INFLUENCE OF SOIL-STRUCTURE INTERACTION ON RESPONSE OF

A MULTI-STORIED BUILDING AGAINST EARTHQUAKE FORCES

Submitted by,

G.Kamala Kumari(14481D8709)

CONTENT Abstract Introduction Literature review Methods for SSI SSI in Seismic codes Proposed work Geotechnical classification on study area Response of structures against earthquake forces Equivalent lateral force method Free vibration analysis Results Conclusions Future scope References

ABSTRACT

In the analysis of structures subjected to earthquake forces, it is usually assumed that the structure is fixed at the base to simplify the mathematical problem. This assumption leads to gross error in assessment of overall response under dynamic loads. The interaction phenomenon is principally affected by the mechanism of energy exchanged between the soil and the structure during an earthquake.

In the present investigation, a multi-storied building which is located in Amaravathi is chosen as the study area which consists of different types of soil / rock profiles at different locations. Many high rise structures are expected in future in the new city.

Earthquake analysis is carried out when similar structure rests on different types of soils and the results of fundamental time periods, base shears and displacements are compared with the results obtained from fixed base condition.

INTRODUCTION:

In seismically active regions like India, there is potential risk for multi- storied RC buildings.

As per the latest seismic zoning map brought out by the Bureau of Indian Standards (BIS), over 65% of the country is prone to moderate to high intensity earthquakes.

Most of the mega cities in India are in seismically active zones and many structures in these cities are designed for gravity loads only.

SOIL-STRUCTURE INTERACTION(SSI)

Most of the civil engineering structures involve some type of structural element with direct contact with ground.

The process in which the response of the soil influences the motion of the structure and the motion of the structure influences the response of the soil is termed as soil-structure interaction. 

In general conventional structural design methods neglect the SSI effects.

The effect of SSI, however, becomes prominent for heavy structures resting on relatively soft soils.

WHY SSI CONSIDERED

In capital region of A.P majority of soils are of black cotton, silty clay and loose soils.

Many high rise structures are expected in the new city in future.

This area falls under seismic zone III.

PARAMETERS FOR SSI AND STRUCTURAL

SSI parameters: Local soil condition Peak ground acceleration Shear wave velocity Frequency content of motion Proximity to fault

Structural parameter: Natural time period Base shear Roof displacement Column moment. Beam moment

LITERATURE REVIEW Response of structures against earthquake forces considering

the effect of soil-structure interaction was carried out by several authors earlier.

S.R.K.Reddy et al, Terrain evaluation and influence of soil-structure interaction on seismic response of structures in urban environs” seismic waves travel through different rock or soil media and reach the foundation layers causing the structure indeed affect the response of the structure apart from the influence of other parameter such as the type of ground excitation, configuration, ductility and quality of construction. Soil is represented by introducing two additional springs, one in horizontal and other in rocking mode.

Milos Novak “Dynamic stiffness and damping of piles” An approximate analytical approach based on linear elasticity is presented, which makes it possible to establish the dimensionless parameters of the problem and to obtain closed form formulas for pile stiffness and damping.

Shehata E.Abdel Raheem, Mohamed M. Ahmed and Tarek M.A.Alazrak ,“Soil-structure interaction effects on seismic response of multi-story buildings on raft foundation” The conventional design procedure usually involves assumption of fixity at the base of foundation neglecting the flexibility of the foundation, the compressibility of soil mass and consequently the effect of foundation settlement on further redistribution of bending moment and shear force demands.

Whiteman.R.V. Richart.F. “design procedure for dynamically loaded foundations” Assuming the foundation of the structure with isolated footings, translational and rocking stiffness formulas are suggested and also a fictitious mass to be added to the soil-structure model in time domain to reduce the error caused by frequency dependent nature of the response.

V.K.Puri and Shamsher Prakash “Foundations for Dynamic loads” Design of foundation in earthquake prone areas needs special considerations sallow foundations many experiences a reduction in bearing capacity and increase in settlement and tilt due to seismic loading. The response of a footing to dynamic load is affected by the nature and magnitude of dynamic load, number of pulses the strain rate response of soil.

METHODS FOR SSI

Direct method Direct approach is one in

which the soil and structure are modeled together in

a single step accounting for both inertial and kinematic interaction.

