A discrete element model for simulating saturated granular soil

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一种三维饱和土--基础--结构动力相互作用分析方法

一种三维饱和土--基础--结构动力相互作用分析方法陈少林;赵宇昕【摘要】地震波入射时土与结构动力相互作用分析是地震工程领域的重要问题。

由于问题的复杂性，以往的研究大多考虑地基土为干土情形。

而实际工程中，土体中经常充满孔隙水，土层往往是含水层或部分含水层。

孔隙水对土层的地震反应影响较大，进而影响支撑于其上的基础和上部结构的响应。

因此，有必要考虑饱和土-基础-结构动力相互作用问题。

基于此，土体采用Biot模型，利用集中质量显式有限元方法并结合多次透射人工边界进行模拟；结构经有限元离散后，采用Newmark隐式时步积分方法进行分析，可通过ANSYS等有限元软件实现；基础假定为刚性，采用显式时步积分进行求解；土体和结构(及基础)可分别采用不同的时间步距；通过FORTRAN程序实现了三维饱和土-基础-结构系统在地震作用下的整体分析。

从饱和多孔介质动力微分方程出发可知，干土是饱和土的特殊情形，通过将流体体积模量及孔隙率置为零，可将饱和土退化到干土，从而将干土统一到饱和土的计算框架中，通过土-结构相互作用算例对此进行了验证，进一步实现了干土与饱和土混合情形时的土-结构动力相互作用分析，使得问题的模拟更贴近实际工程(如考虑地下水位情形)。

通过算例对比了饱和土地基、干土地基、干土覆盖饱和土地基(考虑地下水位)情形时，土-结构相互作用对基础和结构响应的影响，结果表明地下水位对基础和结构响应的影响较大。

%Analysis of soil-structure dynamic interaction subjected to seismic wave is a key problem in earthquake engineering. In general, the soil stratum consists of two-phase saturated porous zones and single-phase viscoelastic zones due to ground water. In most cases of soil-structure dynamic interaction analysis, the soil has been assumed to be a single-phase viscoelastic medium for simplicityand little attention has been paid to the saturated porous soil case, even less to case of the viscoelastic soil layered on saturated soil. In this study, an eﬃcient method for three-dimensional saturated soil-foundation-structure dynamic interaction analysis is proposed. The unbounded saturated soil is modelled by lumped-mass explicit finite element method and transmitting boundary condition the structure is analysed through implicit finite element method, and response of the rigid foundation is calculated through explicit time integration scheme. The different time steps can be chosen for the explicit and implicit integration scheme, which can greatly improve the eﬃciency. In addition, based on the fact that single-phase soil is a special case of two-phase saturated soil, the dynamic analysis of single-phase soil can be unified into the analysis of saturated soil by setting the bulk modulus of pore fluid and porosity to be zero. Thus, the soil-structure interaction analysis for the viscoelastic soil layered on saturated soil case is realized, which can approximate the ground water table in practice. The effects of ground water on the response of foundation and structure are examined through numerical examples of soil-structure interaction analysis for saturated soil, single-phase viscoelastic soil and the viscoelastic soil layered on saturated soil, and the results show that the ground water influences the structure and foundation responses greatly.【期刊名称】《力学学报》【年(卷),期】2016(048)006【总页数】10页(P1362-1371)【关键词】土-结构动力相互作用;饱和多孔介质;显-隐式积分方法;人工边界条件;地震响应分析【作者】陈少林;赵宇昕【作者单位】南京航空航天大学土木工程系，南京210016;南京航空航天大学土木工程系，南京210016【正文语种】中文【中图分类】TU435土-结构相互作用是地震工程领域的重要问题，以往对该问题的研究集中在地基土为干土的情形，对地基土为饱和土情形的研究相对较少.而实际情形中，地下水位以上可视为干土，水位以下可视为饱和土，对该情形的研究更是鲜有报导.地震波输入下土-结构相互作用分析一般采用子结构法[1-4]、集中参数法[5-8]和直接法[9-12].子结构法和集中参数法将土-结构相互作用问题分解为如下可独立求解的子问题：(1)自由场问题，即结构和基础不存在时土层在地震波入射时的响应问题；(2)基础的输入问题，即结构不存在时，无质量刚性基础在地震波入射时的响应问题；(3)刚性基础的动力刚度或动力柔度矩阵；(4)结构响应问题.下面仅就饱和土层自由场分析和饱和地基动力刚度研究的相关工作做一简单介绍.自 Biot[13-15]建立多孔弹性介质波的传播理论以来，Deresiewicz等[16-18]对于波在饱和土界面上的传播特性进行了系统的研究,分析了平面波在自由表面、分层多孔介质界面中的反射和透射.Jocker等[19]通过推广 Thomson-Haskell传递矩阵法，以得到一种封闭形式的解析表达式，用于计算水平成层多孔介质的反射率和透射率.Rajapakse等[20]、Degrande等[21]、Liang等[22]分别给出了饱和土层和半空间的精确动力刚度矩阵，采用直接刚度法可求得饱和水平层状场地的自由场响应.李伟华等[23]采用波函数展开法，求得饱和弹性均匀半空间的自由场，进一步分析了饱和沉积谷场地对SV波的散射问题.赵宇昕等[24]采用传递矩阵法分析了成层饱和土层自由场响应，并探讨了数值结果中的非因果原因.1986年，Halpern等[25]通过对基础所覆盖的单元域上 Green函数数值积分给出了三维饱和弹性半空间表面上刚性板的动力柔度系数.Bougacha等[26]采用基础空间离散振动模态的有限元方法得到了饱和弹性土层上长条形基础和圆形基础的动力刚度.Japon等[27]应用边界元方法分析了长条形基础的动力刚度，并考虑了渗透力、附加密度、地层深度、基础刚度对基础振动的影响.陈少林等[28-29]提出了一种时域求解基础阻抗函数的方法，通过给基础输入脉冲位移，应用集中质量显示有限元方法结合局部透射人工边界，得到地基施加于基础的反力时程，然后根据阻抗函数定义，应用傅里叶变换求得基础阻抗函数.子结构法以频域内的动力刚度为基础，集中参数法通过拟合动力刚度得到参数模型，理论上都只适用于线性系统，不能考虑土体的非线性.直接法将地基、基础和上部结构一并计算，可以方便考虑土体的非均匀性和非线性，但计算量一般较大，尤其是饱和土情形.梁建文等[30-31]将单相土-结构相互作用的研究拓展到饱和土领域[32]，采用间接边界元法分析了二维线性饱和土-结构相互作用问题，分析了P-SV 波斜入射时，孔隙率、土层深度、土层与基岩间的刚度比等参数的影响.本文拟将显-隐式结合的土-结构相互作用分析方法[10]，推广到三维饱和土-结构动力相互作用情形，采用集中质量显示有限元结合透射人工边界的方法分析饱和土体[33-35]，采用隐式方法对上部结构进行分析，实现三维饱和土-基础-结构动力相互作用分析.根据干土是饱和土的特殊情形这一事实，将两者情形的土-结构相互作用分析统一到饱和土-结构相互作用分析框架，进而可分析考虑地下水位情形的土-结构相互作用分析.1.1 土体内节点运动根据Biot[1]理论，饱和弹性多孔介质运动方程可以表示为其中u和U为固液相位移矢量，D，N，Q，R为非负弹性常数，ρ11=ρ1+ρα，ρ22=ρ2+ρα，ρ12=−ρα. ρ1=(1−φ)ρs，ρ2=φρw，ρs为固相质量密度，ρw为液相质量密度，ρα为固、液两相惯性耦合质量密度，φ为孔隙率.衰减系数为流体动力黏度，k0为渗透率.从地基土中取一有限土体，采用八节点三维实体元对其进行空间离散.将土体划分成两个区域，即人工边界区和内部计算区(如图1)，将土体单元节点划分为人工边界点、与基础相连的点和内节点三类.对于内点采用集中质量显式有限单元法.在人工边界上，采用多次透射公式模拟无限域的影响.对于内节点而言，对方程(1)进行有限元空间离散，得到第i个节点的固相运动方程为[33]液相运动方程为其中，和为节点i(全局编号)的固相加速度矢量和液相加速度矢量，为单元e中节点j(单元局部编号)的固相位移和速度矢量，为单元e中节点j的液相位移和速度矢量.Msi和Mwi分别表示集中在i节点上的固相和液相质量阵；是考虑固液两相互相运动所产生的单元阻尼阵的子矩阵，下标k(i)表示节点i(全局编号)在单元中对应的局部节点编号为k，即全局节点编号和单元内的局部节点编号之间的对应关系.表示单元刚度阵的子矩阵，为单元e中分配给节点i的固相载荷矢量和液相载荷矢量.N为包含节点i的单元个数，J为单元e的节点个数.此外，我们可以注意到，上述阻尼矩阵仅考虑固液两相互相运动所产生的阻尼，对固相骨架考虑瑞雷阻尼那么式(2)可修正为对内节点方程(5)和方程(3)采用中心差分与单边结合的积分格式进行时域积分.假定在p+1及其以前时刻节点i的位移矢量已知，时间离散步长用∆t表示，那么p时刻的加速度和速度可以分别表示为其中W=u,U.上式代入式(5)和式(3)可得节点i的位移递推公式1.2 土体边界节点运动对于人工边界上的节点，其运动状态可通过多次透射公式[36]进行确定其中，为边界节点0在p+1时刻的外传波位移(散射位移)，N为透射阶数，二项式可表达为为由人工边界节点及内部节点的散射位移构成的列向量行向量Tn为其中上式中记号“Σ”表示对所有满足以下条件的项求和以一阶Modulation Transfer Function(MTF)为例，那么可知其中S=ca∆t/∆x.式(9)分别用于饱和多孔介质的固相位移和液相位移，可得到边界点在 p+1时刻的散射波场位移，加上边界点的自由场位移，即可得到边界点在p+1时刻的总位移.式(11)中的散射位移向量可通过式(7)和式(8)得到的总位移减去自由场位移得到.对于饱和成层土体的自由场计算可参见文献[24].对于上覆干土，下卧饱和土的情形，可通过满足干土和饱和土分界面上的4个应力位移连续条件，得到相应的传递矩阵.具体计算流程可参见图2.1.3 上部结构的运动对于一般情况下的结构或系统，其动力学方程均可写成在p～p+1时步的间隔∆t内，Newmark积分格式对位移、速度、加速度采用如下的假设关系式中，β和γ为积分参数.因此将式(18)代入式(17)可以得到系统p+1时刻的运动平衡方程由式(19)可以得到up+1，进而通过式(18)可得到p+1时刻速度和加速度.1.4 基础的运动刚性基础作为土体和上部结构的连接部分，起到了承上启下的作用，传递结构与土体之间的作用力.其运动可由6个分量描述，即3个平动分量和3个转动分量土和结构作用在基础上的合力使基础产生刚体运动式中,MF为基础的集中质量阵，对角线元素依次为三方向质量MFx,MFy和MFz，三方向绕质心的转动惯量IFx,IFy和IFz；FS和FD分别为结构和土体作用于基础上的广义力矢量.首先考虑p时刻土体对刚性基础作用力饱和土体与基础接触任一节点k处，没有力矩的传递只有3个方向集中力的传递，这三方向集中力分别由每一时刻固液两相本构力合成因此饱和土体对刚性基础的合力可以表示为其中，m表示土体与基础接触点总数；表示节点k对基础作用力；和是土体对基础三方向的集中作用合力；是土体对基础三方向的转动合力矩；∆Xk,∆Yk和∆Zk是节点k对基础质心的相对坐标；矩阵A是一几何转换矩阵，代表土体接触点或结构接触点和基础质心的相对坐标关系.其次考虑p时刻结构对刚性基础作用力类似于上述的方法，对于任一结构与基础接触节点i处，上部结构对基础作用力可表示为可通过ANSYS分析得到各点反力值因此上部结构对刚性基础的合力可以表示为其中，n表示结构与基础接触点总数；和是结构对基础三方向的集中作用合力；和是结构对基础三方向的转动合力矩.得到p时刻作用力FD与FS后，对式(20)采用中心差分格式积分，可得通过刚性基础位移可得到与其接触的土体点或结构点的位移1.5 饱和土-基础-结构相互作用分析流程上面对饱和土-基础-结构相互作用分析的各个部分计算方法做了详细阐述，下面简述其基本分析步骤.假定p及以前时刻土体、基础与结构位移已知，计算p+1时刻各点的位移，基本步骤可以可描述如下：(1)采用集中质量显式有限元的方法，由式(7)和式(8)得到饱和土体内节点固、液相位移；(2)利用多次透射式(9)和自由场位移得到饱和土体人工边界节点的固、液相位移；(3)根据式(29)得到基础整体位移，进而由式(30)得到与刚性基础相连土体节点位移以及结构节点位移；(4)得到与基础相联的结构节点位移后，将该位移作为结构约束，根据式(19)可得到结构各点位移,进一步可得到该时刻结构对基础的作用力；(5)重复执行步骤(1)～(4)，即可得到饱和土-基础-结构体系在各时刻的动力反应. 根据上述原理，通过编制相应的FORTRAN程序实现了地震波入射时饱和土-基础-结构相互作用分析.其中结构可通过ANSYS有限元软件进行分析，通过FORTRAN调用ANSYS实现饱和土-基础-结构系统的整体分析.当流体体积模量Kf以及孔隙率φ均置为零时，饱和土退化为干土[29].下面采用如下模型对上述退化进行数值验证.上部结构通过 ANSYS进行分析，采用悬臂梁模型，截面尺寸0.1m×0.1m，梁高2m，密度2500kg/m3，弹性模量3.00GPa，泊松比0.2，阻尼比0.05，剪切波速707m/s，一阶振型周期0.226s.刚性基础尺寸6m×6m×4m，密度2500kg/m3.考虑表1中前两类地基土，输入相同的单位脉冲SV波：时间步距dt=0.0002s，脉冲宽度t0=0.15s，步数n=1013(见图 3).土体划分单元尺寸均为1m×1m×1m，满足波动模拟精度要求.结构隐式分析的时间步距dT=0.002s，即FORTRAN每10步对ANSYS执行一次调用.图4和图5分别给出了基础和结构顶部的位移.实线为干土情形的结果，虚线为饱和土退化情形的结果，两者完全吻合.因此，地基土为干土情形的土-基础-结构相互作用分析可纳入到饱和土-基础-结构相互作用分析框架，进而可以分析考虑地下水位的干土覆盖饱和土情形的土-结构相互作用分析.另外，结构在基础有效输入为零后(因为结构柔且小，不足以带动基础做相应运动)做有阻尼的自由振动，其周期正好为结构一阶振型周期0.226s.实际工程中，地下水位位于地表以下一定深度，若直接考虑为干土或饱和土并不合适.以下就地震波入射时土-基础-结构动力相互作用问题，比较地基土分别为干土情形、饱和土情形、干土覆盖饱和土情形对基础和结构响应的影响.仍采用悬臂梁结构及刚性基础，首先考虑地基土为表1中的3号、4号、5号的情形，分别称为CASE1,CASE2,CASE3.其中，3号为饱和土，4号为具有与3号饱和土相同剪切波速和密度的干土，在工程中，常常对饱和土进行如此简化；5号为干土，具有与3号饱和土相同的骨架剪切波速和固相密度.最后考虑由上覆4m厚的5号干土，下卧14m厚的3号饱和土所组成的地基土，这种场地描述了当地下水位为4m时的情况，称其为CASE4.图6(a)和图6(b)分别为以上4种地基土情形时基础的位移时程和频谱.图7(a)和图7(b)为结构顶点的位移时程和频谱，为了比较，图中同时给出了不考虑土结相互作用情形时的结果.由图可知，就本文算例而言，若通过两种干土模型(CASE2,CASE3)代替饱和土模型(CASE1)进行分析，基础与结构的位移均将偏小.由于CASE3中的干土剪切波速更大，其到时也比CASE1与CASE2的情况要早.CASE4与前3种情况相比，基础与结构的位移都有较大幅度减小，并不是介于干土和饱和土情形的结果之间，表明一定深度的地下水位对基础和结构响应的影响较大.不考虑土结相互作用时，脉冲位移从结构底部输入，到时较其他情形早(见图7(a))，最大位移与饱和土-结构相互作用情形CASE1相当，但要大于其他情形(CASE2～CASE4).自由振动阶段的位移幅值小于CASE1，大于其余情形.另外，由图7可知，由于结构柔且小，在脉冲输入结束后，结构独自做有阻尼的自由振动(此时基础反应很小)，此时土-结构相互作用影响较小，与土体情形基本无关，其周期均为结构一阶振型周期0.226s.土体中的孔隙水将影响土体的地震反应，进而影响支撑其上的基础和结构的响应，为此，本文发展了一种饱和土-基础-结构动力相互作用分析的高效方法，主要结论如下：(1)采用集中质量显式有限元方法结合多次透射人工边界模拟半无限饱和土体，利用隐式积分方法分析上部结构，实现了地震波输入时饱和土-基础-结构动力相互作用的高效分析.(2)通过将流体体积模量Kf，孔隙率φ置为零，将干土统一到饱和土计算框架，通过算例验证了这一方案，并实现了地基为干土覆盖饱和土情形的土-结构相互作用分析.(3)对比了饱和土地基、干土地基、干土覆盖饱和土地基(考虑地下水位)情形时，土-结构相互作用对基础和结构响应的影响，算例表明，地下水位对基础和结构响应的影响较大.【相关文献】1 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ITASCA_PFC 复杂模型建模

