Seismic response of arch dams considering infinite radiation damping and joint opening effects

Effects of two important factors on earthquake response of high arch dams are considered and combined into one program. These factors are: effects of radiation damping of the infinite canyon and local non-linearity of the contraction joint opening between the dam monoliths. For modeling of rock canyon, the discrete parameters are obtained based on a curve fitting, thus allowing the nonlinear dam system to be solved in the time domain. The earthquake uniform free-field input at the dam-canyon interface is used. An engineering example is given to demonstrate the significant effects of the radiation damping on the structure response.     

Application of FE-BE-IBE coupling to dynamic interaction between alluvial soil and rock canyons

A method of coupling finite elements (FE), boundary elements (BE) and infinite boundary elements (IBE) in the frequency domain is presented for wave propagation and soil-structure interaction problems. The procedure has the advantage of being suitable for considering non-homogeneous materials in the near region and the radiation condition at the far field. At the same time, the displacement field on the traction free boundary of the semi-plane is simulated by the IBE rather than by additional discretization of the ground surface as is required in the normal BE procedure. Verification examples show that excellent accuracy is achieved compared with the results by Wong¹⁸ who used the generalized inverse method. Finally, the proposed procedure is employed to obtain the response of a semi-elliptical rock canyon-alluvial deposit under seismic P and SV waves. Amplification behaviour due to the alluvial soil is observed to be significant for the given geometric dimensions of the canyon and the mechanical properties of the media under the excitation of the El Centro and Parkfield earthquakes.     

Nonlinear seismic response analysis of arch dam-foundation systems- part I dam-foundation rock interaction

The arch dam–foundation rock dynamic interaction and the nonlinear opening and closing effects of contact joints on arch dam are important to the seismic response analysis of arch dams. Up to date, there is not yet a reasonable and rigorous procedure including the two factors in seismic response analysis. The methods for the analysis of arch dam–foundation rock dynamic interaction in frequency domain are not suitable to the problem with nonlinear behaviors, in this paper, so an analysis method in time domain is proposed by combining the explicit finite element method and the transmitting boundary, and the dynamic relaxation technique is adopted to obtain the initial static response for dynamic analysis. Moreover, the influence of arch dam–foundation dynamic interaction with energy dispersion on seismic response of designed Xiaowan arch dam in China is studied by comparing the results of the proposed method and the conventional method with the massless foundation, and the local material nonlinear and nonhomogeneous behaviors of foundation rock are also considered. The reservoir water effect is assumed as Westergaard added mass model in calculation. The influence of the closing–opening effects of contact joints of arch dam on the seismic response will be studied in another paper.     

Seismic soil–structure interaction of massive flexible strip-foundations embedded in layered soils by hybrid BEM–FEM

A study on the seismic response of massive flexible strip-foundations embedded in layered soils and subjected to seismic excitation is presented. Emphasis is placed on the investigation of the system response with the aid of a boundary element–finite element formulation proper for the treatment of such soil–structure interaction problems. In the formulation, the boundary element method (BEM) is employed to overcome the difficulties that arise from modeling the infinite soil domain, and the finite element method (FEM) is applied to model the embedded massive flexible strip-foundation. The numerical solution for the soil–foundation system is obtained by coupling the FEM with the BEM through compatibility and equilibrium conditions at the soil–foundation and soil layer interfaces. A parametric study is conducted to investigate the effects of foundation stiffness and embedment on the seismic response.     

Seismic response of base-isolated liquid storage tanks considering fluid–structure–soil interaction in time domain

The seismic response analysis of a base-isolated liquid storage tank on a half-space was examined using a coupling method that combines the finite elements and boundary elements. The coupled dynamic system that considers the base isolation system and soil–structure interaction effect is formulated in time domain to evaluate accurately the seismic response of a liquid storage tank. Finite elements for a structure and boundary elements for liquid are coupled using equilibrium and compatibility conditions. The base isolation system is modeled using the biaxial hysteretic element. The homogeneous half-space is idealized using the simple spring-dashpot model with frequency-independent coefficients. Some numerical examples are presented to demonstrate accuracy and applicability of the developed method.Consequently, a general numerical algorithm that can analyze the dynamic response of base-isolated liquid storage tanks on homogeneous half-space is developed in three-dimensional coordinates and dynamic response analysis is performed in time domain.     

