ABAQUS 소프트웨어를 이용한 콘크리트 중력댐의 지진손상해석
Seismic Damage Analysis Of Concrete Gravity Dam Using ABAQUS
신 동 훈*∙Nghia N.T.**∙박 한 규***∙박 경 호****
Dong-Hoon∙Shin, Nguyen Trong∙Nghia, Han-Gyu∙Park, Kyung-Ho∙Park
1)
ABSTRACT
This study deals with 2D and 3D nonlinear seismic damage analysis of a concrete gravity dam using the finite element program ABAQUS and the concrete damaged plasticity model. 2D and 3D spillway sections of the dam are simulated. First the frequency analysis is conducted to compare the fundamental frequency and estimate the value of damping coefficient. Then the seismic analysis is conducted using the simulated ground acceleration motion. The relative displacement between the crest and bottom of the dam is obtained and compared for the maximum value and occurrence time. The results indicate that the plane-stress assumption gives similar results of maximum relative displacement and final damage distribution with 3D analysis.
keywords : Seismic Analysis, Concrete Gravity Dam, Plastic Damage Model
1. Introduction
For the estimation of the seismic damage or fracture of concrete dams, including gravity dams and arch dams, numerical investigations have been conducted in 2D and 3D space using the nonlinear concrete models (Calayir & Karaton, 2005; Leger & Leclerc, 1996; Wu et al., 2008), such as the discrete crack approach and fracture mechanics, the smeared crack approach, the continuum damage mechanics approach, and the plastic damage approach. Usually the plane-stress assumption is used for the seismic analysis of concrete gravity dams, while the full three-dimensional (3D) analysis is performed for concrete arch dams.
This study deals with 2D and 3D nonlinear seismic damage analysis of a concrete gravity dam using the finite element program ABAQUS. The applicability of the conventional plane-stress assumption is evaluated by comparison with 3D analysis using the concrete damaged plasticity model. In order to compare 2D and 3D analyses, two different cases of spillway sections of the dam are considered: (1) Case 1: 2D plane stress analysis for flushing sluice section and (2) Case 2: 3D analysis of three sets of spillway and flushing sluice sections. The similarity and difference of 2D and 3D analyses in fundamental
** 정회원∙한국수자원공사 shindh@kwater.or.kr
* ** Asian Institute of Technology *** 한국수자원공사 hgpark@kwater.or.kr
**** Asian Institute of Technology khpark@ait.ac.th
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frequency, relative displacement and resulting damage distribution are discussed.
2. Numerical modeling
The modeling meshes for two cases are shown in Fig. 1. Case 1 is 2D plane stress analysis for flushing sluice section, using 486 4-noded solid elements. This case is usually used for the seismic analysis of concrete gravity dams. Case 2 is 3D analysis of a combination of three sets of spillway and flushing sluice sections, using 8214 8-noded solid elements.
The damage behavior of the concrete material is modeled using the concrete damaged plasticity model provided by ABAQUS, which is based on the models proposed by Lubliner et al. (1989) and Lee &
Fenves (1998). This model can consider the effects of stiffness degradation and strength reduction due to cracks using the characteristics of concrete material in the concrete tension stiffening and concrete tension damage. The concrete material is assumed uniform with typical values of unit weight=2400 g/cm3, elastic modulus=30 GPa, Poisson's ratio=0.2, dilation angle=36.3o, ultimate tensile strength=2.5 MPa, ultimate compressive strength=15 MPa.
Full-scale concrete gravity dam is modeled with the assumption of rigid foundation. The dam-reservoir interaction is considered by using the Westergaard added mass technique.
Fig 1 Modeling meshes: (a) Case 1 and (b) Case 2
3. Results and discussions
First the frequency analysis is carried out to estimate the fundamental frequency and the value of damping coefficient. Table 1 shows frequency up to the first four modes for two cases. The fundamental modes of Case 1 (2.70 Hz) and Case 2 (2.87 Hz) are similar. The damping coefficient of 0.00347 is used for the seismic analysis using the simulated ground acceleration motion.
The time history of relative displacement between the crest and bottom of the dam is shown in Fig.
2.
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Mode
Frequency (Hz)
Case 1 Case 2
1 2 3 4
2.7004 6.6408 7.1812 7.7382
2.8741 3.2559 4.7760 4.9642 Table 1 Frequency extract
-25 -20 -15 -10 -5 0 5 10 15 20 25
0 5 10 15 20 25 30
Time (sec)
Horizontal displacement
Fc
Sc
Mdd
Mdu
-25 -20 -15 -10 -5 0 5 10 15 20 25
0 5 10 15 20 25 30
Time (sec)
Horizontal displacement
Sc
Fc
Mdd
Mdu
Fig 2 Relative displacement
Fig 3 Damage distribution
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In the figure, Fc indicates the first crack initiation, Sc the second crack initiation, Mdd the maximum relative displacement toward downstream, and Mdu the maximum relative displacement toward upstream.
Case 1 and Case 2 give similar result of maximum relative displacement around 18-22 mm. However, there is a difference for the time and location of first and second damage/crack initiation. For Case 1, the damage is firstly observed at 5.04 sec near the heal, while for Case 2 the first crack initiates at 3.952 sec in the upper part of the dam.
The tensile damage distribution over the dam at the end of the ground motion is shown in Fig. 3.
The tensile damage appears in the upper and base parts of the dam. The resulting damage distributions are similar for the cases.
Acknowledgments
The authors gratefully acknowledge the financial and other support provided by the Royal Thai Government, Korea Water Resources Corporation, and Dodam E&C Co., Ltd..
Reference
Calayir, Y., Karaton, M. (2005) Seismic fracture analysis of concrete gravity dams including dam-reservoir interaction, Computers & Structures, 83, pp.1595-1606.
Leger, P., Leclerc M. (1996) Evaluation of earthquake ground motions to predict cracking response of gravity dams, Engineering Structures, 18, pp.197-200.
Lee, J., Fenves, G.L. (1998) A plastic-damage concrete model for earthquake analysis of dams. Earthquake Engineering and Structural Dynamics, 27, pp.937-956.
Lubliner, J., Oliver, J., Oller, S., Onate, E. (1989) A plastic-damage model for concrete. International Journal of Solids and Structures, 25(3), pp.299-326.
Wu, Y.S., Yu, S.Y., Kung C.S. (2008) Seismic damage analysis of FEI-TSUI arch dam using finite element program ABAQUS, Proceeding EASEC-11, pp.470-471.
