Seismic soil-structure interaction of buildings on hill · PDF fileINTERNATIONAL JOURNAL OF...

INTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING

Volume 2, No 2, 2011

© Copyright 2010 All rights reserved Integrated Publishing services

Research article ISSN 0976 – 4399

Received on September, 2011 Published on November 2011 544

Seismic soil-structure interaction of buildings on hill slopes Pandey A.D

1, Prabhat Kumar

2, Sharad Sharma

3

1- Assistant Professor, Department of Earthquake Engineering, IIT Roorkee, Roorkee,

Uttarakhand, India, 247667

2- Ph.D Student, Research Scholar, Department of Earthquake Engineering, IIT Roorkee,

Roorkee, Uttarakhand, India, 247667

3- Post-Graduate Student, Department of Civil Engineering, IIT Roorkee, Roorkee,

Uttarakhand, India, 247667

[email protected]

doi:10.6088/ijcser.00202010132

ABSTRACT

In hilly regions, engineered construction is constrained by local topography resulting in the

adoption of either a step-back or step-back-set-back configuration as a structural form for

buildings. The adopted form invariably results in a structure which is irregular by virtue of

varying column heights leading to torsion and increased shear during seismic ground motion.

To capture the real behavior of buildings on hill slope a 3-D analysis of the building is

required. In the present study, static pushover analysis and Response spectrum analysis

(RSA) have been conducted on five building i.e. three step back buildings and two step back-

set back buildings with varying support conditions. These buildings have been analyzed for

different soil conditions (hard, medium and soft soils) idealized by equivalent springs. The

response parameters, i.e. total base shear (V), displacement from pushover analysis (δ

performance point), displacement from RSA (δ elastic) and response correction factor (R’) have

been studied with respect to fixed base analysis to compare the effect of soil springs. In

general it is found that response reduction factor decreases with increasing time period, but is

expected to be constant beyond a certain value of time period.

Keywords: Soil-Structure Interaction, Unsymmetrical Buildings, Response-Spectrum

Analysis, Pushover Analysis, Performance Point, Reduction Factor.

1. Introduction

The scarcity of plain ground in hilly areas compels construction activity on sloping ground

resulting in various important buildings such as reinforced concrete framed hospitals,

colleges, hotels and offices resting on hilly slopes. Since, the behavior of buildings during

earthquake depends upon the distribution of mass and stiffness in both horizontal and vertical

planes of the buildings, both of which vary in case of hilly buildings with irregularity and

asymmetry due to step-back and step back-set back configuration (Kumar and Paul, 1996).

The presence of such constructions in seismically prone areas makes them exposed to greater

shears and torsion as compared to conventional construction. In order to highlight the

differences in behavior, which may further be influenced by the characteristics of the locally

available foundation material, a parametric study has been conducted on five different step-

back and step back-set back buildings. Current building codes including IS: 1893 (Part 1):

2002 suggest detailed dynamic analysis of these types of buildings on different soil (hard,

medium and soft soil) types. To assess acceptability of the design it is important to predict the

force and deformation demands imposed on structures and their elements by severe ground

motion by means of static pushover analysis.

Seismic soil-structure interaction of buildings on hill slopes

Pandey A.D, Prabhat Kumar, Sharad Sharma

International Journal of Civil and Structural Engineering

Volume 2 Issue 2 2011

545

2. Modeling and Analysis

The five different buildings are analyzed in SAP2000 as shown in Figure 1 and 2. The slope

of the ground has been taken as 27 degree with horizontal which is neither too steep nor too

flat. The properties of the considered building configurations in the present study are

summarized below (Birajdar, 2004).

Height of each floor: 3.5 m

Plan dimension of each storey block: 7х5m

Floor thickness: 0.15 m

Wall thickness: 230 mm

Parapet wall thickness: 230 mm

Density of concrete: 25 KN/m2

Poisson’s Ratio: 0.2

Damping: 0.05

Size of column: 230mmх500mm

Size of beams: 230mmх500mm

Size of isolate footing taken: 1 m х 1 m

The structural material is assumed to be isotropic and homogenous. Joint between the

building elements (beam and columns) has been modelled by using diaphragm as constraints.

