1

Certificate

This is to certify that Miss. Megha Gupta, Civil OCES -2011, BARC Training School, Mumbai

has completed her Project Work on Response of RC buildings considering soil structure

interaction under seismic loads under my guidance.

Signature _____________________________

Name & Designation_____________________

Division/Unit_________________________________

2

Acknowledgements

I would like to express my sincere gratitude to my guide Dr. V.S. Phanikanth, A&CED for

giving me the opportunity to work with him and also providing excellent guidance and

continuous assistance throughout the project work. His constant advice, assertions, appreciation

were very vital, giving me the motivation without which it wouldnt have been possible to finish

the project. I am thankful to him for his encouragement throughout the project.

I wish to express my gratitude to the Division Head, Mr.K.Srinivas for giving me an opportunity

to work on this project.

I am also thankful to all the staff members of Architectural and Civil Engineering Division

(A&CED) for their continuous support.

Finally I would like to thank my parents and all my friends who stood beside me from the

beginning to the end of this project work.

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Table of Contents

Certificate 1

Acknowledgements 2

Table of contents 3

List of Tables 4

List of figures 5

Abstract 6

Chapter 1 Introduction 7

Chapter 2 Dynamic analysis of RC structures

2.1 Dynamic analysis of RC structures 9

2.2 Description of Structural system 13

2.3 Seismic Analysis of 3-D frame in ETABS 18

Chapter 3 Soil Structure Interaction modeling-Impedance approach

3.1 Soil Properties and Foundation Modeling 24

3.2 Soil Structure analysis in ETABS 26

Chapter 4 Conclusions 30

References 31

4

List of Tables

Table No. Description of the Table Page No.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

Spring Constants for a rectangular mat foundation.

RC Frame Description

Material Description

Parameters for calculation of Seismic loads

Response Spectrum parameters

Total Dead Load

Design Seismic Base Shear

Load combinations as per IS 1893:2002 (Part 1)

Comparison of time periods

Comparison of Base Shear and VB for the three RC frames

Mass participation ratio for RC frame 1(single storey)

Mass participation ratio for RC frame 2 (3-storey)

Mass participation ratio for RC frame 3 (5-storey)

Soil Properties

Column Foundation Dimensions

Equivalent Spring Stiffness for Single Storey Frame

Equivalent Spring Stiffness for Three Storey Frame

Equivalent Spring Stiffness for Five Storey Frame

Variation of Time period with VS for Frame 1 (single storey)

Variation of Time period with VS for Frame 2 (Three storey)

Variation of Time period with VS for Frame 3 (Five storey)

Variation of Response Spectrum acceleration with Vs for Frame

1(single storey)

Variation of Response Spectrum acceleration with Vs for Frame

2(Three storey)

Variation of Response Spectrum acceleration with Vs for Frame

3(Five storey)

8

14

15

15

15

17

18

18

19

19

21

21

22

24

24

25

25

25

26

26

27

28

28

29

5

List of Figures

Figure No. Description of figure Page No.

1

2

3

4

5

6

7

8

9

10

11

12

13

Response spectra for rock and soil sites for 5% damping.

Plan and 3-D view of Frame 1

Plan and 3-D view of Frame 2

Plan and 3-D view of Frame 3

Showing application of Wall load for single storey

Showing waterproofing load

Showing Live Load

Variation of scale factor with height

Significant Mode shapes for single storey

Significant Mode shapes for Three storey

Significant Mode shapes for Five storey

Variation of Time period with VS

Variation of Response Spectrum acceleration with Shear

velocity

12

13

13

14

16

16

17

20

22

23

23

27

28

6

ABSTRACT

The structural design of R.C. buildings under seismic loading in majority of the cases is based on

fixed base analysis assumption. In general this assumption leads to simplified analysis of

structural response under dynamic loads. Whereas the aim is justifiable by avoiding the complex

modeling of soil structure aspects there by using simplified assumptions, the same cannot be

ignored in the design of industrial and safety related structures, which may result in under design

of the structural system.

