international journal of civil and · pdf filethe interaction between foundation and soil ......

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 535

Seismic soilstructure 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 PostGraduate Student, Department of Civil Engineering, IIT Roorkee, Roorkee, Uttarakhand, India, 247667 [email protected]

ABSTRACT

In hilly regions, engineered construction is constrained by local topography resulting in the adoption of either a stepback or stepbacksetback 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 3D 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: SoilStructure Interaction, Unsymmetrical Buildings, ResponseSpectrum 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 stepback and step backset 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 backset 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 soilstructure 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

536

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: 0.15m

Wall thickness: 230 mm

Parapet wall thickness: 230 mm

Density of concrete: 25 KN/m 2

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 nonlinear 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.



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c) 4storey4bay

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

Figure 2: Step backSet 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),



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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 nonlinear static pushover analysis is a comprehensive method of evaluating earthquake response of structures explicitly considering nonlinear 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 nonlinear 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: LoadDeformation 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).



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Spring constant Equivalent radius 32(1ν)GRo (78ν)

Kx Ky = = Af Ro π

= Eq. 3.1

4GRo (1ν)

Kz = Af Ro π

= Eq. 3.2

3 8GRo 3(1 )

KRx ν

= 4 4Iyf Ro

π = Eq. 3.3

3 8GRo 3(1 )

KRy ν

= 4 4Ixf Ro

π = Eq.3.4

3 16GRo 3

KRz = 4 2( ) Iyf Ixf Ro

π +

= 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/m 2 )

Elastic Modulus E (KN/m 2 )

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 nonlinear behaviour is assumed to occur within frame elements at concentrated points or plastichinges. 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 FEMA273/356 or ACT40 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 ATC40 for



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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 stepback and set backstep 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 (StepBack Building4Storey4Bay)



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Figure 5: Sequence of formation and Hinge patterns of shortest column frame “e” (StepBack Building4Storey4Bay)

Figure 6: Sequence of formation and Hinge patterns of frame A, B, C, D and E (SetBackStepBack Building4Storey4Bay)



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Figure 7: Sequence of formation and Hinge patterns of shortest column frame “e” (SetBackStepBack Building4Storey4Bay)

Table 3: Results of Pushover analysis for Step Back Buildings

SoilStructure Interaction Building configuration

Values of VPP & δPP (KN & mm)

Fixed Support

Hard Soil Medium Soil Soft Soil 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

2 storey 2Bay

δy 28.00 60.00 * 388.00 Vx 2225.70 1453.20 916.90 * Vy 1032.80 * 565.10 * δx 17.00 64.00 181.00 *

3 Storey 3Bay

δy 35.00 * 137.00 * Vx 2673.40 1860.14 1101.30 * Vy 1312.30 1101.50 777.10 * δx 28.00 96.00 258.00 *

4Storey 4Bay

δy 49.00 97.00 165.00 *

Table 4: Results of Pushover Analysis for Step BackSet Back Buildings

SoilStructure Interaction Building

configuration Values of VPP & δPP

(KN & mm) Fixed Support Hard Soil Medium Soil Soft Soil

Vx 2035.80 1471.80 797.85 * Vy 1094.00 830.00 * * δx 15.00 61.00 154.00 *

3 Storey 3Bay

δy 28.00 62.00 * * Vx 3988.40 2654.00 1600.20 * Vy 1746.00 1398.00 * * δx 18.00 75.00 204.00 *

4Storey 4Bay

δy 34.00 76.00 * * (pp) Performance Point, V is the total base shear, δ is the displacement, *Result not available.



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The above two tables clearly show that the total base shear in Xdirection for all the considered building models were higher than the base shear in Ydirection 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 Ydirection. Since, the buildings in Xdirection are stiffer, hence they showed lesser displacements and attracts greater shear forces especially in the shorter columns, while in Ydirection the buildings are less stiff due to which higher displacements and less shear forces were obtained. The results exhibit the typical expected behavior for soilstructure 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 Stepback and Step backSet back buildings. The tables clearly shows that for Step BackSet 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 Xdirection but for Ydirection 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 momentresisting 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 (stepback buildings)

δ elastic (mm)

δ pp (mm)

δ'= R* δ elastic (mm) R'=(δ pp/δ')

Support

Building configuration

Xdir Ydir Xdir Ydir Xdir. Ydir Xdir Ydir 2Storey2bay 4.56 3.36 15 28 13.68 10.98 1.10 2.56 3Storey3bay 5.26 20.26 17 35 15.78 60.78 1.08 0.59

Fixed

base

4Storey4bay 14.20 35.18 28 49 42.60 105.54 0.66 0.47 2Storey2bay 18.58 41.41 52 60 55.74 124.23 0.93 0.48 3Storey3bay 24.14 67.71 * 64 72.42 203.13 * 0.32

Hard

soil

4Storey4bay 46.58 104.10 96 97 139.74 312.30 0.69 0.30 2Storey2bay 72.15 130.84 129 * 216.45 392.40 0.60 * 3Storey3bay 81.80 162.80 181 137 245.40 488.40 0.74 0.28

Mediu

m so

il

4Storey4bay 147.9 237.80 258 165 443.70 711 0.58 0.23 2Storey2bay 253.5 411.02 211 388 760.5 1233.0 0.28 0.315

Soft

soil

3Storey3bay 334.0 627.76 * * * * * * 4Storey4bay 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



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Table 6: Displacements from pushover analysis and response spectrum analysis (step backset back buildings)

δ elastic (mm)

δ pp (mm)

δ'= R* δ elastic (mm) R'=(δ pp/δ')

Support

Building configuration

Xdir Ydir Xdir Ydir Xdir Ydir Xdir Ydir 3Storey3bay 4.86 14.81 15 28 14.58 44.43 1.03 0.63

Fixed

base

4Storey4bay 5.37 19.39 18 34 16.11 58.17 1.12 0.59 3Storey3bay 20.69 42.39 61 62 62.07 127.17 1.00 0.49

Hard

soil

4Storey4bay 25.77 65.35 75 76 77.31 196.05 0.97 0.4 3Storey3bay 69.20 111.1 154 * 207.6 333.30 0.75 *

Medium

soil

4Storey4bay 89.00 159.8 204 * 267.0 479.40 0.77 * 3Storey3bay 284.1 417.3 * * 852.3 * * *

Soft

soil

4Storey4bay 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 Xdirection



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Figure 9: Plot between T and R’ Step back building in Ydirection

Figure 10: Plot between T and R’ Step backSet back building in Xdirection

Figure 11: Plot between T and R’ Step backSet back building in Ydirection



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5. Conclusions

In Step backSet 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 Xdirection but for Ydirection 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 13 th 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 312.

6. Kumar, S, (1996), Seismic Analysis of Stepback and Setback Buildings, PhD Thesis, University of Roorkee, India.

7. Pachuau, L.Z., (1992), Seismic Response of RC Framed Building on HillSlopes, 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 SoilStructure Interaction, Soil Dynamics and Earthquake Engineering, 24 (12), pp 893914.

9. Wolf, J. P, (1985), Dynamic SoilStructure Interaction. PrenticeHall, Inc., Englewood Cliffs, New Jersey.

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