Finite element simulations of seismic effects on retaining walls with liquefiable backfills

Finite element simulations of two centrifuge tests on the same cantilever retaining wall model holding liquefiable backfill were conducted using the Biot formulation‐based program DIANA–SWANDYNE II. To demonstrate the effects due to different pore fluids in seismic centrifuge experiments, water was used as the pore fluid in one experiment whereas a substitute pore fluid was used in the second experiment. The cantilever wall model parameters were determined by comparing simulations with measurements from free‐vibration tests performed on the model wall without backfill. The initial stress conditions for dynamic analysis for the soil backfill were obtained by simulating static loads on the retaining wall from the soil backfill. Level‐ground centrifuge model results were used to select the parameters of the Pastor–Zienkiewicz mark III constitutive model used in the dynamic simulations of the soil. The effects due to different pore fluids were captured well by the simulations. The magnitudes of excess pore pressures in the soil, lateral thrust and its line of action on the wall, and wall bending strains, deflections, and accelerations were predicted well. Predictions of settlements and accelerations in the backfill were less satisfactory. Relatively high levels of Rayleigh damping were needed to be used in the retaining wall simulations in order to obtain numerically stable results, which is one of the shortcomings of the model. The procedure may be used for engineering purpose dealing with seismic analysis of flexible retaining walls where lateral pressures, bending strains and deflections in the wall are typically of importance. Copyright © 2008 John Wiley & Sons, Ltd.     

Analytical solution for the response of a flexible retaining structure with an elastic backfill

An extension of an existing analytical solution for the response of a flexible retaining wall subjected to seismic loading is presented. The solution is based on the assumption that the wall and the soil remain elastic and that there are no shear stresses at the wall–soil interface while the contact remains tied. In addition to the wall displacements due to bending, the wall can experience rigid‐body motions due to rotation and horizontal and vertical movements. The solution is verified by comparing its results with those of a finite element method. Results from the analytical solution together with those of the (FEM) are used to identify and quantify the relative importance of key parameters on the seismic response of a wall. The study shows that wall flexibility and horizontal rigid‐body motions of the wall and frequency content of the seismic input have a significant effect on the wall loads. The pressures behind a rigid wall decrease as the wall rotates about its base, whereas for a flexible wall, the soil pressures decrease as the friction between the backfill and the wall increases. The rigid‐body vertical movements of a wall have little impact on the dynamic pressures induced in the wall, except for a flexible wall where, when prevented, the dynamic loads may be reduced. Copyright © 2009 John Wiley & Sons, Ltd.     

考虑土拱效应的刚性挡墙主动土压力分析

以墙后填土为无黏性土的刚性挡土墙为研究对象,考虑墙后土体的土拱效应,修改了Shubhra Geol 抛物线形土拱表达式,推导了对应不同内摩擦角和墙-土摩擦角的挡土墙平动模式下的主动土压力系数。基于水平微分单元法,得到考虑土拱效应的主动土压力分布、合力大小和合力作用点高度的理论表达式,并与现有经典理论解及前人理论研究成果和模型试验数据进行对比分析,结果表明,主动土压力与墙-土接触面摩擦角、土体内摩擦角、土体重度和挡墙高度相关,土压力分布为非线性,与其他结果比较吻合,从而验证了该研究成果的正确性。     

考虑分层填筑及地应力平衡的挡土墙数值仿真

针对重力式挡土墙墙后分层填土对墙身受力影响的问题,深入研究分析墙背土压力动态变化值及规律性,利用大型通用有限元分析软件ADINA,建立了平面应变单元及墙、土接触单元的有限元计算模型,并且综合考虑墙后回填土Mo-hr-Coulomb材料本构模型,初始地应力场平衡、墙后回填土分层碾压填筑,设置墙、土之间的接触受力进行有限元...     

Static and dynamic active earth pressure

Summary The dynamic active earth pressure on retaining structures due to seismic loading is commonly obtained by using the modified Coulomb's approach which is known as the Mononobe-Okabe method. This method has generally been used for cohesionless soils only. A general solution for the determination of total (i.e. static and dynamic) active earth force for a c- soil as backfill was developed by Prakash and Saran in 1966 based on the simplifying assumption that adhesion between the wall-soil interface is equal to the cohesion of the soil, that the surface of the backfill is horizontal, and that the effect of the vertical acceleration can be neglected. This note presents an improved method for calculating the static and dynamic active force behind a rigid retaining wall based on its geometry, inclination of the backfill, surcharge, strength parameters of the backfill, and the adhesion between the wall face and the soil. The effects of adhesion, inclination of backfill, and vertical components of seismic loading for a typical retaining wall are discussed.     