复杂离散颗粒模型构建方法研究石崇1,2，王海礼1,2，王盛年1,2，张玉龙1,2(1. 河海大学岩土力学与堤坝工程教育部重点试验室，南京 210098；2. 河海大学岩土工程研究所，南京 210098)摘要:颗粒流分析中，得到低应力状态、均匀孔隙率的离散颗粒模型是获得良好数值计算结果的前提和基础。

采用AutoCAD 作为处理软件，以polyline 绘制建模范围、3dface 设置粒子投放区域，结合改进的膨胀生成颗粒法编制的程序接口可自动生成PFC2D 边界Wall 、颗粒命令流，并以伺服边界Wall 调整应力状态和空隙率，最终以任意多边形材料边界控制划分颗粒属性即可得到所需的数值计算模型。

该方法可视化程度高，能实现任意二维复杂离散颗粒模型的构建，且生成颗粒间重叠量小、在颗粒间黏结力破坏后亦不会造成飞溢现象，对于复杂离散颗粒模型的构建是有益的补充。

关键词: 离散颗粒；复杂边界；低应力；均匀孔隙率；伺服边界1 前言通过定性分析建立能够获得可靠定量分析结果的计算模型是工程数值模拟分析研究的前提和基础，因此，在采用颗粒离散元PFC2D 进行数值建模工程分析时，如何得到低应力状态、均匀孔隙率的计算模型是获得良好计算结果的首要条件。

目前颗粒离散元最常用的建模方法是膨胀法[1]，该方法先在指定区域内生成小颗粒，然后逐级膨胀，直到充满模型边界。

但采用该方法构建模型时膨胀系数难以控制，常常造成颗粒间有较大的重叠量，内力较高。

虽然当颗粒间的内力小于指定的黏结力或者有边界约束时，仍可用以模拟连续介质的性质。

但是采用颗粒离散元分析边坡滑坡、介质破坏等动力学行为，若颗粒重叠量较大，颗粒间黏结力不足以约束颗粒，颗粒间应变能的释放就会造成大量颗粒飞溢出边界，产生不准确的结果。

本文基于颗粒离散元基本原理，改进了膨胀建模方法，并借助AUTOCAD 可视化操作，研制了复杂离散颗粒模型命令流自动生成技术，可大大简化复杂二维颗粒流模型的构建过程。

Shear behaviour of a geogrid-reinforced coarse-grainedsoil based on large-scale triaxial tests

