Response of RC structures subjected to near fault and far fault earthquake motions considering soil structure interaction Tavakoli.H.R 1, Naeej.M 2, Salari.A 2 1 Assistant Professor, Department of Civil Engineering, Babol University of Technology, Babol, Iran 2 M.S. Students, Department of Civil Engineering, Babol University of Technology, Babol, Iran h_r_tavakoli2003@yahoo.com ABSTRACT Near fault earthquake motions have special characteristics that affect the response of structures. Their importance in earthquake design of civil structures was not fully realized until several failures occurred during the 1994 Northridge and 1995 Kobe earthquake events. The objective of this study is to investigate the effect of near fault and far fault earthquake motions on the response of reinforced concrete structures considering soil structure interaction. In detail, a series of linear time history analysis was carried out for three example buildings. The effects of soil structure interaction were evaluated for a 3 story building, a 7 story building and a 15 story building. The ordinary moment resisting frame system was considered for all example buildings as lateral force resisting system. For all buildings timehistory analysis were performed under 3 example earthquake motions: Tabbas, Kobe and Loma Prieta. The buildings were supported on soft and stiff soils with 100m/s and 900m/s shear wave velocity respectively. For each building and earthquake record, analysis were carried out for both conditions, building supported on soft and stiff soil separately, and compared with fixed base results. For all analysis both near field and far field earthquake were considered. The main evaluated parameters were period of structure, base shear, global displacement and story drifts. Results based on linear time history analysis had shown that considering the soil structure interaction increases period of structure and story drifts and also had noticeable and significant effects on global displacement and base shear. Keywords: Soil structure interaction, Reinforced concrete buildings, Near and far fault Earthquake. 1. Introduction 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. However, the destruction of numerous building in 1985 Mexico earthquake made researchers focus on soil structure interaction effects. Soil structure interaction is a collection of 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. During the last three decades, many studies on the subject have been carried out (Seed et al., 1975; Veletsos and Prasad, 1989; Zhang et al., 1999; Lou and Wu, 1999; Ghiocel and Ghanem, 2002; Gao et al., 2009). In 1980s to 1990s, SSI was studied thoroughly thanks to the impressive development of numerical methods, e.g., Spyrakos and Beskos, Gazentas and Wolf. A detailed discussion on SSI effects and analysis techniques is presented by Johnson. The inclusion of SSI phenomena in seismic analysis and design of structures is addressed in seismic code provision, including the recent FEMA 440 document. 881
The importance of the near source motion characteristics on the elastic and inelastic behaviour of engineered structures has been noted by several researchers, i.e. Naeim (1995), Chopra and Chintanapakdee (2001). The sensitivity of flexible or base isolated structures accommodating the deformation demands of impulsive motion in the near source region has also been addressed in several studies, e.g., Hall et al. (1995). Using simplified mathematical models, a quite extended range of wavelets has been proposed to examine impulsive groundmotion, e.g., Mavroeidis and Papageorgiou (2003). It is broadly accepted that the most severe damage from earthquake activity is localized in a region close to the causative fault, known as the near source region. The expected acceleration amplitude of the ground motion is strongly related to the focal depth of small to moderate magnitude earthquakes in short distances from the source (Hall et al., 1995). Past earthquakes indicated that the bedrock movements could be intensified by the dynamic effects of site and soil structure interaction and also make many changes in structural response. Thus, the influence of foundation flexibility is so much important. Actually soilstructure 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 SSI decreases natural effects on story drifts and damping of structures. Past experiences showed that the soil under foundation can alter dynamic behavior of structure. The dynamic response of structures depends upon soil nature located under foundation, so neglecting of soil structure interaction is a great fault. Also, some