EARTHQUAKE RESPONSE OF MULTISTOREYED RC FRAMES WITH SOIL STRUCTURE INTERACTION EFFECTS

B.R. JayalekshmiFaculty, Department of Civil Engineering , NITK , Surathkal, email:br.jaya@gmail.com

Deepthi Poojary V.G., Katta Venkataramana , R.Shivashankar

AbstractIt is clear from the past earthquakes that the seismic response of a structure is greatly influenced by the soil structure interaction. In this paper, a time history analysis of multi storied building with isolated foundation resting on medium soft, medium stiff and stiff soils is presented. The two dimensional multistory building, its foundation and soil are considered as the parts of single integral system. This system is subjected to modified acceleration time histories recorded during three different real earthquakes. Seismic response of this soil foundation structural system is compared to that of a fixed base structure to isolate the effects of flexibility of soil on multistory frames during ground motions. A finite element analysis of the integrated system is carried out considering a typical two-dimensional frame with foundation and soil below it using finite element software .The soil is characterized by its stiffness, mass density, and poisson’s ratio. The effect on the fundamental natural period due to the incorporation of the effect of flexibility of soil is clarified. The variation in structural response for various parameters like displacements, shear force and bending moments for different types of soil with their time histories is presented and comparisons are made with those obtained from the analysis of a fixed base structure. Key Words: Earthquake response, Time history analysis, soil structure interaction, soil flexibility.

INTRODUCTION

Structures are generally assumed to be fixed at their bases in the process of analysis and design under dynamic loading. But the consideration of actual support flexibility reduces the overall stiffness of the structure and increases the period of the system. Thus the change in natural period may alter the seismic response of any structure considerably [8]. The extent of the fixity offered by the soil at the base of the structure also depends upon the load that is being transferred from the structure to the soil. Such an interdependent behavior between the soil and the structure regulating the overall response is referred to as soil structure interaction [8]. Numerous studies have been made on the effect of soil–structure interaction under dynamic loading. A variety of methods for seismic design of structures have also emerged from these studies, which vary widely in complexity [2]. The current approach has been to develop a two-dimensional finite element simulation of a soil foundation structure system under real earthquake time histories. This study has been carried out for one bay structure models with one, two and three storey with isolated footing subjected to three different modified acceleration time histories of ground motions. The earthquake response of the building frames considering the flexibility of the soil is examined.

IDEALIZATION OF THE SYSTEM

Structural idealization

The building frame elements have been idealized as two dimensional elastic beams, BEAM3 elements with three degrees of freedom at each node, translations in the nodal x and y directions and rotation about the nodal z-axis. The behavior of superstructure is assumed as elastic and is modeled using two parameters, the modulus of elasticity E and poisson’s ratio ν. All the structural members are considered to be reinforced concrete of grade M20.Value of E is taken as 22.36 GPa, ν is taken as 0.15 and density of concrete as 25 kN/m3. The bay length of the building is taken as 4.0 m and height as 3 m for all the cases. Sizes of beams and columns as 230mm X 400 mm. Thickness of slab is taken as 150mm and wall as 230mm with density of 20 kN/m3. The geometric sizes and loadings on the frames have been arrived on the basis of general requirement confirming to design code [4,5,6].The live load is taken as 3 kN/m2. The foundation, which supports the superstructure, is discretised as 4 noded plane element; PLANE42.The element is defined by four nodes having two degrees of freedom at each node, translations in the nodal x and y directions. Square footing of size 2m x 2m with 500mm thickness is considered for all structures. The moment transfer capability is created for a connection between a BEAM 3 elements and PLANE 42, i.e. between the column and the footing. Using the constraint equation, the rotation of the beam element is transferred as force couples to the plane element. The frames considered here are 1 bay structure with 1 storey, 2 storeys and 3 storeys designated as 1x1x1, 1x1x2, 1x1x3 with fixed base and resting on different types of soil models.

Idealization of soil

The structures are assumed to be resting on different types of soil models, in the medium soft, medium stiff to stiff range, based on soil parameters, E and ν [3].They are designated as soil40, soil60 and soil80 with corresponding E of 40000 kN/m2,60000 kN/m2and 80000 kN/m2 respectively and a constant poisson’s ratio of 0.25 is considered. The bearing capacity and density of the soil are taken as 220 kN/m2 and 18 kN/m3. The soil is assumed to be linear, elastic and isotropic material. Width of soil mass beyond the outermost footing is considered as 4 B and depth as 8B, where B is the width of isolated footing [3]. Soil is discretized using 4 nodded plane strain plane elements PLANE42. 5% of the critical damping is considered for the whole system.

