A discrete element model for simulating saturated granular soil

A numerical model is developed to simulate saturated granular soil, based on the discrete element method. Soil particles are represented by Lagrangian discrete elements, and pore fluid, by appropriate discrete elements which represent alternately Lagrangian mass of water and Eulerian volume of space. Macro-scale behavior of the model is verified by simulating undrained biaxial compression tests. Micro-scale behavior is compared to previous literature through pore pressure pattern visualization during shear tests. It is demonstrated that dynamic pore pressure patterns are generated by superposed stress waves. These pore-pressure patterns travel much faster than average drainage rate of the pore fluid and may initiate soil fabric change, ultimately leading to liquefaction in loose sands. Thus, this work demonstrates a tool to roughly link dynamic stress wave patterns to initiation of liquefaction phenomena.     

Discrete simulation and micromechanical analysis of two-dimensional saturated granular media

In this study, a novel approach to incorporate the pore water pressure in the discrete element method (DEM) to comprehensively model saturated granular media was developed. A numerical model was constructed based on the DEM by implanting additional routines in the basic DEM code; pore water pressure calculations were used with a two-dimensional (2D) model to simulate the undrained behavior of saturated granular media. This model coupled the interaction of solid particles and the pore fluid in saturated granular media. Finally, several 2D undrained shear tests were simulated. The test results showed that the model could predict the response of the saturated granular soil to shear loading. The effect of initial compaction was investigated. Biaxial tests on dense and loose specimens were conducted, and the effect of the initial density on the change in shear strength and the volume change of the system was investigated. The overall behavior of loose and dense specimens was phenomenologically similar to the real granular material. Constant volume tests were simulated, and the results were compared to those from the coupled model. Induced anisotropy was micromechanically investigated by studying the contact force orientation. The change in anisotropy depended on the modeling scheme. However, the overall responses of the media obtained using the coupled and constant volume methods were similar.     

Discrete simulation and micromechanical analysis of two-dimensional saturated granular media

In this study, a novel approach to incorporate the pore water pressure in the discrete element method （DEM） to comprehensively model saturated granular media was developed. A numerical model was constructed based on the DEM by implanting additional routines in the basic DEM code; pore water pressure calculations were used with a two-dimensional （2D） model to simulate the undrained behavior of satu- rated granular media. This model coupled the interaction of solid particles and the pore fluid in saturated granular media. Finally, several 2D undrained shear tests were simulated. The test results showed that the model could predict the response of the saturated granular soil to shear loading. The effect of initial compaction was investigated. Biaxial tests on dense and loose specimens were conducted, and the effect of the initial density on the change in shear strength and the volume change of the system was inves- tigated. The overall behavior of loose and dense specimens was phenomenologically similar to the real granular material. Constant volume tests were simulated, and the results were compared to those from the coupled model. Induced anisotropy was micromechanically investigated by studying the contact force orientation. The change in anisotropy depended on the modeling scheme. However, the overall responses of the media obtained usinz the couoled and constant volume methods were similar.     

A model for compaction and shear hysteresis in saturated granular materials

Fluid-saturated sands exhibit irreversible compaction and shear hysteresis under cyclic shear loads in both free draining and undrained conditions. Constitutive relations of differential-type are constructed heuristically from typical qualitative response. An influence of pore pressure on compaction is incorporated, and the generation of pore pressure under cyclic shearing is investigated. Parameter variations in the shear relations allow a variety of hysteresis loop behaviours to be described.     

Mechanical Behaviors of Saturated Sand under Complicated Loading

The different physical states of saturated sand, including shear elasticity, positive dilatancy, and negative dilatancy (preliminary negative dilatancy, secondary negative dilatancy and reversal negative dilatancy) are revealed based on the pore water pressure response of saturated sand in undrained dynamic torsional tests of thin cylinder samples and also checked by the drained cyclic triaxial tests under a given mean effective normal stress. According to the effective stress path of different physical states under the undrained cyclic torsional tests the physical state transformation surface, stress history boundary and yield surface are determined, and the state boundary surface is also determined by the range of effective frictional stress state movement. Based on the moving yield surface without rotation, and the expanding stress history boundary surface relevant to the stress path variations under different physical states in 3D stress space, a physical state model is proposed to provide a new app     

