Solutions for the deformations and stability of elastoplastic hollow cylinders subjected to boundary pressures

In this paper, a closed-form solution is presented for the stress and displacement distributions throughout a hollow cylinder subjected to uniform pressures acting on its internal and external boundary surfaces under plane strain conditions. The material is assumed to be elastoplastic, obeying a Mohr–Coulomb failure criterion, and exhibiting dilatant plastic deformation according to a non-associated flow rule. The newly developed analytical solution is verified through comparison with the solutions obtained from an infinite boundary problem (for which a closed-form solution exists), and numerical analyses using the program FLAC. The solution is also compared with the results of a borehole collapse test on a thick-walled hollow cylinder of synthetic shale. The analytical solution can be used to calculate the stress and displacement distributions around boreholes and other cylindrical cavities under both infinite and finite boundary conditions under both drained and undrained conditions. Copyright © 1999 John Wiley & Sons, Ltd.     

崩塌诱发其下部滑坡变形过程的分析研究

崩塌冲击或崩积物重力加载作用都可能诱发坡脚滑坡的变形或失稳。在查明坡体结构的基础上,采用3DEC离散元数值模拟方法,对高陡斜坡在地下开采作用下崩塌所产生的机理、失稳模式、破坏规模、运动轨迹进行了全过程模拟,特别是斜坡失稳后和坡脚滑坡的相互作用效应进行了深入分析。结果表明:通过地下开采诱发的崩塌过程模拟及其研究,发现斜坡在地下开采的扰动下会产生大规模的崩塌,其滚石会对滑坡体产生强烈的冲击作用,且所形成的崩积物会对滑坡体产生重力加载作用。再通过监测数据以及现场收集的资料分析得出滑坡的蠕滑变形主要是由于崩积物重力加载作用引起的,且有继续变形的趋势,在暴雨季节时,滑坡的变形速率可能会增大,有潜在大规模滑动的危险,需做好相应的防护工作。     

An operator‐split ALE model for large deformation analysis of geomaterials

Analysis of large deformation of geomaterials subjected to time‐varying load poses a very difficult problem for the geotechnical profession. Conventional finite element schemes using the updated Lagrangian formulation may suffer from serious numerical difficulties when the deformation of geomaterials is significantly large such that the discretized elements are severely distorted. In this paper, an operator‐split arbitrary Lagrangian–Eulerian (ALE) finite element model is proposed for large deformation analysis of a soil mass subjected to either static or dynamic loading, where the soil is modelled as a saturated porous material with solid–fluid coupling and strong material non‐linearity. Each time step of the operator‐split ALE algorithm consists of a Lagrangian step and an Eulerian step. In the Lagrangian step, the equilibrium equation and continuity equation of the saturated soil are solved by the updated Lagrangian method. In the Eulerian step, mesh smoothing is performed for the deformed body and the state variables obtained in the updated Lagrangian step are then transferred to the new mesh system. The accuracy and efficiency of the proposed ALE method are verified by comparison of its results with the results produced by an analytical solution for one‐dimensional finite elastic consolidation of a soil column and with the results from the small strain finite element analysis and the updated Lagrangian analysis. Its performance is further illustrated by simulation of a complex problem involving the transient response of an embankment subjected to earthquake loading. Copyright © 2007 John Wiley & Sons, Ltd.     

考虑渗流和变形耦合的黄土湿陷数值计算

以甘肃陇西地区自重湿陷性黄土作为研究对象,建立了渗流和变形耦合的黄土湿陷变形模型,然后利用Galerkin有限元法对基本方程进行空间离散,在时间域内用差分方法离散,并用Fortran语言编程计算。结合具体的试验条件计算得知：渗流计算结果与实际较为吻合;计算湿陷变形量比实测的大,并且土体非饱和程度越大,差异越大。因此,建议在建立湿陷变形本构关系时考虑时间因素。     

搅拌桩加固挤土效应及在地铁隧道保护中的应用

在减小地基变形进行的深层搅拌桩加固时,加固本身的挤土效应对隧道变形产生了影响。为此,模拟了搅拌桩（DCM）侧向挤土效应的4种荷载模式,结合实测资料并采用数值试验验证了侧向挤土荷载模式的合理性。进一步应用该模式,通过有限元模拟了搅拌桩的加固挤土效应,分析讨论了不同加固顺序对地面变形,隧道变形以及长期蠕变变形的影响,结论表明,搅拌桩加固对地面环境影响是不可忽略,隧道周围搅拌桩施工顺序对隧道变形影响较大,搅拌桩加固后长期蠕变效应相对加固过程的变形很小。     

