Research Article Evaluation of Seismic Performance of...
Transcript of Research Article Evaluation of Seismic Performance of...
Research ArticleEvaluation of Seismic Performance of Buildings Constructed onHillside Slope of Doronka Village-Egypt
Ahmed Abdelraheem Farghaly
Civil and Architectural Buildings Faculty of Industrial Education Sohag University Sohag 82524 Egypt
Correspondence should be addressed to Ahmed Abdelraheem Farghaly khodary20002000yahoocom
Received 30 January 2014 Accepted 4 March 2014 Published 10 April 2014
Academic Editors E J Sapountzakis and I Smith
Copyright copy 2014 Ahmed Abdelraheem Farghaly This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited
Construction on the hillside slope ismore challenging to the structural engineer especially under seismic load due to the presence ofa powerful earthquake in addition to the forces of sliding slope itself Regarding the population growth and narrowness of availablelands people take hillside slopes to build their houses One of the main sources of seismic vulnerability in Egypt is representedby the instability of slopes therefore this is a subject of great significance particularly in view of the growing attention that hasbeen recently dedicated to the reduction of seismic hazardThis paper evaluates the seismic performance of Doronka city buildingsconstructed on rocky hillside slope and its foundations system by studying base shear acceleration and displacementsThe stabilityof the slope was first evaluated under seismic loads and then the stability of constructed buildings was checked on the hillside slopeThe results of study show that these buildings will collapse if subjected to earthquake even if its peak ground acceleration (PGA)magnitude is less than 025 g but the hillside slope remains stable within a high earthquake magnitude
1 Introduction
Doronka village is in the south of Cairo (about 375 km)and was subjected to flood in 1996 and most of its houseswere destroyed therefore its people tended to construct theirhouses on the hillside of the town away from the danger offuture flood The nature of the soil of the hillside is a rockysoil which is a very hard soil used to find traditional buildingson it so most of the buildings constructed on hillside inDoronka town were founded as stepped (the foundationfound to be on more than one level in most cases) and raftfoundations
The response of a slope under seismic loading is deter-mined by the temporal and spatial distribution of the seismicforces in the soilmass which in turn depend on the character-istics of the seismic input and on themechanical properties ofthe soil In general any foundation design should meet fouressential requirements (1) adequate Geotechnical capacity ofsoilrock surrounding the foundation with a specified safetyagainst ultimate failure (2) acceptable total or differentialsettlements under static and dynamic loads (3) adequate
overall stability of slopes in the vicinity of a footingmat and(4) constructability with solutions for anticipated problems
The ground response analyses can be performed under 1Dor 2D conditions and the nonlinear soil behavior is usuallydescribed through the equivalent linearmethod that providesa reasonable estimate of soil response for moderate levels ofshearing intensity provided that no significant excess porewater pressure develop during seismic shaking
2 Analysis of Slope Stability Overview
Numerous methods have been developed for assessing thestability of soil slopes most of which are based on the conceptof ideally plastic response when failure is imminent Amongthem the limit equilibrium methods enjoy wide acceptancedue to their reasonable agreement with reality and theirsimplicity [1] Complex soil profiles seepage and a varietyof loading conditions can be easily dealt with [2] Limitequilibrium solutions however are not rigorous To be calledrigorous a solution must satisfy the equilibrium equations
Hindawi Publishing CorporationISRN Civil EngineeringVolume 2014 Article ID 940923 13 pageshttpdxdoiorg1011552014940923
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(a) High slope angle with stepped foundation (b) Small slope angle with stepped foundation
Figure 1 The techniques of constructing building on hillside slope in Doronka village
the compatibility conditions the constitutive relations of allmaterials and the boundary conditions
Limit equilibriummethods often violate the stress bound-ary conditions they do not enforce an appropriate plasticflow rule for the soil while the developing stresses may noteverywhere obey the requirement for nonincidence of soilstrength Moreover the introduction of assumptions neces-sary to remove static indeterminacy leads to kinematicallyinadmissible collapse mechanisms
The finite element (FE)method is an alternative approachemployed with two different methodologies (a) those thatsearch for the critical slip surface using stress fields obtainedfrom the stress and deformation FE analysis and (b) thosethat compute the factor of safety through an iterative finiteelement analysis by the ldquostrength reduction techniquerdquo [3]In the latter category of methods finite elements are utilizedto model the development of shear zones and the progressivefailure of soil The advantages of the FE approach over theconventional slope stability methods can be summarized asfollows
(i) No assumption needs to be made a priori aboutthe shape and location of the slip surface Failureoccurs naturally within the soil when the appliedshear stresses exceed the shear strength of the soilmass
(ii) The solution is kinematically admissible and there areno arbitrary assumptions about the slice side forces
(iii) It can capture progressive failure phenomena andprovide information about the displacement fielduntil the ultimate state
(iv) It can readily (if not easily) handle irregular slopegeometries in 2 and 3 dimensions complex soilstratigraphy and calculation of low quantities (due tosteady seepage or to transient flow)
Pitilakis [4] and Anastasopoulos et al [5] discussed the2D wave propagation effects and it is perhaps leading toldquotopographicrdquo amplification are taken into account in theiranalysis The authors have been shown that such effects maylead to increased amplitude of ground shaking near the crestof the slope
Figure 1 shows the techniques of building constructedin Doronka city (area of study) which clears that they areconstructed on stepped isolated footings or raft foundation
Latha and Garaga [6] proved that the factor of safety forthe slope was reduced by 46 with the application of earth-quake loads in pseudostatic analysis than static conditionsand it is recommended to flatten the slope from 50∘ to 43∘to avoid wedging failures at all pier locations
Pandey et al [7] studied the behavior of buildings onhill slope through a 3D analysis of the building in whichthe static pushover analysis and response spectrum analysishave been conducted on five buildings with varying supportconditions These buildings have been analyzed for differentsoil conditions (hard medium and soft soils) idealized byequivalent springs In general it is found that responsereduction factor decreases with increasing time period but isexpected to be constant beyond a certain value of the timeperiod
Kourkoulis et al [8] studied parametrically the effectsof foundation type (isolated footings versus a rigid raft)on the position of the sliding surface on the foundationtotal and differential displacements and on the distressof the foundation slab and superstructure columns Theauthors showed that a frame structure founded on a properlydesigned raft could survive the combined effects of slopefailure and ground shaking even if the latter is the result ofa strong base excitation amplified by the soil layer and slopetopography
Failure mechanisms caused by shear strength reductionassume different characteristics depending on soil behaviorductile or brittle and soil type granular or cohesive asdiscussed by Rampello et al [9] These mechanisms can beanalyzed in the static condition following the seismic eventusing conventional limit equilibrium methods eventuallyaccounting for the increase of pore water pressure and thedegradation of strength parameters induced by earthquakeloading
On the contrary when slope instability is producedby earthquake-induced inertial forces a progressive devel-opment of slope displacements occurs for the durationof ground motion only Accordingly evaluation of sloperesponse to earthquake loading should be carried out in
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principle using analytical procedures which account fortime-dependent seismic action and that allow an evaluationof the induced displacement to be obtained If a pseudostaticapproach is adopted in this case the equivalent seismiccoefficients used in limit equilibrium calculations must becalibrated against specifying levels of slope performance andin turn defined by specifying threshold values of earthquake-induced displacements In fact in the pseudostatic approachthe safety factor provides an indirect estimate of the seismicperformance of the slope to earthquake loading while understatic conditions it represents a measure of the distance froma potential failure mechanism
In situ soil slopes and embankments are often reinforcedwith nails to improve their static and seismic performanceMichalowski and You [10] developed an approximatemethodbased on the kinematic approach of limit analysis to estimatethe permanent displacement of geosynthetic-reinforced soilslopes subjected to earthquake loading Chavan et al [11]verified this approximatemethod through finite element (FE)analysis of nails and soil slopes considering the soil and thenails as nonlinear and linear elastic materials respectivelyRadiation damping has been considered by using Lysmer-Kuhlemeyer (L-K) dampers at the soil boundaries of theFE model Soil is assumed to be dry and cohesionlessand analyzed under plane strain conditions The permanentdisplacements from approximate method and FE analysishave been compared It is found that the displacements fromFE analysis are considerable (more than 10) less than thosefrom approximate method
Krishnamoorthy [12] obtained a procedure to evaluate thefactor of safety of the slope (1 1) subjected to seismic loadusing Monte Carlo technique The proposed method can beused to obtain simply the factor of safety of the slope anddeformation of the slope
Mavrouli et al [13] presented an analytical methodologyto evaluate rock slope stability under seismic conditions byconsidering the geomechanical and topographic propertiesof a slope The objective is to locate potential rock fall sourceareas and evaluate their susceptibility in terms of probabilityof failure For this purpose the slope face of a study area isdiscretized into cells having homogenous aspect slope anglerock properties and joint set orientations A pseudostaticlimit equilibrium analysis is performed for each cell wherebythe destabilizing effect of an earthquake is represented bya horizontal force The value of this force is calculated bylinear interpolation between the peak horizontal groundacceleration PGA at the base and the top of the slope Theground acceleration at the top of the slope is increased by 50to account for topographic amplification The uncertaintyassociated with the joint dip is taken into account usingthe Monte Carlo method The proposed methodology wasapplied to a study site with moderate seismicity in Solrsquoade Santa Coloma located in the Principality of AndorraThe results of the analysis are consistent with the spatialdistribution of historical rock falls that have occurred since1997 Moreover the results indicate that for the studiedarea (1) the most important factor controlling the rock fallsusceptibility of the slope is the water pressure in jointsand (2) earthquake shaking with PGA of 016 g will cause
a significant increase in rock fall activity only if water levelsin the joints are greater than 50 of the joint height
Figure 2 illustrates the models used for the analysisof different cases for constructing both isolated and raftfoundation cases The angles of slopes 120601 are 60∘ 45∘ and 25∘depending on the slope location in the nature (dimensionsof the models were in m) The finite-element (FE) analysescan be successfully utilized to model the generation ofsliding failure surfaces in the slope reproducing similarfailure surfaces with those derived from limit-equilibriumand limit-analysis methods and leading to similar yieldaccelerations But the capability to treat realistically thedynamic response to ground shaking is an exclusive attributeof the numerical (FE) methodology not of the pseudostaticlimit equilibriumanalysis methods An additional capabilityof the numerical (FE) methodology is that any structure-foundation system can be placed on the slope For thepurpose of the present study a discretization of 05mtimes05mhas been adopted as in Kourkoulis et al [8]
The finite element (FE) method is one of many stresses-deformation methods It is widely accepted for its accuracyin modeling different geological geotechnical phenomena asit implements physical laws During the last decade majorimprovements in efficiency and configuration have made iteasier and cheaper to use and therefore it has become a morecommon tool in science and engineering
3 Selection of Adequate Accelerographs
The recorded accelerographs of Northridge (1989) and ElCentro (1940) earthquakes are shown in Figure 3 Sincethere are no accelerographs available (neither recorded norpredicted based on the seismic risk analyses) in the areathe above accelerographs are selected for seismic analysesof the model According to the Egyptian code of practicefor seismic resistant design of buildings [14] the city ofDoronka is classified as the area by relatively low seismicrisk and the design acceleration of the area is recommendedto 025 g Thus the above mentioned accelerographs havebeen scaled and corrected for this amount Egypt in thelast years was classified as high seismic regions so theresearch will analyse the buildings constructed on hillsideslope subjected to earthquake acceleration 025 05 and 1 g tocover all possibilities of how earthquake force can affect thearea Time history analysis is carried out using SAP200 [15]program considering the factor of acceleration 025 05 and1 g and nonlinear analysis with 4000 step at 40 sec for bothtime history used earthquakes (El Centro and Northridgeearthquakes)The time history corresponding to 5dampingis considered which is reasonable for concrete structure
4 Model Description
The 2D building model consists of frame elements as beamand column The column dimension is 50 times 50 cm andthe beam section is 25 times 50 cm all over the height of thebuildingThe foundation is chosen to be either raft or isolatedfoundation in the analyses A 4-story building was modeled
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Earthquake
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(a) Slope with angle 120601 with directions of earthquakes
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Changeable
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geab
le
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(b) Building on slope constructed on isolated footing
Earthquake
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(c) Stepped buildings on slope constructed on isolated footing (d) Stepped buildings on slopes constructed onraft foundation
Figure 2 Finite element mesh in the area of the slope the discretization is denser (05m times 05m quadrilateral elements)
Acce
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ss
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(a) El Centro
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ss
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(b) Northridge
Figure 3 Acceleration time histories of the earthquakes in N-S direction
with a 3m height (each story) and a 15m length as shown inFigure 2
No matter what type and size of RC structure is underinvestigation the finite element method (FEM) is the mostaccurate and reliable numerical technique for assessing thedemands on structure components in both 2D and 3Ddomains
The inelastic analysis is performed and the failure crite-rion used for both the soil and the structure members has tobe stated as well
Frame members primarily not only serve to carry themajority of gravity loads in a building but also serve as partof lateral resisting systems Bernoulli-Euler beam theory andTimoshenko beam theoryHjelmstad [16] if considering sheareffects of deep beam are widely used and have been imple-mented in most computer-based frame analysis packages
A Beam element was loaded with constant distributed loadsequal to 250 tonm1015840 at all floor levels in addition to ownweight of elements
5 Results and Analysis
To evaluate the performance of buildings constructed onhillside slopes at Doronka city two main parts were studiedthe first part is the performance of the building with adifferent foundation system to seismic loads on the hillsideslope and presenting the straining actions of them resultingfrom two earthquakes (El Centro and Northridge earth-quakes) analyses in steps that is first 025 g 05 g and 1 g inincreasing order of the PGAand the secondpart evaluated theperformance of hillside slope (slope angles 60∘ 45∘ and 25∘)
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Table 1 Description of used symbols in different curves
Symbols Description
I 60∘ Building on 60∘ slope angle founded on isolatedfooting
R 60∘ Building on 60∘ slope angle founded on raft footing
I 45∘ Building on 45∘ slope angle founded on isolatedfooting
R 45∘ Building on 45∘ slope angle founded on raft footing
I 25∘ Building on a 25∘ slope angle founded on isolatedfooting
R 25∘ Building on a 25∘ slope angle founded on isolatedfooting
Fixed ISO Building with fixed stepped isolated footingFixed raft Building with fixed raft footing
under static and seismic loads with and without constructedbuilding to evaluate the static and dynamic stability of thehillside slope
Figure 4 represents the straining actions of the analyzedmodel using El Centro earthquake time history taking intoconsideration the various types of slope angles ground accel-erations and foundation systems (isolated or raft foundationsystem) Figure 4(a) shows variations of normal force in basecolumns for a building founded at a 60∘ slope with raftfoundation and the normal force recorded the highest valuewith respect to the other casesThe greater the slope angle thegreater the normal forces
Figure 4(c) shows bending moment for base column Amaximum bending moment occurs in raft foundation onslope angle 60∘ in 1 g acceleration but in 050 g accelerationthe maximum value was found in raft foundation with 45∘slope angle Figure 4(d) represents the top floor displacementand themaximum value of displacement for the testedmodelwas founded in raft foundation on slope angle 60∘ thisbehavior was repeated in all used accelerations
Table 1 describes the used symbols in different curvesFigure 4(e) shows the values of top floor acceleration of
the building model the maximum top floor acceleration wasregistered in the case of raft foundation on a 25∘ slope anglenearly 24 times the applied acceleration on the model for1 g acceleration 27 times the applied acceleration (050 g)and equals to 2 times the applied acceleration (025 g) fromfigure its can improved that the slope has not effect on thevalues of bending moment of base column except for R 25(raft foundation on hillside slope 25∘) nearly increased by 175times than all cases the bending moments in fixed base casesregistered a lower value with respect to the rest cases
Figure 5 shows the straining actions of the analyzedmod-els using Northridge time history earthquake model takinginto consideration the various types of slope angles groundaccelerations and foundation systems (stepped isolated orraft foundation system) Figure 5(a) shows the variation ofnormal force in base columns and building founded on 60∘slope with raft foundation gives the highest value of thenormal force with respect to the other cases (nearly morethan the other cases by 25 times) the big slope effect on
the oblique of the building so that the high value of normalforce Figure 5(b) illustrates that base shear force at the raftfoundation system in 60∘ slope angle gives the maximumvalue with respect to the other slopes and a foundationsystem this phenomenon was repeated for the three selectedground accelerations
Figure 5(c) shows that base bendingmoment for base col-umn maximum bending moment occurs in raft foundationcase on slope angle 60∘ and rafton slope 25∘ in 1 g accelerationbut in 050 g and 025 g acceleration the values were nearlyconstant Figure 4(d) represents the top floor displacementand themaximumvalue of displacement of the testedmodelsdisplacement of model in 60∘ slope was smaller than in 25∘by 115 times and this behavior was repeated in all usedaccelerations
Figure 5(e) shows the values of top floor accelerationof models and the maximum top floor acceleration wasregistered in the case of raft foundation on a 25∘ slope anglenearly 16 times the applied acceleration on the model for 1 g050 g and 025 g cases of the applied acceleration
The results founded fromEl Centro earthquake excitationwere in the same trend with Northridge earthquake exalta-tion
Figure 6 displays the stress distribution in 119909- and 119911-directions of 2D slopes (angles 60∘ 45∘ and 25∘) under staticcondition Figure 6(c) shows the stress distribution in 119909-and 119911-directions and all stresses are negative (compressionstress) with the allowable stress for the rocky soil of thehillside in Figure 6(b) stress in the hillsidewith slope 45∘ withmoderate compression stress but in Figure 5(a) the stress alsoin compression but with low value that because of the highervalue of slope angle 60∘
To evaluate the effect of different kind of foundationsystem on hillside slopes under El Centro earthquake with025 g 05 g and 1 g PGA (Pick Ground Acceleration) exci-tation there are three actual slopes that were tested (60∘45∘ and 25∘) Only hillside slopes under 1 g PGA are shownin Figure 7 A hillside slope 25∘ subjected to El Centroearthquake with PGA 1 g with raft foundation stress in 119909-direction no tension between foundation and soil under-neath the model and so in 119911-direction generally no tensionstress come out in thewhole of the slopeThe surface of failureappears under raft foundation more straight but for steepedfoundation the surface looks like a quarter circle (criticalcircle of slip) Compression stress in hillside slope underneathsteeped foundation is bigger than raft foundation
For a hillside slope angle 45 the straining action onthe slope is moderate without tension stress between raftfoundation in 119911-direction and the hillside soil will but thereis a tension stress between the raft foundation buildingmodeland the hillside soil in 119909-direction which means collapse ofthe building model there is a tension stress in the hillsideslope in a crest parts and the steeped foundation shows aminimum effect on the slope This appears as a small valueof compression stress in both directions and no tension stressappears underneath the steeped foundation of the model
For hillside slope angle 60∘ deformation of hillside slopewith raft foundation a small part of the hillside will take offa tension stress appears underneath the foundation in both
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05
1015202530354045
I 60 R 25I 25R 45I 45R 60iso
Fixedraft
Foundation system with slope
Fixed
N1 gN05 gN025 g
Nor
mal
forc
e (t)
(a) Base column normal force
02468
10121416
Foundation system with slope
I 60 R 25I 25R 45I 45R 60iso
Fixedraft
Fixed
Shea
r for
ce (t
)
Q 1gQ 05 gQ 025 g
(b) Base column shear force
02468
1012141618
I 60 R 25I 25R 45I 45R 60iso
Fixedraft
Foundation system with slope
Fixed
M1 gM05 gM025 g
Mom
ent (mmiddott
)
(c) Base column bending moment
0
5
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Dis
(cm
)
I 60 R 25I 25R 45I 45R 60iso
Fixedraft
Foundation system with slope
Fixed
Dis 1gDis 05 gDis 025 g
(d) Displacement of top floor
0
05
1
15
2
25
Acce
lera
tion
(g)
I 60 R 25I 25R 45I 45R 60iso
Fixedraft
Foundation system with slope
Fixed
Acceleration 1gAcceleration 05 gAcceleration 025 g
(e) Acceleration of top floor
Figure 4 Straining actions of 2D building with different types of foundation system and slope angle with El Centro earthquake excitation
directions and stepped foundationmodel appears to bemorestable than raft foundation model because there is no tensionbetween foundation and soil
If the PGA equal to 05 g for the hillside slope 25∘no tension between both types of foundation and the soil
underneath both stress are compression in both directionswhich have a large values In hillside slope 45∘ stressunderneath a raft foundation model approximates to zeroin both directions and this means the model is aboutrotation to be destroyed but the steeped foundation was
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0
2
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60 R 25 iso25 R45 iso45 R60 iso R fixed I fixedFoundation system with slope
N1 gN05 gN025 g
Nor
mal
forc
e (t)
(a) Base column normal force
0
05
1
15
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25
3
60 R 25 iso25 R45 iso45 R60 iso R fixed I fixedFoundation system with slope
Base
shea
r (t)
Q 1gQ 05 gQ 025 g
(b) Base column shear force
0
05
1
15
2
25
3
35
60 R 25 iso25 R45 iso45 R60 iso R fixed I fixedFoundation system with slope
M1 gM05 gM025 g
Bend
ing
mom
ent (mmiddott
)
(c) Base column bending moment
002040608
112141618
Dis
(cm
)
60 R 25 iso25 R45 iso45 R60 iso R fixed I fixedFoundation system with slope
Dis 1gDis 05 gDis 025 g
(d) Displacement of top floor
002040608
112141618
Acce
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(g)
60 R 25 iso25 R45 iso45 R60 iso R fixed I fixedFoundation system with slope
Acceleration 1gAcceleration 05 gAcceleration 025 g
(e) Acceleration of top floor
Figure 5 Straining actions of 2D model with different types of foundation and slope angles with Northridge earthquake
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Stress in x direction stress Stress in z direction stress
(c) Slope 25∘
Figure 6 Stress distribution on 2D slope with different slope angles under static load
more stable because there is a small value of compressionstress underneath foundation For a hillside slope angle45 the straining action on the slope is moderate withouttension stress between raft foundation in 119911-direction andthe hillside soil will but there is a tension stress betweenthe raft foundation building model and the hillside soil in119909-direction which means collapse of the building modeland there is a tension stress in the hillside slope in a crestparts and the steeped foundation shows aminimum effect on
the slope This appears as a small value of compression stressin both directions and no tension stress appears underneaththe steeped foundation of the model
Figure 8 illustrates the straining actions of the hillsideslope under Northridge earthquake excitation with differentkinds of foundation systems and slopes For PGA 1 g slope60∘ there is a tension stress between foundation and soil onthe slope this indicated a failure of the model for both kindsof foundation (raft and stepped) deformation for stepped
ISRN Civil Engineering 9
minus102
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Deformation
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(A) Raft foundation x directionz direction
x direction z direction
(a) Straining action on slope 60∘
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Deformation
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(A) Stepped foundation
(B) Raft foundation
x directionz direction
x direction z direction
(b) Straining action on slope 45∘
Figure 7 Continued
10 ISRN Civil Engineering
minus78
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Deformation
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(A) Raft foundation
(B) Raft foundation
x directionz direction
x direction z direction
(c) Straining action on slope 25∘
Figure 7 Straining actions of 2D building with different types of foundation system and slope angle with El Centro earthquake excitationwith PGA equal to 1 g
Table 2 Conclusion of model stable with different earthquake PGA
Earthquakeacceleration
Hillside slopeangle
Static stability of slope only Dynamic stability withconstructed one building
Dynamic stability withconstructed series building
Tension stress Compressionstress
Tension stressunder building
Compressionstress underbuilding
Tension stressunder building
Compressionstress underbuilding
1 g60∘ No Yes Yes mdash Yes mdash45∘ No Yes Yes mdash Yes mdash25∘ No Yes No Yes Yes mdash
050 g60∘ No Yes Yes mdash Yes mdash45∘ No Yes Yes mdash Yes mdash25∘ No Yes No Yes mdash Yes
025 g60∘ No Yes Yes mdash Yes mdash45∘ No Yes No Yes Yes mdash25∘ No Yes No Yes mdash Yes
foundation is bigger than a raft foundation model and thestraining action seems to be lower than the correspondingvalues of El Centro earthquake exaltation For slope 45∘ and1 g PGA there is no tension stress between foundation and soilon the hillside slope but the compression stress in the slope issmall with respect to 60∘ slope and the corresponding valuesin 25∘ slope are bigger than 45∘ and no tension stress appears
The results obtained from Northridge earthquake aresimilar in trend with these founded from El Centro earth-quake excitation
Table 2 concluded the results of model stress founded onthe slopes with the view of stability or not under differentearthquake excitationThe stability of a series of building con-struction on a slope under earthquake excitation was studiedand also concluded in Table 2 It seem that series buildings
can bemore critical than one building and it is shown that theconstruction of series buildings on a slope from60 to 45 anglecan be destroyed under moderate earthquake even so theseries buildings withstand the same earthquake magnitudesif it is founded on a flat land foundation
6 Conclusions
A 2D building model founded on a hillside slope was evalu-ated to check the performance of buildings and slopes undervarious earthquake time history excitation and magnitudestudying a real case of study in a Doronka village in UpperEgypt Two earthquake time histories were used El Centroand Northridge earthquake with 025 g 05 g and 1 g PGAmagnitudeThe models used were prepared to agree with the
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X directionZ direction Deformation
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(ii) Stepped foundation
(iii) Stepped foundation
(iv) Raft foundation
x direction z direction
x direction z direction
x directionz direction
(a) Straining action on slope 45∘
Figure 8 Continued
12 ISRN Civil Engineering
34
17
00
minus17
minus34
minus51
minus68
minus85
minus102
minus119
minus136
minus153
minus170
minus187
45
00
minus45
minus90
minus135
minus180
minus225
minus270
minus315
minus360
minus405
minus450
minus495
