Model identification and parameter estimation of elastoplastic constitutive model by data assimilation using the particle filter

Data assimilation, using the particle filter and incorporating the soil‐water coupled finite element method, is applied to identify the yield function of the elastoplastic constitutive model and corresponding parameters based on the sequential measurements of hypothetical soil tests and an actual construction sequence. In the proposed framework of the inverse analysis, the unknowns are both the particular parameter within the exponential contractancy model, n_E, which parameterizes various shapes for the yield function of the competing constitutive models, including the original/the modified Cam‐Clay models and in‐between models and the parameters of the corresponding constitutive model. An appropriate set, consisting of the yield function of the constitutive model and the parameters of the constitutive model, can be simultaneously identified by the particle filter to describe the most suitable soil behavior. To examine the validity of the proposed procedure, hypothetical and actual measurements for the displacements of a soil specimen were obtained for consolidated and undrained tests through a synthetic FEM computation and for consolidated and drained tests, respectively. After examining the applicability of the proposed procedure to these test results, the present paper then focuses on the actual measured data, ie, the settlement behavior including the lateral deformation of the Kobe Airport Island constructed on reclaimed land.     

Poro‐elasto‐plastic response of an unconsolidated formation confined with stiff seal rocks under radial injection

In this article, we evaluate geomechanics of fluid injection from a fully penetrating vertical well into an unconsolidated formation confined with stiff seal rocks. The coupled behavior of an isotropic, homogeneous sand layer is studied under injection pressures that are high enough to induce plasticity yet not fracturing. Propagation of the significant influence zone surrounding the injection borehole, quantified by the extent of the plastic domain in the elasto‐plastic model, is examined for the first time. First, a new fully coupled axisymmetric numerical model is developed. A comprehensive assessment is performed on pore pressures, stresses/strains, and failure planes during the entire transient period of an injection cycle. Results anticipate existence of five distinctive zones in terms of plasticity state: liquefaction at wellbore; two inner plastic domains surrounding the wellbore, where failure occurs along two planes and major principal stress is in vertical direction; remaining of the plastic domain, where formation fails along one plane and major principal stress is in radial direction; and a non‐plastic region. Failure mechanism at the wellbore is found to be shear followed by liquefaction. Next, a novel methodology is proposed based on which new weakly coupled poro‐elasto‐plastic analytical solutions are derived for all three stress/strain components. Unlike previous studies, extension of the plastic zone is obtained as a function of injection pressure, incorporating plasticity effects on the subsequent elastic domain. Solutions, proven to be a good approximation of numerical simulations, offer a huge advantage as the run time of coupled numerical simulations is considerably long. Copyright © 2016 John Wiley & Sons, Ltd.     

General coupling extended multiscale FEM for elasto‐plastic consolidation analysis of heterogeneous saturated porous media

This paper presents a general coupling extended multiscale FEM (GCEMs) for solving the coupling problem of elasto‐plastic consolidation of heterogeneous saturated porous media. In the GCEMs, the numerical multiscale base functions for the solid skeleton and fluid phase of the coupling system are all constructed on the basis of the equivalent stiffness matrix of the unit cell, which not only contain the interaction between the solid and fluid phases but also consider the time effect. Furthermore, in order to improve the computational accuracy for two‐dimensional problems, a multi‐node coarse element strategy for the GCEMs is proposed, and a two‐scale iteration algorithm for the elasto‐plastic consolidation analysis is developed. Some one‐dimensional and two‐dimensional homogeneous and heterogeneous numerical examples are carried out to validate the proposed method through the comparison with the coupling multiscale FEM and standard FEM. Numerical results show that the newly developed GCEMs can almost preserve the same convergent property as the standard FEM and also possesses the advantages of high computational efficiency. In addition, the GCEMs can be easily applied to other coupling multifield and multiphase transient problems. Copyright © 2014 John Wiley & Sons, Ltd.     

