A NON-LINEAR SEISMIC RESPONSE ANALYSIS METHOD FOR SATURATED SOIL–STRUCTURE SYSTEM WITH ABSORBING BOUNDARY

A non-linear seismic response analysis method for 2-D saturated soil–structure system with an absorbing boundary is presented. According to the 3-D strain space multimechanism model for the cyclic mobility of sandy soil, a constitutive expression for the plane strain condition is first given. Next, based on Biot's two-phase mixture theory, the finite element equations of motion for a saturated soil–structure system with an absorbing boundary during earthquake loadings are derived. A simulation of the shaking table test is performed by applying the proposed constitutive model. The effectiveness of the absorbing boundary is examined for the 2-D non-linear finite element models subjected to random inputs. Finally, a numerical seismic response analysis for a typical saturated soil–structure system is performed as an application of the proposed method.     

阪神地震中大开地铁车站震害机制数值仿真分析

1995年阪神地震中,神户市的地下结构遭受了严重的破坏,尤其是地铁车站的破坏最为严重,其中大开地铁车站有一半以上的中柱发生坍塌,导致地面坍塌近2.5 m。对大开地铁车站的震害进行了全面地描述,基于大型商用有限元软件ABAQUS,采用在该软件上二次开发的土体非线性黏弹性动力本构模型模拟土在循环荷载作用下的动力特性,采用黏塑性动力损伤模型模拟混凝土在循环荷载作用下的拉、压应力-应变关系,对大开地铁车站的非线性地震反应进行了数值仿真分析,给出了破坏演化过程,把有限元分析的结果与大开地铁站的实际震害现象进行了对比,结果表明：数值仿真分析结果能够合理地解释大开地铁车站的主要震害现象,建模方法能够被用来进行地下结构的非线性地震反应分析。     

Earthquake source model using strong motion displacement as response of finite elastic media

The strong motion displacement records available during an earthquake can be treated as the response of the earth as the a structural system to unknown forces acting at unknown locations. Thus, if the part of the earth participating in ground motion is modelled as a known finite elastic medium, one can attempt to model the source location and forces generated during an earthquake as an inverse problem in structural dynamics. Based on this analogy, a simple model for the basic earthquake source is proposed. The unknown source is assumed to be a sequence of impulses acting at locations yet to be found. These unknown impulses and their locations are found using the normal mode expansion along with a minimization of mean square error. The medium is assumed to be finite, elastic, homogeneous, layered and horizontal with a specific set of boundary conditions. Detailed results are obtained for Uttarkashi earthquake. The impulse locations exhibit a linear structure closely associated with the causative fault. The results obtained are shown to be in good agreement with reported values. The proposed engineering model is then used to simulate the acceleration time histories at a few recording stations. The earthquake source in terms of a sequence of impulses acting at different locations is applied on a 2D finite elastic medium and acceleration time histories are found using finite element methods. The synthetic accelerations obtained are in close match with the recorded accelerations.     

随机覆盖下堤坝填筑工程非线性可靠度理论研究

基于Mohr-Coulomb破坏准则下材料的非线性特征,结合粘塑性应力空间内破坏准则被有限超越期间的稳定时间步长,对随机数学覆盖下粘塑性数值算法的逻辑实现过程进行推导,在直接偏微分理论基础上建立了三维及平面应变条件下粘塑性非线性随机有限元的本构关系式,进而提出了基于全量理论的粘塑性非线性随机有限元列式,并以堤防填筑工程为例,分析研究了土质堤坝分阶段逐步填筑过程中的随机演化机理及堤坝结构的可靠度安全性,实现了堤防填筑工程的全程随机模拟。     

近断层强地震动预测中的有限断层震源模型

提出了近断层强地震动预测中建立活断层上设定地震有限断层震源模型的方法和步骤.首先,根据地震地质和地震活动性调查以及地球物理勘探等资料,确定活断层的空间方位和滑动类型; 然后,根据地震定标律确定活断层的宏观震源参数; 第三,将高强体模型与k平方滑动模型相结合,产生断层破裂面上的混合滑动分布.在此基础上,预测了与1994年Northridge地震断层类型、矩震级(M_w6.7)基本一致的设定地震的有限断层震源模型.最后,将预测的有限断层震源模型与基于地震学的、使用动力学拐角频率的地震动随机合成方法相结合,预测了1994年Northridge地震近断层12个基岩台站的加速度时程,并和实际记录进行了对比.结果表明,用上述方法和步骤建立的有限断层震源模型是可行、实用的.      