properties of soil structure such as material are effective on seismic behavior of structure and must be considered. As demonstrated above, assessment of seismic behavior of structure by neglecting of soil structure interaction effects leads to inaccurate results. In recent years comprehensive researches carried out to improve the accuracy of analysis. Due to numerous nonlinear parameters it is necessary to evaluate soil structure interaction by nonlinear soil modeling, offering an appropriate model in soil structure interaction analysis is very important. In order to evaluate soil structure interaction phenomenon while earthquake occurs, different procedures had been submitted. For modeling 3 steps are available: a) Modeling of soil by equivalent mass spring dashpot in foundation. b) Modeling of soil by shear beam with contiguous mass or distributed rigidity. c) Modeling of soil by finite element or finite difference modeling. Modeling of SSI by current methods is a complicated procedure which takes so much time and needs high accuracy. So using a simplified and acceptable procedure is necessary. Analytical procedures including application of equivalent springs under foundation as modeling the soil are one of the dynamic analyses of structure with soil structure interaction considerations which was used in this study. In this method foundation would be substituted with equivalent springs. Then the structure would be subjected to the earthquake records by neglecting of inertia forces and damping. In this study an attempt had been made to probe that how application of equivalent spring method can affect on structural responses. 1.1 Soil structure interaction In classic procedures for a fixed base structure analysis, the applied moment to the base of structure is same to that of free field. This assumption is accurate for structures supported on stiff soils. In structure with flexible base, a rocking and rotational component added to the 882
horizontal motion of structure. In addition, some amount of input seismic energy to structure transmitted to the soil under foundation could be damped due to radiational damping produced by wave propagation and hysteretic damping of soil material. But in classic procedures with this assumption that the located soil in beneath of structure is stiff, the dissipated energy could be neglected. According to the seismic improvement of current structure provision, the members of structure and foundation must be modeled together in unified model to consider soil structure interaction. In this study in nodes of foundation elements, two orthogonal spring, a vertical spring and three rotational springs were used in main direction of structures. The stiffness of each spring is equal to that of given in Table 1 divided by the total area of structure multiplied by area quota of that node. The stiffness quota of each node depends on the area quota of that node. These springs should be modeled in foundation nodes uniformly. 1.2 Richart and Lysmer s model Richart et al. (1970) idealized the foundation as a lumped mass supported on soil which is idealized as frequency independent springs which he described in terms of soil parameter dynamic shear modulus of shear wave velocity of the soil. Table 1 along with Fig. 1 shows the different values of spring as per Richart and Lysmer. In which, G= dynamic shear modulus of soil and is given by; G = s ; = Poisson s ratio of the soil; s = mass density of the soil; K = equivalent spring stiffness of the soil; r = equivalent radius of a circular foundation; L = length of the foundation; and B = width of the foundation. Table 1: Values of soil springs as per Richart and Lysmer (1970) model. Direction Spring Value Equivalent radius Remarks Vertical Horizontal Rocking Rocking Twisting This is in vertical Z direction This induce sliding in horizontal X or Y Direction This produces rocking about Y axis This produces rocking about X axis This produces twisting about vertical Z axis In this study the Table 1 was used to calculate the stiffness of equivalent springs. 2. Software for modeling of soil and structure and drawing charts Discretion of a model to small parts to analyze the elements is not a new idea. Uncoupling these parts and writing the equilibrium and compatibility equations lead to members internal 883