Shear behaviour of a geogrid-reinforced coarse-grained soil based on large-scale triaxial testsXiaobin Chen a,*,Jiasheng Zhang a,Zhiyong Li ba School of Civil Engineering,Central South University,22Shaoshan Road,Changsha410075,PR Chinab Human Communication Research Institute,472Fu Rong Road,Changsha410008,PR Chinaa r t i c l e i n f oArticle history:Received20June2013Received in revised form7May2014Accepted7May2014Available online2June2014Keywords:Weathered mudstone coarse-grained soil Geogrid reinforcementLarge-scale triaxial testShear behaviourReinforcement coefﬁcientSlip surface a b s t r a c tIn China,weathered mudstone geogrid-reinforced coarse-grained soil is used extensively for road em-bankments.However,the microstructure and disintegration process of weathered mudstone remain unclear.Furthermore,few studies have investigated the shear behaviour of this kind of geogrid-reinforcedﬁll through large-scale triaxial tests against grain size effects.To bridge this gap,this study reports results from large scale consolidated undrained(CU)and consolidated drained(CD)triaxial tests as well as scanning electron microscopy(SEM),energy-dispersive X-ray(EDX),and disintegration tests on weathered mudstone geogrid-reinforced coarse-grained soil.EDX spectrograms and SEM images show that coarse grains disintegrate rapidly mainly owing to the high clay mineral content and loose microstructure.Therefore,a suitable disintegration time(w15days)is recommended for embankment sits.The shear behaviour of this geogrid-reinforcedﬁll is investigated in detail through large-scale triaxial tests.The shear deformation tends toward strain hardening behaviour with an increase in the number of geogrid layers and the conﬁning pressure.Geogrids signiﬁcantly improve the apparent cohesive strength of coarse-grained soil.The pore water pressure is found to develop rapidly in the0% e4%axial strain phase but dissipate slowly in the4%e12%axial strain phase.During shear,the pore pressure coefﬁcient A values of0.2e0.4are indicative of the partial saturation of specimens.Conse-quently,pore water pressure development is mainly attributed to the movement and rearrangement of coarse particles in coarse-grained soil.Experimental data show that the geogrid-reinforcement co-efﬁcients increase with the number of geogrid layers,and a20-cm separation between geogrid layers is recommended for embankment construction sites.The number of geogrid layers inﬂuences the geogrid e soil interface’s mobilization and the slip surface type.Test results revealed three types of slip surfaces related to the failure shapes of specimens.Then,based on CU experimental data,the parameters of the Duncan e Chang constitutive model are discussed.Ó2014Elsevier Ltd.All rights reserved.1.IntroductionMudstone,which is widely distributed in the southern part of China,is an extremelyﬁne-grained sedimentary rock consisting of a mixture of clay and silt-sized particles,generally a mixture of clay minerals with any or all of quartz,feldspar,and mica.Mudstone can be subdivided into siltstone and claystone,in which more than50% of the composition is silt-and clay-sized particles,and both of which have similar mechanical properties.Mudstone is a soft rock, commonly with uniaxial compressive strengths less than15MPa and density less than2.65g/cm3.Therefore,it is generally too soft for construction or similar purposes.However,when naturally weathered,it breaks into blockyﬂakes and eventually into residual coarse-grained soil,which is often used as aﬁll for constructing embankments in mountainous areas in China.In recent years,geosynthetics,especially geogrids and geo-textiles,have been increasingly used to reinforce embankments.A geogrid-reinforced embankment,by preventing lateral deforma-tion and distributing trafﬁc loading over a larger subgrade area,can often carry higher trafﬁc loading(U.S.Army Corps of Engineers, 2003).Therefore,when weathered mudstone coarse-grained soil are used in highway embankments subjected to trafﬁc loading,they are usually reinforced with geogrids in top layer.In this study,the shear behaviour and inﬂuences of geogrid reinforcement on clayey mudstone coarse-grained soil are investigated in detail through large-scale triaxial test results.*Corresponding author.Postal address:22Shaoshan Road,Changsha410075, Hunan province,China.Tel./fax:þ86731-82656812.E-mail addresses:cxb528@,chen_xiaobin@,chenxb@illinois. edu(X.Chen).Contents lists available at ScienceDirectGeotextiles and Geomembranesjou rna l homepage:/locate/geotexmem/10.1016/j.geotexmem.2014.05.0040266-1144/Ó2014Elsevier Ltd.All rights reserved.Geotextiles and Geomembranes42(2014)312e328Many studies have investigated granular soil(or granular mixture)reinforcement mechanisms through laboratory andﬁeld tests.Giroud and Noiray(1981)used geogrids and woven geo-textiles as reinforcements for increasing resistance to trafﬁc load. They,along with many other studies(Berg et al.,2000;Hufenus et al.,2006;Subaida et al.,2009),concluded that geogrids mainly provide reinforcement through lateral restraint,improved bearing capacity,and the tensioned membrane effect.Giroud and Han (2004a,b)presented a design method for geogrid-reinforced un-paved roads in which the inﬂuences of the bearing capacity factor (Nc)and interlock among the geogrids were considered.Mekkawy et al.(2011)investigated the shoulder rutting performance of geogrid-reinforced granular shoulders on soft subgrade by per-forming laboratory and full-scale tests.They presented a design chart correlating the rut depth with the number of load cycles to subgrade CBR.This chart was used to optimize granular shoulder design parameters and better predict granular shoulder perfor-mance.Palmeira(2009)analysed the results of large-scale cyclic and monotonic loading tests of unreinforced and geosynthetic-reinforced unpaved roads.They found that the presence of a rein-forcement layer signiﬁcantly reduced the magnitudes of vertical stress increments transferred to and vertical strain in the subgrade. Their experimental investigations showed that geogrids were more efﬁcient than geotextiles in restraining lateral movement of theﬁll material.Perkins and Ismeik(1997a,b)also noted the beneﬁcial effects of geosynthetics on reinforced pavements and unpaved roads.Anderson and Killeavy(1989)and Cancelli et al.(1992)noted that the use of geosynthetic reinforcements could reduce pavement thickness by20%e50%.Knapton and Austin(1996)achieved rut depth reductions of up to50%by using geosynthetic re-inforcements,especially geogrids.Raymond and Ismail(2003) noted that the reinforcement layer position inﬂuences a road’s performance.Yang et al.(2012)conducted accelerated pavement tests on unpaved road sections with geocell-reinforced sand bases and demonstrated that the NPA geocell signiﬁcantly improved the stability of unpaved roads with sand bases and reduced permanent deformation.Gourc et al.(1986)proposed a displacement evalua-tion method based on the effect of reinforcement extensibility on the mobilization of interface mechanisms of fabric-retaining walls. Skinner and Rowe(2005)studied the stability of geosynthetic-reinforced retaining walls by analysing a geosynthetic-reinforced soil wall supporting a bridge abutment and approach road con-structed on clayey soil deposit.Ehrlich et al.(2012)presented a physical model study of the inﬂuence of compaction on the behaviour of geogrid-reinforced soil walls.Their results showed that the position of maximum tensile force mobilized in the re-inforcements was nearer to the face in the wall with heavy compaction.Weggel and Ward(2012)presented the equations for a numerical model that describes the accumulation ofﬁlter cake on a geotextile asﬂow passes through and solved them numerically using an Eulerﬁnite difference scheme and an Excel spreadsheet. Sitharam and Hegde(2013)discussed the geotechnical problems at a site,the design of a geocell foundation based on experimental investigation,and the construction sequences of geocell founda-tions in theﬁeld.Yang et al.(2014)focused on soil-rock mixtures as the backﬁlls of geogrid-reinforced soil retaining walls with due concern for their long-term performance and safety.Wang et al. (2014)conducted a numerical compound tensile test(in sand) with one geogrid tensile member by PFC2D to investigate the load transfer behaviour between the geogrid and sand.Moraci and Recalcati(2006)used a large-scale pullout test setup to study the factors inﬂuencing the behaviours of geogrid reinforcements embedded in granular soil and evaluated the peak and residual pullout resistance values.Fannin et al.(2005)and Chakraborty and Salgado(2010)studied the dilative behaviour of granular soil.The shear behaviour at the geotextile e granular soil interface inﬂuences the stability of a geotextile-reinforced embankment. Many studies conducted direct shear tests on various geotextile interfaces to study their shear stress e shear displacement re-lationships(Gilbert et al.,1996;Triplett and Fox,2001;Zornberg et al.,2005;Bergado et al.,2006;Nye and Fox,2007;Sharma et al.,2007;Suksiripattanaponga et al.,2013).Tran and Meguid (2013)developed a coupledﬁnite-discrete framework to investi-gate the behaviour of a biaxial geogrid sheet embedded in granular material and subjected to pullout loading.Esmaili et al.(2014) presented the descriptions and results of multi-scale pullout and interface shear tests on a woven polypropylene geotextile rein-forcement material in a marginal quality soil.Khoury et al.(2011) presented the results of a laboratory study on the mechanical behaviour of unsaturated soil e geotextile interfaces using a specially modiﬁed direct shear apparatus.Belén et al.(2011)stud-ied the frictional behaviours of geosynthetics used in municipal solid-waste landﬁlls and developed an analytical model to describe the shear behaviour and simulate progressive geomembrane e geotextile interface failure from direct shear tests.Sayeed(2014) used large-size direct shear tests to determine the interfacial shear characteristics of sand e geotextile under three different normal stresses.They investigated the surface morphology of sand particles based on SEM images and quantitatively analysed it using the Wadell roundness and degree of angularity methods.Pitanga et al.(2009)investigated geogrid-reinforced granular soil and found very low dilatancy values between1/300and1/50of the maximum shear displacement in addition to a nonlinear failure envelope in the normal stress ranges.Stark et al.(1996)and Hebeler et al.(2005)studied the geogrid interface interaction mechanisms based on shear tests and found that interbedding and hook control the interface shear strength.Gilbert et al.(1996)and Sharma et al. (2007),among others,developed interface interaction models toﬁt experimental data.Indraratna et al.(2006,2007),among others, demonstrated the effectiveness of geogrid reinforcements on restricting ballast deformation throughﬁeld tests and simple lab-oratory tests.Coleman(1990)and Shukla and Yin(2006)evaluated the effects of interlocking between railway ballast and geogrid apertures on shearing resistance.Indraratna et al.(2011)described how the ballast e geogrid interface copes with fouling by coalﬁnes. They investigated the stress e displacement behaviours of fresh, fouled,and geogrid-reinforced ballast by performing a series of large-scale shear tests.Dombrow et al.(2009)conducted a series of large-scale shear tests with fresh ballast and ballast fouled by coal to varying degrees.They found that the shear strength decreased steadily as the fouling percentage increased.Tutumluer et al.(2012) studied the shear behaviour of ballast under monotonic and cyclic loading.Chen and McDowell(2012)used the discrete element method to simulate the cyclic loading of geogrid-reinforced ballast under conﬁned and unconﬁned conditions.Leshchinsky and Ling (2013),based on prior large-scale laboratory tests of ballast em-bankments with geocell conﬁnement and relevant numerical modelling,validated an acceptable material model for a parametric study usingﬁnite element analysis to investigate the effects of geocell conﬁnement on ballasted embankments when encoun-tering a soft subgrade,weaker ballast,or varying reinforcement stiffnesses.Indraratna et al.(2013)described a novel large-scale process simulation test(PST)apparatus that can capture the lateral strain variation upon loading.They conducted laboratory tests to explore the deformation and degradation response of both unreinforced and reinforced ballast under high-frequency cyclic loading.For coarse-grained soils,Pitman et al.(1994)focused on the ef-fect of the coarse grain content on soil de et al.(1998) investigated the effect of the coarse grain content on theX.Chen et al./Geotextiles and Geomembranes42(2014)312e328313collapsibility of a granular mixture.Vallejo and Mawby (2000)conducted some tests to study the shear strength at different coarse grain contents.Dash and Sitharam (2009)investigated the stress e strain relationships of coarse grained soil,and Bandini and Pham (2011)focused on the critical state characteristics of the same.Zhao and Zhang (2013a,b)conducted drained and undrained triaxial tests on several widely graded soils with different coarse contents at low con ﬁning stress.They found that the soil micro-structure changes from a ﬁne-to a coarse-controlled structure beyond a critical coarse content of w 70%.Zhao and Zhang (2013a,b)investigated the microstructure,compressibility,and shear strength of an unsaturated widely graded coarse-grained soil.Suksiripattanapong et al.(2013)studied the pullout resistance of geogrid reinforcement in coarse-grained soils and presented pullout resistance equations for the bearing reinforcement with different dimensions and spacings between transverse members.Demir et al.