Horizontal Bearing Test and Optimization of Value for...

Research ArticleHorizontal Bearing Test and Optimization of 119898 Value forPrecast Piles in Alluvium Stratum of the Yellow River

Xianzhou Lyu 1 Zhen Chen1 Zenghui Zhao 2 andWeimingWang1

1College of Architecture and Civil Engineering Shandong University of Science and Technology Qingdao 266590 China2State Key Laboratory of Mining Disaster Prevention and Control Cofounded by Shandong Province andthe Ministry of Science and Technology Shandong University of Science and Technology Qingdao 266590 China

Correspondence should be addressed to Zenghui Zhao tgzyzzh163com

Received 20 February 2018 Revised 25 April 2018 Accepted 20 May 2018 Published 21 June 2018

Academic Editor Marek Lefik

Copyright copy 2018 Xianzhou Lyu et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

For a pile foundation design the value of proportional coefficientm to define the soil horizontal resist force is a significant parameterHowever different geological conditions and experimental environment have led to different m values In this paper an in situ testis firstly carried out on the horizontal bearing capacity of large-size precast square-piles The piles deformation is then derived byusing the optimization method from the measured data Secondly a back analysis model is established to calculate the m valueby using the simplex method which reveals the evolution rule of the value of proportional coefficient m Results show that thehorizontal bearing characteristics of precast piles depend on the interaction force of piles and soils The action mechanism of thesoils around the piles is gradually developedwith the increase in the concrete contentThehorizontal critical load and the Eigenvalueof horizontal bearing capacity increased by 167 and 20 respectively It is also seen that the higher the content of the cement-soilaround the piles and the longer the pile length the bigger them value obtainedThe variation of the proportional coefficientmwiththe horizontal displacement of pile top is defined by three stages rapid decaying stage slow decaying stage and balanced stagerespectively The inverse analysis method on the proposedm value can accurately reflect the actual working state of piles and soilsIn the depth of 3sim18m in the west of Jinan the range of m value is recommended as 4sim658 MNsdotmminus4 When Δ takes 12mm thevalues ofm are consistent with the result from the back analysis In summary the obtainedm value can be effectively used to guidethe design of enclosure structure in the super deep foundation pit in the Yellow River alluvial stratum

1 Introduction

The thick alluvial clay stratum in Jirsquonan belongs to thequaternary system with its major content silt silty soil andclay The upper stratum is loose and underconsolidated withpoor physical mechanics properties low bearing capacitycreep and thixotropic property The vein network channelof groundwater extends in all directions and a field deepexcavation shows distinct spatial effect The constructionof metro stations has exacerbated the tension of urbanunderground space making the characteristics of ldquodeep bigtight and nearrdquo of foundation pit more obvious The safetyof foundation pit excavation is facing great challenges Dueto the constant exploitation of super high-rise buildingsand urban underground space super large foundation pitengineering is constantly emerging Design of the foundation

pit enclosure structure with the combination of the supportstructure and the main structure emerges at a historicmoment However few systematic researches on large-sizeprecast piles as principal enclosure structure have beenconducted in deep and large foundation pit The interactionmechanism between prefabricated components and cast-in-situ components is complicated and the design backup ofcritical supporting parameters is insufficient Therefore itis of a vital significance to accurately determine the designparameters of precast piles in deep foundation pit for theconstruction safety of geotechnical engineering in the alluvialstratum of the Yellow River

A pile foundation is supported by a stable soil layeror embedded in bedrock through liquefiable soil layersIn a liquefied and seismic subsidence of the shallow soillayer caused by the earthquake a pile foundation still has

HindawiMathematical Problems in EngineeringVolume 2018 Article ID 3930490 13 pageshttpsdoiorg10115520183930490

2 Mathematical Problems in Engineering

Rebar connector

Precast Concrete Square Pile High pressurejet piles

Concrete lining wall

Cement soil

Figure 1 Pile and wall superposition enclosure structure

sufficient bearing capacity to ensure the stability of thefoundation without excessive deformation [1ndash3] Howeverdetermination of the horizontal and the vertical bearingproperty of the pile foundation is a complicated problemunder pile-soil interaction The bearing characteristic coverstwo aspects the ultimate horizontal bearing capacity ofpile controlled by the strength of soil around piles or theallowable horizontal bearing capacity of pile determinedby the allowable deformation of piles [4] The calculationmethod of the bearing capacity of a single pile mainlyincludes p-y curve method [5ndash7] analytical method [8ndash10]finite element simulation [11ndash15] and artificial intelligencemethod [16] Moreover experimental method is also aneffectiveway to determine the horizontal bearing capacity of apile foundation Huang et al analyzed the horizontal bearingcharacteristics of bored piles by horizontal static loadingtests [17] Haque et al used horizontal static loading test tomeasure the pile strain and analyzed the distribution of pileload transfer under static loading [18] Zhao et al used theindoor model test to study the bearing characteristics of asingle pile under the combination of vertical and horizontalloadings [19] The researches mentioned above show that thescale effect of horizontal bearing capacity of pile foundationin laboratory tests cannot be neglected Also it is difficultfor a model test to insure the reliability In addition theaccuracy of numerical simulation depends on the accuracyof test parameters Comparatively in situ test of piles is moreeffective for testing the bearing capacity of pile foundation

Soils around piles stabilize pile body and resist theexternal lateral force acting on piles Taking the soils aroundpiles as an elastic medium and assuming piles as an elasticbeamwhich supports the soils around piles the soil resistanceforce is determined by the linear elastic reaction methodto derive the elastic resistance property of the soils Thedeformation differential equation of the elastic foundationbeam is as follows [24]

11986411986811988941199101198891199114 minus 119890119886 (119911) = 0 (0 le 119911 le ℎ119899)

11986411986811988941199101198891199114 + 1198981198870 (119911 minus ℎ119899) 119910 minus 119890119886 (119911) = 0 (119911 ge ℎ119899)

(1)

where EI is the flexural rigidity of the enclosure structureE is the elastic modulus of piles I is the section moment of

inertia of the pile y is the lateral displacement of the enclosurestructure z is the excavating depth ea(z) is the active earthpressure at the excavating depth z h119899 is the excavating depthat the step n and m is proportional coefficient of horizontalresistance of foundation soils

The value of m is the proportional coefficient thatdescribes the horizontal resistance coefficient with the depthWhen the pile section type pile stiffness pile length anddepth of pile bottom are determined the m value is entirelydependent on the characteristics of the soils aroundpilesDueto the unreasonable design of row piles accidents frequentlyoccurred in large and deep foundation pits One of the keyfactors is the inappropriate selection of the ratio coefficientof the horizontal resistance of foundation soil (m value)Researches indicate that the value of m is a multifactorand regional parameter which relates to soil properties thepile bearing property under static load dynamic load ormulticycle grade load and displacement etc [25 26] Fora long time researchers have proposed several methods todetermine the value of m Fan et al studied the proportionalcoefficient m in muddy soft rock foundation and provideda reference value through indoor horizontal static load testsand numerical simulations [27] Huang et al consideredcalculating the value of m of the composite pile based onthe design value of horizontal bearing capacity and thecorresponding deformation [28] Xu et al determined theproportional coefficient in vertical elastic subgrade beamby using back analysis software Ucode and finite elementssoftware Abaqus combined with the measured deformationof retaining walls [29]

The above researches provide important reference fordesign of row piles in deep foundation pit However the pilefoundation bearing capacity and the design parameters mvalue present obvious regional featuresmdashthe soil characteris-tics are complex and different soils have different parametersAs the water level decreased in the Yellow River alluviumfor recent years the shallow soil has better performancein self-stability and generates microconsolidation The veinsnetwork of groundwater extends in all directions which aredifferent from the properties of ordinary clays and soft soilsThe excess pore water is commonly observed Given theabove condition a new pile-wall superimposition enclosurestructure is adopted to support the deep foundation pit in thisarea (see Figure 1) The two factors complexity of regional

Mathematical Problems in Engineering 3

Miscellaneous fill

Loess

Silt

Silty clay

Fine sand

Clay

Silty clay

Silty clayClay

Fine sand

1m

Base plate

FloorWater level

Bottom line of piles

Anti-uplift water level

247m

266m

Cement soil

Figure 2 Hydrogeologic conditions and precast piles

Table 1 Formation of physical mechanics parameters

Layers Thicknessm

Bulkdensity

(kNmminus3)