minus540
14
00
minus14
minus28
minus42
minus56
minus70
minus84
minus98
minus112
minus126
minus140
minus154
minus168
45
00
minus45
minus90
minus135
minus180
minus225
minus270
minus315
minus360
minus405
minus450
minus495
minus540
Deformation
Deformation
(v) Raft foundation
(vi) Stepped foundation
x directionz direction
x direction z direction
(b) Straining action on slope 25∘
Figure 8 Straining actions of 2D building with different types of foundation system and slope angle with Northridge earthquake excitationwith PGA equals 1 g
reality of the nature of the case study and the slopes were 60∘45∘ and 25∘ and the foundation system to be stepped isolatedor raft foundations The nonlinear parameters of the rockytype soil were provided to SAP2000 program as a curve of soilunder cyclic loading Applying the two selected earthquaketime histories with different PGA on a free hillside slope frombuilding and with only one building and then with a series ofbuildings the highlight points can be drawn as follows
(i) Static analysis of hillside with different angles ofslopes was found to be stable
(ii) The study gives an overview of the stability of hillsideslopes under earthquake excitations especially forconstruction requirements
(iii) The stability of slopes (without constructing build-ings) (with slope angles range from 60∘ to 25∘) isacceptable in the high PGA for the study of rocky soilno tensile stress was found in the hillside slope
(iv) Compression stress in a hillside slope angle 60∘decreased by 15 times than hillside slope angle 45∘and decreased by 14 times than hillside slope 25∘under seismic excitations
(v) The interplay between dynamic ldquoinertialrdquo effects aris-ing from the ground vibration and the quasistaticldquokinematicrdquo effects arising from the downwardmove-ment of a shallow sliding soil wedge are studied Itwas thus determined that a rigid raft foundationplaced on a big angle slope which is in a precariousequilibrium and fails during very strong shakingcannot protect the superstructure from both falling(being dragged) with the sliding soil mass and fromsuffering large damaging internal forces
(vi) This is in qualitative agreement with several casehistories of structures that have survived the com-bined effects of strong seismic shaking and of soildownward sliding The penalty to pay however is(a) appreciable rotation and lateral displacement ofthe whole system which may impair the serviceabilityof the structure and (b) generation of large bendingmoments and shear forces in the foundation slabby contrast as in fact most engineers would haveintuitively predicted placing a structure with isolatedfootings on a seismically unstable slope would be aprudent decision
(vii) It is recommended to flatten the slope from 60∘ to45∘ to avoid wedge failures at all isolated steppedfoundation locations (normal force decreased by 50for a slope angle 60∘ than slope angle 45∘ and baseshear decreased by 40 in a slope angle 60∘ than slopeangle 45∘)
(viii) The difference in straining action between steps andraft fixed base under dynamic loads is not significant(base shear in raft foundation increased by 2 thanstepping isolated footing 3 in bending moment 5in top displacement and 7 in top floor acceleration)
(ix) Stepped isolated foundation represents the best solu-tion for both dynamic performance of superstructureconstructed on hillside slope and the stability ofthe slope (columns normal force for isolated footingdecreased by 133 times than raft foundation anddecreased by 145 times in base shear) in 2D the effectof the tie beams to connect stepped footing has beenignored
ISRN Civil Engineering 13
(x) Series buildings constructed on a hillside slope espe-cially 60∘ angle normal force increased by nearly 15times than the one building model 175 times forshear force 140 times in bending moment and 125times for displacement and decreased by 020 timesfor top floor acceleration
This conclusion drawn from a 2D analysis remains validfor the 3D cases since more attenuation would be observedif the radiation damping into the third dimension wastaken into consideration These very local conditions are notadequately captured by the analysis However verification isrequired to check the results in 2D and 3D
Conflict of Interests
The author declares that there is no conflict of interestsregarding the publication of this paper
References
[1] E Spencer ldquoA method of analysis of the stability of embank-ments assuming parallel inter slice forcesrdquo Geo-Technique vol17 no 1 pp 11ndash26 1967
[2] H S Yu R Salgado S W Sloan and J M Kim ldquoLimitanalysis versus limit equilibrium for slope stabilityrdquo Journal ofGeotechnical Engineering (ASCE) vol 124 no 1 pp 1ndash11 1998
[3] A Troncone ldquoNumerical analysis of a landslide in soils withstrain-softening behaviourrdquo Geotechnique vol 55 no 8 pp585ndash596 2005
[4] D Pitilakis ldquoTopographic irregularities and soilmdashfoundationmdashstructure interactionrdquo in Proceedings of the 3rd Japan-GreeceWorkshop on Seismic Design Observation and Retrofit of Foun-dations pp 335ndash343 Santorini Greece 2009
[5] I Anastasopoulos G Gazetas M F Bransby M C RDavies and A El Nahas ldquoFault rupture propagation throughsand finite-element analysis and validation through centrifugeexperimentsrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 133 no 8 pp 943ndash958 2007
[6] G M Latha and A Garaga ldquoStability analysis of a rock slopein Himalayasrdquo Geomechanics and Engineering vol 2 no 2 pp125ndash140 2010
[7] A D Pandey P Kumar and S Sharma ldquoSeismic soil structureinteraction of buildings on hill slopesrdquo International Journal ForComputational Civil and Structural Engineering vol 2 no 2 pp544ndash555 2011
[8] R Kourkoulis I Anastasopoulos F Gelagoti and G GazetasldquoInteraction of foundation-structure systems with seismicallyprecarious slopes numerical analysis with strain softeningconstitutivemodelrdquo Soil Dynamics and Earthquake Engineeringvol 30 no 12 pp 1430ndash1445 2010
[9] S Rampello L Callisto and P Fargnoli ldquoEvaluation of seismiccoefficients for slope stability analysis using a displacement-based approachrdquo in Proceedings of the Seismic EngineeringInternational Conference Commemorating the 1908 Messina andReggio Calabria Earthquake (MERCEA rsquo08) 2008
[10] R L Michalowski and L You ldquoDisplacements of reinforcedslopes subjected to seismic loadsrdquo Journal of Geotechnical andGeoenvironmental Engineering vol 126 no 8 pp 685ndash6942000
[11] D S Chavan G Mondal and A Prashant ldquoPermanent dis-placement of nailed soil slopes subjected to earthquake load-ingrdquo in Proceedings of the 15th World Conference on EarthquakeEngineering (WCEE rsquo12) Lisbon Portugal 2012
[12] A Krishnamoorthy ldquoFactor of safety of a slope subjected toseismic loadrdquoElectronic Journal of Geotechnical Engineering vol12 2007
[13] O Mavrouli J Corominas and J Wartman ldquoMethodology toevaluate rock slope stability under seismic conditions at Solade Santa Coloma Andorrardquo Natural Hazards and Earth SystemScience vol 9 no 6 pp 1763ndash1773 2009
[14] ECOL 201 The Egyptian Code For Calculation of Loads andForces in Structural Building Work Housing and BuildingResearch Center Cairo Egypt 2008
[15] SAP200 Nonlinear Version 14 Static and Dynamic Finite Ele-ments Analysis of Structure Computers amp Structures BerkeleyCalif USA 2010
[16] K D Hjelmstad Fundamentals of Structural MechanicsSpringer New York NY USA 2nd edition 2005
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2 ISRN Civil Engineering
(a) High slope angle with stepped foundation (b) Small slope angle with stepped foundation
Figure 1 The techniques of constructing building on hillside slope in Doronka village
the compatibility conditions the constitutive relations of allmaterials and the boundary conditions
Limit equilibriummethods often violate the stress bound-ary conditions they do not enforce an appropriate plasticflow rule for the soil while the developing stresses may noteverywhere obey the requirement for nonincidence of soilstrength Moreover the introduction of assumptions neces-sary to remove static indeterminacy leads to kinematicallyinadmissible collapse mechanisms
The finite element (FE)method is an alternative approachemployed with two different methodologies (a) those thatsearch for the critical slip surface using stress fields obtainedfrom the stress and deformation FE analysis and (b) thosethat compute the factor of safety through an iterative finiteelement analysis by the ldquostrength reduction techniquerdquo [3]In the latter category of methods finite elements are utilizedto model the development of shear zones and the progressivefailure of soil The advantages of the FE approach over theconventional slope stability methods can be summarized asfollows
(i) No assumption needs to be made a priori aboutthe shape and location of the slip surface Failureoccurs naturally within the soil when the appliedshear stresses exceed the shear strength of the soilmass
(ii) The solution is kinematically admissible and there areno arbitrary assumptions about the slice side forces
(iii) It can capture progressive failure phenomena andprovide information about the displacement fielduntil the ultimate state
(iv) It can readily (if not easily) handle irregular slopegeometries in 2 and 3 dimensions complex soilstratigraphy and calculation of low quantities (due tosteady seepage or to transient flow)
Pitilakis [4] and Anastasopoulos et al [5] discussed the2D wave propagation effects and it is perhaps leading toldquotopographicrdquo amplification are taken into account in theiranalysis The authors have been shown that such effects maylead to increased amplitude of ground shaking near the crestof the slope
Figure 1 shows the techniques of building constructedin Doronka city (area of study) which clears that they areconstructed on stepped isolated footings or raft foundation
Latha and Garaga [6] proved that the factor of safety forthe slope was reduced by 46 with the application of earth-quake loads in pseudostatic analysis than static conditionsand it is recommended to flatten the slope from 50∘ to 43∘to avoid wedging failures at all pier locations
Pandey et al [7] studied the behavior of buildings onhill slope through a 3D analysis of the building in whichthe static pushover analysis and response spectrum analysishave been conducted on five buildings with varying supportconditions These buildings have been analyzed for differentsoil conditions (hard medium and soft soils) idealized byequivalent springs In general it is found that responsereduction factor decreases with increasing time period but isexpected to be constant beyond a certain value of the timeperiod
Kourkoulis et al [8] studied parametrically the effectsof foundation type (isolated footings versus a rigid raft)on the position of the sliding surface on the foundationtotal and differential displacements and on the distressof the foundation slab and superstructure columns Theauthors showed that a frame structure founded on a properlydesigned raft could survive the combined effects of slopefailure and ground shaking even if the latter is the result ofa strong base excitation amplified by the soil layer and slopetopography
Failure mechanisms caused by shear strength reductionassume different characteristics depending on soil behaviorductile or brittle and soil type granular or cohesive asdiscussed by Rampello et al [9] These mechanisms can beanalyzed in the static condition following the seismic eventusing conventional limit equilibrium methods eventuallyaccounting for the increase of pore water pressure and thedegradation of strength parameters induced by earthquakeloading
On the contrary when slope instability is producedby earthquake-induced inertial forces a progressive devel-opment of slope displacements occurs for the durationof ground motion only Accordingly evaluation of sloperesponse to earthquake loading should be carried out in
ISRN Civil Engineering 3
principle using analytical procedures which account fortime-dependent seismic action and that allow an evaluationof the induced displacement to be obtained If a pseudostaticapproach is adopted in this case the equivalent seismiccoefficients used in limit equilibrium calculations must becalibrated against specifying levels of slope performance andin turn defined by specifying threshold values of earthquake-induced displacements In fact in the pseudostatic approachthe safety factor provides an indirect estimate of the seismicperformance of the slope to earthquake loading while understatic conditions it represents a measure of the distance froma potential failure mechanism
In situ soil slopes and embankments are often reinforcedwith nails to improve their static and seismic performanceMichalowski and You [10] developed an approximatemethodbased on the kinematic approach of limit analysis to estimatethe permanent displacement of geosynthetic-reinforced soilslopes subjected to earthquake loading Chavan et al [11]verified this approximatemethod through finite element (FE)analysis of nails and soil slopes considering the soil and thenails as nonlinear and linear elastic materials respectivelyRadiation damping has been considered by using Lysmer-Kuhlemeyer (L-K) dampers at the soil boundaries of theFE model Soil is assumed to be dry and cohesionlessand analyzed under plane strain conditions The permanentdisplacements from approximate method and FE analysishave been compared It is found that the displacements fromFE analysis are considerable (more than 10) less than thosefrom approximate method
Krishnamoorthy [12] obtained a procedure to evaluate thefactor of safety of the slope (1 1) subjected to seismic loadusing Monte Carlo technique The proposed method can beused to obtain simply the factor of safety of the slope anddeformation of the slope
Mavrouli et al [13] presented an analytical methodologyto evaluate rock slope stability under seismic conditions byconsidering the geomechanical and topographic propertiesof a slope The objective is to locate potential rock fall sourceareas and evaluate their susceptibility in terms of probabilityof failure For this purpose the slope face of a study area isdiscretized into cells having homogenous aspect slope anglerock properties and joint set orientations A pseudostaticlimit equilibrium analysis is performed for each cell wherebythe destabilizing effect of an earthquake is represented bya horizontal force The value of this force is calculated bylinear interpolation between the peak horizontal groundacceleration PGA at the base and the top of the slope Theground acceleration at the top of the slope is increased by 50to account for topographic amplification The uncertaintyassociated with the joint dip is taken into account usingthe Monte Carlo method The proposed methodology wasapplied to a study site with moderate seismicity in Solrsquoade Santa Coloma located in the Principality of AndorraThe results of the analysis are consistent with the spatialdistribution of historical rock falls that have occurred since1997 Moreover the results indicate that for the studiedarea (1) the most important factor controlling the rock fallsusceptibility of the slope is the water pressure in jointsand (2) earthquake shaking with PGA of 016 g will cause
a significant increase in rock fall activity only if water levelsin the joints are greater than 50 of the joint height
Figure 2 illustrates the models used for the analysisof different cases for constructing both isolated and raftfoundation cases The angles of slopes 120601 are 60∘ 45∘ and 25∘depending on the slope location in the nature (dimensionsof the models were in m) The finite-element (FE) analysescan be successfully utilized to model the generation ofsliding failure surfaces in the slope reproducing similarfailure surfaces with those derived from limit-equilibriumand limit-analysis methods and leading to similar yieldaccelerations But the capability to treat realistically thedynamic response to ground shaking is an exclusive attributeof the numerical (FE) methodology not of the pseudostaticlimit equilibriumanalysis methods An additional capabilityof the numerical (FE) methodology is that any structure-foundation system can be placed on the slope For thepurpose of the present study a discretization of 05mtimes05mhas been adopted as in Kourkoulis et al [8]
The finite element (FE) method is one of many stresses-deformation methods It is widely accepted for its accuracyin modeling different geological geotechnical phenomena asit implements physical laws During the last decade majorimprovements in efficiency and configuration have made iteasier and cheaper to use and therefore it has become a morecommon tool in science and engineering
3 Selection of Adequate Accelerographs
The recorded accelerographs of Northridge (1989) and ElCentro (1940) earthquakes are shown in Figure 3 Sincethere are no accelerographs available (neither recorded norpredicted based on the seismic risk analyses) in the areathe above accelerographs are selected for seismic analysesof the model According to the Egyptian code of practicefor seismic resistant design of buildings [14] the city ofDoronka is classified as the area by relatively low seismicrisk and the design acceleration of the area is recommendedto 025 g Thus the above mentioned accelerographs havebeen scaled and corrected for this amount Egypt in thelast years was classified as high seismic regions so theresearch will analyse the buildings constructed on hillsideslope subjected to earthquake acceleration 025 05 and 1 g tocover all possibilities of how earthquake force can affect thearea Time history analysis is carried out using SAP200 [15]program considering the factor of acceleration 025 05 and1 g and nonlinear analysis with 4000 step at 40 sec for bothtime history used earthquakes (El Centro and Northridgeearthquakes)The time history corresponding to 5dampingis considered which is reasonable for concrete structure
4 Model Description
The 2D building model consists of frame elements as beamand column The column dimension is 50 times 50 cm andthe beam section is 25 times 50 cm all over the height of thebuildingThe foundation is chosen to be either raft or isolatedfoundation in the analyses A 4-story building was modeled
4 ISRN Civil Engineering
Earthquake
X
Z
120601∘
(a) Slope with angle 120601 with directions of earthquakes
2000
2000
200
0
Changeable
Chan
geab
le
500
300
1500
120601∘
(b) Building on slope constructed on isolated footing
Earthquake
X
Z
(c) Stepped buildings on slope constructed on isolated footing (d) Stepped buildings on slopes constructed onraft foundation
Figure 2 Finite element mesh in the area of the slope the discretization is denser (05m times 05m quadrilateral elements)
Acce
lera
tion
(cm
ss
)
600
0
minus600
0 8 16 24 32 40
Time (s)
(a) El Centro
Acce
lera
tion
(cm
ss
)
600
0
minus600
0 8 16 24 32 40
Time (s)
(b) Northridge
Figure 3 Acceleration time histories of the earthquakes in N-S direction
with a 3m height (each story) and a 15m length as shown inFigure 2
No matter what type and size of RC structure is underinvestigation the finite element method (FEM) is the mostaccurate and reliable numerical technique for assessing thedemands on structure components in both 2D and 3Ddomains
The inelastic analysis is performed and the failure crite-rion used for both the soil and the structure members has tobe stated as well
Frame members primarily not only serve to carry themajority of gravity loads in a building but also serve as partof lateral resisting systems Bernoulli-Euler beam theory andTimoshenko beam theoryHjelmstad [16] if considering sheareffects of deep beam are widely used and have been imple-mented in most computer-based frame analysis packages
A Beam element was loaded with constant distributed loadsequal to 250 tonm1015840 at all floor levels in addition to ownweight of elements
5 Results and Analysis
To evaluate the performance of buildings constructed onhillside slopes at Doronka city two main parts were studiedthe first part is the performance of the building with adifferent foundation system to seismic loads on the hillsideslope and presenting the straining actions of them resultingfrom two earthquakes (El Centro and Northridge earth-quakes) analyses in steps that is first 025 g 05 g and 1 g inincreasing order of the PGAand the secondpart evaluated theperformance of hillside slope (slope angles 60∘ 45∘ and 25∘)
ISRN Civil Engineering 5
Table 1 Description of used symbols in different curves
Symbols Description
I 60∘ Building on 60∘ slope angle founded on isolatedfooting
R 60∘ Building on 60∘ slope angle founded on raft footing
I 45∘ Building on 45∘ slope angle founded on isolatedfooting
R 45∘ Building on 45∘ slope angle founded on raft footing
I 25∘ Building on a 25∘ slope angle founded on isolatedfooting
R 25∘ Building on a 25∘ slope angle founded on isolatedfooting
Fixed ISO Building with fixed stepped isolated footingFixed raft Building with fixed raft footing
under static and seismic loads with and without constructedbuilding to evaluate the static and dynamic stability of thehillside slope
Figure 4 represents the straining actions of the analyzedmodel using El Centro earthquake time history taking intoconsideration the various types of slope angles ground accel-erations and foundation systems (isolated or raft foundationsystem) Figure 4(a) shows variations of normal force in basecolumns for a building founded at a 60∘ slope with raftfoundation and the normal force recorded the highest valuewith respect to the other casesThe greater the slope angle thegreater the normal forces
Figure 4(c) shows bending moment for base column Amaximum bending moment occurs in raft foundation onslope angle 60∘ in 1 g acceleration but in 050 g accelerationthe maximum value was found in raft foundation with 45∘slope angle Figure 4(d) represents the top floor displacementand themaximum value of displacement for the testedmodelwas founded in raft foundation on slope angle 60∘ thisbehavior was repeated in all used accelerations
Table 1 describes the used symbols in different curvesFigure 4(e) shows the values of top floor acceleration of
the building model the maximum top floor acceleration wasregistered in the case of raft foundation on a 25∘ slope anglenearly 24 times the applied acceleration on the model for1 g acceleration 27 times the applied acceleration (050 g)and equals to 2 times the applied acceleration (025 g) fromfigure its can improved that the slope has not effect on thevalues of bending moment of base column except for R 25(raft foundation on hillside slope 25∘) nearly increased by 175times than all cases the bending moments in fixed base casesregistered a lower value with respect to the rest cases
Figure 5 shows the straining actions of the analyzedmod-els using Northridge time history earthquake model takinginto consideration the various types of slope angles groundaccelerations and foundation systems (stepped isolated orraft foundation system) Figure 5(a) shows the variation ofnormal force in base columns and building founded on 60∘slope with raft foundation gives the highest value of thenormal force with respect to the other cases (nearly morethan the other cases by 25 times) the big slope effect on
the oblique of the building so that the high value of normalforce Figure 5(b) illustrates that base shear force at the raftfoundation system in 60∘ slope angle gives the maximumvalue with respect to the other slopes and a foundationsystem this phenomenon was repeated for the three selectedground accelerations
Figure 5(c) shows that base bendingmoment for base col-umn maximum bending moment occurs in raft foundationcase on slope angle 60∘ and rafton slope 25∘ in 1 g accelerationbut in 050 g and 025 g acceleration the values were nearlyconstant Figure 4(d) represents the top floor displacementand themaximumvalue of displacement of the testedmodelsdisplacement of model in 60∘ slope was smaller than in 25∘by 115 times and this behavior was repeated in all usedaccelerations
Figure 5(e) shows the values of top floor accelerationof models and the maximum top floor acceleration wasregistered in the case of raft foundation on a 25∘ slope anglenearly 16 times the applied acceleration on the model for 1 g050 g and 025 g cases of the applied acceleration
The results founded fromEl Centro earthquake excitationwere in the same trend with Northridge earthquake exalta-tion
Figure 6 displays the stress distribution in 119909- and 119911-directions of 2D slopes (angles 60∘ 45∘ and 25∘) under staticcondition Figure 6(c) shows the stress distribution in 119909-and 119911-directions and all stresses are negative (compressionstress) with the allowable stress for the rocky soil of thehillside in Figure 6(b) stress in the hillsidewith slope 45∘ withmoderate compression stress but in Figure 5(a) the stress alsoin compression but with low value that because of the highervalue of slope angle 60∘
To evaluate the effect of different kind of foundationsystem on hillside slopes under El Centro earthquake with025 g 05 g and 1 g PGA (Pick Ground Acceleration) exci-tation there are three actual slopes that were tested (60∘45∘ and 25∘) Only hillside slopes under 1 g PGA are shownin Figure 7 A hillside slope 25∘ subjected to El Centroearthquake with PGA 1 g with raft foundation stress in 119909-direction no tension between foundation and soil under-neath the model and so in 119911-direction generally no tensionstress come out in thewhole of the slopeThe surface of failureappears under raft foundation more straight but for steepedfoundation the surface looks like a quarter circle (criticalcircle of slip) Compression stress in hillside slope underneathsteeped foundation is bigger than raft foundation
For a hillside slope angle 45 the straining action onthe slope is moderate without tension stress between raftfoundation in 119911-direction and the hillside soil will but thereis a tension stress between the raft foundation buildingmodeland the hillside soil in 119909-direction which means collapse ofthe building model there is a tension stress in the hillsideslope in a crest parts and the steeped foundation shows aminimum effect on the slope This appears as a small valueof compression stress in both directions and no tension stressappears underneath the steeped foundation of the model
For hillside slope angle 60∘ deformation of hillside slopewith raft foundation a small part of the hillside will take offa tension stress appears underneath the foundation in both
6 ISRN Civil Engineering
05
1015202530354045
I 60 R 25I 25R 45I 45R 60iso
Fixedraft
Foundation system with slope
Fixed
N1 gN05 gN025 g
Nor
mal
forc
e (t)
(a) Base column normal force
02468
10121416
Foundation system with slope
I 60 R 25I 25R 45I 45R 60iso
Fixedraft
Fixed
Shea
r for
ce (t
)
Q 1gQ 05 gQ 025 g
(b) Base column shear force
02468
1012141618
I 60 R 25I 25R 45I 45R 60iso
Fixedraft
Foundation system with slope
Fixed
M1 gM05 gM025 g
Mom
ent (mmiddott
)
(c) Base column bending moment
0
5
10
15
20
Dis
(cm
)
I 60 R 25I 25R 45I 45R 60iso
Fixedraft
Foundation system with slope
Fixed
Dis 1gDis 05 gDis 025 g
(d) Displacement of top floor
0
05
1
15
2
25
Acce
lera
tion
(g)
I 60 R 25I 25R 45I 45R 60iso
Fixedraft
Foundation system with slope
Fixed
Acceleration 1gAcceleration 05 gAcceleration 025 g
(e) Acceleration of top floor
Figure 4 Straining actions of 2D building with different types of foundation system and slope angle with El Centro earthquake excitation
directions and stepped foundationmodel appears to bemorestable than raft foundation model because there is no tensionbetween foundation and soil
If the PGA equal to 05 g for the hillside slope 25∘no tension between both types of foundation and the soil
underneath both stress are compression in both directionswhich have a large values In hillside slope 45∘ stressunderneath a raft foundation model approximates to zeroin both directions and this means the model is aboutrotation to be destroyed but the steeped foundation was
ISRN Civil Engineering 7
0
2
4
6
8
10
12
60 R 25 iso25 R45 iso45 R60 iso R fixed I fixedFoundation system with slope
N1 gN05 gN025 g
Nor
mal
forc
e (t)
(a) Base column normal force
0
05
1
15
2
25
3
60 R 25 iso25 R45 iso45 R60 iso R fixed I fixedFoundation system with slope
Base
shea
r (t)
Q 1gQ 05 gQ 025 g
(b) Base column shear force
0
05
1
15
2
25
3
35
60 R 25 iso25 R45 iso45 R60 iso R fixed I fixedFoundation system with slope
M1 gM05 gM025 g
Bend
ing
mom
ent (mmiddott
)
(c) Base column bending moment
002040608
112141618
Dis
(cm
)
60 R 25 iso25 R45 iso45 R60 iso R fixed I fixedFoundation system with slope
Dis 1gDis 05 gDis 025 g
(d) Displacement of top floor
002040608
112141618
Acce
lera
tion
(g)
60 R 25 iso25 R45 iso45 R60 iso R fixed I fixedFoundation system with slope
Acceleration 1gAcceleration 05 gAcceleration 025 g
(e) Acceleration of top floor
Figure 5 Straining actions of 2D model with different types of foundation and slope angles with Northridge earthquake
8 ISRN Civil Engineering
minus100
minus90
minus80
minus70
minus60
minus50
minus40
minus30
minus20
minus10
0 10
20
30
minus132
minus121
minus110
minus99
minus88
minus77
minus66
minus55
minus44
minus33
minus22
minus11
0 11
Stress in x direction stress Stress in z direction stress
(a) Slope 60∘
minus910
minus840
minus770
minus700
minus630
minus560
minus490
minus420
minus350
minus280
minus210
minus140
minus70
00
minus390
minus360
minus330
minus300
minus270
minus240
minus210
minus180
minus150
minus120
minus90
minus60
minus30
00
Stress in x direction stressStress in z direction stress
(b) Slope 45∘
minus168
minus154
minus140
minus126
minus112
minus98
minus84
minus70
minus56
minus42
minus28
minus14
00
14
minus585
minus540
minus495
minus450
minus405
minus360
minus315
minus270
minus225
minus180
minus135
minus90
minus45
00
Stress in x direction stress Stress in z direction stress
(c) Slope 25∘
Figure 6 Stress distribution on 2D slope with different slope angles under static load
more stable because there is a small value of compressionstress underneath foundation For a hillside slope angle45 the straining action on the slope is moderate withouttension stress between raft foundation in 119911-direction andthe hillside soil will but there is a tension stress betweenthe raft foundation building model and the hillside soil in119909-direction which means collapse of the building modeland there is a tension stress in the hillside slope in a crestparts and the steeped foundation shows aminimum effect on
the slope This appears as a small value of compression stressin both directions and no tension stress appears underneaththe steeped foundation of the model
Figure 8 illustrates the straining actions of the hillsideslope under Northridge earthquake excitation with differentkinds of foundation systems and slopes For PGA 1 g slope60∘ there is a tension stress between foundation and soil onthe slope this indicated a failure of the model for both kindsof foundation (raft and stepped) deformation for stepped
ISRN Civil Engineering 9
minus102
minus94
minus86
minus78
minus70
minus62
minus54
minus46
minus38
minus30