The non-linear static pushover analysis and dynamic analysis (Response Spectrum Analysis)

has been carried out for rigid base (fixed base) and flexible base conditions. The foundation

(base) flexibility in the analysis is considered by means of replacing the foundation by

statically equivalent springs with six degrees of freedom.





546

c) 4storey-4bay

Figure 1: Step back buildings (a, b, c) with increased number of storey and bays in Y-

direction

Figure 2: Step back-Set back buildings (d, e) with increased number of storey and bays in Y-

direction

2.1 Response Spectrum Analysis (Dynamic Analysis)

The dynamic analysis of structures is carried out by two methods, Response Spectrum

Method and Time History Method. The Response Spectrum Method consists of determining

the response in each mode of vibration and then superimposing the responses in various

modes to obtain the total response. The seismic analysis of all buildings was carried out by

Response Spectrum Method in accordance with IS: 1893 (Part 1): 2002, including the effect

of eccentricity (static and accidental). Damping considered for all modes of vibration was

five percent. For determining the response of the buildings in different directions for ground

acceleration the response spectrum analysis was conducted in longitudinal and transverse

direction. The other parameters used in seismic analysis were, moderate seismic zone (III),





547

zone factor 0.16, importance factor 1 and the response reduction factor as 3. Ordinary

moment resistant frame for all configurations was assumed.

2.2 Pushover Analysis

The Nonlinear static pushover analysis is a relatively simple solution to the problem of

predicting force and deformation demands imposed on structures and their elements by

severe ground motion. Nonlinear static methods involve three distinct phases: estimation of

capacity, estimation of demand and correlating the two to decide the performance of the

buildings. The non-linear static pushover analysis is a comprehensive method of evaluating

earthquake response of structures explicitly considering non-linear behavior of structural

elements. The capacity spectrum method is adopted for implementing pushover analysis that

compares structural capacity with ground shaking demand to determine peak response during

an earthquake. The capacity spectrum method estimates peak responses by expressing both

structural capacity and ground shaking demand in terms of spectral acceleration and

displacement. The capacity spectrum method assumes peak response of the non-linear

structure to be equal to the modal displacement of an equivalent elastic system with an

effective period, Teff based on secant stiffness. The intersection of capacity curve and demand

curve established the performance point. Under incrementally increasing loads some

elements may yield sequentially. Consequently, at each event, the structures experiences a

stiffness change as shown in Figure 3, where IO, LS and CP stand for immediate occupancy,

life safety and collapse prevention respectively.

Figure 3: Load-Deformation Curve

3. Foundation Characteristics

Dynamic analysis of the structure and its interaction with the material (foundation soil) under

the structure affects the response of structure. The interaction between foundation and soil

depends on the elastic properties of foundation soil and foundation dimensions. The

foundation flexibility in the analysis is considered by means of replacing the foundation by

statically equivalent springs. Modeling of foundation soil has been done by using spring

constants as shown below, according to the equations given by Wolf (1985).





548

Spring constant Equivalent radius

32(1-ν)GRo

(7-8ν)Kx Ky

AfRo

Eq. 3.1

4GRo

(1-ν)Kz

AfRo

Eq. 3.2

38GRo

3(1- )KRx

4

4IyfRo

Eq. 3.3

38GRo

3(1- )KRy

4

4IxfRo

Eq.3.4

316GRo

3KRz 4

2( )Iyf IxfRo

Eq.3.5

Where, G is shear modulus of soil, ν is the Poisson’s ratio of soil and Ro is the equivalent

radius; Af is the area of the footing and Ixf and Iyf are moments of inertia of the footing

about X and Y axis, respectively. The values of Poisson’s ratio (ν) and shear modulus (G) for

three different kinds of soil, hard, medium and soft are taken from Prakash and Barken

(Verma, 1989). The elastic properties of foundation soil for hard, medium and soft soil are

tabulated in Table 1 and the numerical values of spring constants for different type of

foundation soil for isolated footing are summarized in Table 2.