Seismic response analysis of geosynthetic reinforced soil segmental retaining walls by finite element method

The paper presents the results of a finite element analysis of the dynamic response of a geosynthetic reinforced soil retaining wall that is constructed with dry-stacked modular concrete blocks as the facia system. In the finite element model, the cyclic shear behavior of the backfill soil is described by a hyperbolic stress-strain relationship with Masing hysteretic unload-reload behavior. The reinforcement material is modelled using a similar hysteretic model which takes into account the measured response of cyclic load-extension tests performed on unconfined geogrid specimens in the laboratory. Interface shear between wall components is simulated using slip elements. The results of finite element analyses giving the seismic response of a typical geogrid reinforced segmental retaining wall subjected to prescribed acceleration records are presented. The results of analyses highlight the influence of dynamic loading on: (1) wall displacement; (2) cumulative interface shear force and displacement between facing units; (3) tensile forces developed in the reinforcement and; (4) acceleration response over the height of the wall. A number of implications to the design of these structures are identified based on the results of these simulations.     

Estimation of static earth pressures for a sloping cohesive backfill using extended Rankine theory with a composite log-spiral failure surface

The Rankine earth pressure theory is extended herein to an inclined c–? backfill. An analytical approach is then proposed to compute the static passive and active lateral earth pressures for a sloping cohesive backfill retained by a vertical wall, with the presence of wall–soil interface adhesion. The proposed method is based on a limit equilibrium analysis coupled with the method of slices wherein the assumed profile of the backfill failure surface is a composite of log-spiral and linear segments. The geometry of the failure surface is determined using the stress states of the soil at the two boundaries of the mobilized soil mass. The resultant lateral earth thrust, the point of application, and the induced moment on the wall are computed considering global and local equilibrium of forces and moments. Results of the proposed approach are compared with those predicted by a number of analytical models currently adopted in the design practice for various combinations of soil’s frictional angles, wall–soil interface frictional angles, inclined angles of backfill and soil cohesions. The predicted results are also verified against those obtained from finite element analyses for several scenarios under the passive condition. It is found that the magnitude of earth thrust increases with the backfill inclination angle under both the passive and active conditions.

     

挡土墙主动土压力的库仑统一解

基于极限平衡理论,视墙后填土为服从Mohr-Coulomb屈服准则的理想弹塑性材料,指出库仑土压力理论存在的一些缺陷,明确提出极限土压力是由墙后塑性土体产生,并假定塑性区的一族滑移线为直线,即平面滑裂面,建立了更为完善的滑楔分析模型,求解了在一般情况下考虑黏性土作用的挡土墙主动土压力、滑裂面土反力以及它们的分布,而经典库仑和朗肯主动土压力为其特例。     

基于颗粒抗转动模型的刚性挡墙被动土压力临界状态离散元分析

简要介绍了颗粒抗转动模型,并将其引入离散元程序中,通过建立挡墙地基模型和合理选取模型参数,分别考虑了地基填土不同密实度和挡墙不同位移模式（被动T模式、RB模式、RT模式）情况下,刚性挡墙被动土压力随挡墙位移增长发展到达临界状态时,土压力系数 随位移发展的变化规律及墙后填土剪切带的形成规律,并与其他学者的研究成果进行对比分析。研究结果表明,土压力系数 随着挡墙位移增长的变化规律与填土的孔隙比（或相对密实度）和挡墙的位移模式紧密相关。随着孔隙比的减小或相对密实度的增大,土压力系数 会逐渐由位移硬化特性过渡为位移软化特性。尽管中密试样在双轴压缩试验中呈现出应变软化特性,而中密样的土压力系数 随着挡墙平动位移的增长可能呈现出位移软化特性,也可能呈现位移硬化特性。随着刚性挡墙向墙后土体推移,试样中的剪应变随之增大,并会在墙后形成应变局部化,即剪切带的出现。与室内试验剪应变云图相似,离散元较好地模拟了土压力临界状态时剪切带分布规律。同时,墙后土体表面不再是光滑的平面,而是逐渐隆起的凹凸面;随着挡墙位移增长,土体表面隆起量越来越大,直至土体破坏。     

Numerical solution of active earth pressures on rigid retaining walls built near rock faces

For retaining walls built in mountainous regions, narrow backfill spaces are often encountered. The space to fully develop the active wedge is restricted for walls with a limited backfill space. This paper presents a numerical study on the behaviour of active earth pressures behind a rigid retaining wall with limited backfill space of various geometries. The active earth pressure for a wall built with limited backfill space is considerably less than that of the Coulomb solution, and the location of the resultant of active earth pressures is noticeably higher than one-third of the wall height. The coefficient of active earth pressures is as low as 0.5–0.6 times the Coulomb solution and the h/H value reaches up to 0.4–0.37 if aspect ratio of the fill space is in the range from 0.1 to 0.2. A clear trend between the ratio of the coefficient of active earth pressures at constrained fill conditions over the Coulomb K_a value and the aspect ratio of the fill-space geometry is obtained.     