(2013)conducted 16ﬁeld tests to evaluate the effects of replacing natural clay soil with a stiffer granular ﬁll layer and single-multiple layers of geogrid reinforcement placed into the granular ﬁll below circular footings.Moraci and Cardile (2012)analysed the effects of the tensile cyclic load,frequency,and amplitude;vertical con ﬁning stress;and geogrid structure on the pullout behaviour in terms of accumulated displacements and deformations.Shivashankar and Jayaraj (2014)investigated the effects of prestressing the rein-forcement on the strength improvement and settlement reduction of a reinforced granular bed overlying weak soil.Many studies have investigated the effect of the coarse grain content on the stress e strain relationships,shear strength,and critical state properties of coarse grained soil.However,few studies have focused on geogrid-reinforced coarse-grained soils;in particular,few large-scale triaxial experimental investigations have been rge specimens are rarely used to diminish coarse grains ’size effects on the shear behaviour in triaxial tests.Furthermore,the disintegration of coarse grains is always neglec-ted.To better understand the shear behaviour and effects of geogrid-reinforced coarse-grained soil during triaxial testing,a series of large-scale triaxial tests (CU and CD)were conducted in this study.SEM images and EDX spectrograms of mudstone were obtained using a ﬁeld-emission gun environmental scanning elec-tron microscope (FEG-ESEM).In addition,disintegration tests were conducted to investigate the mudstone grain ’s disintegration when exposed to air and water.In the triaxial experiments,the di-mensions of each specimen are as follows:diameter ¼300mm,height ¼600mm,and thickness of rubber membrane encasing specimen ¼2mm.The relationships between the specimen failure shapes and numbers of geogrid layers were studied,and the pa-rameters of the Duncan and Chang constitutive model were discussed.2.Materials and specimen preparation 2.1.Mudstone grain ’s propertiesMudstone consists of silt-,mud-,and clay-sized particles.The chemical compositions of mudstone grains are summarized in Table 1.The microstructure of the mudstone grain ’s mineral matrix was investigated by SEM,as shown in Fig.1(a e d).These images show that the microstructure of the mudstone grain ’s mineral matrix is relatively loose,and the shape of the clay ’s mineral matrix is mainly blocky and laminated.The loose microstructure suggests that water and air could easily penetrate the mudstone grains,in turn easilyTable 1Chemical compositions of mudstone grains (%,percentage by dry weight).Sample no.Compositions S i O 2Al 2O 3Fe 2O 3CaO MgO Burning loss Others A1(at k6þ060)65.0514.537.80.74 1.647.32 2.92A2(at k14þ130)69.3413.587.270.54 1.13 5.23 2.91A3(at k17þ090)67.2014.057.510.65 1.20 6.86 2.53A4(at k23þ400)69.5013.987.400.55 1.32 4.75 2.50Average67.7714.047.500.621.326.042.71Fig.1.SEM images of weathered mudstone.X.Chen et al./Geotextiles and Geomembranes 42(2014)312e 328314Fig.2.EDX spectrums of weathered mudstone.X.Chen et al./Geotextiles and Geomembranes 42(2014)312e 328315leading to their disintegration.The main minerals in the mudstone grains were analysed based on the EDX spectrograms obtained using an FEG-ESEM,as shown in Fig.2(a e d).The EDX spectrum analysis shows that the minerals in the mudstone grains mainly include clay,quartz (50%e 58%),chlorite (15%e 18%),isinglass (14%e 18%),and feldspar (11%e 12%)by weight.Among these,clay-type minerals d including chlorite,isinglass,and feldspar d constitute 40%e 48%.These fractions can easily be weathered into clayey ﬁne soil.When mudstone grains are exposed to air and water,they disintegrate quickly mainly owing to their high clay mineral con-tent.This disintegration is probably bene ﬁcial for constructing geogrid-reinforced embankments because ﬁlls with higher density and degree of compaction can be obtained with the same compaction energy.In this study,the disintegration time and its effects on mudstone grains were investigated through tests.The disintegration test involves the following steps:(1)Weatheredmudstone grains are dried in an electronic oven.(2)Particle size distribution analysis tests are performed using different sieve aperture diameters (63,37.5,19,9.5,2.36,0.6,and 0.3mm),and the initial particle size distribution diagrams are drawn.(3)Dried mudstone grain samples are exposed to air with constant moisture for 2,3,9,15,24,and 35days.(4)After varying exposures intervals,each sample is subjected to particle size distribution analysis again as in step (2),and the disintegrated particle size distribution dia-grams are plotted again.(5)The disintegration is discussed by comparing the particle size distribution diagrams.Fig.3(a)shows a plot of the particle size distributions of mudstone grains during disintegration tests and Fig.3(b)shows the uniformity coef ﬁcients.Fig.3(a)clearly shows that mudstone grain disintegration in-creases with the exposure time.Disintegration is more obvious in the early phase (ﬁrst 15days),indicating that mudstone grains disintegrate rapidly initially.After 15days,the disintegration speed decreases and most grains (diameter:>60mm)are almost dis-integrated.For instance,when the median grain diameter (d 50)decreases to 50,25,20,6,4,3.1,and 2.0mm,the disintegration times increase to 2,3,9,15,24,and 35days,respectively.Fig.3(b)shows the increase in the uniformity coef ﬁcient of mudstone grain with the disintegration time in the early phase and the decrease in the same with the disintegration time in the later phase (after the ﬁrst 15days),which also demonstrates that most large grains had already been disintegrated in the early phase.Based on the results,the recommended disintegration time is w 15days for embank-ment construction sites.2.2.Specimen preparationThe properties of commercially available polyvinyl chloride (PVC)geogrids with longitudinal and transverse ribs are summa-rized in Table 2.Field weathered mudstone residual soil is a yellow-cyan coarse-grained soil with irregular oblong-,pyramid-,or chip-shaped grains.This weathered mudstone coarse-grained soil has a me-dian grain size diameter (d 50)of 55mm and a uniformity coef ﬁcient (C u )of 4.0.The maximum void ratio (e max )is 0.85,and the mini-mum void ratio (e min )is 0.46.The ﬁeld void ratio (e )is 0.72,and the relative density (D r )is 0.31,which indicates the relatively loose condition in ﬁeld.The basic physical parameters of weathered mudstone coarse-grained soil are listed in Table 3,and its grain size distribution is shown in Fig.4.Not all coarse grains in ﬁeld can be directly accepted for labo-ratory testing,and the coarse grains ’size effects are obvious (Zekkosa et al.,2008,2012).Several studies have recommended that the largest grain diameter be not greater than 1/6or even 1/10of the specimen diameter for minimizing scale effects (Varadaraja et al.,2003).In this study,the diameter of the largest grain in the sample was not greater than 1/5of the specimen diameter,and the size effects were acceptable (Guo,1999).The specimen dimensions are as follows:diameter ¼300mm,height ¼600mm,and a common height-to-diameter ratio of 2according to ASTM D3999-91.The ﬁeld grain size distribution was highly imitated using the weight equivalence method (Guo.1999)in this study,and the large-scale triaxial testing samples were prepared by ﬁltering the ﬁeld mudstone coarse-grained soil with a 60-mm aperturediameterFig. 3.Particle size distribution and uniformity coef ﬁcients during disintegration testing.Table 2Physical dimensions and tensile parameters of polyvinyl chloride geogrids.Aperture length (mm)Aperture width (mm)Longitudinal rib width (mm)Tranverse rib Width (mm)Thickness of rib (mm)Ultimate tensile strength (kN/m)2%Strain tensile strength (kN/m)Longitudinal Tranverse Longitudinal Tranverse 40.038.05.04.03.081.272.568.368.9X.Chen et al./Geotextiles and Geomembranes 42(2014)312e 328316sieve.Theﬁeld and experimental grain size distribution diagrams for weathered mudstone coarse-grained soils are plotted in Fig.4. Although there is a little difference between theﬁeld grain size distribution and the experimental grain size distribution,the de-viation of the testing results and the coarse grain size effects could be acceptable(Guo,1999;Varadaraja et al.,2003).The dry tamping method,moist tamping method,dry pluviation method,and wet pluviation method are commonly used for large-scale reconstituted specimen preparation(Wichtmann et al.,2005). Among these,the moist tamping method allows for specimen preparation with arbitrary relative density and achieves sufﬁcient homogeneity through the application of different compaction ef-forts on each layer,thus compacting each layer to the same density. Considering the characteristics of these methods,the moist tamp-ing method was selected for large-scale triaxial soil specimen preparation in this study.All samples were thoroughly mixed with optimum moisture content(12%).They were then sitting in a curing tank with the same moisture content for at least24h before specimen making.The mudstone coarse-grained soil samples were poured layer-by-layer(ﬁve layers)into cylindrical steel moulds. Then,the mudstone coarse-grained soil samples were compacted such that all layers had the same speciﬁc density,and the surfaces of each layer were scratched to ensure better bonding with the next layer.The degree of compaction of each layer was95%,and poly-vinyl chloride geogrids were embedded at suitable heights(sepa-ration of30,20,and15cm between layers,respectively).To examine the effects of geogrid reinforcement,specimens with no geogrids as well as one,two,and three layers of geogrids were prepared in this study.The specimen symbols and testing programs used in these large-scale triaxial tests are summarized in Table4.2.3.Experimental procedureCU and CD triaxial tests were conducted using a large-scale triaxial setup based on the BS1377-8standards(1990,Methods of test for soils for civil engineering purposes Shear strength tests). Most of the tests performed are CU tests,with CD tests only being performed for volumetric strain analysis.All specimens were tested under fully saturated conditions.A combination of the back pres-sure saturation method and the CO2ﬂushing saturation method was used for achieving sufﬁcient degrees of saturation.The Skempton pore pressure parameter(B¼D u/Ds3)was used as an indicator of the degree of saturation as the specimen was saturated. It is widely accepted that when B>0.95in testing,the degree of saturation,S,reaches100%(Karg and Haegeman,2009).However,it is very difﬁcult to achieve B!0.95for the laboratory testing of large-scale coarse-grained soil specimens,especially for the clayey soils.In practice,it is presumed that B>0.85indicates a degree of saturation of at least99.5%(Thooft,1991).In the mudstone geogrid-reinforced coarse-grained soil triaxial tests,the B values of all samples were0.90e0.95,indicating that all the samples were sufﬁciently saturated.When the saturation procedure was completed,the isotropic consolidation procedure was applied with the specimen drainage valves left open;the time required for full consolidation was8e12h during testing.After consolidation,a shear deviator stress(s1e s3)was applied to the specimens,and the resulting shear behaviours were observed.In the shear test,the shearing speeds were controlled by the axial deformation rates of 0.01cm/min(CU)and0.005cm/min(CD).The shear test was terminated when the axial strain reached15%or the stress reached the critical condition(Torav,1985;Zhu,2003).During testing,the shear stress,shear strain,pore water pressure,and specimen failure shapes were investigated.The obtained critical stress states are summarized in Table5.3.Tests results and analysis3.1.Shear behaviourThe failure shapes of specimens are shown in pared with the original shape,three main types of failure shapes are typically observed:shear banding,middle bulging,and top bulging. These failure shapes are likely related to the embedded geogrid layers.For example,shear banding failure is more likely to occur in non-reinforced specimens;middle bulging failure,in specimens reinforced with two geogrid layers;and top bulging failure,in specimens reinforced with three geogrid layers.The middle and top bulging failure specimens show a clear bulge at a height of0.5e 0.7H and0.7e0.8H,respectively.The experimental principal stresses,principal strains,and pore water pressures during shear testing were focused on,and all of them were automatically recorded by the triaxial setup.Under different conﬁning pressures,the critical deviatoric stresses,axial strains,and shear e induced pore water pressures of mudstone geogrid-reinforced coarse-grained soil specimens are plotted in Fig.6.In determining the specimens’shear behaviour,the effects of geogrids are as evident as those of the conﬁning pressure.As shown in Fig.6,the S1group specimens exhibit a strain-softening trendTable3Basic physical parameters of weathered mudstone coarse-grained soil.Density/g/cm3Relative density/Dr Natural water content/%Optimum water content/%Fine particles liquid limit/%Fine particles plastic limit/%1.930.3117123215.9C.B.R.value at different compact degree MLR(Sulphate invading)/%Void ratio Saturation degree90%93%95%n(%)S r(%)39.645.547.0 1.57267.5Note:C.B.R.is the California Bearing Ratio Test.MLR is the Mass Loss Rate when sulphate corrosioninvade.Fig.4.Particle size distribution of weathered mudstone coarse-grained soil.X.Chen et al./Geotextiles and Geomembranes42(2014)312e328317under low con ﬁning pressures;however,the geogrid-reinforced specimens tend to undergo strain hardening,especially the S3group specimens.These experimental results show that the geogrid likely leads to strain hardening under shearing,and the magnitude of this strain hardening is possibly related to the extensile force applied to the geogrid.However,the geogrid ’s extensile force takes obvious effect until its strains accumulate to a suitable level.During shearing,the effect of the geogrid is not obvious when the total axial strain is less than 1%(εa <1%),and the shear curves are very close (as shown in Fig.6).The effect of geogrids becomes more obvious when the axial strain is larger than 1%(εa >1%).Under a con ﬁning pressure of 50kPa,when the shear strain reaches 5%,the shear force (s 1e s 3)reaches 153,195.3,214.4,and 233.1kPa,respectively,for the unreinforced specimen and specimens rein-forced with one,two,and three geogrid layers.The extensile force of the geogrid gradually contributes to the improvement of the reinforced specimens ’shear strength with an increase in the shear strain.Shear deformation leads to strain hardening as the con ﬁning pressure and number of reinforcing geogrid layers increase.Based on experimental data,εa vs.(s 1Às 3)/εa curves of the weathered mudstone coarse-grained soil specimens are plotted in Fig.7.The values of (s 1Às 3)/εa decrease with an increase in the axial strain,and the number of geogrid layers in ﬂuences the curves ’slopes as well as the con ﬁning pressure.The εa vs.(s 1Às 3)/εa curves for the unreinforced samples are linear,as shown in Fig.7(a),which suggests that these specimens ’shear behaviours potentially tend toward shear dilatancy and strain softening.With the presence of geogrid layers,εa vs.(s 1Às 3)/εa curves of the reinforced samples become nonlinear (Fig.7(c e d)).The nonlinear shapes of the curves indicate that the shear behaviour tends toward shear contractancy or strain hardening because of geogrid reinforcement.It is commonly accepted that the volume deformation of a specimen equals the volume of water drained from the specimen in the CD triaxial tests.Therefore,the volume deformation of spec-imen can be determined by measuring the volume of drained wa-ter.During the large-scale consolidated drained triaxial tests,the volume of drained water was measured.Therefore,the specimen ’s volume deformation was obtained indirectly,and the relationshipsTable 4Programs for mudstone coarse-grained soil in large-scale triaxial tests.Test methodSpecimen symbol Embedded geogridsDry density (g/cm 3)Con ﬁning pressure s 3/kPa (CU and CD)method outlined in Standard ASTM D3999-91S1group No geogrid1.8950,100,150,200S2group One layer of geogrid (30cm per layer)50,100,150,200S3group Two layers of geogrid (20cm per layer)50,100,150,200S4groupThree layers of geogrid (15cm per layer)50,100,150,200Table 5Critical stress conditions and residual pore water pressure during axial CU testing.Specimen group Load step s 3(kPa)s 1(kPa)s 1e s 3(kPa)Max pore water pressure u w (kPa)Failure shape description S1150156.2106.238.5Shear band 2100251.5151.539.5Shear band 3150309.4159.459.1Shear band 4200399.2199.263.8Middle bulge S2150186.4136.441.8Middle bulge 2100287.6187.642.3Shear band 3150381.0231.070.2Middle bulge 4200447.2247.273.5Middle bulge S3150231.0181.048.6Middle bulge 2100322.5222.559.2Middle bulge 3150411.5261.578.7Top bulge 4200478.3278.386.9eS4150261.5211.553.5Top bulge 2100360.5260.569.3Top bulge 3150434.1284.192.0Total bulge 4200500.0300.0105.2TopbulgeFig.5.Sketch of specimen failure shapes.X.Chen et al./Geotextiles and Geomembranes 42(2014)312e 328318。

