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A Study on Seismic Analysis Methods in the Cross Section of Underground Structures Using Static Finite Element Method

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A Study on Seismic Analysis Methods in the Cross Section of Underground Structures Using Static Finite Element Method Structural Eng./Earthquake Eng., JSCE, Vol.22, No. 1, 41s-53s, 2005 April A STUDY ON SEISMIC ANALYSIS METHODS IN THE CROSS SECTION OF UNDERGROUND STRUCTURES USING STATIC FINITE ELEMENT METHOD Akira TATEISHI1 1Member of JSCE, Dr. Eng., Civil Engineering Research Institute, TAISEI CORPORATION (344-1, Nase-cho, Totsuka-ku, Yokohama 245-0051, Japan) Based on the dynamic substructure technique, the author proposes a static seismic analysis method, the Ground Response Method, for underground structures modeled on the structure and surrounding soil that is expressed using finite elements. By comparing existing static seismic analysis methods, it is veri- fied that the Ground Response Acceleration Method for Buried Structures provides results almost equivalent to those obtained from the Ground Response Method. However, the FEM Seismic Deforma- tion Method yields different results. Thus, the author proposes a new seismic load that is equivalent to seismic ground strains and modifies the FEM Seismic Deformation Method. Key Words : underground structure, seismic design, substructure method, static finite element method, seismic load 1. OUTLINE above knowledge and these can be classified into two groups in terms of modeling techniques for the The dynamic behavior of underground structures surrounding soil. One of these techniques is of soil- has been demonstrated through verification studies spring type, in which the surrounding soil is mod- such as the several earthquake observations and eled using springs; the representative method is the model vibration experiments. Based on the results, seismic deformation method. The seismic deforma- the characteristics of this behavior of underground tion method has been primarily adapted to the seis- structures have been identified as: mic design of slender underground structures in the a) Underground structures have no predominant longitudinal direction, such as that of a buried pipe, vibration modes themselves and are dependent as described in Establishment of New Aseismic De- on the surrounding soil. sign Method 1). In 1985, the method was modified b) The deformation of underground structures is for the seismic design of underground structures in controlled by relative displacements or strains the transverse direction of nuclear power plants and of the surrounding soil. its applicability was shown2). The advantages of the A few static seismic analysis methods for under- methods of the soil-spring type are that the model- ground structures have been proposed based on the ing is relatively easy and that the resulting stresses of underground structures can be expressed by sim- ple equations. Hence, this type is widely used for This paper is translated into English from the Japa- the seismic design of underground structures. The nese paper, which originally appeared on J. Struct. other type is the soil-FEM type, in which the sur- Mech. Earthquake Eng., JSCE, No.519/I-32, pp.139- rounding soil is modeled with finite elements. One 148, 1995.7. 41s of the representative methods of this type is the ground structure based on the dynamic substructure seismic deformation method proposed by Hamada method is proposed. Through a comparison between et al.3), 4), which is used for design of underground the seismic loads of the static substructure method rock caverns in the transverse direction. The other is and the existing methods, the author proposes a new Ground Response Acceleration Method for Buried method of seismic load application and verifies the Structures (GRAMBS) proposed by Katayama5), 6). validity through numerical analyses of the under- In this paper, the seismic deformation method of the ground duct. Finally, characteristics of the existing soil-FEM type is called the FEM Seismic Deforma- methods and the methods proposed in this paper are tion Method (FSDM) in order to distinguish it from compared. the seismic deformation method of the soil-spring type. The advantages of the soil-FEM type are that the calculation of soil-spring constants is not neces- 2. STATIC SEISMIC ANALYSIS METH- sary and that the seismic stability of surrounding ODS OF THE SOIL-FEM TYPE soil can be obtained using the resulting stresses of FEM elements of soil as well as those of under- (1) FEM seismic deformation method ground structures. Hamada et al.3), 4) demonstrated that the seismic In general, the dynamic substructure method 7) is strains of the surrounding soil was statically trans- one of the most effective methods for analyzing ferred to an underground rock cavern according to dynamic interaction behavior of a finite region such the record of earthquake motions at a mountain tun- as a structure or the soil surrounding the structure, nel. This phenomenon had been already introduced which, in reality, is