In this study an attempt has been made to investigate the influence of soil structure interaction in

the dynamic behavior of R.C. structures using the impedance approach as suggested by

TECDOC 1347/ASCE 4-98.The detailed dynamic analysis is evaluated with the help of

commercial Finite element software ETABS using beam elements. As brick in-fill panel effects

are not modeled, the amplification in the base shear as per IS1893-2002 is also investigated for

different storeys considered. The influence of soil-structure interaction in the analysis and

design of a single, 3 storey and 5 storey reinforced concrete frame building is also investigated.

Finite element models simulating two different conditions: namely soil-structure interaction and

fixed-base behavior are considered. The results show an increase in the vibration period in

comparison with the fixed-base model, which does not consider the supporting soil. This shows

that the aspects may be ignored for flexible structures whereas the same cannot be applicable for

rigid structures like nuclear power plants where the increase in time period may result in

amplification of dynamic forces.

7

1. Introduction

The analysis of R.C. structures require consideration of various loads such as dead loads, live

loads, superimposed loads if any, wind loads or earthquake loads etc. The analysis of structures

to earthquake forces in turn may be based on seismic coefficient method for conventional

structures and may need detailed dynamic analysis using response spectrum method as suggested

by the code or site specific spectrum as applicable. Usually the designers carry out fixed base

analysis due to simplicity. However the soil effects are ignored in this assumption.

The effect of Soil structure interaction (SSI) on the response of buildings has been focus of

attention for more than 30 years. It is also well recognized that SSI could play a significant role

on structural response particularly for rigid structures on soft soil. Soil structure interaction is a

coupled phenomena in the response of structures caused by the flexibility of the foundation soils,

as well as in the response of soil region caused by the presence of structures.

Past earthquakes indicated that the bedrock movements could be intensified by the dynamic

effects of site and due to these effects of SSI changes in structural response is required to be

evaluated. The consideration of the influence of foundation flexibility is essential for accurate

representation of soil structure system. Soil structure interaction is an important issue, especially

for stiff and massive structures constructed on the relatively soft ground, which may alter the

dynamic characteristics of the structural response significantly. The dynamic response of

structures depend on the soil properties beneath the foundation, so the representation of soil

properties along with the structure in the FE model gives realistic estimation of dynamic

response. Some of the important parameters that change the dynamic response of the structure

are shear modulus, Poissons ratio etc. As discussed above, assessment of seismic behavior of

structure by neglecting soil structure interaction effects may lead to un-conservative results. In

recent years several researches carried out comprehensive studies on effects of SSI to improve

the accuracy of analysis. In order to evaluate SSI phenomenon for earthquake loading, elastic

half space approach is to be carried out. However this procedure is quite complex due to

modeling inherent non-linearity in the soil, alternative simplified approach using Impedance

method, is usually carried out by the designers due to the simplicity. These procedures are

8

recommended by ASCE4-98/TECDOC1347-2003.The impedance approach involved replacing

the soil stiffness by equivalent soil springs (frequency independent) in all rotational and

translational directions and the expressions for evaluating the spring stiffness and damping

values have been suggested for rigid circular/rectangular foundations in ASCE4-98.

Table 1: Spring Constants for a rectangular mat foundation. (TECDOC1347-2002/ASCE4-98)

Movement Foundation Stiffness

Horizontal sliding

Vertical

Rocking

Here,

= Poissons ratio of soil medium

G = Shear modulus of soil medium

B = width of the foundation perpendicular to the direction of horizontal excitation

L = length of the foundation in the direction of horizontal excitation

9

2. Dynamic analysis of RC structures

Dynamic analysis is related to the inertia forces developed by a structure when it is excited by

means of dynamic loads applied suddenly (e.g., wind blasts, explosion, and earthquake).

Dynamic analysis for simple structures can be carried out manually, but for complex structures

finite element analysis can be used. In a 3-D structure there are three dynamic degrees of

freedom (DDOF) for every unrestrained node with non-zero mass and there is potentially a

natural vibration mode for each DDOF. Thus, there may be hundreds of potential vibration

modes in a typical structure, but usually, it is only a small number of vibration modes with the

lowest frequencies that are of interest. In a multi-storey building, for example, it might be only a

few in each of two horizontal directions, plus one or two torsional modes that have to be

considered. The natural frequency of a system is dependent only on the stiffness of the structure

and the mass which participates with the structure (including self-weight). It is not dependent on

the load function.