基于尖点突变模型的地震液化和孔压研究

地震液化是一种严重的自然灾害，然而如何准确判断液化目前作的还很不成功。本文以经过持时修正的能量函数和经过粘粒及上覆压力修正的标贯击数为控制变量，以孔压发展为状态变量，根据液化的物理意义、室内孔压发展曲线的特点和国内外实测液化资料，建立了基于修正Zeeman突变方程的孔压液化发展模型。在此基础上，利用统计学中控制“弃真”概率的方法，确定了分叉曲线和新旧坐标之间的转换关系并且从统计的角度给出了不同土的孔压发展曲线。从孔压发展曲线看，对于R＞0的任何土，超静水压力均达不到1，其实这正好反映了宏观液化现象。在宏观震害中，只要有喷水冒砂现象即认为是液化，超静水压力只要能克服埋深而无须达到上覆压力即可使地下水到达地面从而显现宏观液化现象。检验结果表明这一模型是合理的。     

ROTATIONAL RESISTANCE AND SHEAR-INDUCED ANISOTROPY IN GRANULAR MEDIA

This paper presents a micromechanical study on the behavior of granular materials under confined shear using a three-dimensional Discrete Element Method （DEM）. We consider rotational resistance among spherical particles in the DEM code as an approximate way to account for the effect of particle shape. Under undrained shear, it is found rotational resistance may help to increase the shear strength of a granular system and to enhance its resistance to liquefaction. The evolution of internal structure and anisotropy in granular systems with different initial conditions depict a clear bimodal character which distinguishes two contact subnetworks. In the presence of rotational resistance, a good correlation is found between an analytical stress-force-fabric relation and the DEM results, in which the normal force anisotropy plays a dominant role. The unique properties of critical state and liquefaction state in relation to granular anisotropy are also explored and discussed.     

剪胀性砂土边界面模型的研究

剪胀性对于砂土,尤其是中密以及密实砂土,是一个非常显著的特性。相变线是剪胀性砂土的特征曲线,能够反映砂土的围压以及初时孔隙比对变形特性的影响。本文在边界面塑性理论的框架内,把相变状态参量引入到剪胀方程以及塑性硬化模量中,建立了一个能够描述砂土剪胀性以及循环特性的本构模型。本模型采用一套参量可以模拟不同初时孔隙比、不同围压、排水(或不排水)条件下单调(或循环)加载的应力-应变特性。验证表明本模型数值计算与试验结果相吻合。     

不排水条件下土石混合料双轴压缩离散元模拟

基于离散单元法构建了考虑碎石形状的柔性边界不排水双轴压缩模型,研究了11组不同含石量土石混合料在不排水条件下的宏细观力学特性。研究发现,(1)土石混合料强度随含石量增加先增后减,含石量超过约60%时形成碎石骨架,强度快速增长;含石量约80%时强度和内摩擦角最大;含石量增加,混合料黏聚力逐渐减小。(2)不排水受载下,土石混合料孔隙水压力先正后负、先增后减。含石量较小时,含石量增加,混合料孔隙水压力变化较小,混合料在碎石骨架形成初期孔隙水压力增加;碎石骨架完全形成后最大孔隙水压力减小。(3)含石量小于约30%时,混合料应变局部化呈规则剪切带,随后含石量增加破坏规则剪切带,当含石量约为80%时,混合料再次形成规则剪切带。含石量增加,配位数逐渐减小,颗粒间接触力在含石量小于60%时随含石量增加缓慢增长,超过70%时则快速增长。     

Pore pressure generation in a saturated sand layer subjected to a cyclic horizontal acceleration at its base

A compaction theory for saturated sand, of differential type, is applied to shear wave propagation through a layer induced by cyclic horizontal acceleration of its base. The compaction relation incorporates dependence on the pore fluid pressure, and in turn the pore pressure is related to the compaction through the elastic compression relations. An assumption of undrained flow, which will yield the maximum pore pressures, allows straightforward numerical solution of the simplified dynamic equations. A variety of results are computed for comparison with alternative predictions.     

