Characterizing soil properties by the meshless local Petrov-Galerkin method

This study presents a preliminary development of a direct back analysis procedure by the meshless local Petrov-Galerkin (MLPG) method and its application to characterize soil properties using in-situ test results. As compared to a direct back analysis based on the finite element method (FEM), it is intended to show that doing a direct back analysis by the MLPG method may reduce the computation costs or treat with the non-homogeneity of characterized soil properties more easily. Taking a two-dimensional (2D) solute transport problem as an illustration, an MLPG1 model of such a problem is derived to predict the solute concentration with trial coefficients of dispersion. To account for the non-homogeneity of these coefficients, variation of them is described by the moving least-squares interpolation. The Akaike information criterion is then introduced to find those coefficients of dispersion with which errors between predicted and measured data are minimized. A benchmark problem is studied to test the precision of numerical results provided by the proposed MLPG1 model. Another example illustrates the experiences of doing an MLPG-based direct back analysis. Comparison of MLPG-based and FEM-based direct back analyses is taken.     

Direct back analysis by the meshless local Petrov‐Galerkin method and Bayesian statistics

This study presents a preliminary development of a direct back analysis procedure by the meshless local Petrov–Galerkin (MLPG) method and Bayesian statistics and the application of resulting procedure to characterize soil properties using laboratory results. As compared to direct back analyses that are based on the finite element method (FEM), it is intended to show that MLPG‐based direct back analyses may be more suitable for some kinds of characterization problems; for example, involving a complex subsurface stratification or the characterization of soil properties of just an inclusion of a soil profile. The existing MLPG method is first slightly modified to analyse time‐dependent problems. Using the resulting method, quantities to be characterized are evaluated so that they give numerical results as close to measured data as possible. The Akaike information criterion is introduced for simplifying the evaluation. A one‐dimensional finite strain consolidation problem is introduced to do an error analysis for prediction by the proposed MLPG method. Another example illustrates experiences of performing an MLPG‐based direct back analysis. Comparison of MLPG‐based and FEM‐based direct back analyses is taken. Copyright © 2006 John Wiley & Sons, Ltd.     

Three‐dimensional simulations of tensile cracks in geomaterials by coupling meshless and finite element method

Failure in geotechnical engineering is often related to tension‐induced cracking in geomaterials. In this paper, a coupled meshless method and FEM is developed to analyze the problem of three‐dimensional cracking. The radial point interpolation method (RPIM) is used to model cracks in the smeared crack framework with an isotropic damage model. The identification of the meshless region is based on the stress state computed by FEM, and the adaptive coupling of RPIM and FEM is achieved by a direct algorithm. Mesh‐bias dependency, which poses difficulties in FEM‐based cracking simulations, is circumvented by a crack tracking algorithm. The performance of our scheme is demonstrated by two numerical examples, that is, the four‐point bending test on concrete beam and the surface cracks caused by tunnel excavation. Copyright © 2014 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.     

Inverse analysis of an embankment on soft clay by extended Bayesian method

A new type of indirect inverse analysis procedure is proposed to overcome the difficulties the geotechnical inverse analyses are encountering (such as unstability and non-uniqueness of the solutions as well as multicollinearity). These difficulties are eased by combining the objective information (i.e. the observation data) and the subjective information (i.e. the prior information) in an appropriate manner by so-called extended Bayesian method. The method is based on a new view on Bayesian model proposed by Akaike. The problem of model identification in the inverse analysis is also tackled by applying well-known AIC but of the Bayesian version. A case study on an embankment on soft clay is presented to illustrate the effectiveness of the new method. A rather thorough review on the geotechnical inverse analysis is also presented to indicate the necessity of the proposed procedure. An appendix is attached to summarize the statistical background of the new method.     