minus22
minus14
minus6
00
minus102
minus94
minus86
minus78
minus70
minus62
minus54
minus46
minus38
minus30
minus22
minus14
minus6
00
480
420
360
300
240
180
120
6000minus60
minus120
minus180
minus240
minus300
420
360
300
240
180
120
6000minus60
minus120
minus180
minus240
minus300
minus360
Deformation
Deformation
(B) Stepped foundation
(A) Raft foundation x directionz direction
x direction z direction
(a) Straining action on slope 60∘
400
350
300
250
200
150
100
5000minus50
minus100
minus150
minus200
minus250
160
8000minus80
minus160
minus240
minus320
minus400
minus480
minus560
minus640
minus720
minus800
360
315
270
225
180
135
904500minus45
minus90
minus135
minus180
minus225
minus16
minus24
minus32
minus40
minus48
minus56
minus64
minus70
minus78
minus86
minus94
minus102
minus110
Deformation
Deformation
(A) Stepped foundation
(B) Raft foundation
x directionz direction
x direction z direction
(b) Straining action on slope 45∘
Figure 7 Continued
10 ISRN Civil Engineering
minus78
minus52
minus26
00265278104
130
156
182
208
234
260
603000minus30
minus60
minus90
minus120
minus150
minus180
minus210
minus240
minus270
minus300
minus330
minus80
minus60
minus40
minus20
0020406080100
120
140
160
180
84562800minus28
minus56
minus84
minus112
minus140
minus168
minus196
minus224
minus252
minus280
Deformation
Deformation
(A) Raft foundation
(B) Raft foundation
x directionz direction
x direction z direction
(c) Straining action on slope 25∘
Figure 7 Straining actions of 2D building with different types of foundation system and slope angle with El Centro earthquake excitationwith PGA equal to 1 g
Table 2 Conclusion of model stable with different earthquake PGA
Earthquakeacceleration
Hillside slopeangle
Static stability of slope only Dynamic stability withconstructed one building
Dynamic stability withconstructed series building
Tension stress Compressionstress
Tension stressunder building
Compressionstress underbuilding
Tension stressunder building
Compressionstress underbuilding
1 g60∘ No Yes Yes mdash Yes mdash45∘ No Yes Yes mdash Yes mdash25∘ No Yes No Yes Yes mdash
050 g60∘ No Yes Yes mdash Yes mdash45∘ No Yes Yes mdash Yes mdash25∘ No Yes No Yes mdash Yes
025 g60∘ No Yes Yes mdash Yes mdash45∘ No Yes No Yes Yes mdash25∘ No Yes No Yes mdash Yes
foundation is bigger than a raft foundation model and thestraining action seems to be lower than the correspondingvalues of El Centro earthquake exaltation For slope 45∘ and1 g PGA there is no tension stress between foundation and soilon the hillside slope but the compression stress in the slope issmall with respect to 60∘ slope and the corresponding valuesin 25∘ slope are bigger than 45∘ and no tension stress appears
The results obtained from Northridge earthquake aresimilar in trend with these founded from El Centro earth-quake excitation
Table 2 concluded the results of model stress founded onthe slopes with the view of stability or not under differentearthquake excitationThe stability of a series of building con-struction on a slope under earthquake excitation was studiedand also concluded in Table 2 It seem that series buildings
can bemore critical than one building and it is shown that theconstruction of series buildings on a slope from60 to 45 anglecan be destroyed under moderate earthquake even so theseries buildings withstand the same earthquake magnitudesif it is founded on a flat land foundation
6 Conclusions
A 2D building model founded on a hillside slope was evalu-ated to check the performance of buildings and slopes undervarious earthquake time history excitation and magnitudestudying a real case of study in a Doronka village in UpperEgypt Two earthquake time histories were used El Centroand Northridge earthquake with 025 g 05 g and 1 g PGAmagnitudeThe models used were prepared to agree with the
ISRN Civil Engineering 11
13
0minus13
minus26
minus39
minus52
minus65
minus78
minus91
minus104
minus117
minus130
minus143
minus156
0minus22
minus44
minus66
minus88
minus110
minus132
minus154
minus176
minus198
minus220
minus242
minus262
minus286
12
0minus12
minus24
minus36
minus48
minus60
minus72
minus84
minus96
minus108
minus120
minus132
minus144
minus44
minus66
minus88
minus110
minus132
minus154
minus176
minus198
minus220
minus242
minus262
minus286
minus600
minus550
minus500
minus450
minus400
minus350
minus300
minus250
minus200
minus150
minus100
minus50
00
50
0minus9
minus18
minus27
minus36
minus45
minus54
minus63
minus72
minus81
minus90
minus99
minus108
minus117
60
00
minus60
minus120
minus180
minus240
minus300
minus360
minus420
minus480
minus540
minus600
minus660
minus720
12
0minus12
minus24
minus36
minus48
minus60
minus72
minus84
minus96
minus108
minus120
minus132
minus144
X directionZ direction Deformation
Deformation
Deformation
Deformation
(i) Raft foundation
(ii) Stepped foundation
(iii) Stepped foundation
(iv) Raft foundation
x direction z direction
x direction z direction
x directionz direction
(a) Straining action on slope 45∘
Figure 8 Continued
12 ISRN Civil Engineering
34
17
00
minus17
minus34
minus51
minus68
minus85
minus102
minus119
minus136
minus153
minus170
minus187
45
00
minus45
minus90
minus135
minus180
minus225
minus270
minus315
minus360
minus405
minus450
minus495
minus540
14
00
minus14
minus28
minus42
minus56
minus70
minus84
minus98
minus112
minus126
minus140
minus154
minus168
45
00
minus45
minus90
minus135
minus180
minus225
minus270
minus315
minus360
minus405
minus450
minus495
minus540
Deformation
Deformation
(v) Raft foundation
(vi) Stepped foundation
x directionz direction
x direction z direction
(b) Straining action on slope 25∘
Figure 8 Straining actions of 2D building with different types of foundation system and slope angle with Northridge earthquake excitationwith PGA equals 1 g
reality of the nature of the case study and the slopes were 60∘45∘ and 25∘ and the foundation system to be stepped isolatedor raft foundations The nonlinear parameters of the rockytype soil were provided to SAP2000 program as a curve of soilunder cyclic loading Applying the two selected earthquaketime histories with different PGA on a free hillside slope frombuilding and with only one building and then with a series ofbuildings the highlight points can be drawn as follows
(i) Static analysis of hillside with different angles ofslopes was found to be stable
(ii) The study gives an overview of the stability of hillsideslopes under earthquake excitations especially forconstruction requirements
(iii) The stability of slopes (without constructing build-ings) (with slope angles range from 60∘ to 25∘) isacceptable in the high PGA for the study of rocky soilno tensile stress was found in the hillside slope
(iv) Compression stress in a hillside slope angle 60∘decreased by 15 times than hillside slope angle 45∘and decreased by 14 times than hillside slope 25∘under seismic excitations
(v) The interplay between dynamic ldquoinertialrdquo effects aris-ing from the ground vibration and the quasistaticldquokinematicrdquo effects arising from the downwardmove-ment of a shallow sliding soil wedge are studied Itwas thus determined that a rigid raft foundationplaced on a big angle slope which is in a precariousequilibrium and fails during very strong shakingcannot protect the superstructure from both falling(being dragged) with the sliding soil mass and fromsuffering large damaging internal forces
(vi) This is in qualitative agreement with several casehistories of structures that have survived the com-bined effects of strong seismic shaking and of soildownward sliding The penalty to pay however is(a) appreciable rotation and lateral displacement ofthe whole system which may impair the serviceabilityof the structure and (b) generation of large bendingmoments and shear forces in the foundation slabby contrast as in fact most engineers would haveintuitively predicted placing a structure with isolatedfootings on a seismically unstable slope would be aprudent decision
(vii) It is recommended to flatten the slope from 60∘ to45∘ to avoid wedge failures at all isolated steppedfoundation locations (normal force decreased by 50for a slope angle 60∘ than slope angle 45∘ and baseshear decreased by 40 in a slope angle 60∘ than slopeangle 45∘)
(viii) The difference in straining action between steps andraft fixed base under dynamic loads is not significant(base shear in raft foundation increased by 2 thanstepping isolated footing 3 in bending moment 5in top displacement and 7 in top floor acceleration)
(ix) Stepped isolated foundation represents the best solu-tion for both dynamic performance of superstructureconstructed on hillside slope and the stability ofthe slope (columns normal force for isolated footingdecreased by 133 times than raft foundation anddecreased by 145 times in base shear) in 2D the effectof the tie beams to connect stepped footing has beenignored
ISRN Civil Engineering 13
(x) Series buildings constructed on a hillside slope espe-cially 60∘ angle normal force increased by nearly 15times than the one building model 175 times forshear force 140 times in bending moment and 125times for displacement and decreased by 020 timesfor top floor acceleration
This conclusion drawn from a 2D analysis remains validfor the 3D cases since more attenuation would be observedif the radiation damping into the third dimension wastaken into consideration These very local conditions are notadequately captured by the analysis However verification isrequired to check the results in 2D and 3D
Conflict of Interests
The author declares that there is no conflict of interestsregarding the publication of this paper
References
[1] E Spencer ldquoA method of analysis of the stability of embank-ments assuming parallel inter slice forcesrdquo Geo-Technique vol17 no 1 pp 11ndash26 1967
[2] H S Yu R Salgado S W Sloan and J M Kim ldquoLimitanalysis versus limit equilibrium for slope stabilityrdquo Journal ofGeotechnical Engineering (ASCE) vol 124 no 1 pp 1ndash11 1998
[3] A Troncone ldquoNumerical analysis of a landslide in soils withstrain-softening behaviourrdquo Geotechnique vol 55 no 8 pp585ndash596 2005
[4] D Pitilakis ldquoTopographic irregularities and soilmdashfoundationmdashstructure interactionrdquo in Proceedings of the 3rd Japan-GreeceWorkshop on Seismic Design Observation and Retrofit of Foun-dations pp 335ndash343 Santorini Greece 2009
[5] I Anastasopoulos G Gazetas M F Bransby M C RDavies and A El Nahas ldquoFault rupture propagation throughsand finite-element analysis and validation through centrifugeexperimentsrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 133 no 8 pp 943ndash958 2007
[6] G M Latha and A Garaga ldquoStability analysis of a rock slopein Himalayasrdquo Geomechanics and Engineering vol 2 no 2 pp125ndash140 2010
[7] A D Pandey P Kumar and S Sharma ldquoSeismic soil structureinteraction of buildings on hill slopesrdquo International Journal ForComputational Civil and Structural Engineering vol 2 no 2 pp544ndash555 2011
[8] R Kourkoulis I Anastasopoulos F Gelagoti and G GazetasldquoInteraction of foundation-structure systems with seismicallyprecarious slopes numerical analysis with strain softeningconstitutivemodelrdquo Soil Dynamics and Earthquake Engineeringvol 30 no 12 pp 1430ndash1445 2010
[9] S Rampello L Callisto and P Fargnoli ldquoEvaluation of seismiccoefficients for slope stability analysis using a displacement-based approachrdquo in Proceedings of the Seismic EngineeringInternational Conference Commemorating the 1908 Messina andReggio Calabria Earthquake (MERCEA rsquo08) 2008
[10] R L Michalowski and L You ldquoDisplacements of reinforcedslopes subjected to seismic loadsrdquo Journal of Geotechnical andGeoenvironmental Engineering vol 126 no 8 pp 685ndash6942000
[11] D S Chavan G Mondal and A Prashant ldquoPermanent dis-placement of nailed soil slopes subjected to earthquake load-ingrdquo in Proceedings of the 15th World Conference on EarthquakeEngineering (WCEE rsquo12) Lisbon Portugal 2012
[12] A Krishnamoorthy ldquoFactor of safety of a slope subjected toseismic loadrdquoElectronic Journal of Geotechnical Engineering vol12 2007
[13] O Mavrouli J Corominas and J Wartman ldquoMethodology toevaluate rock slope stability under seismic conditions at Solade Santa Coloma Andorrardquo Natural Hazards and Earth SystemScience vol 9 no 6 pp 1763ndash1773 2009
[14] ECOL 201 The Egyptian Code For Calculation of Loads andForces in Structural Building Work Housing and BuildingResearch Center Cairo Egypt 2008
[15] SAP200 Nonlinear Version 14 Static and Dynamic Finite Ele-ments Analysis of Structure Computers amp Structures BerkeleyCalif USA 2010
[16] K D Hjelmstad Fundamentals of Structural MechanicsSpringer New York NY USA 2nd edition 2005
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ISRN Civil Engineering 3
principle using analytical procedures which account fortime-dependent seismic action and that allow an evaluationof the induced displacement to be obtained If a pseudostaticapproach is adopted in this case the equivalent seismiccoefficients used in limit equilibrium calculations must becalibrated against specifying levels of slope performance andin turn defined by specifying threshold values of earthquake-induced displacements In fact in the pseudostatic approachthe safety factor provides an indirect estimate of the seismicperformance of the slope to earthquake loading while understatic conditions it represents a measure of the distance froma potential failure mechanism
In situ soil slopes and embankments are often reinforcedwith nails to improve their static and seismic performanceMichalowski and You [10] developed an approximatemethodbased on the kinematic approach of limit analysis to estimatethe permanent displacement of geosynthetic-reinforced soilslopes subjected to earthquake loading Chavan et al [11]verified this approximatemethod through finite element (FE)analysis of nails and soil slopes considering the soil and thenails as nonlinear and linear elastic materials respectivelyRadiation damping has been considered by using Lysmer-Kuhlemeyer (L-K) dampers at the soil boundaries of theFE model Soil is assumed to be dry and cohesionlessand analyzed under plane strain conditions The permanentdisplacements from approximate method and FE analysishave been compared It is found that the displacements fromFE analysis are considerable (more than 10) less than thosefrom approximate method
Krishnamoorthy [12] obtained a procedure to evaluate thefactor of safety of the slope (1 1) subjected to seismic loadusing Monte Carlo technique The proposed method can beused to obtain simply the factor of safety of the slope anddeformation of the slope
Mavrouli et al [13] presented an analytical methodologyto evaluate rock slope stability under seismic conditions byconsidering the geomechanical and topographic propertiesof a slope The objective is to locate potential rock fall sourceareas and evaluate their susceptibility in terms of probabilityof failure For this purpose the slope face of a study area isdiscretized into cells having homogenous aspect slope anglerock properties and joint set orientations A pseudostaticlimit equilibrium analysis is performed for each cell wherebythe destabilizing effect of an earthquake is represented bya horizontal force The value of this force is calculated bylinear interpolation between the peak horizontal groundacceleration PGA at the base and the top of the slope Theground acceleration at the top of the slope is increased by 50to account for topographic amplification The uncertaintyassociated with the joint dip is taken into account usingthe Monte Carlo method The proposed methodology wasapplied to a study site with moderate seismicity in Solrsquoade Santa Coloma located in the Principality of AndorraThe results of the analysis are consistent with the spatialdistribution of historical rock falls that have occurred since1997 Moreover the results indicate that for the studiedarea (1) the most important factor controlling the rock fallsusceptibility of the slope is the water pressure in jointsand (2) earthquake shaking with PGA of 016 g will cause
a significant increase in rock fall activity only if water levelsin the joints are greater than 50 of the joint height
Figure 2 illustrates the models used for the analysisof different cases for constructing both isolated and raftfoundation cases The angles of slopes 120601 are 60∘ 45∘ and 25∘depending on the slope location in the nature (dimensionsof the models were in m) The finite-element (FE) analysescan be successfully utilized to model the generation ofsliding failure surfaces in the slope reproducing similarfailure surfaces with those derived from limit-equilibriumand limit-analysis methods and leading to similar yieldaccelerations But the capability to treat realistically thedynamic response to ground shaking is an exclusive attributeof the numerical (FE) methodology not of the pseudostaticlimit equilibriumanalysis methods An additional capabilityof the numerical (FE) methodology is that any structure-foundation system can be placed on the slope For thepurpose of the present study a discretization of 05mtimes05mhas been adopted as in Kourkoulis et al [8]
The finite element (FE) method is one of many stresses-deformation methods It is widely accepted for its accuracyin modeling different geological geotechnical phenomena asit implements physical laws During the last decade majorimprovements in efficiency and configuration have made iteasier and cheaper to use and therefore it has become a morecommon tool in science and engineering
3 Selection of Adequate Accelerographs
The recorded accelerographs of Northridge (1989) and ElCentro (1940) earthquakes are shown in Figure 3 Sincethere are no accelerographs available (neither recorded norpredicted based on the seismic risk analyses) in the areathe above accelerographs are selected for seismic analysesof the model According to the Egyptian code of practicefor seismic resistant design of buildings [14] the city ofDoronka is classified as the area by relatively low seismicrisk and the design acceleration of the area is recommendedto 025 g Thus the above mentioned accelerographs havebeen scaled and corrected for this amount Egypt in thelast years was classified as high seismic regions so theresearch will analyse the buildings constructed on hillsideslope subjected to earthquake acceleration 025 05 and 1 g tocover all possibilities of how earthquake force can affect thearea Time history analysis is carried out using SAP200 [15]program considering the factor of acceleration 025 05 and1 g and nonlinear analysis with 4000 step at 40 sec for bothtime history used earthquakes (El Centro and Northridgeearthquakes)The time history corresponding to 5dampingis considered which is reasonable for concrete structure
4 Model Description
The 2D building model consists of frame elements as beamand column The column dimension is 50 times 50 cm andthe beam section is 25 times 50 cm all over the height of thebuildingThe foundation is chosen to be either raft or isolatedfoundation in the analyses A 4-story building was modeled
4 ISRN Civil Engineering
Earthquake
X
Z
120601∘
(a) Slope with angle 120601 with directions of earthquakes
2000
2000
200
0
Changeable
Chan
geab
le
500
300
1500
120601∘
(b) Building on slope constructed on isolated footing
Earthquake
X
Z
(c) Stepped buildings on slope constructed on isolated footing (d) Stepped buildings on slopes constructed onraft foundation
Figure 2 Finite element mesh in the area of the slope the discretization is denser (05m times 05m quadrilateral elements)
Acce
lera
tion
(cm
ss
)
600
0
minus600
0 8 16 24 32 40
Time (s)
(a) El Centro
Acce
lera
tion
(cm
ss
)
600
0
minus600
0 8 16 24 32 40
Time (s)
(b) Northridge
Figure 3 Acceleration time histories of the earthquakes in N-S direction
with a 3m height (each story) and a 15m length as shown inFigure 2
No matter what type and size of RC structure is underinvestigation the finite element method (FEM) is the mostaccurate and reliable numerical technique for assessing thedemands on structure components in both 2D and 3Ddomains
The inelastic analysis is performed and the failure crite-rion used for both the soil and the structure members has tobe stated as well
Frame members primarily not only serve to carry themajority of gravity loads in a building but also serve as partof lateral resisting systems Bernoulli-Euler beam theory andTimoshenko beam theoryHjelmstad [16] if considering sheareffects of deep beam are widely used and have been imple-mented in most computer-based frame analysis packages
A Beam element was loaded with constant distributed loadsequal to 250 tonm1015840 at all floor levels in addition to ownweight of elements
5 Results and Analysis
To evaluate the performance of buildings constructed onhillside slopes at Doronka city two main parts were studiedthe first part is the performance of the building with adifferent foundation system to seismic loads on the hillsideslope and presenting the straining actions of them resultingfrom two earthquakes (El Centro and Northridge earth-quakes) analyses in steps that is first 025 g 05 g and 1 g inincreasing order of the PGAand the secondpart evaluated theperformance of hillside slope (slope angles 60∘ 45∘ and 25∘)
ISRN Civil Engineering 5
Table 1 Description of used symbols in different curves
Symbols Description
I 60∘ Building on 60∘ slope angle founded on isolatedfooting
R 60∘ Building on 60∘ slope angle founded on raft footing
I 45∘ Building on 45∘ slope angle founded on isolatedfooting
R 45∘ Building on 45∘ slope angle founded on raft footing
I 25∘ Building on a 25∘ slope angle founded on isolatedfooting
R 25∘ Building on a 25∘ slope angle founded on isolatedfooting
Fixed ISO Building with fixed stepped isolated footingFixed raft Building with fixed raft footing
under static and seismic loads with and without constructedbuilding to evaluate the static and dynamic stability of thehillside slope
Figure 4 represents the straining actions of the analyzedmodel using El Centro earthquake time history taking intoconsideration the various types of slope angles ground accel-erations and foundation systems (isolated or raft foundationsystem) Figure 4(a) shows variations of normal force in basecolumns for a building founded at a 60∘ slope with raftfoundation and the normal force recorded the highest valuewith respect to the other casesThe greater the slope angle thegreater the normal forces
Figure 4(c) shows bending moment for base column Amaximum bending moment occurs in raft foundation onslope angle 60∘ in 1 g acceleration but in 050 g accelerationthe maximum value was found in raft foundation with 45∘slope angle Figure 4(d) represents the top floor displacementand themaximum value of displacement for the testedmodelwas founded in raft foundation on slope angle 60∘ thisbehavior was repeated in all used accelerations
Table 1 describes the used symbols in different curvesFigure 4(e) shows the values of top floor acceleration of
the building model the maximum top floor acceleration wasregistered in the case of raft foundation on a 25∘ slope anglenearly 24 times the applied acceleration on the model for1 g acceleration 27 times the applied acceleration (050 g)and equals to 2 times the applied acceleration (025 g) fromfigure its can improved that the slope has not effect on thevalues of bending moment of base column except for R 25(raft foundation on hillside slope 25∘) nearly increased by 175times than all cases the bending moments in fixed base casesregistered a lower value with respect to the rest cases
Figure 5 shows the straining actions of the analyzedmod-els using Northridge time history earthquake model takinginto consideration the various types of slope angles groundaccelerations and foundation systems (stepped isolated orraft foundation system) Figure 5(a) shows the variation ofnormal force in base columns and building founded on 60∘slope with raft foundation gives the highest value of thenormal force with respect to the other cases (nearly morethan the other cases by 25 times) the big slope effect on
the oblique of the building so that the high value of normalforce Figure 5(b) illustrates that base shear force at the raftfoundation system in 60∘ slope angle gives the maximumvalue with respect to the other slopes and a foundationsystem this phenomenon was repeated for the three selectedground accelerations
Figure 5(c) shows that base bendingmoment for base col-umn maximum bending moment occurs in raft foundationcase on slope angle 60∘ and rafton slope 25∘ in 1 g accelerationbut in 050 g and 025 g acceleration the values were nearlyconstant Figure 4(d) represents the top floor displacementand themaximumvalue of displacement of the testedmodelsdisplacement of model in 60∘ slope was smaller than in 25∘by 115 times and this behavior was repeated in all usedaccelerations
Figure 5(e) shows the values of top floor accelerationof models and the maximum top floor acceleration wasregistered in the case of raft foundation on a 25∘ slope anglenearly 16 times the applied acceleration on the model for 1 g050 g and 025 g cases of the applied acceleration
The results founded fromEl Centro earthquake excitationwere in the same trend with Northridge earthquake exalta-tion
Figure 6 displays the stress distribution in 119909- and 119911-directions of 2D slopes (angles 60∘ 45∘ and 25∘) under staticcondition Figure 6(c) shows the stress distribution in 119909-and 119911-directions and all stresses are negative (compressionstress) with the allowable stress for the rocky soil of thehillside in Figure 6(b) stress in the hillsidewith slope 45∘ withmoderate compression stress but in Figure 5(a) the stress alsoin compression but with low value that because of the highervalue of slope angle 60∘
To evaluate the effect of different kind of foundationsystem on hillside slopes under El Centro earthquake with025 g 05 g and 1 g PGA (Pick Ground Acceleration) exci-tation there are three actual slopes that were tested (60∘45∘ and 25∘) Only hillside slopes under 1 g PGA are shownin Figure 7 A hillside slope 25∘ subjected to El Centroearthquake with PGA 1 g with raft foundation stress in 119909-direction no tension between foundation and soil under-neath the model and so in 119911-direction generally no tensionstress come out in thewhole of the slopeThe surface of failureappears under raft foundation more straight but for steepedfoundation the surface looks like a quarter circle (criticalcircle of slip) Compression stress in hillside slope underneathsteeped foundation is bigger than raft foundation
For a hillside slope angle 45 the straining action onthe slope is moderate without tension stress between raftfoundation in 119911-direction and the hillside soil will but thereis a tension stress between the raft foundation buildingmodeland the hillside soil in 119909-direction which means collapse ofthe building model there is a tension stress in the hillsideslope in a crest parts and the steeped foundation shows aminimum effect on the slope This appears as a small valueof compression stress in both directions and no tension stressappears underneath the steeped foundation of the model
For hillside slope angle 60∘ deformation of hillside slopewith raft foundation a small part of the hillside will take offa tension stress appears underneath the foundation in both
6 ISRN Civil Engineering
05
1015202530354045
I 60 R 25I 25R 45I 45R 60iso
Fixedraft
Foundation system with slope
Fixed
N1 gN05 gN025 g
Nor
mal
forc
e (t)
(a) Base column normal force
02468
10121416
Foundation system with slope
I 60 R 25I 25R 45I 45R 60iso
Fixedraft
Fixed
Shea
r for
ce (t
)
Q 1gQ 05 gQ 025 g
(b) Base column shear force
02468
1012141618
I 60 R 25I 25R 45I 45R 60iso
Fixedraft
Foundation system with slope
Fixed
M1 gM05 gM025 g
Mom
ent (mmiddott
)
(c) Base column bending moment
0
5
10
15
20
Dis
(cm
)
I 60 R 25I 25R 45I 45R 60iso
Fixedraft
Foundation system with slope
Fixed
Dis 1gDis 05 gDis 025 g
(d) Displacement of top floor
0
05
1
15
2
25
Acce
lera
tion
(g)
I 60 R 25I 25R 45I 45R 60iso
Fixedraft
Foundation system with slope
Fixed
Acceleration 1gAcceleration 05 gAcceleration 025 g
(e) Acceleration of top floor
Figure 4 Straining actions of 2D building with different types of foundation system and slope angle with El Centro earthquake excitation
directions and stepped foundationmodel appears to bemorestable than raft foundation model because there is no tensionbetween foundation and soil
If the PGA equal to 05 g for the hillside slope 25∘no tension between both types of foundation and the soil
underneath both stress are compression in both directionswhich have a large values In hillside slope 45∘ stressunderneath a raft foundation model approximates to zeroin both directions and this means the model is aboutrotation to be destroyed but the steeped foundation was
ISRN Civil Engineering 7
0
2
4
6
8
10
12
60 R 25 iso25 R45 iso45 R60 iso R fixed I fixedFoundation system with slope
N1 gN05 gN025 g
Nor
mal
forc
e (t)
(a) Base column normal force
0
05
1
15
2
25
3
60 R 25 iso25 R45 iso45 R60 iso R fixed I fixedFoundation system with slope
Base
shea
r (t)
Q 1gQ 05 gQ 025 g
(b) Base column shear force
0
05
1
15
2
25
3
35
60 R 25 iso25 R45 iso45 R60 iso R fixed I fixedFoundation system with slope
M1 gM05 gM025 g
Bend
ing
mom
ent (mmiddott
)
(c) Base column bending moment
002040608
112141618
Dis
(cm
)
60 R 25 iso25 R45 iso45 R60 iso R fixed I fixedFoundation system with slope
Dis 1gDis 05 gDis 025 g
(d) Displacement of top floor
002040608
112141618
Acce
lera
tion
(g)
60 R 25 iso25 R45 iso45 R60 iso R fixed I fixedFoundation system with slope
Acceleration 1gAcceleration 05 gAcceleration 025 g
(e) Acceleration of top floor
Figure 5 Straining actions of 2D model with different types of foundation and slope angles with Northridge earthquake
8 ISRN Civil Engineering
minus100
minus90
minus80
minus70
minus60
minus50
minus40
minus30
minus20
minus10
0 10
20
30
minus132
minus121
minus110
minus99
minus88
minus77
minus66
minus55
minus44
minus33
minus22
minus11
0 11
Stress in x direction stress Stress in z direction stress
(a) Slope 60∘
minus910
minus840
minus770
minus700
minus630
minus560
minus490
minus420
minus350
minus280
minus210
minus140
minus70
00
minus390
minus360
minus330
minus300
minus270
minus240
minus210
minus180
minus150
minus120
minus90
minus60
minus30
00
Stress in x direction stressStress in z direction stress
(b) Slope 45∘
minus168
minus154
minus140
minus126
minus112
minus98
minus84
minus70
minus56
minus42
minus28
minus14
00
14
minus585
minus540
minus495
minus450
minus405
minus360
minus315
minus270
minus225
minus180
minus135
minus90
minus45
00
Stress in x direction stress Stress in z direction stress
(c) Slope 25∘
Figure 6 Stress distribution on 2D slope with different slope angles under static load
more stable because there is a small value of compressionstress underneath foundation For a hillside slope angle45 the straining action on the slope is moderate withouttension stress between raft foundation in 119911-direction andthe hillside soil will but there is a tension stress betweenthe raft foundation building model and the hillside soil in119909-direction which means collapse of the building modeland there is a tension stress in the hillside slope in a crestparts and the steeped foundation shows aminimum effect on