土-地下结构体系地震反应的简化分析方法

基于Penzien提出的土-结构动力相互作用分析的集中质量模型,考虑等价土体的层间剪切刚度与阻尼效应,提出了土-地下结构动力相互作用体系地震反应分析的简化分析方法,选取具有不同地震动特性的Taft波、汶川地震什邡八角波和松潘波作为基岩水平向输入地震动,采用该简化方法和二维有限元法对土-地铁地下车站结构体系的地震加速度反应特性进行了对比分析,结果表明：简化方法计算的地铁地下车站结构峰值加速度反应大于二维有限元法计算的地铁地下车站结构峰值加速度反应,两者的差异与输入地震动特性有关,但其随地铁地下车站结构高度变化的总体趋势较为一致;随着输入地震动强度的增大,其差异程度也有所加大。该简化方法可合理反映土-地下结构体系的动力相互作用效应,可作为地下结构抗震设计分析的一种辅助方法。     

Numerical modeling of dredging effect on berthing structure

Piles and diaphragm wall-supported berthing structure on marine soils are loaded laterally from horizontal soil movements generated by dredging. The literature on the adequacy of the finite element method modeling of berthing structure to analyze their behavior during dredging is limited. This paper describes a finite element approach for analyzing the lateral response of pile and diaphragm wall during dredging. Piles are represented by equivalent sheet-pile walls and a plane strain analysis using the finite element method is performed. Results from the finite element method are compared with full-scale field test data. Full-scale field test was conducted on a bearing structure to measure the lateral deflection on pile and diaphragm wall for their full length using inclinometer during dredging in sequence. The finite element method results are in good agreement with full-scale field results. Conclusions are drawn regarding application of the analytical method to study the effect of dredging on piles and diaphragm wall-supported berthing structures.     

Stochastic modeling of seismic surface rotations

In this paper, a stochastic analysis of surface rotations during earthquakes is presented. The surface motion is modeled by a spacetime random field. A method to obtain rotation based on direct differentiation of the random field is proposed with a reference to a second method based on wave decomposition. The first method leads to a spectral density of surface rotations in terms of point translation spectral density, coherence function and apparent waves velocity, while the second method formulates the rotational spectrum in terms of point translation spectral density and wave parameters. The advantages and disadvantages of both methods are discussed in detail.On leave from: Faculty of Civil Engineering, Technical University, ul. Katowicka 48, 45–951 Opole Poland.     

盾构地铁隧道区间在地震作用下的三维动力时程响应分析

地铁已成为城市地下空间结构和轨道交通网络的重要组成部分。为预估和降低地震灾害的影响,以西安盾构地铁区间隧道为例,建立了地铁隧道区间三维计算模型,进行三维抗震时程响应分析。采用粘弹性局部人工边界模拟地基结构的半无限性,利用不同超越概率水平下的地震动参数作为参考,考虑相位随机性影响,拟合地震动时程样本,建立了地基与结构相互作用的三维有限元模型。计算结果表明,地震发生时,顶部、底面、侧面、以及联络通道处虽产生变形影响,但均在规范规定范围内;位移时程曲线、位移分布云图、拉压应力云图清楚显示区间结构在地震持续时的抗震情况,数据表明结构最不利位置在联络通道处,而内力和变形均满足规范安全要求。     

软土地下结构的地震土压力分析研究

在软土室内动力试验和有限元有效应力动力反应分析基础上,采用一种能够全面考虑软土振动孔压上升及消散、震陷、土-结构动力相互作用等因素的软土地下建筑物抗震稳定分析方法,对上海地铁一号线典型地铁车站结构进行地震土压力计算分析。据此对各类常用地震土压力简化计算方法进行评价,为今后改进地震土压力计算方法、提高软土地下建筑抗震设计水平提供了依据。     

Dynamics of unsaturated soils using various finite element formulations

Unsaturated soils are three‐phase porous media consisting of a solid skeleton, pore liquid, and pore gas. The coupled mathematical equations representing the dynamics of unsaturated soils can be derived based on the theory of mixtures. Solution of these fully coupled governing equations for unsaturated soils requires tremendous computational resources because three individual phases and interactions between them have to be taken into account. The fully coupled equations governing the dynamics of unsaturated soils are first presented and then two finite element formulations of the governing equations are presented and implemented within a finite element framework. The finite element implementation of all the terms in the governing equations results in the complete formulation and is solved for the first time in this paper. A computationally efficient reduced formulation is obtained by neglecting the relative accelerations and velocities of liquid and gas in the governing equations to investigate the effects of fluid flow in the overall behavior. These two formulations are used to simulate the behavior of an unsaturated silty soil embankment subjected to base shaking and compared with the results from another commonly used partially reduced formulation that neglects the relative accelerations, but takes into account the relative velocities. The stress–strain response of the solid skeleton is modeled as both elastic and elastoplastic in all three analyses. In the elastic analyses no permanent deformations are predicted and the displacements of the partially reduced formulation are in between those of the reduced and complete formulations. The frequency of vibration of the complete formulation in the elastic analysis is closer to the predominant frequency of the base motion and smaller than the frequencies of vibration of the other two analyses. Proper consideration of damping due to fluid flows in the complete formulation is the likely reason for this difference. Permanent deformations are predicted by all three formulations for the elastoplastic analyses. The complete formulation, however, predicts reductions in pore fluid pressures following strong shaking resulting in somewhat smaller displacements than the reduced formulation. The results from complete and reduced formulations are otherwise comparable for elastoplastic analyses. For the elastoplastic analysis, the partially reduced formulation leads to stiffer response than the other two formulations. The likely reason for this stiffer response in the elastoplastic analysis is the interpolation scheme (linear displacement and linear pore fluid pressures) used in the finite element implementation of the partially reduced formulation. Copyright © 2008 John Wiley & Sons, Ltd.     