SUB STRUCTURE METHOD Substructure method is one in which the

analysis broken down into several steps. That is the principal of superposition is used

to isolate the two primary causes of soil - structure interaction.

SSI IN SEISMIC CODES The important cases in which SSI has a pronounced

effect need to be considered according to part five of Eurocode 8. These cases are as follows: Structure where P-Δ effects play a significant role. Structures with massive or deep-seated

foundations, such as bridge piers, offshore caissons, and silos.

Slender tall structures, such as towers and chimneys.

Structures supported on very soft soils, with average shear wave velocity less than 100m/s, such as clayey soils.

FEMA 450

It has incorporated a procedure to take into account the flexibility of foundation and soil to evaluate the equivalent lateral force.

By finding an effective period considering the motion of the first mode of vibration a reduction of base shear is introduced which results to reduction of lateral forces and overturning moments.

FEMA 273, 1997

It is also suggests to consider SSI for near-field and soft soil sites in which the increase in the fundamental period due to SSI increases.

But it is commented that soil-structure interaction cannot be used to reduce component and element actions by more than 25%.

PROPOSED WORK In the present study, a twelve storied building (multi-

storied building), with lower two stories for parking (soft stories) and the remaining ten stories for commercial and residential purpose, resting on five different types of homogeneous soils, is chosen for the analysis.

The dimensions and properties and the structural element of the building are presented in table. The building consists of 3 bays in X-direction and 6 bays in Z-direction, plan and elevation of building is shown in figure.

DIMENSIONS OF STRUCTURAL ELEMENTS

Parameter Dimension/sHeight of the building 38.4m

Height of each storey 3.2m

Number of stories 12(2 soft +10 )

Column size 0.23m x 0.5m

Longitudinal beams 0.23m x 0.35m

Transverse beams 0.23m x 0.5m

Plinth beams 0.23m x o.35m

Slab thickness 0.12m

Exterior wall thickness 0.23 m

Interior wall thickness 0.115m

Parapet wall height 1m

PROPERTIES OF MATERIALS AND DIFFERENT LOADS

Grade of concrete M25Grade of steel Fe 415Unit weight of RCC 25 KN/ m3

Unit weight of brick work 19 KN/ m3

Live load (floor) 4.00 KN/ m2

Live load (terrace) 1.50 KN/ m2

floor finish 1.0 KN/ m2

Terrace finish 1.5KN/ m2

CALCULATION OF EQUIVALENT U.D.L ON BEAMS Loads onto beam are considered as

Trapezoidal section of slab / triangular section of slab or both from one side or two sides.

From Wall, if any Self-weight of rib of Beam

Formulae for equivalent U.D.L on beam

  B.M CONSIDERATIONS S.F CONSIDERATIONS

FOR TRIANGLE

FOR TRAPEZOIDAL

GRAVITY LOAD CALCULATION ON COLUMN

Loads onto the columns are considered to be Load from the beams that are connected to the column Self-weight of column Point loads if any Loads on critical column

A1 column load = 1059 KNA2 column load = 1268 KNB1 column load = 1535 KNB2 column load = 1833 KN

GEOTECHNICAL CLASSIFICATION IN STUDY AREA

The study area is covered by different types of geomorphic units/ landforms. The seismic response of similar building behaves differently in different soil units during an earthquake

Type S1 – Clay, Silty Clay Type S2 – Stiff clay Type S3 – Coarse gravel & murrum (soft rock) Type S4 – Sand stone or laterite Type S5 – Hard rock (granite)

GEO-TECHNICAL PROPERTIES OF VARIOUS GEOMORPHIC UNITS

Property of the materialunits Soil / rock type

S1 S2 S3 S4 S5

Shear wave velocity Vs m/s 60 150 400 1250 2700

Mass density (ρ) KN-m2/m4 1.7 1.8 1.9 2.1 2.6

Poisson’s ratio (µ) - 0.4 0.4 0.33 0.30 0.30

Shear modulus (Gs ) = ρVs

2

KN/m2x 105 0.0612 0.405 3.04 32.812 189.54

Young’s modulus (Es) KN/m2x 105 0.1775 1.134 8.086 85.31 492.804

Bearing capacity (p) KN/m2 60 200 300 400 500

Variation of shear modulus (G) with shear wave velocity (Vs)

In general, Earthquake motion causes both horizontal and vertical ground motions.

