Numerical stability for modelling of dynamic two‐phase interaction

Dynamic two‐phase interaction of soil can be modelled by a displacement‐based, two‐phase formulation. The finite element method together with a semi‐implicit Euler–Cromer time‐stepping scheme renders a discrete equation that can be solved by recursion. By experience, it is found that the CFL stability condition for undrained wave propagation is not sufficient for the considered two‐phase formulation to be numerically stable at low values of permeability. Because the stability analysis of the two‐phase formulation is onerous, an analysis is performed on a simplified two‐phase formulation that is derived by assuming an incompressible pore fluid. The deformation of saturated porous media is now captured in a single, second‐order partial differential equation, where the energy dissipation associated with the flow of the fluid relative to the soil skeleton is represented by a damping term. The paper focuses on the different options to discretize the damping term and its effect on the stability criterion. Based on the eigenvalue analyses of a single element, it is observed that in addition to the CFL stability condition, the influence of the permeability must be included. This paper introduces a permeability‐dependent stability criterion. The findings are illustrated and validated with an example for the dynamic response of a sand deposit. Copyright © 2015 John Wiley & Sons, Ltd.     

Unsaturated slope stability analysis with steady infiltration or evaporation using elasto‐plastic finite elements

The paper presents results of unsaturated slope stability analyses using elasto‐plastic finite elements in conjunction with a novel analytical formulation for the suction stress above the water table. The suction stress formula requires four parameters, three for the soil type and one for the steady infiltration (or evaporation) due to environmental effects. The suction stress approach enables the analysis to proceed in the context of classical effective stress, while maintaining the advantages of a general non‐linear finite element approach in which no advance assumptions need to be made about the shape or location of the critical failure surface. The results show the extent to which suctions above the water table can increase the factor of safety of a slope for a variety of different soil types and infiltration rates. All stability analyses that include the effects of suction stresses are contrasted with more traditional approaches in which water pressures above the water table are ignored. Copyright © 2005 John Wiley & Sons, Ltd.     

隧道开挖与支护有限差分法分析

根据景德镇-黄山高速公路某隧道现场工程地质条件和隧道结构设计参数,采用有限差分法对喷射500 mm普通混凝土支护和喷射200 mm厚聚丙烯纤维混凝土支护两种支护结构,进行了施工过程的数值模拟分析。从围岩的应力、位移和塑性区分布3个方面对隧道围岩的稳定性进行了分析。模拟计算结果表明,采用喷射200 mm厚聚丙烯纤维混凝土支护结构的隧道围岩能够处于稳定状态。     

Upper bound finite element analysis of slope stability using a nonlinear failure criterion

In this study, upper bound finite element (FE) limit analysis is applied to stability problems of slopes using a nonlinear criterion. After formulating the upper bound analysis as the dual form of a second-order cone programming (SOCP) problem, the stress field and corresponding shear strength parameters can be determined iteratively. Thus, the nonlinear failure criterion is represented by the shear strength parameters associated with stress so that the analysis of slope stability using a nonlinear failure criterion can be transformed into the traditional upper bound method with a linear Mohr–Coulomb failure criterion. Comparison with published solutions illustrates the accuracy and feasibility of the proposed method for a simple homogeneous slope stability problem. The proposed approach is also applied to a seismic stability problem for a rockfill dam to study the influence of different failure criterions on the upper bound solutions. The results show that the seismic stability coefficients obtained using two different nonlinear failure criteria are similar but that the convergence differs significantly.     

土体本构模型对强度折减法分析基坑整体稳定性的影响

运用有限元强度折减法对基坑工程进行整体稳定性分析时,已有研究主要采用摩尔-库伦模型对土体进行模拟,由于摩尔-库伦模型给出的基坑变形曲线与实测不符,故据此得到的基坑整体稳定安全系数也不甚合理。采用Plaxis硬化模型模拟开挖过程,在强度折减分析中采用特征点位移突变对基坑整体稳定性进行收敛判断,通过分析对比所选取的不同特征点的位移与折减系数的关系曲线,提出采用挡墙内侧开挖面附近土体作为收敛判断的判别点较为合理,其安全系数的取值与采用极限平衡法得到的结果比较接近,而摩尔-库伦模型所得到的计算结果则偏大。最后分析了基坑宽度、基底软土层厚度、挡墙插入深度和挡墙刚度等因素对基坑整体稳定性的影响,并比较了采用这两种不同土体本构模型对分析结果的影响     

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。     

3D key‐group method for slope stability analysis

Because of the simplicity and the speed of execution, methods used in static stability analyses have yet remained relevant. The key‐block method, which is the most famous of them, is used for the stability analysis of fractured rock masses. The KBM method is just based on finding key blocks, and if no such blocks are found to be unstable, it is concluded that the whole of the rock mass is stable. Literally, though groups of ‘stable’ blocks are taken together into account, in some cases, it may prove to be unstable. An iterative and progressive stability analysis of the discontinuous rock slopes can be performed using the key‐group method, in which groups of collapsible blocks are combined. This method is literally a two‐dimensional (2D) limit equilibrium approach. Because of the normally conservational results of 2D analysis, a three‐dimensional (3D) analysis seems to be necessary. In this paper, the 2D key‐group method is developed into three dimensions so that a more literal analysis of a fractured rock mass can be performed. Using Mathematica software, a computer program was prepared to implement the proposed methodology on a real case. Then, in order to assess the proposed 3D procedure, its implementation results are compared with the outcomes of the 2D key‐group method. Finally, tectonic block No.2 of Choghart open pit mine was investigated as a case study using the proposed 3D methodology. Results of the comparison revealed that the outcomes of the 3D analysis of this block conform to the reality and the results of 2D analysis. Copyright © 2011 John Wiley & Sons, Ltd.     