A modal analysis calculates the frequency modes or natural frequencies of a given system. The

vibration mode shapes are normalized. This means that the largest value in each tabulated mode

shape is +1.0. Modal analysis of a structure comprises of following steps:

1. Find the natural modes (the shape adopted by a structure) and natural frequencies

2. Calculate the response of each mode

3. Optionally superpose the response of each mode to find the full modal response to a

given loading.

Determining the natural mode shapes and frequencies does not provide any quantitative

information about the response of the structure to excitation, but in some cases it may be

sufficient to know what the natural frequencies are so they can be avoided.

2.1 Seismic Evaluation Methods

Equivalent Static Method

Response Spectrum Method

10

2.1.1 Response Spectrum Method

Response spectrum analysis is a procedure for computing the statistical maximum response of a

structure to a base excitation. Each of the vibration modes that are considered may be assumed to

respond independently as a single-degree-of-freedom system. Design codes specify response

spectra which determine the base acceleration applied to each mode according to its period (the

number of seconds required for a cycle of vibration).Having determined the response of each

vibration mode to the excitation, it is necessary to obtain the response of the structure by

combining the effects of each vibration mode because the maximum response of each mode will

not necessarily occur at the same instant, the statistical maximum response, where damping is

zero, is taken as the square root of the sum of the squares (SRSS) of the individual responses.

Response spectrum analysis produces a set of results for each earthquake load case which is

really in the nature of an envelope. It is apparent from the calculation, that all results will be

absolute values - they are all positive. Each value represents the maximum absolute value of

displacement, moment, shear, etc. that is likely to occur during the event which corresponds to

the input response spectrum.

2.1.2 Equivalent Static Method

The equivalent static method is the simplest method of analysis because the forces depend on the

code based fundamental period of structures with some empirical modifiers. The design base

shear is to be computed as whole, then it is distributed along the height of the building based on

some simple formulae appropriate for buildings with regular distribution of mass and stiffness.

The design lateral force obtained at each floor shall then be distributed to individual lateral load

resisting elements depending upon the floor diaphragm action.

Following are the major steps in determining the seismic forces:

Determination of Base shear:

The total design lateral force or design base shear along any principal direction shall be

determined by this expression:

(1)

11

Where,

Ah = design horizontal seismic coefficient for a structure

W= seismic weight of building.

The design horizontal seismic coefficient for a structure Ah is given by:

(

) (

) (

) for Design Basis Earthquake (DBE) (2)

Z is the zone factor given in Table 2 of IS 1893:2002 (part 1) for the maximum considered

earthquake (MCE) and service life of a structure in a zone. The factor 2 is to reduce the MCE to

the factor for design base earthquake (DBE).

I is the importance factor, depending upon the functional use of the structure, characterized by

hazardous consequences of its failure, post-earthquake functional needs, historical or economic

importance. The minimum values of importance factor are given in Table 6 of IS 1893:2002

R is the response reduction factor, depending on the perceived seismic damage performance of

the structure, characterized by ductile or brittle deformations. The need for introducing R in base

shear formula is an attempt to consider the structures inelastic characteristics in linear analysis

as it is undesirable as well as uneconomical to design a structure on the basis that it will remain

in elastic range for all major earthquakes. Note: IS code recommends that the value of I/R should

not exceed 1.0 the values of R are given in Table 7 of IS 1893:2002 (part 1).

Sa/g is the average response acceleration coefficient for rock and soil sites as given in figure 2 of

IS 1893:2002 (part 1). The values are given for 5 % of damping of the structure.

12

Figure 1: Response spectra for rock and soil sites for 5% damping.