Usually vertical ground motion has much smaller magnitudes than that of horizontal. The vertical ground motion due to the earthquakes can be resisted by the factor of safety provided in the design of structures.

The structures which are designed to carry only the gravity loads will not be able to resist the horizontal ground motion.

The horizontal ground motion causes the most significant effect on the structure by shaking the foundation.

RESPONSE OF STRUCTURE AGAINST EARTHQUAKE FORCES

BUILDING MODEL

SEISMIC ANALYSIS OF THE STRUCTURE FOR FIXED BASE CONDITION

Seismic Weight: The Seismic weight of a floor is its full dead

load plus appropriate amount of imposed load, as specified in Clause 8.3.1 and 8.3.2 of IS 1893 (Part I) : 2002.

Following reduced live loads are used for analysis:

Zero on terrace and 50% on other floors.

STIFFNESS OF EACH STOREY

 The total equivalent stiffness of each storey is taken as, k = ∑ kc + ∑ kw.

Stiffness of column kc =12EI/l3

Stiffness of wall kw

= d

m

lAE 2cos

MASS AND STIFFNESS VALUES OF STRUCTURE

Stiffness (KN/m)x106

k1,2 1.02

k3-12 5.11

Mass (KN-sec2/m)m1 206.3m2 276

m3-11 343.3m12 226

EQUIVALENT LATERAL FORCE METHOD It is the simplest method of analysis and requires less computational

effort The code recommends the use of the design spectrum method for

determination of lateral forces. The following is the step-by-step procedure for analysis of the frame : Step 1: Calculation of Lumped Masses to Various Floor Level.

Step 2: Determination Of Fundamental Natural Period

Ta = 0.085h 0.75 (Moment resisting steel frame building without brick infill walls)

Ta = 0.085h 0.75 (Moment resisting RC frame building without brick infill walls

Ta = (all other buildings including moment resisting RC frame buildings

with brick infill walls)

Step 3: Determination of Design Base Shear VB = Ah W (Clause 7.5 of IS 1893:2002) Ah = x x (Clause 6.4.2 of IS 1893:2002)

Zone factor, Z (Clause 6.4.2 of IS 1893:2002)

Importance factor, I (Clause 6.4.2 of IS 1893:2002)

Seismic zone II III IV V

Seismic Intensity

(Z)

Low

0.10

Moderate

0.16

Severe

0.24

Very severe

0.36

Structure Importance FactorImportant service and community buildings, such as

hospitals; schools; monumental structures;

emergency buildings like telephone exchange,

television stations, radio stations, railway stations,

fire station buildings; large community halls like

cinemas, assembly halls and subway stations, power

stations.

1.5

All other buildings 1.0

Step 4 : Vertical Distribution of Base Shear Qi = VB .

DISTRIBUTION OF DESIGN FORCE

Storey no Wi hi Wi hi2 Wi hi

2/ΣWi hi2 Qi (kN) Vi (kN)

12 2217 38.4 3269099.52 0.1581 272.04 272.40

11 3368 35.2 4173086.72 0.2018 347.7 620.10

10 3368 32.0 3448832 0.1667 287.2 907.30

9 3368 28.8 2793553.92 0.1351 232.6 1140.0

8 3368 25.6 2207252.48 0.1067 183.8 1323.7

7 3368 22.4 1689927.68 0.0817 140.76 1464.4

6 3368 19.2 1241579.52 0.0601 103.5 1568.0

5 3368 16.0 862208 0.0417 72 1640.0

4 3368 12.8 551813.12 0.0267 46 1686.0

3 3368 9.6 310394.88 0.015 26 1712.0

2 2703 6.4 110714.88 0.0054 9.3 1721.3

1 2024 3.2 20725.76 0.0010 1.7 1723.0

BASE SHEARS AT EACH FLOOR

TYPE OF FOUNDATION

Type of soil Type of foundation

S1 Pile/Mat/isolated footing

S2

S3 Mat/isolated footing

S4 isolated footings

S5

SOIL MODEL The dynamic model of soil requires the representation of

soil mass, soil stiffness and damping factors allowing for strain dependence and variation of soil properties.