the slope This appears as a small value of compression stressin both directions and no tension stress appears underneaththe steeped foundation of the model
Figure 8 illustrates the straining actions of the hillsideslope under Northridge earthquake excitation with differentkinds of foundation systems and slopes For PGA 1 g slope60∘ there is a tension stress between foundation and soil onthe slope this indicated a failure of the model for both kindsof foundation (raft and stepped) deformation for stepped
ISRN Civil Engineering 9
minus102
minus94
minus86
minus78
minus70
minus62
minus54
minus46
minus38
minus30
minus22
minus14
minus6
00
minus102
minus94
minus86
minus78
minus70
minus62
minus54
minus46
minus38
minus30
minus22
minus14
minus6
00
480
420
360
300
240
180
120
6000minus60
minus120
minus180
minus240
minus300
420
360
300
240
180
120
6000minus60
minus120
minus180
minus240
minus300
minus360
Deformation
Deformation
(B) Stepped foundation
(A) Raft foundation x directionz direction
x direction z direction
(a) Straining action on slope 60∘
400
350
300
250
200
150
100
5000minus50
minus100
minus150
minus200
minus250
160
8000minus80
minus160
minus240
minus320
minus400
minus480
minus560
minus640
minus720
minus800
360
315
270
225
180
135
904500minus45
minus90
minus135
minus180
minus225
minus16
minus24
minus32
minus40
minus48
minus56
minus64
minus70
minus78
minus86
minus94
minus102
minus110
Deformation
Deformation
(A) Stepped foundation
(B) Raft foundation
x directionz direction
x direction z direction
(b) Straining action on slope 45∘
Figure 7 Continued
10 ISRN Civil Engineering
minus78
minus52
minus26
00265278104
130
156
182
208
234
260
603000minus30
minus60
minus90
minus120
minus150
minus180
minus210
minus240
minus270
minus300
minus330
minus80
minus60
minus40
minus20
0020406080100
120
140
160
180
84562800minus28
minus56
minus84
minus112
minus140
minus168
minus196
minus224
minus252
minus280
Deformation
Deformation
(A) Raft foundation
(B) Raft foundation
x directionz direction
x direction z direction
(c) Straining action on slope 25∘
Figure 7 Straining actions of 2D building with different types of foundation system and slope angle with El Centro earthquake excitationwith PGA equal to 1 g
Table 2 Conclusion of model stable with different earthquake PGA
Earthquakeacceleration
Hillside slopeangle
Static stability of slope only Dynamic stability withconstructed one building
Dynamic stability withconstructed series building
Tension stress Compressionstress
Tension stressunder building
Compressionstress underbuilding
Tension stressunder building
Compressionstress underbuilding
1 g60∘ No Yes Yes mdash Yes mdash45∘ No Yes Yes mdash Yes mdash25∘ No Yes No Yes Yes mdash
050 g60∘ No Yes Yes mdash Yes mdash45∘ No Yes Yes mdash Yes mdash25∘ No Yes No Yes mdash Yes
025 g60∘ No Yes Yes mdash Yes mdash45∘ No Yes No Yes Yes mdash25∘ No Yes No Yes mdash Yes
foundation is bigger than a raft foundation model and thestraining action seems to be lower than the correspondingvalues of El Centro earthquake exaltation For slope 45∘ and1 g PGA there is no tension stress between foundation and soilon the hillside slope but the compression stress in the slope issmall with respect to 60∘ slope and the corresponding valuesin 25∘ slope are bigger than 45∘ and no tension stress appears
The results obtained from Northridge earthquake aresimilar in trend with these founded from El Centro earth-quake excitation
Table 2 concluded the results of model stress founded onthe slopes with the view of stability or not under differentearthquake excitationThe stability of a series of building con-struction on a slope under earthquake excitation was studiedand also concluded in Table 2 It seem that series buildings
can bemore critical than one building and it is shown that theconstruction of series buildings on a slope from60 to 45 anglecan be destroyed under moderate earthquake even so theseries buildings withstand the same earthquake magnitudesif it is founded on a flat land foundation
6 Conclusions
A 2D building model founded on a hillside slope was evalu-ated to check the performance of buildings and slopes undervarious earthquake time history excitation and magnitudestudying a real case of study in a Doronka village in UpperEgypt Two earthquake time histories were used El Centroand Northridge earthquake with 025 g 05 g and 1 g PGAmagnitudeThe models used were prepared to agree with the
ISRN Civil Engineering 11
13
0minus13
minus26
minus39
minus52
minus65
minus78
minus91
minus104
minus117
minus130
minus143
minus156
0minus22
minus44
minus66
minus88
minus110
minus132
minus154
minus176
minus198
minus220
minus242
minus262
minus286
12
0minus12
minus24
minus36
minus48
minus60
minus72
minus84
minus96
minus108
minus120
minus132
minus144
minus44
minus66
minus88
minus110
minus132
minus154
minus176
minus198
minus220
minus242
minus262
minus286
minus600
minus550
minus500
minus450
minus400
minus350
minus300
minus250
minus200
minus150
minus100
minus50
00
50
0minus9
minus18
minus27
minus36
minus45
minus54
minus63
minus72
minus81
minus90
minus99
minus108
minus117
60
00
minus60
minus120
minus180
minus240
minus300
minus360
minus420
minus480
minus540
minus600
minus660
minus720
12
0minus12
minus24
minus36
minus48
minus60
minus72
minus84
minus96
minus108
minus120
minus132
minus144
X directionZ direction Deformation
Deformation
Deformation
Deformation
(i) Raft foundation
(ii) Stepped foundation
(iii) Stepped foundation
(iv) Raft foundation
x direction z direction
x direction z direction
x directionz direction
(a) Straining action on slope 45∘
Figure 8 Continued
12 ISRN Civil Engineering
34
17
00
minus17
minus34
minus51
minus68
minus85
minus102
minus119
minus136
minus153
minus170
minus187
45
00
minus45
minus90
minus135
minus180
minus225
minus270
minus315
minus360
minus405
minus450
minus495
minus540
14
00
minus14
minus28
minus42
minus56
minus70
minus84
minus98
minus112
minus126
minus140
minus154
minus168
45
00
minus45
minus90
minus135
minus180
minus225
minus270
minus315
minus360
minus405
minus450
minus495
minus540
Deformation
Deformation
(v) Raft foundation
(vi) Stepped foundation
x directionz direction
x direction z direction
(b) Straining action on slope 25∘
Figure 8 Straining actions of 2D building with different types of foundation system and slope angle with Northridge earthquake excitationwith PGA equals 1 g
reality of the nature of the case study and the slopes were 60∘45∘ and 25∘ and the foundation system to be stepped isolatedor raft foundations The nonlinear parameters of the rockytype soil were provided to SAP2000 program as a curve of soilunder cyclic loading Applying the two selected earthquaketime histories with different PGA on a free hillside slope frombuilding and with only one building and then with a series ofbuildings the highlight points can be drawn as follows
(i) Static analysis of hillside with different angles ofslopes was found to be stable
(ii) The study gives an overview of the stability of hillsideslopes under earthquake excitations especially forconstruction requirements
(iii) The stability of slopes (without constructing build-ings) (with slope angles range from 60∘ to 25∘) isacceptable in the high PGA for the study of rocky soilno tensile stress was found in the hillside slope
(iv) Compression stress in a hillside slope angle 60∘decreased by 15 times than hillside slope angle 45∘and decreased by 14 times than hillside slope 25∘under seismic excitations
(v) The interplay between dynamic ldquoinertialrdquo effects aris-ing from the ground vibration and the quasistaticldquokinematicrdquo effects arising from the downwardmove-ment of a shallow sliding soil wedge are studied Itwas thus determined that a rigid raft foundationplaced on a big angle slope which is in a precariousequilibrium and fails during very strong shakingcannot protect the superstructure from both falling(being dragged) with the sliding soil mass and fromsuffering large damaging internal forces
(vi) This is in qualitative agreement with several casehistories of structures that have survived the com-bined effects of strong seismic shaking and of soildownward sliding The penalty to pay however is(a) appreciable rotation and lateral displacement ofthe whole system which may impair the serviceabilityof the structure and (b) generation of large bendingmoments and shear forces in the foundation slabby contrast as in fact most engineers would haveintuitively predicted placing a structure with isolatedfootings on a seismically unstable slope would be aprudent decision
(vii) It is recommended to flatten the slope from 60∘ to45∘ to avoid wedge failures at all isolated steppedfoundation locations (normal force decreased by 50for a slope angle 60∘ than slope angle 45∘ and baseshear decreased by 40 in a slope angle 60∘ than slopeangle 45∘)
(viii) The difference in straining action between steps andraft fixed base under dynamic loads is not significant(base shear in raft foundation increased by 2 thanstepping isolated footing 3 in bending moment 5in top displacement and 7 in top floor acceleration)
(ix) Stepped isolated foundation represents the best solu-tion for both dynamic performance of superstructureconstructed on hillside slope and the stability ofthe slope (columns normal force for isolated footingdecreased by 133 times than raft foundation anddecreased by 145 times in base shear) in 2D the effectof the tie beams to connect stepped footing has beenignored
ISRN Civil Engineering 13
(x) Series buildings constructed on a hillside slope espe-cially 60∘ angle normal force increased by nearly 15times than the one building model 175 times forshear force 140 times in bending moment and 125times for displacement and decreased by 020 timesfor top floor acceleration
This conclusion drawn from a 2D analysis remains validfor the 3D cases since more attenuation would be observedif the radiation damping into the third dimension wastaken into consideration These very local conditions are notadequately captured by the analysis However verification isrequired to check the results in 2D and 3D
Conflict of Interests
The author declares that there is no conflict of interestsregarding the publication of this paper
References
[1] E Spencer ldquoA method of analysis of the stability of embank-ments assuming parallel inter slice forcesrdquo Geo-Technique vol17 no 1 pp 11ndash26 1967
[2] H S Yu R Salgado S W Sloan and J M Kim ldquoLimitanalysis versus limit equilibrium for slope stabilityrdquo Journal ofGeotechnical Engineering (ASCE) vol 124 no 1 pp 1ndash11 1998
[3] A Troncone ldquoNumerical analysis of a landslide in soils withstrain-softening behaviourrdquo Geotechnique vol 55 no 8 pp585ndash596 2005
[4] D Pitilakis ldquoTopographic irregularities and soilmdashfoundationmdashstructure interactionrdquo in Proceedings of the 3rd Japan-GreeceWorkshop on Seismic Design Observation and Retrofit of Foun-dations pp 335ndash343 Santorini Greece 2009
[5] I Anastasopoulos G Gazetas M F Bransby M C RDavies and A El Nahas ldquoFault rupture propagation throughsand finite-element analysis and validation through centrifugeexperimentsrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 133 no 8 pp 943ndash958 2007
[6] G M Latha and A Garaga ldquoStability analysis of a rock slopein Himalayasrdquo Geomechanics and Engineering vol 2 no 2 pp125ndash140 2010
[7] A D Pandey P Kumar and S Sharma ldquoSeismic soil structureinteraction of buildings on hill slopesrdquo International Journal ForComputational Civil and Structural Engineering vol 2 no 2 pp544ndash555 2011
[8] R Kourkoulis I Anastasopoulos F Gelagoti and G GazetasldquoInteraction of foundation-structure systems with seismicallyprecarious slopes numerical analysis with strain softeningconstitutivemodelrdquo Soil Dynamics and Earthquake Engineeringvol 30 no 12 pp 1430ndash1445 2010
[9] S Rampello L Callisto and P Fargnoli ldquoEvaluation of seismiccoefficients for slope stability analysis using a displacement-based approachrdquo in Proceedings of the Seismic EngineeringInternational Conference Commemorating the 1908 Messina andReggio Calabria Earthquake (MERCEA rsquo08) 2008
[10] R L Michalowski and L You ldquoDisplacements of reinforcedslopes subjected to seismic loadsrdquo Journal of Geotechnical andGeoenvironmental Engineering vol 126 no 8 pp 685ndash6942000
[11] D S Chavan G Mondal and A Prashant ldquoPermanent dis-placement of nailed soil slopes subjected to earthquake load-ingrdquo in Proceedings of the 15th World Conference on EarthquakeEngineering (WCEE rsquo12) Lisbon Portugal 2012
[12] A Krishnamoorthy ldquoFactor of safety of a slope subjected toseismic loadrdquoElectronic Journal of Geotechnical Engineering vol12 2007
[13] O Mavrouli J Corominas and J Wartman ldquoMethodology toevaluate rock slope stability under seismic conditions at Solade Santa Coloma Andorrardquo Natural Hazards and Earth SystemScience vol 9 no 6 pp 1763ndash1773 2009
[14] ECOL 201 The Egyptian Code For Calculation of Loads andForces in Structural Building Work Housing and BuildingResearch Center Cairo Egypt 2008
[15] SAP200 Nonlinear Version 14 Static and Dynamic Finite Ele-ments Analysis of Structure Computers amp Structures BerkeleyCalif USA 2010
[16] K D Hjelmstad Fundamentals of Structural MechanicsSpringer New York NY USA 2nd edition 2005
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4 ISRN Civil Engineering
Earthquake
X
Z
120601∘
(a) Slope with angle 120601 with directions of earthquakes
2000
2000
200
0
Changeable
Chan
geab
le
500
300
1500
120601∘
(b) Building on slope constructed on isolated footing
Earthquake
X
Z
(c) Stepped buildings on slope constructed on isolated footing (d) Stepped buildings on slopes constructed onraft foundation
Figure 2 Finite element mesh in the area of the slope the discretization is denser (05m times 05m quadrilateral elements)
Acce
lera
tion
(cm
ss
)
600
0
minus600
0 8 16 24 32 40
Time (s)
(a) El Centro
Acce
lera
tion
(cm
ss
)
600
0
minus600
0 8 16 24 32 40
Time (s)
(b) Northridge
Figure 3 Acceleration time histories of the earthquakes in N-S direction
with a 3m height (each story) and a 15m length as shown inFigure 2
No matter what type and size of RC structure is underinvestigation the finite element method (FEM) is the mostaccurate and reliable numerical technique for assessing thedemands on structure components in both 2D and 3Ddomains
The inelastic analysis is performed and the failure crite-rion used for both the soil and the structure members has tobe stated as well
Frame members primarily not only serve to carry themajority of gravity loads in a building but also serve as partof lateral resisting systems Bernoulli-Euler beam theory andTimoshenko beam theoryHjelmstad [16] if considering sheareffects of deep beam are widely used and have been imple-mented in most computer-based frame analysis packages
A Beam element was loaded with constant distributed loadsequal to 250 tonm1015840 at all floor levels in addition to ownweight of elements
5 Results and Analysis
To evaluate the performance of buildings constructed onhillside slopes at Doronka city two main parts were studiedthe first part is the performance of the building with adifferent foundation system to seismic loads on the hillsideslope and presenting the straining actions of them resultingfrom two earthquakes (El Centro and Northridge earth-quakes) analyses in steps that is first 025 g 05 g and 1 g inincreasing order of the PGAand the secondpart evaluated theperformance of hillside slope (slope angles 60∘ 45∘ and 25∘)
ISRN Civil Engineering 5
Table 1 Description of used symbols in different curves
Symbols Description
I 60∘ Building on 60∘ slope angle founded on isolatedfooting
R 60∘ Building on 60∘ slope angle founded on raft footing
I 45∘ Building on 45∘ slope angle founded on isolatedfooting
R 45∘ Building on 45∘ slope angle founded on raft footing
I 25∘ Building on a 25∘ slope angle founded on isolatedfooting
R 25∘ Building on a 25∘ slope angle founded on isolatedfooting
Fixed ISO Building with fixed stepped isolated footingFixed raft Building with fixed raft footing
under static and seismic loads with and without constructedbuilding to evaluate the static and dynamic stability of thehillside slope
Figure 4 represents the straining actions of the analyzedmodel using El Centro earthquake time history taking intoconsideration the various types of slope angles ground accel-erations and foundation systems (isolated or raft foundationsystem) Figure 4(a) shows variations of normal force in basecolumns for a building founded at a 60∘ slope with raftfoundation and the normal force recorded the highest valuewith respect to the other casesThe greater the slope angle thegreater the normal forces
Figure 4(c) shows bending moment for base column Amaximum bending moment occurs in raft foundation onslope angle 60∘ in 1 g acceleration but in 050 g accelerationthe maximum value was found in raft foundation with 45∘slope angle Figure 4(d) represents the top floor displacementand themaximum value of displacement for the testedmodelwas founded in raft foundation on slope angle 60∘ thisbehavior was repeated in all used accelerations
Table 1 describes the used symbols in different curvesFigure 4(e) shows the values of top floor acceleration of
the building model the maximum top floor acceleration wasregistered in the case of raft foundation on a 25∘ slope anglenearly 24 times the applied acceleration on the model for1 g acceleration 27 times the applied acceleration (050 g)and equals to 2 times the applied acceleration (025 g) fromfigure its can improved that the slope has not effect on thevalues of bending moment of base column except for R 25(raft foundation on hillside slope 25∘) nearly increased by 175times than all cases the bending moments in fixed base casesregistered a lower value with respect to the rest cases
Figure 5 shows the straining actions of the analyzedmod-els using Northridge time history earthquake model takinginto consideration the various types of slope angles groundaccelerations and foundation systems (stepped isolated orraft foundation system) Figure 5(a) shows the variation ofnormal force in base columns and building founded on 60∘slope with raft foundation gives the highest value of thenormal force with respect to the other cases (nearly morethan the other cases by 25 times) the big slope effect on
the oblique of the building so that the high value of normalforce Figure 5(b) illustrates that base shear force at the raftfoundation system in 60∘ slope angle gives the maximumvalue with respect to the other slopes and a foundationsystem this phenomenon was repeated for the three selectedground accelerations
Figure 5(c) shows that base bendingmoment for base col-umn maximum bending moment occurs in raft foundationcase on slope angle 60∘ and rafton slope 25∘ in 1 g accelerationbut in 050 g and 025 g acceleration the values were nearlyconstant Figure 4(d) represents the top floor displacementand themaximumvalue of displacement of the testedmodelsdisplacement of model in 60∘ slope was smaller than in 25∘by 115 times and this behavior was repeated in all usedaccelerations
Figure 5(e) shows the values of top floor accelerationof models and the maximum top floor acceleration wasregistered in the case of raft foundation on a 25∘ slope anglenearly 16 times the applied acceleration on the model for 1 g050 g and 025 g cases of the applied acceleration
The results founded fromEl Centro earthquake excitationwere in the same trend with Northridge earthquake exalta-tion
Figure 6 displays the stress distribution in 119909- and 119911-directions of 2D slopes (angles 60∘ 45∘ and 25∘) under staticcondition Figure 6(c) shows the stress distribution in 119909-and 119911-directions and all stresses are negative (compressionstress) with the allowable stress for the rocky soil of thehillside in Figure 6(b) stress in the hillsidewith slope 45∘ withmoderate compression stress but in Figure 5(a) the stress alsoin compression but with low value that because of the highervalue of slope angle 60∘
To evaluate the effect of different kind of foundationsystem on hillside slopes under El Centro earthquake with025 g 05 g and 1 g PGA (Pick Ground Acceleration) exci-tation there are three actual slopes that were tested (60∘45∘ and 25∘) Only hillside slopes under 1 g PGA are shownin Figure 7 A hillside slope 25∘ subjected to El Centroearthquake with PGA 1 g with raft foundation stress in 119909-direction no tension between foundation and soil under-neath the model and so in 119911-direction generally no tensionstress come out in thewhole of the slopeThe surface of failureappears under raft foundation more straight but for steepedfoundation the surface looks like a quarter circle (criticalcircle of slip) Compression stress in hillside slope underneathsteeped foundation is bigger than raft foundation
For a hillside slope angle 45 the straining action onthe slope is moderate without tension stress between raftfoundation in 119911-direction and the hillside soil will but thereis a tension stress between the raft foundation buildingmodeland the hillside soil in 119909-direction which means collapse ofthe building model there is a tension stress in the hillsideslope in a crest parts and the steeped foundation shows aminimum effect on the slope This appears as a small valueof compression stress in both directions and no tension stressappears underneath the steeped foundation of the model
For hillside slope angle 60∘ deformation of hillside slopewith raft foundation a small part of the hillside will take offa tension stress appears underneath the foundation in both
6 ISRN Civil Engineering
05
1015202530354045
I 60 R 25I 25R 45I 45R 60iso
Fixedraft
Foundation system with slope
Fixed
N1 gN05 gN025 g
Nor
mal
forc
e (t)
(a) Base column normal force
02468
10121416
Foundation system with slope
I 60 R 25I 25R 45I 45R 60iso
Fixedraft
Fixed
Shea
r for
ce (t
)
Q 1gQ 05 gQ 025 g
(b) Base column shear force
02468
1012141618
I 60 R 25I 25R 45I 45R 60iso
Fixedraft
Foundation system with slope
Fixed
M1 gM05 gM025 g
Mom
ent (mmiddott
)
(c) Base column bending moment
0
5
10
15
20
Dis
(cm
)
I 60 R 25I 25R 45I 45R 60iso
Fixedraft
Foundation system with slope
Fixed
Dis 1gDis 05 gDis 025 g
(d) Displacement of top floor
0
05
1
15
2
25
Acce
lera
tion
(g)
I 60 R 25I 25R 45I 45R 60iso
Fixedraft
Foundation system with slope
Fixed
Acceleration 1gAcceleration 05 gAcceleration 025 g
(e) Acceleration of top floor
Figure 4 Straining actions of 2D building with different types of foundation system and slope angle with El Centro earthquake excitation
directions and stepped foundationmodel appears to bemorestable than raft foundation model because there is no tensionbetween foundation and soil
If the PGA equal to 05 g for the hillside slope 25∘no tension between both types of foundation and the soil
underneath both stress are compression in both directionswhich have a large values In hillside slope 45∘ stressunderneath a raft foundation model approximates to zeroin both directions and this means the model is aboutrotation to be destroyed but the steeped foundation was
ISRN Civil Engineering 7
0
2
4
6
8
10
12
60 R 25 iso25 R45 iso45 R60 iso R fixed I fixedFoundation system with slope
N1 gN05 gN025 g
Nor
mal
forc
e (t)
(a) Base column normal force
0
05
1
15
2
25
3
60 R 25 iso25 R45 iso45 R60 iso R fixed I fixedFoundation system with slope
Base
shea
r (t)
Q 1gQ 05 gQ 025 g
(b) Base column shear force
0
05
1
15
2
25
3
35
60 R 25 iso25 R45 iso45 R60 iso R fixed I fixedFoundation system with slope
M1 gM05 gM025 g
Bend
ing
mom
ent (mmiddott
)
(c) Base column bending moment
002040608
112141618
Dis
(cm
)
60 R 25 iso25 R45 iso45 R60 iso R fixed I fixedFoundation system with slope
Dis 1gDis 05 gDis 025 g
(d) Displacement of top floor
002040608
112141618
Acce
lera
tion
(g)
60 R 25 iso25 R45 iso45 R60 iso R fixed I fixedFoundation system with slope
Acceleration 1gAcceleration 05 gAcceleration 025 g
(e) Acceleration of top floor
Figure 5 Straining actions of 2D model with different types of foundation and slope angles with Northridge earthquake
8 ISRN Civil Engineering
minus100
minus90
minus80
minus70
minus60
minus50
minus40
minus30
minus20
minus10
0 10
20
30
minus132
minus121
minus110
minus99
minus88
minus77
minus66
minus55
minus44
minus33
minus22
minus11
0 11
Stress in x direction stress Stress in z direction stress
(a) Slope 60∘
minus910
minus840
minus770
minus700
minus630
minus560
minus490
minus420
minus350
minus280
minus210
minus140
minus70
00
minus390
minus360
minus330
minus300
minus270
minus240
minus210
minus180
minus150
minus120
minus90
minus60
minus30
00
Stress in x direction stressStress in z direction stress
(b) Slope 45∘
minus168
minus154
minus140
minus126
minus112
minus98
minus84
minus70
minus56
minus42
minus28
minus14
00
14
minus585
minus540
minus495
minus450
minus405
minus360
minus315
minus270
minus225
minus180
minus135
minus90
minus45
00
Stress in x direction stress Stress in z direction stress
(c) Slope 25∘
Figure 6 Stress distribution on 2D slope with different slope angles under static load
more stable because there is a small value of compressionstress underneath foundation For a hillside slope angle45 the straining action on the slope is moderate withouttension stress between raft foundation in 119911-direction andthe hillside soil will but there is a tension stress betweenthe raft foundation building model and the hillside soil in119909-direction which means collapse of the building modeland there is a tension stress in the hillside slope in a crestparts and the steeped foundation shows aminimum effect on
the slope This appears as a small value of compression stressin both directions and no tension stress appears underneaththe steeped foundation of the model
Figure 8 illustrates the straining actions of the hillsideslope under Northridge earthquake excitation with differentkinds of foundation systems and slopes For PGA 1 g slope60∘ there is a tension stress between foundation and soil onthe slope this indicated a failure of the model for both kindsof foundation (raft and stepped) deformation for stepped
ISRN Civil Engineering 9
minus102
minus94
minus86
minus78
minus70
minus62
minus54
minus46
minus38
minus30
minus22
minus14
minus6
00
minus102
minus94
minus86
minus78
minus70
minus62
minus54
minus46
minus38
minus30
minus22
minus14
minus6
00
480
420
360
300
240
180
120
6000minus60
minus120
minus180
minus240
minus300
420
360
300
240
180
120
6000minus60
minus120
minus180
minus240
minus300
minus360
Deformation
Deformation
(B) Stepped foundation
(A) Raft foundation x directionz direction
x direction z direction
(a) Straining action on slope 60∘
400
350
300
250
200
150
100
5000minus50
minus100
minus150
minus200
minus250
160
8000minus80
minus160
minus240
minus320
minus400
minus480
minus560
minus640
minus720
minus800
360
315
270
225
180
135
904500minus45
minus90
minus135
minus180
minus225
minus16
minus24
minus32
minus40
minus48
minus56
minus64
minus70
minus78
minus86
minus94
minus102
minus110
Deformation
Deformation
(A) Stepped foundation
(B) Raft foundation
x directionz direction
x direction z direction
(b) Straining action on slope 45∘
Figure 7 Continued
10 ISRN Civil Engineering
minus78
minus52
minus26
00265278104
130
156
182
208
234
260
603000minus30
minus60
minus90
minus120
minus150
minus180
minus210
minus240
minus270
minus300
minus330
minus80
minus60
minus40
minus20
0020406080100
120
140
160
180
84562800minus28
minus56
minus84
minus112
minus140
minus168
minus196
minus224
minus252
minus280
Deformation
Deformation
(A) Raft foundation
(B) Raft foundation
x directionz direction
x direction z direction
(c) Straining action on slope 25∘
Figure 7 Straining actions of 2D building with different types of foundation system and slope angle with El Centro earthquake excitationwith PGA equal to 1 g
Table 2 Conclusion of model stable with different earthquake PGA
Earthquakeacceleration
Hillside slopeangle
Static stability of slope only Dynamic stability withconstructed one building
Dynamic stability withconstructed series building
Tension stress Compressionstress
Tension stressunder building
Compressionstress underbuilding
Tension stressunder building
Compressionstress underbuilding
1 g60∘ No Yes Yes mdash Yes mdash45∘ No Yes Yes mdash Yes mdash25∘ No Yes No Yes Yes mdash
050 g60∘ No Yes Yes mdash Yes mdash45∘ No Yes Yes mdash Yes mdash25∘ No Yes No Yes mdash Yes
025 g60∘ No Yes Yes mdash Yes mdash45∘ No Yes No Yes Yes mdash25∘ No Yes No Yes mdash Yes
foundation is bigger than a raft foundation model and thestraining action seems to be lower than the correspondingvalues of El Centro earthquake exaltation For slope 45∘ and1 g PGA there is no tension stress between foundation and soilon the hillside slope but the compression stress in the slope issmall with respect to 60∘ slope and the corresponding valuesin 25∘ slope are bigger than 45∘ and no tension stress appears
The results obtained from Northridge earthquake aresimilar in trend with these founded from El Centro earth-quake excitation
Table 2 concluded the results of model stress founded onthe slopes with the view of stability or not under differentearthquake excitationThe stability of a series of building con-struction on a slope under earthquake excitation was studiedand also concluded in Table 2 It seem that series buildings
can bemore critical than one building and it is shown that theconstruction of series buildings on a slope from60 to 45 anglecan be destroyed under moderate earthquake even so theseries buildings withstand the same earthquake magnitudesif it is founded on a flat land foundation
6 Conclusions
A 2D building model founded on a hillside slope was evalu-ated to check the performance of buildings and slopes undervarious earthquake time history excitation and magnitudestudying a real case of study in a Doronka village in UpperEgypt Two earthquake time histories were used El Centroand Northridge earthquake with 025 g 05 g and 1 g PGAmagnitudeThe models used were prepared to agree with the
ISRN Civil Engineering 11
13
0minus13
minus26
minus39
minus52
minus65
minus78
minus91
minus104
minus117
minus130
minus143
minus156
0minus22
minus44
minus66
minus88
minus110
minus132
minus154
minus176
minus198
minus220
minus242
minus262
minus286
12
0minus12
minus24
minus36
minus48
minus60
minus72
minus84
minus96
minus108
minus120
minus132
minus144
minus44
minus66
minus88
minus110
minus132
minus154
minus176
minus198
minus220
minus242
minus262
minus286
minus600
minus550
minus500
minus450
minus400
minus350
minus300
minus250
minus200
minus150
minus100
minus50
00
50
0minus9
minus18
minus27
minus36
minus45
minus54
minus63
minus72
minus81
minus90
minus99
minus108
minus117
60
00
minus60
minus120
minus180
minus240
minus300
minus360
minus420
minus480
minus540
minus600
minus660
minus720
12
0minus12
minus24
minus36
minus48
minus60
minus72
minus84
minus96
minus108
minus120
minus132
minus144
X directionZ direction Deformation
Deformation
Deformation
Deformation
(i) Raft foundation
(ii) Stepped foundation
(iii) Stepped foundation
(iv) Raft foundation
x direction z direction