ElasticmodulusMpa

Poissonrsquosratios C kPa 120601(∘)

Undrainedshear

strengthkPa

CompressioncoefficientMPaminus1

Voidration

Watercontent

Miscellaneousfill 28 180 8 035 -- -- -- -- -- --

Loess 32 193 12 032 360 160 933 032 0750 245Silt 10 196 20 028 150 200 878 018 0697 232Silty clay 60 195 30 029 500 140 999 032 0766 264Fine sand 20 212 80 025 00 300 -- -- -- --Silty clay 56 195 35 030 500 140 999 027 0796 273Clay 97 192 50 028 60 18 1250 028 0780 265

stratum conditions and the new support method make someresults not clear such as horizontal bearing characteristics ofprecast piles and the selection rule of the m value This isan urgent problem for the construction of extra-large deepfoundation pit in alluvial stratumofYellowRiver In this studyfirstly a variable unique research of large-size precast square-piles by in situ test is conducted to analyze the bearing charac-teristics of the new pile-wall superimposition structureThena calculation model is established to determine the m valuebased on the engineering survey data and the optimizationmethod The obtained results can provide theoretical andtechnical guidance for the enclosure structure design ofthe deep foundation pit in the alluvial stratum and similarstratum

2 Field Test

21 Parameters of Stratum and Soil The testing site is locatedat the Yan Mazhuang Station Metro line R1 Jirsquonan Thedesign depth of foundation pit is 16sim18m and the maximumlength of precast piles is 266m with 700mm in diameterThe main enclosure structure adopts cement-soil cast-in-place piles with 1100mm in diameter where precast piles with

700times700 mm rectangle section are inserted The standardinterval between piles is 15mThe waterproof curtain adoptstriple-pipe jet grouting piles with 800mm in diameter and 550mm in spacing Enclosure piles are inserted into the cement-soil cast-in-place pile and the length of the cement-soil pileis as long as the enclosure piles The alluvial stratum is thealluvial-diluvial geomorphic units of the Yellow River andXiaoqing River The covering layer is the quaternary alluvial-diluvial strata which is mainly composed of silty clay siltyclay and clay or sandy soil and pebbles in some regionsThe base bearing soil layer is compressible and mainly claylayer and the local is silt Generally the foundation soils arestable and homogeneous Hydrogeologic conditions and thedistribution of precast piles are shown in Figure 2 and therelevant parameters of each layer are shown in Table 1

22 Test Equipment Layout of the horizontal static loadingtest is shown in Figure 3 In the test the horizontal force isapplied by the lifting jack A spherical hinge seat is placedat the contact between the jack and the test pile to ensurethat the jack force can pass horizontally through the axisof the pile body The horizontal displacement of the pile ismeasured by large range dial gauges Two dial gauges are


Ball-twist

Reactionpile

Reactionpile

TestpileBase Pile

Dial gauges Lifting jack

(a) Overlook of test device (b) Field test

Figure 3 Horizontal static loading test of single pile

Table 2 Basic parameters of in situ test

NoCement soil between piles Precast pile core

Diameter Length Cement content mixture ratio Pile Cross section Pile length Concrete type Pile end bearing layerm m m m

PCSP1 11 242 167 300 1028 465 07times07 247 C50 ClayPCSP2 11 261 256 500 900 550 07times07 266 C50 ClayPCSP3 11 242 256 500 900 550 07times07 247 C50 ClayNote the mixture ratio is the ratio of cement soil water and the water content of the soil is 17

installed on the plane surface and 50cm above the planeLower gauge is used to measure the horizontal displacementof the pile on the ground while the upper one is used tomeasure the horizontal displacement on the top of the pileThe rotation angle of the pile body above the ground can beobtained according to the ratio of the displacement differencebetween the two tables and the distance of the two tablesThe base pile for fixing the dial gauges is set in the oppositedirection of the test pile while the net distance to the test pileis less than one time of the pile diameter With the excavationof the foundation pit the stress balance is destroyed andthe superposition enclosure structure is mainly deformedtowards the inside of the foundation pitTherefore horizontalloads are applied perpendicularly to the outside of the pitin the test The horizontal counterforce is developed fromthe consolidated soils The horizontal thrust is applied bythe hydraulic jack with a spherical joint while the horizontalaction line coincides with the top elevation (plusmn 000m) of thepile foundation

23 TestMethod According to the requirements of TechnicalCode for Testing of Building Foundation Piles (JGJ106-2014)[30] one-way multicycle graded loading method is adoptedin the test The loading capacity of each grade is 110 of thedesign bearing capacity of pile foundation After each gradeof load is applied the load remains unchanged for 4 minutesbefore the horizontal displacement is measured After datarecording unloading is conducted to zero and the load ismaintained for 2 minutes when the residual deformation isrecorded A load cycle is completed according to the abovesteps Deformation detection of the first grade loading iscompleted after five cycles

24 Test Pile Type and Basic Parameters The pile testsare based on the principle of unique variable Three pilesare selected to conduct the experiment in which two areequipped into one group Three groups are adopted in totalin the experiment Specific parameters are listed in Table 2where the PCSP is the abbreviation of precast concretesquare-pile

3 Test Results

31 Relation between Displacement of Piles and HorizontalLoad Figure 4 shows the relationship between the pile topdisplacementY0 and the horizontal loadHThe displacementtrajectory of PCSP No2 and PCSP No3 is the same beforeloading to 500kN Due to the breakage of PCSP No2 theloading process is stopped and the maximum horizontaldisplacement is 1133mm

Compared with the displacement curves of PCSP No1and PCSP No3 the displacement of pile top increases grad-ually during loading process and the curve shows a parabolictrend Under the same stress level the displacement of PCSPNo1 pile with lower cement content ismore than that of PCSPNo3 from the beginning to the end and the displacementdifference increases gradually Finally the differential valueof the maximum displacement is 661mm When the pilesare subjected to the lateral load the cemented soils aroundpiles play important roles for stabilizing piles and resistingthe external force transfer from piles

In order to more intuitively reveal the effect of horizontalloads on the deformation of retaining structures the ratioof horizontal load change per displacement unit (ΔY ΔH)over the horizontal increment is summarized as shown in


100 200 300 400 500 600 700 8000

5

10

15

20

25

30

Horizontal load H(kN)

PCSP No 1-loading to 2778mmPCSP No 2-loading to 1133mmPCSP No 3-loading to 2175mm

Disp

lace

men

t of p

ile to

pY0

(mm

)

Figure 4 Horizontal static loading test Y0-H curve of single pile

0 100 200 300 400 500 600 700 800000

002

004

006

008

010

Lateral load H(kN)

PCSP No 3PCSP No 2PCSP No 1

ΔYΔ

H(m

mmiddotＥ

minus1)

Figure 5 ΔY ΔH-H curve of single pile

Figure 5 The ordinate represents the characterization ofdisplacement grade under loading that is the displacementvariation amplitude under a unit force The abscissa repre-sents the applied horizontal load in the test

From the pile displacement grade curve of PCSP No3(Figure 5) it is seen that in the range of 100kN to 400kNthe variation of the displacement grade is not large Themaximum displacement grade observed after the appliedhorizontal load is more than 400kN Similar to that of PCSPNo3 the displacement grade of the PCSP No2 increasessuddenly and tends to increase with a higher rate whenloading is beyond 400kN On the contrary PCSP No1without the cement-soil mixture has a significant increase inthe grade curve The grade curve has the same trend in the

loading interval between 160kN and 480kN After loadingto 480kN the slope of the grade curve suddenly increaseswhich indicates that the use of cement-soil enhances thebearing capacity of the pile in a certain range

32 Analysis of the Relationship between the Displacement(Y0) and lgt Figures 6(a) 6(b) and 6(c) show the Y0-lgtrelationship curves of PCSP Nos1 2 and 3 in static loadingtests respectively It is seen that when loading is applied to400kN 400kN and 480kN respectively the displacement isobviously higher than the displacement differencementionedin the previous section According to Technical Code forTesting of Building Foundation Piles [30] the horizontalcritical loads Hcr of PCSP Nos1 2 and 3 can be judged as400kN 400kN and 480kN respectively and the Eigenvalueof horizontal bearing capacity Rℎ is 300kN 300kN and360kN accordingly It is seen that the maintenance effectof soils around the piles is improved by 89 while thehorizontal critical load and the Eigenvalue of horizontalbearing capacity increase by 167 and 20 respectively