A multilaminate constitutive model accounting for anisotropic small strain stiffness

In this paper an extension of existing multilaminate soil models is presented, which can account for inherent and stress‐induced cross‐anisotropic elasticity in the small strain range and its dependency on the load history. In the multilaminate framework, material behaviour is formulated on a number of local planes in each stress point, and the macroscopic response of the material is obtained by integration of the local contributions. Strain‐induced anisotropy, which adds to the stiffness anisotropy inherently present in the material, is therefore intrinsically taken into account. Micro–macro relations between local parameters on plane level and global parameters on macroscopic level are obtained by the spectral decomposition of the global elastic compliance matrix. The model is implemented into a finite‐element code, and model predictions are compared with experimental data of triaxial tests on different soils involving small and large load cycles. The importance of cross‐anisotropic elasticity within the small strain range for predicting ground deformations in geotechnical boundary value problems is discussed at the example of an excavation problem. Copyright © 2012 John Wiley & Sons, Ltd.     

岩体弹粘塑性显式波动有限元分析

真实反映地震动传播特性的分析方法是准确描述岩体地震反应的基础。基于显式波动有限元,采用能够考虑应变率影响的弹粘塑性本构模型,提出了一种用于分析岩体地震反应的新方法,编制了相应的计算程序。以均质岩石边坡为例,计算了EL-CENTRO波输入下边坡的位移和应力反应,并将计算结果与采用粘弹性本构模型的结果进行了比较,初步验证了程序的可靠性。计算结果表明,所提出的新方法能够较合理地计算出地震作用下边坡的永久位移和残余应力。      

浅基础沉降可靠性的摄动随机有限元法

将二阶非线性摄动随机有限元理论和土性参数随机场的离散技术相结合,可以处理岩土工程中由多种不确定因素带来的结果的不确定性。与一阶摄动随机有限元相比,二阶摄动随机有限元具有较高的计算精度。笔者探讨了这一方法,考虑土性分布参数和荷载变异性,用二阶摄动随机有限元法进行了浅地基沉降的概率分析。     

青藏铁路冻土路基温度场随机有限元分析

从一阶Taylor展开式入手,结合冻土温度场计算有限元法,推导了冻土路基温度场随机有限元方程及有关计算公式,并对青藏铁路北麓河试验段冻土路基温度场进行了随机有限元分析,结果表明温度标准差与温度场的分布趋势大致相同,在垂直方向上,最大值都出现在路基上部,向下逐渐减小,但两者分布范围略有不同,路基内部标准差的分布范围明显较大,在一定深度处达到均化。     

多地貌单元复合场地非线性地震效应特征二维分析

针对由河漫滩、阶地、波状起伏的丘陵地带和残丘等组成的典型复合地形场地,基于ABAQUS软件的显式有限元并行计算集群平台,考虑土体的非线性特征,采用黏弹性人工边界模拟切除的无限域对地震波动的影响,建立了大尺度复合地形真实场地的二维有限元模型,并将基岩地震动视为SH波,分析了不同地貌单元复合场地地震效应特征。结果表明：地形差异引起地表各测点峰值加速度(PGA)及峰值位移(PGD)不同;在相同地震波入射下,河漫滩区地表PGA大于Ⅰ级阶地区域,但其PGD明显小于Ⅰ级阶地区域,且河漫滩区的峰值位移差动较小;场地地表水平加速度反应谱呈双峰及多峰现象,加速度在0.4～1.2 Hz频段放大较多,且加速度反应谱特性与输入地震动相关;特定频段（0.5～1.75 Hz）地震动放大效应与聚集效应比较明显,频率小于0.2 Hz及大于2 Hz时,场地地震动放大特征不显著。低丘区的敏感频率段宽于河漫滩区;观测点的位置影响相应的水平加速度持时大小,局部地形变化将引起地震动持时差异,且持时和输入地震动特性相关。     