forces. Now development in structural analysis software, make it possible to model soil and structure and design them with very high accuracy. Figure 1: 3D view of the block foundation So soil structure interaction analysis is conceivable. In this study, modeling of soil structure phenomenon was performed using the SAP2000 program (version 12) which is powerful software for solving soil and structural problems. Graphs and charts in this study were drawn with EXCEL software which is a powerful program for drawing graphs and charts. 2.1 Description of structures and loading In this study 3 reinforced concrete buildings had been investigated. They were 3 story, 7 story and 15 story buildings. The buildings elevations were 9.9m, 21.3 and 49.5m, respectively. As shown in Figure 2 all buildings have the same symmetric floor plan (3*3 bays) with 4 m bay spacing. The 3D models of 7 story building as example model are shown in Figure 3 and 4. As shown in Figure 3, the building is supported on fixed base while the building which is shown in Figure 7 is rested on flexible base modeled by equivalent spring. Figure 2: Plan of 3, 7 and 15 story building The moment resisting frame system had been considered as lateral force resisting system for all buildings. At first step the example buildings had been modeled in SAP2000 software assuming that the columns were supported on rigid base. Next time this modeling performed assuming that the columns were supported on flexible base which were modeled by equivalent springs. Then in accordance with Iranian loading code the building were loaded by gravity loading and designed in accordance with Iranian concrete code. For uniform gravity loading of floors 750kg/m 2 and 200kg/m 2 were assumed as dead load and live load, respectively. Also 884
for uniform gravity loading of roof, 650kg/m 2 and 150kg/m 2 were assumed as dead load and live load, respectively. Designed sections of buildings were verified by the Iranian seismic design code (2800 code) to control story drifts. In next step time history analysis had been performed to analyze buildings. Figure 3: 3D model of example 7 story building with fixed base Figure 4: 3D model of example 7 story building with flexible base 2.2 Description of foundation system and soil In this study two types of soils as earth type representative namely soil type 1 and soil type 4 in accordance with seismic design code classification (2800 code) had been selected. The assumed properties of soils are listed in Table 2. In which, V s = shear wave velocity; s = mass density of the soil and = Poisson s ratio of the soil. As the shear wave velocity (V s ) gets more the soil becomes stiffer. Table 2: The assumed properties of soils Soil type V s (m/s) ρ s (kg/m 3 ) ν Soil 1 900 2000 0.4 Soil 4 100 1600 0.33 2.3 Earthquake records for Dynamic analysis Comparing the results of dynamic structural analysis, considering the soil structure interaction by equivalent spring method is the purpose of this study. Thus the example buildings and foundation were modeled together for soil type 1 and type 4. The buildings had been analyzed under Tabas, Kobe and Loma Prieta earthquake records. These records are listed in Table 3 and 4. These Tables contain specification of far fault earthquake and near fault earthquake, respectively. In which, PGA = peak ground acceleration; PGV = peak ground velocity; PGD 885
= peak ground displacement and RMS Distance = Root Mean Square Distance. The peak ground acceleration (PGA) of earthquake record in bedrock with recurrence interval of 475 years, equal to 0.35g had been considered. Table 3: characteristics of considered far fault earthquake motions Earthquake Tabas, Iran 1978 09 16 Kobe, Japan 1995 01 16 Loma Prieta 1989 10 18 Magnitud e PGA(g) PGV(cm/s) PGD(cm ) Station RMS Distance(km ) 7.35 0.1084 7.0800 7.1800 71 Ferdows 108.70 6.90 0.0373 4.9200 1.6200 99999 FUK 185.06 6.93 0.1268 17.5400 3.6900 Olema Point Reyes Station 136.42 Table 4: characteristics of considered near fault earthquake motions Earthquake Magnitude PGA(g) PGV(cm/s) PGD(cm) Station Tabas, Iran 1978 09 16 Kobe, Japan 1995 01 16 Loma Prieta 1989 10 18 RMS Distance(km) 7.35 0.8128 98.2000 62.1500 9101 Tabas 21.13 6.90 0.7105 77.8300 18.8700 6.93 0.4975 41.9200 10.1200 3. Discussion and comparison of results Dynamic structural analysis leads to: JMA 99999 KJMA CDMG 57007 Corralitos 11.19 13.68 1. As shown in Table 5, considering the soil structure interaction increased the natural period of structures. But this effect of soil structure interaction was not noticeable in soil type 1 while it had significant effect on soil type 4 which is softer and more flexible than soil type 1. So as the soil gets softer the importance of SSI becomes more. Therefore, neglecting of SSI for stiff soil is acceptable while it should be considered in soft soil. Table 5: natural periods (vibration period of first mode) corresponding to example buildings Soil type 1 Soil type 4 Fixed Base flexible Base Fixed Base flexible Base 3 Story 0.95 0.95 0.95 0.99 7 Story 1.6 1.6 1.22 1.34 15 Story 2.75 2.76 1.89 2.43 886