基于单位分解的扩展径向点插值无网格法

针对线弹性断裂力学问题,提出扩展径向点插值无网格法（X-RPIM）。该方法基于单位分解思想,在传统径向点插值无网格法的位移模式中加入扩展项来描述裂纹两侧的不连续位移场和裂尖奇异场。由于其形函数具有Kronecker ? 函数性质,易于施加本质边界条件。详细描述了X-RPIM不连续位移模式的建立,支配方程的离散形式以及J积分计算混合模式裂纹的应力强度因子的实现过程,讨论了不同积分区域对应力强度因子的影响。数值算例分析证明了该方法在求解断裂问题时的可行性和有效性,同时说明扩展径向点插值无网格法在模拟裂纹扩展问题时具有良好的前景。     

Groundwater management using a new coupled model of meshless local Petrov-Galerkin method and modified artificial bee colony algorithm

To develop sustainable groundwater management strategies, generally coupled simulation-optimization (SO) models are used. In this study, a new SO model is developed by coupling moving least squares (MLS)-based meshless local Petrov-Galerkin (MLPG) method and modified artificial bee colony (MABC) algorithm. The MLPG simulation model utilizes the advantages of meshless methods over the grid-based techniques such as finite difference (FDM) and finite element method (FEM). For optimization, the basic artificial bee colony algorithm is modified to balance the exploration and exploitation capacity of the model more effectively. The performance of the developed MLPG-MABC model is investigated by applying it to hypothetical and field problems with three different management scenarios. The model results are compared with other available SO model solutions for its accuracy. Further, sensitivity analyses of various model parameters are carried out to check the robustness of the SO model. The proposed model gave quite promising results, showing the applicability of the present approach.     

Statistical inverse analysis based on genetic algorithm and principal component analysis: Method and developments using synthetic data

This study concerns the identification of parameters of soil constitutive models from geotechnical measurements by inverse analysis. To deal with the non‐uniqueness of the solution, the inverse analysis is based on a genetic algorithm (GA) optimization process. For a given uncertainty on the measurements, the GA identifies a set of solutions. A statistical method based on a principal component analysis (PCA) is, then, proposed to evaluate the representativeness of this set. It is shown that this representativeness is controlled by the GA population size for which an optimal value can be defined. The PCA also gives a first‐order approximation of the solution set of the inverse problem as an ellipsoid. These developments are first made on a synthetic excavation problem and on a pressuremeter test. Some experimental applications are, then, studied in a companion paper, to show the reliability of the method. Copyright © 2009 John Wiley & Sons, Ltd.     

弹性地基上水工结构各向异性Mindlin底板计算分析的无单元法（EFGM）

无单元法（element free galerkin method）是一种基于滑动最小二乘法构造插值函数的无网格数值方法。以该方法中插值函数及其导函数为基础,从变分原理出发,建立了弹性地基上正交各向异性Mindlin板的无单元法求解控制方程,其中弹性地基采用Winkler地基模型。对该理论方法进行了相应的程序实现,最后通过算例分析表明了提出方法用于水工结构中弹性地基板问题分析的可行性和有效性。     

Determination of Trace Element Mass Fractions in Ultramafic Rocks by HR‐ICP‐MS: A Combined Approach Using a Direct Digestion/Dilution Method and Preconcentration by Coprecipitation

A procedure is described for the determination of thirty‐seven minor and trace elements (LILE, REE, HFSE, U, Th, Pb, transition elements and Ga) in ultramafic rocks. After Tm addition and acid sample digestion, compositions were determined both following a direct digestion/dilution method (without element separation) and after a preconcentration procedure using a double coprecipitation process. Four ultramafic reference materials were investigated to test and validate our procedure (UB‐N, MGL‐GAS [GeoPT12], JP‐1 and DTS‐2B). Results obtained following the preconcentration procedure are in good agreement with previously published work on REE, HFSE, U, Th, Pb and some of the transition elements (Sc, Ti, V). This procedure has two major advantages: (a) it avoids any matrix effect resulting from the high Mg content of peridotite, and (b) it allows the preconcentration of a larger trace element set than with previous methods. Other elements (LILE, other transition elements Cr, Mn, Co, Ni, Cu, Zn, as well as Ga) were not fully coprecipitated with the preconcentration method and could only be accurately determined through the direct digestion/dilution method.     

