A practical numerical method for large strain liquefaction analysis of saturated soils

Accurate prediction of the liquefaction of saturated soils is based on strong coupling between the pore fluid phase and soil skeleton. A practical numerical method for large strain dynamic analysis of saturated soils is presented. The u–p formulation is used for the governing equations that describe the coupled problem in terms of soil skeleton displacement and excess pore pressure. A mixed finite element and finite difference scheme related to large strain analysis of saturated soils based on the updated Lagrangian method is given. The equilibrium equation of fluid-saturated soils is spatially discretized by the finite element method, whereas terms associated with excess pore pressure in the continuity equation are spatially discretized by the finite difference method. An effective cyclic elasto-plastic constitutive model is adopted to simulate the non-linear behavior of saturated soils under dynamic loading. Several numerical examples that include a saturated soil column and caisson-type quay wall are presented to verify the accuracy of the method and its usefulness and applicability to solutions of large strain liquefaction analysis of saturated soils in practical problems.     

Dynamic responses of coastal structures during earthquakes including sediment–sea–structure interaction

The effects of the interaction among sea water, sediment, backfill-soil and coastal structures (embankments) were included in the present study. The formulation is derived from fundamental theories in various fields, including marine hydrodynamics, flow in porous medium, and structural dynamics. The hybrid finite-difference and finite element methods were used in the analysis. The finite-difference method was used to calculate the nonlinear hydrodynamic pressures of sea water as well as the pore water in the sediment acting on the coastal embankment faces by seismic-wave actions. The fluid-filled solid mixture was used to model sediment and back-fill soil and the corresponding dynamic responses were also evaluated by finite difference method. The dynamic response of the coastal structures was calculated by finite element method. The numerical results are presented for various water depths and ground motion intensities. The significant dynamic forces on coastal structures were calculated during earthquakes and the possible sliding of the coastal embankment will occur and the special foundation treatment should be made.     

软件ABAQUS在饱和土体动力响应分析中的应用

研究表明:地震作用下土体的动力特性及变形特性与超静孔隙水压力的发展变化密切相关,因此,在土体动力分析过程中考虑孔隙水压的影响是非常必要的。本文通过对基本方程的推导,借助于大型有限元软件ABAQUS,进行了饱和土体在动力作用下孔隙水压变化的数值模拟。计算结果表明,ABAQUS完全适用于此类问题的数值模拟,并且稳定性和收敛性较好。     

Energy approach to unsaturated cyclic strength of sand

The mechanical response to cyclic loading of saturated cohesionless soils is usually investigated by means of effective stress method considering pore water pressure changes that lead to reduced strength and stiffness. On the other hand, the behavior of partially saturated sands is different from the behavior of saturated sand deposits. The development of negative pore water pressures in particular makes it difficult to estimate the behavior of partially saturated sands. The response of partially saturated sands, however, can be examined in a physically understandable manner by investigating their energy characteristics independently of pore pressure behavior. To establish a general framework for understanding the behavior of partially saturated sand, a total of 52 resonant column and dynamic torsional shear tests were conducted under undrained conditions. The effects of factors such as the amplitude of shear strain, relative density, saturation ratio and confining pressure on the dynamic characteristics of the sand and on energy dissipation were studied. The use of the energy concept in the evaluation of partially saturated soils is shown to be a promising method for the evaluation of the cyclic behavior of partially saturated sands.     

Adaptive element free Galerkin method applied to analysis of earthquake induced liquefaction

An automatically adaptive element free method is presented to analyze the seismic response of liquefiable soils.The method is based on the element free Galerkin method (EFGM) and the fission procedure that is part of h-refinement,indicated by error estimation. In the proposed method, a posteriori error estimate procedure that depends on the energy normof stress and the T-Belytschko (TB) stress recovery scheme is incorporated. The effective cyclic elasto-plastic constitutivemodel is used to describe the nonlinear behavior of the saturated soil. The governing equations are established by u-pformulation. The proposed method can effectively avoid the volumetric locking due to large deformation that usually occursin numerical computations using the finite element method (FEM). The efficiency of the proposed method is demonstratedby evaluating the seismic response of an embankment and comparing it to results obtained through FEM. It is shown that theproposed method provides an accurate seismic analysis of saturated soil that includes the effects of liquefaction     