Homogenization framework for three‐dimensional elastoplastic finite element analysis of a grouted pipe‐roofing reinforcement method for tunnelling

This paper deals with the grouted pipe‐roofing reinforcement method that is used in the construction of tunnels through weak grounds. This system consists on installing, prior to the excavation of a length of tunnel, an array of pipes forming a kind of ‘umbrella’ above the area to be excavated. In some cases, these pipes are later used to inject grout to strengthen the ground and ‘connect’ the pipes. This system has proven to be very efficient in reducing tunnel convergence and water inflow when tunnelling through weak grounds. However, due to the geometrical and mechanical complexity of the problem, existing finite element frameworks are inappropriate to simulate tunnelling using this method. In this paper, a mathematical framework based on a homogenization technique to simulate ‘grouted pipe‐roofing reinforced ground’ and its implementation into a 3‐D finite element programme that can consider stage construction situations are presented. The constitutive model developed allows considering the main design parameters of the problem and only requires geometrical and mechanical properties of the constituents. Additionally, the use of a homogenization approach implies that the generation of the finite element mesh can be easily produced and that re‐meshing is not required as basic geometrical parameters such as the orientation of the pipes are changed. The model developed is used to simulate tunnelling with the grouted pipe‐roofing reinforcement method. From the analyses, the effects of the main design parameters on the elastic and the elastoplastic analyses are considered. Copyright © 2004 John Wiley & Sons, Ltd.     

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.     

Inter‐relations between experimental and computational aspects of slope stability analysis

Most conventional slope stability calculations are based on the linear Mohr–Coulomb failure criterion. However, a substantial amount of experimental evidence suggests that failure criteria of many soils are not linear particularly in the range of small normal stresses. This departure from linearity is significant for slope stability calculations since for a wide range of practical stability problems, critical slip surfaces are shallow and normal stresses acting on such surfaces are small. There exists a technical difficulty in performing strength measurements in the range of small normal stresses relevant to such slope stability problems. As a result, in many practical situations strength measurements are performed at much larger normal stresses then those relevant for the stability problem under consideration. When this is the case, use of the Mohr–Coulomb criterion amounts to a linear extrapolation of experimental information (obtained at large normal stresses), into the range of small normal stresses, which is relevant to the problem. This extrapolation results with very significant overestimation of calculated safety factors in cases when there is large mismatch between experimental and relevant ranges of normal stresses. The present work delineates the extent of this problem and suggests a practical way to overcome it. Copyright © 2003 John Wiley & Sons, Ltd.     

Iterative analysis of pore‐dynamic models discretized by finite elements

This work proposes an iterative procedure to analyze dynamic linear/nonlinear fully saturated porous media considering time‐domain finite element discretization. In this iterative approach, each phase of the coupled problem is treated separately, uncoupling the governing equations of the model. Thus, simpler, smaller, and better conditioned systems of equations are obtained, rendering more attractive techniques. A relaxation parameter is introduced in order to improve the efficiency and robustness of the iterative solution, and an expression to compute optimal values for the relaxation parameter is discussed. At the end of the paper, numerical examples are presented, illustrating the effectiveness and potentialities of the proposed methodology. Copyright © 2013 John Wiley & Sons, Ltd.     

东巨寺沟隧道湿喷纤维混凝土支护结构和围岩稳定性位移模糊判别

湿法喷射混凝土可有效地改善隧道内作业环境、反弹量小、喷射质量高,是隧道支护结构施工值得推广的工艺。首次在宝鸡－兰州铁路复线东巨寺沟铁路隧道选取试验段,实施湿喷工艺喷射聚丙烯纤维混凝土,作为支护结构兼作永久性支护,免除二次衬砌工作,并进行水平位移收敛监测。采用非线性最小二乘法对该隧道水平收敛曲线进行回归分析,同时采用隧道稳定性模糊概率分析理论对不同断面位置处的隧道围岩稳定性进行判别分析。分析结果表明,采用湿喷纤维混凝土支护的隧道围岩处于稳定状态,可靠度指标高。     

Scaled boundary finite‐element analysis of a non‐homogeneous axisymmetric domain subjected to general loading

The scaled boundary finite‐element method is derived for elastostatic problems involving an axisymmetric domain subjected to a general load, using a Fourier series to model the variation of displacement in the circumferential direction of the cylindrical co‐ordinate system. The method is particularly well suited to modelling unbounded problems, and the formulation allows a power‐law variation of Young's modulus with depth. The efficiency and accuracy of the method is demonstrated through a study showing the convergence of the computed solutions to analytical solutions for the vertical, horizontal, moment and torsion loading of a rigid circular footing on the surface of a homogeneous elastic half‐space. Computed solutions for the vertical and moment loading of a smooth rigid circular footing on a non‐homogeneous half‐space are compared to analytical ones, demonstrating the method's ability to accurately model a variation of Young's modulus with depth. Copyright © 2003 John Wiley & Sons, Ltd.     

