EFFECT OF SSI ON SEISMIC RESPONSE OF FLYOVER: A CASE STUDY

4th International Conference on Advances in Civil Engineering 2018 (ICACE 2018) 19 –21 December 2018 CUET, Chittagong, Bangladesh www.cuet.ac.bd EFFECT OF SSI ON SEISMIC RESPONSE OF FLYOVER: A CASE STUDY M. R. Mukhlis1*&M. A. R. Bhuiyan2 1 Institute of Earthquake Engineering Research, Chittagong University of Engineering and Technology, Chittagong-4349, Bangladesh. E-mail: [email protected] 2 Department of Civil Engineering, Chittagong University of Engineering and Technology Chittagong-4349, Bangladesh *Corresponding Author ABSTRACT The soil structure interaction (SSI) has become an important measure in the seismic response evaluation of engineering structures with the emergence of massive constructions on soft soils such as dams, flyovers, tunnels, etc. This study investigates the effects of SSI on the non-linear seismic response of flyover pier for different far field ground motion history. Yield and ultimate displacements of pier have been evaluated by developing the force-displacement relationship through pushover analysis of a pile supported typical pier of a multispan simply supported flyover. Effect of SSI has been included in the study by calculating the stiffness of equivalent soil springs for pile foundation recommended by Japan Road Association (JRA). The non linear time history analysis has been adopted to measure the seismic response of the pier. Finally, maximum displacement of the pier top and corresponding displacement ductility demand has been used to evaluate the damage state of the pier with and without considering the effect of SSI in the modeling of flyover pier. From the analytical investigation, it can be concluded that, consideration of SSI in the modeling of flyover pier increases the seismic response. Keywords: flyover pier; soil structure interaction; displacement ductility; seismic response. INTRODUCTION Flyover is one kind of bridge, which is an elevated structure carrying highway over roads, railways and other features. Since bridges are one of the most critical components of highway systems, it is necessary to evaluate the seismic safety of highway bridges (Hwang et al., 2001).Most of the structures involve some type of contact with ground. When the external forces, such as earthquakes, act on these systems, neither the structural displacements nor the ground displacements, are independent of each other. Conventional structural analysis neglect the SSI effects, while neglecting SSI is reasonable for light structures in relatively stiff soil such as low rise buildings but effect of SSI, however, becomes prominent for heavy structures resting on relatively soft soils for example high-rise buildings and elevated-highways on soft soil (Wolf, 1985). Methods that can be used to evaluate the SSI effects can be categorized as direct and substructure approaches. In a direct analysis, the soil and structure are included within the same model and analyzed as a complete system. In a substructure approach, the SSI problem is partitioned into distinct parts that are combined to formulate the complete solution. Based on the above background, the study aims at evaluating the seismic response of a pile supported typical pier of Kadamtali flyover, constructed in Chittagong city of Bangladesh, with and without considering SSI. Initially, the yield and ultimate displacement of pier from pushover analysis and maximum displacement of pier tops from non linear time history analysis for three different ground motion history have been evaluated for both considerations of SSI. Effect of SSI has been included in the study through direct approach by calculating the stiffness of equivalent soil springs for pile 624 foundation recommended by JRA (2002). Finally, the seismic performance of the pier has been evaluated based on displacement ductility demand expressed in terms of damage states. MODELING OF PIER Physical Model Kadamtali flyover (22.34°N; 91.82°E) was constructed to reduce traffic jam in Chittagong city of Bangladesh. Figure 1 shows a 3D view of the flyover. The flyover is approximately 1127 m long and 