Poroelastic-plastic consolidation — analytical solution

Consolidation of a poroelastic material that yields according to Drucker–Prager or Mohr–Coulomb criteria leads to a Stefan problem for time-dependent pore fluid pressure. The solution to the Stefan problem for a column of infinite depth is known and is adapted to poroelastic/plastic consolidation of a weightless material under a uniform surface load applied instantaneously and subsequently maintained constant. In this approach, the plastic potential and yield criterion need not be the same. If yielding occurs concurrently with application of load, then collapse is instantaneous. Otherwise, yielding may occur during the consolidation period. If so, then the elastic–plastic zone first appears at the surface and subsequently moves down the column. Depth to the elastic–plastic boundary is given by the simple expression Z = 2β√t where β is a constant determined from continuity conditions at the elastic–plastic boundary. Time-dependent surface displacement that occurs during consolidation is directly proportional to Z. There is little difference between elastic–plastic and purely elastic results in a numerical example because there is little difference in the respective consolidation coefficients. Elastic–plastic finite element results obtained from a column of finite depth are in close agreement with analytical results as long as the pore pressure at the bottom of the column does not change significantly from the value induced by application of the surface load. The analytical solution provides for: (1) efficient evaluation of material properties effects on consolidation, including strength and fluid compressibility, and (2) an accurate way of validating poroelastic/plastic computer codes that are based on Drucker–Prager and Mohr–Coulomb criteria. Copyright © 1999 John Wiley & Sons, Ltd.     

A variational approach for vertical deformation analysis of pile group

A variational approach for the analysis of vertical deformation of pile groups is presented. The method assumes that the deformation of piles can be represented by a finite series. The method applies the principle of minimum potential energy to determine the deformation of piles. Using this method, an analytical solution for pile groups in soil modelled by the theoretical load–transfer curves can be obtained rigorously. Analysis of field tests indicates that the method can predict the performance of pile groups reasonably well.     

三峡库区大坪滑坡变形对前缘塌岸的响应分析

随着三峡水库的长期运行,受库水位涨落和波浪作用影响,三峡水库土质岸坡的塌岸问题愈发严重,塌岸不仅造成了水土流失,甚至会诱发滑坡复活。大坪滑坡是三峡库区前缘塌岸发育最为明显的滑坡之一,以三峡库区大坪滑坡为例,结合大坪滑坡的地表宏观变形、地表GPS位移等数据,分析滑坡变形特征以及塌岸对滑坡变形的影响,在此基础上通过ABAQUS生死单元功能实现前缘塌岸对滑坡稳定性影响的数值模拟,进一步探索滑坡变形对前缘塌岸的响应关系。结果表明:大坪滑坡的变形主要受库水位涨落影响,前缘塌岸较发育,塌岸一侧GPS监测点地表位移变化较明显,显然塌岸对大坪滑坡地表变形影响较大;ABAQUS的有限元计算结果表明,塌岸对滑坡的变形影响十分明显,影响大小主要与塌岸方量相关;塌岸导致的滑坡变形主要集中在滑坡前部,并向后部逐渐扩展;ABAQUS中的生死单元法可以很好地实现塌岸对滑坡稳定性影响的模拟。     

水平受荷桩的弹性有限元虚拟加载上限分析

基于将塑性上限分析等效为弹性迭代计算的总量虚拟加载上限分析理论,在商业化有限元软件ABAQUS中实现了弹性有限元虚拟加载上限方法（弹性有限元T-EMSD）。应用弹性有限元T-EMSD法分析了不排水黏土中的二维水平受荷桩,其获得的荷载-位移曲线与弹塑性有限元分析结果一致,其极限承载力与塑性解相近。在极限位移加载量下弹性有限元T-EMSD法对应的上限机构从弹性始速度场开始随迭代逐渐演化,迭代收敛后的速度场和解析塑性破坏机构相似。与其他基于可变强度概念（MSD）的方法相比,弹性有限元T-EMSD法对水平受荷桩桩身的分析具有更高的精度。弹性有限元T-EMSD法最大的优势在于可在计算中自然地获得塑性机构,因而可被用于研究一些塑性机构难以构造的复杂问题,并对弹塑性数值方法进行验证。     

Proposed nonlinear 3-D analytical method for piled raft foundations

The load distribution and deformation of piled raft foundations subjected to axial and lateral loads were investigated by a numerical analysis and field case studies. Special attention is given to the improved analytical method (YSPR) proposed by considering raft flexibility and soil nonlinearity. A load transfer approach using p–y, t–z and q–z curves is used for the analysis of piles. An analytical method of the soil–structure interaction is developed by taking into account the soil spring coupling effects based on the Filonenko-Borodich model. The proposed method has been verified by comparing the results with other numerical methods and field case studies on piled raft. Through comparative studies, it is found that the proposed method in the present study is in good agreement with general trend observed by field measurements and, thus, represents a significant improvement in the prediction of piled raft load sharing and settlement behavior.     