基于地形分区IDW的复垦排土场土壤养分空间分布

准确掌握土壤养分的空间分布，对于评价复垦排土场土壤质量，并制定相应的复垦措施具有重要意义，但是排土场的复杂地形导致一般插值方法的预测效果较差。以内蒙古锡林浩特盟胜利一号露天矿北排土场为例，采用基于地形分区的反距离权重法对土壤养分（速效氮、速效钾、有效磷和有机质）进行空间插值并与常规反距离权重法和克里金插值法进行比较。结果表明，使用分区反距离权重法插值得到的交叉验证精度均高于克里金插值法与反距离权重法，除此之外，有效磷的R2值为0.22，速效氮的R2值为0.37，速效钾以及有机质的R2值分别为0.34与0.14，同样高于克里金插值法与反距离权重法。插值结果显示，排土场速效氮含量整体由北至南逐渐减少；有效磷含量仅在中心地区稍高；速效钾在研究区东北部含量偏高；土壤有机质在中心地区含量相对偏低。研究成果为露天矿排土场土壤养分评价提供借鉴。      

基于紧支径向基函数的点插值无网格方法

紧支径向基函数能使支配方程中的刚度矩阵具有稀疏性,很适合应用于无网格方法中,其缺点是在插值计算时精度不高.点插值方法的插值函数具有Delta函数性质,可以很方便的施加本质边界条件,但在计算插值函数时矩阵易出现奇异.为了提高计算精度并避免点插值法的局限性,首先对紧支径向基函数进行完备性修正,然后用完备性修正的紧支径向基函数代替多项式来形成插值函数,建立了紧支径向基函数点插值方法.由于该方法中的形函数满足Delta函数性质,因此本质边界条件可以像传统的有限元方法一样很容易施加.然后将该方法用于二维弹性静力问题的求解,导出了其相应的离散方程.最后将该方法应用于一个悬臂梁的分析中,初步验证了该方法的有效性与合理性.     

基于Chebyshev走时逼近的三维多次反射射线计算

在利用有限差分等基于网格的数值分析方法解地震波走时所满足的程函方程时,由于速度模型的网格化离散等原因,会使走时在各网格节点之间不具有计算射线路径所要求的光滑性,即走时在邻近网格节点之间不具有连续的一阶导数。因此,直接利用网格节点走时计算射线路径会使最终的射线路径不光滑。为解决这个问题,已有研究者提出了基于B样条插值的逆向梯度方案（法）。然而,在速度发生突变时,B样条逆向梯度法所计算出的射线路径会具有较大的误差。针对这个问题,首先采用适合于解最小零偏差逼近及最佳平方逼近问题的Chebyshev多项式取代B样条对来自于分区多级计算方案的网格节点走时进行最佳逼近,得到在最小平方意义下的最优走时公式;然后采用与B样条逆向梯度法类似的计算过程得到光滑的射线路径。数值实验表明,利用Chebyshev多项式逼近走时可以得到具有很高精度的多次反射射线路径,在多次波偏移成像研究中具有潜在的价值。     

Fully coupled poromechanical back analysis of the pulse test by inverse method

In this paper, we investigate the pulse test, which is usually considered as efficient for measuring the permeability of weakly permeable porous media. The pulse is first analyzed and we show that it is a fully poromechanical coupled problem. Owing to those couplings, the problem is 2D‐axisymmetrical, rather than 1D as is usually considered to be the case. As a consequence, the 1D solutions, for example under constant mean stress hypothesis, although giving good approximates of permeability and storage coefficient, are not rigorous and an enhanced back analysis of the test requires 2D solutions. Therefore, no analytical solution exists, and the problem has to be solved using 2D‐axisymmetrical numerical modelings of the pulse test. The finite element method is considered in this paper. We then proceed to formulate the pulse test back analysis as a parameter identification problem, and we focus on intrinsic permeability, Biot coefficient, drained Young's modulus and reservoir compressibility levels. This parameter identification problem is solved by an inverse method consisting of the minimization of a cost‐functional, through a gradient‐based algorithm. This new method of interpretation of the pulse test is finally applied to laboratory tests on Meuse/Haute–Marne argillite and is shown to give encouraging results. Copyright © 2010 John Wiley & Sons, Ltd.     

