岩石边坡稳定的块体单元极限分析上限法

将块体单元法与极限分析上限法相结合,提出了岩石边坡稳定的块体单元极限分析上限法。借助于块体单元法离散计算区域,通过块体系统速度场在结构面上满足Mohr-Coulomb屈服条件、关联流动法则、速度边界条件以及块体系统虚功原理,构成求解边坡强度储备安全系数上限解的非线性规划模型,模型的求解采用复合形法。最后研究了一个岩质楔形体边坡算例和小湾水电站进水口边坡实例,通过将块体单元法上限分析计算结果与刚体极限平衡法相比较,验证了该方法的正确性。     

三维块体元塑性极限分析下限法

基于块体元离散思想,将三维边坡离散为块体-结构面组成的块体系统,假定块体为刚体,以结构面上的应力为未知量;从下限定理出发,构造满足平衡条件、边界条件和屈服条件的静力许可场,平衡方程严格满足3方向力平衡及绕3个主轴方向的力矩平衡条件,为避免非线性规划,对屈服条件进行线性化处理;最后,建立了下限法数学规划模型,通过线性及非线性规划获得边坡稳定严格的下限解。用几个典型算例验证了文中方法的正确性及可行性。     

考虑孔隙水压力的土坡稳定性的有限元下限分析

以极限分析下限法理论为基础,应用有限单元思想离散结构物,建立了同时满足平衡条件、应力边界条件、屈服条件和应力间断条件的静力许可应力场,其中孔隙水压力被当作一种类似于重力的外力荷载。引入线性数学规划手段后,得到了考虑孔隙水压力的边坡稳定的下限法数学规划模型,由此可以求出安全系数的下限解及其对应的应力场。最后,以2个经典的土坡为算例,与多种方法的分析结果比较,论证了该方法的正确性。     

不连续边界形状下土压力的严密解法

分析不连续边界形状下土体中不连续应力场和速度场特征,根据应力不连续线和速度不连续的性质,在考虑有重土、土和墙体摩擦情况下,同时利用上、下限定理,构建算法;通过数值计算解三类边值问题,求得挡土墙绕基底转动下,墙后不连续边界形状下土体的静力场,同时对对应的机动场进行分析,找出了满足所有速度边界条件和静力边界条件的应力场,得到绕墙基转动下挡土墙土压力的严密解。算例表明：求解极限平衡问题真解的算法是可行的。     

边坡稳定的有限元塑性极限分析

系统地介绍了结构塑性极限分析的原理和方法。借助有限单元法和线性规划,运用塑性极限分析的下限法,可求解岩土边坡的极限承载力和安全系数。算例表明了该方法的正确性并具有较高的精度,同时,分析了该方法的困难所在。     

三维塑性极限分析下限法原理及应用

介绍了三维塑性极限分析下限法的基本原理。将计算区域离散为有限个三维空间单元,利用极限分析中的下限定理,借助有限元思想建立数学规划模型,并引入非线性规划的数值方法寻求问题的下限解。以均匀土质边坡的极限荷载作为算例,比较了所得数值解与经典塑性力学理论解,论证了该方法的正确性。     

基于非线性规划的有限元塑性极限分析下限法研究

在分析Sloan建立的有限元塑性极限分析线性规划数学模型存在的局限性基础上,提出了基于非线性规划的有限元塑性极限分析下限法数学模型。采用非线性屈服条件构建了下限法静力容许应力场,建立了求解超载系数、强度储备系数的下限法数学模型,并提出了针对塑性极限分析非线性规划数学模型的求解策略;最后对一个经典算例进行了深入分析,验证了方法的正确性。     

基于极限分析法求解基坑支护墙入土深度下限解

基于极限分析下限法构建满足一定规则的静力许可应力场,以极限平衡方程与屈服准则为基础,确定坑底土体的下限极限承载力,并根据其与基坑支护墙入土深度的关系推导出支护墙入土深度的下限解,并提出了基坑抗隆起稳定性分析的计算式。采用工程实例验证了支护墙入土深度的下限解及基坑抗隆起稳定性分析计算的可行性。     

基于塑性极限分析上限法理论的土质边坡可靠度分析

将极限分析的上限定理、有限元离散思想、随机规划理论和蒙特卡洛方法这四者结合起来,提出了一种土质边坡可靠度分析的上限数值方法。首先采用三节点有限单元离散土质边坡,然后将土体的抗剪参数设为随机变量,根据上限定理构建同时满足三角形单元的塑性流动约束条件、单元公共边的塑性流动约束条件和单元速度边界条件的机动许可速度场,并根据内功功率等于外功功率条件建立目标函数,构建土质边坡可靠度分析的上限法随机规划模型。采用蒙特卡洛方法求解上限法随机规划模型,同时提出了一种基于上限法速度场的边坡失效风险系数估算方法,该方法特别适用于具有多种失效模式的边坡风险分析。对2个经典算例进行了深入分析,验证了方法的正确性。     