T, the fundamental natural period for buildings are calculated as per Clause 7.6 of IS 1893:2002

(part 1).

for moment resisting frame without brick infill panels. (3)

for resisting steel frame building without brick infill panels. (4)

for all other buildings including moment resisting RC frames. (5)

h is the height of the building in m and d is the base dimension of building at plinth level in m

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0

IS1893,Hard rock

S DJ /g

Time(sec)

Normalised spectra of TECDOC and IS1893-2002

13

2.2 Description of Structural system

Three RC frames are modeled as single storey, 3 storey and 5 storey in ETABS. Appropriate

beam and column dimensions are chosen and secondary beams are provided to reduce the span

of the slab. The following section shows an overview of the model showing the plan and 3-D

view of the model.

2.2.1 Model Overview

Frame 1 Single Storey

Figure 2: Plan and 3-D view of Frame 1

Frame 2 Three storey

Figure 3 : Plan and 3-D view of Frame 2

14

Frame 3 Five storey

Figure 4 : Plan and 3-D view of Frame 3

2.2.2 Description of model geometry and material properties

The RC frames are modeled considering the dimensions as shown in Table 1. Secondary beams

are provided so as to reduce the span of the slab and thus ensure two way action of the slab.

Table 2: RC Frame Description

Frame 1 Frame2 Frame 3

Number of stories 1 3 5

Plan Dimensions 6mx6m 6mx6m 6mx6m

Plinth Depth 3.0m 3.0m 3.0m

Storey Height 3.5m 3.5m 3.5m

Total Height from the

base 6.5m 13.5m 20.5m

Beam Dimensions

(mm) 300x600 300x600 300x600

Column Dimensions

(mm) 300x500 300x500 300x500

Slab Depth (mm) 120 120 120

15

Table 3 gives a brief description of the materials for the beams and columns. The concrete used

is of M30 grade and steel of Fe 415 grade is used.

Table 3: Material Description

Concrete Steel

Grade 30 Fe 415

Unit Weight (kN/m3) 25 77

Modulus of Elasticity (kN/m2) 27.386X10

3 2x10

8

Poisson Ratio, 0.2 0.3

2.2.3 Seismic evaluation parameters

The parameters considered for the calculation of seismic loads are listed in Table 4. The structure

is considered to be in Zone III and an Importance factor of 1.5 is assigned to the structure.

Table 4: Parameters for calculation of Seismic loads

Zone III

Zone Factor 0.16

Importance Factor,I 1.5

Response reduction Factor,R 3

Spectrum IS-1893:2002

The response spectrum corresponding to 5% damping value is chosen and is applied in all three

directions, i.e. x, y, and z directions. For the directional combination of the responses SRSS

method is applied and the responses from the various modes are combined through CQC

combination. Table 5 gives a brief description of the various response spectrum parameters

applied to the model.

Table 5: Response Spectrum parameters

Directional Combination SRSS

Modal Combination CQC

Spectrum type Acceleration

Direction X, Y, Z

Damping 5%

16

2.2.4 Loading on the structure

Dead Load

Includes self-weight of all members + Brick Load + Water Proofing load from the

slab.Self weight of members include the weight of columns, beams and that of the

slabs.Wall load due to 3.5 m high wall and of thickness 230mm and of 20 kN/m3 density,

WL= 20x.23x3.5=16kN/m.

Figure 5: Showing application of Wall load for single storey

Waterproofing Load considering average waterproofing thickness of 100mm and density of

24kN/m3= 24x0.1=2.4 kN/m

2.

Figure 6: Showing waterproofing load

17

The values of Self weight of members, wall load and waterproofing load calculated for the RC

frames are shown in Table 6.

Table 6: Total Dead Load

Frame 1 Frame 2 Frame 3

Self weight of members (kN) 434.1 1010.70 1587.3

Wall load (kN) 384.0 1152.0 1920.0

Waterproofing load (kN) 86.4 86.4 86.4

Total Dead load (kN) 904.5 2249.1 3593.7

Live Load

Live load is taken as 1.5 kN/m2 with a live load reduction factor of 25%.

Figure 7: Showing Live Load

Seismic Load

The design seismic base shear was calculated as per IS 1893:2002 (Part 1) for equivalent

static procedure. The values of base shear calculated are tabulated below for the RC

18

frames. The design shear is calculated for both cases of with infill walls and without infill

walls based on Equations 3 and 4.