加筋土挡土墙边坡的稳定性分析

加筋挡土墙边坡是一种新型的复合边坡加固技术,用传统的方法很难设计这种复杂的结构。以一工程实例叙述了采用弹塑性有限元法预测加筋土边坡的稳定性的方法;给出了不同设计方案下的位移;分析了土体力学参数对边坡最大水平位移的影响。结果表明,土体的弹性模量、内摩擦角与粘聚力是影响边坡位移的重要因素。这些土力学参数与边坡最大水平位移是非线性关系,且有呈现临界点的趋势。因此,适当控制填土的力学性能参数有助于达到安全节省的设计目标。      

考虑挡墙位移效应的被动侧土压力计算方法

挡土结构上土压力的计算是土力学和岩土工程领域的基本研究课题之一。实际工程中的土压力通常是介于主动土压力和被动土压力之间的某一值,墙后填土由于碾压具有较高的密实度。经典的朗肯和库仑土压力理论只能计算极限状态下的土压力,没有考虑挡墙的位移以及剪切过程中密砂的强度从峰值强度降低到残余强度这一强度变化特性对于土压力的影响。给出了考虑挡墙位移效应的被动侧土压力计算方法,该方法能够同时考虑剪切过程中密砂的强度从峰值强度降低为残余强度这一强度变化特性对被动土压力的影响。通过土压力模型试验结果对计算方法进行了初步验证,计算结果和试验结果吻合较好,表明了该方法的有效性。     

The effect of interface properties on retaining wall behaviour

A series of finite element analyses have been undertaken to investigate the effects of interface properties on the behaviour of a vertical retaining wall and the deformation of the ground around it. The boundary between a rigid embedded wall and the soil is modelled with zero thickness interface elements. Uniform translation of the wall has been studied. The analyses show the predicted limiting active and passive pressure on the wall are dependent on the maximum wall friction angle and are in reasonable agreement with accepted approximate analytical solutions. The limiting pressure is independent of the stiffness and dilation properties of the interface elements. The dilation properties of the interface have a significant effect on the ground surface deformation around the wall. © 1998 John Wiley & Sons, Ltd.     

Pseudo-dynamic approach of seismic active earth pressure behind retaining wall

Knowledge of seismic active earth pressure behind rigid retaining wall is very important in the design of retaining wall in earthquake prone region. Commonly used Mononobe-Okabe method considers pseudo-static approach, which gives the linear distribution of seismic earth pressure in an approximate way. In this paper, the pseudo-dynamic method is used to compute the distribution of seismic active earth pressure on a rigid retaining wall supporting cohesionless backfill in more realistic manner by considering time and phase difference within the backfill. Planar rupture surface is considered in the analysis. Effects of a wide range of parameters like wall friction angle, soil friction angle, shear wave velocity, primary wave velocity and horizontal and vertical seismic accelerations on seismic active earth pressure have been studied. Results are provided in tabular and graphical non-dimensional form with a comparison to pseudo-static method to highlight the realistic non-linearity of seismic active earth pressures distribution.     

Modeling the 2D behavior of dry‐stone retaining walls by a fully discrete element method

The dry‐stone retaining walls (DSRW) have been tipped as a promising solution for sustainable development. However, before recently, their behavior is relatively obscure. In this study, discrete element method (DEM) approach was applied to simulate the plane strain failure of these walls. A commercial DEM package (PFC2D™) was used throughout this study. The authors used a fully discrete approach; thus, both the wall and the backfill were modeled as discrete elements. The methodology for obtaining the micromechanical parameters was discussed in detail; this includes the three mechanical sub‐systems of DSRWs: wall, backfill and interface. The models were loaded progressively until failure, and then the results were compared with the full‐scale experimental results where the walls were loaded, respectively, with hydrostatic load and backfill. Despite its complexity and its intensive calculation time, DEM model can then be used to validate a more simplified approach. Copyright © 2015 John Wiley & Sons, Ltd.     