x direction z direction
x directionz direction
(a) Straining action on slope 45∘
Figure 8 Continued
12 ISRN Civil Engineering
34
17
00
minus17
minus34
minus51
minus68
minus85
minus102
minus119
minus136
minus153
minus170
minus187
45
00
minus45
minus90
minus135
minus180
minus225
minus270
minus315
minus360
minus405
minus450
minus495
minus540
14
00
minus14
minus28
minus42
minus56
minus70
minus84
minus98
minus112
minus126
minus140
minus154
minus168
45
00
minus45
minus90
minus135
minus180
minus225
minus270
minus315
minus360
minus405
minus450
minus495
minus540
Deformation
Deformation
(v) Raft foundation
(vi) Stepped foundation
x directionz direction
x direction z direction
(b) Straining action on slope 25∘
Figure 8 Straining actions of 2D building with different types of foundation system and slope angle with Northridge earthquake excitationwith PGA equals 1 g
reality of the nature of the case study and the slopes were 60∘45∘ and 25∘ and the foundation system to be stepped isolatedor raft foundations The nonlinear parameters of the rockytype soil were provided to SAP2000 program as a curve of soilunder cyclic loading Applying the two selected earthquaketime histories with different PGA on a free hillside slope frombuilding and with only one building and then with a series ofbuildings the highlight points can be drawn as follows
(i) Static analysis of hillside with different angles ofslopes was found to be stable
(ii) The study gives an overview of the stability of hillsideslopes under earthquake excitations especially forconstruction requirements
(iii) The stability of slopes (without constructing build-ings) (with slope angles range from 60∘ to 25∘) isacceptable in the high PGA for the study of rocky soilno tensile stress was found in the hillside slope
(iv) Compression stress in a hillside slope angle 60∘decreased by 15 times than hillside slope angle 45∘and decreased by 14 times than hillside slope 25∘under seismic excitations
(v) The interplay between dynamic ldquoinertialrdquo effects aris-ing from the ground vibration and the quasistaticldquokinematicrdquo effects arising from the downwardmove-ment of a shallow sliding soil wedge are studied Itwas thus determined that a rigid raft foundationplaced on a big angle slope which is in a precariousequilibrium and fails during very strong shakingcannot protect the superstructure from both falling(being dragged) with the sliding soil mass and fromsuffering large damaging internal forces
(vi) This is in qualitative agreement with several casehistories of structures that have survived the com-bined effects of strong seismic shaking and of soildownward sliding The penalty to pay however is(a) appreciable rotation and lateral displacement ofthe whole system which may impair the serviceabilityof the structure and (b) generation of large bendingmoments and shear forces in the foundation slabby contrast as in fact most engineers would haveintuitively predicted placing a structure with isolatedfootings on a seismically unstable slope would be aprudent decision
(vii) It is recommended to flatten the slope from 60∘ to45∘ to avoid wedge failures at all isolated steppedfoundation locations (normal force decreased by 50for a slope angle 60∘ than slope angle 45∘ and baseshear decreased by 40 in a slope angle 60∘ than slopeangle 45∘)
(viii) The difference in straining action between steps andraft fixed base under dynamic loads is not significant(base shear in raft foundation increased by 2 thanstepping isolated footing 3 in bending moment 5in top displacement and 7 in top floor acceleration)
(ix) Stepped isolated foundation represents the best solu-tion for both dynamic performance of superstructureconstructed on hillside slope and the stability ofthe slope (columns normal force for isolated footingdecreased by 133 times than raft foundation anddecreased by 145 times in base shear) in 2D the effectof the tie beams to connect stepped footing has beenignored
ISRN Civil Engineering 13
(x) Series buildings constructed on a hillside slope espe-cially 60∘ angle normal force increased by nearly 15times than the one building model 175 times forshear force 140 times in bending moment and 125times for displacement and decreased by 020 timesfor top floor acceleration
This conclusion drawn from a 2D analysis remains validfor the 3D cases since more attenuation would be observedif the radiation damping into the third dimension wastaken into consideration These very local conditions are notadequately captured by the analysis However verification isrequired to check the results in 2D and 3D
Conflict of Interests
The author declares that there is no conflict of interestsregarding the publication of this paper
References
[1] E Spencer ldquoA method of analysis of the stability of embank-ments assuming parallel inter slice forcesrdquo Geo-Technique vol17 no 1 pp 11ndash26 1967
[2] H S Yu R Salgado S W Sloan and J M Kim ldquoLimitanalysis versus limit equilibrium for slope stabilityrdquo Journal ofGeotechnical Engineering (ASCE) vol 124 no 1 pp 1ndash11 1998
[3] A Troncone ldquoNumerical analysis of a landslide in soils withstrain-softening behaviourrdquo Geotechnique vol 55 no 8 pp585ndash596 2005
[4] D Pitilakis ldquoTopographic irregularities and soilmdashfoundationmdashstructure interactionrdquo in Proceedings of the 3rd Japan-GreeceWorkshop on Seismic Design Observation and Retrofit of Foun-dations pp 335ndash343 Santorini Greece 2009
[5] I Anastasopoulos G Gazetas M F Bransby M C RDavies and A El Nahas ldquoFault rupture propagation throughsand finite-element analysis and validation through centrifugeexperimentsrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 133 no 8 pp 943ndash958 2007
[6] G M Latha and A Garaga ldquoStability analysis of a rock slopein Himalayasrdquo Geomechanics and Engineering vol 2 no 2 pp125ndash140 2010
[7] A D Pandey P Kumar and S Sharma ldquoSeismic soil structureinteraction of buildings on hill slopesrdquo International Journal ForComputational Civil and Structural Engineering vol 2 no 2 pp544ndash555 2011
[8] R Kourkoulis I Anastasopoulos F Gelagoti and G GazetasldquoInteraction of foundation-structure systems with seismicallyprecarious slopes numerical analysis with strain softeningconstitutivemodelrdquo Soil Dynamics and Earthquake Engineeringvol 30 no 12 pp 1430ndash1445 2010
[9] S Rampello L Callisto and P Fargnoli ldquoEvaluation of seismiccoefficients for slope stability analysis using a displacement-based approachrdquo in Proceedings of the Seismic EngineeringInternational Conference Commemorating the 1908 Messina andReggio Calabria Earthquake (MERCEA rsquo08) 2008
[10] R L Michalowski and L You ldquoDisplacements of reinforcedslopes subjected to seismic loadsrdquo Journal of Geotechnical andGeoenvironmental Engineering vol 126 no 8 pp 685ndash6942000
[11] D S Chavan G Mondal and A Prashant ldquoPermanent dis-placement of nailed soil slopes subjected to earthquake load-ingrdquo in Proceedings of the 15th World Conference on EarthquakeEngineering (WCEE rsquo12) Lisbon Portugal 2012
[12] A Krishnamoorthy ldquoFactor of safety of a slope subjected toseismic loadrdquoElectronic Journal of Geotechnical Engineering vol12 2007
[13] O Mavrouli J Corominas and J Wartman ldquoMethodology toevaluate rock slope stability under seismic conditions at Solade Santa Coloma Andorrardquo Natural Hazards and Earth SystemScience vol 9 no 6 pp 1763ndash1773 2009
[14] ECOL 201 The Egyptian Code For Calculation of Loads andForces in Structural Building Work Housing and BuildingResearch Center Cairo Egypt 2008
[15] SAP200 Nonlinear Version 14 Static and Dynamic Finite Ele-ments Analysis of Structure Computers amp Structures BerkeleyCalif USA 2010
[16] K D Hjelmstad Fundamentals of Structural MechanicsSpringer New York NY USA 2nd edition 2005
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ISRN Civil Engineering 5
Table 1 Description of used symbols in different curves
Symbols Description
I 60∘ Building on 60∘ slope angle founded on isolatedfooting
R 60∘ Building on 60∘ slope angle founded on raft footing
I 45∘ Building on 45∘ slope angle founded on isolatedfooting
R 45∘ Building on 45∘ slope angle founded on raft footing
I 25∘ Building on a 25∘ slope angle founded on isolatedfooting
R 25∘ Building on a 25∘ slope angle founded on isolatedfooting
Fixed ISO Building with fixed stepped isolated footingFixed raft Building with fixed raft footing
under static and seismic loads with and without constructedbuilding to evaluate the static and dynamic stability of thehillside slope
Figure 4 represents the straining actions of the analyzedmodel using El Centro earthquake time history taking intoconsideration the various types of slope angles ground accel-erations and foundation systems (isolated or raft foundationsystem) Figure 4(a) shows variations of normal force in basecolumns for a building founded at a 60∘ slope with raftfoundation and the normal force recorded the highest valuewith respect to the other casesThe greater the slope angle thegreater the normal forces
Figure 4(c) shows bending moment for base column Amaximum bending moment occurs in raft foundation onslope angle 60∘ in 1 g acceleration but in 050 g accelerationthe maximum value was found in raft foundation with 45∘slope angle Figure 4(d) represents the top floor displacementand themaximum value of displacement for the testedmodelwas founded in raft foundation on slope angle 60∘ thisbehavior was repeated in all used accelerations
Table 1 describes the used symbols in different curvesFigure 4(e) shows the values of top floor acceleration of
the building model the maximum top floor acceleration wasregistered in the case of raft foundation on a 25∘ slope anglenearly 24 times the applied acceleration on the model for1 g acceleration 27 times the applied acceleration (050 g)and equals to 2 times the applied acceleration (025 g) fromfigure its can improved that the slope has not effect on thevalues of bending moment of base column except for R 25(raft foundation on hillside slope 25∘) nearly increased by 175times than all cases the bending moments in fixed base casesregistered a lower value with respect to the rest cases
Figure 5 shows the straining actions of the analyzedmod-els using Northridge time history earthquake model takinginto consideration the various types of slope angles groundaccelerations and foundation systems (stepped isolated orraft foundation system) Figure 5(a) shows the variation ofnormal force in base columns and building founded on 60∘slope with raft foundation gives the highest value of thenormal force with respect to the other cases (nearly morethan the other cases by 25 times) the big slope effect on
the oblique of the building so that the high value of normalforce Figure 5(b) illustrates that base shear force at the raftfoundation system in 60∘ slope angle gives the maximumvalue with respect to the other slopes and a foundationsystem this phenomenon was repeated for the three selectedground accelerations
Figure 5(c) shows that base bendingmoment for base col-umn maximum bending moment occurs in raft foundationcase on slope angle 60∘ and rafton slope 25∘ in 1 g accelerationbut in 050 g and 025 g acceleration the values were nearlyconstant Figure 4(d) represents the top floor displacementand themaximumvalue of displacement of the testedmodelsdisplacement of model in 60∘ slope was smaller than in 25∘by 115 times and this behavior was repeated in all usedaccelerations
Figure 5(e) shows the values of top floor accelerationof models and the maximum top floor acceleration wasregistered in the case of raft foundation on a 25∘ slope anglenearly 16 times the applied acceleration on the model for 1 g050 g and 025 g cases of the applied acceleration
The results founded fromEl Centro earthquake excitationwere in the same trend with Northridge earthquake exalta-tion
Figure 6 displays the stress distribution in 119909- and 119911-directions of 2D slopes (angles 60∘ 45∘ and 25∘) under staticcondition Figure 6(c) shows the stress distribution in 119909-and 119911-directions and all stresses are negative (compressionstress) with the allowable stress for the rocky soil of thehillside in Figure 6(b) stress in the hillsidewith slope 45∘ withmoderate compression stress but in Figure 5(a) the stress alsoin compression but with low value that because of the highervalue of slope angle 60∘
To evaluate the effect of different kind of foundationsystem on hillside slopes under El Centro earthquake with025 g 05 g and 1 g PGA (Pick Ground Acceleration) exci-tation there are three actual slopes that were tested (60∘45∘ and 25∘) Only hillside slopes under 1 g PGA are shownin Figure 7 A hillside slope 25∘ subjected to El Centroearthquake with PGA 1 g with raft foundation stress in 119909-direction no tension between foundation and soil under-neath the model and so in 119911-direction generally no tensionstress come out in thewhole of the slopeThe surface of failureappears under raft foundation more straight but for steepedfoundation the surface looks like a quarter circle (criticalcircle of slip) Compression stress in hillside slope underneathsteeped foundation is bigger than raft foundation
For a hillside slope angle 45 the straining action onthe slope is moderate without tension stress between raftfoundation in 119911-direction and the hillside soil will but thereis a tension stress between the raft foundation buildingmodeland the hillside soil in 119909-direction which means collapse ofthe building model there is a tension stress in the hillsideslope in a crest parts and the steeped foundation shows aminimum effect on the slope This appears as a small valueof compression stress in both directions and no tension stressappears underneath the steeped foundation of the model
For hillside slope angle 60∘ deformation of hillside slopewith raft foundation a small part of the hillside will take offa tension stress appears underneath the foundation in both
6 ISRN Civil Engineering
05
1015202530354045
I 60 R 25I 25R 45I 45R 60iso
Fixedraft
Foundation system with slope
Fixed
N1 gN05 gN025 g
Nor
mal
forc
e (t)
(a) Base column normal force
02468
10121416
Foundation system with slope
I 60 R 25I 25R 45I 45R 60iso
Fixedraft
Fixed
Shea
r for
ce (t
)
Q 1gQ 05 gQ 025 g
(b) Base column shear force
02468
1012141618
I 60 R 25I 25R 45I 45R 60iso
Fixedraft
Foundation system with slope
Fixed
M1 gM05 gM025 g
Mom
ent (mmiddott
)
(c) Base column bending moment
0
5
10
15
20
Dis
(cm
)
I 60 R 25I 25R 45I 45R 60iso
Fixedraft
Foundation system with slope
Fixed
Dis 1gDis 05 gDis 025 g
(d) Displacement of top floor
0
05
1
15
2
25
Acce
lera
tion
(g)
I 60 R 25I 25R 45I 45R 60iso
Fixedraft
Foundation system with slope
Fixed
Acceleration 1gAcceleration 05 gAcceleration 025 g
(e) Acceleration of top floor
Figure 4 Straining actions of 2D building with different types of foundation system and slope angle with El Centro earthquake excitation
directions and stepped foundationmodel appears to bemorestable than raft foundation model because there is no tensionbetween foundation and soil
If the PGA equal to 05 g for the hillside slope 25∘no tension between both types of foundation and the soil
underneath both stress are compression in both directionswhich have a large values In hillside slope 45∘ stressunderneath a raft foundation model approximates to zeroin both directions and this means the model is aboutrotation to be destroyed but the steeped foundation was
ISRN Civil Engineering 7
0
2
4
6
8
10
12
60 R 25 iso25 R45 iso45 R60 iso R fixed I fixedFoundation system with slope
N1 gN05 gN025 g
Nor
mal
forc
e (t)
(a) Base column normal force
0
05
1
15
2
25
3
60 R 25 iso25 R45 iso45 R60 iso R fixed I fixedFoundation system with slope
Base
shea
r (t)
Q 1gQ 05 gQ 025 g
(b) Base column shear force
0
05
1
15
2
25
3
35
60 R 25 iso25 R45 iso45 R60 iso R fixed I fixedFoundation system with slope
M1 gM05 gM025 g
Bend
ing
mom
ent (mmiddott
)
(c) Base column bending moment
002040608
112141618
Dis
(cm
)
60 R 25 iso25 R45 iso45 R60 iso R fixed I fixedFoundation system with slope
Dis 1gDis 05 gDis 025 g
(d) Displacement of top floor
002040608
112141618
Acce
lera
tion
(g)
60 R 25 iso25 R45 iso45 R60 iso R fixed I fixedFoundation system with slope
Acceleration 1gAcceleration 05 gAcceleration 025 g
(e) Acceleration of top floor
Figure 5 Straining actions of 2D model with different types of foundation and slope angles with Northridge earthquake
8 ISRN Civil Engineering
minus100
minus90
minus80
minus70
minus60
minus50
minus40
minus30
minus20
minus10
0 10
20
30
minus132
minus121
minus110
minus99
minus88
minus77
minus66
minus55
minus44
minus33
minus22
minus11
0 11
Stress in x direction stress Stress in z direction stress
(a) Slope 60∘
minus910
minus840
minus770
minus700
minus630
minus560
minus490
minus420
minus350
minus280
minus210
minus140
minus70
00
minus390
minus360
minus330
minus300
minus270
minus240
minus210
minus180
minus150
minus120
minus90
minus60
minus30
00
Stress in x direction stressStress in z direction stress
(b) Slope 45∘
minus168
minus154
minus140
minus126
minus112
minus98
minus84
minus70
minus56
minus42
minus28
minus14
00
14
minus585
minus540
minus495
minus450
minus405
minus360
minus315
minus270
minus225
minus180
minus135
minus90
minus45
00
Stress in x direction stress Stress in z direction stress
(c) Slope 25∘
Figure 6 Stress distribution on 2D slope with different slope angles under static load
more stable because there is a small value of compressionstress underneath foundation For a hillside slope angle45 the straining action on the slope is moderate withouttension stress between raft foundation in 119911-direction andthe hillside soil will but there is a tension stress betweenthe raft foundation building model and the hillside soil in119909-direction which means collapse of the building modeland there is a tension stress in the hillside slope in a crestparts and the steeped foundation shows aminimum effect on
the slope This appears as a small value of compression stressin both directions and no tension stress appears underneaththe steeped foundation of the model
Figure 8 illustrates the straining actions of the hillsideslope under Northridge earthquake excitation with differentkinds of foundation systems and slopes For PGA 1 g slope60∘ there is a tension stress between foundation and soil onthe slope this indicated a failure of the model for both kindsof foundation (raft and stepped) deformation for stepped
ISRN Civil Engineering 9
minus102
minus94
minus86
minus78
minus70
minus62
minus54
minus46
minus38
minus30
minus22
minus14
minus6
00
minus102
minus94
minus86
minus78
minus70
minus62
minus54
minus46
minus38
minus30
minus22
minus14
minus6
00
480
420
360
300
240
180
120
6000minus60
minus120
minus180
minus240
minus300
420
360
300
240
180
120
6000minus60
minus120
minus180
minus240
minus300
minus360
Deformation
Deformation
(B) Stepped foundation
(A) Raft foundation x directionz direction
x direction z direction
(a) Straining action on slope 60∘
400
350
300
250
200
150
100
5000minus50
minus100
minus150
minus200
minus250
160
8000minus80
minus160
minus240
minus320
minus400
minus480
minus560
minus640
minus720
minus800
360
315
270
225
180
135
904500minus45
minus90
minus135
minus180
minus225
minus16
minus24
minus32
minus40
minus48
minus56
minus64
minus70
minus78
minus86
minus94
minus102
minus110
Deformation
Deformation
(A) Stepped foundation
(B) Raft foundation
x directionz direction
x direction z direction
(b) Straining action on slope 45∘
Figure 7 Continued
10 ISRN Civil Engineering
minus78
minus52
minus26
00265278104
130
156
182
208
234
260
603000minus30
minus60
minus90
minus120
minus150
minus180
minus210
minus240
minus270
minus300
minus330
minus80
minus60
minus40
minus20
0020406080100
120
140
160
180
84562800minus28
minus56
minus84
minus112
minus140
minus168
minus196
minus224
minus252
minus280
Deformation
Deformation
(A) Raft foundation
(B) Raft foundation
x directionz direction
x direction z direction
(c) Straining action on slope 25∘
Figure 7 Straining actions of 2D building with different types of foundation system and slope angle with El Centro earthquake excitationwith PGA equal to 1 g
Table 2 Conclusion of model stable with different earthquake PGA
Earthquakeacceleration
Hillside slopeangle
Static stability of slope only Dynamic stability withconstructed one building
Dynamic stability withconstructed series building
Tension stress Compressionstress
Tension stressunder building
Compressionstress underbuilding
Tension stressunder building
Compressionstress underbuilding
1 g60∘ No Yes Yes mdash Yes mdash45∘ No Yes Yes mdash Yes mdash25∘ No Yes No Yes Yes mdash
050 g60∘ No Yes Yes mdash Yes mdash45∘ No Yes Yes mdash Yes mdash25∘ No Yes No Yes mdash Yes
025 g60∘ No Yes Yes mdash Yes mdash45∘ No Yes No Yes Yes mdash25∘ No Yes No Yes mdash Yes
foundation is bigger than a raft foundation model and thestraining action seems to be lower than the correspondingvalues of El Centro earthquake exaltation For slope 45∘ and1 g PGA there is no tension stress between foundation and soilon the hillside slope but the compression stress in the slope issmall with respect to 60∘ slope and the corresponding valuesin 25∘ slope are bigger than 45∘ and no tension stress appears
The results obtained from Northridge earthquake aresimilar in trend with these founded from El Centro earth-quake excitation
Table 2 concluded the results of model stress founded onthe slopes with the view of stability or not under differentearthquake excitationThe stability of a series of building con-struction on a slope under earthquake excitation was studiedand also concluded in Table 2 It seem that series buildings
can bemore critical than one building and it is shown that theconstruction of series buildings on a slope from60 to 45 anglecan be destroyed under moderate earthquake even so theseries buildings withstand the same earthquake magnitudesif it is founded on a flat land foundation
6 Conclusions
A 2D building model founded on a hillside slope was evalu-ated to check the performance of buildings and slopes undervarious earthquake time history excitation and magnitudestudying a real case of study in a Doronka village in UpperEgypt Two earthquake time histories were used El Centroand Northridge earthquake with 025 g 05 g and 1 g PGAmagnitudeThe models used were prepared to agree with the
ISRN Civil Engineering 11
13
0minus13
minus26
minus39
minus52
minus65
minus78
minus91
minus104
minus117
minus130
minus143
minus156
0minus22
minus44
minus66
minus88
minus110
minus132
minus154
minus176
minus198
minus220
minus242
minus262
minus286
12
0minus12
minus24
minus36
minus48
minus60
minus72
minus84
minus96
minus108
minus120
minus132
minus144
minus44
minus66
minus88
minus110
minus132
minus154
minus176
minus198
minus220
minus242
minus262
minus286
minus600
minus550
minus500
minus450
minus400
minus350
minus300
minus250
minus200
minus150
minus100
minus50
00
50
0minus9
minus18
minus27
minus36
minus45
minus54
minus63
minus72
minus81
minus90
minus99
minus108
minus117
60
00
minus60
minus120
minus180
minus240
minus300
minus360
minus420
minus480
minus540
minus600
minus660
minus720
12
0minus12
minus24
minus36
minus48
minus60
minus72
minus84
minus96
minus108
minus120
minus132
minus144
X directionZ direction Deformation
Deformation
Deformation
Deformation
(i) Raft foundation
(ii) Stepped foundation
(iii) Stepped foundation
(iv) Raft foundation
x direction z direction
x direction z direction
x directionz direction
(a) Straining action on slope 45∘
Figure 8 Continued
12 ISRN Civil Engineering
34
17
00
minus17
minus34
minus51
minus68
minus85
minus102
minus119
minus136
minus153
minus170
minus187
45
00
minus45
minus90
minus135
minus180
minus225
minus270
minus315
minus360
minus405
minus450
minus495
minus540
14
00
minus14
minus28
minus42
minus56
minus70
minus84
minus98
minus112
minus126
minus140
minus154
minus168
45
00
minus45
minus90
minus135
minus180
minus225
minus270
minus315
minus360
minus405
minus450
minus495
minus540
Deformation
Deformation
(v) Raft foundation
(vi) Stepped foundation
x directionz direction
x direction z direction
(b) Straining action on slope 25∘
Figure 8 Straining actions of 2D building with different types of foundation system and slope angle with Northridge earthquake excitationwith PGA equals 1 g
reality of the nature of the case study and the slopes were 60∘45∘ and 25∘ and the foundation system to be stepped isolatedor raft foundations The nonlinear parameters of the rockytype soil were provided to SAP2000 program as a curve of soilunder cyclic loading Applying the two selected earthquaketime histories with different PGA on a free hillside slope frombuilding and with only one building and then with a series ofbuildings the highlight points can be drawn as follows
(i) Static analysis of hillside with different angles ofslopes was found to be stable
(ii) The study gives an overview of the stability of hillsideslopes under earthquake excitations especially forconstruction requirements
(iii) The stability of slopes (without constructing build-ings) (with slope angles range from 60∘ to 25∘) isacceptable in the high PGA for the study of rocky soilno tensile stress was found in the hillside slope
(iv) Compression stress in a hillside slope angle 60∘decreased by 15 times than hillside slope angle 45∘and decreased by 14 times than hillside slope 25∘under seismic excitations
(v) The interplay between dynamic ldquoinertialrdquo effects aris-ing from the ground vibration and the quasistaticldquokinematicrdquo effects arising from the downwardmove-ment of a shallow sliding soil wedge are studied Itwas thus determined that a rigid raft foundationplaced on a big angle slope which is in a precariousequilibrium and fails during very strong shakingcannot protect the superstructure from both falling(being dragged) with the sliding soil mass and fromsuffering large damaging internal forces
(vi) This is in qualitative agreement with several casehistories of structures that have survived the com-bined effects of strong seismic shaking and of soildownward sliding The penalty to pay however is(a) appreciable rotation and lateral displacement ofthe whole system which may impair the serviceabilityof the structure and (b) generation of large bendingmoments and shear forces in the foundation slabby contrast as in fact most engineers would haveintuitively predicted placing a structure with isolatedfootings on a seismically unstable slope would be aprudent decision
(vii) It is recommended to flatten the slope from 60∘ to45∘ to avoid wedge failures at all isolated steppedfoundation locations (normal force decreased by 50for a slope angle 60∘ than slope angle 45∘ and baseshear decreased by 40 in a slope angle 60∘ than slopeangle 45∘)
(viii) The difference in straining action between steps andraft fixed base under dynamic loads is not significant(base shear in raft foundation increased by 2 thanstepping isolated footing 3 in bending moment 5in top displacement and 7 in top floor acceleration)
(ix) Stepped isolated foundation represents the best solu-tion for both dynamic performance of superstructureconstructed on hillside slope and the stability ofthe slope (columns normal force for isolated footingdecreased by 133 times than raft foundation anddecreased by 145 times in base shear) in 2D the effectof the tie beams to connect stepped footing has beenignored
ISRN Civil Engineering 13
(x) Series buildings constructed on a hillside slope espe-cially 60∘ angle normal force increased by nearly 15times than the one building model 175 times forshear force 140 times in bending moment and 125times for displacement and decreased by 020 timesfor top floor acceleration
This conclusion drawn from a 2D analysis remains validfor the 3D cases since more attenuation would be observedif the radiation damping into the third dimension wastaken into consideration These very local conditions are notadequately captured by the analysis However verification isrequired to check the results in 2D and 3D
Conflict of Interests
The author declares that there is no conflict of interestsregarding the publication of this paper
References
[1] E Spencer ldquoA method of analysis of the stability of embank-ments assuming parallel inter slice forcesrdquo Geo-Technique vol17 no 1 pp 11ndash26 1967
[2] H S Yu R Salgado S W Sloan and J M Kim ldquoLimitanalysis versus limit equilibrium for slope stabilityrdquo Journal ofGeotechnical Engineering (ASCE) vol 124 no 1 pp 1ndash11 1998
[3] A Troncone ldquoNumerical analysis of a landslide in soils withstrain-softening behaviourrdquo Geotechnique vol 55 no 8 pp585ndash596 2005
[4] D Pitilakis ldquoTopographic irregularities and soilmdashfoundationmdashstructure interactionrdquo in Proceedings of the 3rd Japan-GreeceWorkshop on Seismic Design Observation and Retrofit of Foun-dations pp 335ndash343 Santorini Greece 2009
[5] I Anastasopoulos G Gazetas M F Bransby M C RDavies and A El Nahas ldquoFault rupture propagation throughsand finite-element analysis and validation through centrifugeexperimentsrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 133 no 8 pp 943ndash958 2007
[6] G M Latha and A Garaga ldquoStability analysis of a rock slopein Himalayasrdquo Geomechanics and Engineering vol 2 no 2 pp125ndash140 2010
[7] A D Pandey P Kumar and S Sharma ldquoSeismic soil structureinteraction of buildings on hill slopesrdquo International Journal ForComputational Civil and Structural Engineering vol 2 no 2 pp544ndash555 2011
[8] R Kourkoulis I Anastasopoulos F Gelagoti and G GazetasldquoInteraction of foundation-structure systems with seismicallyprecarious slopes numerical analysis with strain softeningconstitutivemodelrdquo Soil Dynamics and Earthquake Engineeringvol 30 no 12 pp 1430ndash1445 2010
[9] S Rampello L Callisto and P Fargnoli ldquoEvaluation of seismiccoefficients for slope stability analysis using a displacement-based approachrdquo in Proceedings of the Seismic EngineeringInternational Conference Commemorating the 1908 Messina andReggio Calabria Earthquake (MERCEA rsquo08) 2008
[10] R L Michalowski and L You ldquoDisplacements of reinforcedslopes subjected to seismic loadsrdquo Journal of Geotechnical andGeoenvironmental Engineering vol 126 no 8 pp 685ndash6942000
[11] D S Chavan G Mondal and A Prashant ldquoPermanent dis-placement of nailed soil slopes subjected to earthquake load-ingrdquo in Proceedings of the 15th World Conference on EarthquakeEngineering (WCEE rsquo12) Lisbon Portugal 2012
[12] A Krishnamoorthy ldquoFactor of safety of a slope subjected toseismic loadrdquoElectronic Journal of Geotechnical Engineering vol12 2007
[13] O Mavrouli J Corominas and J Wartman ldquoMethodology toevaluate rock slope stability under seismic conditions at Solade Santa Coloma Andorrardquo Natural Hazards and Earth SystemScience vol 9 no 6 pp 1763ndash1773 2009
[14] ECOL 201 The Egyptian Code For Calculation of Loads andForces in Structural Building Work Housing and BuildingResearch Center Cairo Egypt 2008
[15] SAP200 Nonlinear Version 14 Static and Dynamic Finite Ele-ments Analysis of Structure Computers amp Structures BerkeleyCalif USA 2010
[16] K D Hjelmstad Fundamentals of Structural MechanicsSpringer New York NY USA 2nd edition 2005
