Method of deformation analysis for composite structures of soils and masonry stones

The coupled numerical manifold method (NMM) and discontinuous deformation analysis (DDA) are enhanced to simulate deformations of continuous soil and discontinuous masonry structures. An elasto-plastic NMM-DDA is formulated that incorporates elasto-plastic constitutive laws into incremental forms of the equation of motion. A node-based uniform strain element is applied to avoid volumetric locking, which often occurs in conventional NMM-DDA. The proposed method is applied to three fundamental boundary value problems: a beam bending problem, a bearing capacity problem of a footing, and a bearing capacity problem of a masonry structure. The method is verified through comparisons with conventional solutions.     

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。     

A critical assessment of methods of correcting for drift from the yield surface in elasto-plastic finite element analysis

The analysis of elasto-plastic boundary value problems using the finite element method involves many discretizations. These lead to the problem of yield surface drift in which the stress state predicted at the end of an elasto-plastic increment of loading does not lie on the current yield surface. As such discrepancies are comulative it is important to ensure that the stresses are corrected back to the yield surface during each increment of loading. In this paper five methods of accounting for this drift are examined. These involve correcting the stresses by projecting back along the plastic flow, the total strain increment and the accumulated effective stress direction. In addition a ‘correct’, method which accounts for the changes in elastic strains which accompany any stress correction is considered. This method is theoretically more sound than the other approximate approaches. All five methods have been used in finite element analyses of the stress changes that occur adjacent to a single pile installed in a uniform deposit of soil on pile loading. The soil was assumed to be normally consolidated and was modelled using a form of modified Cam Clay. Comparison of these results with an analysis, in which yield surface drift was negligible indicated that only the ‘correct’ method and the method involving projecting back along the plastic flow direction give accurate predictions. Substantiai errors occur if the other methods of correcting for yield surface drift are employed. It is recommended that the ‘correct’ method be adopted for finite element calculations.     

The analysis of finite elasto-plastic consolidation

A theoretical formulation and a numerical solution method are proposed for the problem of the time dependent consolidation of an elasto-plastic soil subject to finite deformations. The soil is assumed to be a two-phase material with a skeleton which may yield according to a general yield criterion with plastic flow governed by a general flow law, and whose pore fluid flows according to Darcy's Law. Governing equations are cast in a rate form and constitutive laws are expressed in a frame indifferent manner. The method of analysis is illustrated by several examples of practical interest for both a soil with an elastic skeleton and a soil with an elasto-plastic skeleton which obeys a Morh–Coulomb yield criterion and a non-associated flow law.     

Elasto-plastic analysis of an underground opening by FEM and coupled FEBEM

The elasto-plastic analysis of a circular underground opening using the finite element method (FEM), the coupled finite element and the boundary element method (FEBEM) is presented. The coupling procedure and elasto-plastic formulation are discussed. The effect of in situ stress ratio on yielded zone, displaced shape and principal stresses is presented. The results of FEBEM analysis are compared with those obtained from FEM. The computation time and the number of iterations as required by FEBEM and FEM are compared.     

Numerical stability of non-local viscoplastic FEM analyses for the study of localisation processes

As is well known, numerically handling, by means of finite element codes, localisation problems involving softening materials is still quite delicate. As soon as strain localisation occurs, mesh dependence and serious problems of convergence take place. This paper deals with this type of problem in the case where localisation occurs in an ideal naturally cemented granular specimen tested under plane strain conditions. Different versions (a local elasto-plastic, a local viscoplastic and a non-local viscoplastic) of the same strain softening model are taken into consideration and the relative numerical results are critically discussed and compared. The snap-back problem is numerically taken into account and it has been demonstrated to be affected not only by the softening parameters but also by the viscous nucleus definition. To highlight the relationship between viscosity and non-locality, the results of a numerical parametric analysis are finally discussed.     

边坡变形破坏过程的大变形有限元分析

在用有限元法分析边坡稳定性时,引入计算大变形问题的更新的拉格朗日方法,推导了边坡大变形弹塑性有限元分析的方程式。采用边坡某一幅值的等效塑性剪应变区,从坡脚到坡顶贯通前的折减系数作为边坡安全系数。在此基础上,采用弹塑性大变形有限元分析软件计算了均质土坡不同坡角的安全系数,将其与小变形分析的结果进行了对比分析,结果表明：用弹塑性大变形有限元分析边坡失稳破坏的过程中,既考虑了岩土材料的非线性,又考虑了边坡的几何非线性,使计算结果更趋合理。并结合东深供水改造工程BIII2边坡进行了大变形有限元分析,计算结果与勘查到的实际边坡的滑动面分布位置比较接近。研究表明：该方法尤其适宜于软土类边坡或基坑的稳定性分析。     

An edge-based smoothed point interpolation method for elasto-plastic coupled hydro-mechanical analysis of saturated porous media

An edge-based smoothed point interpolation method is adopted for coupled hydro-mechanical analysis of saturated porous media with elasto-plastic behaviour. A novel approach for the evaluation of the coupling matrix of the porous media is adopted. Stress integration is performed using the substepping method, and the modified Newton-Raphson approach is utilised to address the nonlinearities arising from the elasto-plastic constitutive model used in the formulation. Numerical examples are studied and the results are compared with analytical solutions and those obtained from the conventional finite element method (FEM) to evaluate the performance of the proposed model.     