4 Analysis of the Value of 119898 in ThickAlluvial Foundation Soils

Support design of a deep foundation pit in thick alluviumareais always a very complex common problem The determina-tion of the ratio coefficient m of the horizontal resistance forfoundation soils also has great controversy in various areasdue to different geological conditions The initial value ofm in each region in China was recommended by Xilin etal (former Soviet Union) which was then adopted by theTechnical Code for Design of Railway Highway and UrbanRoad Bridges andCulverts of the former Soviet Union [31] In1974 the China research center corrected the recommendedvalue of m by single pile horizontal static loading tests TheCode for Design of Foundation and Foundation of HighwayBridge Culvert (JTJ024-85) [22] adopted the revised value in1985 and the railway ministry took the same value as thebenchmark Now the various codes and the research contentsof scholars are used in this study for comparison and collectedin Table 3

Although the current specifications and guidelinespresent recommended values for m values they are onlyobtained by test statistics The suggested m values for eachtype of soils are in a large range and it is still difficult toaccurately determine the values

41 Calculation of m Value Based on the Horizontal StaticLoading Tests Thetarget objective of vertical elastic subgradebeam method is used to solve plane strain problems Inthis method the enclosure structure is assumed as a verticalelastic foundation beamThe effect to the enclosure structureinduced by the soil mass below the excavating surface isstimulated by a series of Winkler springs while the support-ing effect to the enclosure structure induced by the lateralbracing (steel shotcrete or concrete support) is stimulatedby the elastic mountings In order to achieve the balance ofcalculation the effect of the soils behind the wall acting on


24 26 28 30 32 340

5

10

15

20

25

lgt (s)

Loading 100kN

Loading 200kN

Loading 300kNLoading 400kNLoading 500kN

Loading 600kNLoading 700kN

Y0

(mm

)

(a) 1198840-lgt curve of PCSP No1

lgt (s)24 26 28 30 32 34

0

2

4

6

8

10

12

Loading 100kN

Loading 200kNLoading 300kNLoading 400kNLoading 500kN

Y0

(mm

)(b) 1198840-lgt curve of PCSP No2

lgt (s)24 26 28 30 32 34

0

5

10

15

20

25

30

Loading160kN

Loading 240kN



Y0

(mm

)

(c) 1198840-lgt curve of PCSP No3

Figure 6 Relationship between the displacement of single pile and the logarithm of time

the enclosure structure is represented by the Rankine earthpressure

Due to the soil stratification the values ofm are differentin different layers Therefore the beam element in the finiteelement method is adopted That is the elastic foundationbeam will be divided into some units based on the soil layersalong the vertical direction and the differential equationsabove of each unit are listed to solve them subsequently

The method of flat vertical elastic foundation beam forthe foundation pit enclosure structure is substantially evolvedfrom the computational method of laterally loaded pilesTherefore the determination of the value of m is actuallybased on the results from the horizontal load tests

According to Technical Code for Testing of BuildingFoundation Piles (JGJ106-2014) [30] the computationalequation of m value and the horizontal deformation coeffi-cient 120572 are

119898 = (119867V119909119909)53

[1198870 (119864119868)23] (2)

120572 = (1198981198870119864119868 )15

(3)

where H is the horizontal thrust of single pile x is thehorizontal displacement caused by pile under loading b0 is


Table 3 Range of experiential value ofm for various types of soil

Sources Classification of foundation soil mMNsdotmminus4

Horizontaldisplace-ment ofpile topΔmm

Applicablearea

Technicalspecification forbuilding pilefoundation(JGJ94-94)[20]

Silt silty soil saturated loess 25sim6 6sim12Plastic flow soft plastic clay loose silt siltysand(egt09) Loose slightly dense filling 6sim14 4sim8

Plastic clay silt (e=075sim09) collapsible loessmedium dense fill slightly fine sand 14sim35 3sim6 Various

regionsHard plastic hard clay collapsible loess silt(elt09) medium thick medium and coarse

sand dense old fill35sim100 2sim5

Dense dense gravel gravel soil 100sim300 15sim3

Feng et al (2005)[21]

Viscous soil with flow plastic 0sim15 --HangzhouChina

Soft plastic clay loose silty soil and sand 3sim4 --Plastic clay mildly densely silty soil and sand 5sim6 --

Hard clay dense silty soil sand 9sim10 --

Designspecification forfoundation andfoundation ofhighway bridgeand culvert(JTJ024-85) [22]

Plastic Clayey Soil ILge 1 silt 3sim5

X maxle6Soft plastic clay 1gtILge05 Silty sand 5sim10

Hard plastic clay 05gtILge0 Fine sand andmedium sand 10sim20 Tianjin

ChinaHard semi hard clayey soil ILlt0 Coarse sand 20sim30

Gravel breccia Boulder gravel pebbles 30sim80Dense pebbles dense pebbles 80sim120

Design rules offoundation pitengineering inShanghai(DBJ08-61-97)[23]

Viscous soil with flow plastic 1sim2 --Soft plastic clay loose silt soil and sand 2sim4

Plastic clay mildly densely silty soil and sand 4sim6 --

Hard clay dense silty soil sand 6sim10 -- ShanghaiChina

Cement soil mixing pilereinforcement

Replacement rategt25Cement content

lt8 2sim4 --Cement content

gt12 4sim6Note (1) According to the highway bridge and culvert standard the maximum displacement of the structure at the surface is not more than 6mm When thedisplacement is larger it is should be reduced (2) e is a void ratio IL is a liquid index

Table 4 Reference value of pile top displacement coefficient

Converting 120572h ge40 35 30 28 26 24V119909 2441 2502 2727 2905 3163 3526

the calculative width of pile v119909 is the displacement coefficientat the pile top according to the Technical Code for BuildingPile Foundations [30]120572 is calculated by comparing the valuesof 120572h and finding the corresponding values in Table 4 and his the injection depth of pile

For circular pile when pile diameter D is less thanor equal to 1m b0=09(15D+05) When pile diameter ismore than 1m b0=09(D+1) For precast concrete square-pilewhen the sectional dimension B is less than or equal to 1mb0=15B+05 When B is more than 1m b0=B+1

Determination of flexural rigidity (EI) of piles isexplained as follows In the loading process on the precast

concrete square-piles the cemented soils and the precast corepile work together Comparing the effects of flexural rigidityit is seen that the flexural rigidity of core pile (119864119868)con is 69times105kNsdotm2 while the flexural rigidity of cement-soil (119864119868)cem is032times105 kNsdotm2 so the (119864119868)con (119864119868)cem=46 Obviously theflexural rigidity of cement-soil is relatively tiny so that it isreplaced by the flexural rigidity in this paper

According to (2) the variation trend of the value of m indifferent loading grades is obtained as shown in Figure 7The relationship between the value of m and horizontalforce is resembled in an inverse proportion relation Whenloading to 200kN the m value of PCSP Nos 1 2 and 3 is2773MNm4 1574 MNm4 and 100 MNm4 respectivelyWith the increase of the horizontal loading the value ofm ineach case gradually decreases and eventually tends to be thesame In the case of large displacement of piles the coefficientof horizontal resistance of the pile from the soils around piles


0 100 200 300 400 500 600 700 8000

100

200

300

400

500

Lateral load H(kN)

m-H PCSP No 1m-H PCSP No 2m-H PCSP No 3

m (M

NmiddotＧ

minus4)

No

Figure 7 Relation between the value of m and the horizontal loadH

0 5 10 15 20 25 300

100

200

300

400

500

m (M

NmiddotＧ

minus4)

Horizontal displacement of pile top Y0 (mm)

1ＭＮ stage

2Ｈ＞ stage

2Ｌ＞ stage

m-Y0 PCSP No 1m-Y0 PCSP No 2m-Y0 PCSP No 3

Figure 8 Relation between the value of m and the horizontaldisplacement of pile top Y0

is gradually reduced and it gradually tends to be a stablevalue

It is also found that the values of m vary with theformation and environment It seems that there is a specialrelationship between the value of m and the load magnitudein the test such as the displacement at the pile top Fromthe test data the relation between the value of m and thehorizontal displacement at the pile top is described as shownin Figure 8