土石坝地震响应的非线性剪切条模型与对比分析

对一维剪切条计算模型进行改进,提出了土石坝非线性地震反应的简化计算方法。首先将坝体沿坝高离散为一系列的具有不同剪切刚度与阻尼比等参数特性的层状体系,建立了各层的振动控制方程及其边值条件,进而采用数学物理方程方法进行了求解,确定了体系的振动特性,并根据振型叠加原理和Duhamel积分确定了坝体地震反应的线弹性解。采用等价线性化方法考虑坝料的动力非线性性质,通过对线弹性地震响应的反复迭代计算,使得各层土的模量和阻尼比与其相应的剪应变水平相协调,确定出与非线性坝体系统相等效的线性解答,并将所得到的地震响应作为非线性地震响应的近似解。最后,以均质坝和心墙坝作为算例进行了具体的数值计算,将所得结果与有限元数值解进行对比分析,论证了所提方法的适用性和合理性。     

SV波在饱和土体自由表面的反射

基于饱和两相介质弹性波动方程分析SV波在饱和土体自由表面的反射问题,引入波动方程的势函数解答,求解出二维问题中SV波入射情况下饱和土体自由场的位移、速度、加速度和应力响应。在饱和土体自由场响应解析解基础上,建立SV波入射下饱和土体自由场静、动力有限元模型。建模中考虑了如下几方面因素:(1)在不同分析步,对土体单元赋予不同材料本构。通过*model change命令进行单元生死设定,从而实现在初始应力场平衡的静力状态下采用DuncanChang本构模型,而地震波动输入时采用Davidenkov动力本构模型;(2)采用多孔介质黏弹性人工边界条件,在人工边界上分别施加固相和液相介质的弹簧和阻尼来模拟饱和土体中能量的传播;(3)将地震波转化为作用在人工边界上的等效地震荷载,施加到人工边界节点上;(4)土体单元采用4结点平面应变孔压单元(CPE4P)。有限元计算与解析解比较结果表明:SV波在垂直入射和掠入射时,竖向位移响应为零;在45°左右入射时,水平位移响应最大;60°左右入射时,竖向位移响应最大。这些结论与解析解吻合较好,本文模型为建立土-结构动力相互作用模型打下良好的基础。     

饱和南京细砂永久应变势模型的试验研究

土单元永久应变势的预测模型是土动力学的重要研究内容之一。现有的土单元永久应变势模型没有反映振动孔压增长的影响,难以合理解释地震动作用引起的饱和砂土地基永久变形一般是由土层软化或再固结变形所致的机理。基于饱和南京细砂永久变形动三轴试验结果的有效应力状态分析,研究了试样的永久变形与振动孔压增长的关系,建立了一个能反映振动孔压增长影响的土单元永久应变势模型,给出了土单元永久应变势的数学表达式,分析了土单元永久应变势模型参数的影响因素。初步的验证性试验表明:模型预测与试验测得的试样永久应变势与振动孔压增长曲线比较接近,说明该模型具有一定的合理性。     

饱和土体瞬态响应有限元分析

给出基于Biot多孔介质理论分析饱和土体在动载荷作用下瞬态响应的有限元公式,数值计算部分采用本文有限元法分别计算一维饱和土柱在两种不同类型动载荷作用下的瞬态响应,并将数值计算结果与文献中的解析解进行比较,二者结果十分吻合,从而验证本文方法的可行性。     

可液化土层隧道围岩的动力响应及液化区发展分析

隧道可液化土层围岩对地震动作用非常敏感,可液化土层动孔压的产生和发展使得地下结构受到上浮作用,从而影响地下结构的稳定性.通过对可液化土层中隧道动力响应计算,研究了不同静应力场隧道围岩动孔压场分布、围岩液化区域分布以及衬砌结构仰拱底与拱顶的动孔压差变化.研究结果表明,不同静应力场对围岩可液化土的动孔压分布、液化区域分布及...     

Fully coupled numerical analysis of repeated shake-consolidation process of earth embankment on liquefiable foundation

It is known that a series of aftershocks might follow a mainshock, which may cause further damages on civil engineering structures. So it is necessary to investigate the dynamic response of structures undergone several shocks. This study presents a numerical analysis of repeated shake-consolidation process for an earth embankment founded on liquefiable foundation soils. Analysis is carried out using an effective stress-based, fully coupled, finite element method. The behaviors of the foundation soils are described by means of a cyclic mobility constitutive model which was developed at the bases of modified Cam-clay model by introducing concepts such as stress-induced anisotropy, over-consolidation, and structure. Results show that the cyclic mobility constitutive model can reflect the dynamic response of liquefiable soils. Special emphasis is given to analyze the result of excess pore water pressures, stress path, acceleration, and deformations during the two seismic excitation and consolidation process.     