Modeling the hydro-mechanical responses of strip and circular punch loadings on water-saturated collapsible geomaterials

A stabilized enhanced strain finite element procedure for poromechanics is fully integrated with an elasto-plastic cap model to simulate the hydro-mechanical interactions of fluid-infiltrating porous rocks with associative and non-associative plastic flow. We present a quantitative analysis on how macroscopic plastic volumetric response caused by pore collapse and grain rearrangement affects the seepage of pore fluid, and vice versa. Results of finite element simulations imply that the dissipation of excess pore pressure may significantly affect the stress path and thus alter the volumetric plastic responses.     

Computational model for the simulation of the shield tunneling process in cohesive soils

A two-dimensional computational model is developed here in order to simulate the continuous advance of the Earth Pressure Balance (EPB) Shield during the tunneling process in cohesive soils. The model is based on the combination of the plane strain “transverse–longitudinal” sections that can incorporate the three-dimensional deformation of the soil around and ahead of the shield face. This model is capable of prediciting the soil response due to the shield tunneling before the event, especially in soft ground conditions. An elasto-plastic finite element analysis that is based on the coupled theory of mixtures for inelastic porous media for finite deformation is used in this work to describe the time-dependent deformation of the saturated cohesive soils. The results of this model are compared with the in situ field measurements of the N-2 tunnel project excavated in 1981 in San Francisco using the EPB shield tunneling machine. Reasonable agreement is found between the observed field measurements and the predicted deformations of the soil using the proposed numerical simulation. Copyright © 1999 John Wiley & Sons, Ltd.     

Strain space formulation of the elasto-plastic theory and its finite element implementation

this paper systematically presents the research work of the authors in strain space formulation of elasto-plastic theory and its numerical implementation in the context of geotechnical problems. The following aspects are mainly discussed: the advantages of the theory, the relations between stress space and strain space, the generalized yield, constitutive relations in strain space, the strain path and strain path method. The theory has been implemented in a finite element program. Two numerical examples are given which prove that the proposed theory and method are not only simple and convenient but also practical. It opens up a new approach for the application of strain space theory in the geotechnical engineering.     

边坡渗流耦合变形分析方法的研究及其应用

边坡在渗流作用下应力场会发生变化,是渗流场耦合应力场的作用结果。给出了一种考虑饱和-非饱和流渗影响的边坡弹塑性有限元分析方法,采用了不同含水量对抗剪强度影响的模型,求解带有渗透力作用项的土体弹塑性平衡方程得到边坡的应力应变分布,并应用于某滑坡的实际降雨分析。该实例分析证实,由于渗流作用影响,边坡变形加大,最后形成潜在滑动面。利用渗流耦合变形的弹塑性有限元法分析大气降雨造成土体滑坡的变形和发展是可行的,其在实际工程中的应用是成功的。     

边坡大变形损伤破坏的高效无网格模拟

首先讨论了Lagrangian和Eulerian无网格近似的联系和区别,然后基于稳定节点积分和增量本构理论,建立了分析边坡静动力破坏的高效大变形无网格法,并给出了详细的计算流程。该方法采用弹塑性损伤耦合本构关系来模拟岩土类材料的破坏演化过程,其中屈服函数采用Drucker-Prager准则,损伤准则为基于应变的各项同性损伤函数。由于无网格近似和稳定节点积分具有非局部近似的特性,在保证空间离散稳定性和提高计算效率的同时,也可准确有效地模拟应变集中所形成的剪切带的发生与扩展,通过数值算例验证了方法的有效性。     

Transient analysis of excavations in soil

A finite element approach is used to assess the transient stability of excavation in elasto-plastic soils. Stability is shown to be a function of the rate of excavation, the soil permeability and the drainage path lengths. Sequential excavation has been modelled rigorously in the finite element analysis, together with the transient effects through a fully coupled Biot formulation. Results are presented which demonstrate the effects of the rate of excavation and permeability on stability. Both drained and undrained behaviour of the problem are retrieved as special cases of the transient analysis, and comparisons made with classical solutions where available.     

