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.     

A Generalized Backward Euler algorithm for the numerical integration of an isotropic hardening elastoplastic model for mechanical and chemical degradation of bonded geomaterials

An extended version of the classical Generalized Backward Euler (GBE) algorithm is proposed for the numerical integration of a three‐invariant isotropic‐hardening elastoplastic model for cemented soils or weak rocks undergoing mechanical and non‐mechanical degradation processes. The restriction to isotropy allows to formulate the return mapping algorithm in the space of principal elastic strains. In this way, an efficient and robust integration scheme is developed which can be applied to relatively complex yield surface and plastic potential functions. Moreover, the proposed algorithm can be linearized in closed form, thus allowing for quadratic convergence in the global Newton iteration. A series of numerical experiments are performed to illustrate the accuracy and convergence properties of the algorithm. Selected results from a finite element analysis of a circular footing on a soft rock layer undergoing chemical weathering are then presented to illustrate the algorithm performance at the boundary value problem level. Copyright © 2002 John Wiley & Sons, Ltd.     

An improved implicit numerical integration of a non‐associated,three‐invariant cap plasticity model with mixed isotropic–kinematic hardening for geomaterials

The Sandia GeoModel is a continuum elastoplastic constitutive model that captures many features of the mechanical response for geological materials over a wide range of porosities and strain rates. Among the specific features incorporated into the formulation are a smooth compression cap, isotropic/kinematic hardening, nonlinear pressure dependence, strength differential effect, and rate sensitivity. This study attempts to provide enhancements regarding computational tractability, domain of applicability, and robustness of the model. A new functional form is presented for the yield and plastic potential functions. This reformulation renders a more accurate, robust, and efficient model as it eliminates spurious solutions attributed to the original form. In addition, we achieve a high‐performance implementation, because the local iterative method is allowed to recast residual vectors with a uniform dimensionality. The model is also furnished with a smooth, elliptical tension cap to account for the tensile yielding. Moreover, an efficient algorithm is introduced, which decreases the computational cost by differentiating the updated shear yield surface from the cap surface based on the trial relative stress state. Finally, various numerical examples including a large‐scale boundary value problem are presented to demonstrate the fidelity of the modified model and to analyze its numerical performance. Copyright © 2015 John Wiley & Sons, Ltd.     

岩体初始应力场的遗传算法与有限元联合反演法

岩土工程问题的有限元分析一般需要考虑初始应力场。实际工程中,岩体往往为非线性。本文采用遗传算法与有限元联合反演法求解非线性岩体初始应力场,通过算例说明文中所提方法是合理的,可在工程应用中推广。     

A high strain‐rate constitutive model for sand and its application in finite‐element analysis of tunnels subjected to blast

The paper presents a constitutive model for simulating the high strain‐rate behavior of sands. Based on the concepts of critical‐state soil mechanics, the bounding surface plasticity theory and the overstress theory of viscoplasticity, the constitutive model simulates the high strain‐rate behavior of sands under uniaxial, triaxial and multi‐axial loading conditions. The model parameters are determined for Ottawa and Fontainebleau sands, and the performance of the model under extreme transient loading conditions is demonstrated through simulations of split Hopkinson pressure bar tests up to a strain rate of 2000/s. The constitutive model is implemented in a finite‐element analysis software Abaqus to analyze underground tunnels in sandy soil subjected to internal blast loads. Parametric studies are conducted to examine the effect of relative density and type of sand and of the depth of tunnel on the variation of stresses and deformations in the soil adjacent to the tunnels. Copyright © 2012 John Wiley & Sons, Ltd.