According to the m value curves of PCSP Nos 1 2 and3 the relation between the coefficient m and the horizontaldisplacement at the pile top can be divided into three stages

rapid decaying stage slow decaying stage and balanced stagerespectively

(a)When the horizontal displacement of the pile head Y0ranges from 0 to 5mm the value of m is on the first rapiddecaying stage

(b)When the horizontal displacement of the pile head Y0ranges from 5 to 15mm the value of m is on the second slowdecaying stage

(c) When the horizontal displacement of the pile headY0 is more than 15mm the value of m is on the third slowdecaying stage balanced stage

It is found that the values of m for three groups ofpiles are eventually maintained at the section between 10and 30 MNsdotmminus4 along with the increase in the horizontaldisplacement at the pile top On the one hand the value ofm of the precast pile with different variables varies greatlyin the first stage The relative values of the second and thirdphases decreased rapidly tending to be in a uniform stableinterval On the other hand although the piles are underdifferent circumstances they vary following the same trendThe three change stages of m value and the displacement atthe pile top referred to in this paper all apply to the differentcircumstances for both precast piles and bored piles

42 Displacement Back Analysis of the Value of m The prin-ciple of the displacement back analysis calculation methodadopts the displacement obtained from the actual measure-ment of the project and the original stress or mechanicalparameters are back-derived according to the selected calcu-lation model This method was put forward in 1971 by K TKavanagh and RW Clough [32] Due to themaneuverabilityand reliability of the displacement measurement in recentyears the displacement back analysismethod is appliedwidelyin the field of geotechnical engineering [33ndash37]The displace-ment inversion of m value is based on the compiling of theacquisition information of pile displacementThe lsquomrsquo methodand the boundary conditions of the mechanical model ofthe enclosure structure are optimally selected to serve theobjective function The difference between the theoreticalvalue and the measured value is minimized by the constantcorrection on a given initial value Finally optimizationtechnique is used to derive the resistance coefficient of eachsoil layer In order to make the calculated value mostly closeto all the measured values the square sum of deviations isrequired to be the smallest thus the objective function canbe described as

119891 (119898) =119872

sum119895=1

119873

sum119894=1

(119906119894(119895) minus 119906lowast119894(119895))2 997888rarr min (4)

where M is the construction step N is the test numberand 119906119894(119895) and 119906lowast119894(119895) are the calculated value of horizontaldisplacement and the measured displacement of piles basedon the test measuring point i in the construction step jrespectively The measured values are obtained by using theinclinometer along the precast piles

In (4) the soil layer parameters m1m2m3 m119899 mini-mized by the objective function are the parameters to be


Initial value of the ratio coefficient m

Calculation of horizontal displacement of support

structure

Calculating the minimum value of the objective

function f (m)

Measured horizontal displacement of support

structure

Iterative calculation by simplex method

Convergence accuracy

discrimination

Adjusting the m value

NO

YESTrial calculation m

value meets the requirements

Prediction of support structure

displacement

Figure 9 Flowchart of back analysis

Table 5 Excavation sequence of foundation ditch

No Excavation steps1 Excavate to 39m2 Construct the first support and excavate to 85m3 Construct the second support and excavate to 131m4 Construct the third support and excavate to the bottom of the foundation pit

sought and they can be solved by the simplex optimizationmethod [38ndash40] Specifically a group of initial values usedto develop the initial simplex according to certain rules isprovided first And then the optimal value is obtained bysearching the step length The accuracy of the convergenceis controlled by the step length

As the proportional coefficient is quite different betweenthe upper and lower limits of the soil layers the m value ofvarious types of soil mass has great limitationsThe followingconstraints are introduced

119898min119894 le 119898119894 le 119898max

119894 (119894 = 1 2 sdot sdot sdot 119899) (5)

where 119898min119894 and 119898max

119894 are the upper and lower bound of119898119894 values for the foundation soil in the layer i Combining(4) and (5) a set of nonlinear programming problems isobtained eg the problem of function optimizing underconstraint conditions This method can not only fully exploitthe characteristics of the back analysis algorithm but alsomake the obtained m values meet the requirements Theflowchart of back analysis is shown in Figure 9

43 A Calculating Example In this paper the deep foun-dation pit in the Yanmazhuang west station of Jirsquonan railtransit line R1 is taken as an example The deep excavationadopts the cut-and-cover method with 165m in excavationdepth The enclosure structure is composed of 700times700mmprecast square-piles and two steel braces and a concretesupport The 400times400mm precast core columns are used inthe middle of the enclosure structure After the excavation ofthe foundation pit the encased concrete forms the permanentstructural columns The excavation sequence of foundationpit is shown in Table 5

The back analysis is based on the measured displacementof the inclinometer pipe of the support structure underdifferent working conditions The initial value of the pro-portionality coefficient m is substituted into the calculationprocess of back analysis as shown in Figure 9 for iterativecomputations until a reasonable m value of the foundationsoil is obtained Figure 10 shows the influence curve of theiterations for the optimal value of the inversion It is seenthat the convergence of the inversion process meets therequirements


0 2 4 6 8 10 124

5

6

7

8

9

Iterative number

m(M

NmiddotＧ

minus4)

Figure 10 Inversion process ofm value of foundation soil

minus24

minus20

minus16

minus12

minus8

minus4

0minus2 0 2 4 6 8 10 12

Horizontal displacement (mm)

Dep

th (m

)

Inversion m valueMeasured displacementInitial m value

Figure 11 Comparison between the measured deformation and thecalculated deformation by initialm value and inversem value

Figure 11 shows the comparison between the deformationof the enclosure structure calculated from the initialm valueand inverse m value and the measured deformation whenexcavating to the bottom of the foundation pit Results showthat the measured deformation is much larger than that ofthe deformation calculated from the initial m value Themaximum horizontal displacement difference is more than42mmThemeasured data is 66 higher than the calculateddata It is believed the m value of the foundation soil isobviously larger After the iteration of the back analysis therange of m value for each soil layer in this area is in the

range of 4sim8MNsdotmminus4 It has been found that the deformationobtained by the inversion of m values is consistent with themeasured one

5 Discussion on the EmpiricalEquation of 119898 Value

The thick alluvium stratum of the Yellow River in Jirsquonanarea is similar to the soft soil stratum with obvious regionalcharacteristics Whenm value is applied in the calculation ofelastic foundation beam the recommended values of buildingcodes or other local codes should not be copied directly Atpresent experiences have been achieved for the calculationof m value in soft soil and clay areas in southern China Inthe absence of any single horizontal static load test and lackof experience the following empirical calculation methodis used according to the Technical Specification for Retain-ing and Protection of Building Foundation Excavations[41]

119898 = 1Δ (021205932 minus 120593 + c) (6)

where 120593 is the standard value of internal friction angle (∘)c is the standard value of cohesion (kPa) and Δ is thedisplacement at the bottom of foundation pit which can beevaluated by the regional experience 10mm is suggested inthe absence of engineering experience

By taking the typical soil layer the different frictionalangles and cohesiveness of natural quick shear test andconsolidation quick shear test are obtained by consultingthe geological survey data The m value is obtained bysubstituting it into the empirical equation Results are shownin Table 6

It is obvious that the value of m obtained by applyingthe cohesive and the internal friction angle under the naturalfast shear test is close to the value obtained from the backanalysis However the value of m obtained by consolidatedquick shear test is significantly larger than that of theback analysis method The empirical equation deserves afurther optimization by the parameters of natural fast sheartest

Figure 12 is the experiential correction curve of (6) Asthe value of Δ in the equation is difficult to determine thecalculated value of m is quite different from that of theregional experience value Yang et al pointed out that the mvalue of the rock stratum in Guangzhou is obviously lowerby using empirical equation [42] while in the local standardfoundation pit engineering technical specification of Hubeiprovince the above empirical equation had multiplied anempirical coefficient Specifically the empirical coefficientstake 10 for general cohesive and sandy soil 18 sim 20 for oldcohesive soil and the gravel stratumovermediumdensity and06 to 08 for silt and mucky soil In view of the blank in thecorrection of the empirical equation ofm value in the alluvialstratum of Yellow River the experience value of Δ is verifiedand the obtained results are compared with the value of mobtained from back analysis It is seen that the value obtainedby (6) is larger which is contrary to that in Guangzhou