Table 1 Elastic Properties of Foundation Soil

Type of soil Shear Modulus

G (KN/m2)

Elastic Modulus

E (KN/m2)

Poisson’s Ratio

ν

HARD 2700.0 6750.0 0.25

MEDIUM 451.1 1200.0 0.33

SOFT 84.5 250.0 0.48

Table 2: Spring Constants for Isolated Footing

Type of

soil

Kx

(KN/m)

Ky

(KN/m)

Kz

(KN/m)

KRx

(KN/rad)

KRy

(KN/rad)

KRz

(KN/rad)

HARD 7309.4 7309.4 8121.6 1777.8 1777.8 2666.7

MEDIUM 1251.1 1251.1 1518.9 334.1 334.1 444.5

SOFT 251.0 251.0 366.6 80.3 80.3 83.5

4. Result and Discussion

In SAP 2000, a non-linear behaviour is assumed to occur within frame elements at

concentrated points or plastic-hinges. The default types include an uncoupled moment hinges,

an uncoupled axial hinge, an uncoupled shear hinge and a coupled axial force and biaxial

bending moment hinge, as PMM, PM and M. The default hinge properties designated are

typically based on FEMA-273/356 or ACT-40 criteria, these default properties are section

dependent. Default PMM hinges to each end of the moment frame columns and default M3

hinges to each end of the moment frame beams were assigned as described in ATC-40 for





549

pushover analysis. The development of the pushover curve includes the evaluation of force

distribution along the height of the structure. In the static pushover analysis, load cases were

defined for the gravity load and other two cases are defined for the lateral load distribution in

X and Y direction. The load application is defined to be displacement control while defining

the load cases for the pushover analysis. In the present analysis the formation of hinges in the

buildings shows almost similar pattern for different types of foundation media. In X-

direction, the hinge formation starts with beams from the end of shortest column frame. In the

beginning of the hinge formation, first few hinges are developed in the shortest columns in Y-

direction. The formation of hinges started from the shortest columns and then reached to the

last longest frame. The hinges in the shortest columns exhibit rotations corresponding to

immediate occupancy level and essentially reaching the collapse prevention level for all the

types of support condition. Sometimes the hinges in these columns reached the collapse

prevention level directly after the immediate occupancy level and jumping the life safety

zone. The data obtained from pushover analysis is tabulated in Table 3 and Table 4. The

sequence of formation and hinge patterns of step-back and set back-step back buildings are

shown in Figure 4, 5, 6 and 7.

Figure 4: Sequence of formation and Hinge patterns of frame A, B, C, D and E

(Step-Back Building-4-Storey-4-Bay)





550

Figure 5: Sequence of formation and Hinge patterns of shortest column frame “e”

(Step-Back Building-4-Storey-4-Bay)

Figure 6: Sequence of formation and Hinge patterns of frame A, B, C, D and E

(Set-Back-Step-Back Building-4-Storey-4-Bay)





551

Figure 7: Sequence of formation and Hinge patterns of shortest column frame “e”

(Set-Back-Step-Back Building-4-Storey-4-Bay)

Table 3: Results of Pushover analysis for Step Back Buildings

Building

configuration

Values of VPP & δPP

(KN & mm)

Fixed

Support

Soil-Structure Interaction

Hard Soil Medium Soil Soft Soil

2 storey-

2Bay

Vx 961.70 689.30 428.60 174.09

Vy 528.30 388.80 * 215.00

δx 15.00 52.00 129.00 211.00

δy 28.00 60.00 * 388.00

3 Storey-

3Bay

Vx 2225.70 1453.20 916.90 *

Vy 1032.80 * 565.10 *

δx 17.00 64.00 181.00 *

δy 35.00 * 137.00 *

4Storey-

4Bay

Vx 2673.40 1860.14 1101.30 *

Vy 1312.30 1101.50 777.10 *

δx 28.00 96.00 258.00 *

δy 49.00 97.00 165.00 *

Table 4: Results of Pushover Analysis for Step Back-Set Back Buildings

Building

configuration

Values of VPP & δPP

(KN & mm)

Fixed

Support

Soil-Structure Interaction

Hard Soil Medium Soil Soft Soil

3 Storey-

3Bay

Vx 2035.80 1471.80 797.85 *

Vy 1094.00 830.00 * *

δx 15.00 61.00 154.00 *

δy 28.00 62.00 * *

4Storey-

4Bay

Vx 3988.40 2654.00 1600.20 *

Vy 1746.00 1398.00 * *

δx 18.00 75.00 204.00 *

δy 34.00 76.00 * *

(pp)- Performance Point, V is the total base shear, δ is the displacement, *Result not available.