挡土墙主动土压力分布与侧压力系数

采用库仑土压力理论的假设：挡土墙土压力是由墙后填土在极限平衡状态下出现的滑动楔体产生,在该滑动楔体上沿竖向取水平薄层作为微分单元体,通过作用在单元体上的水平力、竖向力和力矩平衡条件,建立挡土墙上土压力强度的一阶微分方程式,给出了土侧压力系数、土压力强度、土压力合力和土压力合力作用点高度的理论公式,并分析了填土内摩擦角和墙背摩擦角对土侧压力系数、土压力强度、土压力合力、土压力合力作用点和墙底抗倾稳定性的影响。     

Analytical solutions for the earth pressure of narrow cohesive backfill with retaining walls rotating about the top

Currently, knowledge of the failure mechanisms of narrow backfills with retaining walls rotating about the top (RT mode) is still lacking which leads to inaccurate estimations of the earth pressure. Numerical simulations using finite element limit analysis find that under the effects of backfill geometries, interface strengths, and soil properties, the upper soil layer supported by soil arching retains its integrity and the lower soil layer is sheared by multiple curved sliding surfaces in the limit state. Based on the failure mechanisms of narrow backfills, a calculation model is established which considers the soil arching effect, curved sliding surface, and cohesive soils. Analytical solutions for the earth pressure of narrow cohesive backfills with retaining walls rotating about the top are derived by using the limit equilibrium horizontal slice method. Compared with previous studies, the present method predicts the earth pressure distribution with higher accuracy. Several extensive parametric studies have also been conducted. Thus, decreasing the aspect ratio of backfills, increasing the inclined angle of natural slopes, interface strengths, and soil cohesion are beneficial for maintaining backfill integrity and reducing earth pressure against retaining walls.

     

整体刚性面板加筋土挡墙基频影响因素计算分析

作为一种柔性支挡结构,加筋土挡墙相较于传统重力式挡墙具有优越的抗震性能。由于结构在地震等动荷载作用下的动力响应大小与其自身的固有频率大小有关,因此,固有频率的研究显得尤为重要,特别是其最小值基频。以整体刚性面板加筋土挡墙为研究对象,分别用弹性地基梁模型、线性弹簧模型表示面板、填土及筋材,提出了一种加筋土挡墙固有频率计算方法。计算求得的基频值与既有瑞利能量法计算值具有较好的一致性。参数分析表明：填土中铺设筋材可以增大墙体的基频;对于加筋土挡墙,筋材长度以及筋材-填土界面摩擦系数对墙体基频影响较小;随着筋材竖向间距的增大,加筋密度对加筋土挡墙基频的影响逐渐减小;墙体基频随着面板宽度的增大先减小后增大;随着面板模量的减小,墙体基频趋于恒值。     

Lateral force and centroid location caused by horizontal and vertical surcharge strip loads on a cross‐anisotropic backfill

This work presents analytical solutions for determining lateral force (force per unit length) and centroid location caused by horizontal and vertical surcharge surface loads acting on a cross‐anisotropic backfill. The surcharge loading types are point load, line load, uniform strip load, upward linear‐varying strip load, upward nonlinear‐varying strip load, downward linear‐varying strip load, and downward nonlinear‐varying strip load. The planes of cross‐anisotropy are assumed parallel to the backfill ground surface. The proposed solutions, derived by integrating the lateral stress solutions (Int. J. Numer. Anal. Meth. Geomech. 2005; 29 :1341–1361), do not exist in literature. Clearly, the type and degree of material anisotropy, loading distance from the retaining wall, and loading types markedly impact the proposed solutions. Two examples are utilized to illustrate the type and degree of soil anisotropy, and the loading types on the lateral force and centroid location in the isotropic/cross‐anisotropic backfills generated by the horizontal and vertical uniform, upward linear‐varying and upward nonlinear‐varying strip loads. The parametric study results demonstrate that the lateral force and centroid location accounting for soil anisotropy, loading distance from the retaining wall, dimension of the loading strip, and loading directions and types differ significantly from those estimated using existing isotropic solutions. The derived solutions can be added to other lateral pressures, such as earth pressure or water pressure, required for stability and structural analysis of a retaining wall. Additionally, they can simulate realistically actual surcharge loading problems in geotechnical engineering when backfill materials are cross‐anisotropic. Copyright © 2007 John Wiley & Sons, Ltd.     

基于薄层单元法主动土压力计算的复合遗传算法

作用于挡土墙侧土压力的计算一直沿用经典的土压力理论,其土压力分布沿墙高呈直线分布,但实践证明它们与实际情况不符。在已有研究成果的基础上,为提高计算精度,假定挡土墙后土体潜在滑裂面为由对数螺线面和平面组合而成,根据挡土墙后土体薄层单元的极限平衡条件推导出土压力的计算公式。由于土压力计算值与滑裂面的位置有关,为寻找潜在最危险滑裂面,在简单遗传算法中引入复合形搜索法得到一种高效的复合形遗传算法,并将其用于墙后填土潜在最危险滑裂面搜索和相应主动土压力计算。最后,对室内模型挡墙和现场实际挡墙后填土土压力进行了分析计算,计算值与实测值吻合很好,这表明该方法不仅可行,而且可靠。