裂隙岩体渗流场的无单元法模拟及渗流特性研究

裂隙岩体因含有发育程度不同的裂隙、节理和断层等不连续面,致其渗透性具有各向异性、不连续性等特点,因此传统的有限元法对分布密集的裂隙岩体渗流场求解有一定的难度。本文提出了采用无单元Glaerkin法求解有自由面裂隙渗流问题,并推导了无单元法求解渗流场的基本方程和积分格式,给出了应用罚函数法处理渗流边界条件和自由面处理方法。采用IDL语言编制了二维无单元法计算软件LIDAREFM。文中以北京怀柔桥梓镇某裂隙岩体边坡渗流场计算为例,研究了复杂裂隙共同作用下渗流场特性和自由面分布,讨论了不同开度、不同连通程度的裂隙对渗流场的影响。研究结果表明:无单元法可以较好地解决有密集裂隙的岩体渗流场的求解问题,实现了裂隙处结点任意加密以及积分网格的独立布置,避免了对有自由面和裂隙穿越的子域的重新处理,简化了渗流问题的求解过程。     

岩土体渗流自由面问题的重心插值无网格方法

岩土体的渗透破坏、地下工程的防渗设计等无不与渗流计算有关。针对渗流自由面问题,提出一种重心拉格朗日插值的配点型无网格方法。由于渗流自由面问题的求解区域是不规则区域,该方法通过将不规则求解区域嵌入一个正则矩形区域,在正则区域上采用重心拉格朗日插值近似未知函数,利用配点法离散渗流问题的控制方程,将重心拉格朗日插值的微分矩阵离散成代数方程表达的矩阵形式。将自由面上的边界条件通过重心拉格朗日插值离散,通过置换方程法和附加方程法施加边界条件,利用正则区域上的重心插值配点法,通过迭代确定最终自由面的位置。数值算例表明所提出的无网格方法对于求解渗流自由面问题的正确性和高精度。     

Certified solutions for hydraulic structures using the node‐based smoothed point interpolation method (NS‐PIM)

A meshfree node‐based smoothed point interpolation method (NS‐PIM), which has been recently developed for solid mechanics problems, is applied to obtain certified solutions with bounds for hydraulic structure designs. In this approach, shape functions for displacements are constructed using the point interpolation method (PIM), and the shape functions possess the Kronecker delta property and permit the straightforward enforcement of essential boundary conditions. The generalized smoothed Galerkin weak form is then applied to construct discretized system equations using the node‐based smoothed strains. As a very novel and important property, the approach can obtain the upper bound solution in energy norm for hydraulic structures. A 2D gravity dam problem and a 3D arch dam problem are solved, respectively, using the NS‐PIM and the simulation results of NS‐PIM are found to be the upper bounds. Together with standard fully compatible FEM results as a lower bound, we have successfully determined the solution bounds to certify the accuracy of numerical solutions. This confirms that the NS‐PIM is very useful for producing certified solutions for the analysis of huge hydraulic structures. Copyright © 2009 John Wiley & Sons, Ltd.     

Identifying parameters controlling soil delayed behaviour from laboratory and in situ pressuremeter testing

The aim of this paper is to present a methodology for identifying the soil parameters controlling the delayed behaviour from laboratory and in situ pressuremeter tests by using an elasto‐viscoplastic model (EVP‐MCC) based on Perzyna's overstress theory and on the elasto‐plastic Modified Cam Clay model. The influence of both the model parameters and the soil permeability was studied under the loading condition of pressuremeter tests by coupling the proposed model equations with Biot's consolidation theory. On the basis of the parametric study, a methodology for identifying model parameters and soil permeability by inverse analysis from three levels of constant strain rate pressuremeter tests was then proposed and applied on tests performed on natural Saint‐Herblain clay. The methodology was validated by comparing the optimized values of soil parameters and the values of the same parameters obtained from laboratory test results, and also by using the identified parameters to simulate other tests on the same samples. The analysis of the drainage condition and the strain rate effect during a pressuremeter test demonstrated the coupled influence of consolidation and viscous effects on the test results. The numerical results also showed that the inverse analysis procedure could successfully determine the parameters controlling the time‐dependent soil behaviour. Copyright © 2008 John Wiley & Sons, Ltd.