Multiscale modeling of large deformation in geomechanics

Large deformation soil behavior underpins the operation and performance for a wide range of key geotechnical structures and needs to be properly considered in their modeling, analysis, and design. The material point method (MPM) has gained increasing popularity recently over conventional numerical methods such as finite element method (FEM) in tackling large deformation problems. In this study, we present a novel hierarchical coupling scheme to integrate MPM with discrete element method (DEM) for multiscale modeling of large deformation in geomechanics. The MPM is employed to treat a typical boundary value problem that may experience large deformation, and the DEM is used to derive the nonlinear material response from small strain to finite strain required by MPM for each of its material points. The proposed coupling framework not only inherits the advantages of MPM in tackling large deformation engineering problems over the use of FEM (eg, no need for remeshing to avoid mesh distortion in FEM), but also helps avoid the need for complicated, phenomenological assumptions on constitutive material models for soil exhibiting high nonlinearity at finite strain. The proposed framework lends great convenience for us to relate rich grain-scale information and key micromechanical mechanisms to macroscopic observations of granular soils over all deformation levels, from initial small-strain stage en route to large deformation regime before failure. Several classic geomechanics examples are used to demonstrate the key features the new MPM/DEM framework can offer on large deformation simulations, including biaxial compression test, rigid footing, soil-pipe interaction, and soil column collapse.     

Nonlinear three-dimensional analysis of pile group supported columns considering pile cap flexibility

A numerical method that takes into account the coupling between the rigidities of the piles, the cap, and the column has been developed for analyzing the response of pile group supported columns. Special attention is given to consideration of pile cap flexibility. A load transfer approach using t–z/q–z and p–y curves is used for the analysis of single piles. The finite element technique is used to combine the pile stiffness with the stiffness of the cap and column. The numerical method developed has been verified by comparing the results with other numerical methods for pile groups. Through comparative studies, it has been found that the maximum load on the individual piles in a group is highly influenced by pile cap flexibility. The prediction of the lateral loads and bending moments in the pile cap is much more conservative in the present analysis than in FBPier 3.0 and shows a definitely larger lateral load and bending moment for various cap thicknesses.     

钙质石灰岩中桩基轴向承载特性的有限元分析

为了研究钙质石灰岩中桩基的合理设计理论及开发相关的变形破坏数值分析方法,利用弹塑性有限元方法对以硫球石灰岩作为持力层的桩基现场轴向载荷试验进行了数值分析。有限元分析中钙质石灰岩被假定为理想弹塑性材料。结果表明,如果能在有限元解析中合理地考虑桩侧摩阻力的低减效果,弹塑性有限元计算可以较好地模拟与分析钙质砂土中桩基的轴向承载力特性。最后还对开口钢管桩基的土塞效应的发生机制进行了分析。     

路堤荷载下地基的侧向变形计算分析

目前关于路基侧向变形研究,大都是基于现场测试或数值模拟,却鲜有理论上的计算与分析。为深入研究路堤荷载下地基的侧向变形,基于布辛奈斯克等弹性理论解及平面应变问题,推导出无限长线荷载、均布条形荷载、三角形分布条形荷载及梯形分布条形荷载下地基侧向变形解析表达式,并与有限元数值计算结果对比验证了解析解的正确性。在此基础上,重点分析了土体的泊松比、路堤宽度以及路堤边坡宽度等参数对地基侧向位移场的影响。计算结果表明,路堤荷载下地基同一垂直线上土体的侧向变形沿深度呈弓形状,变形最大值在地表下某深度处。泊松比对地基侧向位移有较显著的影响：在坡脚附近地表浅层处,随着泊松比的增加,土体侧向变形的方向由向路堤内逐渐转为向路堤外;另泊松比越大,土体的水平位移也相对越大,且最大位移发生位置逐渐上移。研究结果可为类似路堤工程地基变形分析及稳定性控制监测提供一定理论支撑。     