International Journal of
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Navigation and Observation
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DistributedSensor Networks
International Journal of
6 ISRN Civil Engineering
05
1015202530354045
I 60 R 25I 25R 45I 45R 60iso
Fixedraft
Foundation system with slope
Fixed
N1 gN05 gN025 g
Nor
mal
forc
e (t)
(a) Base column normal force
02468
10121416
Foundation system with slope
I 60 R 25I 25R 45I 45R 60iso
Fixedraft
Fixed
Shea
r for
ce (t
)
Q 1gQ 05 gQ 025 g
(b) Base column shear force
02468
1012141618
I 60 R 25I 25R 45I 45R 60iso
Fixedraft
Foundation system with slope
Fixed
M1 gM05 gM025 g
Mom
ent (mmiddott
)
(c) Base column bending moment
0
5
10
15
20
Dis
(cm
)
I 60 R 25I 25R 45I 45R 60iso
Fixedraft
Foundation system with slope
Fixed
Dis 1gDis 05 gDis 025 g
(d) Displacement of top floor
0
05
1
15
2
25
Acce
lera
tion
(g)
I 60 R 25I 25R 45I 45R 60iso
Fixedraft
Foundation system with slope
Fixed
Acceleration 1gAcceleration 05 gAcceleration 025 g
(e) Acceleration of top floor
Figure 4 Straining actions of 2D building with different types of foundation system and slope angle with El Centro earthquake excitation
directions and stepped foundationmodel appears to bemorestable than raft foundation model because there is no tensionbetween foundation and soil
If the PGA equal to 05 g for the hillside slope 25∘no tension between both types of foundation and the soil
underneath both stress are compression in both directionswhich have a large values In hillside slope 45∘ stressunderneath a raft foundation model approximates to zeroin both directions and this means the model is aboutrotation to be destroyed but the steeped foundation was
ISRN Civil Engineering 7
0
2
4
6
8
10
12
60 R 25 iso25 R45 iso45 R60 iso R fixed I fixedFoundation system with slope
N1 gN05 gN025 g
Nor
mal
forc
e (t)
(a) Base column normal force
0
05
1
15
2
25
3
60 R 25 iso25 R45 iso45 R60 iso R fixed I fixedFoundation system with slope
Base
shea
r (t)
Q 1gQ 05 gQ 025 g
(b) Base column shear force
0
05
1
15
2
25
3
35
60 R 25 iso25 R45 iso45 R60 iso R fixed I fixedFoundation system with slope
M1 gM05 gM025 g
Bend
ing
mom
ent (mmiddott
)
(c) Base column bending moment
002040608
112141618
Dis
(cm
)
60 R 25 iso25 R45 iso45 R60 iso R fixed I fixedFoundation system with slope
Dis 1gDis 05 gDis 025 g
(d) Displacement of top floor
002040608
112141618
Acce
lera
tion
(g)
60 R 25 iso25 R45 iso45 R60 iso R fixed I fixedFoundation system with slope
Acceleration 1gAcceleration 05 gAcceleration 025 g
(e) Acceleration of top floor
Figure 5 Straining actions of 2D model with different types of foundation and slope angles with Northridge earthquake
8 ISRN Civil Engineering
minus100
minus90
minus80
minus70
minus60
minus50
minus40
minus30
minus20
minus10
0 10
20
30
minus132
minus121
minus110
minus99
minus88
minus77
minus66
minus55
minus44
minus33
minus22
minus11
0 11
Stress in x direction stress Stress in z direction stress
(a) Slope 60∘
minus910
minus840
minus770
minus700
minus630
minus560
minus490
minus420
minus350
minus280
minus210
minus140
minus70
00
minus390
minus360
minus330
minus300
minus270
minus240
minus210
minus180
minus150
minus120
minus90
minus60
minus30
00
Stress in x direction stressStress in z direction stress
(b) Slope 45∘
minus168
minus154
minus140
minus126
minus112
minus98
minus84
minus70
minus56
minus42
minus28
minus14
00
14
minus585
minus540
minus495
minus450
minus405
minus360
minus315
minus270
minus225
minus180
minus135
minus90
minus45
00
Stress in x direction stress Stress in z direction stress
(c) Slope 25∘
Figure 6 Stress distribution on 2D slope with different slope angles under static load
more stable because there is a small value of compressionstress underneath foundation For a hillside slope angle45 the straining action on the slope is moderate withouttension stress between raft foundation in 119911-direction andthe hillside soil will but there is a tension stress betweenthe raft foundation building model and the hillside soil in119909-direction which means collapse of the building modeland there is a tension stress in the hillside slope in a crestparts and the steeped foundation shows aminimum effect on
the slope This appears as a small value of compression stressin both directions and no tension stress appears underneaththe steeped foundation of the model
Figure 8 illustrates the straining actions of the hillsideslope under Northridge earthquake excitation with differentkinds of foundation systems and slopes For PGA 1 g slope60∘ there is a tension stress between foundation and soil onthe slope this indicated a failure of the model for both kindsof foundation (raft and stepped) deformation for stepped
ISRN Civil Engineering 9
minus102
minus94
minus86
minus78
minus70
minus62
minus54
minus46
minus38
minus30
minus22
minus14
minus6
00
minus102
minus94
minus86
minus78
minus70
minus62
minus54
minus46
minus38
minus30
minus22
minus14
minus6
00
480
420
360
300
240
180
120
6000minus60
minus120
minus180
minus240
minus300
420
360
300
240
180
120
6000minus60
minus120
minus180
minus240
minus300
minus360
Deformation
Deformation
(B) Stepped foundation
(A) Raft foundation x directionz direction
x direction z direction
(a) Straining action on slope 60∘
400
350
300
250
200
150
100
5000minus50
minus100
minus150
minus200
minus250
160
8000minus80
minus160
minus240
minus320
minus400
minus480
minus560
minus640
minus720
minus800
360
315
270
225
180
135
904500minus45
minus90
minus135
minus180
minus225
minus16
minus24
minus32
minus40
minus48
minus56
minus64
minus70
minus78
minus86
minus94
minus102
minus110
Deformation
Deformation
(A) Stepped foundation
(B) Raft foundation
x directionz direction
x direction z direction
(b) Straining action on slope 45∘
Figure 7 Continued
10 ISRN Civil Engineering
minus78
minus52
minus26
00265278104
130
156
182
208
234
260
603000minus30
minus60
minus90
minus120
minus150
minus180
minus210
minus240
minus270
minus300
minus330
minus80
minus60
minus40
minus20
0020406080100
120
140
160
180
84562800minus28
minus56
minus84
minus112
minus140
minus168
minus196
minus224
minus252
minus280
Deformation
Deformation
(A) Raft foundation
(B) Raft foundation
x directionz direction
x direction z direction
(c) Straining action on slope 25∘
Figure 7 Straining actions of 2D building with different types of foundation system and slope angle with El Centro earthquake excitationwith PGA equal to 1 g
Table 2 Conclusion of model stable with different earthquake PGA
Earthquakeacceleration
Hillside slopeangle
Static stability of slope only Dynamic stability withconstructed one building
Dynamic stability withconstructed series building
Tension stress Compressionstress
Tension stressunder building
Compressionstress underbuilding
Tension stressunder building
Compressionstress underbuilding
1 g60∘ No Yes Yes mdash Yes mdash45∘ No Yes Yes mdash Yes mdash25∘ No Yes No Yes Yes mdash
050 g60∘ No Yes Yes mdash Yes mdash45∘ No Yes Yes mdash Yes mdash25∘ No Yes No Yes mdash Yes
025 g60∘ No Yes Yes mdash Yes mdash45∘ No Yes No Yes Yes mdash25∘ No Yes No Yes mdash Yes
foundation is bigger than a raft foundation model and thestraining action seems to be lower than the correspondingvalues of El Centro earthquake exaltation For slope 45∘ and1 g PGA there is no tension stress between foundation and soilon the hillside slope but the compression stress in the slope issmall with respect to 60∘ slope and the corresponding valuesin 25∘ slope are bigger than 45∘ and no tension stress appears
The results obtained from Northridge earthquake aresimilar in trend with these founded from El Centro earth-quake excitation
Table 2 concluded the results of model stress founded onthe slopes with the view of stability or not under differentearthquake excitationThe stability of a series of building con-struction on a slope under earthquake excitation was studiedand also concluded in Table 2 It seem that series buildings
can bemore critical than one building and it is shown that theconstruction of series buildings on a slope from60 to 45 anglecan be destroyed under moderate earthquake even so theseries buildings withstand the same earthquake magnitudesif it is founded on a flat land foundation
6 Conclusions
A 2D building model founded on a hillside slope was evalu-ated to check the performance of buildings and slopes undervarious earthquake time history excitation and magnitudestudying a real case of study in a Doronka village in UpperEgypt Two earthquake time histories were used El Centroand Northridge earthquake with 025 g 05 g and 1 g PGAmagnitudeThe models used were prepared to agree with the
ISRN Civil Engineering 11
13
0minus13
minus26
minus39
minus52
minus65
minus78
minus91
minus104
minus117
minus130
minus143
minus156
0minus22
minus44
minus66
minus88
minus110
minus132
minus154
minus176
minus198
minus220
minus242
minus262
minus286
12
0minus12
minus24
minus36
minus48
minus60
minus72
minus84
minus96
minus108
minus120
minus132
minus144
minus44
minus66
minus88
minus110
minus132
minus154
minus176
minus198
minus220
minus242
minus262
minus286
minus600
minus550
minus500
minus450
minus400
minus350
minus300
minus250
minus200
minus150
minus100
minus50
00
50
0minus9
minus18
minus27
minus36
minus45
minus54
minus63
minus72
minus81
minus90
minus99
minus108
minus117
60
00
minus60
minus120
minus180
minus240
minus300
minus360
minus420
minus480
minus540
minus600
minus660
minus720
12
0minus12
minus24
minus36
minus48
minus60
minus72
minus84
minus96
minus108
minus120
minus132
minus144
X directionZ direction Deformation
Deformation
Deformation
Deformation
(i) Raft foundation
(ii) Stepped foundation
(iii) Stepped foundation
(iv) Raft foundation
x direction z direction
x direction z direction
x directionz direction
(a) Straining action on slope 45∘
Figure 8 Continued
12 ISRN Civil Engineering
34
17
00
minus17
minus34
minus51
minus68
minus85
minus102
minus119
minus136
minus153
minus170
minus187
45
00
minus45
minus90
minus135
minus180
minus225
minus270
minus315
minus360
minus405
minus450
minus495
minus540
14
00
minus14
minus28
minus42
minus56
minus70
minus84
minus98
minus112
minus126
minus140
minus154
minus168
45
00
minus45
minus90
minus135
minus180
minus225
minus270
minus315
minus360
minus405
minus450
minus495
minus540
Deformation
Deformation
(v) Raft foundation
(vi) Stepped foundation
x directionz direction
x direction z direction
(b) Straining action on slope 25∘
Figure 8 Straining actions of 2D building with different types of foundation system and slope angle with Northridge earthquake excitationwith PGA equals 1 g
reality of the nature of the case study and the slopes were 60∘45∘ and 25∘ and the foundation system to be stepped isolatedor raft foundations The nonlinear parameters of the rockytype soil were provided to SAP2000 program as a curve of soilunder cyclic loading Applying the two selected earthquaketime histories with different PGA on a free hillside slope frombuilding and with only one building and then with a series ofbuildings the highlight points can be drawn as follows
(i) Static analysis of hillside with different angles ofslopes was found to be stable
(ii) The study gives an overview of the stability of hillsideslopes under earthquake excitations especially forconstruction requirements
(iii) The stability of slopes (without constructing build-ings) (with slope angles range from 60∘ to 25∘) isacceptable in the high PGA for the study of rocky soilno tensile stress was found in the hillside slope
(iv) Compression stress in a hillside slope angle 60∘decreased by 15 times than hillside slope angle 45∘and decreased by 14 times than hillside slope 25∘under seismic excitations
(v) The interplay between dynamic ldquoinertialrdquo effects aris-ing from the ground vibration and the quasistaticldquokinematicrdquo effects arising from the downwardmove-ment of a shallow sliding soil wedge are studied Itwas thus determined that a rigid raft foundationplaced on a big angle slope which is in a precariousequilibrium and fails during very strong shakingcannot protect the superstructure from both falling(being dragged) with the sliding soil mass and fromsuffering large damaging internal forces
(vi) This is in qualitative agreement with several casehistories of structures that have survived the com-bined effects of strong seismic shaking and of soildownward sliding The penalty to pay however is(a) appreciable rotation and lateral displacement ofthe whole system which may impair the serviceabilityof the structure and (b) generation of large bendingmoments and shear forces in the foundation slabby contrast as in fact most engineers would haveintuitively predicted placing a structure with isolatedfootings on a seismically unstable slope would be aprudent decision
(vii) It is recommended to flatten the slope from 60∘ to45∘ to avoid wedge failures at all isolated steppedfoundation locations (normal force decreased by 50for a slope angle 60∘ than slope angle 45∘ and baseshear decreased by 40 in a slope angle 60∘ than slopeangle 45∘)
(viii) The difference in straining action between steps andraft fixed base under dynamic loads is not significant(base shear in raft foundation increased by 2 thanstepping isolated footing 3 in bending moment 5in top displacement and 7 in top floor acceleration)
(ix) Stepped isolated foundation represents the best solu-tion for both dynamic performance of superstructureconstructed on hillside slope and the stability ofthe slope (columns normal force for isolated footingdecreased by 133 times than raft foundation anddecreased by 145 times in base shear) in 2D the effectof the tie beams to connect stepped footing has beenignored
ISRN Civil Engineering 13
(x) Series buildings constructed on a hillside slope espe-cially 60∘ angle normal force increased by nearly 15times than the one building model 175 times forshear force 140 times in bending moment and 125times for displacement and decreased by 020 timesfor top floor acceleration
This conclusion drawn from a 2D analysis remains validfor the 3D cases since more attenuation would be observedif the radiation damping into the third dimension wastaken into consideration These very local conditions are notadequately captured by the analysis However verification isrequired to check the results in 2D and 3D
Conflict of Interests
The author declares that there is no conflict of interestsregarding the publication of this paper
References
[1] E Spencer ldquoA method of analysis of the stability of embank-ments assuming parallel inter slice forcesrdquo Geo-Technique vol17 no 1 pp 11ndash26 1967
[2] H S Yu R Salgado S W Sloan and J M Kim ldquoLimitanalysis versus limit equilibrium for slope stabilityrdquo Journal ofGeotechnical Engineering (ASCE) vol 124 no 1 pp 1ndash11 1998
[3] A Troncone ldquoNumerical analysis of a landslide in soils withstrain-softening behaviourrdquo Geotechnique vol 55 no 8 pp585ndash596 2005
[4] D Pitilakis ldquoTopographic irregularities and soilmdashfoundationmdashstructure interactionrdquo in Proceedings of the 3rd Japan-GreeceWorkshop on Seismic Design Observation and Retrofit of Foun-dations pp 335ndash343 Santorini Greece 2009
[5] I Anastasopoulos G Gazetas M F Bransby M C RDavies and A El Nahas ldquoFault rupture propagation throughsand finite-element analysis and validation through centrifugeexperimentsrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 133 no 8 pp 943ndash958 2007
[6] G M Latha and A Garaga ldquoStability analysis of a rock slopein Himalayasrdquo Geomechanics and Engineering vol 2 no 2 pp125ndash140 2010
[7] A D Pandey P Kumar and S Sharma ldquoSeismic soil structureinteraction of buildings on hill slopesrdquo International Journal ForComputational Civil and Structural Engineering vol 2 no 2 pp544ndash555 2011
[8] R Kourkoulis I Anastasopoulos F Gelagoti and G GazetasldquoInteraction of foundation-structure systems with seismicallyprecarious slopes numerical analysis with strain softeningconstitutivemodelrdquo Soil Dynamics and Earthquake Engineeringvol 30 no 12 pp 1430ndash1445 2010
[9] S Rampello L Callisto and P Fargnoli ldquoEvaluation of seismiccoefficients for slope stability analysis using a displacement-based approachrdquo in Proceedings of the Seismic EngineeringInternational Conference Commemorating the 1908 Messina andReggio Calabria Earthquake (MERCEA rsquo08) 2008
[10] R L Michalowski and L You ldquoDisplacements of reinforcedslopes subjected to seismic loadsrdquo Journal of Geotechnical andGeoenvironmental Engineering vol 126 no 8 pp 685ndash6942000
[11] D S Chavan G Mondal and A Prashant ldquoPermanent dis-placement of nailed soil slopes subjected to earthquake load-ingrdquo in Proceedings of the 15th World Conference on EarthquakeEngineering (WCEE rsquo12) Lisbon Portugal 2012
[12] A Krishnamoorthy ldquoFactor of safety of a slope subjected toseismic loadrdquoElectronic Journal of Geotechnical Engineering vol12 2007
[13] O Mavrouli J Corominas and J Wartman ldquoMethodology toevaluate rock slope stability under seismic conditions at Solade Santa Coloma Andorrardquo Natural Hazards and Earth SystemScience vol 9 no 6 pp 1763ndash1773 2009
[14] ECOL 201 The Egyptian Code For Calculation of Loads andForces in Structural Building Work Housing and BuildingResearch Center Cairo Egypt 2008
[15] SAP200 Nonlinear Version 14 Static and Dynamic Finite Ele-ments Analysis of Structure Computers amp Structures BerkeleyCalif USA 2010
[16] K D Hjelmstad Fundamentals of Structural MechanicsSpringer New York NY USA 2nd edition 2005
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
ISRN Civil Engineering 7
0
2
4
6
8
10
12
60 R 25 iso25 R45 iso45 R60 iso R fixed I fixedFoundation system with slope
N1 gN05 gN025 g
Nor
mal
forc
e (t)
(a) Base column normal force
0
05
1
15
2
25
3
60 R 25 iso25 R45 iso45 R60 iso R fixed I fixedFoundation system with slope
Base
shea
r (t)
Q 1gQ 05 gQ 025 g
(b) Base column shear force
0
05
1
15
2
25
3
35
60 R 25 iso25 R45 iso45 R60 iso R fixed I fixedFoundation system with slope
M1 gM05 gM025 g
Bend
ing
mom
ent (mmiddott
)
(c) Base column bending moment
002040608
112141618
Dis
(cm
)
60 R 25 iso25 R45 iso45 R60 iso R fixed I fixedFoundation system with slope
Dis 1gDis 05 gDis 025 g
(d) Displacement of top floor
002040608
112141618
Acce
lera
tion
(g)
60 R 25 iso25 R45 iso45 R60 iso R fixed I fixedFoundation system with slope
Acceleration 1gAcceleration 05 gAcceleration 025 g
(e) Acceleration of top floor
Figure 5 Straining actions of 2D model with different types of foundation and slope angles with Northridge earthquake
8 ISRN Civil Engineering
minus100
minus90
minus80
minus70
minus60
minus50
minus40
minus30
minus20
minus10
0 10
20
30
minus132
minus121
minus110
minus99
minus88
minus77
minus66
minus55
minus44
minus33
minus22
minus11
0 11
Stress in x direction stress Stress in z direction stress
(a) Slope 60∘
minus910
minus840
minus770
minus700
minus630
minus560
minus490
minus420
minus350
minus280
minus210
minus140
minus70
00
minus390
minus360
minus330
minus300
minus270
minus240
minus210
minus180
minus150
minus120
minus90
minus60
minus30
00
Stress in x direction stressStress in z direction stress
(b) Slope 45∘
minus168
minus154
minus140
minus126
minus112
minus98
minus84
minus70
minus56
minus42
minus28
minus14
00
14
minus585
minus540
minus495
minus450
minus405
minus360
minus315
minus270
minus225
minus180
minus135
minus90
minus45
00
Stress in x direction stress Stress in z direction stress
(c) Slope 25∘
Figure 6 Stress distribution on 2D slope with different slope angles under static load
more stable because there is a small value of compressionstress underneath foundation For a hillside slope angle45 the straining action on the slope is moderate withouttension stress between raft foundation in 119911-direction andthe hillside soil will but there is a tension stress betweenthe raft foundation building model and the hillside soil in119909-direction which means collapse of the building modeland there is a tension stress in the hillside slope in a crestparts and the steeped foundation shows aminimum effect on
the slope This appears as a small value of compression stressin both directions and no tension stress appears underneaththe steeped foundation of the model
Figure 8 illustrates the straining actions of the hillsideslope under Northridge earthquake excitation with differentkinds of foundation systems and slopes For PGA 1 g slope60∘ there is a tension stress between foundation and soil onthe slope this indicated a failure of the model for both kindsof foundation (raft and stepped) deformation for stepped
ISRN Civil Engineering 9
minus102
minus94
minus86
minus78
minus70
minus62
minus54
minus46
minus38
minus30
minus22
minus14
minus6
00
minus102
minus94
minus86
minus78
minus70
minus62
minus54
minus46
minus38
minus30
minus22
minus14
minus6
00
480
420
360
300
240
180
120
6000minus60
minus120
minus180
minus240
minus300
420
360
300
240
180
120
6000minus60
minus120
minus180
minus240
minus300
minus360
Deformation
Deformation
(B) Stepped foundation
(A) Raft foundation x directionz direction
x direction z direction
(a) Straining action on slope 60∘
400
350
300
250
200
150
100
5000minus50
minus100
minus150
minus200
minus250
160
8000minus80
minus160
minus240
minus320
minus400
minus480
minus560
minus640
minus720
minus800
360
315
270
225
180
135
904500minus45
minus90
minus135
minus180
minus225
minus16
minus24
minus32
minus40
minus48
minus56
minus64
minus70
minus78
minus86
minus94
minus102
minus110
Deformation
Deformation
(A) Stepped foundation
(B) Raft foundation
x directionz direction
x direction z direction
(b) Straining action on slope 45∘
Figure 7 Continued
10 ISRN Civil Engineering
minus78
minus52
minus26
00265278104
130
156
182
208
234
260
603000minus30
minus60
minus90
minus120
minus150
minus180
minus210
minus240
minus270
minus300
minus330
minus80
minus60
minus40
minus20
0020406080100
120
140
160
180
84562800minus28
minus56
minus84
minus112
minus140
minus168
minus196
minus224
minus252
minus280
Deformation
Deformation
(A) Raft foundation
(B) Raft foundation
x directionz direction
x direction z direction
(c) Straining action on slope 25∘
Figure 7 Straining actions of 2D building with different types of foundation system and slope angle with El Centro earthquake excitationwith PGA equal to 1 g
Table 2 Conclusion of model stable with different earthquake PGA
Earthquakeacceleration
Hillside slopeangle
Static stability of slope only Dynamic stability withconstructed one building
Dynamic stability withconstructed series building
Tension stress Compressionstress
Tension stressunder building
Compressionstress underbuilding
Tension stressunder building
Compressionstress underbuilding
1 g60∘ No Yes Yes mdash Yes mdash45∘ No Yes Yes mdash Yes mdash25∘ No Yes No Yes Yes mdash
050 g60∘ No Yes Yes mdash Yes mdash45∘ No Yes Yes mdash Yes mdash25∘ No Yes No Yes mdash Yes
025 g60∘ No Yes Yes mdash Yes mdash45∘ No Yes No Yes Yes mdash25∘ No Yes No Yes mdash Yes
foundation is bigger than a raft foundation model and thestraining action seems to be lower than the correspondingvalues of El Centro earthquake exaltation For slope 45∘ and1 g PGA there is no tension stress between foundation and soilon the hillside slope but the compression stress in the slope issmall with respect to 60∘ slope and the corresponding valuesin 25∘ slope are bigger than 45∘ and no tension stress appears
The results obtained from Northridge earthquake aresimilar in trend with these founded from El Centro earth-quake excitation
Table 2 concluded the results of model stress founded onthe slopes with the view of stability or not under differentearthquake excitationThe stability of a series of building con-struction on a slope under earthquake excitation was studiedand also concluded in Table 2 It seem that series buildings
can bemore critical than one building and it is shown that theconstruction of series buildings on a slope from60 to 45 anglecan be destroyed under moderate earthquake even so theseries buildings withstand the same earthquake magnitudesif it is founded on a flat land foundation
6 Conclusions
A 2D building model founded on a hillside slope was evalu-ated to check the performance of buildings and slopes undervarious earthquake time history excitation and magnitudestudying a real case of study in a Doronka village in UpperEgypt Two earthquake time histories were used El Centroand Northridge earthquake with 025 g 05 g and 1 g PGAmagnitudeThe models used were prepared to agree with the
ISRN Civil Engineering 11
13
0minus13
minus26
minus39
minus52
minus65
minus78
minus91
minus104
minus117
minus130
minus143
minus156
0minus22
minus44
minus66
minus88
minus110
minus132
minus154
minus176
minus198
minus220
minus242
minus262
minus286
12
0minus12
minus24
minus36
minus48
minus60
minus72
minus84
minus96
minus108
minus120
minus132
minus144
minus44
minus66
minus88
minus110
minus132
minus154
minus176
minus198
minus220
minus242
minus262
minus286
minus600
minus550
minus500
minus450
minus400
minus350
minus300
minus250
minus200
minus150
minus100
minus50
00
50
0minus9
minus18
minus27
minus36
minus45
minus54
minus63
minus72
minus81
minus90
minus99
minus108
minus117
60
00
minus60
minus120
minus180
minus240
minus300
minus360
minus420
minus480
minus540
minus600
minus660
minus720
12
0minus12
minus24
minus36
minus48
minus60
minus72
minus84
minus96
minus108
minus120
minus132
minus144
X directionZ direction Deformation
Deformation
Deformation
Deformation
(i) Raft foundation
(ii) Stepped foundation
(iii) Stepped foundation
(iv) Raft foundation
x direction z direction
x direction z direction
x directionz direction
(a) Straining action on slope 45∘
Figure 8 Continued
12 ISRN Civil Engineering
34
17
00
minus17
minus34
minus51
minus68
minus85
minus102
minus119
minus136
minus153
minus170
minus187
45
00
minus45
minus90
minus135
minus180
minus225
minus270
minus315
minus360
minus405
minus450
minus495
minus540
14
00
minus14
minus28
minus42
minus56
minus70
minus84
minus98
minus112
minus126
minus140
minus154
minus168
45
00
minus45
minus90
minus135
minus180
minus225
minus270
minus315
minus360
minus405
minus450
minus495
minus540
Deformation
Deformation
(v) Raft foundation
(vi) Stepped foundation
x directionz direction
x direction z direction
(b) Straining action on slope 25∘
Figure 8 Straining actions of 2D building with different types of foundation system and slope angle with Northridge earthquake excitationwith PGA equals 1 g
reality of the nature of the case study and the slopes were 60∘45∘ and 25∘ and the foundation system to be stepped isolatedor raft foundations The nonlinear parameters of the rockytype soil were provided to SAP2000 program as a curve of soilunder cyclic loading Applying the two selected earthquaketime histories with different PGA on a free hillside slope frombuilding and with only one building and then with a series ofbuildings the highlight points can be drawn as follows
(i) Static analysis of hillside with different angles ofslopes was found to be stable
(ii) The study gives an overview of the stability of hillsideslopes under earthquake excitations especially forconstruction requirements
(iii) The stability of slopes (without constructing build-ings) (with slope angles range from 60∘ to 25∘) isacceptable in the high PGA for the study of rocky soilno tensile stress was found in the hillside slope
(iv) Compression stress in a hillside slope angle 60∘decreased by 15 times than hillside slope angle 45∘and decreased by 14 times than hillside slope 25∘under seismic excitations
(v) The interplay between dynamic ldquoinertialrdquo effects aris-ing from the ground vibration and the quasistaticldquokinematicrdquo effects arising from the downwardmove-ment of a shallow sliding soil wedge are studied Itwas thus determined that a rigid raft foundationplaced on a big angle slope which is in a precariousequilibrium and fails during very strong shakingcannot protect the superstructure from both falling(being dragged) with the sliding soil mass and fromsuffering large damaging internal forces
(vi) This is in qualitative agreement with several casehistories of structures that have survived the com-bined effects of strong seismic shaking and of soildownward sliding The penalty to pay however is(a) appreciable rotation and lateral displacement ofthe whole system which may impair the serviceabilityof the structure and (b) generation of large bendingmoments and shear forces in the foundation slabby contrast as in fact most engineers would haveintuitively predicted placing a structure with isolatedfootings on a seismically unstable slope would be aprudent decision
(vii) It is recommended to flatten the slope from 60∘ to45∘ to avoid wedge failures at all isolated steppedfoundation locations (normal force decreased by 50for a slope angle 60∘ than slope angle 45∘ and baseshear decreased by 40 in a slope angle 60∘ than slopeangle 45∘)
(viii) The difference in straining action between steps andraft fixed base under dynamic loads is not significant(base shear in raft foundation increased by 2 thanstepping isolated footing 3 in bending moment 5in top displacement and 7 in top floor acceleration)
(ix) Stepped isolated foundation represents the best solu-tion for both dynamic performance of superstructureconstructed on hillside slope and the stability ofthe slope (columns normal force for isolated footingdecreased by 133 times than raft foundation anddecreased by 145 times in base shear) in 2D the effectof the tie beams to connect stepped footing has beenignored
ISRN Civil Engineering 13
(x) Series buildings constructed on a hillside slope espe-cially 60∘ angle normal force increased by nearly 15times than the one building model 175 times forshear force 140 times in bending moment and 125times for displacement and decreased by 020 timesfor top floor acceleration
This conclusion drawn from a 2D analysis remains validfor the 3D cases since more attenuation would be observedif the radiation damping into the third dimension wastaken into consideration These very local conditions are notadequately captured by the analysis However verification isrequired to check the results in 2D and 3D
Conflict of Interests
The author declares that there is no conflict of interestsregarding the publication of this paper
References
[1] E Spencer ldquoA method of analysis of the stability of embank-ments assuming parallel inter slice forcesrdquo Geo-Technique vol17 no 1 pp 11ndash26 1967
[2] H S Yu R Salgado S W Sloan and J M Kim ldquoLimitanalysis versus limit equilibrium for slope stabilityrdquo Journal ofGeotechnical Engineering (ASCE) vol 124 no 1 pp 1ndash11 1998
[3] A Troncone ldquoNumerical analysis of a landslide in soils withstrain-softening behaviourrdquo Geotechnique vol 55 no 8 pp585ndash596 2005
[4] D Pitilakis ldquoTopographic irregularities and soilmdashfoundationmdashstructure interactionrdquo in Proceedings of the 3rd Japan-GreeceWorkshop on Seismic Design Observation and Retrofit of Foun-dations pp 335ndash343 Santorini Greece 2009
[5] I Anastasopoulos G Gazetas M F Bransby M C RDavies and A El Nahas ldquoFault rupture propagation throughsand finite-element analysis and validation through centrifugeexperimentsrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 133 no 8 pp 943ndash958 2007