On finite volume method implementation of poro‐elasto‐plasticity soil model

Accurate prediction of the interactions between the nonlinear soil skeleton and the pore fluid under loading plays a vital role in many geotechnical applications. It is therefore important to develop a numerical method that can effectively capture this nonlinear soil‐pore fluid coupling effect. This paper presents the implementation of a new finite volume method code of poro‐elasto‐plasticity soil model. The model is formulated on the basis of Biot's consolidation theory and combined with a perfect plasticity Mohr‐Coulomb constitutive relation. The governing equation system is discretized in a segregated manner, namely, those conventional linear and uncoupled terms are treated implicitly, while those nonlinear and coupled terms are treated explicitly by using any available values from previous time or iteration step. The implicit–explicit discretization leads to a linearized and decoupled algebraic system, which is solved using the fixed‐point iteration method. Upon the convergence of the iterative method, fully nonlinear coupled solutions are obtained. Also explored in this paper is the special way of treating traction boundary in finite volume method compared with FEM. Finally, three numerical test cases are simulated to verify the implementation procedure. It is shown in the simulation results that the implemented solver is capable of and efficient at predicting reasonable soil responses with pore pressure coupling under different loading situations. Copyright © 2015 John Wiley & Sons, Ltd.     

Single‐and multi‐objective genetic algorithm optimization for identifying soil parameters

This paper discusses the quality of the procedure employed in identifying soil parameters by inverse analysis. This procedure includes a FEM‐simulation for which two constitutive models—a linear elastic perfectly plastic Mohr–Coulomb model and a strain‐hardening elasto‐plastic model—are successively considered. Two kinds of optimization algorithms have been used: a deterministic simplex method and a stochastic genetic method. The soil data come from the results of two pressuremeter tests, complemented by triaxial and resonant column testing. First, the inverse analysis has been performed separately on each pressuremeter test. The genetic method presents the advantage of providing a collection of satisfactory solutions, among which a geotechnical engineer has to choose the optimal one based on his scientific background and/or additional analyses based on further experimental test results. This advantage is enhanced when all the constitutive parameters sensitive to the considered problem have to be identified without restrictions in the search space. Second, the experimental values of the two pressuremeter tests have been processed simultaneously, so that the inverse analysis becomes a multi‐objective optimization problem. The genetic method allows the user to choose the most suitable parameter set according to the Pareto frontier and to guarantee the coherence between the tests. The sets of optimized parameters obtained from inverse analyses are then used to calculate the response of a spread footing, which is part of a predictive benchmark. The numerical results with respect to both the constitutive models and the inverse analysis procedure are discussed. Copyright © 2011 John Wiley & Sons, Ltd.     

Three dimensional elasto‐plastic interface for embedded beam elements with interaction surface for the analysis of lateral loading of piles

This paper presents a numerical formulation for a three dimensional elasto‐plastic interface, which can be coupled with an embedded beam element in order to model its non‐linear interaction with the surrounding solid medium. The formulation is herein implemented for lateral loading of piles but is able to represent soil‐pile interaction phenomena in a general manner for different types of loading conditions or ground movements. The interface is formulated in order to capture localized material plasticity in the soil surrounding the pile within the range of small to moderate lateral displacements. The interface is formulated following two different approaches: (i) in terms of beam degrees of freedoms; and (ii) considering the displacement field of the solid domain. Each of these alternatives has its own advantages and shortcomings, which are discussed in this paper. The paper presents a comparison of the results obtained by means of the present formulation and by other well‐established analysis methods and test results published in the literature. Copyright © 2016 John Wiley & Sons, Ltd.     