滑坡稳定性导论

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Different constitutive relations can be employed. No assumption needs to be made in advance about the shape or location of the failure surface. Failure occurs `naturally" through the zones within the soil mass in which the soil shear strength is unable to sustain the applied shear stresses.
(cohesion and friction angle) Model Behavior
Continuum modelling
Typical Input required
• Moduls of Elasticity for rock and joints
• Poision ratio for rock and joints
Limitation
Software based on Limit equilibrium Method
SLIDE (rocscience group) GALENA GEO-SLOPE GEO5 GGU SOILVISION
Software based on Numerical modeling
• Density
• Shear strength for rock and joints

基于物质点法的土体流动大变形过程数值模拟

基于物质点法的土体流动大变形过程数值模拟杨婷婷;杨永森;邱流潮【期刊名称】《工程地质学报》【年(卷),期】2018(026)006【摘要】土体滑坡作为一种自然地质灾害,受自然因素和人类活动的影响在我国时有发生,给周围居民的生命和财产安全带来了很大威胁,日益受到人们的广泛关注.滑坡防治也逐渐成为工程研究的热点之一.土体本质上是一种具有复杂组成结构的颗粒材料堆积体,通过对颗粒流动的模拟可以深入理解自然界中的土体流动现象,如滑坡、泥石流等,进而预测灾害破坏范围及改进相应工程防护措施.但由于土体流动是一个涉及大变形及大位移的复杂流动过程,传统的基于网格的有限元法(FEM)由于网格畸变,并不适合这类问题的研究.本文采用物质点法(MPM)模拟土体流动大变形问题.作为一种源于particle-in-cell(PIC)法的无网格法,兼具欧拉法和拉格朗日法的优点,因而,物质点法在处理大变形问题上具有独特的优势.目前,国内外利用物质点法模拟边坡滑动问题已有不少研究,但对相关参数进行敏感性分析的较少.本文基于物质点法模拟了黏性土体及无黏性土体流动大变形问题,并进行了参数敏感性分析,包括土体材料的内摩擦角、黏聚力、高宽比、底面坡度对土体滑动距离的影响规律.本文计算中采用Drucker-Prager(DP)弹塑性本构模型描述土的非线性特性.研究结果表明:(1)基于物质点法得到的土体的流动形态、滑动距离以及自然休止角等数值模拟结果均与文献中的实验结果基本吻合,验证了物质点法模拟土体大变形力学行为的精度及有效性;(2)随着内摩擦角、黏聚力的增大,滑动距离相应减小;(3)坡度对边坡稳定的影响是显著的,随着底面坡度的增大,滑动距离相应增大;(4)当土柱高宽比较小时,与滑动距离呈线性增长关系.其中,内摩擦角和黏聚力反映了土体的抗剪切性能,因此通过工程措施提高土体的抗剪能力可以降低土体滑坡带来的危害.研究结果为探索土体滑动破坏规律,降低滑动破坏范围提供了可靠的参考.%As a natural geologic disaster, soil landslide is affected by natural factors and human activities. It brings a great threat to the safety of the surrounding residents' life and property, attracting more worries from ndslide prevention and control are also one of the hot spots in engineering research. Soil is essentially a kind of deposits consists of granular material with complicated composition and structure. By means of numerical simulation of granular material flows, we can well understand the phenomena of soil flows in the nature, such as landslide and debris flows. It is therefore possible to predict the landslide hazard zone and to improve the design of engineeringprotection measurements. However, the finite element method (FEM) is not suitable for simulating soil flow with large deformation and large displacement due to the finite element method is sensitive to mesh distortion. In this paper, we simulate the soil flows using the material point method (MPM). MPM is a mesh-free method and originating from the particle-in-cell (PIC) method. It combines the Eulerian description and Lagrangian description and has distinct advantages in solving the large deformation and large displacement problem. Currently, there have been many studies on the simulation of slope sliding using MPM, but less attentions has paid to sensitivity analysis on relevant parameters. In this paper, the large deformations of the cohesive soil and the non-cohesive soil slopes due to gravity are numerically investigated with MPM. The influence of the internal friction angle, the cohesive force,the aspect ratio and bottom surface gradient on the landslide run-out are analysed. In this MPM simulation, the elasto-palstic constitutive models based on the Drucker-Prager (DP) yield criterion is used for modeling nonlinear characters of soil flows. The Drucker-Prager yield criterion is a pressure-dependent model for determining whether a material has failed or undergone plastic yielding. The yielding surface of the Drucker-Prager criterion may be considered depending on the internal friction angle of the material and its cohesion. The simulated results show the following featurs.(a) There are well agreements in the flow pattern, the sliding distance and natural angle of repose between the simulated results and the corresponding experimental results, which validates the ability of MPM to modeling soil flows. (b) The sliding distance decreases with the increase of the internal friction angle and cohesive force. (c) The steepness of the soil slope has significant influence on its stability. The sliding distance increases with the increase of the steepness of the soil slope. (d) For a comparatively small aspect ratio, the sliding distance increases linearly with aspect ratio. It is noteworthy that the internal friction angle and cohesive force of soil reflect its shear resistance. Therefore, the damage due to landslide can be reduced by improving the shear resistance of soil through engineering measurements. The results of the simulation provide a reliable reference to explore the law of the soil sliding hazardous behavior and reduce the sliding damage range.【总页数】10页(P1463-1472)【作者】杨婷婷;杨永森;邱流潮【作者单位】中国农业大学水利与土木工程学院, 北京 100083;中国农业大学水利与土木工程学院, 北京 100083;中国农业大学水利与土木工程学院, 北京 100083【正文语种】中文【中图分类】TU36【相关文献】1.基于有限点法的自由面流动的数值模拟 [J], 卢雨;胡安康;刘亚冲2.基于物质点法的弹体侵彻靶板破甲特性数值模拟 [J], 秦业志;姚熊亮;王志凯;王莹3.基于物质点法的钛合金高速切削数值模拟技术研究 [J], 谷骁勇; 王大勇; 程坦4.基于物质点法的土体强度对边坡失稳滑动距离影响研究 [J], 宰德志;庞锐5.盾构掘进过程土体变形特性数值模拟 [J], 张利民;李大勇因版权原因，仅展示原文概要，查看原文内容请购买。

离散元法及其在岩土工程中的应用综述_王卫华

文章编号:1007-2993(2005)04-0177-05离散元法及其在岩土工程中的应用综述王卫华　李夕兵(中南大学资源与安全工程学院,湖南长沙　410083) 【摘　要】　离散元法是基于不连续性假设的数值方法,它特别适合于求解节理岩体中的非连续性问题。

在介绍离散元法基本原理的基础上,着重对离散元法在岩土工程领域的应用现状作了叙述和分析,并对其发展趋势进行了探讨。

【关键词】　离散元法;岩土工程;数值方法【中图分类号】　T B 115A Review on Fundamentals of Distinct Element Methodand Its Applications in Geotechnical EngineeringWang Weihua Li Xibing(School of Resources and Safe ty Engineering ,Central South U niversity ,Changsha Hunan 410083China )【Abstract 】　The Distinct Element M ethod (DEM )is a discontinuum -based numerical method especially applicable to solve the discontinuity problems in jointed rock mass .Firstly the fundamentals of DEM are introduced ,and then its applications in geo -technical engineering are summarzied emphatically ,and finally the development trends of DEM are discussed .【Key Words 】　Distinct Element M ethod ;geo -technical eng ineering ;numerical method0　引　言岩体是一种具有不连续性、非均质性、各向异性和非线性的天然地质体[1～3]。

砂土振冲密实的细观颗粒流模拟

2009年4月水利学报SH UI LI X UE BAO 第40卷　第4期收稿日期:2008204224基金项目:国家自然科学基金资助项目(50578122);上海市重点学科建设项目资助(B308)作者简介:贾敏才(1973-),男,河南泌阳人,工学博士,主要从事地基处理和离散元数值模拟等方面的研究。

E 2mail :mincai —jia @文章编号:055929350(2009)0420421209砂土振冲密实的细观颗粒流模拟贾敏才1,2,王　磊1,周　健1,2(11同济大学地下建筑与工程系,上海　200092;21同济大学岩土及地下工程教育部重点实验室,上海　200092)摘要:对二维颗粒流程序PFC 2D 进行二次开发,采用其内置的Fishtank 函数库和FISH 语言,定义了模拟砂粒和振冲棒的颗粒块,建立了模拟砂土地基振冲加固过程的细观颗粒流模型以及相应的边界条件,研究了振动频率和振冲方向等对加固效果的影响,并对振冲密实前后砂样的孔隙率、颗粒排列等细观结构特征进行了研究。

与室内细观模型试验对比结果表明,颗粒流理论能够较好地揭示砂土振冲密实的宏细观变化,振冲后砂土的孔隙率、颗粒排列定向性和有序性等细观特性变化与其宏观密实程度具有一定的对应关系。

验证了采用颗粒流理论探索砂土振冲加固的可行性和有效性。

关键词:砂土;振冲密实;细观模拟;机理;颗粒流中图分类号:T U41文献标识码:A1　研究背景因工艺简单、经济实用和不用“三材”等优点,振冲密实法已成为软弱地基特别是吹填砂性土地基最为常用的加固措施之一[1]。

有关学者曾从波和能量的传播[2]、动力液化[3]、循环密实[4]的角度或通过现场试验[1,5-6]、模型试验[7]、有限元方法计算[8]等对砂土的振冲密实及其影响因素进行了大量的研究。