[6] G M Latha and A Garaga ldquoStability analysis of a rock slopein Himalayasrdquo Geomechanics and Engineering vol 2 no 2 pp125ndash140 2010
[7] A D Pandey P Kumar and S Sharma ldquoSeismic soil structureinteraction of buildings on hill slopesrdquo International Journal ForComputational Civil and Structural Engineering vol 2 no 2 pp544ndash555 2011
[8] R Kourkoulis I Anastasopoulos F Gelagoti and G GazetasldquoInteraction of foundation-structure systems with seismicallyprecarious slopes numerical analysis with strain softeningconstitutivemodelrdquo Soil Dynamics and Earthquake Engineeringvol 30 no 12 pp 1430ndash1445 2010
[9] S Rampello L Callisto and P Fargnoli ldquoEvaluation of seismiccoefficients for slope stability analysis using a displacement-based approachrdquo in Proceedings of the Seismic EngineeringInternational Conference Commemorating the 1908 Messina andReggio Calabria Earthquake (MERCEA rsquo08) 2008
[10] R L Michalowski and L You ldquoDisplacements of reinforcedslopes subjected to seismic loadsrdquo Journal of Geotechnical andGeoenvironmental Engineering vol 126 no 8 pp 685ndash6942000
[11] D S Chavan G Mondal and A Prashant ldquoPermanent dis-placement of nailed soil slopes subjected to earthquake load-ingrdquo in Proceedings of the 15th World Conference on EarthquakeEngineering (WCEE rsquo12) Lisbon Portugal 2012
[12] A Krishnamoorthy ldquoFactor of safety of a slope subjected toseismic loadrdquoElectronic Journal of Geotechnical Engineering vol12 2007
[13] O Mavrouli J Corominas and J Wartman ldquoMethodology toevaluate rock slope stability under seismic conditions at Solade Santa Coloma Andorrardquo Natural Hazards and Earth SystemScience vol 9 no 6 pp 1763ndash1773 2009
[14] ECOL 201 The Egyptian Code For Calculation of Loads andForces in Structural Building Work Housing and BuildingResearch Center Cairo Egypt 2008
[15] SAP200 Nonlinear Version 14 Static and Dynamic Finite Ele-ments Analysis of Structure Computers amp Structures BerkeleyCalif USA 2010
[16] K D Hjelmstad Fundamentals of Structural MechanicsSpringer New York NY USA 2nd edition 2005
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
8 ISRN Civil Engineering
minus100
minus90
minus80
minus70
minus60
minus50
minus40
minus30
minus20
minus10
0 10
20
30
minus132
minus121
minus110
minus99
minus88
minus77
minus66
minus55
minus44
minus33
minus22
minus11
0 11
Stress in x direction stress Stress in z direction stress
(a) Slope 60∘
minus910
minus840
minus770
minus700
minus630
minus560
minus490
minus420
minus350
minus280
minus210
minus140
minus70
00
minus390
minus360
minus330
minus300
minus270
minus240
minus210
minus180
minus150
minus120
minus90
minus60
minus30
00
Stress in x direction stressStress in z direction stress
(b) Slope 45∘
minus168
minus154
minus140
minus126
minus112
minus98
minus84
minus70
minus56
minus42
minus28
minus14
00
14
minus585
minus540
minus495
minus450
minus405
minus360
minus315
minus270
minus225
minus180
minus135
minus90
minus45
00
Stress in x direction stress Stress in z direction stress
(c) Slope 25∘
Figure 6 Stress distribution on 2D slope with different slope angles under static load
more stable because there is a small value of compressionstress underneath foundation For a hillside slope angle45 the straining action on the slope is moderate withouttension stress between raft foundation in 119911-direction andthe hillside soil will but there is a tension stress betweenthe raft foundation building model and the hillside soil in119909-direction which means collapse of the building modeland there is a tension stress in the hillside slope in a crestparts and the steeped foundation shows aminimum effect on
the slope This appears as a small value of compression stressin both directions and no tension stress appears underneaththe steeped foundation of the model
Figure 8 illustrates the straining actions of the hillsideslope under Northridge earthquake excitation with differentkinds of foundation systems and slopes For PGA 1 g slope60∘ there is a tension stress between foundation and soil onthe slope this indicated a failure of the model for both kindsof foundation (raft and stepped) deformation for stepped
ISRN Civil Engineering 9
minus102
minus94
minus86
minus78
minus70
minus62
minus54
minus46
minus38
minus30
minus22
minus14
minus6
00
minus102
minus94
minus86
minus78
minus70
minus62
minus54
minus46
minus38
minus30
minus22
minus14
minus6
00
480
420
360
300
240
180
120
6000minus60
minus120
minus180
minus240
minus300
420
360
300
240
180
120
6000minus60
minus120
minus180
minus240
minus300
minus360
Deformation
Deformation
(B) Stepped foundation
(A) Raft foundation x directionz direction
x direction z direction
(a) Straining action on slope 60∘
400
350
300
250
200
150
100
5000minus50
minus100
minus150
minus200
minus250
160
8000minus80
minus160
minus240
minus320
minus400
minus480
minus560
minus640
minus720
minus800
360
315
270
225
180
135
904500minus45
minus90
minus135
minus180
minus225
minus16
minus24
minus32
minus40
minus48
minus56
minus64
minus70
minus78
minus86
minus94
minus102
minus110
Deformation
Deformation
(A) Stepped foundation
(B) Raft foundation
x directionz direction
x direction z direction
(b) Straining action on slope 45∘
Figure 7 Continued
10 ISRN Civil Engineering
minus78
minus52
minus26
00265278104
130
156
182
208
234
260
603000minus30
minus60
minus90
minus120
minus150
minus180
minus210
minus240
minus270
minus300
minus330
minus80
minus60
minus40
minus20
0020406080100
120
140
160
180
84562800minus28
minus56
minus84
minus112
minus140
minus168
minus196
minus224
minus252
minus280
Deformation
Deformation
(A) Raft foundation
(B) Raft foundation
x directionz direction
x direction z direction
(c) Straining action on slope 25∘
Figure 7 Straining actions of 2D building with different types of foundation system and slope angle with El Centro earthquake excitationwith PGA equal to 1 g
Table 2 Conclusion of model stable with different earthquake PGA
Earthquakeacceleration
Hillside slopeangle
Static stability of slope only Dynamic stability withconstructed one building
Dynamic stability withconstructed series building
Tension stress Compressionstress
Tension stressunder building
Compressionstress underbuilding
Tension stressunder building
Compressionstress underbuilding
1 g60∘ No Yes Yes mdash Yes mdash45∘ No Yes Yes mdash Yes mdash25∘ No Yes No Yes Yes mdash
050 g60∘ No Yes Yes mdash Yes mdash45∘ No Yes Yes mdash Yes mdash25∘ No Yes No Yes mdash Yes
025 g60∘ No Yes Yes mdash Yes mdash45∘ No Yes No Yes Yes mdash25∘ No Yes No Yes mdash Yes
foundation is bigger than a raft foundation model and thestraining action seems to be lower than the correspondingvalues of El Centro earthquake exaltation For slope 45∘ and1 g PGA there is no tension stress between foundation and soilon the hillside slope but the compression stress in the slope issmall with respect to 60∘ slope and the corresponding valuesin 25∘ slope are bigger than 45∘ and no tension stress appears
The results obtained from Northridge earthquake aresimilar in trend with these founded from El Centro earth-quake excitation
Table 2 concluded the results of model stress founded onthe slopes with the view of stability or not under differentearthquake excitationThe stability of a series of building con-struction on a slope under earthquake excitation was studiedand also concluded in Table 2 It seem that series buildings
can bemore critical than one building and it is shown that theconstruction of series buildings on a slope from60 to 45 anglecan be destroyed under moderate earthquake even so theseries buildings withstand the same earthquake magnitudesif it is founded on a flat land foundation
6 Conclusions
A 2D building model founded on a hillside slope was evalu-ated to check the performance of buildings and slopes undervarious earthquake time history excitation and magnitudestudying a real case of study in a Doronka village in UpperEgypt Two earthquake time histories were used El Centroand Northridge earthquake with 025 g 05 g and 1 g PGAmagnitudeThe models used were prepared to agree with the
ISRN Civil Engineering 11
13
0minus13
minus26
minus39
minus52
minus65
minus78
minus91
minus104
minus117
minus130
minus143
minus156
0minus22
minus44
minus66
minus88
minus110
minus132
minus154
minus176
minus198
minus220
minus242
minus262
minus286
12
0minus12
minus24
minus36
minus48
minus60
minus72
minus84
minus96
minus108
minus120
minus132
minus144
minus44
minus66
minus88
minus110
minus132
minus154
minus176
minus198
minus220
minus242
minus262
minus286
minus600
minus550
minus500
minus450
minus400
minus350
minus300
minus250
minus200
minus150
minus100
minus50
00
50
0minus9
minus18
minus27
minus36
minus45
minus54
minus63
minus72
minus81
minus90
minus99
minus108
minus117
60
00
minus60
minus120
minus180
minus240
minus300
minus360
minus420
minus480
minus540
minus600
minus660
minus720
12
0minus12
minus24
minus36
minus48
minus60
minus72
minus84
minus96
minus108
minus120
minus132
minus144
X directionZ direction Deformation
Deformation
Deformation
Deformation
(i) Raft foundation
(ii) Stepped foundation
(iii) Stepped foundation
(iv) Raft foundation
x direction z direction
x direction z direction
x directionz direction
(a) Straining action on slope 45∘
Figure 8 Continued
12 ISRN Civil Engineering
34
17
00
minus17
minus34
minus51
minus68
minus85
minus102
minus119
minus136
minus153
minus170
minus187
45
00
minus45
minus90
minus135
minus180
minus225
minus270
minus315
minus360
minus405
minus450
minus495
minus540
14
00
minus14
minus28
minus42
minus56
minus70
minus84
minus98
minus112
minus126
minus140
minus154
minus168
45
00
minus45
minus90
minus135
minus180
minus225
minus270
minus315
minus360
minus405
minus450
minus495
minus540
Deformation
Deformation
(v) Raft foundation
(vi) Stepped foundation
x directionz direction
x direction z direction
(b) Straining action on slope 25∘
Figure 8 Straining actions of 2D building with different types of foundation system and slope angle with Northridge earthquake excitationwith PGA equals 1 g
reality of the nature of the case study and the slopes were 60∘45∘ and 25∘ and the foundation system to be stepped isolatedor raft foundations The nonlinear parameters of the rockytype soil were provided to SAP2000 program as a curve of soilunder cyclic loading Applying the two selected earthquaketime histories with different PGA on a free hillside slope frombuilding and with only one building and then with a series ofbuildings the highlight points can be drawn as follows
(i) Static analysis of hillside with different angles ofslopes was found to be stable
(ii) The study gives an overview of the stability of hillsideslopes under earthquake excitations especially forconstruction requirements
(iii) The stability of slopes (without constructing build-ings) (with slope angles range from 60∘ to 25∘) isacceptable in the high PGA for the study of rocky soilno tensile stress was found in the hillside slope
(iv) Compression stress in a hillside slope angle 60∘decreased by 15 times than hillside slope angle 45∘and decreased by 14 times than hillside slope 25∘under seismic excitations
(v) The interplay between dynamic ldquoinertialrdquo effects aris-ing from the ground vibration and the quasistaticldquokinematicrdquo effects arising from the downwardmove-ment of a shallow sliding soil wedge are studied Itwas thus determined that a rigid raft foundationplaced on a big angle slope which is in a precariousequilibrium and fails during very strong shakingcannot protect the superstructure from both falling(being dragged) with the sliding soil mass and fromsuffering large damaging internal forces
(vi) This is in qualitative agreement with several casehistories of structures that have survived the com-bined effects of strong seismic shaking and of soildownward sliding The penalty to pay however is(a) appreciable rotation and lateral displacement ofthe whole system which may impair the serviceabilityof the structure and (b) generation of large bendingmoments and shear forces in the foundation slabby contrast as in fact most engineers would haveintuitively predicted placing a structure with isolatedfootings on a seismically unstable slope would be aprudent decision
(vii) It is recommended to flatten the slope from 60∘ to45∘ to avoid wedge failures at all isolated steppedfoundation locations (normal force decreased by 50for a slope angle 60∘ than slope angle 45∘ and baseshear decreased by 40 in a slope angle 60∘ than slopeangle 45∘)
(viii) The difference in straining action between steps andraft fixed base under dynamic loads is not significant(base shear in raft foundation increased by 2 thanstepping isolated footing 3 in bending moment 5in top displacement and 7 in top floor acceleration)
(ix) Stepped isolated foundation represents the best solu-tion for both dynamic performance of superstructureconstructed on hillside slope and the stability ofthe slope (columns normal force for isolated footingdecreased by 133 times than raft foundation anddecreased by 145 times in base shear) in 2D the effectof the tie beams to connect stepped footing has beenignored
ISRN Civil Engineering 13
(x) Series buildings constructed on a hillside slope espe-cially 60∘ angle normal force increased by nearly 15times than the one building model 175 times forshear force 140 times in bending moment and 125times for displacement and decreased by 020 timesfor top floor acceleration
This conclusion drawn from a 2D analysis remains validfor the 3D cases since more attenuation would be observedif the radiation damping into the third dimension wastaken into consideration These very local conditions are notadequately captured by the analysis However verification isrequired to check the results in 2D and 3D
Conflict of Interests
The author declares that there is no conflict of interestsregarding the publication of this paper
References
[1] E Spencer ldquoA method of analysis of the stability of embank-ments assuming parallel inter slice forcesrdquo Geo-Technique vol17 no 1 pp 11ndash26 1967
[2] H S Yu R Salgado S W Sloan and J M Kim ldquoLimitanalysis versus limit equilibrium for slope stabilityrdquo Journal ofGeotechnical Engineering (ASCE) vol 124 no 1 pp 1ndash11 1998
[3] A Troncone ldquoNumerical analysis of a landslide in soils withstrain-softening behaviourrdquo Geotechnique vol 55 no 8 pp585ndash596 2005
[4] D Pitilakis ldquoTopographic irregularities and soilmdashfoundationmdashstructure interactionrdquo in Proceedings of the 3rd Japan-GreeceWorkshop on Seismic Design Observation and Retrofit of Foun-dations pp 335ndash343 Santorini Greece 2009
[5] I Anastasopoulos G Gazetas M F Bransby M C RDavies and A El Nahas ldquoFault rupture propagation throughsand finite-element analysis and validation through centrifugeexperimentsrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 133 no 8 pp 943ndash958 2007
[6] G M Latha and A Garaga ldquoStability analysis of a rock slopein Himalayasrdquo Geomechanics and Engineering vol 2 no 2 pp125ndash140 2010
[7] A D Pandey P Kumar and S Sharma ldquoSeismic soil structureinteraction of buildings on hill slopesrdquo International Journal ForComputational Civil and Structural Engineering vol 2 no 2 pp544ndash555 2011
[8] R Kourkoulis I Anastasopoulos F Gelagoti and G GazetasldquoInteraction of foundation-structure systems with seismicallyprecarious slopes numerical analysis with strain softeningconstitutivemodelrdquo Soil Dynamics and Earthquake Engineeringvol 30 no 12 pp 1430ndash1445 2010
[9] S Rampello L Callisto and P Fargnoli ldquoEvaluation of seismiccoefficients for slope stability analysis using a displacement-based approachrdquo in Proceedings of the Seismic EngineeringInternational Conference Commemorating the 1908 Messina andReggio Calabria Earthquake (MERCEA rsquo08) 2008
[10] R L Michalowski and L You ldquoDisplacements of reinforcedslopes subjected to seismic loadsrdquo Journal of Geotechnical andGeoenvironmental Engineering vol 126 no 8 pp 685ndash6942000
[11] D S Chavan G Mondal and A Prashant ldquoPermanent dis-placement of nailed soil slopes subjected to earthquake load-ingrdquo in Proceedings of the 15th World Conference on EarthquakeEngineering (WCEE rsquo12) Lisbon Portugal 2012
[12] A Krishnamoorthy ldquoFactor of safety of a slope subjected toseismic loadrdquoElectronic Journal of Geotechnical Engineering vol12 2007
[13] O Mavrouli J Corominas and J Wartman ldquoMethodology toevaluate rock slope stability under seismic conditions at Solade Santa Coloma Andorrardquo Natural Hazards and Earth SystemScience vol 9 no 6 pp 1763ndash1773 2009
[14] ECOL 201 The Egyptian Code For Calculation of Loads andForces in Structural Building Work Housing and BuildingResearch Center Cairo Egypt 2008
[15] SAP200 Nonlinear Version 14 Static and Dynamic Finite Ele-ments Analysis of Structure Computers amp Structures BerkeleyCalif USA 2010
[16] K D Hjelmstad Fundamentals of Structural MechanicsSpringer New York NY USA 2nd edition 2005
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
ISRN Civil Engineering 9
minus102
minus94
minus86
minus78
minus70
minus62
minus54
minus46
minus38
minus30
minus22
minus14
minus6
00
minus102
minus94
minus86
minus78
minus70
minus62
minus54
minus46
minus38
minus30
minus22
minus14
minus6
00
480
420
360
300
240
180
120
6000minus60
minus120
minus180
minus240
minus300
420
360
300
240
180
120
6000minus60
minus120
minus180
minus240
minus300
minus360
Deformation
Deformation
(B) Stepped foundation
(A) Raft foundation x directionz direction
x direction z direction
(a) Straining action on slope 60∘
400
350
300
250
200
150
100
5000minus50
minus100
minus150
minus200
minus250
160
8000minus80
minus160
minus240
minus320
minus400
minus480
minus560
minus640
minus720
minus800
360
315
270
225
180
135
904500minus45
minus90
minus135
minus180
minus225
minus16
minus24
minus32
minus40
minus48
minus56
minus64
minus70
minus78
minus86
minus94
minus102
minus110
Deformation
Deformation
(A) Stepped foundation
(B) Raft foundation
x directionz direction
x direction z direction
(b) Straining action on slope 45∘
Figure 7 Continued
10 ISRN Civil Engineering
minus78
minus52
minus26
00265278104
130
156
182
208
234
260
603000minus30
minus60
minus90
minus120
minus150
minus180
minus210
minus240
minus270
minus300
minus330
minus80
minus60
minus40
minus20
0020406080100
120
140
160
180
84562800minus28
minus56
minus84
minus112
minus140
minus168
minus196
minus224
minus252
minus280
Deformation
Deformation
(A) Raft foundation
(B) Raft foundation
x directionz direction
x direction z direction
(c) Straining action on slope 25∘
Figure 7 Straining actions of 2D building with different types of foundation system and slope angle with El Centro earthquake excitationwith PGA equal to 1 g
Table 2 Conclusion of model stable with different earthquake PGA
Earthquakeacceleration
Hillside slopeangle
Static stability of slope only Dynamic stability withconstructed one building
Dynamic stability withconstructed series building
Tension stress Compressionstress
Tension stressunder building
Compressionstress underbuilding
Tension stressunder building
Compressionstress underbuilding
1 g60∘ No Yes Yes mdash Yes mdash45∘ No Yes Yes mdash Yes mdash25∘ No Yes No Yes Yes mdash
050 g60∘ No Yes Yes mdash Yes mdash45∘ No Yes Yes mdash Yes mdash25∘ No Yes No Yes mdash Yes
025 g60∘ No Yes Yes mdash Yes mdash45∘ No Yes No Yes Yes mdash25∘ No Yes No Yes mdash Yes
foundation is bigger than a raft foundation model and thestraining action seems to be lower than the correspondingvalues of El Centro earthquake exaltation For slope 45∘ and1 g PGA there is no tension stress between foundation and soilon the hillside slope but the compression stress in the slope issmall with respect to 60∘ slope and the corresponding valuesin 25∘ slope are bigger than 45∘ and no tension stress appears
The results obtained from Northridge earthquake aresimilar in trend with these founded from El Centro earth-quake excitation
Table 2 concluded the results of model stress founded onthe slopes with the view of stability or not under differentearthquake excitationThe stability of a series of building con-struction on a slope under earthquake excitation was studiedand also concluded in Table 2 It seem that series buildings
can bemore critical than one building and it is shown that theconstruction of series buildings on a slope from60 to 45 anglecan be destroyed under moderate earthquake even so theseries buildings withstand the same earthquake magnitudesif it is founded on a flat land foundation
6 Conclusions
A 2D building model founded on a hillside slope was evalu-ated to check the performance of buildings and slopes undervarious earthquake time history excitation and magnitudestudying a real case of study in a Doronka village in UpperEgypt Two earthquake time histories were used El Centroand Northridge earthquake with 025 g 05 g and 1 g PGAmagnitudeThe models used were prepared to agree with the
ISRN Civil Engineering 11
13
0minus13
minus26
minus39
minus52
minus65
minus78
minus91
minus104
minus117
minus130
minus143
minus156
0minus22
minus44
minus66
minus88
minus110
minus132
minus154
minus176
minus198
minus220
minus242
minus262
minus286
12
0minus12
minus24
minus36
minus48
minus60
minus72
minus84
minus96
minus108
minus120
minus132
minus144
minus44
minus66
minus88
minus110
minus132
minus154
minus176
minus198
minus220
minus242
minus262
minus286
minus600
minus550
minus500
minus450
minus400
minus350
minus300
minus250
minus200
minus150
minus100
minus50
00
50
0minus9
minus18
minus27
minus36
minus45
minus54
minus63
minus72
minus81
minus90
minus99
minus108
minus117
60
00
minus60
minus120
minus180
minus240
minus300
minus360
minus420
minus480
minus540
minus600
minus660
minus720
12
0minus12
minus24
minus36
minus48
minus60
minus72
minus84
minus96
minus108
minus120
minus132
minus144
X directionZ direction Deformation
Deformation
Deformation
Deformation
(i) Raft foundation
(ii) Stepped foundation
(iii) Stepped foundation
(iv) Raft foundation
x direction z direction
x direction z direction
x directionz direction
(a) Straining action on slope 45∘
Figure 8 Continued
12 ISRN Civil Engineering
34
17
00
minus17
minus34
minus51
minus68
minus85
minus102
minus119
minus136
minus153
minus170
minus187
45
00
minus45
minus90
minus135
minus180
minus225
minus270
minus315
minus360
minus405
minus450
minus495
minus540
14
00
minus14
minus28
minus42
minus56
minus70
minus84
minus98
minus112
minus126
minus140
minus154
minus168
45
00
minus45
minus90
minus135
minus180
minus225
minus270
minus315
minus360
minus405
minus450
minus495
minus540
Deformation
Deformation
(v) Raft foundation
(vi) Stepped foundation
x directionz direction
x direction z direction
(b) Straining action on slope 25∘
Figure 8 Straining actions of 2D building with different types of foundation system and slope angle with Northridge earthquake excitationwith PGA equals 1 g
reality of the nature of the case study and the slopes were 60∘45∘ and 25∘ and the foundation system to be stepped isolatedor raft foundations The nonlinear parameters of the rockytype soil were provided to SAP2000 program as a curve of soilunder cyclic loading Applying the two selected earthquaketime histories with different PGA on a free hillside slope frombuilding and with only one building and then with a series ofbuildings the highlight points can be drawn as follows
(i) Static analysis of hillside with different angles ofslopes was found to be stable
(ii) The study gives an overview of the stability of hillsideslopes under earthquake excitations especially forconstruction requirements
(iii) The stability of slopes (without constructing build-ings) (with slope angles range from 60∘ to 25∘) isacceptable in the high PGA for the study of rocky soilno tensile stress was found in the hillside slope
(iv) Compression stress in a hillside slope angle 60∘decreased by 15 times than hillside slope angle 45∘and decreased by 14 times than hillside slope 25∘under seismic excitations
(v) The interplay between dynamic ldquoinertialrdquo effects aris-ing from the ground vibration and the quasistaticldquokinematicrdquo effects arising from the downwardmove-ment of a shallow sliding soil wedge are studied Itwas thus determined that a rigid raft foundationplaced on a big angle slope which is in a precariousequilibrium and fails during very strong shakingcannot protect the superstructure from both falling(being dragged) with the sliding soil mass and fromsuffering large damaging internal forces
(vi) This is in qualitative agreement with several casehistories of structures that have survived the com-bined effects of strong seismic shaking and of soildownward sliding The penalty to pay however is(a) appreciable rotation and lateral displacement ofthe whole system which may impair the serviceabilityof the structure and (b) generation of large bendingmoments and shear forces in the foundation slabby contrast as in fact most engineers would haveintuitively predicted placing a structure with isolatedfootings on a seismically unstable slope would be aprudent decision
(vii) It is recommended to flatten the slope from 60∘ to45∘ to avoid wedge failures at all isolated steppedfoundation locations (normal force decreased by 50for a slope angle 60∘ than slope angle 45∘ and baseshear decreased by 40 in a slope angle 60∘ than slopeangle 45∘)
(viii) The difference in straining action between steps andraft fixed base under dynamic loads is not significant(base shear in raft foundation increased by 2 thanstepping isolated footing 3 in bending moment 5in top displacement and 7 in top floor acceleration)
(ix) Stepped isolated foundation represents the best solu-tion for both dynamic performance of superstructureconstructed on hillside slope and the stability ofthe slope (columns normal force for isolated footingdecreased by 133 times than raft foundation anddecreased by 145 times in base shear) in 2D the effectof the tie beams to connect stepped footing has beenignored
ISRN Civil Engineering 13
(x) Series buildings constructed on a hillside slope espe-cially 60∘ angle normal force increased by nearly 15times than the one building model 175 times forshear force 140 times in bending moment and 125times for displacement and decreased by 020 timesfor top floor acceleration
This conclusion drawn from a 2D analysis remains validfor the 3D cases since more attenuation would be observedif the radiation damping into the third dimension wastaken into consideration These very local conditions are notadequately captured by the analysis However verification isrequired to check the results in 2D and 3D
Conflict of Interests
The author declares that there is no conflict of interestsregarding the publication of this paper
References
[1] E Spencer ldquoA method of analysis of the stability of embank-ments assuming parallel inter slice forcesrdquo Geo-Technique vol17 no 1 pp 11ndash26 1967
[2] H S Yu R Salgado S W Sloan and J M Kim ldquoLimitanalysis versus limit equilibrium for slope stabilityrdquo Journal ofGeotechnical Engineering (ASCE) vol 124 no 1 pp 1ndash11 1998
[3] A Troncone ldquoNumerical analysis of a landslide in soils withstrain-softening behaviourrdquo Geotechnique vol 55 no 8 pp585ndash596 2005
[4] D Pitilakis ldquoTopographic irregularities and soilmdashfoundationmdashstructure interactionrdquo in Proceedings of the 3rd Japan-GreeceWorkshop on Seismic Design Observation and Retrofit of Foun-dations pp 335ndash343 Santorini Greece 2009
[5] I Anastasopoulos G Gazetas M F Bransby M C RDavies and A El Nahas ldquoFault rupture propagation throughsand finite-element analysis and validation through centrifugeexperimentsrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 133 no 8 pp 943ndash958 2007
[6] G M Latha and A Garaga ldquoStability analysis of a rock slopein Himalayasrdquo Geomechanics and Engineering vol 2 no 2 pp125ndash140 2010
[7] A D Pandey P Kumar and S Sharma ldquoSeismic soil structureinteraction of buildings on hill slopesrdquo International Journal ForComputational Civil and Structural Engineering vol 2 no 2 pp544ndash555 2011
[8] R Kourkoulis I Anastasopoulos F Gelagoti and G GazetasldquoInteraction of foundation-structure systems with seismicallyprecarious slopes numerical analysis with strain softeningconstitutivemodelrdquo Soil Dynamics and Earthquake Engineeringvol 30 no 12 pp 1430ndash1445 2010
[9] S Rampello L Callisto and P Fargnoli ldquoEvaluation of seismiccoefficients for slope stability analysis using a displacement-based approachrdquo in Proceedings of the Seismic EngineeringInternational Conference Commemorating the 1908 Messina andReggio Calabria Earthquake (MERCEA rsquo08) 2008
[10] R L Michalowski and L You ldquoDisplacements of reinforcedslopes subjected to seismic loadsrdquo Journal of Geotechnical andGeoenvironmental Engineering vol 126 no 8 pp 685ndash6942000
[11] D S Chavan G Mondal and A Prashant ldquoPermanent dis-placement of nailed soil slopes subjected to earthquake load-ingrdquo in Proceedings of the 15th World Conference on EarthquakeEngineering (WCEE rsquo12) Lisbon Portugal 2012
[12] A Krishnamoorthy ldquoFactor of safety of a slope subjected toseismic loadrdquoElectronic Journal of Geotechnical Engineering vol12 2007
[13] O Mavrouli J Corominas and J Wartman ldquoMethodology toevaluate rock slope stability under seismic conditions at Solade Santa Coloma Andorrardquo Natural Hazards and Earth SystemScience vol 9 no 6 pp 1763ndash1773 2009
[14] ECOL 201 The Egyptian Code For Calculation of Loads andForces in Structural Building Work Housing and BuildingResearch Center Cairo Egypt 2008
[15] SAP200 Nonlinear Version 14 Static and Dynamic Finite Ele-ments Analysis of Structure Computers amp Structures BerkeleyCalif USA 2010
[16] K D Hjelmstad Fundamentals of Structural MechanicsSpringer New York NY USA 2nd edition 2005
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
10 ISRN Civil Engineering
minus78
minus52
minus26
00265278104
130
156
182
208
234
260
603000minus30
minus60
minus90
minus120
minus150
minus180
minus210
minus240
minus270
minus300
minus330
minus80
minus60
minus40
minus20
0020406080100
120
140
160
180
84562800minus28
minus56
minus84
minus112
minus140
minus168
minus196
minus224
minus252
minus280
Deformation
Deformation
(A) Raft foundation
(B) Raft foundation
x directionz direction
x direction z direction
(c) Straining action on slope 25∘
Figure 7 Straining actions of 2D building with different types of foundation system and slope angle with El Centro earthquake excitationwith PGA equal to 1 g
Table 2 Conclusion of model stable with different earthquake PGA
Earthquakeacceleration
Hillside slopeangle
Static stability of slope only Dynamic stability withconstructed one building
Dynamic stability withconstructed series building
Tension stress Compressionstress
Tension stressunder building
Compressionstress underbuilding
Tension stressunder building
Compressionstress underbuilding
1 g60∘ No Yes Yes mdash Yes mdash45∘ No Yes Yes mdash Yes mdash25∘ No Yes No Yes Yes mdash
050 g60∘ No Yes Yes mdash Yes mdash45∘ No Yes Yes mdash Yes mdash25∘ No Yes No Yes mdash Yes
025 g60∘ No Yes Yes mdash Yes mdash45∘ No Yes No Yes Yes mdash25∘ No Yes No Yes mdash Yes
