Seismic Response Analysis of Structure Supported by Piles Subjected to Very Large Earthquake Based on 3D-FEM

Transcription

1 Seismic Response Analysis of Structure Supported by Piles Subjected to Very Large Earthquake Based on 3D-FEM *Hisatoshi Kashiwa 1) and Yuji Miyamoto 2) 1), 2) Dept. of Architectural Engineering Division of Global Architecture, Osaka Univ., Osaka, Japan 1) ABSTRACT This paper presents the simulation analysis about the damaged structure supported by pile in Hyogo-ken Nanbu (Kobe) earthquake. The major findings obtained from analyses are summarized as follows; 1) The deformation of piles for FE analysis is a little larger than the observation. However, the deformation of pile which has low stiffness was largest in both the FE analysis and the observation. 2) The damage at pile cap may be understood from the following consideration: the shear force and the ground displacement applied at the same time 3) The reduction of pile response was caused by the ground improvement which led the increase of the lateral resistance of the surface layer and the decrease of the displacement of ground. 1. Introduction Many structures supported by pile were damaged seriously in Hyogo-ken Nanbu earthquake and the results of the investigation were summarized by Kinki Branch of AIJ (1996). However, the reasons of damage have not been cleared yet. The strong nonlinear behavior of pile-soil systems, which is the separation between the pile and the soil, slip in the soil or the yielding of the pile cap, will occur under the strong ground motions. The nonlinearity of soil-pile-structure dynamic interaction has a strong influence on the structural behavior during earthquake. It is considered that the 3D FEM is very effective in the evaluation of behavior of structure during earthquake with nonlinear soil-structure interaction. On the other hand, the structure built on the improved ground suffered very little to minor damage, so the ground improvement has been applied to many structures after Hyogo-ken 1) 2) Assistant Professor Professor

2 Nanbu earthquake. Therefore, we conducted the centrifugal model tests for the structure supported by piles in dry sand subjected large earthquake and the simulation analysis by elasticplastic 3-D FEM (Hidekawa 211). This paper presents the simulation analysis about the damaged structure supported by pile in Hyogo-ken Nanbu (Kobe) earthquake. In addition, the influence of the ground improvement on the behavior of soil-pile-structure system is discussed. 2. Simulation analysis by 3D-FEM 2.1. Description of model The FE analysis was conducted about the collective housing which was a six story reinforced concrete structure and was supported by prestressed high strength concrete pile groups which consisted of two, three, or four piles (Kinki Branch 1996). The pile had 6mm outer diameter. Figure 1 shows the finite element mesh for the structure supported by piles and subsurface layers. In this simulation analysis, only N-S direction which was short side direction of superstructure was considered because N-S component of seismic ground motion in this area might be dominant by considered tipping condition of gravestone. So, the superstructure assumed to be linear. For the superstructure, the slabs and base foundation were modeled using 8-node rectangular solid elements with reduced integration, and the columns were modeled using 2-node beam elements. The properties of superstructure used in the analysis were summarized in Table 1. The slabs and base foundation were assumed to be rigid body with density and contact property, and the columns assumed to be linearly elastic with elastic modules E and Poisson s ratio. The natural period of 1 st mode under base fixed condition was.17 second. The piles were modeled using shell element, and assumed to have elastic-plastic bilinear model with coefficient of strain hardening and yield stress. The elastic module E and the coefficient of strain hardening and the yield stress were determined as the moment-curvature relationship of pile by FE analysis simulated that of pile by fiber analysis, as shown Figure 2. Each pile group was modeled one concentrated pile without a pile group effect. The edges of piles were fixed in all rotated coordinate directions and vertical direction, and were free in horizontal direction. The pile caps were fixed to base foundation rigidly. The contact condition, which allowed the slip and the separation of the contacting surfaces, was applied between the pile and the soil. The properties of surface layers used in the analysis were summarized in Table 2. The surface layers were modeled four layer on the basis of the result of borehole survey, and bedrock was modeled using elastic solid element, where the shear wave velocity Vs=45(m/s). The soil of which the surface layers consist was assumed to be a Mohr-Coulomb elastic-plastic constitutive model with no associated flow rule. For the side boundaries, the nodes which were same depth were constrained in all three coordinate directions. For the bottom boundaries, the nodes were fixed without short side direction in the superstructure, and the model was shaken under a one-direction input motion, as shown Figure 3.