Stability analysis of membrane‐reinforced curved earth retaining walls,using a multiphase approach

The stability analysis of curved earth retaining walls, stabilized by reinforcing membranes, is investigated by means of a multiphase model developed in the framework of the yield design approach. This model is an extension of that previously developed for soils reinforced by linear inclusions. It combines the advantage of a homogenization approach in terms of improved computational efficiency, with its capability to account for a specific soil–reinforcement failure condition, in a rational and systematic way. Application of this model is performed on the illustrative example of a cylindrical‐reinforced retaining wall by means of the kinematic approach of yield design, which provides upper bound estimates for the retaining wall stability factor. Nondimensional charts are finally presented assessing the influence of relevant parameters such as the curvature of the wall, the length of the reinforcing membranes or the reinforcement pull‐out resistance. Copyright © 2009 John Wiley & Sons, Ltd.     

Upper bound limit analysis using simplex strain elements and second‐order cone programming

In geomechanics, limit analysis provides a useful method for assessing the capacity of structures such as footings and retaining walls, and the stability of slopes and excavations. This paper presents a finite element implementation of the kinematic (or upper bound) theorem that is novel in two main respects. First, it is shown that conventional linear strain elements (6‐node triangle, 10‐node tetrahedron) are suitable for obtaining strict upper bounds even in the case of cohesive‐frictional materials, provided that the element sides are straight (or the faces planar) such that the strain field varies as a simplex. This is important because until now, the only way to obtain rigorous upper bounds has been to use constant strain elements combined with a discontinuous displacement field. It is well known (and confirmed here) that the accuracy of the latter approach is highly dependent on the alignment of the discontinuities, such that it can perform poorly if an unstructured mesh is employed. Second, the optimization of the displacement field is formulated as a standard second‐order cone programming (SOCP) problem. Using a state‐of‐the‐art SOCP code developed by researchers in mathematical programming, very large example problems are solved with outstanding speed. The examples concern plane strain and the Mohr–Coulomb criterion, but the same approach can be used in 3D with the Drucker–Prager criterion, and can readily be extended to other yield criteria having a similar conic quadratic form. Copyright © 2006 John Wiley & Sons, Ltd.     

Three‐dimensional finite elements for the analysis of soil contamination using a multiple‐porosity approach

A three‐dimensional finite‐element model of contaminant migration in fissured clays or contaminated sand which includes multiple sources of non‐equilibrium processes is proposed. The conceptual framework can accommodate a regular network of fissures in 1D, 2D or 3D and immobile solutions in the macro‐pores of aggregated topsoils, as well as non‐equilibrium sorption. A Galerkin weighted‐residual statement for the three‐dimensional form of the equations in the Laplace domain is formulated. Equations are discretized using linear and quadratic prism elements. The system of algebraic equations is solved in the Laplace domain and solution is inverted to the time domain numerically. The model is validated and its scope is illustrated through the analysis of three problems: a waste repository deeply buried in fissured clay, a storage tank leaking into sand and a sanitary landfill leaching into fissured clay over a sand aquifer. Copyright © 2005 John Wiley & Sons, Ltd.     

Generation of a realistic 3D sand assembly using X‐ray micro‐computed tomography and spherical harmonic‐based principal component analysis

Three‐dimensional particle morphology is a significant problem in the discrete element modeling of granular sand. The major technical challenge is generating a realistic 3D sand assembly that is composed of a large number of random‐shaped particles containing essential morphological features of natural sands. Based on X‐ray micro‐computed tomography data collected from a series of image processing techniques, we used the spherical harmonics (SH) analysis to represent and reconstruct the multi‐scale features of real 3D particle morphologies. The SH analysis was extended to some highly complex particles with sharp corners and surface cavities. We then proposed a statistical approach for the generation of realistic particle assembly of a given type of sand based on the principle component analysis (PCA). The PCA aims to identify the major pattern of the coefficient matrix, which is made up of the SH coefficients of all the particles involved in the analysis. This approach takes into account the particle size effect on the variation of particle morphology, which is observed from the available results of micro‐computed tomography and QICPIC analyses of sand particle morphology. Using the aforementioned approach, two virtual sand samples were generated, whose statistics of morphological parameters were compared with those measured from real sand particles. The comparison shows that the proposed approach is capable of generating a realistic sand assembly that retains the major morphological features of the mother sand. Copyright © 2016 John Wiley & Sons, Ltd.