Ground Motions considered

The effect of soil structure interaction on the building frames is studied under three different types of ground motions. The analysis has been carried out for the modified acceleration time histories that correspond to a peak ground acceleration of 0.5 g of the following earthquake ground motions, Yerba buena island (Loma Prieta) Earthquake San Francisco, Station Yerba (1989), Imperial Valley Earthquake, Station Elcentro (1940) and Treasure Island (Loma Prieta) earthquake, Station Treas (1991). Response spectrum curves for the earthquake ground motions are represented in the fig1.

METHODOLOGY

Finite element modeling of the whole structure –foundation –soil system is generated using the software ANSYS as shown in fig.2. The seismic analysis of the building frames is carried

Fig1.Response spectrum curves for the earthquake ground motions

Fig2. Finite element Model of a 1bay 3 storey RC frame –foundation soil system.

out with transient dynamic analysis using mode superposition method. For the mode superpo-sition type of transient analysis, Alpha and Beta damping have to be calculated. These values are not known directly but are calculated from modal damping ratios, i. i is the ratio of ac-tual damping to critical damping for a particular mode of vibration i. if i is the natural circu-lar frequency of mode i, and should satisfy the relation, i = / 2i + i /2 , based on Rayleigh Damping [1], such that the critical damping is taken as 5%.

RESULTS AND DISCUSSIONS

The variation of natural period and structural response for various parameters like floor dis-placements, shear force and bending moments for the first floor beams and ground storey col-umns of the building models resting on different types of soil with their time histories is pre-sented and comparisons are made with those obtained from the analysis of a fixed base struc-ture.

Variation in Natural Period

The variation in natural period due to the effect of soil flexibility is studied on different build-ing models with 1 to 3 storeys on isolated footing resting on medium soft to stiff soils and tabulated in table 1. It is observed that the natural period increases by the incorporation of soil flexibility. An increase of 58% is observed for medium soft soil and this increase is gradually decreasing with increase in stiffness i.e., 16% for stiff soil.

Effect of number of storey

It is observed here that, natural period increases as the number of storeys increases and the percentage variation of natural period decreases with increase in number of storey for the building models.

Table 1. Values of Natural period for different buildings with fixed base and with consideration of soil flexibility

No. of Natural period (sec) % Variation in periodstories Fixed soil 80 soil 60 soil 40 soil 80 soil 60 soil 40

1 0.255 0.298 0.330 0.404 16.84 29.10 58.122 0.561 0.612 0.629 0.639 9.14 12.22 13.863 0.926 0.997 1.020 1.066 7.70 10.20 15.11

Variation in Structural Response

The seismic structural response of one storey, two storey and three storey building for Elcentro motion considering soil flexibility is presented in table 2. Variation of structural response quantities for different earthquakes are plotted in fig.3 to fig.8 and fig.9 and fig10 represent the variation for different building models. Fig 11 to fig 15 represent the time

Table 2. Variation of Structural response quantities for Elcentro Earthquake

FrameType

 Parameters

 

Models % Variation

Fixed soil 80 soil 60 soil 40 soil 80 soil 60 soil 401x1x1 i Displacement (mm)  

 @ roof 28.95 47.6 62.97 82.34 64.42 117.51 184.42 @ base 0 9.59 13.14 22 - - -

ii Base shear(kN) 101.96 129.42 152.55 186.22 26.94 49.62 82.64iii Beam Shear (kN) 34.975 54.029 63.91 79.86 54.48 82.73 128.34iv Beam moment (kNm) 71.9 109.84 129.45 162.65 52.77 80.04 126.22v Column Shear (kN) 50.48 73.68 86.485 108.02 45.96 71.33 113.99vi Column Moment( kNm) 101.2 146.58 170.3 207.77 44.84 68.28 105.31

1x1x2 i Displacement (mm)  

 