8.54 m wide. The reinforcement with yield strength of 413 N/mm2 and concrete with compressive strength of 30 N/mm2 are used to construct the flyover. It is spanning around 630 m with 22 spans of variable length from 21.3 m to 42.0 m. There are 21 piers with variable heights ranging from 4.66 m to 8.5 m. Figure 2 shows the transverse section of the typical pier of the flyover. The deck of the flyover is comprised of four pre-stressed concrete girders with 200 mm reinforced concrete slab. The girders rest on elastomeric neoprene bearing over concrete bearing pad installed on top of each pier. Each elastomeric neoprene bearing with a cross-section of 500 mm × 350 mm consists of 4 numbers of 3 mm steel plates with a total thickness of 70 mm. For this study, a typical pier (Pier 7 as shown in Figure 1) of the flyover has been selected for analysis purpose. Geometric dimensions of the typical pier are presented in Table 1. Table 1: Geometric dimensions of a typical pier of Kadamtali flyover Pier No. 7 Pier height, H (m) 8.27 Pier Dimension (m x m) 1.2 x 2.5 Longitudinal Reinforcement 66-Y25 bar Fig. 1: 3-D view of Kadamtali flyover (Mukhlis and Bhuiyan, 2017) Fig. 2: Transverse section of typical pier Fig. 3: Analytical model of typical pier without considering SSI Fig. 4: Analytical model of typical pier considering SSI Analytical Model 625 The pier-girder system is approximated as a continuous 2-D finite element frame using the SeismoStruct nonlinear analysis program. The superstructure and substructure of the system are modelled as a lumped mass system divided into a number of small discrete segments. The mass of each segment is assumed to be distributed between two adjacent nodes. The body of the flyover pier is modelled using fiber elements. The loads from deck, prestressed concrete girders and pier caps are calculated and modelled as lumped mass element on the pier top. The base of the pier is assumed to be fixed neglecting the foundation movement effect when SSI is not considered in the analysis. On the other hand, the base of the pier is modeled with zero length spring elements when SSI is considered in the analysis. At that case, the mass of the pile cap are simply put on the base node of the pier using lumped mass element in SeismoStruct. Analytical model of the typical pier without and with considering SSI are shown in Fig. 3 and Fig. 4 respectively. PUSHOVER ANALYSIS OF PIER The sectional analysis has been conducted by response 2000 to obtain the moment-curvature (M-) relationship of pier cross section as shown in Fig. 5 which is used to derive the force-displacement relationship of the pier. In addition, SeismoStruct 2016 is used to conduct the pushover analysis to derive the force-displacement relationships of the pier. This typical pier is modelled as single degree of freedom system with a lumped mass on the pier top carrying all the seismic dead load coming from deck, girder and pier cap. Fig. 6 shows the pushover model of the typical pier in SeismoStruct 2016 and Fig. 7 shows the force displacement relationship of the typical pier obtained from pushover analysis. This bilinear idealization of force displacement relationship can be easily found in the analysis result in SeismoStruct 2016, from which yield displacement (y), ultimate displacement (u) and ultimate strength (Pu) are obtained as shown in Fig. 8 and tabulated in Table 2 for the typical pier. Moment (kN-m) 25000 Pier cross-section 1.2 m x 2.5 m 20000 15000 10000 5000 0 0 5 10 15 20 Curvature (rad/km) 25 Fig. 5: Moment-curvature (M-) relationship for the typical pier cross-section Fig. 6: Pushover model of the typical pier (SeismoStruct 2016) Force (kN) 3000 2000 1000 0 0 100 200 Displacement (mm) 300 Fig. 7: Force-displacement relationship of typical pier Pier no. Fig. 8: Bilinear idealization of force-displacement relationship Table 2: Ultimate strength of typical pier Ultimate displacement, u Yield displacement, y 626 Ultimate strength, Pu 7 (mm) (mm) (kN) 37 175 2454 SEISMIC RESPONSE EVALUATION OF PIER Seismic performance of bridge components are generally expressed in terms of damage conditions of