The role of a realistic volume constraint in modelling a two dimensional granular assembly

This paper presents a deceptively simple mathematical model for the deformation of granular materials composed of rigid particles. The model captures many of the diverse features of the behaviour of such a material and emphasises the importance of volume constraints in situations where the deformation is mainly by particle rearrangement. It is constructed using a simple dissipation function and a rather more complicated dilatancy rule containing an updateable reference strain. This allows the solid-like and fluid-like properties of granular materials to be reconciled in a single model.The model has been used to simulate experiments that use an analogue of an ideal granular material [Joer, H.A., Lanier, J., Fahey, M., 1998. Deformation of granular materials due to rotation of principal axes. Geotechnique 48 (5), 605-619] consisting of a two dimensional assembly of thin PVC rods. These experiments clearly illustrate: partially reversible dilatancy in direct shear tests; cyclic shearing leading to liquefaction in constant volume shear tests; and non-coaxiality of the principal axes of stress and strain increment in circular loading tests. These radically different modes of deformation provide a challenging data set that allows the model's potential to be clearly demonstrated.The authors believe that the comparison of these experimental results and our simulations give strong support to the assertion that volume changes associated with shear deformation are responsible for the rotational kinematic hardening seen in granular materials, and hence, the non-coaxiality of the stress and strain-rate tensors.     

A numerical investigation into the behavior of ground-supported concrete silos filled with saturated solids

This paper introduces a finite-element solution for simulating the filling process of ground-supported concrete silos filled with saturated granular material. An elasto-plastic axisymmetric finite-element model is used to represent both the granular material and the concrete silo. The interaction between the two materials is modeled using interface elements to allow for relative movement. The filling process is idealized via a multi-stage numerical technique capable of representing both undrained and drained conditions for the granular material. The effects of the relative stiffness between the foundation and wall are examined, as are the boundary conditions at the top of the structure (the roof details).Depending on the drainage properties of the stored material, the effect of the filling process may be time-dependent. The excess pore water pressure resulting from the filling process may cause a substantial increase in the hoop stresses in the wall. The predicted internal forces may be influenced by the foundation rigidity, but not by the boundary condition at the top of the wall.The results of these analyses may be used to design experiments to evaluate existing silos, or to develop filling strategies to minimize loads on existing structures.     

FEM-FDM coupled liquefaction analysis of a porous soil using an elasto-plastic model

The phenomenon of liquefaction is one of the most important subjects in Earthquake Engineering and Coastal Engineering. In the present study, the governing equations of such coupling problems as soil skeleton and pore water are obtained through application of the two-phase mixture theory. Using au-p (displacement of the solid phase-pore water pressure) formulation, a simple and practical numerical method for the liquefaction analysis is formulated. The finite difference method (FDM) is used for the spatial discretization of the continuity equation to define the pore water pressure at the center of the element, while the finite element method (FEM) is used for the spatial discretization of the equilibrium equation. FEM-FDM coupled analysis succeeds in reducing the degrees of freedom in the descretized equations. The accuracy of the proposed numerical method is addressed through a comparison of the numerical results and the analytical solutions for the transient response of saturated porous solids. An elasto-plastic constitutive model based on the non-linear kinematic hardening rule is formulated to describe the stress-strain behavior of granular materials under cyclic loading. Finally, the applicability of the proposed numerical method is examined. The following two numerical examples are analyzed in this study: (1) the behavior of seabed deposits under wave action, and (2) a numerical simulation of shaking table test of coal fly ash deposit.     

垂向动载下饱和砂土液化发展的数值模拟

针对一维应变情况,建立了垂向荷载作用时饱和砂土的一维应变动力学模型,然后进行了分析。得到了在垂向荷载作用下,饱和砂土液化发展过程的特性。结果表明,渗透系数越小,骨架强度越低,扰动强度越大,液化发展越快。     

Numerical study of shear band instability and effect of cavitation on the response of a specimen under undrained biaxial loading

This paper presents an extension of the local second gradient model to multiphasic materials (solids particles, air, water) and including the cavitation phenomenon. This new development was made in order to model the response of saturated dilatant materials under deviatoric stress and undrained conditions and possibly, in future, the behavior of unsaturated soils. Some experiments have showed the significance of cavitation for the hydromechanical response of materials. However, to date and as far as we are aware, no attempt was made to implement the cavitation as a phase change mechanism with a control of pore pressure. The first part of the results section explores the effects of permeability, dilation angle and loading rate on the stability of shear bands during a localization event. The reasons underlying the band instability are discussed in detail, which helps defining the conditions required to maintain stability and investigating the effects of cavitation without parasite effect of materials parameters or loading rate. The model showed that, if a uniform response is obtained, cavitation triggers localization. However, in case of a localized solution, cavitation follows the formation of the shear band, with the two events being quite distinct.     