A seismic free field input model for FE-SBFE coupling in time domain

A seismic free field input formulation of the coupling procedure of the finite element (FE) and the scaled boundary finite-element (SBFE) is proposed to perform the unbounded soil-structure interaction analysis in time domain. Based on the substructure technique, seismic excitation of the soil-structure system is represented by the free-field motion of an elastic half-space. To reduce the computational effort, the acceleration unit-impulse response function of the unbounded soil is decomposed into two functions; linear and residual. The latter converges to zero and can be truncated as required. With the prescribed tolerance parameter, the balance between accuracy and efficiency of the procedure can be controlled. The validity of the model is verified by the scattering analysis of a hemi-spherical canyon subjected to plane harmonic P, SV and SH wave incidence. Numerical results show that the new procedure is very efficient for seismic problems within a normal range of frequency. The coupling procedure presented herein can be applied to linear and nonlinear earthquake response analysis of practical structures which are built on unbounded soil. Supproted by: the National Key Basic Research and Development Program under Grant No. 2002CB412709     

Three-dimensional analysis of spatially varying ground motions around a uniform canyon in a homogeneous half-space

Department of Civil Engineering, University of California, Berkeley, CA 94720, U.S.A. A direct boundary element method to determine the three-dimensional seismic response of an infinitely-long canyon of arbitrary but uniform cross-section cut in a homogeneous viscoelastic half-space is presented. The seismic excitation is represented by P, SV, SH or Rayleigh waves at arbitrary angles with respect to the axis of the canyon. The accuracy of the procedure and implementing computer program is demonstrated by comparison with previous solutions for the limiting case of two-dimensional response, recently obtained three-dimensional response results for infinitely-long canyons, and three-dimensional boundary method solutions presented in this paper for finite canyons.     

Two-dimensional dynamic analysis of concrete gravity and embankment dams including hydrodynamic effects

An analysis procedure in the frequency domain is developed for determining the earthquake response of two-dimensional concrete gravity and embankment dams including hydrodynamic effects; responses of the elastic dams and compressible water are assumed linear. The dam and fluid domain are treated as substructures and modelled with finite elements. The only geometric restriction is that an infinite fluid domain must maintain a constant depth beyond some point in the upstream direction. For such an infinite uniform region, a finite element discretization over the depth is combined with a continuum representation in the upstream direction. The fluid domain model approximately accounts for interaction between the fluid and underlying foundation medium through a damping boundary condition applied along the reservoir bottom, while the dam foundation is assumed rigid. Several examples are presented to demonstrate the accuracy of the fluid domain model and to illustrate dam responses obtained from the analysis procedure.     

Analytic solutions for soil-structure interaction in layered media

The total system studied in this paper is a layered soil stratum with a rigid bedrock and a cylindrical cavity on the surface. Analytic solutions for the layered medium with prescribed harmonic displacement time history on the surface of the cylindrical cavity are presented. The whole soil domain is divided into interior and exterior domains. The interior domain is the projection of the cylindrical cavity down to the rigid bedrock, whereas the exterior domain is then the soil medium complement to the interior domain. The displacement and stress fields in both domains are expanded as an infinite series of Fourier components with respect to the azimuth. For each Fourier component in the infinite series, the solutions for both domains are found independently by solving the general differential equations of wave propagation satisfying the boundary conditions of the top surface and the lower rigid boundary. Displacement and stress continuity conditions are then imposed on the vertical interface between the two domains using the formulation of a weighted residual. For the soil-structure interaction problem, the impedance matrix at the interface between the structure and the soil medium can be easily generated using the analytic solutions, which can then be combined with the finite element model of the structure. A simple example is presented to demonstrate the effectiveness of the procedure presented.     