吸力式沉箱基础极限拉拔承载力的数值分析

作为新型的深水海洋基础型式,吸力式沉箱基础被广泛地用于系泊深水海洋设施中,从而承受巨大的倾斜上拔荷载。在上拔荷载水平分量与竖向分量的共同作用下,吸力式沉箱的承载特性及其工作性能评价是海洋工程设计与建设中的关键技术问题之一。然而现有的理论分析与试验研究并不能满足工程实践的需要,因此,对吸力式沉箱基础的极限承载力分析建立了有限元数值计算方法。当沉箱基础在快速拔出过程中,正常固结黏土处于完全不排水状态,沉箱基础发生整体破坏时表现出反向地基承载力失稳模式,此时沉箱基础所发挥的极限承载能力往往最大。为此,在数值计算中直接假定沉箱基础及其周围土体处于完全不排水状态,针对不同的沉箱长径比,分别确定了在竖向上拔荷载和水平拉拔的单独作用下沉箱基础极限承载力。对比发现：竖向上拔极限承载力有限元解能够较好地与理论计算结果相符合,而水平极限承载力解与理论计算结果存在一定的差异。     

Analytical and numerical analyses of the load‐bearing capacity of retaining walls laterally supported at both ends

This paper investigates the load‐bearing capacity of a perfectly smooth retaining wall laterally supported at both ends assuming that the wall fails by the development of three plastic hinges. The study considers the case of a cohesionless elastic–perfectly plastic backfill with a Mohr–Coulomb yield criterion and an associative flow rule in drained conditions. A kinematically admissible soil–structure failure mechanism is proposed and compared with the conventional solutions and with results from a numerical finite element modelling. The study shows that the proposed solution and the numerical solution are in good agreement. These solutions are found to be much more favourable for the wall than the conventional solutions. Copyright © 2010 John Wiley & Sons, Ltd.     

Analysis of axial pile-soil interaction in clay

A method for predicting the maximum mobilized side resistance and unit shaft resistance-displacement curves (load transfer functions) on piles in clay is described. The method was derived using a numerical solution to model pile installation effects and a finite element scheme to model pile loading. Results of three well-documented pile load tests on steel piles were used to develop intermediate steps and final solutions, and the method was verified by comparing predicted results to two other load tests. An expression is proposed to represent load transfer functins for use by practitioners for the design of bridge and other foundations in clay.     

Numerical analysis of seepage–deformation in unsaturated soils

A coupled elastic–plastic finite element analysis based on simplified consolidation theory for unsaturated soils is used to investigate the coupling processes of water infiltration and deformation. By introducing a reduced suction and an elastic–plastic constitutive equation for the soil skeleton, the simplified consolidation theory for unsaturated soils is incorporated into an in-house finite element code. Using the proposed numerical method, the generation of pore water pressure and development of deformation can be simulated under evaporation or rainfall infiltration conditions. Through a parametric study and comparison with the test results, the proposed method is found to describe well the characteristics during water evaporation/infiltration into unsaturated soils. Finally, an unsaturated soil slope with water infiltration is analyzed in detail to investigate the development of the displacement and generation of pore water pressure.     

Analytical and numerical solution of the elastodynamic strip load problem

Analytical and numerical solutions of the elastodynamic problem of an instantaneous strip load on a half space are presented and compared. The analytical solution is obtained using the De Hoop–Cagniard method, and the numerical solution is obtained using the dynamic module of the finite element package Plaxis. The purpose of the paper is to validate the numerical solution by comparison with a completely analytical solution, and to verify that the main characteristics of the analytical solution are also obtained in the numerical solution. Particular attention is paid to the magnitude, the velocity, and the shape of the Rayleigh wave disturbances. Copyright © 2007 John Wiley & Sons, Ltd.     

基于两阶段法的堆载对公路桥梁桩基础影响分析

首先基于布西奈斯克解,将表面作用有集中荷载时半无限弹性体的应力变形解在荷载作用区域利用复合辛普森公式进行数值积分,得到了表面处于不同形式的分布荷载作用下土体自由场水平及竖直方向应力和变形的计算公式。结合有限差分法及Mindlin位移解分别推导出弹性地基中桩顶作用有集中荷载时单桩桩、土单元的位移,两者结合便得到主动桩的分析方法。通过将堆载作用下的土体自由场位移施加于桩上把上述自由场分析及主动桩分析结合起来,推导出堆载作用下被动单桩的竖向和水平向承载特性的分析方法。选取地表附近作用有矩形均布荷载的计算工况,通过与有限元计算结果的对比验证了所提出的分析方法的正确性;将所提出的方法计算结果与某处工程案例中实测数据结果进行对比,分析表明利用该方法分析堆载对邻近桩基的水平及竖向影响是合理可靠的。