循环剪切荷载作用下软土的力学性状研究

利用从现场取得的原状土样,通过室内动三轴试验对循环荷载作用下的变形、孔压和强度特性进行研究。试验研究主要考虑了周围固结压力、循环剪切应力比、荷载频率和循环次数等因素的影响。研究表明,在循环荷载作用下,孔隙水压力和轴向应变均是一个波动上升的过程。当循环应力比增大时,动孔隙水压力变化幅值显著增加,而残余孔压也较大。同时,孔隙水压力值也随着周围压力的增大而明显增大。当作用荷载频率比较大时,需要更多的循环次数才能达到小频率作用荷载能达到的孔隙水压力值。但是,随着循环荷载作用次数的增加,频率对孔隙水压力的影响有减小的趋势。     

Effect of dilatancy on the strain localization of water-saturated elasto-viscoplastic soil

It is well known that geomaterials such as soils exhibit an increase in volume during shearing deformation, referred to as dilatancy. Dilatancy is a typical property of such granular materials as soils and is closely related to changes in the microstructure. Normally consolidated clay exhibits negative dilatancy or contractancy, namely, a decrease in volume during shearing. On the other hand, overconsolidated clay shows positive dilatancy, namely, an increase in volume during shearing. The aim of the present paper is to study the effects of the microstructure, such as dilatancy and permeability, on the strain localization of water-saturated clay using an elasto-viscoplastic constitutive model. Based on the non-linear kinematic hardening theory and a Chaboche type of viscoplasticity model, an elasto-viscoplastic model for both normally consolidated and overconsolidated clays is proposed; the model can address both negative and positive dilatancies. Firstly, the instability of the model under undrained creep conditions is analyzed in terms of the accelerating creep failure. The analysis shows that clay with positive dilatancy is more unstable than clay with negative dilatancy. Secondly, a finite element analysis of the deformation of water-saturated clay is presented with focus on the numerical results under plane strain conditions. From the present numerical analysis, it is found that both dilatancy and permeability prominently affect shear strain localization behavior.     

Static liquefaction of a saturated loose sand stratum

The ideal case of an infinite horizontal, homogeneous oedometrically consolidated saturated loose sand stratum, sheared in displacement controlled conditions is numerically analysed. The phenomenon of the stratum liquefaction, which is due to both the material mechanical instability and the water presence within pores, is discussed. The numerical results have been obtained by means of a spatial one dimension finite difference numerical code within which both the local and the non-local versions of the same elasto-viscoplastic constitutive model are implemented. Both pore water and shear strain wave propagation within the soil layer is described.     

考虑热渗效应的有限长圆柱热固结解

在作者已建立的饱和多孔介质耦合非线性热弹性理论基础上,考虑热渗效应,建立了饱和多孔介质耦合热弹性固结方程,并推导了有限长圆柱热固结问题的解析解,进而以温控三轴试验的试样为例进行了算例分析,同时利用COMSOL软件进行了数值模拟,并将解析结果和数值结果进行对比．结果表明：在不排水条件下,影响试样最终孔压大小的参数是：土的泊松比>弹性模量>水的体膨胀系数,渗透系数对孔压变化影响不大,考虑与不考虑水土压缩性不影响孔压的计算;相对线弹性情况,考虑非线弹性膨胀系数随温度变化时的孔压有所下降,轴向应变变化很小．     

透水与隔水夹层对粉质土液化影响试验研究

黄河三角洲沉积物以粉质土为主,循环荷载作用下隔水夹层与透水夹层的存在对粉质土孔压累积、消散及液化的影响如何,目前尚不清楚。本文针对4种隔水夹层与透水夹层的组合情况,利用现场原位振动和室内土样振动试验,研究隔水夹层与透水夹层的存在对循环荷载作用下黄河口粉质海床土液化过程影响,发现循环荷载导致黄河三角洲粉质土孔隙水压力、粒度成分、密度、含水量及孔隙比等物性指标发生的变化,因夹层的不同有明显的差异,并且其液化性能因夹层结构的不同而不同,有透水夹层时,相对提高了粉土的抗液化性能,隔水夹层则相反。