基于流固耦合动力模型的饱和土体-隧道体系地震反应研究

基于ABAQUS软件平台,应用自行开发的流固耦合动力模型孔压单元模拟场地土体,并通过黏弹性人工边界方法实现地震动的输入,对饱和土体场地中的双孔隧道结构在地震荷载作用下的动力反应进行研究。计算结果表明:在地震反应结束时刻,场地土体位移幅值在两隧道之间以及两隧道的附近区域较大,而远离隧道的区域则较小;场地底部区域土体的孔压幅值较大,而场地顶部区域土体则较小;隧道左右两侧拱腰部位的衬砌的应力较大,而拱顶部位则较小。计算结果同时表明了流固耦合动力模型孔压单元在饱和土体-隧道体系地震反应研究中的适用性。     

横观各向同性饱和地基中埋置荷载的非轴对称瞬态响应

基于孔隙介质的Biot理论,首先利用Laplace变换,给出圆柱坐标系下横观各向同性饱和弹性多孔介质在变换域上的波动方程;将波动方程解耦后,根据方位角的Fourier展开和径向Hankel变换,求解了Biot波动方程,得到以土骨架位移、孔隙水压力和土介质总应力分量的积分形式的一般解;借助一般解,建立了有限厚度饱和土层和饱和半空间的精确动力刚度矩阵,并由土层的层间界面连续条件建立三维非轴对称层状饱和地基的总刚度方程;在此基础上,系统研究了横观各向同性饱和半空间体在内部集中荷载激励下的动力响应,并给出了问题的瞬态解答.该研究为运用边界元法求解饱和地基动力响应奠定了理论基础.     

The Mechanical Coupling of Fluid-Filled Granular Material Under Shear

The coupled mechanics of fluid-filled granular media controls the physics of many Earth systems, for example saturated soils, fault gouge, and landslide shear zones. It is well established that when the pore fluid pressure rises, the shear resistance of fluid-filled granular systems decreases, and, as a result, catastrophic events such as soil liquefaction, earthquakes, and accelerating landslides may be triggered. Alternatively, when the pore pressure drops, the shear resistance of these geosystems increases. Despite the great importance of the coupled mechanics of grain–fluid systems, the basic physics that controls this coupling is far from understood. Fundamental questions that must be addressed include: what are the processes that control pore fluid pressurization and depressurization in response to deformation of the granular skeleton? and how do variations of pore pressure affect the mechanical strength of the grains skeleton? To answer these questions, a formulation for the pore fluid pressure and flow has been developed from mass and momentum conservation, and is coupled with a granular dynamics algorithm that solves the grain dynamics, to form a fully coupled model. The pore fluid formulation reveals that the evolution of pore pressure obeys viscoelastic rheology in response to pore space variations. Under undrained conditions elastic-like behavior dominates and leads to a linear relationship between pore pressure and overall volumetric strain. Viscous-like behavior dominates under well-drained conditions and leads to a linear relationship between pore pressure and volumetric strain rate. Numerical simulations reveal the possibility of liquefaction under drained and initially over-compacted conditions, which were often believed to be resistant to liquefaction. Under such conditions liquefaction occurs during short compactive phases that punctuate the overall dilative trend. In addition, the previously recognized generation of elevated pore pressure under undrained compactive conditions is observed. Simulations also show that during liquefaction events stress chains are detached, the external load becomes completely supported by the pressurized pore fluid, and shear resistance vanishes.     

自适应时间步长法及三维堤坝地震液化数值模拟

三维大模型数值计算因巨大的单元和结点数目而非常耗时,在地震响应分析中受计算时间步长的限值则更加耗时。在饱和砂土动力液化计算平台上开发时域离散误差评估方法和时间步长自适应调整的计算程序,并成功应用于三维堤坝地震液化响应分析。时域离散误差包括土骨架的位移误差和单元孔压误差,通过定义孔压误差影响系数计算出混合误差,根据混合误差和设定的误差允许值进行计算步长的自适应调整。在三维堤坝地震液化数值模拟中,采用自适应时间步长法有效避免小步长精确但耗时、大步长省时而不精确的缺点。在大模型和超大模型计算中,最优调整每一步的计算时间步长,完美实现既节省时间又不失精度的时域离散策略。     

Seismic behavior of breakwaters on complex ground by numerical tests: Liquefaction and post liquefaction ground settlements

A large number of breakwaters have been constructed along coasts to protect humans and infrastructures from tsunamis.There is a risk that foundation soils of these structures may liquefy,or partially liquefy during the earthquake preceding a tsunami,which would greatly reduce the structures’capacity to resist the tsunami.It is necessary to consider not only the soil’s liquefaction behavior due to earthquake motions but also its post-liquefaction behavior because this behavior will affect the breakwater’s capacity to resist an incoming tsunami.In this study,numerical tests based on a sophisticated constitutive model and a soil-water coupled finite element method are used to predict the mechanical behavior of breakwaters and the surrounding soils.Two real breakwaters subjected to two different seismic excitations are examined through numerical simulation.The simulation results show that,earthquakes affect not only the immediate behavior of breakwaters and the surrounding soils but also their long-term settlements due to post-earthquake consolidation.A soil profile with thick clayey layers beneath liquefied soil is more vulnerable to tsunami than a soil profile with only sandy layers.Therefore,quantitatively evaluating the seismic behavior of breakwaters and surrounding soils is important for the design of breakwater structures to resist tsunamis.     