The structure is assumed to rest on uniform elastic half-space and soil-spring approach is used to model the soil-structure interaction.

Since the structures are usually designed for gravity loads and plan of the building is symmetrical, only horizontal and rocking springs are considered .

STIFFNESS OF SOIL (ISOLATED FOOTING) Horizontal stiffness, kx (KN/m) = 2(1+ ν) Gβx (BL)½

Rocking stiffness, kψ (KN-m) =[G/(1- ν)] βψ BL2

Constants for rectangular basis (Whitmen and Richart)

CALCULATION OF STIFFNESS OF PILE

Calculation of stiffness of pile by using Novak and EI-Sharnouby Formulae (1983)

Translational stiffness Kx=[ ] *fx Rocking stiffness Kψ =[ ] *fψ1

Where Ep = modulus of elasticity of pile materialIp= moment of inertia of single pile about X

or Y axis ro = pile radius

fx1 , fψ1 are Novak’s coefficients

MASS AND STIFFNESS VALUES OF SOIL

parameter Type of foundation

Mo I kx k φ

Units KN.sec2

/mKN.m.s

ec2KN/m*

106KN.m*

106

Typeof

soil

S1 Pile 972 57242 1368 35890Mat 1110 58901 0.298 19.04

S2 Pile 863 55931 4694 54000Footing 670 53616 8.57 30.618

S3 Mat 955 57037 13.47 490.9Footing 530 51937 46.1 255.3

S4 Isolated footing

431 50749 407 1717

S5 401 50380 2091 5680

FREE VIBRATION ANALYSIS:

Using the combined mathematical model of both structure and soil with masses and springs , the equilibrium equations are formulated and put them in matrix form

.. [M] x + [k] x = 0

Where [M] – Mass matrix,[k] – Stiffness matrix,

..x – Horizontal acceleration, x – Horizontal displacement

MASS MATRIX

I-mass Moment Of Inertia Of All Storey Masses

STIFFNESS MATRIX

=

RESULTSParameter Frequency

(Hz)Time

period(sec)Displacements (mm)

Shears absorb by

soil (kN)

Net base Shears (kN)

S1 Pile 1.628 0.614 5.0 224.2 1498.8

Mat 0.436 2.29 63.5 261.2 1461.8

S2 Pile 1.629 0.6138 5.2 214.1 1508.9

Footing 0.558 1.79 37.2 217 1506.0

S3 Mat 1.35 0.7394 6.57 242 1481.0

Footing 1.2 0.8332 7.97 201 1522.0

S4 Footing 1.54 0.6485 5.1 198 1525.0

S5 1.6 0.6235 4.8 194 1529.0

Fixed base 1.63 0.6126 4.5 172 1551.0

Graph 1(a) time period Vs shear wave velocity 

Graph 1(b) storey shear Vs shear wave velocity

Graph 1(c) rocking stiffness vs shear wave velocity(pile to footing)

Graph 1(d) rocking stiffness vs shear wave velocity (mat to footing)

Graph 1(e) horizontal stiffness vs shear wave velocity

D1 D2 D3 D4 D5 D6 D7 D8 D9 D10 D11 D12 D13 D140

1

2

3

4

5

6

7

8

9

10

pile (S1)mat (S1)

Displacements at storey level

disp

lace

men

ts (m

m)

D1 D2 D3 D4 D5 D6 D7 D8 D9 D10 D11 D12 D13 D140

1

2

3

4

5

6

pile (S2)isolated footing(S2)

Displacements at storey level

disp

lace

men

ts (m

m)

D1 D2 D3 D4 D5 D6 D7 D8 D9 D10 D11 D12 D13 D140

0.2

0.4

0.6

0.8

1

1.2

mat (S3)isolated footing (S3)

Displacements storey level

disp

lace

men

ts (m

m)

D1 D2 D3 D4 D5 D6 D7 D8 D9 D10 D11 D12 D13 D140

0.1

0.2

0.3

0.4

0.5

0.6

0.7

isolated S4isolated S5fixed base

storey level

disp

lace

men

ts

(mm

)

CONCLUSION The shear wave velocity influences significantly in

changing the shear modulus of different soils from static to dynamic state. It is noticed that dynamic shear modulus exponentially increases with the increase of shear wave velocity.