Table 7: Design Seismic Base Shear (VB)

Frame 1 Frame2 Frame 3

Time Period (sec) 0.3053 0.5282 0.7226

Ah 0.1 0.0750 0.0554

Seismic Weight (KN) 918 2289.6 3661.2

VB (kN)(without

infills) 91.8 171.72 202.83

VB (kN)(without

infills) 91.8 184.63 194.48

2.2.5 Load Combinations applied

Table 8 shows the load combinations applied to the model.

Table 8: Load combinations as per IS 1893:2002 (Part 1)

1.5(DL + LL)

1.2(DL + LL EL)

1.5(DL EL)

0.9DL 1.5EL

2.3 Seismic Analysis of 3-D Frame in ETABS

After the loading on the structure is complete, fixed base and SSI analysis is done for the

structure.

2.3.1 Comparison of Fundamental Time periods obtained through ETABS with that of IS-

1893:2002

Time Period calculated by the Equivalent Static Method as prescribed by the code is compared

with the fundamental time period calculated by ETABS for the three RC frames.

The comparison shown in Table 9 indicates that ETABS predict a higher value of the time

periods than given by the code.The value of time period given by the code takes in account only

19

the height and plan dimensions (in case of infills) of the structure. There is no provision to

capture the mass or stiffness of the structure. Therefore, a detailed dynamic analysis of the

structure will provide more accurate results.

Table 9: Comparison of time periods

ETABS IS-1893:2002

Frame 1 0.3615 0.3053

Frame 2 0.8812 0.5282

Frame 3 1.4094 0.7226

2.3.2 Comparison of Seismic Base shear as computed by IS-1893:2002(Part-1) with ETABS.

Design seismic base shears ( ) were calculated using IS 1893:2002 in the X and Y directions

(EQx and EQy). Base shear from response spectrum analysis (VB) was calculated from the modal

combination of the first twelve modes (EQ). VXand VYare the components in X- and Y- directions,

respectively. As VBwas lessthan , the seismic force demands in the frame elements from

response spectrum analysis were scaledup by a factor equal to the ratio of the two base shears

( . In case of without infills the base shear needs to be amplified by 16%, 36.5% and

60.5% in X- direction and an amplification of 19.3%, 73.8% and 99% is required in Y- direction.

Table 10: Comparison of Base Shear and VB for the three RC frames.

Frame 1 Frame 2 Frame 3

Vx (kN) Vy(kN) Vx (kN) Vy(kN) Vx (kN) Vy(kN)

Equivalent Static ( )(without infills) EQx 91.80 91.80 171.72 171.72 202.83 202.83

Equivalent Static ( ) (with infills) EQx 91.80 91.80 184.63 184.63 194.48 194.48

Response Spectra (VB)

EQ 79.13 76.95 120.12 94.34 120.64 97.30

(without

infills)

1.160 1.193 1.365 1.738 1.605 1.990

(with infills)

1.160 1.193 1.467 1.869 1.539 1.908

20

From the analysis, the scale factor is found to be increasing with height of the structure.

Figure 8: Variation of scale factor with height ( without infills).

2.3.3 Comparison of Mass participation ratios for the three frames.

The mass participation ratios (%) for the first twelve modes are tabulated in Table 11,12 and 13

for the three RC frames. The significant modes for single storey frames are mode 1 (Y-direction)

and mode 3 (X-direction) while that for 3 and 5 storey frame are mode 1 (Y- direction) and mode

2 (X-direction). Rest all modes are insignificant as their mass participation is less than 20%. For

simplicity the mass participation in Z direction has been ignored in this analysis, otherwise, it has

to be considered.

0

0.5

1

1.5

2

2.5

1 storey 3 storey 5 storey

Scal

e F

acto

r

X-dir

Y-dir

21

Table 11: Mass participation ratio for RC frame 1(single storey).

Mode

no.