foundation is bigger than a raft foundation model and thestraining action seems to be lower than the correspondingvalues of El Centro earthquake exaltation For slope 45∘ and1 g PGA there is no tension stress between foundation and soilon the hillside slope but the compression stress in the slope issmall with respect to 60∘ slope and the corresponding valuesin 25∘ slope are bigger than 45∘ and no tension stress appears
The results obtained from Northridge earthquake aresimilar in trend with these founded from El Centro earth-quake excitation
Table 2 concluded the results of model stress founded onthe slopes with the view of stability or not under differentearthquake excitationThe stability of a series of building con-struction on a slope under earthquake excitation was studiedand also concluded in Table 2 It seem that series buildings
can bemore critical than one building and it is shown that theconstruction of series buildings on a slope from60 to 45 anglecan be destroyed under moderate earthquake even so theseries buildings withstand the same earthquake magnitudesif it is founded on a flat land foundation
6 Conclusions
A 2D building model founded on a hillside slope was evalu-ated to check the performance of buildings and slopes undervarious earthquake time history excitation and magnitudestudying a real case of study in a Doronka village in UpperEgypt Two earthquake time histories were used El Centroand Northridge earthquake with 025 g 05 g and 1 g PGAmagnitudeThe models used were prepared to agree with the
ISRN Civil Engineering 11
13
0minus13
minus26
minus39
minus52
minus65
minus78
minus91
minus104
minus117
minus130
minus143
minus156
0minus22
minus44
minus66
minus88
minus110
minus132
minus154
minus176
minus198
minus220
minus242
minus262
minus286
12
0minus12
minus24
minus36
minus48
minus60
minus72
minus84
minus96
minus108
minus120
minus132
minus144
minus44
minus66
minus88
minus110
minus132
minus154
minus176
minus198
minus220
minus242
minus262
minus286
minus600
minus550
minus500
minus450
minus400
minus350
minus300
minus250
minus200
minus150
minus100
minus50
00
50
0minus9
minus18
minus27
minus36
minus45
minus54
minus63
minus72
minus81
minus90
minus99
minus108
minus117
60
00
minus60
minus120
minus180
minus240
minus300
minus360
minus420
minus480
minus540
minus600
minus660
minus720
12
0minus12
minus24
minus36
minus48
minus60
minus72
minus84
minus96
minus108
minus120
minus132
minus144
X directionZ direction Deformation
Deformation
Deformation
Deformation
(i) Raft foundation
(ii) Stepped foundation
(iii) Stepped foundation
(iv) Raft foundation
x direction z direction
x direction z direction
x directionz direction
(a) Straining action on slope 45∘
Figure 8 Continued
12 ISRN Civil Engineering
34
17
00
minus17
minus34
minus51
minus68
minus85
minus102
minus119
minus136
minus153
minus170
minus187
45
00
minus45
minus90
minus135
minus180
minus225
minus270
minus315
minus360
minus405
minus450
minus495
minus540
14
00
minus14
minus28
minus42
minus56
minus70
minus84
minus98
minus112
minus126
minus140
minus154
minus168
45
00
minus45
minus90
minus135
minus180
minus225
minus270
minus315
minus360
minus405
minus450
minus495
minus540
Deformation
Deformation
(v) Raft foundation
(vi) Stepped foundation
x directionz direction
x direction z direction
(b) Straining action on slope 25∘
Figure 8 Straining actions of 2D building with different types of foundation system and slope angle with Northridge earthquake excitationwith PGA equals 1 g
reality of the nature of the case study and the slopes were 60∘45∘ and 25∘ and the foundation system to be stepped isolatedor raft foundations The nonlinear parameters of the rockytype soil were provided to SAP2000 program as a curve of soilunder cyclic loading Applying the two selected earthquaketime histories with different PGA on a free hillside slope frombuilding and with only one building and then with a series ofbuildings the highlight points can be drawn as follows
(i) Static analysis of hillside with different angles ofslopes was found to be stable
(ii) The study gives an overview of the stability of hillsideslopes under earthquake excitations especially forconstruction requirements
(iii) The stability of slopes (without constructing build-ings) (with slope angles range from 60∘ to 25∘) isacceptable in the high PGA for the study of rocky soilno tensile stress was found in the hillside slope
(iv) Compression stress in a hillside slope angle 60∘decreased by 15 times than hillside slope angle 45∘and decreased by 14 times than hillside slope 25∘under seismic excitations
(v) The interplay between dynamic ldquoinertialrdquo effects aris-ing from the ground vibration and the quasistaticldquokinematicrdquo effects arising from the downwardmove-ment of a shallow sliding soil wedge are studied Itwas thus determined that a rigid raft foundationplaced on a big angle slope which is in a precariousequilibrium and fails during very strong shakingcannot protect the superstructure from both falling(being dragged) with the sliding soil mass and fromsuffering large damaging internal forces
(vi) This is in qualitative agreement with several casehistories of structures that have survived the com-bined effects of strong seismic shaking and of soildownward sliding The penalty to pay however is(a) appreciable rotation and lateral displacement ofthe whole system which may impair the serviceabilityof the structure and (b) generation of large bendingmoments and shear forces in the foundation slabby contrast as in fact most engineers would haveintuitively predicted placing a structure with isolatedfootings on a seismically unstable slope would be aprudent decision
(vii) It is recommended to flatten the slope from 60∘ to45∘ to avoid wedge failures at all isolated steppedfoundation locations (normal force decreased by 50for a slope angle 60∘ than slope angle 45∘ and baseshear decreased by 40 in a slope angle 60∘ than slopeangle 45∘)
(viii) The difference in straining action between steps andraft fixed base under dynamic loads is not significant(base shear in raft foundation increased by 2 thanstepping isolated footing 3 in bending moment 5in top displacement and 7 in top floor acceleration)
(ix) Stepped isolated foundation represents the best solu-tion for both dynamic performance of superstructureconstructed on hillside slope and the stability ofthe slope (columns normal force for isolated footingdecreased by 133 times than raft foundation anddecreased by 145 times in base shear) in 2D the effectof the tie beams to connect stepped footing has beenignored
ISRN Civil Engineering 13
(x) Series buildings constructed on a hillside slope espe-cially 60∘ angle normal force increased by nearly 15times than the one building model 175 times forshear force 140 times in bending moment and 125times for displacement and decreased by 020 timesfor top floor acceleration
This conclusion drawn from a 2D analysis remains validfor the 3D cases since more attenuation would be observedif the radiation damping into the third dimension wastaken into consideration These very local conditions are notadequately captured by the analysis However verification isrequired to check the results in 2D and 3D
Conflict of Interests
The author declares that there is no conflict of interestsregarding the publication of this paper
References
[1] E Spencer ldquoA method of analysis of the stability of embank-ments assuming parallel inter slice forcesrdquo Geo-Technique vol17 no 1 pp 11ndash26 1967
[2] H S Yu R Salgado S W Sloan and J M Kim ldquoLimitanalysis versus limit equilibrium for slope stabilityrdquo Journal ofGeotechnical Engineering (ASCE) vol 124 no 1 pp 1ndash11 1998
[3] A Troncone ldquoNumerical analysis of a landslide in soils withstrain-softening behaviourrdquo Geotechnique vol 55 no 8 pp585ndash596 2005
[4] D Pitilakis ldquoTopographic irregularities and soilmdashfoundationmdashstructure interactionrdquo in Proceedings of the 3rd Japan-GreeceWorkshop on Seismic Design Observation and Retrofit of Foun-dations pp 335ndash343 Santorini Greece 2009
[5] I Anastasopoulos G Gazetas M F Bransby M C RDavies and A El Nahas ldquoFault rupture propagation throughsand finite-element analysis and validation through centrifugeexperimentsrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 133 no 8 pp 943ndash958 2007
[6] G M Latha and A Garaga ldquoStability analysis of a rock slopein Himalayasrdquo Geomechanics and Engineering vol 2 no 2 pp125ndash140 2010
[7] A D Pandey P Kumar and S Sharma ldquoSeismic soil structureinteraction of buildings on hill slopesrdquo International Journal ForComputational Civil and Structural Engineering vol 2 no 2 pp544ndash555 2011
[8] R Kourkoulis I Anastasopoulos F Gelagoti and G GazetasldquoInteraction of foundation-structure systems with seismicallyprecarious slopes numerical analysis with strain softeningconstitutivemodelrdquo Soil Dynamics and Earthquake Engineeringvol 30 no 12 pp 1430ndash1445 2010
[9] S Rampello L Callisto and P Fargnoli ldquoEvaluation of seismiccoefficients for slope stability analysis using a displacement-based approachrdquo in Proceedings of the Seismic EngineeringInternational Conference Commemorating the 1908 Messina andReggio Calabria Earthquake (MERCEA rsquo08) 2008
[10] R L Michalowski and L You ldquoDisplacements of reinforcedslopes subjected to seismic loadsrdquo Journal of Geotechnical andGeoenvironmental Engineering vol 126 no 8 pp 685ndash6942000
[11] D S Chavan G Mondal and A Prashant ldquoPermanent dis-placement of nailed soil slopes subjected to earthquake load-ingrdquo in Proceedings of the 15th World Conference on EarthquakeEngineering (WCEE rsquo12) Lisbon Portugal 2012
[12] A Krishnamoorthy ldquoFactor of safety of a slope subjected toseismic loadrdquoElectronic Journal of Geotechnical Engineering vol12 2007
[13] O Mavrouli J Corominas and J Wartman ldquoMethodology toevaluate rock slope stability under seismic conditions at Solade Santa Coloma Andorrardquo Natural Hazards and Earth SystemScience vol 9 no 6 pp 1763ndash1773 2009
[14] ECOL 201 The Egyptian Code For Calculation of Loads andForces in Structural Building Work Housing and BuildingResearch Center Cairo Egypt 2008
[15] SAP200 Nonlinear Version 14 Static and Dynamic Finite Ele-ments Analysis of Structure Computers amp Structures BerkeleyCalif USA 2010
[16] K D Hjelmstad Fundamentals of Structural MechanicsSpringer New York NY USA 2nd edition 2005
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
ISRN Civil Engineering 11
13
0minus13
minus26
minus39
minus52
minus65
minus78
minus91
minus104
minus117
minus130
minus143
minus156
0minus22
minus44
minus66
minus88
minus110
minus132
minus154
minus176
minus198
minus220
minus242
minus262
minus286
12
0minus12
minus24
minus36
minus48
minus60
minus72
minus84
minus96
minus108
minus120
minus132
minus144
minus44
minus66
minus88
minus110
minus132
minus154
minus176
minus198
minus220
minus242
minus262
minus286
minus600
minus550
minus500
minus450
minus400
minus350
minus300
minus250
minus200
minus150
minus100
minus50
00
50
0minus9
minus18
minus27
minus36
minus45
minus54
minus63
minus72
minus81
minus90
minus99
minus108
minus117
60
00
minus60
minus120
minus180
minus240
minus300
minus360
minus420
minus480
minus540
minus600
minus660
minus720
12
0minus12
minus24
minus36
minus48
minus60
minus72
minus84
minus96
minus108
minus120
minus132
minus144
X directionZ direction Deformation
Deformation
Deformation
Deformation
(i) Raft foundation
(ii) Stepped foundation
(iii) Stepped foundation
(iv) Raft foundation
x direction z direction
x direction z direction
x directionz direction
(a) Straining action on slope 45∘
Figure 8 Continued
12 ISRN Civil Engineering
34
17
00
minus17
minus34
minus51
minus68
minus85
minus102
minus119
minus136
minus153
minus170
minus187
45
00
minus45
minus90
minus135
minus180
minus225
minus270
minus315
minus360
minus405
minus450
minus495
minus540
14
00
minus14
minus28
minus42
minus56
minus70
minus84
minus98
minus112
minus126
minus140
minus154
minus168
45
00
minus45
minus90
minus135
minus180
minus225
minus270
minus315
minus360
minus405
minus450
minus495
minus540
Deformation
Deformation
(v) Raft foundation
(vi) Stepped foundation
x directionz direction
x direction z direction
(b) Straining action on slope 25∘
Figure 8 Straining actions of 2D building with different types of foundation system and slope angle with Northridge earthquake excitationwith PGA equals 1 g
reality of the nature of the case study and the slopes were 60∘45∘ and 25∘ and the foundation system to be stepped isolatedor raft foundations The nonlinear parameters of the rockytype soil were provided to SAP2000 program as a curve of soilunder cyclic loading Applying the two selected earthquaketime histories with different PGA on a free hillside slope frombuilding and with only one building and then with a series ofbuildings the highlight points can be drawn as follows
(i) Static analysis of hillside with different angles ofslopes was found to be stable
(ii) The study gives an overview of the stability of hillsideslopes under earthquake excitations especially forconstruction requirements
(iii) The stability of slopes (without constructing build-ings) (with slope angles range from 60∘ to 25∘) isacceptable in the high PGA for the study of rocky soilno tensile stress was found in the hillside slope
(iv) Compression stress in a hillside slope angle 60∘decreased by 15 times than hillside slope angle 45∘and decreased by 14 times than hillside slope 25∘under seismic excitations
(v) The interplay between dynamic ldquoinertialrdquo effects aris-ing from the ground vibration and the quasistaticldquokinematicrdquo effects arising from the downwardmove-ment of a shallow sliding soil wedge are studied Itwas thus determined that a rigid raft foundationplaced on a big angle slope which is in a precariousequilibrium and fails during very strong shakingcannot protect the superstructure from both falling(being dragged) with the sliding soil mass and fromsuffering large damaging internal forces
(vi) This is in qualitative agreement with several casehistories of structures that have survived the com-bined effects of strong seismic shaking and of soildownward sliding The penalty to pay however is(a) appreciable rotation and lateral displacement ofthe whole system which may impair the serviceabilityof the structure and (b) generation of large bendingmoments and shear forces in the foundation slabby contrast as in fact most engineers would haveintuitively predicted placing a structure with isolatedfootings on a seismically unstable slope would be aprudent decision
(vii) It is recommended to flatten the slope from 60∘ to45∘ to avoid wedge failures at all isolated steppedfoundation locations (normal force decreased by 50for a slope angle 60∘ than slope angle 45∘ and baseshear decreased by 40 in a slope angle 60∘ than slopeangle 45∘)
(viii) The difference in straining action between steps andraft fixed base under dynamic loads is not significant(base shear in raft foundation increased by 2 thanstepping isolated footing 3 in bending moment 5in top displacement and 7 in top floor acceleration)
(ix) Stepped isolated foundation represents the best solu-tion for both dynamic performance of superstructureconstructed on hillside slope and the stability ofthe slope (columns normal force for isolated footingdecreased by 133 times than raft foundation anddecreased by 145 times in base shear) in 2D the effectof the tie beams to connect stepped footing has beenignored
ISRN Civil Engineering 13
(x) Series buildings constructed on a hillside slope espe-cially 60∘ angle normal force increased by nearly 15times than the one building model 175 times forshear force 140 times in bending moment and 125times for displacement and decreased by 020 timesfor top floor acceleration
This conclusion drawn from a 2D analysis remains validfor the 3D cases since more attenuation would be observedif the radiation damping into the third dimension wastaken into consideration These very local conditions are notadequately captured by the analysis However verification isrequired to check the results in 2D and 3D
Conflict of Interests
The author declares that there is no conflict of interestsregarding the publication of this paper
References
[1] E Spencer ldquoA method of analysis of the stability of embank-ments assuming parallel inter slice forcesrdquo Geo-Technique vol17 no 1 pp 11ndash26 1967
[2] H S Yu R Salgado S W Sloan and J M Kim ldquoLimitanalysis versus limit equilibrium for slope stabilityrdquo Journal ofGeotechnical Engineering (ASCE) vol 124 no 1 pp 1ndash11 1998
[3] A Troncone ldquoNumerical analysis of a landslide in soils withstrain-softening behaviourrdquo Geotechnique vol 55 no 8 pp585ndash596 2005
[4] D Pitilakis ldquoTopographic irregularities and soilmdashfoundationmdashstructure interactionrdquo in Proceedings of the 3rd Japan-GreeceWorkshop on Seismic Design Observation and Retrofit of Foun-dations pp 335ndash343 Santorini Greece 2009
[5] I Anastasopoulos G Gazetas M F Bransby M C RDavies and A El Nahas ldquoFault rupture propagation throughsand finite-element analysis and validation through centrifugeexperimentsrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 133 no 8 pp 943ndash958 2007
[6] G M Latha and A Garaga ldquoStability analysis of a rock slopein Himalayasrdquo Geomechanics and Engineering vol 2 no 2 pp125ndash140 2010
[7] A D Pandey P Kumar and S Sharma ldquoSeismic soil structureinteraction of buildings on hill slopesrdquo International Journal ForComputational Civil and Structural Engineering vol 2 no 2 pp544ndash555 2011
[8] R Kourkoulis I Anastasopoulos F Gelagoti and G GazetasldquoInteraction of foundation-structure systems with seismicallyprecarious slopes numerical analysis with strain softeningconstitutivemodelrdquo Soil Dynamics and Earthquake Engineeringvol 30 no 12 pp 1430ndash1445 2010
[9] S Rampello L Callisto and P Fargnoli ldquoEvaluation of seismiccoefficients for slope stability analysis using a displacement-based approachrdquo in Proceedings of the Seismic EngineeringInternational Conference Commemorating the 1908 Messina andReggio Calabria Earthquake (MERCEA rsquo08) 2008
[10] R L Michalowski and L You ldquoDisplacements of reinforcedslopes subjected to seismic loadsrdquo Journal of Geotechnical andGeoenvironmental Engineering vol 126 no 8 pp 685ndash6942000
[11] D S Chavan G Mondal and A Prashant ldquoPermanent dis-placement of nailed soil slopes subjected to earthquake load-ingrdquo in Proceedings of the 15th World Conference on EarthquakeEngineering (WCEE rsquo12) Lisbon Portugal 2012
[12] A Krishnamoorthy ldquoFactor of safety of a slope subjected toseismic loadrdquoElectronic Journal of Geotechnical Engineering vol12 2007
[13] O Mavrouli J Corominas and J Wartman ldquoMethodology toevaluate rock slope stability under seismic conditions at Solade Santa Coloma Andorrardquo Natural Hazards and Earth SystemScience vol 9 no 6 pp 1763ndash1773 2009
[14] ECOL 201 The Egyptian Code For Calculation of Loads andForces in Structural Building Work Housing and BuildingResearch Center Cairo Egypt 2008
[15] SAP200 Nonlinear Version 14 Static and Dynamic Finite Ele-ments Analysis of Structure Computers amp Structures BerkeleyCalif USA 2010
[16] K D Hjelmstad Fundamentals of Structural MechanicsSpringer New York NY USA 2nd edition 2005
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
12 ISRN Civil Engineering
34
17
00
minus17
minus34
minus51
minus68
minus85
minus102
minus119
minus136
minus153
minus170
minus187
45
00
minus45
minus90
minus135
minus180
minus225
minus270
minus315
minus360
minus405
minus450
minus495
minus540
14
00
minus14
minus28
minus42
minus56
minus70
minus84
minus98
minus112
minus126
minus140
minus154
minus168
45
00
minus45
minus90
minus135
minus180
minus225
minus270
minus315
minus360
minus405
minus450
minus495
minus540
Deformation
Deformation
(v) Raft foundation
(vi) Stepped foundation
x directionz direction
x direction z direction
(b) Straining action on slope 25∘
Figure 8 Straining actions of 2D building with different types of foundation system and slope angle with Northridge earthquake excitationwith PGA equals 1 g
reality of the nature of the case study and the slopes were 60∘45∘ and 25∘ and the foundation system to be stepped isolatedor raft foundations The nonlinear parameters of the rockytype soil were provided to SAP2000 program as a curve of soilunder cyclic loading Applying the two selected earthquaketime histories with different PGA on a free hillside slope frombuilding and with only one building and then with a series ofbuildings the highlight points can be drawn as follows
(i) Static analysis of hillside with different angles ofslopes was found to be stable
(ii) The study gives an overview of the stability of hillsideslopes under earthquake excitations especially forconstruction requirements
(iii) The stability of slopes (without constructing build-ings) (with slope angles range from 60∘ to 25∘) isacceptable in the high PGA for the study of rocky soilno tensile stress was found in the hillside slope
(iv) Compression stress in a hillside slope angle 60∘decreased by 15 times than hillside slope angle 45∘and decreased by 14 times than hillside slope 25∘under seismic excitations
(v) The interplay between dynamic ldquoinertialrdquo effects aris-ing from the ground vibration and the quasistaticldquokinematicrdquo effects arising from the downwardmove-ment of a shallow sliding soil wedge are studied Itwas thus determined that a rigid raft foundationplaced on a big angle slope which is in a precariousequilibrium and fails during very strong shakingcannot protect the superstructure from both falling(being dragged) with the sliding soil mass and fromsuffering large damaging internal forces
(vi) This is in qualitative agreement with several casehistories of structures that have survived the com-bined effects of strong seismic shaking and of soildownward sliding The penalty to pay however is(a) appreciable rotation and lateral displacement ofthe whole system which may impair the serviceabilityof the structure and (b) generation of large bendingmoments and shear forces in the foundation slabby contrast as in fact most engineers would haveintuitively predicted placing a structure with isolatedfootings on a seismically unstable slope would be aprudent decision
(vii) It is recommended to flatten the slope from 60∘ to45∘ to avoid wedge failures at all isolated steppedfoundation locations (normal force decreased by 50for a slope angle 60∘ than slope angle 45∘ and baseshear decreased by 40 in a slope angle 60∘ than slopeangle 45∘)
(viii) The difference in straining action between steps andraft fixed base under dynamic loads is not significant(base shear in raft foundation increased by 2 thanstepping isolated footing 3 in bending moment 5in top displacement and 7 in top floor acceleration)
(ix) Stepped isolated foundation represents the best solu-tion for both dynamic performance of superstructureconstructed on hillside slope and the stability ofthe slope (columns normal force for isolated footingdecreased by 133 times than raft foundation anddecreased by 145 times in base shear) in 2D the effectof the tie beams to connect stepped footing has beenignored
ISRN Civil Engineering 13
(x) Series buildings constructed on a hillside slope espe-cially 60∘ angle normal force increased by nearly 15times than the one building model 175 times forshear force 140 times in bending moment and 125times for displacement and decreased by 020 timesfor top floor acceleration
This conclusion drawn from a 2D analysis remains validfor the 3D cases since more attenuation would be observedif the radiation damping into the third dimension wastaken into consideration These very local conditions are notadequately captured by the analysis However verification isrequired to check the results in 2D and 3D
Conflict of Interests
The author declares that there is no conflict of interestsregarding the publication of this paper
References
[1] E Spencer ldquoA method of analysis of the stability of embank-ments assuming parallel inter slice forcesrdquo Geo-Technique vol17 no 1 pp 11ndash26 1967
[2] H S Yu R Salgado S W Sloan and J M Kim ldquoLimitanalysis versus limit equilibrium for slope stabilityrdquo Journal ofGeotechnical Engineering (ASCE) vol 124 no 1 pp 1ndash11 1998
[3] A Troncone ldquoNumerical analysis of a landslide in soils withstrain-softening behaviourrdquo Geotechnique vol 55 no 8 pp585ndash596 2005
[4] D Pitilakis ldquoTopographic irregularities and soilmdashfoundationmdashstructure interactionrdquo in Proceedings of the 3rd Japan-GreeceWorkshop on Seismic Design Observation and Retrofit of Foun-dations pp 335ndash343 Santorini Greece 2009
[5] I Anastasopoulos G Gazetas M F Bransby M C RDavies and A El Nahas ldquoFault rupture propagation throughsand finite-element analysis and validation through centrifugeexperimentsrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 133 no 8 pp 943ndash958 2007
[6] G M Latha and A Garaga ldquoStability analysis of a rock slopein Himalayasrdquo Geomechanics and Engineering vol 2 no 2 pp125ndash140 2010
[7] A D Pandey P Kumar and S Sharma ldquoSeismic soil structureinteraction of buildings on hill slopesrdquo International Journal ForComputational Civil and Structural Engineering vol 2 no 2 pp544ndash555 2011
[8] R Kourkoulis I Anastasopoulos F Gelagoti and G GazetasldquoInteraction of foundation-structure systems with seismicallyprecarious slopes numerical analysis with strain softeningconstitutivemodelrdquo Soil Dynamics and Earthquake Engineeringvol 30 no 12 pp 1430ndash1445 2010
[9] S Rampello L Callisto and P Fargnoli ldquoEvaluation of seismiccoefficients for slope stability analysis using a displacement-based approachrdquo in Proceedings of the Seismic EngineeringInternational Conference Commemorating the 1908 Messina andReggio Calabria Earthquake (MERCEA rsquo08) 2008
[10] R L Michalowski and L You ldquoDisplacements of reinforcedslopes subjected to seismic loadsrdquo Journal of Geotechnical andGeoenvironmental Engineering vol 126 no 8 pp 685ndash6942000
[11] D S Chavan G Mondal and A Prashant ldquoPermanent dis-placement of nailed soil slopes subjected to earthquake load-ingrdquo in Proceedings of the 15th World Conference on EarthquakeEngineering (WCEE rsquo12) Lisbon Portugal 2012
[12] A Krishnamoorthy ldquoFactor of safety of a slope subjected toseismic loadrdquoElectronic Journal of Geotechnical Engineering vol12 2007
[13] O Mavrouli J Corominas and J Wartman ldquoMethodology toevaluate rock slope stability under seismic conditions at Solade Santa Coloma Andorrardquo Natural Hazards and Earth SystemScience vol 9 no 6 pp 1763ndash1773 2009
[14] ECOL 201 The Egyptian Code For Calculation of Loads andForces in Structural Building Work Housing and BuildingResearch Center Cairo Egypt 2008
[15] SAP200 Nonlinear Version 14 Static and Dynamic Finite Ele-ments Analysis of Structure Computers amp Structures BerkeleyCalif USA 2010
[16] K D Hjelmstad Fundamentals of Structural MechanicsSpringer New York NY USA 2nd edition 2005
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
ISRN Civil Engineering 13
(x) Series buildings constructed on a hillside slope espe-cially 60∘ angle normal force increased by nearly 15times than the one building model 175 times forshear force 140 times in bending moment and 125times for displacement and decreased by 020 timesfor top floor acceleration
This conclusion drawn from a 2D analysis remains validfor the 3D cases since more attenuation would be observedif the radiation damping into the third dimension wastaken into consideration These very local conditions are notadequately captured by the analysis However verification isrequired to check the results in 2D and 3D
Conflict of Interests
The author declares that there is no conflict of interestsregarding the publication of this paper
References
[1] E Spencer ldquoA method of analysis of the stability of embank-ments assuming parallel inter slice forcesrdquo Geo-Technique vol17 no 1 pp 11ndash26 1967
[2] H S Yu R Salgado S W Sloan and J M Kim ldquoLimitanalysis versus limit equilibrium for slope stabilityrdquo Journal ofGeotechnical Engineering (ASCE) vol 124 no 1 pp 1ndash11 1998
[3] A Troncone ldquoNumerical analysis of a landslide in soils withstrain-softening behaviourrdquo Geotechnique vol 55 no 8 pp585ndash596 2005
[4] D Pitilakis ldquoTopographic irregularities and soilmdashfoundationmdashstructure interactionrdquo in Proceedings of the 3rd Japan-GreeceWorkshop on Seismic Design Observation and Retrofit of Foun-dations pp 335ndash343 Santorini Greece 2009
[5] I Anastasopoulos G Gazetas M F Bransby M C RDavies and A El Nahas ldquoFault rupture propagation throughsand finite-element analysis and validation through centrifugeexperimentsrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 133 no 8 pp 943ndash958 2007
[6] G M Latha and A Garaga ldquoStability analysis of a rock slopein Himalayasrdquo Geomechanics and Engineering vol 2 no 2 pp125ndash140 2010
[7] A D Pandey P Kumar and S Sharma ldquoSeismic soil structureinteraction of buildings on hill slopesrdquo International Journal ForComputational Civil and Structural Engineering vol 2 no 2 pp544ndash555 2011
[8] R Kourkoulis I Anastasopoulos F Gelagoti and G GazetasldquoInteraction of foundation-structure systems with seismicallyprecarious slopes numerical analysis with strain softeningconstitutivemodelrdquo Soil Dynamics and Earthquake Engineeringvol 30 no 12 pp 1430ndash1445 2010
[9] S Rampello L Callisto and P Fargnoli ldquoEvaluation of seismiccoefficients for slope stability analysis using a displacement-based approachrdquo in Proceedings of the Seismic EngineeringInternational Conference Commemorating the 1908 Messina andReggio Calabria Earthquake (MERCEA rsquo08) 2008
[10] R L Michalowski and L You ldquoDisplacements of reinforcedslopes subjected to seismic loadsrdquo Journal of Geotechnical andGeoenvironmental Engineering vol 126 no 8 pp 685ndash6942000
[11] D S Chavan G Mondal and A Prashant ldquoPermanent dis-placement of nailed soil slopes subjected to earthquake load-ingrdquo in Proceedings of the 15th World Conference on EarthquakeEngineering (WCEE rsquo12) Lisbon Portugal 2012
[12] A Krishnamoorthy ldquoFactor of safety of a slope subjected toseismic loadrdquoElectronic Journal of Geotechnical Engineering vol12 2007
[13] O Mavrouli J Corominas and J Wartman ldquoMethodology toevaluate rock slope stability under seismic conditions at Solade Santa Coloma Andorrardquo Natural Hazards and Earth SystemScience vol 9 no 6 pp 1763ndash1773 2009
[14] ECOL 201 The Egyptian Code For Calculation of Loads andForces in Structural Building Work Housing and BuildingResearch Center Cairo Egypt 2008
[15] SAP200 Nonlinear Version 14 Static and Dynamic Finite Ele-ments Analysis of Structure Computers amp Structures BerkeleyCalif USA 2010
[16] K D Hjelmstad Fundamentals of Structural MechanicsSpringer New York NY USA 2nd edition 2005
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International Journal of
RotatingMachinery
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Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of