@ roof 135.1 161.3 168.7 170.05 19.39 24.87 25.87@ first floor  73.5  90.42  92.61  102.2 23.02 26 39.05@ base 0 13.10 21 32.7  -  -  -

ii Base shear(kN) 216.51 239.47 238.24 227.37 10.60 10.03 5.02iii Beam Shear (kN) 109.31 116.47 117.7 111.66 6.55 7.67 2.15iv Beam moment (kNm) 221.35 237.59 240.02 228.1 7.34 8.43 3.05v Column Shear(kN) 100.75 118.87 121.34 112.73 17.98 20.44 11.89vi Column Moment (kNm) 210.66 236.56 235.9 211.01 12.30 11.98 0.16

1x1x3 

i Displacement (mm)  

 

@roof 242.3 263.15 274.23 277.2 8.60 13.18 14.40@second floor 186.2 209.34 213.12 208 12.43 14.45 11.71@first floor 82.45 108.02 110.74 110.74 31.09 33.52 34.39@base  0 10.97 14.38 26.74  -  -  -

ii Base shear(kN) 235.1 248.04 237.85 250.4 5.504 1.169 6.51iii Beam Shear (kN) 145.8 145.5 143.2 115.13 -0.206 -1.78 -21.03iv Beam moment (kNm) 292.9 292.7 288.57 268.38 -0.06 -1.47 -8.37v Column Shear( kN) 115.1 127.69 125.28 121.26 10.93 8.84 5.35vi Column Moment (kNm) 261.48 273.15 266.37 256.99 4.46 1.87 -1.72

Fig 3. Variation of roof displacement for different input motions

Fig 4. Variation of Base shear for different input motions

Fig 5. Variation of Beam shear force for different input motions

Fig 6. Variation of Column shear force for different input motions

Fig 7. Variation of Beam bending moment for different input motions

Fig 8. Variation of Column bending moment for different input motions

Fig 9. Variation of roof displacement for different storeys

Fig 10. Variation of Base shear for different storeys

Fig 11. Time history of displacement at different floor levels of a 1x1x3 building for soil 40

Fig 12. Time history of Base shear of a 1x1x1 building for different soils

Fig 13. Time history of Beam shear of a 1x1x1 building for different soils

Fig 14. Time history of Beam moment of a 1x1x1 building for different soils

Fig 15. Time history of Column moment of a 1x1x1 building for different soils

history of structural response for Elcentro earthquake motion. It is seen that the percentage increase in various quantities is more for medium soft soil compared to stiff in the case of 1x1x1 model and this decreases as the number of storey increases. Two to three times increase in the structural response quantities are observed for a single story building resting on medium soft soil. The fundamental natural period of a two storied buildings coincides with the peak period of the earthquake motions, hence resonance will develop and the response increases dramatically with the values being more than three storied building. The Treas response spectrum intensity is more than Yerba and Elcentro, therefore the response quantities for Treas is seen to be more. Since natural period of three storied building lies in the falling part of response spectrum curve for all motions its seismic response is less compared to two storied building and decreases with the flexibility of the soil.

CONCLUSION

It is concluded that the first storey building shows considerable increase in the member forces for all earthquake motions considered based on the characteristics of the input motion. The seismic response of all the buildings considering soil flexibility exhibits variation based on the frequency content of the input motion and stiffness of soil.

REFERENCES

[1] Anil, K. Chopra (2003) “ Dynamics of structures “ , Theory and application to Earthquake Engineering , Prentice hall , New Delhi.[2] Amir M. Haalabian and M. Hesham El Naggar (2002). “Effect of non-linear soil-structure interaction on seismic response of tall slender structures”, Soil Dynamics and Earthquake Engineering , Vol 22, 639-658.

[3] Bowles, J.E.(1998).”Foundation Analysis and design” ,McGraw Hills, New York.

[4] IS 1893 (Part I): 2002 Criteria for Earthquake Resistant Design of Structures - General provisions and Buildings , Bureau of Indian Standards , New Delhi.

[5] IS 456:2000 Plain and Reinforced Concrete – Code of Practice, Bureau of Indian standards, New Delhi.

[6] IS 875 : 1987 (Part I & Part II ) Code of practice for design Loads ( Other than Earthquake ) for buildings and structures , Bureau of Indian Standards , New Delhi.

[7] John P. Wolf (1985) , “ Dynamic Soil-Structure Interaction” , Prentice- Hall, Inc , Englewood Cliffs, New Jersey

[8] Koushik Bhattacharya and S C Dutta ( 2004),“ Assesing lateral period of building frames incorporating soil-flexibility” Journal of sound and vibration ,vol269,795-821.