一般认为振冲加固地基主要体现在挤密和振密效应、排水减压效应和预振效应等方面[9],但是限于研究手段或测试技术的限制,这些机理研究多停留于宏观假设的水平上。

+++DEM Analysis of Stresses and Deformations of

DEM Analysis of Stresses and Deformations of Geogrid-Reinforced Embankments over PilesJie Han,Ph.D.,M.ASCE 1;Anil Bhandari 2;and Fei Wang 3Abstract:The geosynthetic-reinforced pile-supported embankment is one of the favorable ground improvement techniques used in the construction of earth structures over a compressible soil when limited construction time is available and limited deformation is permissible.Various methods are available for the design of the geosynthetic-reinforced platform based on various load transfer mechanisms from the embankment to the piles and the compressible soil.The existence of the geosynthetic layer makes the mechanisms more complex.This study focuses on the behavior of geogrid-reinforced embankments over piles compared with the behavior of unreinforced embankments.The numerical simulations of the unreinforced and reinforced pile-supported embankments were conducted using the discrete element method (DEM).The embankment fill was simulated using unbonded graded aggregates of diameters ranging from 9.2to 20.8mm and the geogrid was simulated using bonded particles.This study investigated the changes of vertical and horizontal stresses and porosities,the vertical displacements within the embankment fill,and the deflection and tension in the geogrid.The simulation results showed that the coefficient of lateral earth pressure in the embankment fill changed from an initial at rest condition to a passive condition at certain locations after the compression of the compressible soil.The embankment fill dilated during the development of soil arching.The embankment load was transferred to the piles owing to the reorientation of the principal stresses.The results also showed that the geogrid reinforcement significantly reduced the total and differential settlements at the top of the embankment.DOI:10.1061/(ASCE)GM.1943-5622.0000050.©2012American Society of Civil Engineers.CE Database subject headings:Geosynthetics;Geogrids;Piles;Embankments;Soil deformation.Author keywords:DEM;Embankment;Geogrid;Pile;Soil arching.IntroductionThe geosynthetic-reinforced pile-supported embankment is an eco-nomic and effective solution to solving the total and differential settlement problems encountered in the construction of earth struc-tures over a compressible soil when limited construction time is available and limited deformation is permissible (Han and Gabr 2002).This construction technique is equally useful in addressing the challenges posed by an existing large sinkhole under a proposed highway alignment (Wang et al.2009).Soil arching is a key mecha-nism in transferring the load owing to the embankment weight and surface loadings to the piles that would otherwise rely on support from the soft soil or a void area.The details of soil arching and the governing factors can be found in Giroud et al.(1990),McKelvey (1994),Han and Gabr (2002),Jenck et al.(2007),and Chen et al.(2008).Various design methods for the load transfer platformabove piles have been proposed based on various assumptions of load transfer mechanisms in the embankment fill to the piles and the compressible soil.For example,Chen et al.(2008)com-pared three design methods based on Terzaghi (1943),Low et al.(1994),and BS8006(BSI 1995)with experimental results and found significant deviations in the calculated stress concentration ratios from the measured ones.Understanding the load transfer mechanisms of pile-supported embankments is one of the keys to improving these design methods.Huang et al.(2009)coupled mechanical and hydraulic models to investigate the short-and long-term behavior of geosynthetic-reinforced pile-supported embankments.Recent research has used a coupled finite-discrete element model to investigate the behavior of geosynthetic-reinforced em-bankments over piles.The coupled finite-discrete element model accommodates the fibrous structure of the geosynthetic including its tensile and membrane effect.Meanwhile,the discrete element method (DEM)model of the embankment fill evaluates the force transfer between the particles at a particle contact level as the key mechanism of soil arching (Le Hello and Villard 2009;Villard et al.2009).Le Hello and Villard (2009)observed that the stiffness of the geosynthetic had a minor influence on the load transfer mechanism but governed the maximum geosynthetic deformation.This finding signifies that the load transfer to the pile caps as a result of soil arching develops at a small particle movement in the embankment.The displacement vectors of the particles in the embankment indicated a triangular shape of soil arching,which is similar to the finding of Bhandari et al.(2009).Jenck et al.(2009)presented two-dimensional (2D)small-scale model studies of the pile supported granular platform and the discrete element and continuum-based numerical modeling.They found that the DEM model better predicted the behavior of the1Professor,Dept.of Civil,Environmental,and Architectural Engineer-ing (CEAE),Univ.of Kansas,Lawrence,KS 66045-7609(corresponding author).E-mail:jiehan@ 2Geotechnical Project Manager,Terracon Consultants,Inc.,14505th St.West,North Charleston,SC 29405;formerly,Graduate Research Assistant,GSI fellow,Dept.of Civil,Environmental,and Architectural Engineering (CEAE),Univ.of Kansas,Lawrence,KS 66045-7609.E-mail:abhandari@ 3Lecturer,Institute of Geotechnical Engineering,Southeast Univ.,Nanjing 210096,China.E-mail:feiwangseu@Note.This manuscript was submitted on November 14,2009;approved on April 29,2011;published online on May 2,2011.Discussion period open until January 1,2013;separate discussions must be submitted for individual papers.This paper is part of the International Journal of Geo-mechanics ,V ol.12,No.4,August 1,2012.©ASCE,ISSN 1532-3641/2012/4-340–350/$25.00.340/INTERNATIONAL JOURNAL OF GEOMECHANICS ©ASCE /JULY/AUGUST 2012D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y U N I VE R S I T I P U T R A M A L A Y S I A o n 05/21/14. C o p y r i g h t A S C E .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .platform (for example,the efficacy;i.e.,the ratio of the load shared by the piles to the total load of the platform),than the continuum model even though both approaches overpredicted the experimen-tal values.Furthermore,they pointed out that the stress and strain are coupled in the continuum model while the discrete element model has less restriction on the stress and strain relationship.As a consequence,an increased friction angle of the platform material increased the efficacy and reduced the settlement in the continuum model while the reduction in the settlement was insignificant in the discrete element model.The pictorial presentation of the contact forces in the embank-ment illustrates the load transfer mechanism (Bhandari et al.2009;Jenck et al.2009).Bhandari et al.(2009)showed that the contact forces were concentrated over the pile caps compared with the soil between the pile caps in both unreinforced and reinforced embank-ments.However,the geogrid in the reinforced embankment re-duced the contact forces transmitted to the compressible soil below the geogrid.Tensile forces developed in the geogrid,which acted as a tensioned membrane.These studies clearly demonstrated the merits of using the DEM to investigate the soil arching mecha-nism,which involves the relative movement of particles in the embankment.However,most studies thus far have focused on the stress trans-fer between the soil and the pile using the parameters such as the stress reduction ratio,efficacy,and stress concentration ratio above the geosynthetic layer and the deflection of the geosynthetic layer at the pile head level.The stress distribution within the embankment fill in the vertical and horizontal directions,orientations of the contacts,normal forces and shear forces between particles,change of the fill porosity,particle movement within the embankment fill,and effect of the geosynthetic have not been well investigated,which are important for the understanding of soil arching in geosynthetic-reinforced pile-supported embankments.Therefore,they deserve a further study and will be discussed in this paper.In this study,the geogrid was modeled using a series of bonded particles.Numerical SimulationThe particle flow code,PFC2D,developed by Itasca (2004)and based on the DEM (Cundall and Strack 1979),was used in this study.PFC2D is based on rigid body and soft contact approaches.The soft contact approach allows calculating deformations at the contacts.PFC2D utilizes two successive cycles to compute the forces and displacements of the particles.The motion of each particle is calculated from the resultant contact and body forces acting on the particle using Newton ’s second law of motion.The contact and body forces are then updated for the resulting motion by applying the force-displacement law (Itasca 2004).The model preparation and determination of the micromechanical parameters for the model used in this study are discussed subsequently.Material PropertiesThe micromechanical properties of materials are usually calibrated using known macromechanical responses.Biaxial tests and shear tests have been commonly used to evaluate and back-calculate the micromechanical properties of geomaterials (Chareyre and Villard 2002;Zhang and Thornton 2007).In this study,biaxial test simu-lation was used to calibrate the micromechanical parameters of the embankment fill while tensile test simulation was used to calibrate the micromechanical parameters of the geogrid.The parameters of stiffness and contact bond strength of the particles were calculated using the following relationships (Itasca 2004;Potyondy and k n ¼2tE c ;ϕ¼2t σc R ;ϕ¼2t τc Rð1Þwhere k n =normal stiffness of the particles;t =thickness of particles along the plane of paper;E c =Young ’s modulus of the particle/particle contact;ϕn =parameter of the contact bond normal strength (σc )between particles;R =radius of the particle;and ϕs =parameter of the contact bond shear strength (τc )between particles.Here,ϕn and ϕs are expressed in the unit of force.Embankment FillThe biaxial sample used to calibrate the embankment fill had a width of 0.6m and a height of 1.2m.Particles with diameters ranging from 9.2to 20.8mm were generated at a porosity of 0.16under the gravity deposition method.The particle size distri-bution followed a normal distribution curve with a mean particle size (d 50)of 15.0mm.The dimensions (width and height)of the biaxial sample were not realistic for a laboratory test;however,they were chosen to permit the generation of a sufficient number of particles (number of particles ¼3;422)for the biaxial test simula-tion.The micromechanical parameters governing the response of the materials at the macrolevel are presented in Table 1.The devia-toric stress versus the axial strain and the volumetric strain versus the axial strain are shown in Figs.1and 2.The contraction of the sample was plotted as a negative volumetric strain while the dila-tion of the sample was plotted as a positive volumetric strain in Fig.2.These plots were obtained at three confining stresses:10,20,and 40kPa.The confining stresses mimic a typical stress level in the embankment of the selected dimension.Fig.2shows the large dilation of the sample,indicating the dense behavior of the granular material.At this research stage,no experimental data are available for a comparison with the simulation results.The q Àp 0plot of this test is shown in Fig.3,and the friction angle of the assembly can be calculated as follows:qp 0¼sin Ø¼0:44ð2Þwhere Ø¼26°.The obtained assembled friction angle (Ø¼26°)was much smaller than the friction angle of the particle/particle contact.The differences between the assembled friction angle and the contact friction angle of particles have been observed in experimental and numerical simulations of biaxial compression tests (Bathurst and Rothenburg 1990;Masson and Martinez 2000).Particles in a 2D arrangement have contributed to thisTable 1.Micromechanical Properties for the DEM Analysis ParameterValue SoilNormal stiffness of particles,k n 75MN/m Shear stiffness of particles,k s 62.5MN/m Friction coefficient,μ0.80GeogridNormal stiffness of particles,k n 645MN/m Shear stiffness of particles,k s 645MN/m Friction coefficient,μ0.64Parameter of contact bond normal strength,ϕn 23.74kN Parameter of contact bond shear strength,ϕs 23.74kN Parallel bond normal stiffness,k np 1;290GN ∕m 3Parallel bond shear stiffness,k sp 1;290GN ∕m 3Parallel bond normal strength,σnp 94:9MN ∕m 2Parallel bond shear strength,σsp 94:9MN ∕m 2Parallel bond radius multiplier,r pb0.5D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y U N I VE R S I T I P U T R A M A L A Y S I A o n 05/21/14. C o p y r i g h t A S C E .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .low friction angle as well.Jenck et al.(2007)obtained a friction angle of 24°for steel rods in biaxial compression tests.Even though the friction angle of natural granular materials with an inherent sur-face roughness is typically higher than the friction angle of the biaxial rods,use of biaxial rods (also called the Schneebeli soil)is well accepted in geotechnical research when studying the behav-ior of granular materials.The use of clump particles to achieve a higher friction angle for embankment fill will be investigated in future research.GeogridChareyre and Villard (2005)proposed a dynamic spar element model to simulate the interface between geosynthetics and soilroughness.This model was verified with flat geosyn-such as geotextiles.However,this model has not been with geogrids.For geogrids,the large dimensions of the play an important role in the interface friction.In this the geogrid was modeled using a series of bonded particles,mm in diameter at a rib and 2.6mm in diameter at the junctions,typical geogrids in the market.The contact bond forcethe geogrid particles corresponds to the tensile strength of geogrid.Similarly,the tensile stiffness of the geogrid corre-to the normal stiffness between particles.It is worth men-that the stiffness of a viscoelastic material such as a geogrid on the strain rate (Walters et al.2002).However,the model used an elastic spring at the contact between two (i.e.,the contact-bond model);therefore,the viscoelastic of the geogrid was not captured.The micromechanical of the geogrid were calibrated by simulating a tensile test.Because the geogrid has some bending resistance,par-allel bonds with a radius of 0.25mm were considered in the sim-ulation of the tensile strength test.However,this parallel bond had no influence on the tensile strength of the geogrid at the low strain (up to 5%)used in the calibration.The particles generated for the tensile test simulation are shown in Fig.4.Thirty particles were generated to cover a span of 33.2mm to simulate an aperture of the geogrid without any overlap between the particles.The center-to-center distance,L ,between the adjacent junctions would be 30.6mm,which is the aperture dimension in the cross-machine direction for a selected punched-drawn biaxial geogrid.The cali-brated parameters of the geogrid are provided in Table 1.During the simulation,the starting and ending particles in the row were given a small velocity,v ,of 10À8m ∕step to simulate the tension test.The resulting forces between the particles were recorded.102030405060708000.020.040.060.08D e v i a t o r i c s t r e s s (k P a )Axial strain402010Confining pressure (kPa)Fig.1.Deviatoric stress versus axial strain from PFC2D biaxial test simulationsV o l u m e t r i c s t r a i nAxial strainFig.2.Volumetric strain versus axial strain from PFC2D biaxial test simulationsq= 0.44p'5101520253035020406080q =(σ1-σ2)/2, k P ap'=(σ1+σ2)/2, kPaFig.3.Deviatoric stress q versus mean effective stress p 0plotFig.4.Particle assembly for a tensile-test simulation of a geogridD o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y U N I VE R S I T I P U T R A M A L A Y S I A o n 05/21/14. C o p y r i g h t A S C E .