2. The predominant period of earthquake records are addressed in Table 6. This Table presents that the predominant periods of far fault earthquake records were more than near ones. In this study all of the predominant periods for 3 earthquakes and in 2 directions (X and Y) and for near and far fault earthquake were evaluated and the predominant earthquake were considered which are more effective on seismic response of RC buildings. Table 6: Predominant period of earthquake records Kobe Loma Prieta Tabas X Direction Y Direction Far field 0.46 0.56 Near field 0.34 0.38 Far field 0.78 0.72 Near field 1.18 2.28 Far field 0.32 0.24 Near field 0.24 0.2 3.1. Base shear force The dynamic base shear force estimated for soil type 1 and type 4 and fixed base are shown in Figs. 5 to 10. As it can be seen from these figures, overall the magnitude of base shear force increases as the soil gets softer. It shows that base shear may also be critical parameter especially for softer soils. Figure 5: Variation of Base Shear in 3 story RC building located on soil type 1 887
Figure 6: Variation of Base Shear in 3 story RC building located on soil type 4 Figure 7: Variation of Base Shear in 7 story RC building located on soil type 1 Figure 8: Variation of Base Shear in 7 story RC building located on soil type 4 888
Figure 9: Variation of Base Shear in 15 story RC building located on soil type 1 Figure 10: Variation of Base Shear in 15 story RC building located on soil type 4 3.2 The story drift As shown in Figs. 11 to 15 considering the soil structure interaction had noticeable effects on behavior of structures. The value of effects depended on story height and earthquakes field. In overall view the story drift got more as the soil became stiffer. But this result cannot be 889
generalized and depends on other condition as number of story. However the results prove that soil structure interaction had a significant effect on the response of structures. Figure 11: Variation of story drift in 3 story RC building located on soil type 4 Figure 12: Variation of story drift in 3 story RC building located on soil type 1 Figure 13: Variation of story drift in 7 story RC building located on soil type 1 890
Figure 14: Variation of story drift in 7 story RC building located on soil type 4 Figure 15: Variation of story drift in 15 story RC building located on soil type 1 Figure 15: Variation of story drift in 15 story RC building located on soil type 4 891
3.3 Global displacement to base The roof displacement to base estimated for soil type 1 and type 4 and fixed base are shown in Figs. 16 to 21. As it can be seen from these figures, overall the magnitude of global displacement to base increases as the soil gets softer. It shows that global displacement to base may also be critical parameter especially for softer soils. Figure 16: Variation of global displacement in 3 story RC building located on soil type 1 Figure 17: Variation of global displacement in 3 story RC building located on soil type 4 892
Figure 18: Variation of global displacement in 7 story RC building located on soil type 1 Figure 19: Variation of global displacement in 7 story RC building located on soil type 4 Figure 20: Variation of global displacement in 15 story RC building located on soil type 1 893
Figure 21: Variation of global displacement in 15 story RC building located on soil type 4 4. Conclusion The effects of various soil conditions and base rigidity on the structure behaviors have been investigated and the preparation results obtained for different height ratios of buildings in terms of different soil stiffness and different shear wave velocities are used. Various analyses are performed for different soil properties, number of building stories, the near and far fault earthquake motions, the change of results of lateral displacement of global (last story of building) and natural periods with respect to soil conditions are presented by graphs and results are discussed. This paper suggests a simple approach for modeling the soil and structures and considering the soil structure interaction. The results of this study can be summarized as follows: 1. In general, as the soil under structure gets softer, soil structure interaction becomes more effective. This conclusion is valid for all response parameters investigated in this study, namely the story drift and base shear, global displacement to base, period of structure and the earthquake field effects. 