Table 6 Comparison ofm value between natural quick shear test and consolidated quick shear test

Layer Natural quick shear m Consolidated quick shear m119888119903 120593119903 119888119896 120593119896Loess (Plastic) 23 14 48 41 22 116Silt 19 20 79 15 20 75Silty clayH 36 16 71 46 22 121Silty clay0 35 15 65 40 17 84Clay (Plastic) 35 15 65 42 18 89Note silty clayH in plastic-hard plastic state silty clay0 in plastic state Unit of the Cohesion c internal friction angle 120593 and m is kPa ∘ and MNsdotmminus3respectively

minus22

minus20

minus18

minus16

minus14

minus12

minus10

minus8

minus6

minus4

2 4 6 8 10 12

Dep

th(m

)

Inversion value

m

= 14

= 12

= 10

= 8

= 6

Figure 12 Comparison ofm value by corrected empirical equationand inversion method

When Δ takes 12mm the values of m are consistent with theresult of the back analysis Therefore it is more reasonablefor the horizontal displacement Δ to take 12mm in thisproblem

6 Conclusions

This paper raises the research issue on the horizontal bearingcapacity of the precast pile and the key supporting parametersof the deep foundation pit in the Yellow River alluvium Vari-able unique analysis for the large-size precast square-piles isconducted by in situ test and the bearing characteristics ofthe new pile-wall superimposition structure are explored Acalculationmodel is established for resistance coefficientm offoundation soil based on the engineering survey data and theoptimization method The conclusions are drawn as follows

(a)As a new type of precast piles the increase in cementedsoils can strengthen the bearing capacity of a single pile to

some extent Under the joint action of pile and cementedsoils the envelop effect of the soils around piles increaseby 89 while the horizontal critical load and Eigenvalueof horizontal bearing capacity increase by 167 and 20respectively

(b) According to the test results the ratio coefficient ofthe horizontal resist force in foundation soils is not a constantThehigher the intensity of the cemented soils around the pilesand the insertion ration the bigger the value of m With theincrease in the horizontal displacement at the pile top thevalue ofm undergoes three stages rapid decaying stage slowdecaying stage and balanced stageThe change mode of eachstage is different

(c) A back analysis model is established for the m valuecalculated by using the simplex method which reflects themvalue in real work conditions In the west area of Jinan citythe alluvial stratum of the Yellow River in the depth of 3sim18mis regarded as a normally consolidated viscous stratum andthe range of m value is recommended to be in the range of 4sim 658 MNsdotmminus4

(d) Based on the measured data the displacement of thesupport structure is predicted by the calculation parameterwhich proves that the value of m is more accurate withthe internal friction angle and cohesive force under thenatural quick shear When Δ takes 12mm the values ofm areconsistent with that from the back analysis

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This paper is supported by the National Natural ScienceFoundation of China [Grant nos 51774196 and 41472280]China Postdoctoral Science Foundation [Grant no2016M592221] and SDUST Young Teachers TeachingTalent Training Plan [Grant no BJRC20160501]


References

[1] A M Kaynia and S Mahzooni ldquoForces in pile foundationsunder seismic loadingrdquo Journal of Engineering Mechanics vol122 no 1 pp 46ndash53 1996

[2] G Cai S Liu L Tong and G Du ldquoAssessment of direct CPTandCPTUmethods for predicting the ultimate bearing capacityof single pilesrdquo Engineering Geology vol 104 no 3-4 pp 211ndash222 2009

[3] G G Meyerhof and A S Yalcin ldquoPile capacity for eccentricinclined load in clayrdquoCanadianGeotechnical Journal vol 21 no3 pp 389ndash396 1984

[4] J Lee M Kim and D Kyung ldquoEstimation of lateral loadcapacity of rigid short piles in sands using CPT resultsrdquo Journalof Geotechnical and Geoenvironmental Engineering vol 136 no1 pp 48ndash56 2010

[5] M Ashour and G Norris ldquoModeling lateral soil-pile responsebased on soil-pile interactionrdquo Journal of Geotechnical andGeoenvironmental Engineering vol 126 no 5 pp 420ndash4282000

[6] B Zhu R-P Chen J-F Guo L-G Kong and Y-M ChenldquoLarge-Scale Modeling andTheoretical Investigation of LateralCollisions onElevated Pilesrdquo Journal of Geotechnical andGeoen-vironmental Engineering vol 138 no 4 pp 461ndash471 2012

[7] K Gavin D Igoe and W Li ldquoEvaluation of CPT-based pymodels for laterally loaded piles in siliceous sandrdquoGeotechniqueLetters no 4 pp 110ndash117 2014

[8] T Ito and TMatsui ldquoMethods to estimate lateral force acting onstabilizing pilesrdquo Soils and Foundations vol 15 no 4 pp 43ndash591975

[9] H Poulos and E Davis Pile Foundation Analysis And DesignGeotechnical Engineering Wiley 1980

[10] W D Guo and F H Lee ldquoLoad transfer approach for laterallyloaded pilesrdquo International Journal for Numerical and AnalyticalMethods in Geomechanics vol 25 no 11 pp 1101ndash1129 2001

[11] A B Dan and C F Shie ldquoThree dimensional nite elementmodel of laterally loaded pilesrdquoComputers and Geotechnics vol10 no 1 pp 59ndash79 1990

[12] W L Ye and B L Shi ldquoA practical non-linear calculationmethod pilersquos lateral bearing capacity-NL methodrdquo Rock andSoil Mechanics vol 21 no 2 pp 97ndash101 2000

[13] E M Comodromos and K D Pitilakis ldquoResponse evaluationfor horizontally loaded fixed-head pile groups using 3-D non-linear analysisrdquo International Journal for Numerical and Analyt-ical Methods in Geomechanics vol 29 no 6 pp 597ndash625 2005

[14] MNHussien T Tobita S Iai andKMRollins ldquoVertical loadseffect on the lateral pile group resistance in sandrdquoGeomechanicsand Geoengineering An International Journal vol 7 no 4 pp263ndash282 2012

[15] M Abu-Farsakh A Souri G Voyiadjis and F Rosti ldquoCompar-ison of static lateral behavior of three pile group configurationsusing three-dimensional finite element modelingrdquo CanadianGeotechnical Journal vol 55 no 1 pp 107ndash118 2018

[16] P KMuduli S KDas andMRDas ldquoPrediction of lateral loadcapacity of piles using extreme learningmachinerdquo InternationalJournal of Geotechnical Engineering vol 7 no 4 pp 388ndash3942013

[17] Y-B Huang H-B Zhao C-C Gu and J Shao ldquoField experi-mental study of lateral load capacity of filling pile enhanced bysoil-cement pilerdquo Yantu LixueRock and Soil Mechanics vol 34no 4 pp 1109ndash1115 2013

[18] Q Chen N Haque M Abu-Farsakh and B A FernandezldquoField investigation of pile setup in mixed soilrdquo GeotechnicalTesting Journal vol 37 no 2 2014

[19] C F Zhao FM Liu Z X Qiu C Zhao andW ZWang ldquoStudyon bearing behavior of a single pile under combined verticaland lateral loads in sandrdquo Chinese Journal of GeotechnicalEngineering vol 37 no 1 pp 183ndash190 2015

[20] ldquoTechnical Code for Building Pile Foundationrdquo Housing andUrban-Rural Development JGJ94-94 Beijing china 1994

[21] J F Feng J L Yu X L Yang and X N Gong ldquoBack analysisand prediction of deep pit foundation excavation consideringdynamic factorsrdquo Rock Soil Mechanics vol 26 no 3 pp 455ndash460 2005

[22] ldquoSpecifications for design of ground base and foundation ofhighway bridges and culvertsrdquo Ministry of Communications ofPR China JTJ024-85 Beijing China 1985

[23] Shanghai Standard Code for Design of Excavation EngineeringDBJ08-61-97 Shanghai China 1997

[24] F Ma and Z Y Ai ldquoThe finite element method of elasticsubgrade beamwith the contact friction effect consideredrdquoRockSoil Mechanics vol 23 no 1 pp 93ndash96 2012

[25] Y J Yin X W Xie and Y M Qian ldquoThe research of horizontalresistance coefficient of pile lateral soil in horizontal loadsrdquoApplied Mechanics and Materials vol 501-504 pp 228ndash2332014