those components subjected to seismic ground motions. Piers are generally the most critical components of bridges and different forms of engineering demand parameters (EDP) such as displacement ductility demands (d) are generally used to measure the damage state (DS) of the bridge piers (Bhuiyan and Alam 2012, Bhuiyan and Alim 2017). Table 3 summarizes the definitions of various damage states and their corresponding damage criteria available in the literature. Table 3: Damage states of bridge pier Bridge Component Pier Reference EDP (Displacement Ductility, d) d  1.0 1.0  d  1.2 1.2  d  1.76 1.76  d  4.76 d  4.76 Hwang et al. 2001 Damage States (DS) No Damage Slight (DS 1) Moderate (DS 2) Extensive (DS 3) Collapse (DS 4) FEMA 2003 Physical Phenomenon No Physical phenomenon Cracking and spalling Moderate cracking and spalling Degradation without collapse Failure leading to collapse FEMA 2003 Displacement ductility demand (d) has been estimated from the results of time history analysis (THA) for specific ground motion history with and without considering soil structure interaction (SSI) using Eq. (1), where, du = maximum pier displacement from THA, dy = yield displacement of pier. 𝑑 = 𝑑𝑢 𝑑𝑦 (1) Selection of Ground Motions As sufficient seismic data is not available for this region, the time history analysis is conducted by applying three selected earthquake ground motion records with different peak ground acceleration (PGA) as shown in Table 4. The time histories of these three earthquakes are shown in Fig. 9. Table 4: Earthquake ground motions for time history analysis Ground Acceleration (g) Earthquake No. EQ-1 EQ-2 EQ-3 Earthquake Name El Centro-1940 Northridge-1994 Kobe-1995 Magnitude, Mw 6.9 6.7 6.9 PGA (g) 0.35 0.45 0.24 Occurrence time of PGA (s) 2.12 4.06 15.16 EL Centro-1940 Northridge-1994 Kobe-1995 0.50 0.25 0.00 -0.25 -0.50 0 5 10 15 Time (sec) 20 25 30 Fig. 9: Selected earthquake ground motion records for THA THA without Considering Soil Structure Interaction (SSI) Rayleigh damping has been chosen for THA of the pier with 5% damping using two fundamental modes in transverse and longitudinal direction with a period of 0.525 s and 0.252 s respectively found in the eigenvalue analysis. THA has been conducted by applying three selected ground motions shown in 627 Pier displacement (mm) Fig. 9 at the base of the pier in three separate models. The displacement response at the top of piers are represented with respect to time as shown in Figure 10 with peak displacements of 86 mm at 2.86 s, 154 mm at 7.28 s and 89 mm at 15.42 s for EQ-1, EQ-2 and EQ-3 respectively without considering SSI. 160 El Centro-1940 Northridge-1994 Kobe-1995 80 0 -80 -160 0 5 10 15 Time (sec) 20 25 30 Fig. 10: Displacement response at pier top (without considering SSI) THA Considering Soil Structure Interaction (SSI) Soil structure interaction is considered in seismic analysis by modeling the soil medium. According to JRA (2002), spring constants for ground can be evaluated using the geometric properties of pile foundation and physical properties of underlying soil layer by following equations. 𝐾𝑥 = 𝑛𝑘1 ; 𝐾𝑧 = 𝑛𝑘𝑣𝑝 ; 𝐾𝑦 = 𝑛𝑘4 + 𝑘𝑣𝑝 ∑𝑛𝑖=1 𝑥𝑖 2 ; 𝐾𝑥𝑦 = −𝑛𝑘2 when, pile head is assumed to be hinged, 𝑘1 = where, 𝑘𝑣𝑝 = 𝑘𝐻0 = 𝐸𝐷 30 𝑎𝐴𝑝 𝐸𝑝 (tf/m); 𝐿𝑝 4 𝑘𝐻 𝐷𝑝  = √4𝐸  𝑝 𝐼𝑝 2𝐸𝑝 𝐼𝑝 3 ; 𝑘2 = 𝑘3 = 𝑘4 = 0 (m ); 𝑘𝐻 = -1 3 𝐵 −4 𝑘𝐻0 ( 30𝐻 ) 1 (kgf/cm3); 𝐵𝐻 = √ 𝐷𝑝 (cm);  𝑆 (Kgf/cm3); 𝐸𝐷 = 2(1 + 𝐷 ) 10𝑔 𝑉𝑆𝐷 2 (kgf/cm2); 𝑉𝑆𝐷 = 0.8 (100𝑁 1⁄ 3) (m/s) here, Kx = translational constant of ground along x-axis (tf/m); Kz = vertical constant of ground along z-axis (tf/m); Ky = rotational constant of foundation around the y-axis (tf-m/rad); Kxy = coupling constant of foundation of the displacement along x-axis and rotation around the y-axis (tf-m/m); n = 4, representing the total number of piles. Coefficient for distribution of soil vertical stiffness along the length of pile (a) is assumed to be 1. Poisson’s ratio of soil (D) is taken as 0.5, considering saturated clay & also the maximum value. Unit weight of soil (S) is taken as 1.27 (tf/m3), considering soft silty clayed sand layer. Finally, Kx, Kz and Ky are found to