非均质土坡的有限元塑性极限分析

在评价现有边坡稳定分析方法的基础上,提出了边坡稳定的有限元塑性极限分析方法。借助有限单元思想和线性规划,建立了边坡稳定的数学规划模型,由此可以求出安全系数的上下限解,从而,界定了边坡的安全范围,同时,可以给出下限状态下的应力场和上限状态下的速度场。以一个经典非均质土坡的边坡稳定作为算例,比较了多种方法的分析结果,论证了本方法的正确性。     

A novel computational approach for large deformation and post‐failure analyses of segmental retaining wall systems

Segmental retaining wall (SRW) systems are commonly used in geotechnical practice to stabilize cut and fill slopes. Because of their flexibility, these systems can tolerate minor movements and settlements without incurring damage or crack. Despite these advantages, very few numerical studies of large deformations and post‐failure behavior of SRW systems are found in the current literature. Traditional numerical methods, such as the finite element method, suffer from mesh entanglement, thus are unable to simulate large deformations and flexible behavior of retaining wall blocks in SRW systems. To overcome the above limitations, a novel computational framework based on the smoothed particle hydrodynamics (SPH) method was developed to simulate large deformations and post‐failure behavior of soils and retaining wall blocks in SRW systems. The proposed numerical framework is a hybrid continuum/discontinuum approach that can model soil as an elasto‐plastic material and retaining wall blocks as independent rigid bodies associated with both translational and rotational degrees of freedom. A new contact model is proposed within the SPH framework to simulate the interaction between the soil and the blocks and between the blocks. As an application of the proposed numerical method, a two‐dimensional simulation of an SRW collapse was simulated and compared to experimental results conducted under the same conditions. The results showed that the proposed computational approach provided satisfactory agreement with the experiment. This suggests that the new framework is a promising numerical approach to model SRW systems. Copyright © 2014 John Wiley & Sons, Ltd.     

考虑土体硬化的基坑开挖性状及隆起稳定性分析

基坑开挖过程中,土体应力路径、卸载回弹再压缩特性与简单加载或卸载不同,采用常规的理想弹塑性模型模拟基坑开挖,得到的围护墙位移、坑内土体回弹以及坑外沉降较大。分析了基坑开挖不同区域土体的性状,采用土体硬化模型模拟基坑开挖的卸载与土体硬化行为,结合工程算例,对比土体硬化模型和理想弹塑性模拟以及实测的围护结构土压力、围护墙水平位移和坑外土体沉降,并利用强度折减法分析基坑的稳定性。计算结果表明,考虑土体硬化的HS模型有限元方法能体现土体卸载再加载与开挖的特性,所得土压力、围护结构水平位移以及基坑抗隆起稳定性符合软土地区基坑工程的实践。     

基于二阶锥规划有限元增量加载法的条形浅基础极限承载力分析

地基极限承载力分析是土力学研究中的一个经典课题。基于Hellinger-Reissner混合变分原理和有限元方法,将岩土体弹塑性问题构造成基于有限元框架的二阶锥规划（second-order cone programming,SOCP）问题,进而提出一种基于二阶锥规划理论的增量有限元法,即FEM-SOCP法。将岩土体弹塑性问题构造成二阶锥规划的数学优化问题,可以避免采用传统弹塑性计算中复杂的应力点积分等算法和屈服面棱角的平滑处理。此外,对于二阶锥规划问题,可以采用具有原始?对偶内点求解法的标准数学规划求解器MOSEK进行求解。将增量加载FEM-SOCP法应用于经典的基底粗糙的条形浅基础地基极限承载力分析中,分别考虑了关联和非关联塑性条件下的Mohr-Coulomb屈服准则。数值结果表明：所提出的增量加载FEM-SOCP法获得的地基承载力系数及地基承载力与传统FEM计算结果基本一致,而与常规有限元计算结果相比,基于增量加载的FEM-SOCP法所获得的屈服区更加平滑。     

Fully coupled elastoplastic hydro-mechanical analysis of unsaturated porous media using a meshfree method

This paper presents the first application of an advanced meshfree method, ie, the edge-based smoothed point interpolation method (ESPIM), in simulation of the coupled hydro-mechanical behaviour of unsaturated porous media. In the proposed technique, the problem domain is spatially discretised using a triangular background mesh, and the polynomial point interpolation method combined with a simple node selection scheme is adopted for creating nodal shape functions. Smoothing domains are formed on top of the background mesh, and a constant smoothed strain, created by applying the smoothing operation over the smoothing domains, is assigned to each smoothing domain. The deformation and flow models are developed based on the equilibrium equation of the mixture, and linear momentum and mass balance equations of the fluid phases, respectively. The effective stress approach is followed to account for the coupling between the flow and deformation models. Further coupling among the phases is captured through a hysteretic soil water retention model that evolves with changes in void ratio. An advanced elastoplastic constitutive model within the context of the bounding surface plasticity theory is employed for predicting the nonlinear behaviour of soil skeleton. Time discretisation is performed by adopting a three-point discretisation method with growing time steps to avoid temporal instabilities. A modified Newton-Raphson framework is designed for dealing with nonlinearities of the discretised system of equations. The performance of the numerical model is examined through a number of numerical examples. The state-of-the-art computational scheme developed is useful for simulation of geotechnical engineering problems involving unsaturated soils.     