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .The DEM results were compared with the tensile force of the geogrid as mentioned on the product specification for this selected geogrid.Fig.5shows a reasonable agreement between the DEM results and the experimental data.Numerical Modeling of Embankment over PilesA 1.6-m-high and 1.5-m-long rectangular box was created using four walls (Fig.6).Particles,ranging from 9.2to 20.8mm in dia-meter,were generated at a porosity of 0.16using the radial expansion technique described in Itasca (2004).The particle size distribution followed a normal distribution curve with a mean par-condition,a geogrid sheet was placed by generating bonded par-ticles with a diameter of 2.6mm on the nodes and 1.0mm between the nodes inside the guided walls (created at 1.3m below the top wall).The geogrid was optional depending on whether an unrein-forced or reinforced case was studied.A 0:3×0:3m pile cap was placed on either side of the model using walls and the particles inside the pile caps were deleted because they did not interact with particles outside the walls.The deletion of these particles was also needed for the calculation of the unbalanced force on the walls from the particles outside.The remaining particles in the model were subjected to the gravity field and brought to an equilibrium condition.Furthermore,the porosity of the assembly below 1.3m (i.e.,between the pile caps)was increased to 0.35from an initial porosity of 0.16by randomly deleting the particles within this zone.The high porosity within this zone was to simulate the compressible soil.Because of this compressible soil in the lower part,the embankment fill undergoes displacements to achieve a new equi-librium of the system (embankment).Twenty-three measurement circles were installed in the model as shown in Fig.6to measure the horizontal and vertical stresses at various stages of the simula-tion.It is worth mentioning that the unit cell concept has been com-monly used by researchers to analyze pile-supported embankments (see,for example,Han and Gabr 2002;Smith and Filz 2007).Because the widths of most embankments are much larger than the spacing of the piles,it is reasonable to use the unit cell concept to analyze central piles,which have larger settlements than the edge piles.When the piles are closer to the centerline of the embank-ment,the horizontal displacements of the piles are small.Analysis of the ResultsStresses in the EmbankmentDevelopment of soil arching in an embankment changes its stress these stresses are not readily measureable in the simulation.In a discrete collection of particles,only the at the physical contacts can be computed.These be converted to the equivalent continuum stresses over circle using the volume average method.Eq.(3)forces at the contacts to the average stresses ð σij Þin circle (Itasca 2004)σij ¼1ÀnP N pV!"X N pX N p cx ðc Þi Àx ðp Þi F ðc ;p Þj#ð3Þsummation is taken over N p particles whose centroids lie measurement circle.Here,V ðp Þ=volume of the particle;inside the measurement circle;N p c =number of con-the surface of particle p ;x ðc Þi and x ðp Þi =locations ofand the contact of particle p ,respectively;and F ðc ;p Þj =on particle p at contact c .7shows the vertical and horizontal stress contours within before the development of soil arching.The par-subjected to the gravity field and brought to an equilib-The force equilibrium of the embankment was ensured total weight of the embankment was the same as the of the loads transferred to the pile caps and the bottom fluctuations on the stresses at equal vertical heights but expected,because contact forces may develop preferential path in the discrete simulation.Almost equally stress contours in Fig.7show the linear gradient vertical stress under the influence of the gravity field.parison of DEM and experimental results for a geogrid in a tensile testOF GEOMECHANICS ©ASCE /JULY/AUGUST 2012/343D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y U N I VE R S I T I P U T R A M A L A Y S I A o n 05/21/14. C o p y r i g h t A S C E .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .The horizontal stresses were approximately one-half of the vertical stresses throughout the embankment.Fig.8shows the contours of the vertical and horizontal stresses after the development of soil arching in the unreinforced embank-ment.Fig.9shows similar plots for the reinforced embankment.In both cases,the vertical stresses increased significantly over the pile caps but decreased between the pile caps.The horizontal stresses also increased over the pile caps but largely remained unaffected in the portion of the embankment between the pile caps.Therefore,the horizontal stresses follow the trend of the vertical stresses only in a loading path but behave differently in an unloading path.This effect leads to the locked-in horizontal stresses in the soil mass.Stress concentration ratio (n )is often used to characterize the degree of stress transfer and soil arching and defined as a ratio of the stress on the pile cap,σc ,to the stress on the soil,σs ,(Han and Gabr 2002).The initial stress concentration ratio (n )was 3.5for the unreinforced model and 7.5for the geogrid rein-forced model.This result is consistent with that of the Han and Gabr (2002)numerical study,in which the geosynthetic increased the stress concentration ratio compared with the unreinforced case.A ratio of the horizontal stress to the vertical stress,defined as the coefficient of lateral earth pressure (k ),is often used to evaluate the stress condition in the soil mass.The coefficients of lateral earth pressure at various embankment heights were calculated before and after the development of soil arching for the unreinforced and reinforced embankments as shown in Fig.10.Three sections were considered at distances of 0.20,0.40,and 0.75m away from the left wall.Before the development of soil arching,the coefficient of lat-eral earth pressure fluctuated in a narrow range,which may be con-sidered uniform for practical purposes.The average coefficient of lateral earth pressure was 0.49.The coefficient of lateral earth pres-sure at rest may be calculated using Jaky ’s formula as follows:K o ¼1Àsin Ø¼1Àsin 26°¼0:56ð4Þwhere Ø=friction angle of the granular media.The theoretical value of K o was reasonably close to the average value obtained from the numerical simulation.After the development of soil arching,the coefficient of lateral earth pressure varied in a wide range of 0.5–2.7as shown in Fig.10.The coefficient of 2.7is the same as the coefficient of passive earthDistance (m)(a)(b)E m b a n k m e n t h e i g h t (m )00.31.2 1.500.30.60.91.21.5Distance (m)0.31.2 1.500.3Fig.7.Stress contours in the embankment before the development of soil arching:(a)vertical stress (kPa);(b)horizontal stress (kPa)Distance (m)(a)(b)E m b a n k m e n t h e i g h t (m )00.31.2 1.50Distance (m)00.31.21.50.3Fig.8.Stress contours in the unreinforced embankment after development of soil arching:(a)vertical stress (kPa);(b)horizontal stress (kPa)344/INTERNATIONAL JOURNAL OF GEOMECHANICS ©ASCE /JULY/AUGUST 2012D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y U N I VE R S I T I P U T R A M A L A Y S I A o n 05/21/14. C o p y r i g h t A S C E .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .pressure.In both unreinforced and reinforced embankments,the maximum coefficient of lateral earth pressure occurred at the top level of the embankments along the midspan between the pile caps.As a result of the development of soil arching,the vertical stresses along the midspan of the embankments decreased signifi-cantly as shown in Figs.8and 9.Therefore,the reduced vertical stresses coupled with the relatively unaffected horizontal stresses resulted in the maximum coefficient of lateral earth pressure at the top of the embankments.Contact Forces and OrientationsForces in granular media transfer through an interconnected net-work of force chains via contact points.Fig.11shows the contact force distributions for the unreinforced and reinforced embank-ments at the development of soil arching.The contact forces were plotted on the same scale.In Fig.11,the arrows point to compres-sive contact forces and tensile contact forces.The thickness of the lines represents the relative magnitude of the contact forces.For example,the maximum compressive contact forces were 714and 730N in the unreinforced and the reinforced embankments,respectively.The maximum tensile force was 1,009N in the rein-forced embankment.The weight of the embankment portion be-tween the pile caps was transferred to the adjacent pile caps owing to the reorientation of the contact forces.Therefore,the com-pressive contact forces were concentrated over the pile caps for both unreinforced and reinforced embankments.The remaining weight of the embankment portion between the pile caps trans-ferred to the underlying compressible soil in the unreinforced embankment.The geogrid transferred the remaining weight of the embankment portion between the pile caps to the pile caps through the cable action of the geogrid in the case of the reinforced embankment.A negligible amount of forces was transferred to the compressible soil because the geogrid barely rested over the com-pressible soil.Furthermore,it is evident that the contact forces at the midspan of the embankments were increasingly aligned on a horizontal direction toward the top of the embankments.The con-sequence of this load transfer was the occurrence of the maximum lateral earth pressure coefficient at the top of the embankments as explained in the preceding section.The polar histogram of the contact forces shown in Fig.11can be obtained by collecting the contact force information at aDistance (m)(a)(b)E m b a n k m e n t h e i g h t (m )00.31.2 1.50Distance (m)00.31.2 1.50.3Fig.9.Stress contours in the geogrid-reinforced embankment after the development of soil arching:(a)vertical stress (kPa);(b)horizontal stress (kPa)1.21.5Coefficient of lateral earth pressure (k)Coefficient of lateral earth pressure (k)(a)(b)E m b a n k m e n t h e i g h t (m )Fig.10.Coefficient of lateral earth pressure at various sections of the embankments before and after the development of soil arching:(a)unreinforced;(b)reinforcedINTERNATIONAL JOURNAL OF GEOMECHANICS ©ASCE /JULY/AUGUST 2012/345D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y U N I VE R S I T I P U T R A M A L A Y S I A o n 05/21/14. C o p y r i g h t A S C E .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .orientation was normalized by the total number of contacts.Similarly,the polar histograms for the contact normal forces and tangential forces were normalized by the average normal force over all contacts in the assembly.Fig.12shows the normalized histo-grams for the orientations of the contacts and the forces for the embankment at an initial equilibrium condition and after the devel-opment of soil arching in the cases of unreinforced and reinforced embankments.Fig.12also shows the Fourier series approximation of these normalized orientations of the contacts and forces.Because Zones A and B in Fig.11showed various contact force orienta-tions,they were evaluated separately.The observation of the normalized orientations of the contacts and contact forces led to the following Fourier series approximations (Rothenburg and Bathurst 1989;Bathurst and Rothenburg 1990):E ðθÞ¼12π½1þa cos 2ðθÀθ0Þ ð5Þ f n ðθÞ¼ f o ½1þa n cos 2ðθÀθf Þ ð6Þ f t ðθÞ¼ f o ½Àa t cos 2ðθÀθt Þ ð7Þf o ðθÞ¼12πZ2π0 f n ðθÞd θ¼1NX N cf k nð8Þwhere E ðθÞ=contact density distribution function; f n ðθÞ=averagenormal force density distribution function; f t ðθÞ=average tangen-tial force density distribution function; f t ðθÞ=average contact force of all contacts in the region of interest;a ,a n ,and a t =magnitudes of the directional variations of the contacts,the average normal force,and the average tangential force;θa ,θf ,and θt =corresponding major principal directions of anisotropy;N =total number of particles;and f k n =contact normal force.Table 2shows the coefficients of the Fourier series approxima-tion of the contact and the force orientations at various stages of simulation.At the initial equilibrium under the application of the gravity field,Zones A and B in the embankment had identical density distributions for the contacts and for the normal as well as the tangential forces as shown in Fig.12(a).The density distribu-tion of the contacts was isotropic,the normal contact forces had aoped more contacts in the horizontal direction than in the vertical direction [Fig.12(b)and 12(d)].The contact normal force was slightly higher in the horizontal direction than in the vertical direc-tion for the unreinforced embankment but was isotropic for the reinforced embankment.The isotropic distribution of the stresses beneath the soil arch was proposed for the analytical solution of the piled embankment by Hewlett and Randolph (1988).Within Zone B inclined principal directions of the contacts and the contact normal forces developed at angles of 74.5and 86.2°for the unrein-forced embankment and 80.9and 83.9°for the reinforced embank-ment,respectively.Similarly,the directions of the zero average tangential force inclined at angles of 82.5and 81.4°for the unrein-forced and reinforced embankments,respectively.The normalized tangential forces after the development of soil arching did not show any marked increase compared with those before the development of soil arching.The previous discussion demonstrates that the load transfer of the embankment to the pile caps is a result of the reorientation of the major principal stresses.Porosity Changes in the EmbankmentGranular materials show volumetric dilation or contraction behav-ior under the influence of external disturbances (force or displace-ment field)depending upon their initial packing conditions.In general,an initially dense-packed system shows volumetric dilation while a loose-packed system shows volumetric contraction.It is extremely challenging to measure the volumetric changes within the embankment owing to the development of soil arching.How-ever,this information can be readily obtained in a discrete element ing the porosities monitored at various measurement circles,the percentage porosity changes in the embankment before and after the development of soil arching could be calculated and are presented in Fig.13.Both the unreinforced and reinforced embankments showed increased porosities (i.e.,dilation)to a maxi-mum percentage change of 2%.The maximum dilation occurred at the midspan between the pile caps and at the height equal to one-half of the clear spacing.Higher dilation also developed near the edge of the pile caps.The influence area of the increased porosity for the unreinforced embankment was more spread out than that for the reinforced embankment.The dilation of the embankment fill346/INTERNATIONAL JOURNAL OF GEOMECHANICS ©ASCE /JULY/AUGUST 2012D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y U N I VE R S I T I P U T R A M A L A Y S I A o n 05/21/14. C o p y r i g h t A S C E .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .。