The horizontal and rocking soil spring constant values increase when type of soil varies from loose soil to hard rock. It is also noticed that these values are high in case of pile foundations when compared to the isolated footing type of foundation.

Fundamental time period of the building invariably decreases with the increase of soil stiffness. In loose soils like silty clay and silty sand, where normally pile foundations are preferred, these time period values decrease compared to the values obtained when isolated footing type and mat foundation is provided.

The base shear values obtained are the lateral shears transferred from soil to the base of the structure due to effect of soil – structure interaction.

It is noticed that the shears and displacements are high in case of loose soils compared to those of very stiff/ hard soils.

In general, it can be concluded that structure resting on stiff soils or rock behave well during earthquake than structures resting on loose soils.

FUTURE SCOPE In this experimental study a multi storey building rests on

different soil conditions (hard rock granite, coarse gravel, silty clay) have been considered, for further experimental investigations different combinations of soil conditions can be carried out.

In this present study the soil in and around the foundation has been considered as a spring one in horizontal and rocking mode, for further study spring can modeled including torsion effects this can modeled as used in different softwares like ANSYS,SAP200, and ETABS or inelastic continuum method.

The soil is considered as single media but layered soil types exist below is not single, so different linear equilibrium effects can also be considered.

REFERENCES[1] S.R.K.Reddy, et al, “Terrain evaluation and influence of soil-structure interaction on

seismic response of structures in urban environs” proc of 3 rd International conference (2006)Venice, Italy, pp235-242.

[2] Whiteman. R.V, Richart.F.E, “Design procedure for dynamically loaded foundations” journal of soil mechanics and foundation engg., Division, ASCE 93, 1967, pp167-191.

[3] Shehata E.Abdel Raheem, Mohamed M. Ahmed and Tarek M.A.Alazrak, “Soil-structure interaction effects on seismic response of multi-story buildings on raft foundation”, Journal of Engineering aSciences Assiut University Faculty of Engineering vol.42, No. 4, pp 905-930, July 2014.

[4] P.A Dode, H.S.Chore and D.K.Agraual, “Space frame – pile foundation –soil interaction analysis”, Journal of structural engg. Vol.42, No.3, August – September 2015.pp.246-255.

[5] Vidya.V, B, K, Raghu Prasad and Amarnath.K, “Seismic response of high rise structure due to interaction between soil and structure”, International Journal of Research in Engineering and Applied Sciences, Volume 5, Issue 5-May-2015.

[6] Milos Novak “Dynamic stiffness and damping of piles” (1974) Canadian Geo Technical Engineering, journal, 1974, pp 574-598.

[7] V.K.Puri and Shamsher Prakash “Foundations for Dynamic loads”.

[8]A Criterion For Considering Soil-structure Interaction Effects In Seismic Design Of Ductile Rc-mrfs According To Iranian Codes By Massumi 1 And H.R. Tabatabaiefar 2

[9] Bharath Bhushan Prasad, “Fundamentals of Soil Dynamics and Earthquake Engineering’’, PHI learning private limited,2009.

[10] Joseph E Bowles, “Foundation analysis and design”, The McGraw-Hill Companies, Inc.,5th Edition, pp. 501-505, 1996.

[11] Ketan Bajaj, JiteshT Chavda, Bhavik M Vyas, “seismic behaviour of buildings on different types of soil”.

[12] Bureau of Indian Standards IS 1893 (Part I): 2002. Criteria for earthquake resistant design of structures. Part I General provisions and Buildings, 2002.

[13] IS 456:2002 “Plain and Reinforced Concrete - Code of Practice” fourth revised edition.

[14] IS 13920 (1993)”Ductile detailing of reinforces concrete structures subjected to earthquake forces”

[15] IS 875(PART 1 & 2) : 1987 code of practice for design loads for building and structures.

[16] Soil mechanics and foundation engineering DR.K.R.Arorass[16] Earthquake resistant design by Punkaj Agarwal.

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