be 1.93109 kN/m, 6.03106 kN/m and 1.95107 kN-m/rad respectively. These spring constants of ground and foundation in longitudinal direction have been used at the base of the piers as zero length spring elements in the modeling of piers followed by THA by applying three selected ground motions shown in Fig. 9 at those spring elements of the pier in three separate models. The displacement response at the top of piers are represented with respect to time as shown in Figure 11 with peak displacements of 88 mm at 2.88 s, 158 mm at 7.29 s and 93 mm at 15.43 s for EQ-1, EQ-2 and EQ-3 respectively considering SSI. Pier displacement (mm) 160 El Centro-1940 Northridge-1994 Kobe-1995 80 0 -80 -160 0 5 10 15 Time (sec) 20 25 30 Fig. 11: Displacement response at pier top (considering SSI) Damage State Evaluation of Pier Damage states of the pier are evaluated based on displacement ductility demand (d). Displacement ductility demands of pier models with and without considering SSI are shown in Table 5 using Eq. (1) and comparison of displacement ductility demands are shown in Fig. 12. It has been observed that d 628 values increases up to 4.49% for EQ-3 due to SSI considerations though the physical damage state remains the same with extensive damage state (DS 3) representing degradation without collapse in response to all applied ground motions for both modeling considerations. Table 5: Displacement ductility demand (d) of typical pier Displacement Ductility Demand (d) Increase in d Earthquake No. EQ-1 EQ-2 EQ-3 Earthquake Name Without Considering SSI 2.32 4.16 2.41 El Centro-1940 Northridge-1994 Kobe-1995 4.16 2.32 considering SSI (%) 2.33 2.60 4.49 4.27 2.41 2.38 EQ - 1 Considering SSI 2.38 4.27 2.51 EQ - 2 Without Considering SSI 2.51 EQ - 3 Considering SSI Fig. 12: Comparison of displacement ductility demand (d) of typical pier CONCLUSIONS Interaction between soil and structure is considered in the modeling procedure of a typical pier of a flyover through equivalent spring constants. Pushover analysis of the pier has been conducted to determine the yield and ultimate displacement of the pier. Three selected earthquake ground motions of different PGA are used to compare the response of the pier models through time history analysis with and without considering SSI. From the time history analysis maximum top displacement of the pier models are used to determine the displacement ductility demands. These displacement ductility demands are used to evaluate the seismic performance of piers in terms of damage states. For all three earthquake ground motions, displacement ductility demands of piers show higher value when SSI is considered in the pier model though, physically the pier indicating towards damage with degradation without collapse with extensive damage state (DS-3) for both type of model. Hence, from the analytical results, it has been revealed that soil structure interaction has great impact on seismic response analysis of bridge piers and should be carefully taken into account in the modeling procedure. REFERENCES Bhuiyan, MAR and Alam, MS. 2012. Seismic Vulnerability Assessment of a Multi-Span Continuous Highway Bridge Fitted with Shape Memory Alloy Bars and Laminated Rubber Bearings. Earthquake Spectra, 28(4): 1379-1404. Bhuiyan, MAR and Alim, H. 2017. Seismic Safety Evaluation of Abdul Mannan Overpass in Chittagong, Bangladesh. Malaysian Journal of Civil Engineering, 29(3): 250-272. FEMA. 2003. HAZUS-MH MR1: Technical Manual, Earthquake Model. Federal Emergency Management Agency, WA, USA. Hwang, H; Liu, JB and Chiu, Y. 2001. Seismic Fragility Analysis of Highway Bridges. Technical Report of MAEC RR-4 project. Mid-America Earthquake Center, USA. JRA. 2002. Specifications for Highway Bridges - Part V: Seismic design. Japan Road Association, Tokyo, Japan. Mukhlis, MR and Bhuiyan, MAR. 2017. Lateral Strength and Safety Evaluation of Piers of Kadamtali Flyover in Chittagong, Bangladesh. International Journal of Advanced Structures and Geotechnical Engineering, 6(2): 45-56. Wolf, JP. 1985. Dynamic Soil-Structure Interaction. Prentice-Hall, Inc., Englewood Cliffs, New Jersey, USA. 629