3 Bending Moment (MN m) Superstructure Surface layer Direction of input motion (a) 3-D meshes for FEM Bedrock N S (b) Cross section view N S 58 (a) Plan view of soil around piles Fig.1 Layout of analysis model (unit:mm) Table1 Properties of structure Slab Collumn (6 6) GL Width Weight Hight Weight Young's Module (mm) (mm) (t) (mm) (t) (N/mm 2 ) RF F F F F F Foundation f (1/m) Fig.2 M-f relationship of pile Table2 Properties of surface layers GL N Vs (mm) Value (t/m 3 ) (mm) ~-2.m ~-5.m ~-1.m m~ Vs=8m/s Vs=11m/s Vs=25m/s

4 Acc. (m/s 2 ) Acc. (m/s 2 ) Acc. res. spectrum (m/s 2 ) 4 1 Input motion AIJ (a) Time history Fig.3 Input Motion 5 Period (s) (b) Acceleration response spectrum The input ground motion which was the bedrock motions at GL.-1m was evaluated by 2D FE Analysis using deep irregular underground model with vertical discontinuity, and the observation record at Motoyama elementary school. The input ground motion was acceleration record in N-S direction. Maximum acceleration value of the input motion is 8.23 m/s 2. As shown Figure 3 (b), the input ground motion is far larger than the seismic acceleration of the Japanese code. This superstructure suffered very little to minor damage and the pile caps suffered visible structural damage. Figure 4 shows the summary of damage investigation of pile cap at 1995 Hyogo-ken Nanbu (Kobe) earthquake. Pile caps which were suffered serious structural damage were 5 by visual check by Kinki Branch of AIJ and damaged piles were the member of pile groups which consisted of two or three piles Result of FE analysis Figure 5 shows the calculated acceleration responses of the superstructure (Base and RF) and the acceleration time history of input ground motion. The calculated results of superstructure are close to the input ground motion because the natural period of soil-pile-structure interaction system was shorter than the predominant period of input ground motion. X Y Z (a) Plan view of pile foundation (b) Summary of damage investigation by visual check( :serious damage) Fig.4 Summary of damage investigation of pile cap 15 Input Base RF Fig.5 Time history of acceleration

5 1. F all / W all Fig.6 Sum of the inertial forces over 1 st story (normalized by weight of structure) Figure 6 shows the time history of F all /W all, where F all =sum of the inertia forces of slabs and columns over 1 st story, W all =sum of the weight of slabs and columns over 1 st story. F all contains the shear force at 1 st story column and the inertia force by rocking behaviour. The maximum value of F all /W all is about.9 which is comparable to the base shear coefficient at Japan Level 2 Design Earthquake, and this result indicates that the superstructure may suffer some structural damage under this input motion. This result is not consistent with the investigation result by Kinki Branch. Figure 7 shows the distribution of maximum curvature for X, Y and Z pile in Figure 3, where f y = the curvature of yielding starting, f p = the curvature of full plasticity. The curvature at pile cap at X pile is greater than f p, whereas that at Y or Z pile is smaller than f p and greater than f y. On the other hand, as shown Figure 4, X pile which is the pile group model comprised of two piles suffered serious structural damage at pile cap, whereas Y and Z pile which are respectively the pile group model comprised of three and four piles suffered no visible structural damage. Therefore, the evaluations for FE analysis were larger than the observation. However, the deformation of X pile which has lower stiffness than Y or Z pile is largest in both the FE analysis and the observation. Figure 8 shows the distribution of maximum displacement of surface layer. The deformation of surface layer is large at the boundary where the shear wave velocity changes substantially, about G.L.-5m. The displacement at G.L.-m is about 7mm. Figure 9 shows the time histories of the result, Figure 9(a) shows the sum of the external force at the base foundation F ft, Figure 9(b) shows the displacement of ground surface and foundation and Figure 9(c) shows the curvature at pile cap at X pile. The inertial force peaks at 4.54s, and then the displacement of base foundation and the ground surface peaks at 4.8s and the curvature at the pile cap in X pile peaks at the same time. Figure 1 shows the time history of external force applying on base foundation. The sum of subgrade reaction acting on base foundation was calculated by subtracting the sum of shear force at pile caps from the sum of the inertial force at the base foundation. The sum of subgrade reaction is larger than the shear force.

6 Force (MN) f (1/m) Disp. (mm) F ft (MN) Depth (m) Depth (m) Curvature (1/m) Displacement (mm) X Y Z f y f p Fig.7 Distribution of maximum curvature -1 Fig.8 Distribution of maximum displacement of surface layer (a) Sum of external force at base foundation (b) Displacements of ground surface and foundation (c) Curvature at pile cap (Pile-X) Fig.9 Time histories of responses of soil-pile-structure system 25 Shearforce at pile cap Subgrade reaction at footing Fig.1 Time history of external force acting on base foundation