月壤静力学特性的离散元模拟

第38卷第2期吉林大学学报(工学版)Vol.38 No.22008年3月Jour nal of Jilin U niversity (Eng ineer ing and T echnolog y Editio n)M ar.2008收稿日期:2007-05-10.基金项目:教育部科学技术研究重点项目(107035);吉林大学/985工程0项目.作者简介:邹猛(1978-),男,博士研究生.研究方向:车辆地面力学.E -mail:zoumeng 0001@通讯联系人:李建桥(1953-),男,教授,博士生导师.研究方向:地面机械仿生及控制.E -mail:jqli@月壤静力学特性的离散元模拟邹猛1,李建桥1,贾阳2,任露泉1,李因武1(1.吉林大学地面机械仿生技术教育部重点实验室,长春130022; 2.中国空间技术研究院,北京100094)摘要:以典型月壤的物理力学性质为参照标准,采用颗粒流程序PFC3D 对月壤静力学特性进行了离散元模拟研究。

通过离散元模拟三轴试验反复调整颗粒细观参数,建立了月壤离散元接触力学模型;描述了月面探测车辆行驶下的月壤承压特性模型与剪切特性模型;从月面探测车辆的行驶观点出发,模拟压板试验,得出了载荷-沉降关系;通过模拟履带板试验得出了剪切应力-位移关系。

最后,计算出了月壤的变形模量K 为1635kN/m n +2、变形指数n 为1.22,剪切变形模量k 为1.35cm 。

结果表明,模拟试验值与模型预测趋势一致。

关键词:农业工程;月壤;剪切特性;承压特性;PFC3D中图分类号:S152.9;T P391 文献标识码:A 文章编号:1671-5497(2008)02-0383-05Statics characteristics of lunar soil by DEM simulationZou M eng 1,Li Jian -qiao 1,Jia Yang 2,Ren Lu -quan 1,Li Yin -w u 1(1.K ey Labor ator y of T er r ain -machine Bionics E ngineer ing,M inis tr y of Ed ucation ,J ilin Univer sity ,Changchun 130022,China;2.China A cademy of Sp ace T echnology ,B eij ing 100094,China)Abstract:According to its physical m echanics properties,the statics char acteristic o f lunar soil is studied using DEM softw are PFC3D.T he DEM contacting m echanics mo del o f lunar soil w as built by triax -test to adjust the particle m icro par am eters.T he pressure -sinkag e m odel and shear mo del o f the lunar ro ver passing on lunar surface w er e descr ibed.Then the plate -sinkag e -test w as sim ulated to obtain the relationship betw een load and sinkage;and the shear -test w as simulated to obtain the relatio nship betw een shear and displacement.Finally the terra -m echanics parameters of the lunar soil w ere calculated as:the deformation modulus K =1635kN/m n +2,the sinkag e ex ponent n =1.22and the shearing strength displacement m odulus k =1.35cm.These values o btained by DEM simulation ar e close to that obtained by prediction model.Key words:ag ricultur al engineering;lunar so il;shear char acteristics;pressure -sinkage characteristics;PFC3D深空探测车辆是各种探测仪器的载体,最基本的要求是能够具有在未知的复杂路面行走的能力,以满足科学探测考察的需要[1]。

岩土工程硕士论文-砂土地基静压沉桩三维颗粒流PFC_'3D_离散元模拟分析模板

simulation，large deforma兹呈交的学位论文是本人在导师指导下完成的研究成果。论文写作中不包含其他人已经发表或撰写过的研究内容，如参考他人或集体的科研成果，均在论文中以明确的方式说明。本人依法享有和承担由此论文所产生的权利和责任。
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华侨大学 2010 届硕士学位论文
砂土地基静压沉桩三维颗粒流 PFC3D 离散元模拟分析
第一章
绪
论
1.1 前言
华侨大学硕士学位论文砂土地基静压沉桩三维颗粒流PFC<'3D>离散元模拟分析姓名：黄晨亮申请学位级别：硕士专业：岩土工程指导教师：郭力群 20100601
摘
要
对静压沉桩过程的数值模拟研究以往主要是建立在传统连续介质力学模型宏观连续性假设的基础上,应用有限元对沉桩规律进行计算分析。但是工程中静压沉桩是桩土之间倾倒、滑移、裂缝不断发展的过程，桩和桩周土都会产生大位移及大变形，因而采用连续介质假设的有限元模拟分析方法很不适用。而离散元颗粒流方法克服了连续介质力学模型宏观连续性假设，可以模拟沉桩过程中桩周土体颗粒非均质、不连续和大变形位移流动的特性。能够解决传统数值方法忽略的和无法解决的问题，能对静压沉桩过程进行更为符合实际的模拟。对静压沉桩过程的数值模拟已有部分学者采用离散元颗粒流分析，但都是基于平面状态二维分析，与实际三维沉桩情况有很大差别。因此有必要利用离散元三维颗粒流 PFC3D 方法对静压沉桩全过程进行模拟分析，目前尚未见相关研究报道。本文从细观力学角度出发利用离散元三维颗粒流 PFC3D 方法对砂土地基静压沉桩全过程进行模拟。首先，模拟分析了单桩在整个沉桩贯入过程桩周不同区域土体位移、孔隙率、颗粒滑动数、接触数和应力的变化规律。通过改变土体参数、压桩参数和桩体参数不同因素去分析对静压沉桩贯入的影响，同时将数值模拟结果与前人室内模型试验进行对比。发现在模拟试验中桩周土体的孔隙率、应力与位移变化与模型实验中的变化趋势非常接近，分析对比结果较为吻合。表明利用三维颗粒流 PFC3D 方法分析砂土中静压沉桩是可行的。其次，对邻近桩基的先后沉桩对不同区域土体的影响进行了分析，并对后桩沉桩对前桩不同区域处的土体细观参数影响进行了研究，分析结果可以

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Particuology9 (2011) 650–658ContentslistsavailableatScienceDirectParticuology

journalhomepage:www.elsevier.com/locate/partic

AdiscreteelementmodelforsimulatingsaturatedgranularsoilMahanLamei,AliAsgharMirghasemi∗SchoolofCivilEngineering,CollegeofEngineering,UniversityofTehran,P.O.Box11155-4563,Tehran,Iran

articleinfoArticlehistory:Received21June2010Receivedinrevisedform14September2010Accepted21April2011Keywords:DiscreteelementmethodGranularsoilSaturatedsoilPorepressureabstract

Anumericalmodelisdevelopedtosimulatesaturatedgranularsoil,basedonthediscreteelementmethod.SoilparticlesarerepresentedbyLagrangiandiscreteelements,andporeﬂuid,byappropriatediscreteelementswhichrepresentalternatelyLagrangianmassofwaterandEulerianvolumeofspace.Macro-scalebehaviorofthemodelisveriﬁedbysimulatingundrainedbiaxialcompressiontests.Micro-scale

behavioriscomparedtopreviousliteraturethroughporepressurepatternvisualizationduringshear

tests.Itisdemonstratedthatdynamicporepressurepatternsaregeneratedbysuperposedstresswaves.Thesepore-pressurepatternstravelmuchfasterthanaveragedrainagerateoftheporeﬂuidandmayinitiatesoilfabricchange,ultimatelyleadingtoliquefactioninloosesands.Thus,thisworkdemonstrates

atooltoroughlylinkdynamicstresswavepatternstoinitiationofliquefactionphenomena.

1.IntroductionGranularsoils,becauseoftheirfavorableandreliablemechan-icalproperties,aremajormaterialingeotechnicalengineering.Phenomenologicalresearchonmicrostructureofthesewidelyusedconstructionmaterialhasbeenofgreatinterestingeotechnicallit-erature.Researchinthisareahasbeencarriedoutbymeansofinnovativelaboratorytechniques(DeJosselindeJong&Verruijt,1969;Oda&Konishi,1974;Oda,Takemura,&Takahashi,2004;Rechenmacher&Finno,2004)orbymeansofnumericalsimula-tions(Bagherzadeh-Khalkhali&Mirghasemi,2009;Mirghasemi,Rothenburg,&Matyas,2002;Ng&Dobry,1994;Rothenburg&Bathurst,1991;Strack&Cundall,1978).Inmanyimportantgeotechnicalstructures,asindams,offshoreretainingwalls,andtailingdams,granularsoilisimmersedinwater.Inthesestruc-tures,interactionofsoilgrainsandporewatermayleadtolossofshearstrengthandﬁnalcollapseofthesoilstructureundersomeloadingssuchasearthquakes.Stateoftheartresearchisaimedatacquiringcomprehensiveknowledgeaboutbehaviorofimmersedgranularmaterial.Withrecentprogressincomputationaltoolsandmethods,itisreasonabletomakenumericalinvestigationsatthescaleofconstituentelementsofasoilbodywhichissaturatedwithwater.Microstructuralinvestigationofsaturatedsoildeformationispossiblevianumericalsimulations,andhasalwaysbeenconducted∗Correspondingauthor.Tel.:+982166957783;fax:+982166957787.E-mailaddress:aghasemi@ut.ac.ir(A.A.Mirghasemi).bymeansofthediscreteelementmethod,withsoilparticlesasdiscreteelementsandporewaterasasurroundingmediumthatappliesforcestograinsaccordingtosomeappropriateassump-tions.Hakuno(1995),inatwodimensionalanalysis,determinedeachandeveryindividualporeasareainsideaclosedchainofgrains.Volume(areain2Dsimulations)oftheseporesiscalcu-latedforeachDEMcycle.Changeinvolumesleadstochangeinporewaterpressure,whichinturn,leadstoexertionofforcetograinsandwillbecoupledtoDEMforcecalculationinthecurrentcycle.BeforeproceedingtothenextDEMcycle,porepressuresalloverthesampleareequalized,ignoringanyﬂowpatternthatmaystillremainattheendofthecurrentDEMcycle.Nakase,Takeda,andOda(1999),deﬁnedaﬁxedmeshofsquares,eachsquarecellcontainingabout15soilparticles.Theporevolumechangeineachcelliscomputedonthebasisofparticledisplace-mentsintheneighboringcells,andcauseschangeinthepressureofthecell.Thepressuredifferenceamongcellsgeneratesagra-dientthatdriveswaterﬂow.Aﬁnitedifferenceschemehasbeenusedtosolvetheequationsdescribingporepressuredissipation.

Oncepressuredissipationhasoccurredafteratimeincrement,theremainingpressuresareconvertedintoforcesactingonparticles.Bonilla(2004)usedtheporedeterminingapproachandfurtherassumedneighboringporesasinterconnectedbypipesofdiffer-entlengthsbutsamediameteracrossthespecimen.Thisnetworkofreservoirsandpipesdissipatesgeneratedexcessporepressuresaccordingtoaﬁnitedifferencescheme.Remainingporepressuresateachcyclearetransformedtoforcesonparticles.ThisapproachcanbeusedinthreedimensionsemployingtheDelaunaytessella-tionfordeﬁnitionofporesinthreedimensions(Yang,Zou,Yu,&

1674-2001/$–seefrontmatter© 2011 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved.doi:10.1016/j.partic.2011.04.001