基于流固耦合统一计算框架的三维大规模海域场地地震反应分析?以东京湾为例

海域场地地震响应分析是确定海洋工程结构抗震设计地震动输入的重要环节。然而,针对海水、饱和土、基岩之间的流固耦合分析,目前一般通过对3种介质方程进行离散,然后整体求解或分区耦合求解的方式进行,过程复杂而低效。因此,大规模海域场地地震反应分析仍是一个挑战性问题。本文基于流固耦合统一计算框架求解海域近场波动问题,采用透射边界模拟无限域,通过将海水和基岩视为孔隙率分别等于1和0的广义饱和多孔介质,使得海水、饱和土、基岩之间的相互耦合可在统一计算框架中实现,避免不同介质求解器之间的数据交换。采用集中质量显式有限元并行计算,不同进程之间采用MPI进行数据交换,提高计算效率;采用逐元技术,按单元类别存储单元刚度,大大节省了内存,便于大规模计算。通过自编程,输入界面高程数据和材料参数,实现建模-自由场-三维地震动模拟全流程自动化。以东京湾为例,使用该方法和程序在超级计算机上模拟SV波垂直入射时的地震响应,证实了该方法用于三维大规模海域地震波场模拟的高效性和可行性。     

Dam-reservoir-massed foundation system and travelling wave along reservoir bottom

In the present paper, effects of non-uniform excitation due to spatially variation of seismic waves under the reservoir bottom on linear and nonlinear responses of arch dams are studied. Foundation is assumed to be massed and infinite elements are utilized to model semi-infinite medium via the far-end boundary of the foundation FE model. A continuum crack propagation model based on the smeared crack approach in 3D space is introduced. Reservoir's water is assumed compressible and the coupled system is solved using the staggered method. As a case study, Amir-Kabir double curvature arch dam in Iran is selected to investigate seismic behavior of the system. Two cases are analyzed in which wave travelling velocities are taken as 650 m/s and infinity. According to the results, non-uniform excitation leads to reduction in seismic response of the system and, in addition, frequency content of the response is different completely in comparison with the system under the uniform excitation.     

Seismic analysis of underground tunnels by the 2.5D finite/infinite element approach

A procedure for the seismic analysis of underground tunnels using recorded free-field earthquakes based on the 2.5D finite/infinite element approach is presented. The near and far fields of the half space are modeled by finite and infinite elements, respectively. Using the 1D wave theory, the nodal force and displacement on the near-field boundary are computed for each spectral frequency of the earthquake. Then, equivalent seismic forces are computed for the near-field boundary for the earthquake spectrum. By assuming the soil-tunnel system to be uniform along the tunnel axis, the 2.5D approach can account for the wave transmission along the tunnel axis, which reduces to the 2D case for infinite transmission velocity. The horizontal and vertical components of the 1999 Chi-Chi Earthquake (TCU068) are adopted as the free-field motions in the numerical analysis. The maximal stresses and distribution patterns of the tunnel section under the P- and SV-waves are thoroughly studied by the 2.5D and 2D approaches, which should prove useful to the design of underground tunnels.     

Efficient seismic analysis for nonlinear soil-structure interaction with a thick soil layer

The direct finite element method is a type commonly used for nonlinear seismic soil-structure interaction(SSI) analysis. This method introduces a truncated boundary referred to as an artificial boundary meant to divide the soilstructure system into finite and infinite domains. An artificial boundary condition is used on a truncated boundary to achieve seismic input and simulate the wave radiation effect of infinite domain. When the soil layer is particularly thick, especially for a three-dimensional problem, the computational efficiency of seismic SSI analysis is very low due to the large size of the finite element model, which contains an whole thick soil layer. In this paper, an accurate and efficient scheme is developed to solve the nonlinear seismic SSI problem regarding thick soil layers. The process consists of nonlinear site response and SSI analysis. The nonlinear site response analysis is still performed for the whole thick soil layer. The artificial boundary at the bottom of the SSI analysis model is subsequently relocated upward from the bottom of the soil layer(bedrock surface) to the location nearest to the structure as possible. Finally, three types of typical sites and underground structures are adopted with seismic SSI analysis to evaluate the accuracy and efficiency of the proposed efficient analysis scheme.     