X-Trans

(%mass)

Y-Trans

(%mass)

Z-Trans

(%mass)

Sum

X(%mass)

Sum

Y(%mass)

Sum

Z(%mass)

1 0.00 87.32 0.00 0.00 87.32 0.00

2 0.00 0.00 0.00 0.00 87.32 0.00

3 84.39 0.00 0.00 84.39 87.32 0.00

4 0.00 12.68 0.00 84.39 100.00 0.00

5 0.00 0.00 0.00 84.39 100.00 0.00

6 0.00 0.00 0.00 84.39 100.00 0.00

7 15.61 0.00 0.00 100.00 100.00 0.00

8 0.00 0.00 0.00 100.00 100.00 0.00

9 0.00 0.00 0.00 100.00 100.00 0.00

10 0.00 0.00 0.00 100.00 100.00 0.00

11 0.00 0.00 0.00 100.00 100.00 0.00

12 0.00 0.00 0.00 100.00 100.00 0.00

Table 12: Mass participation ratio for RC frame 2 (3-storey).

Mode

no.

X-Trans

(%mass)

Y-Trans

(%mass)

Z-Trans

(%mass)

Sum

X(%mass)

Sum

Y(%mass)

Sum

Z(%mass)

1 0.00 85.64 0.00 0.00 85.64 0.00

2 83.97 0.00 0.00 83.97 85.64 0.00

3 0.00 0.00 0.00 83.97 85.64 0.00

4 0.00 8.19 0.00 83.97 93.83 0.00

5 0.00 0.00 0.00 83.97 93.83 0.00

6 9.07 0.00 0.00 93.04 93.83 0.00

7 0.00 2.40 0.00 93.04 96.24 0.00

8 0.00 0.00 0.00 93.04 96.24 0.00

9 0.00 3.76 0.00 93.04 100.00 0.00

10 0.00 0.00 0.00 93.04 100.00 0.00

11 3.00 0.00 0.00 96.04 100.00 0.00

12 0.00 0.00 0.00 96.04 100.00 0.00

22

Table 13: Mass participation ratio for RC frame 3 (5-storey).

Mode

no.

X-Trans

(%mass)

Y-Trans

(%mass)

Z-Trans

(%mass)

Sum

X(%mass)

Sum

Y(%mass)

Sum

Z(%mass)

1 0.00 84.06 0.00 0.00 84.06 0.00

2 82.53 0.00 0.00 82.53 84.06 0.00

3 0.00 0.00 0.00 82.53 84.06 0.00

4 0.00 9.07 0.00 82.53 93.13 0.00

5 9.79 0.00 0.00 92.32 93.13 0.00

6 0.00 0.00 0.00 92.32 93.13 0.00

7 0.00 2.75 0.00 92.32 95.88 0.00

8 0.00 0.00 0.00 92.32 95.88 0.00

9 0.00 1.28 0.00 92.32 97.17 0.00

10 3.09 0.00 0.00 95.41 97.17 0.00

11 0.00 0.59 0.00 95.41 97.75 0.00

12 0.00 0.00 0.00 95.41 97.75 0.00

Significant Mode Shapes:

Single Storey:

Figure 9: Significant Mode shapes for single storey.

23

Three Storey:

Figure 10: Significant Mode shapes for Three storey.

Five Storey:

Figure 11: Significant Mode shapes for 5 storey.

24

Chapter 3 Soil Structure Modeling- Impedance approach.

Soil Structure Interaction plays a significant role in case of rigid structures and hence needs to be

modeled with the structure for accurate results. Impedance approach for soil structure interaction models

the soil in the form of equivalent springs. Soil stiffness is considered by providing springs in horizontal

and vertical direction for translation and for rotational and torsional degrees of freedom.

3.1 Soil Properties and Foundation Modeling

The properties of soil considered for calculation of soil spring stiffness are as given in Table 14.

Table 14: Soil Properties

Unit Weight (kN/m3) 18

Poisson Ratio, 0.3

Safe Bearing Capacity

@3m below G.L.(kN/m2)

200

Assuming the aspect ratio of the column foundation to be same as that of column i.e. 5:3, the

dimensions of foundation are calculated as given in Table 15.For Kx and KRy, the ratio is

used in the calculation of X and and for Ky andKRx , ratio of is used.