A transient finite element analysis of linear viscoelastic material model

Since the attenulation of propagating waves through soil/rock is related to the localized material properties as well as the strain developed, the commonly used Rayleigh-type damping model and its variations are not suitable for dynamic finite element analysis of such materials. A linear viscoelastic material model based on the concept of the relaxation spectrum is manipualted in place of the damping model in this paper. The method proposed by Day and Minster¹¹ to transform the convolutional form of the stress–strain relationship to a set of differential operators using the Pade approximant method is generalized to non-scalar waves and implemented for transient finite element analyses. A time-marching scheme is also proposed to incorporate the resultant differential operators into the governing equation of motion. The accuracy related to the Pade approximant method and the time-marching scheme is investigated by critically analysing some scalar wave propagation problems. The proposed technique is further verified using two one-dimensional stress wave propagation problems and a two-dimensional transient propagating wave through an unbounded linear viscoelastic medium. Some encouraging results have been obtained using the proposed technique and guidelines for using this technique are also presented. Comparisons of analytical solutions obtained by Fourier synthesis and numerical results have been provided.     

Large deformation FEMLIP drained analysis of a vertical cut

Understanding and modelling the whole instability mechanisms of a slope are fundamental issues from a scientific and technical viewpoint. To date, small strain Lagrangian approaches have mostly been used in solid mechanics for modelling the failure stage, whereas Eulerian approaches are common in fluid mechanics for propagation analysis. A combination of both approaches allows the stability, failure and propagation stages of a slope to be analysed in a unique mathematical framework. To this end, this paper adopts a finite element method with Lagrangian integration points (FEMLIP), which is currently implemented in the ELLIPSIS code and has been used in geophysics and civil engineering applications. The method combines the robustness of an Eulerian mesh with the flexibility of a set of Lagrangian particles, which allows the history of the material to be taken into account. FEMLIP is first validated with reference to benchmarks with analytical solutions, and is then tested in a large deformation drained analysis of a vertical cut in coarse-grained soils. The results are compared with those provided by the standard engineering methods (1) the limit equilibrium method (LEM) and (2) standard stress–strain elasto-plastic FEM analysis. The comparison shows that FEMLIP is a reliable method for the analysis of both the stability and the instability of a vertical cut, and can be confidently used to analyse more complex problems related to natural slopes.     

Rheological structure and dynamical response of the DSS profile BALTIC in the SE Fennoscandian Shield

Numerical modelling was applied to study the present-day state of stress and deformation under different tectonic loading conditions at the seismic BALTIC–SKJ profile in south-eastern Finland and in Estonia. The finite element method was used to solve the numerical problem. The two-dimensional model was constructed using the results from both seismic and thermal studies along the profile. The model is 700 km long and 200 km deep, and is roughly divided into an inhomogeneous, laterally layered crust and a homogeneous mantle lithosphere. Both the linear elastic and non-linear elasto-plastic rheologies were used. Elasto-plasticity was achieved by calculating a rheological strength as a function of depth along the profile. Different tectonic load cases were analysed with displacement, force and pressure type boundary conditions. Also, the effect of different strain rates was investigated. The results suggest that even with relatively low compressive stress levels the lower crust deforms in a plastic manner for a wet crustal rheology. When applying a dry crustal rheology, plastic yielding is attained only with much higher stress fields.     

Translation and the resolution of the pluton space problem

The Late Cretaceous Mono Creek granite has a pronounced NW–SE elongate shape, 60 km long by 10 km wide, characteristic of plutons from the eastern Sierra Nevada batholith. An 8 km-wide bulge exists on the NE side of this pluton, which exhibits evidence of forceful emplacement (or in-situ ballooning), such as deflection of metamorphic wallrock and igneous foliation, and the orientation of fracture patterns. Three-dimensional strain analysis indicates that wallrock strains do not provide enough volume to accommodate the emplacement of the bulge, a recurring problem in studies of plutonic terranes.We suggest that emplacement of the Mono Creek bulge was accommodated by all components of the three-dimensional displacement field—including translation, rotation, and pure strain (shape change)—of the surrounding units. Classical strain analysis only addresses the rotation and pure strain components, and is incapable of quantifying the translation component. However, our analysis suggests that translation plays the dominant role in the emplacement process. A shell model of translation of the surrounding igneous and metamorphic units is proposed for the Mono Creek bulge, which suggests that the translation component decreases dramatically away from the intrusion, consistent with the observed geology and finite strain analysis. We propose that translation is the solution to the recurring pluton `space' problem, either through tectonically controlled (passive) or magmatically controlled (active) movement of the wallrocks. Translation is generally the neglected component of the displacement field, but it may often be evaluated through judicious use of finite strain analysis and tectonic reconstruction.