Simulation of long‐term consolidation behavior of soft sensitive clay using an elasto‐viscoplastic constitutive model

The phenomenon of excess pore water pressure increase or stagnation and continuing large ground deformation in soft sensitive clay following the completion of construction of embankment is simulated for a case study at Saint Alban, Quebec, Canada. The present model employs an updated Lagrangian finite element framework and is combined with an automatic time increment selection scheme. The simulation based on an elasto‐viscoplastic constitutive model considers soil‐structure degradation effect. It is shown that without consideration for the microstructural degradation effect, it is not possible to reproduce the field responses of soft sensitive clay even during the construction of the embankment. When the soil‐structure degradation effect is considered, the present model can offer reasonably accurate prediction for the consolidation behavior of soft sensitive clay, including the so‐called anomalous pore water pressure generation and continuing large deformation even after the end of construction, which has been posing numerous uncertainties on the long‐term performance of earth structures. Copyright © 2013 John Wiley & Sons, Ltd.     

Efficient solution algorithms for multiaxial probabilistic elasto‐plastic constitutive simulations of soils

A Fokker‐Planck‐Kolmogorov (FPK) equation approach has recently been developed to probabilistically solve any elastic‐plastic constitutive equation with uncertain material parameters by transforming the nonlinear, stochastic constitutive rate equation into a linear, deterministic partial differential equation (PDE) and thereby simplifying the numerical solution process. For an uniaxial problem, conventional numerical techniques, such as the finite difference or finite element methods, may be used to solve the resulting univariate FPK PDE. However, for a multiaxial problem, an efficient algorithm is necessary for tractability of the numerical solution of the multivariate FPK PDE. In this paper, computationally efficient algorithms, based on a Fourier spectral approach, are presented for solving FPK PDEs in (stress) space and (pseudo) time, having space‐independent but time‐dependent coefficients and both space‐ and time‐dependent coefficients, that commonly arise in probabilistic elasto‐plasticity. The algorithms are illustrated by probabilistically simulating 2 common laboratory constitutive experiments in geotechnical engineering, namely, the unconfined compression test and the unconsolidated undrained triaxial compression test.     

Some numerical issues using element‐free Galerkin mesh‐less method for coupled hydro‐mechanical problems

A new formulation of the element‐free Galerkin (EFG) method is developed for solving coupled hydro‐mechanical problems. The numerical approach is based on solving the two governing partial differential equations of equilibrium and continuity of pore water simultaneously. Spatial variables in the weak form, i.e. displacement increment and pore water pressure increment, are discretized using the same EFG shape functions. An incremental constrained Galerkin weak form is used to create the discrete system equations and a fully implicit scheme is used for discretization in the time domain. Implementation of essential boundary conditions is based on a penalty method. Numerical stability of the developed formulation is examined in order to achieve appropriate accuracy of the EFG solution for coupled hydro‐mechanical problems. Examples are studied and compared with closed‐form or finite element method solutions to demonstrate the validity of the developed model and its capabilities. The results indicate that the EFG method is capable of handling coupled problems in saturated porous media and can predict well both the soil deformation and variation of pore water pressure over time. Some guidelines are proposed to guarantee the accuracy of the EFG solution for coupled hydro‐mechanical problems. Copyright © 2008 John Wiley & Sons, Ltd.     

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 self‐consistent approach for micro–macro modeling of elastic–plastic deformation in polycrystalline geomaterials

This paper is devoted to multi‐scale modeling of elastic–plastic deformation of a class of geomaterials with a polycrystalline microstructure. We have extended and improved the simplified polycrystalline model presented in [Zeng T. et al., 2014. Mech. Mater. 69 (1):132–145]. A rigorous and fully consistent self‐consistent (SC) scheme is proposed to describe the interaction among plastic mineral grains. We have also deeply discussed the numerical issues related to the numerical implementation of the proposed micromechanical model. The efficiency of the proposed model and the related numerical procedure is evaluated in several representative cases. We have compared the numerical results respectively obtained from the fully SC model and two simplified ones. It is found that the SC model produces a softer stress–strain response than that of the simplified models. The comparisons between the estimation of overall behavior of a granite in different loading conditions and experimental data are also conducted. Copyright © 2015 John Wiley & Sons, Ltd.     