7 Depth (m) 2.3. Influence of inertia force and ground displacement on piles damage As shown Figure 1, the stresses in piles under the horizontal seismic motion can estimate to superpose the stresses generated by the shear force at pile cap (inertial) and one generated by the ground displacement (Kinematic). Figure 11 shows the comparison of maximum curvature in different calculation methods. Dynamic is the result that is mentioned in section 2.2. Inertial is the result of other analysis (static analysis) in which the base foundation was subjected monotonic displacement statically using the analysis model as Figure 1, changed the boundary condition of surface layer to fix in all coordination. The Inertial result is under loading maximum inertial force in Dynamic analysis. Kinematic is the result of another analysis in which the superstructure is cleared from the Dynamic analysis model and the weight of the base foundation is assumed.1 times as large as one in the default. This analysis is considered with the nonlinear state, and so it is not possible to superpose the stresses in a precise sense which are calculated in the different method. However, it may be possible to investigate the influence of inertia force and ground displacement on piles damage qualitatively. The curvature of Kinematic at the pile cap is about.25 times as large as one of Dynamic, and one of Inertial at the pile cap is about.4 times as large as one of Dynamic and the influence of inertial force is larger than on of ground displacement in this analysis. However, the curvature of Inertial at the pile cap is smaller than f y and the pile cap didn t become inelastic state under loading only the inertial force. The damage at pile cap may be understood from the following consideration: the shear force and the ground displacement applied at the same time as shown Figure 9(b). Shear force at pile cap Displacement of surface layers Curvature (1/m) Dynamic Inertial Kinematic Fig.11 Schematic of pile stresses induced by earthquake -11 Fig.12 Comparison of maximum curvature in different calculation methods f y f p 3. Effect of response reduction by ground improvement 3.1. Analysis model Figure 13 shows the pattern of ground improvement. Two analysis cases were conducted. In case of 1layer, the ground improvement was applied to 1 st layer in the model represented in

8 P (MN) Figure 1. In case of 2layer, the ground improvement was applied to 1 st and 2 nd layer. In both cases, all of soils in the layer were improved. Figure 14 shows shear stress shear strain relationships of improved soil. The improved soil was assumed to be a Mohr-Coulomb elastic-plastic constitutive model as in the case with surface layer and the curve was fitted to the result of the simple shear test. The improved soil model had the shear wave velocity Vs=14m/s, the friction angle f=8.9dgree and the cohesion c=.212n/mm 2. The maximum shear stress of improved soil was 2.5 times as large as that of the no improved soil at G.L.-5m, and 5times as large as at G.L.-2m Figure 15 shows the horizontal load displacement relationships at base foundation based on the static analysis. In figure 15, it can be seen that the load for 1layer or 2layer case was larger than that for no improved case (Normal). This can be interpreted as the increase of the lateral resistance of the surface layer. Improved ground Vs=11m/s Vs=25m/s (a) 1Layer (b) 2Layer Fig.13 Pattern of ground improvement.25 (N/mm 2 ) Test Analysis 6 Normal 1Layer 2Layer 6 (%) Fig.14 - curve of improved soil 6 (mm) Fig.15 Lateral force - displacement relationship of foundation 3.2. Result of analysis Figure 16 shows the result of the analysis about the effect of improved soil. Figure 16(a) shows the comparison of the time histories of the acceleration at RF, and Figure 16(b) shows that of the sum of the external force at the base foundation. In Figures 16(a) and (b), it can be seen that the acceleration and the external force for 1layer or 2layer case were larger than that for Normal case. Figure 16(c) shows the comparison of the distribution of the maximum curvature for X pile. In Figures 16(c), it can be seen that the maximum curvature for 1layer or 2layer case were smaller than that for Normal case. It is noted that the curvature at pile cap for 2layer is smaller than the f p, and especially that for 2layer is smaller than the f y. Figure 16(d) shows the comparison of the distribution of the maximum displacement of the surface layer. In Figure

9 F all (MN) Depth (m) Depth (m) Acc. (gal) 16(c), it can be seen that the displacement at ground surface for 2 layer case was smaller than that for 1layer case or Normal case. Figure 17 shows the distribution of plastic strain at the time about 4.8s when the maximum curvature occurred. It can be seen that the area of plasticity for 1layer or 2layer case were smaller than that for Normal case. Therefore, the displacement of surface layer was decreased by improved the ground. Thus, the reduction of pile response was caused by the ground improvement which led the increase of the lateral resistance of the surface layer as shown Figure 15 and the decrease of the displacement of ground as shown Figure 16(c). 2 Nomal 1Layer 2Layer Curvature (1/m) Displacement (cm) (a) Time histories of acceleration at RF Normal 1Layer 2Layer (b) Time histories of external force at base foundation -11 Fig.16 Effect of ground improvement -7-9 Normal 1Layer 2Layer f y f p (c) maximum curvature Normal 1Layer 2Layer (d) maximum displacement of subsurface layer (a) No improvement (b) 1Layer (c) 2Layer Fig.17 Distribution of plastic strain at time occurred maximum curvature 4. Conclusion The major findings obtained from analyses are summarized as follows; 1) The deformation of piles for FE analysis is a little larger than the observation. However, the deformation of pile which has low stiffness was largest in both the FE analysis and the observation.

10 2) The damage at pile cap may be understood from the following consideration: the shear force and the ground displacement applied at the same time 3) The reduction of pile response was caused by the ground improvement which led the increase of the lateral resistance of the surface layer and the decrease of the displacement of ground. Acknowledgements This work was supported in part of activities by Kinki Branch of AIJ. The authors express their sincere thanks to the above organization. References Kinki Branch of AIJ (1997). The reports of damaged structures, AIJ. Hidekawa, T., J.C., Kishimoto, M, Kashiwa, H., Miyamoto, Y. and Tamura, S. (1992). Earthquake response of building supported on piles considered with nonlinearity of pile-soil system, Journal of Structural and Construction Engineering, AIJ, No. 661,