[26] H J Yu S Q Peng Q H Zhao H Wu Z H Ding and H HMu ldquoStudy on coefficient of horizontal resistance for gravel soilfoundation on slopesrdquo Chinese Soil Mechanics vol 38 no 6 pp1682ndash1687 2017

[27] Q Y Fan Q J Yang and Z Zhen ldquoStudy of foundationhorizontal resistance coefficient for argillaceous soft rocksrdquoRock Soil Mechanics vol 3 no 8 pp 137ndash142 2011

[28] X L Huang J W Yue L D Li and X S Sun ldquoCalculationmethod for horizontal resistance coefficient of foundation soilwith composite pilesrdquo Chinese Journal of Geotechnical Engineer-ing vol 584 no 2 pp 693ndash704 2011

[29] Z-H Xu J Li andW-D Wang ldquoBack analysis of proportionalcoefficient of horizontal resistance in vertical elastic subgradebeam method for deep excavationsrdquo Yantu LixueRock and SoilMechanics vol 35 pp 398ndash411 2014

[30] ldquoTechnical Code for Building Pile Foundationrdquo Housing andUrban-Rural Development JGJ106 Beijing China 2014

[31] ldquoTechnical Code for Design of Railwayrdquo Highway and UrbanRoad Bridges and Culverts CH200-62 Moscow Russia 1962

[32] K T Kavanagh and R W Clough ldquoFinite element applicationsin the characterization of elastic solidsrdquo International Journal ofSolids amp Structures vol 7 no 1 pp 11ndash23 1971

[33] Y Yu B Zhang and H Yuan ldquoAn intelligent displacementback-analysis method for earth-rockfill damsrdquo Computers ampGeosciences vol 34 no 6 pp 423ndash434 2007

[34] M Ghorbani and M Sharifzadeh ldquoLong term stability assess-ment of Siah Bisheh powerhouse cavern based on displacementback analysis methodrdquo Tunnelling and Underground SpaceTechnology vol 24 no 5 pp 574ndash583 2009

[35] M Sharifzadeh A Tarifard and M A Moridi ldquoTime-dependent behavior of tunnel lining in weak rock mass basedon displacement back analysis methodrdquo Tunnelling and Under-ground Space Technology vol 38 pp 348ndash356 2013

[36] R J Finno and M Calvello ldquoSupported excavations Observa-tional method and inverse modelingrdquo Journal of Geotechnicaland Geoenvironmental Engineering vol 131 no 7 pp 826ndash8362016


[37] Y Luo J Chen Y Chen P Diao and X Qiao ldquoLongitudinaldeformation profile of a tunnel in weak rock mass by usingthe back analysis methodrdquo Tunnelling and Underground SpaceTechnology vol 71 pp 478ndash493 2018

[38] J A Nelder and R Mead ldquoA simplex method for functionminimizationrdquoThe Computer Journal vol 7 no 4 pp 308ndash3131965

[39] M J Santos-Delgado E Crespo-Corral and L M Polo-DıezldquoDetermination of herbicides in soil samples by gas chromatog-raphy Optimization by the simplex methodrdquo Talanta vol 53no 2 pp 367ndash377 2000

[40] Z Zhao Q Ma Y Tan and X Gao ldquoLoad transfer mechanismand reinforcement effect of segmentally yieldable anchorage inweakly consolidated soft rockrdquo Simulation Transactions of theSociety for Modeling and Simulation International 2018

[41] ldquoTechnical Specification for Retaining and Protection of Build-ing Foundation Excavationsrdquo Housing and Urban-Rural Devel-opment JGJ120-2012 Beijing China 2012

[42] G H Yang Y Jiang Y C Zhang and E Q Wang ldquoMethod fordetermination of bearing capacity of soil foundationrdquo ChineseJournal of Geotechnical Engineering vol 36 no 4 pp 597ndash6032014

Hindawiwwwhindawicom Volume 2018

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International Journal of Mathematics and Mathematical Sciences


Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

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Dierential EquationsInternational Journal of

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Decision SciencesAdvances in


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Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom


Rebar connector

Precast Concrete Square Pile High pressurejet piles

Concrete lining wall

Cement soil

Figure 1 Pile and wall superposition enclosure structure

sufficient bearing capacity to ensure the stability of thefoundation without excessive deformation [1ndash3] Howeverdetermination of the horizontal and the vertical bearingproperty of the pile foundation is a complicated problemunder pile-soil interaction The bearing characteristic coverstwo aspects the ultimate horizontal bearing capacity ofpile controlled by the strength of soil around piles or theallowable horizontal bearing capacity of pile determinedby the allowable deformation of piles [4] The calculationmethod of the bearing capacity of a single pile mainlyincludes p-y curve method [5ndash7] analytical method [8ndash10]finite element simulation [11ndash15] and artificial intelligencemethod [16] Moreover experimental method is also aneffectiveway to determine the horizontal bearing capacity of apile foundation Huang et al analyzed the horizontal bearingcharacteristics of bored piles by horizontal static loadingtests [17] Haque et al used horizontal static loading test tomeasure the pile strain and analyzed the distribution of pileload transfer under static loading [18] Zhao et al used theindoor model test to study the bearing characteristics of asingle pile under the combination of vertical and horizontalloadings [19] The researches mentioned above show that thescale effect of horizontal bearing capacity of pile foundationin laboratory tests cannot be neglected Also it is difficultfor a model test to insure the reliability In addition theaccuracy of numerical simulation depends on the accuracyof test parameters Comparatively in situ test of piles is moreeffective for testing the bearing capacity of pile foundation

Soils around piles stabilize pile body and resist theexternal lateral force acting on piles Taking the soils aroundpiles as an elastic medium and assuming piles as an elasticbeamwhich supports the soils around piles the soil resistanceforce is determined by the linear elastic reaction methodto derive the elastic resistance property of the soils Thedeformation differential equation of the elastic foundationbeam is as follows [24]

11986411986811988941199101198891199114 minus 119890119886 (119911) = 0 (0 le 119911 le ℎ119899)

11986411986811988941199101198891199114 + 1198981198870 (119911 minus ℎ119899) 119910 minus 119890119886 (119911) = 0 (119911 ge ℎ119899)

(1)

where EI is the flexural rigidity of the enclosure structureE is the elastic modulus of piles I is the section moment of

inertia of the pile y is the lateral displacement of the enclosurestructure z is the excavating depth ea(z) is the active earthpressure at the excavating depth z h119899 is the excavating depthat the step n and m is proportional coefficient of horizontalresistance of foundation soils

The value of m is the proportional coefficient thatdescribes the horizontal resistance coefficient with the depthWhen the pile section type pile stiffness pile length anddepth of pile bottom are determined the m value is entirelydependent on the characteristics of the soils aroundpilesDueto the unreasonable design of row piles accidents frequentlyoccurred in large and deep foundation pits One of the keyfactors is the inappropriate selection of the ratio coefficientof the horizontal resistance of foundation soil (m value)Researches indicate that the value of m is a multifactorand regional parameter which relates to soil properties thepile bearing property under static load dynamic load ormulticycle grade load and displacement etc [25 26] Fora long time researchers have proposed several methods todetermine the value of m Fan et al studied the proportionalcoefficient m in muddy soft rock foundation and provideda reference value through indoor horizontal static load testsand numerical simulations [27] Huang et al consideredcalculating the value of m of the composite pile based onthe design value of horizontal bearing capacity and thecorresponding deformation [28] Xu et al determined theproportional coefficient in vertical elastic subgrade beamby using back analysis software Ucode and finite elementssoftware Abaqus combined with the measured deformationof retaining walls [29]

The above researches provide important reference fordesign of row piles in deep foundation pit However the pilefoundation bearing capacity and the design parameters mvalue present obvious regional featuresmdashthe soil characteris-tics are complex and different soils have different parametersAs the water level decreased in the Yellow River alluviumfor recent years the shallow soil has better performancein self-stability and generates microconsolidation The veinsnetwork of groundwater extends in all directions which aredifferent from the properties of ordinary clays and soft soilsThe excess pore water is commonly observed Given theabove condition a new pile-wall superimposition enclosurestructure is adopted to support the deep foundation pit in thisarea (see Figure 1) The two factors complexity of regional