552

The above two tables clearly show that the total base shear in X-direction for all the

considered building models were higher than the base shear in Y-direction except for soft soil

for which sufficient amount of results have not emerged. Further the displacements in X-

direction were less than the displacements in Y-direction. Since, the buildings in X-direction

are stiffer, hence they showed lesser displacements and attracts greater shear forces especially

in the shorter columns, while in Y-direction the buildings are less stiff due to which higher

displacements and less shear forces were obtained. The results exhibit the typical expected

behavior for soil-structure interaction. As the foundation moves from the fixed support to

hard soil, medium soil then soft soil support, the shear forces go on decreasing in both X and

Y direction, while the displacement goes on increasing.

The displacements from pushover analysis (δ performance point (δ pp)) and response spectrum

analysis (δ elastic) have been tabulated in Table 5 and 6 for Step-back and Step back-Set back

buildings. The tables clearly shows that for Step Back-Set Back buildings the value of

displacement at the performance point, δ pp is always greater than δ elastic, i.e., (δ pp/ δ elastic >

1) in both X and Y direction for all type of support. While in Step back buildings this ratio is

valid perfectly in X-direction but for Y-direction this relation is valid up to only two storey

and two bay for hard soil support after that this ratio becomes less than one. The correction

factor R’ has been calculated by dividing the displacement at performance point (inelastic

displacement) by the elastic displacement multiplying by the response reduction factor R

whose value is 3 for Ordinary moment-resisting frame (OMRF) as per IS 1893: 2002.

R'= (δ pp/ R* δ elastic)

The relationship between T and R’ has been shown in Figures 8, 9, 10 and 11.

Table 5: Displacements from pushover analysis and response spectrum analysis

(step-back buildings)

Su

pp

ort

Building

configuration

δ elastic

(mm)

δ pp

(mm)

δ'= R* δ elastic

(mm) R'=(δ pp/δ')

X-dir Y-dir X-dir Y-dir X-dir. Y-dir X-dir Y-dir

Fix

ed

base

2Storey-2bay 4.56 3.36 15 28 13.68 10.98 1.10 2.56

3Storey-3bay 5.26 20.26 17 35 15.78 60.78 1.08 0.59

4Storey-4bay 14.20 35.18 28 49 42.60 105.54 0.66 0.47

Hard

soil

2Storey-2bay 18.58 41.41 52 60 55.74 124.23 0.93 0.48

3Storey-3bay 24.14 67.71 * 64 72.42 203.13 * 0.32

4Storey-4bay 46.58 104.10 96 97 139.74 312.30 0.69 0.30

Med

iu

m s

oil

2Storey-2bay 72.15 130.84 129 * 216.45 392.40 0.60 *

3Storey-3bay 81.80 162.80 181 137 245.40 488.40 0.74 0.28

4Storey-4bay 147.9 237.80 258 165 443.70 711 0.58 0.23

Soft

soil

2Storey-2bay 253.5 411.02 211 388 760.5 1233.0 0.28 0.315

3Storey-3bay 334.0 627.76 * * * * * *

4Storey-4bay 610.1 891.82 * * * * * *

*Result not available, (pp) - performance point, δ elastic is the displacement in response

spectrum analysis, R is the response reduction factor





553

Table 6: Displacements from pushover analysis and response spectrum analysis

(step back-set back buildings) S

up

port

Building

configuration

δ elastic

(mm)

δ pp

(mm)

δ'= R* δ elastic

(mm) R'=(δ pp/δ')