Table 15: Column Foundation Dimensions.

Frame 1 Frame 2 Frame3

Length,L(m) 1.8 3.1 3.8

Breadth,B(m) 1.1 1.8 2.3

Table 16, 17 and 18 shows the values of the Equivalent Spring Stiffness for the three frames

calculated using the equations as per Table 1 and foundations dimensions as per Table 5. The

soil properties considered are given in Table 14.

25

Table 16: Equivalent Spring Stiffness for Single Storey Frame

Soil

name

Vs

(m/s)

Soil

type

Kx x 106

(kN/m)

Ky x

106

(kN/m)

Kz x

106

(kN/m)

KRx x 106

(kNm/rad)

KRy x 106

(kNm/rad)

KT x10-5

(kNm/rad)

A 1100 7.797 8.122 4.284 6.630 11.303 1.000 B 1000 II 6.444 6.712 3.541 5.479 9.341 1.000

C 800 II 4.124 4.296 2.266 3.507 5.979 1.000

D 600 II 2.320 2.416 1.275 1.973 3.363 1.000

E 400 II 1.031 1.074 0.566 0.877 1.495 1.000

F 200 III 0.258 0.268 0.142 0.219 0.374 1.000

Table 17: Equivalent Spring Stiffness for Three Storey Frame

Soil

name

Vs

(m/s)

Soil

type

Kx x 106

(kN/m)

Ky x

106

(kN/m)

Kz x

106

(kN/m)

KRx x 106

(kNm/rad)

KRy x 106

(kNm/rad)

KT x10-5

(kNm/rad)

A 1100 I 12.953 13.635 7.117 30.261 54.86 1.000

B 1000 II 10.705 11.268 5.882 25.009 45.338 1.000

C 800 II 6.851 7.212 3.764 16.006 29.016 1.000

D 600 II 3.854 4.057 2.117 9.003 16.322 1.000

E 400 II 1.711 1.801 0.940 3.997 7.247 1.000

F 200 III 0.428 0.460 0.235 0.999 1.812 1.000

Table 18: Equivalent Spring Stiffness for Five Storey Frame

Soil

name

Vs

(m/s)

Soil

type

Kx x 106

(kN/m)

Ky x

106

(kN/m)

Kz x

106

(kN/m)

KRx x 106

(kNm/rad)

KRy x 106

(kNm/rad)

KT x10-5

(kNm/rad)

A 1100 I 16.200 17.064 8.907 60.564 105.329 1.000

B 1000 II 13.388 14.102 7.361 50.050 87.044 1.000

C 800 II 8.568 9.025 4.711 32.032 55.708 1.000

D 600 II 4.819 5.076 2.650 18.018 31.336 1.000

E 400 II 2.142 2.254 1.177 8.000 13.913 1.000

F 200 III 0.535 0.564 0.294 2.000 3.478 1.000

26

3.2 Soil Structure analysis in ETABS.

3.2.1 Variation of Time period with shear velocity (VS) for the significant modes.

The variation of time period of the structure with the shear velocity for the significant modes is

shown in Figure 12. It is indicated that the time period decreases with increase in shear wave

velocity,i.e. as the soil stiffness increases, frequency increases, hence time period decreases.

Table 19, 20 and 21 show the time period values corresponding to different soil types for the

three RC frames.

Table 19: Variation of Time period with VS for Frame 1 (single storey).

VS

(m/s)

Mode 1

(Y-dir) (sec)

Mode 3

(X-dir) (sec)

200 0.3882 0.2930

400 0.3684 0.2719

600 0.3646 0.2676

800 0.3633 0.2660

1000 0.3627 0.2653

1100 0.3625 0.2651

Table 20: Variation of Time period with VS for Frame 2 (Three storey).

VS

(m/s)

Mode 1

(Y-dir) (sec)

Mode 2

(X-dir) (sec)

200 0.9187 0.7186

400 0.8907 0.6857

600 0.8855 0.6795

800 0.8836 0.6772

1000 0.8828 0.6762

1100 0.8825 0.6759

27

Table 21: Variation of Time period with VS for Frame 3 (Five storey).