2. It is worth mentioning that as the structural period increases the ratio of peak responses of flexible base systems to the responses of fixed base condition. Considering the soil structure interaction increases period of structure and decreases the base shear of it. 3. According to this study, the importance degree of soil structure interaction for soil type1 and soil type2 can be suggested as below: 1. The soil structure interaction could be neglected for regular flexible buildings on rock or very stiff soil as soil type1. 2. Considering the soil structure interaction for structures supported on relatively soft soil, such as soil type 4 is necessary. In this way accurate analysis and design are available. 894
5. References 1. Chopra AK. (1995), Dynamics of structures: theory and applications to earthquake engineering. 2. Englewood Cliffs, NJ: Prentice Hall. 3. Clough RW, Penzien J. (1993), Dynamics of structures. New York: McGraw Hill. 4. De Barros, F.C.P., Luco, J.E. (1990), Discrete models for vertical vibrations of surface and embedded foundation, Earthquake Engineering and Structural Dynamics, 19(2), pp 289 303. 5. Housner, G.W.(1957), Interaction of building and ground during an earthquake. Bulletin of the Seismological Society of America, 47 (3), pp 179 186. 6. Hradilek, and P.J., Luco,J.E.(1970). Dynamic soil structure interaction. IDIEM Technical Report No.14, University of Chile, Santiago, Chile. 7. Iguchi, M., (1982).An approximate analysis of input motions for rigid embedded foundations. Transactions of the Architectural Institute of Japan, 315, pp 61 75. 8. Iranian seismic code (2800 code), 2008. 9. Kausel, E. (1976). Soil structure interaction. Soil Dynamics for Earthquake Design. International Centre for Computer. 10. Kuhlemeyer RL, Lysmer J.(1973), Finite element method accuracy for wave propagation problems. Soil Mech Found, ASCE 99, pp 421 7. 11. Lin CC, Chung LL, Lu KH. Optimal discrete time structural control using direct output feedback. Engineering Structures 18(6), pp 472 80. 12. Lysmer, J. and Richart, F.E.(1966), Dynamic response of footings to vertical loading. Journal of the Soil Mechanics and Foundations Division, ASCE, 92, SM1. 13. Massumi,A. and Tabatabaiefar,H.R. (2007), Effects of Soil Structure Interaction on Seismic Behavior of Ductile Reinforced Concrete Moment Resisting Frames,Proceedings of World Housing Congress on Affordable Quality Housing (WHC2007):Challenges and Issues in the Provision of Shelter for All, Housing. 14. Ro esset,j.m.,whitman,r.v.,and Dobry,R.(1973), Modal analysis of structures for foundation interaction. Journal of the Structural Division, ASCE, 99 (ST3), pp 399 416. 15. Seed, H.B., Hwang, R.N., Lysmer, J. (1975), Soil Structure Interaction Analyses for Seismic Response, Journal of the Geotechnical Engineering Division, 101(5), pp 439 457. 895
16. Spyrakos CC, Beskos DE. (1986). Dynamic response of flexible strip foundations by boundary and finite elements. Soil Dynamics Earthquake Engineering, 5(2), pp 84 96. 17. Stewart PJ, Seed RB, Fenves GL. (1999). Seismic soil structure interaction in buildings. II: empirical findings. J Geotechn Geoenviron Eng, 125(1): pp 38 48. aideddesign (ICCAD),Santa Margherita, Italy. 18. Veletsos, A, and Nair,V.V.D.(1975), Seismic interaction of structures on hysteretic foundations. Journal of the Structural Division, ASCE, 101 (ST1), pp 109 129. 19. Veletsos, A.S., Prasad, A.M. (1989) Seismic interaction of structures and soils: stochastic approach, Journal of Structural Engineering, 115(4), pp 935 956. 20. Zhang, X., Wegner, J.L., Haddow, J.B. (1999) Three dimensional dynamic soilstructure interaction analysis in the time domain, Earthquake Engineering and Structural Dynamics, 28(12), pp 1501 1524. 21. Wakabayashi,M.,(1985), Design of Earthquake Resistant Building,Mc Graw Hill (TX). 22. Wolf JP. (1994), Foundation vibration analysis using simple physical models. New Jersey: Prentice Hall. 23. Wolf JP. (1985), Dynamic soil structure interaction. New Jersey: Prentice Hall. 24. Wolf JP. (1987), Soil structure interaction analysis in time domain. NewJersey: Prentice Hall. pp 65 91. 25. Wolf, J.P., Somaini, D.R.(1983), Approximate dynamic model of embedded foundation in time domain, Earthquake Engineering and Structural Dynamics, 14(5): 683 703. Vol. 13, Bund. G 18. 26. Wong HL, Luco JE. (1976), Dynamic response of rigid foundations of arbitrary shape. Earthquake Eng Struct Dyn, 4, pp 587 97. 27. Wu WH, Smith HA. (1995), Efficient modal analysis for structures with soil structure interaction, Earthquake Engineering Structural Dynamics, 24, pp 735 56. 896