An elasto‐plastic three phase model for partially saturated soil for the finite element simulation of compressed air support in tunnelling

This paper presents a fully coupled finite element formulation for partially saturated soil as a triphasic porous material, which has been developed for the simulation of shield tunnelling with heading face support using compressed air. While for many numerical simulations in geotechnics use of a two‐phase soil model is sufficient, the simulation of compressed air support demands the use of a three‐phase model with the consideration of air as a separate phase. A multiphase model for soft soils is developed, in which the individual constituents of the soil—the soil skeleton, the fluid and the gaseous phase—and their interactions are considered. The triphasic model is formulated within the framework of the theory of porous media, based upon balance equations and constitutive relations for the soil constituents and their mixture. An elasto‐plastic, cam–clay type model is extended to partially saturated soil conditions by incorporating capillary pressure according to the Barcelona basic model. The hydraulic properties of the soil are described via DARCY 's law and the soil–water characteristic curve after VAN GENUCHTEN . Water is modelled as an incompressible and air as a compressible phase. The model is validated by means of selected benchmark problems. The applicability of the model to geotechnical problems is demonstrated by results from the simulation of a compressed air intervention in shield tunnelling. Copyright © 2009 John Wiley & Sons, Ltd.     

A non‐coaxial and unbalanced plastic flow rule for geomaterials and its application to the shear band orientation prediction

In this paper, the non‐coaxial relation between the principal plastic strain increments and the principal stresses, which results from the internal friction in geomaterials, is analyzed, and the phenomenon of the unbalanced development of plastic flow in two conjugate directions is discussed. A non‐coaxial, unbalanced plastic flow model for Coulomb frictional materials is developed and used to determine the orientation of shear band in geomaterials. It is shown that the unbalanced index r of plastic flow has important effect on the orientation of the shear band, and the orientation determined by the conventional plastic flow theory is only a special case of the proposed model when r=0. This result soundly explains the reason that the geomaterials with the same internal friction angle and dilatancy angle can have very different shear band orientations. In addition, the difference between the intrinsic and apparent dilatancy angles is analyzed, and it is emphasized that the dilatancy angle commonly used in practice is indeed the apparent dilatancy angle. Copyright © 2010 John Wiley & Sons, Ltd.     

Investigation of influence of particle characteristics on the non‐coaxiality of anisotropic granular materials using DEM

As a result of deposition process and particle characteristics, granular materials can be inherently anisotropic. Many researchers have strongly suggested that the inherent anisotropy is the main reason for the deformation non‐coaxiality of granular materials. However, their relationships are not unanimous because of the limited understanding of the non‐coaxial micro‐mechanism. In this study, we investigated the influence of inherent anisotropy on the non‐coaxial angle using the discrete element method. Firstly, we developed a new discrete element method approach using rough elliptic particles and proposed a novel method to produce anisotropic specimens. Secondly, the effects of initial specimen density and particle characteristics, such as particle aspect ratio A _m, rolling resistance coefficient β , and bedding plane orientation δ , were examined by a series of biaxial tests and rotational principal axes tests. Findings from the numerical simulations are summarized as follows: (1) the peak internal friction angle ? _p and the non‐coaxial angle i both increase with the initial density, A _m and β , and they both increase initially and then decrease with δ in the range of 0–90°; (2) among the particle characteristics, the influence of A _m is the most significant; and (3) for anisotropic specimens, the non‐coaxial angle can be calculated using the double slip and rotation rate model. Then, an empirical formula was proposed based on the simulation results to depict the relationship between the non‐coaxial angle and the particle characteristics. Finally, the particle‐scale mechanism of non‐coaxiality for granular materials was discussed from the perspective of energy dissipation. Copyright © 2016 John Wiley & Sons, Ltd.     