VS

(m/s)

Mode 1

(Y-dir) (sec)

Mode 2

(X-dir) (sec)

200 1.4761 1.1842

400 1.4263 1.1253

600 1.4169 1.1140

800 1.4136 1.1100

1000 1.4121 1.1081

1100 1.4116 1.1076

Figure 12: Variation of Time period with VS

0.0000

0.2000

0.4000

0.6000

0.8000

1.0000

1.2000

1.4000

1.6000

200 400 600 800 1000 1100

Tim

e P

eri

od

(se

c) Mode 1 (Y-dir) Frame 1

Mode 3(X-dir) Frame 1

Mode1 (Y-dir) Frame 2

Mode 3 (X-dir) Frame 2

Mode 1 (Y-dir) Frame 3

Mode 2 (X-dir) Frame 3

Shear velocity (m/s)

28

3.2.2 Variation of Response Spectrum accelerations with shear velocity (VS) for the significant

modes.

Table 22, 23 and 24 show the variation of Response spectrum acceleration with shear velocity.

There is no variation in response spectrum accelerations for single storey frame as the time

period values for the different shear wave velocities fall in the range corresponding to the

maximum value of spectral acceleration.

Table 22: Variation of Response Spectrum acceleration with Vs for Frame 1(single storey).

Vs (m/s)

Mode 1(Y-dir)

(m/s2)

Mode 3 (X-dir)

(m/s2)

200 1.1692 1.1368

400 1.1692 1.1368

600 1.1692 1.1368

800 1.1692 1.1368

1000 1.1692 1.1368

1100 1.1692 1.1368

In case of 3 and 5 storey frames, for Vs values between 400 m/s to 1000 m/sthe response

spectrum accelerations are found to increase with the shear velocity which can be explained by

the corresponding decrease in the time period.

Table 23: Variation of Response Spectrum acceleration with Vs for Frame 2(Three storey).

Vs (m/s)

Mode 1(Y-dir)

(m/s2)

Mode 2 (X-dir)

(m/s2)

200 1.2534 1.2567

400 1.0531 1.1052

600 1.0592 1.1160

800 1.0609 1.1198

1000 1.0623 1.1215

1100 0.7814 0.8071

29

Table 24: Variation of Response Spectrum acceleration (Sa) with Vs for Frame 3(Five storey).

Vs (m/s)

Mode 1(Y-dir)

(m/s2)

Mode 2 (X-dir)

(m/s2)

200 0.8862 0.8893

400 0.7452 0.7663

600 0.7497 0.7743

800 0.7513 0.7772

1000 0.7520 0.7785

1100 0.5531 0.5727

Figure 13: Variation of Response Spectrum acceleration with Shear velocity

0.0000

0.2000

0.4000

0.6000

0.8000

1.0000

1.2000

1.4000

200 400 600 800 1000 1100

Re

spo

nse

sp

ect

rum

acc

ele

rati

on

(m

/s2 )

Mode 1(Y-dir)-Frame 1Mode 3 (X-dir)Frame 1Mode 1(Y-dir) Frame2Mode 2 (X-dir)Frame 2Mode 1(Y-dir) Frame3Mode 2 (X-dir)Frame 3

Shear Velocity (m/s)

30

Chapter 4 Conclusions

An attempt has been made to incorporate the soil stiffness in the finite element model of the

structure by introducing equivalent soil springs. In general, the effect of soil structure interaction

increases the time period of the structure. This effect of soil structure interaction is found to be

insignificant for flexible structures and significant for the rigid structures. Detailed comparison

of time period for fixed base is performed in ETABS.A comparative study of response spectrum

acceleration and Time period variation with shear velocity is also performed.

31

REFERENCES

1. ASCE4-98/TECDOC1347-2003.

2. IS 1893 (Part 1):2002, Criteria for Earthquake Resistant Design of Structures.

3. ETABS, Commercial package Finite Element Software.

4. Tavakoli ,H.R. ,Naeej, M. , Salari.A ,(2011), Response of RC structures subjected to near fault

and far fault earthquake motions considering Soil structure Interaction.