有限元法模拟开挖引起的基坑水平位移和邻近建筑物沉降

以徐州某采用水泥土墙支护的基坑为例,采用有限元数值模拟的方法,对基坑开挖引起的水平位移量和邻近建筑物沉降量进行了计算,并与实际监测值进行了对比分析,得到了一些关于如何控制基坑水平位移和减少基坑周边建筑沉降的结论。     

Upper bound limit analysis of cohesive soils using mesh-free method

A mesh-free based limit analysis approach is proposed, to determine the upper bound solutions for the collapse loads associated with cohesive soils, under plane strain conditions. In the presented technique, the geometry of problem is just simulated by nodes and there is no need of mesh in the traditional sense. The process of finding an upper bound solution consists of combining limit analysis theory and a mesh-free numerical technique as a discretisation tool. To satisfy the required conditions for the admissibility of the discretised velocity field at the entire problem domain, a strain rate smoothing technique has been adopted. The outcome of proposed combination is a nonlinear optimisation problem which is solved by a direct iterative technique. The solution found by an iterative algorithm is an upper bound for limit load of the stability problem. The efficiency of the proposed method is demonstrated by solving different example problems in the soil mechanics engineering field, at the end of the paper.     

Lower bound limit analysis of an anisotropic undrained strength criterion using second‐order cone programming

In this paper, the formulation of the lower bound limit analysis of an anisotropic undrained strength criterion using second‐order cone programming is described. The finite element concept was used to discretize the soil mass into 3‐noded triangular elements. The stress field was modeled using a linear interpolation within the elements while stress discontinuities were permitted to occur at the shared edges of adjacent elements. An elliptical yield criterion was adopted to model the anisotropic undrained strength of the clay. A statically admissible stress field was defined by enforcing the equilibrium equations within all triangular elements and along all shared edges of adjacent elements, stress boundary conditions, and no stress violation of the anisotropic strength envelope cast in the form of a conic quadratic constraint. The lower bound solution of the proposed formulation was solved by second‐order cone programming. The proposed formulation of the anisotropic undrained strength criterion was validated through comparison of the model's predictions with the known exact solutions of strip footings, and was applied to solve undrained stability of a shallow unlined square tunnel. Computational performance between the proposed approach of second‐order cone programming and linear programming was examined and discussed.     

基于主应力迹线分层的有限土体土压力计算

为了研究挡墙后有限土体的主动土压力,以墙后无黏性土体为研究对象,假定破裂面为通过墙踵的平面,且在挡墙平动模式下,墙后土体形成圆弧形小主应力拱。采用沿小主应力迹线分层的方法,将挡墙后土体划分为若干个圆弧形曲线薄层单元,考虑了单元体上下表面应力分布的不均匀性,提出了一种有限土体挡墙主动土压力计算方法,给出了主动土压力合力及其作用点高度的表达式,并验证了该方法的正确性。研究结果表明：采用曲线薄层单元法可以准确考虑单元体复杂的受力情况,能更好地反映挡墙后有限土体主动土压力的变化规律;有限填土时主动土压力沿墙高 呈非线性分布,土压力先随着土体深度增加呈单调递增趋势,然后在接近墙底位置处呈单调递减趋势。分析参数敏感性时取不同土体宽高比与墙背粗糙程度对挡墙主动土压力分布及合力作用点高度进行分析,结果表明：随着土体宽高比n的增大,主动土压力值逐渐增大,土压力分布曲线非线性越来越明显,合力作用点高度逐渐降低且恒大于 。当 0.71时,均趋于稳定。可将 0.71作为有限土体与半无限土体的临界宽高比。随着摩擦角 的增大,主动土压力值逐渐减小,土压力分布曲线非线性越来越明显,合力作用点高度逐渐增大且恒大于 。     

基于尖点突变理论的浆砌块石边坡稳定性研究

根据影响浆砌块石挡土墙边坡稳定性的主要控制变量：挡土墙的垂直度i、挡土墙高度h、填料的内摩擦角 、墙后边坡土的重度 、土对挡土墙基底的摩擦系数 、土对挡土墙墙背的摩擦角 等6个因素变量,利用正交设计原理优化试验设计方案,结合库仑理论与力的多边形法,分析计算浆砌块石挡土墙边坡的安全系数,最后用尖点突变理论的突变级数法进一步判断边坡的稳定性。研究结果表明：影响挡土墙边坡稳定性的6个主要控制变量因素的主次关系为 ;在分析挡土墙边坡稳定性时,采用突变级数法进行计算判断,可以直观地判断边坡的稳定情况,从而弥补工程中运用传统的最小安全系数法进行判断出现的模糊不确定的情况。