Miscellaneous fill

Loess

Silt

Silty clay

Fine sand

Clay

Silty clay

Silty clayClay

Fine sand

1m

Base plate

FloorWater level



247m

266m

Cement soil



Layers Thicknessm

Bulkdensity

(kNmminus3)

ElasticmodulusMpa


Undrainedshear

strengthkPa


Voidration

Watercontent




2 Field Test





Ball-twist

Reactionpile

Reactionpile

TestpileBase Pile











3 Test Results





100 200 300 400 500 600 700 8000

5

10

15

20

25

30



Disp

lace

men

t of p

ile to

pY0

(mm

)


0 100 200 300 400 500 600 700 800000

002

004

006

008

010

Lateral load H(kN)


ΔYΔ

H(m

mmiddotＥ

minus1)











24 26 28 30 32 340

5

10

15

20

25

lgt (s)

Loading 100kN

Loading 200kN



Y0

(mm

)


lgt (s)24 26 28 30 32 34

0

2

4

6

8

10

12

Loading 100kN


Y0

(mm


lgt (s)24 26 28 30 32 34

0

5

10

15

20

25

30

Loading160kN

Loading 240kN



Y0

(mm

)







119898 = (119867V119909119909)53

[1198870 (119864119868)23] (2)

120572 = (1198981198870119864119868 )15

(3)






Applicablearea







Feng et al (2005)[21]



















Converting 120572h ge40 35 30 28 26 24V119909 2441 2502 2727 2905 3163 3526







0 100 200 300 400 500 600 700 8000

100

200

300

400

500

Lateral load H(kN)


m (M

NmiddotＧ

minus4)

No


0 5 10 15 20 25 300

100

200

300

400

500

m (M

NmiddotＧ

minus4)


1ＭＮ stage

2Ｈ＞ stage

2Ｌ＞ stage












119891 (119898) =119872

sum119895=1

119873

sum119894=1







structure


function f (m)


structure



discrimination


NO




displacement






119898min119894 le 119898119894 le 119898max

119894 (119894 = 1 2 sdot sdot sdot 119899) (5)






0 2 4 6 8 10 124

5

6

7

8

9

Iterative number

m(M

NmiddotＧ

minus4)


minus24

minus20

minus16

minus12

minus8

minus4

0minus2 0 2 4 6 8 10 12


Dep

th (m

)







119898 = 1Δ (021205932 minus 120593 + c) (6)








minus22

minus20

minus18

minus16

minus14

minus12

minus10

minus8

minus6

minus4

2 4 6 8 10 12

Dep

th(m

)

Inversion value

m

= 14

= 12

= 10

= 8

= 6



6 Conclusions







Data Availability




Acknowledgments



References



















































Journal of












Journal of







Volume 2018






Volume 2018









Miscellaneous fill

Loess

Silt

Silty clay

Fine sand

Clay

Silty clay

Silty clayClay

Fine sand

1m

Base plate

FloorWater level



247m

266m

Cement soil



Layers Thicknessm

Bulkdensity

(kNmminus3)

ElasticmodulusMpa


Undrainedshear

strengthkPa


Voidration

Watercontent




2 Field Test





Ball-twist

Reactionpile

Reactionpile

TestpileBase Pile











3 Test Results





100 200 300 400 500 600 700 8000

5

10

15

20

25

30



Disp

lace

men

t of p

ile to

pY0

(mm

)


0 100 200 300 400 500 600 700 800000

002

004

006

008

010

Lateral load H(kN)


ΔYΔ

H(m

mmiddotＥ

minus1)











24 26 28 30 32 340

5

10

15

20

25

lgt (s)

Loading 100kN

Loading 200kN



Y0

(mm

)


lgt (s)24 26 28 30 32 34

0

2

4

6

8

10

12

Loading 100kN


Y0

(mm


lgt (s)24 26 28 30 32 34

0

5

10

15

20

25

30

Loading160kN

Loading 240kN



Y0

(mm

)







119898 = (119867V119909119909)53

[1198870 (119864119868)23] (2)

120572 = (1198981198870119864119868 )15

(3)






Applicablearea







Feng et al (2005)[21]



















Converting 120572h ge40 35 30 28 26 24V119909 2441 2502 2727 2905 3163 3526







0 100 200 300 400 500 600 700 8000

100

200

300

400

500

Lateral load H(kN)


m (M

NmiddotＧ

minus4)

No


0 5 10 15 20 25 300

100

200

300

400

500

m (M

NmiddotＧ

minus4)


1ＭＮ stage

2Ｈ＞ stage

2Ｌ＞ stage












119891 (119898) =119872

sum119895=1

119873

sum119894=1







structure


function f (m)


structure



discrimination


NO




displacement






119898min119894 le 119898119894 le 119898max

119894 (119894 = 1 2 sdot sdot sdot 119899) (5)






0 2 4 6 8 10 124

5

6

7

8

9

Iterative number

m(M

NmiddotＧ

minus4)


minus24

minus20

minus16

minus12

minus8

minus4

0minus2 0 2 4 6 8 10 12


Dep

th (m

)







119898 = 1Δ (021205932 minus 120593 + c) (6)








minus22

minus20

minus18

minus16

minus14

minus12

minus10

minus8

minus6

minus4

2 4 6 8 10 12

Dep

th(m

)

Inversion value

m

= 14

= 12

= 10

= 8

= 6



6 Conclusions







Data Availability




Acknowledgments



References



















































Journal of












Journal of







Volume 2018






Volume 2018









Ball-twist

Reactionpile

Reactionpile

TestpileBase Pile











3 Test Results





100 200 300 400 500 600 700 8000

5

10

15

20

25

30



Disp

lace

men

t of p

ile to

pY0

(mm

)


0 100 200 300 400 500 600 700 800000

002

004

006

008

010

Lateral load H(kN)


ΔYΔ

H(m

mmiddotＥ

minus1)











24 26 28 30 32 340

5

10

15

20

25

lgt (s)

Loading 100kN

Loading 200kN



Y0

(mm

)


lgt (s)24 26 28 30 32 34

0

2

4

6

8

10

12

Loading 100kN


Y0

(mm


lgt (s)24 26 28 30 32 34

0

5

10

15

20

25

30

Loading160kN

Loading 240kN



Y0

(mm

)







119898 = (119867V119909119909)53

[1198870 (119864119868)23] (2)

120572 = (1198981198870119864119868 )15

(3)






Applicablearea







Feng et al (2005)[21]



















Converting 120572h ge40 35 30 28 26 24V119909 2441 2502 2727 2905 3163 3526







0 100 200 300 400 500 600 700 8000

100

200

300

400

500

Lateral load H(kN)


m (M

NmiddotＧ

minus4)

No


0 5 10 15 20 25 300

100

200

300

400

500

m (M

NmiddotＧ

minus4)


1ＭＮ stage

2Ｈ＞ stage

2Ｌ＞ stage












119891 (119898) =119872

sum119895=1

119873

sum119894=1







structure


function f (m)


structure



discrimination


NO




displacement






119898min119894 le 119898119894 le 119898max

119894 (119894 = 1 2 sdot sdot sdot 119899) (5)






0 2 4 6 8 10 124

5

6

7

8

9

Iterative number

m(M

NmiddotＧ

minus4)


minus24

minus20

minus16

minus12

minus8

minus4

0minus2 0 2 4 6 8 10 12


Dep

th (m

)







119898 = 1Δ (021205932 minus 120593 + c) (6)








minus22

minus20

minus18

minus16

minus14

minus12

minus10

minus8

minus6

minus4

2 4 6 8 10 12

Dep

th(m

)

Inversion value

m

= 14

= 12

= 10

= 8

= 6



6 Conclusions







Data Availability




Acknowledgments



References



















































Journal of












Journal of







Volume 2018






Volume 2018









100 200 300 400 500 600 700 8000

5

10

15

20

25

30



Disp

lace

men

t of p

ile to

pY0

(mm

)


0 100 200 300 400 500 600 700 800000

002

004

006

008

010

Lateral load H(kN)


ΔYΔ

H(m

mmiddotＥ

minus1)











24 26 28 30 32 340

5

10

15

20

25

lgt (s)

Loading 100kN

Loading 200kN



Y0

(mm

)


lgt (s)24 26 28 30 32 34

0

2

4

6

8

10

12

Loading 100kN


Y0

(mm


lgt (s)24 26 28 30 32 34

0

5

10

15

20

25

30

Loading160kN

Loading 240kN



Y0

(mm

)