Stochastic Modeling of Variably Saturated Transient Flow in Fractal Porous Media

This work presents the application of a Monte Carlo simulation method to perform an statistical analysis of transient variably saturated flow in an hypothetical random porous media. For each realization of the stochastic soil parameters entering as coefficients in Richards' flow equation, the pressure head and the flow field are computed using a mixed finite element procedure for the spatial discretization combined with a backward Euler and a modified Picard iteration in time. The hybridization of the mixed method provides a novel way for evaluating hydraulic conductivity on interelement boundaries. The proposed methodology can handle both large variability and fractal structure in the hydraulic parameters. The saturated conductivity K _s and the shape parameter _vg in the van Genuchten model are treated as stochastic fractal functions known as fractional Brownian motion (fBm) or fractional Gaussian noise (fGn). The statistical moments of the pressure head, water content, and flow components are obtained by averaging realizations of the fractal parameters in Monte Carlo fashion. A numerical example showing the application of the proposed methodology to characterize groundwater flow in highly heterogeneous soils is presented.     

Stochastic finite element modelling of water flow in variably saturated heterogeneous soils

Water flow is greatly influenced by the characteristics of the domain through which the process occurs. It is generally accepted that earth materials have extreme variations from point to point in space. Consequently, this heterogeneity results in high variation in hydraulic properties of soil. In order to develop an accurate predictive model for transport processes in soil, the effects of this variability should be considered. In this study a two‐dimensional stochastic finite element flow model was developed for simulation of water flow through unsaturated soils. In this model, the stochastic partial differential governing equation of water flow, obtained from implementation of the perturbation‐spectral stochastic method on classical Richard's equation, was solved using a finite element method in the space domain and a finite difference scheme in the time domain. The effective hydrological parameters embedded in the mathematical model depend on time derivatives of capillary tension head; this makes possible to consider the hysteresis due to large‐scale variability of soil hydrological properties. The model is also capable of simulating infiltration and evaporation events and rapid change in the land surface boundary condition from one type event to another, based on a scheme used in the model for implementation of land surface boundary condition. The model was validated with the data obtained from a layered lysimeter test. The model was also used to simulate water flow under a long irrigation furrow. The results obtained with this model show better agreement with experimental measurements in comparison with a deterministic model. The possible reason for this agreement is that in the developed model, the influence of the variability of the properties of soil and effects of parameter hysteresis on water flow and water content redistribution are considered. Copyright © 2010 John Wiley & Sons, Ltd.     

Performance of mixed and enhanced finite elements for strain localization in hypoplasticity

Displacement and mixed finite element formulations of shear localization in materials are presented. The formulations are based on hypoplastic constitutive laws for soils and the mixed enhanced treatment involving displacement, strain and stress rates as independently varied fields. Included in these formulations are the standard displacement method, the three‐field mixed formulation, the enhanced assumed strain method and the mixed enhanced strain method. Several numerical examples demonstrating the capability and performance of the different finite element formulations are presented. The numerical results are compared with available experimental data for Hostun RF sand and numerical results for Karlsruhe sand on biaxial tests. Copyright © 2011 John Wiley & Sons, Ltd.     

Reliability analysis of serviceability performance for an underground cavern using a non-intrusive stochastic method

This paper proposes a non-intrusive stochastic analysis procedure for reliability analysis of the serviceability performance of an underground cavern with an implicit limit state function. This procedure is formulated on the basis of the stochastic response surface method (SRSM) and the deterministic finite element method. First, the SRSM is briefly introduced and implemented through a MATLAB code. Then, the software SIGMA/W is used to perform a deterministic finite element analysis. Next, a link between the MATLAB code and SIGMA/W is developed to automatically pass exchange data between the two platforms. Finally, two examples are presented to illustrate the capacity and validity of the proposed procedure. In the first example, a closed-form limit state function is adopted to validate the SRSM by comparing it with the results obtained from a direct Monte Carlo simulation. In the second example, the serviceability performance of an underground cavern is analyzed to illustrate the capacity of the proposed procedure to handle a reliability problem with an implicit limit state function. The proposed procedure does not require the user to modify the existing deterministic finite element code. The deterministic finite element analysis and the probabilistic analysis are decoupled. This is a major practical advantage because realistic probabilistic analyses are made possible. The SRSM can produce sufficiently accurate reliability results. Furthermore, the method is much more efficient than the direct Monte Carlo simulation. Sensitivity analyses show the effect of the variability of input random variables and the correlation between them on: (1) the probability density functions, (2) the first four order statistical moments, and (3) the probability of failure, which is investigated and discussed.