A unified CFD‐DEM approach for modeling of debris flow impacts on flexible barriers

This paper presents a unified modeling framework to investigate the impacts of debris flow on flexible barriers, based on coupled computational fluid dynamics and discrete element method (CFD‐DEM). We consider a debris flow as a mixture of fluid and particles where the fluid and particle phases are modeled by the CFD and the DEM, respectively. The fluid‐particle coupling is considered by the exchange of interaction forces between CFD and DEM calculations. The flexible barrier is simulated by the DEM as a network of bonded particles with remote interactions. The proposed coupled CFD‐DEM approach enables us to conveniently handle the complicated three‐way interactions among the fluid, the particles, and the flexible barrier structure for debris flow impact simulations. The proposed approach is first used to investigate the influences of channel inclination and the volumetric solid fraction in a debris mixture on the impact force, the resultant deformation, and the retained mass in a flexible barrier. The predictions agree well with existing experimental and numerical studies. We further examine the possible failure modes of a flexible barrier under debris flow impact and their underlying mechanisms. The performance of different components in a flexible barrier system, including single wires, double twists and cables, and their load sharing mechanisms, are carefully evaluated. The proposed unified framework offers a novel, promising pathway towards physically based, quantitative analysis and design of flexible barriers for debris flow mitigation.     

数据同化算法在青藏高原高寒生态系统能量—水分平衡分析中的应用

位于青藏高原腹地的多年冻土地带,其冻融过程中的土壤含水量和土壤冻结深度的变化对气候强烈响应并产生显著的陆面能—水平衡变化,进而又对全球气候产生较大的反馈作用。为了能准确模拟这种变化,选取青藏高原多年冻土分布区的风火山左冒孔流域（长江源）进行了相关的野外数据采集和试验,以考虑土壤冻融影响的水—热耦合陆面过程模型——SHAW为动力学约束框架,验证集合卡尔曼滤波算法在改进模型对土壤冻融过程中土壤水分和冻土深度的计算效果。基于试验点的数据同化计算结果表明：数据同化方法可以融合观测信息显著提高水—热耦合模型对土壤冻融过程中状态变量（土壤水分和冻深）的模拟,并进而改善模型对其它相关能量—水分变量的计算,为在高寒冻土地区利用多源信息进行融合监测提供了理论依据。     

集合卡尔曼滤波估计水文地质参数的局域化修正

集合卡尔曼滤波(Ensemble Kalman Filter,EnKF)作为一种有效的数据同化方法,在众多数值实验中体现优势的同时,也暴露了它使用小集合估计协方差情况下精度较低的缺陷。为了降低取样噪声对协方差估计的干扰并提高滤波精度,应用局域化函数对小集合估计的协方差进行修正,即在协方差矩阵中以舒尔积的形式增加空间距离权重以限制远距离相关。在一个二维理想孔隙承压含水层模型中的运行结果表明,局域化对集合卡尔曼滤波估计地下水参数的修正十分有效,局域化可以很好地过滤小集合估计中噪声的影响,节省计算量的同时又可以防止滤波发散。相关长度较小的水文地质参数(如对数渗透系数)更容易受到噪声的干扰,更有必要进行局域化修正。     

Coupled formulation and algorithms for the simulation of non‐planar three‐dimensional hydraulic fractures using the generalized finite element method

This paper presents a coupled hydro‐mechanical formulation for the simulation of non‐planar three‐dimensional hydraulic fractures. Deformation in the rock is modeled using linear elasticity, and the lubrication theory is adopted for the fluid flow in the fracture. The governing equations of the fluid flow and elasticity and the subsequent discretization are fully coupled. A Generalized/eXtended Finite Element Method (G/XFEM) is adopted for the discretization of the coupled system of equations. A Newton–Raphson method is used to solve the resulting system of nonlinear equations. A discretization strategy for the fluid flow problem on non‐planar three‐dimensional surfaces and a computationally efficient strategy for handling time integration combined with mesh adaptivity are also presented. Several three‐dimensional numerical verification examples are solved. The examples illustrate the generality and accuracy of the proposed coupled formulation and discretization strategies. Copyright © 2015 John Wiley & Sons, Ltd.