X-dir Y-dir X-dir Y-dir X-dir Y-dir X-dir Y-dir

Fix

ed

base

3Storey-3bay 4.86 14.81 15 28 14.58 44.43 1.03 0.63

4Storey-4bay 5.37 19.39 18 34 16.11 58.17 1.12 0.59

Hard

soil

3Storey-3bay 20.69 42.39 61 62 62.07 127.17 1.00 0.49

4Storey-4bay 25.77 65.35 75 76 77.31 196.05 0.97 0.4

Med

ium

soil

3Storey-3bay 69.20 111.1 154 * 207.6 333.30 0.75 *

4Storey-4bay 89.00 159.8 204 * 267.0 479.40 0.77 *

Soft

soil

3Storey-3bay 284.1 417.3 * * 852.3 * * *

4Storey-4bay 396.2 602.7 * * 1188 * * *

*Result not available, (pp) - performance point, δ elastic is the displacement in response

spectrum analysis, R is the response reduction factor

For the adopted building configuration, as the value of time period “T” increase the value of

correction factor R’ decreases. In the present study due to availability of limited data, the

extrapolation of correction factor R’ beyond the range of “T” shown on plot is quite difficult.

Consistency in general trend of decreasing value of R’ with the increasing value of “T” has

been noted. Pushover analysis for type of irregularity considered requires modification. The

correction is considered on the basis of the observation of relation between elastic and

inelastic displacement for regular symmetric frame for which the value of correction factor is

0.7. Due to irregularity, it is expected that this value will decrease for irregular frame which

is confirmed by the variation in Figure 8 to 11.

Figure 8: Plot between T and R’ Step back building in X-direction





554

Figure 9: Plot between T and R’ Step back building in Y-direction

Figure 10: Plot between T and R’ Step back-Set back building in X-direction

Figure 11: Plot between T and R’ Step back-Set back building in Y-direction





555

5. Conclusions

In Step back-Set back buildings, the value of the displacement at performance point, δpp is

always greater than elastic displacement for all types of support. However, in Step back

buildings this is valid perfectly in X-direction but for Y-direction this is valid up to only two

storeys and two bays for hard soil. For the adopted building configurations, as the value of

time period T increase the value of correction factor R’ decreases. Pushover analysis for type

of irregularity considered requires modification.

6. Acknowledgements

The authors are indebted to Head, Department of Earthquake Engineering, Indian Institute of

Technology, Roorkee for providing facilities to carry out the research work reported in this

paper work. The second author acknowledges with thanks the research fellowship received

from the Ministry of Human Resource Development (Government of India) to allow perusing

the Ph.D.

References

1. ATC 40, (1996), Seismic evaluation and Retrofit of Concrete Buildings, Volume1.

2. Birajdar, B.G, and S.S. Nalawade, (2004), Seismic Analysis of Buildings Resting on

Sloping Ground, Proceedings of 13th

World Conference on Earthquake Engineering,

Vancouver, B.C., Canada, Paper no. 1472.

3. Verma, R.K., (1989), Earthquake Response Spectrum Analysis of Buildings on Hill

Slopes, M.E Dissertation, Department of Earthquake Engineering, University of Roorkee.

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

Revision, BIS New Delhi.

5. Barros, R. C, and R. Almeida, (2005), Pushover analysis of asymmetric three dimensional

building frames, Journal of Civil Engineering and Management, 11 (1) , pp 3-12.

6. Kumar, S, (1996), Seismic Analysis of Step-back and Set-back Buildings, PhD Thesis,

University of Roorkee, India.

7. Pachuau, L.Z., (1992), Seismic Response of RC Framed Building on Hill-Slopes, M.E

Dissertation, Department of Earthquake Engineering, University of Roorkee.

8. Dutta, S.C., K. Bhattacharya, and R. Roy, (2004), Response of Low Rise Buildings under

Seismic Ground Excitation Incorporating Soil-Structure Interaction, Soil Dynamics and

Earthquake Engineering, 24 (12), pp 893-914.

9. Wolf, J. P, (1985), Dynamic Soil-Structure Interaction. Prentice-Hall, Inc., Englewood

Cliffs, New Jersey.

Seismic soil-structure interaction of buildings on hill · PDF fileINTERNATIONAL JOURNAL OF...

Documents

Transcript of Seismic soil-structure interaction of buildings on hill · PDF fileINTERNATIONAL JOURNAL OF...