Study of pore pressure variation during liquefaction using two constitutive models for sand

Numerical analyses of liquefiable sand are presented in this paper. Liquefaction phenomenon is an undrained response of saturated sandy soils when they are subjected to static or dynamic loads. A fully coupled dynamic computer code is developed to predict the liquefaction potential of a saturated sandy layer. Coupled dynamic field equations of extended Biot's theory with u–P formulation are used to determine the responses of pore fluid and soil skeleton. Generalized Newmark method is employed for integration in time. The soil behavior is modelled by two constitutive models; a critical state two-surface plasticity model, and a densification model. A class ‘B’ analysis of a centrifuge experiment is performed to simulate the dynamic response of level ground sites. The results of the numerical analyses demonstrate the capability of the critical sate two-surface plasticity model in producing pore pressures that are consistent with observations of the behavior of liquefiable sand in the centrifuge test.     

Uplift mechanism for a shallow-buried structure in liquefiable sand subjected to seismic load: centrifuge model test and DEM modeling

Based on a centrifuge model test and distinct element method(DEM), this study provides new insights into the uplift response of a shallow-buried structure and the liquefaction mechanism for saturated sand around the structure under seismic action. In the centrifuge test, a high-speed microscopic camera was installed in the structure model, by which the movements of particles around the structure were monitored. Then, a two-dimensional digital image processing technology was used to analyze the microstructure of saturated sand during the shaking event. Herein, a numerical simulation of the centrifuge experiment was conducted using a two-phase(solid and fl uid) fully coupled distinct element code. This code incorporates a particle-fl uid coupling model by means of a "fi xed coarse-grid" fl uid scheme in PFC3D(Particle Flow Code in Three Dimensions), with the modeling parameters partially calibrated based on earlier studies. The physical and numerical models both indicate the uplifts of the shallow-buried structure and the sharp rise in excess pore pressure. The corresponding micro-scale responses and explanations are provided. Overall, the uplift response of an underground structure and the occurrence of liquefaction in saturated sand are predicted successfully by DEM modeling. However, the dynamic responses during the shaking cannot be modeled accurately due to the restricted computer power.     

Fully fluid-solid coupling dynamic model for seismic response of underground structures in saturated soils

The seismic response characteristics of underground structures in saturated soils are investigated. A fully fluid-solid coupling dynamic model is developed and implemented into ABAQUS with a user-defined element to simulate the dynamic behavior of saturated soils. The accuracy of the model is validated using a classic example in literature. The performance of the model is verified by its application on simulating the seismic response characteristics of a subway station built in saturated soils. The merits of the model are demonstrated by comparing the difference of the seismic response of an underground structure in saturated soils between using the fully coupling model and a single-phase medium model. The study finds that the fully coupling model developed herein can simulate the dynamic response characteristics of the underground structures in saturated soils with high accuracy. The seismic response of the underground structure tends to be underestimated by using the single-phase medium model compared with using the fully coupling model, which provides a weaker confining action to the underground structure.     

Dynamic analysis of slab track on multi-layered transversely isotropic saturated soils subjected to train loads

The dynamic responses of a slab track on transversely isotropic saturated soils subjected to moving train loads are investigated by a semi-analytical approach. The track model is described as an upper Euler beam to simulate the rails and a lower Euler beam to model the slab. Rail pads between the rails and slab are represented by a continuous layer of springs and dashpots. A series of point loads are formulated to describe the moving train loads. The governing equations of track-ground systems are solved using the double Fourier transform, and the dynamic responses in the time domain are obtained by the inverse Fourier transform. The results show that a train load with high velocity will generate a larger response in transversely isotropic saturated soil than the lower velocity load, and special attention should be paid on the pore pressure in the vicinity of the ground surface. The anisotropic parameters of a surface soil layer will have greater influence on the displacement and excess pore water pressure than those of the subsoil layer. The traditional design method taking ground soil as homogeneous isotropic soil is unsafe for the case of RE 1 and RG 1, so a transversely isotropic foundation model is of great significance to the design for high train velocities.