徐淮地区煤矿井筒破裂原因初探

本用震源力学理论和方法研究了徐淮地区从１９７０年以来构造应力场的方向和强度的时空变化过程。结果表明：以唐山地震为分界线，本区的应力场Ｐ轴取向由震前平均６１．８°变为震后平均７７．７°。如果将本区以宿北断裂为界分为南区和北区两个部分，则北区的Ｐ轴取向从６８．１°变７１．２°，而南区的Ｐ轴取向由６２．５°变到８３．６°，南区的变化明显于北区。     

Seismic analysis of base-isolated liquid storage tanks using the BE–FE–BE coupling technique

A three-dimensional soil–structure–liquid interaction problem is numerically simulated in order to analyze the dynamic behavior of a base-isolated liquid storage tank subjected to seismic ground motion. A dynamic analysis of a liquid storage tank is carried out using a hybrid formulation, which combines the finite shell elements for structures and the boundary elements for liquid and soil. The system is composed of three parts: the liquid–structure interaction part, the soil–foundation interaction part, and the base-isolation part. In the liquid–structure interaction part, the tank structure is modeled using the finite elements and the liquid is modeled using the internal boundary elements, which satisfy the free surface boundary condition. In the soil–foundation interaction part, the foundation is modeled using the finite elements and the half-space soil media are modeled using the external boundary elements, which satisfy the radiation condition in the infinite domain. Finally, above two parts are connected with the base-isolation system to solve the system's behavior. Numerical examples are presented to demonstrate the accuracy of the developed method, and an earthquake response analysis is carried out to demonstrate the applicability of the developed technique. The properties of a real LNG tank located in the west coast of Korea are used. The effects of the ground and the base-isolation system on the behavior of the tank are analyzed.     

Analytical and numerical analysis of pressure drawdown in a poroelastic reservoir with complete overburden effect considered

Starting from an analytical reservoir model that incorporates full interaction with an elastic overburden, a new hybrid mathematical approach is developed by combining two numerical discretization methods. A tabular reservoir (petroleum reservoir or an aquifer) in an infinite or semi-infinite domain is viewed as a macroscopic displacement discontinuity, allowing use of the efficient displacement discontinuity mathematical method to calculate stresses and displacements that arise because of pressure changes. A 3-D finite element method using a poroelastic formulation is used to discretize the reservoir itself. By coupling the displacement discontinuity and finite element methods, a 3-D large-scale poroelastic reservoir can be simulated within an infinite or semi-infinite domain. The numerical model has been verified through comparison to known solutions, and some time-dependent pressure drawdown problems are analyzed. Results indicate that including the complete overburden (reservoir surroundings) response has a significant effect on pressure drawdown in a poroelastic reservoir during pumping, and should be incorporated in appropriate applications such as well test equations and subsidence analyses.     

考虑坝体材料非线性的混凝土拱坝地震反应分析

本文基于可信概率水准的破坏性强震作用,针对小湾高拱坝进行了考虑坝体材料非线性的拱坝地震反应分析。在分析模型中,同时考虑了无约束域地震能量辐射效应和近域地基材料非均匀性的影响。为了实现非线性条件下的静、动力组合分析,利用显式有限元结合修正的黏弹性人工边界的开放系统时域静、动力统一分析方法进行了求解,对在自重作用下的初始静力解计算采用了动力松弛技术。     

高拱坝体系整体抗震安全评价方法研究

采用非线性地震波动反应分析方法，将坝体、地基、库水的强震反应本质上作为满足体系中接触面边界约束条件的波传播问题，在时域内以显式有限元方法求解。在不同概率水平的地震波作用下进行高拱坝与地基体系的有限元时程分析，并建议了以坝体位移反应发生突变为依据的拱坝体系整体失稳判断准则，从而建立了进行高拱坝体系整体抗震安全评价的方法，并以小湾拱坝为算例，对其抗震安全度作出初步评价。     

斜入射条件下地下结构时域地震反应分析初探

通过采用平面波和远场散射波混合透射的应力人工边界条件,得到了地震波斜入射的解析方式,以此为基础建立了地震波斜入射条件下,土体与地下结构动力相互作用的时域计算分析模型。以实际建设的南京地铁某车站结构为研究对象,应用大型通用有限元分析软件ANSYS,进行了地震波斜入射条件下地下结构时域地震反应的计算和分析。初步结果表明:在地震波斜入射的情况下,地下结构的动力反应与地震波垂直入射时有较为明显的差异。