continuous in a half-space. With in a seismic design method of a tunnel structure in regard to the static seismic analysis method of the the longitudinal direction. Based on these findings, soil-spring type, the author studied a seismic load FSDM was proposed. In this method, the maximum for the seismic deformation method based on the seismic strains of soil are calculated, the under- dynamic substructure method and verified that ground structure is not modeled (termed as a free seismic stresses and seismic deformation of soil field), and then the relative displacements obtained should be applied to an underground structure. The from the calculated strains are applied to the outer author then proposed the modified method 8). boundaries of an FEM model that expresses the sur- On the other hand, with regard to the static seis- rounding soil of an underground rock cavern. The mic analysis method of the soil-FEM type, Hibino surrounding soil is modeled with finite elements in et al. conducted dynamic FEM analyses and static order to study the seismic stability of the surround- FEM analyses using FSDM and GRAMBS for a ing soil as well as the tunnel structure. A conceptual large underground rock cavern. The results showed figure of a seismic load of FSDM is shown in Fig. 1. that the maximum stresses of the concrete lining of the cavern obtained using GRAMBS were in good (2) Ground response acceleration method for agreement with those obtained using the dynamic buried structures FEM; however, the stresses obtained using FSDM Katayama5), 6) insisted that existing empirical cal- were not in good agreement9). There is a big differ- culation methods of a subgrade reaction spring for ence between FSDM and GRAMBS in terms of the seismic deformation method didn't have enough seismic load application; the former is a seismic accuracy. Hence, in place of the seismic deforma- displacement of soil and the latter is an inertia force tion method, he proposed GRAMBS based on the of soil respectively. It can be seen that there remains characteristics of the dynamic behavior of under- an unsolved problem in the static seismic analysis ground structures. In this method, the surrounding method of the soil-FEM type. Therefore, the author soil is modeled by means of finite elements and ac- attempts to theoretically demonstrate the seismic celerations are calculated in a free field. The calcu- load application of a static seismic analysis method lated accelerations are then applied to the FEM of the soil-FEM type based on the dynamic sub- model, including an underground structure, in which structure method. horizontal rollers are set at side boundaries in the Following is an outline of the paper. First, existing case of horizontal earthquake motions. A conceptual static seismic analysis methods of the soil-FEM type figure of a seismic load of GRAMBS is shown in are introduced, and then comparative analyses of an Fig. 2. This method has been adapted to the seismic underground duct in the transverse direction are design of underground ducts, shafts, and rock cav- conducted using the existing methods, in order to erns. examine the unsolved problem. Second, a static sub- structure method of the soil-FEM type for an under- 42s Ground GL GL displacement GL-15 m Sandy layer Sandy layer GL-30 Table m 1 Physical propertiesGL-30 of mduct Rocky layer Rocky layer Material Reinforced concrete (a) Covered duct model (b) Uncovered duct model Density 2.4 t/m3 Fig. 3 Ground and duct model7 2 Young modulus 2.65×10 kN/m Fig. 1 Seismic load of FSDM Poisson ratio 0.2 Ground damping ratio 0.05 acceleration 3.2 4.8 0.8 0.8 0.83.40.4 3.4 0.8 8.8 Unit ; m Horizontal Horizontal roller roller Fig. 4 Dimensions of duct model model of the ground and the duct is shown in Fig. 3 and the dimensions of the duct are shown in Fig. 4. The duct is modeled using a linear elastic beam element. The physical properties of the duct mate- rial are shown in Table 1. In the case of the sandy Fig. 2 Seismic load of GRAMBS layer, an effective overburden stress dependency of modulus and the strain dependency of modulus re- duction and damping are taken into consideration. The rocky layer is modeled using a linear elastic material. The physical properties of the soil are 3. COMPARATIVE STUDY THROUGH shown in Table 2. NUMERICAL ANALYSES The input earthquake motion is the acceleration time history of the EL CENTRO NS-component whose maximum acceleration is normalized to 300 In order to identify problems in existing static cm/sec2; the acceleration time history is input to the seismic analysis methods of the soil-FEM type, nu- rock surface at a depth of GL-30m as a shear wave. merical analyses by means of a dynamic FEM, FSDM, and GRAMBS were conducted using an (2) Numerical methods underground duct in the transverse direction as an First, one-dimensional site response analysis object of study. The maximum seismic section based on the multi-reflection theory for layered soil forces obtained from the numerical analyses were (termed as the multi-reflection analysis) is con- then compared.
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