119898 = (119867V119909119909)53

[1198870 (119864119868)23] (2)

120572 = (1198981198870119864119868 )15

(3)






Applicablearea







Feng et al (2005)[21]



















Converting 120572h ge40 35 30 28 26 24V119909 2441 2502 2727 2905 3163 3526







0 100 200 300 400 500 600 700 8000

100

200

300

400

500

Lateral load H(kN)


m (M

NmiddotＧ

minus4)

No


0 5 10 15 20 25 300

100

200

300

400

500

m (M

NmiddotＧ

minus4)


1ＭＮ stage

2Ｈ＞ stage

2Ｌ＞ stage












119891 (119898) =119872

sum119895=1

119873

sum119894=1







structure


function f (m)


structure



discrimination


NO




displacement






119898min119894 le 119898119894 le 119898max

119894 (119894 = 1 2 sdot sdot sdot 119899) (5)






0 2 4 6 8 10 124

5

6

7

8

9

Iterative number

m(M

NmiddotＧ

minus4)


minus24

minus20

minus16

minus12

minus8

minus4

0minus2 0 2 4 6 8 10 12


Dep

th (m

)







119898 = 1Δ (021205932 minus 120593 + c) (6)








minus22

minus20

minus18

minus16

minus14

minus12

minus10

minus8

minus6

minus4

2 4 6 8 10 12

Dep

th(m

)

Inversion value

m

= 14

= 12

= 10

= 8

= 6



6 Conclusions







Data Availability




Acknowledgments



References



















































Journal of












Journal of







Volume 2018






Volume 2018









24 26 28 30 32 340

5

10

15

20

25

lgt (s)

Loading 100kN

Loading 200kN



Y0

(mm

)


lgt (s)24 26 28 30 32 34

0

2

4

6

8

10

12

Loading 100kN


Y0

(mm


lgt (s)24 26 28 30 32 34

0

5

10

15

20

25

30

Loading160kN

Loading 240kN



Y0

(mm

)







119898 = (119867V119909119909)53

[1198870 (119864119868)23] (2)

120572 = (1198981198870119864119868 )15

(3)






Applicablearea







Feng et al (2005)[21]



















Converting 120572h ge40 35 30 28 26 24V119909 2441 2502 2727 2905 3163 3526







0 100 200 300 400 500 600 700 8000

100

200

300

400

500

Lateral load H(kN)


m (M

NmiddotＧ

minus4)

No


0 5 10 15 20 25 300

100

200

300

400

500

m (M

NmiddotＧ

minus4)


1ＭＮ stage

2Ｈ＞ stage

2Ｌ＞ stage












119891 (119898) =119872

sum119895=1

119873

sum119894=1







structure


function f (m)


structure



discrimination


NO




displacement






119898min119894 le 119898119894 le 119898max

119894 (119894 = 1 2 sdot sdot sdot 119899) (5)






0 2 4 6 8 10 124

5

6

7

8

9

Iterative number

m(M

NmiddotＧ

minus4)


minus24

minus20

minus16

minus12

minus8

minus4

0minus2 0 2 4 6 8 10 12


Dep

th (m

)







119898 = 1Δ (021205932 minus 120593 + c) (6)








minus22

minus20

minus18

minus16

minus14

minus12

minus10

minus8

minus6

minus4

2 4 6 8 10 12

Dep

th(m

)

Inversion value

m

= 14

= 12

= 10

= 8

= 6



6 Conclusions







Data Availability




Acknowledgments



References



















































Journal of












Journal of







Volume 2018






Volume 2018












Applicablearea







Feng et al (2005)[21]



















Converting 120572h ge40 35 30 28 26 24V119909 2441 2502 2727 2905 3163 3526







0 100 200 300 400 500 600 700 8000

100

200

300

400

500

Lateral load H(kN)


m (M

NmiddotＧ

minus4)

No


0 5 10 15 20 25 300

100

200

300

400

500

m (M

NmiddotＧ

minus4)


1ＭＮ stage

2Ｈ＞ stage

2Ｌ＞ stage












119891 (119898) =119872

sum119895=1

119873

sum119894=1







structure


function f (m)


structure



discrimination


NO




displacement






119898min119894 le 119898119894 le 119898max

119894 (119894 = 1 2 sdot sdot sdot 119899) (5)






0 2 4 6 8 10 124

5

6

7

8

9

Iterative number

m(M

NmiddotＧ

minus4)


minus24

minus20

minus16

minus12

minus8

minus4

0minus2 0 2 4 6 8 10 12


Dep

th (m

)







119898 = 1Δ (021205932 minus 120593 + c) (6)








minus22

minus20

minus18

minus16

minus14

minus12

minus10

minus8

minus6

minus4

2 4 6 8 10 12

Dep

th(m

)

Inversion value

m

= 14

= 12

= 10

= 8

= 6



6 Conclusions







Data Availability




Acknowledgments



References



















































Journal of












Journal of







Volume 2018






Volume 2018









0 100 200 300 400 500 600 700 8000

100

200

300

400

500

Lateral load H(kN)


m (M

NmiddotＧ

minus4)

No


0 5 10 15 20 25 300

100

200

300

400

500

m (M

NmiddotＧ

minus4)


1ＭＮ stage

2Ｈ＞ stage

2Ｌ＞ stage












119891 (119898) =119872

sum119895=1

119873

sum119894=1







structure


function f (m)


structure



discrimination


NO




displacement






119898min119894 le 119898119894 le 119898max

119894 (119894 = 1 2 sdot sdot sdot 119899) (5)






0 2 4 6 8 10 124

5

6

7

8

9

Iterative number

m(M

NmiddotＧ

minus4)


minus24

minus20

minus16

minus12

minus8

minus4

0minus2 0 2 4 6 8 10 12


Dep

th (m

)







119898 = 1Δ (021205932 minus 120593 + c) (6)








minus22

minus20

minus18

minus16

minus14

minus12

minus10

minus8

minus6

minus4

2 4 6 8 10 12

Dep

th(m

)

Inversion value

m

= 14

= 12

= 10

= 8

= 6



6 Conclusions







Data Availability




Acknowledgments



References



















































Journal of












Journal of







Volume 2018






Volume 2018











structure


function f (m)


structure



discrimination


NO




displacement






119898min119894 le 119898119894 le 119898max

119894 (119894 = 1 2 sdot sdot sdot 119899) (5)






0 2 4 6 8 10 124

5

6

7

8

9

Iterative number

m(M

NmiddotＧ

minus4)


minus24

minus20

minus16

minus12

minus8

minus4

0minus2 0 2 4 6 8 10 12


Dep

th (m

)







119898 = 1Δ (021205932 minus 120593 + c) (6)








minus22

minus20

minus18

minus16

minus14

minus12

minus10

minus8

minus6

minus4

2 4 6 8 10 12

Dep

th(m

)

Inversion value

m

= 14

= 12

= 10

= 8

= 6



6 Conclusions







Data Availability




Acknowledgments



References



















































Journal of












Journal of







Volume 2018






Volume 2018









0 2 4 6 8 10 124

5

6

7

8

9

Iterative number

m(M

NmiddotＧ

minus4)


minus24

minus20

minus16

minus12

minus8

minus4

0minus2 0 2 4 6 8 10 12


Dep

th (m

)







119898 = 1Δ (021205932 minus 120593 + c) (6)








minus22

minus20

minus18

minus16

minus14

minus12

minus10

minus8

minus6

minus4

2 4 6 8 10 12

Dep

th(m

)

Inversion value

m

= 14

= 12

= 10

= 8

= 6



6 Conclusions







Data Availability




Acknowledgments



References



















































Journal of












Journal of







Volume 2018






Volume 2018











minus22

minus20

minus18

minus16

minus14

minus12

minus10

minus8

minus6

minus4

2 4 6 8 10 12

Dep

th(m

)

Inversion value

m

= 14

= 12

= 10

= 8

= 6



6 Conclusions







Data Availability




Acknowledgments



References



















































Journal of












Journal of







Volume 2018






Volume 2018









References



















































Journal of












Journal of







Volume 2018






Volume 2018






















Journal of












Journal of







Volume 2018






Volume 2018








Horizontal Bearing Test and Optimization of Value for...

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