Finite element formulation and algorithms for unsaturated soils. Part II: Verification and application

The finite‐element formulation and integration algorithms developed in Part I are used to analyse a number of practical problems involving unsaturated and saturated soils. The formulation and algorithms perform well for all the cases analysed, with the robustness of the latter being largely insensitive to user‐defined parameters such as the number of coarse time steps and error control tolerances. The efficiency of the algorithms, as measured by the CPU time consumed, does not depend on the number of coarse time steps, but may be influenced by the error control tolerances. Based on the analyses presented here, typical values for the error control tolerances are suggested. It is also shown that the constitutive modelling framework presented in Part I can, by adjusting one constitutive equation and one or two material parameters, be used to simulate soils that expand or collapse upon wetting. Treating the suction as a strain variable instead of a stress variable proves to be an efficient and robust way of solving suction‐dependent plastic yielding. Moreover, the concept of the constitutive stress is a particularly convenient way of handling the transition between saturation and unsaturation. Copyright © 2003 John Wiley & Sons, Ltd.     

Uncoupling of coupled flows in soil—a finite element method

Coupled flow of water, chemicals, heat and electrical potential in soil are of significance in a variety of circumstances. The problem is characterized by the coupling between different flows, i.e. a flow of one type driven by gradients of other types, and by the dual nature of certain flows, i.e. combined convection and conduction. Effective numerical solutions to the problem are challenged due to the coupling and the dual nature. In this paper, we first present a general expression that can be used to represent various types of coupled flows in soil. A finite element method is then proposed to solve the generalized coupled flows of convection-conduction pattern. The unknown vector is first decomposed into two parts, a convective part forming a hyperbolic system and a conductive part forming a parabolic system. At each time step, the hyperbolic system is solved analytically to give an initial solution. To solve the multi-dimensional hyperbolic system, we assume that a common eigenspace exists for the coefficient matrices, so that the system can be uncoupled by transforming the unknown vector to the common eigenspace. The uncoupled system is solved by the method of characteristics. Using the solution of the hyperbolic system as the initial condition, we then solve the parabolic system by a Galerkin finite element method for space discretization and a finite difference scheme for time stepping. The proposed technique can be used for solving multi-dimensional, transient, coupled or simultaneous flows of convection-conduction type. Application to a flow example shows that the technique indeed exhibits optimality in convergence and in stability.     

Use of photo-based 3D photogrammetry in analysing the results of laboratory pressure grouting tests

This paper presents a non-destructive, low-cost, photo-based, 3D reconstruction technique for characterizing geo-materials with irregular shapes of a relatively large size. After being validated against two traditional volume measurement methods, namely the vernier caliper method and the fluid displacement method for regular and irregular shapes, respectively, 3D photogrammetry was used to analyse the grout bulbs formed in laboratory pressure grouting tests. The reconstructed 3D mesh model of the sample provides accurate and detailed 3D vertex data, which allowed the volume, densification efficiency and bleeding behaviour of the grout bulbs to be analysed. Comparing the bulb section views at different grouting pressures also offers an intuitive observation of the grout development and propagation process. Moreover, the 3D vertex data and surface area included in the model are of great importance in validating numerical predictions of the pressure grouting process and analysing the interface shear resistance of grouted soil nails or anchors. Compared to existing approaches, the new 3D photogrammetry method possesses several key advantages: (a) it does not require expensive, specialized equipment; (b) samples are not destroyed or modified during testing; (c) it allows to reconstruct objects of various scales and (d) the software is public domain. Therefore, the adoption of this 3D photogrammetry method will facilitate research in the pressure grouting process and can be extended to other problems in geotechnical engineering.     

Finite element formulation and algorithms for unsaturated soils. Part I: Theory

This paper presents a complete finite‐element treatment for unsaturated soil problems. A new formulation of general constitutive equations for unsaturated soils is first presented. In the incremental stress–strain equations, the suction or the pore water pressure is treated as a strain variable instead of a stress variable. The global governing equations are derived in terms of displacement and pore water pressure. The discretized governing equations are then solved using an adaptive time‐stepping scheme which automatically adjusts the time‐step size so that the integration error in the displacements and pore pressures lies close to a specified tolerance. The non‐linearity caused by suction‐dependent plastic yielding, suction‐dependent degree of saturation, and saturation‐dependent permeability is treated in a similar way to the elastoplasticity. An explicit stress integration scheme is used to solve the constitutive stress–strain equations at the Gauss point level. The elastoplastic stiffness matrix in the Euler solution is evaluated using the suction as well as the stresses and hardening parameters at the start of the subincrement, while the elastoplastic matrix in the modified Euler solution is evaluated using the suction at the end of the subincrement. In addition, when applying subincrementation, the same rate is applied to all strain components including the suction. Copyright © 2003 John Wiley & Sons, Ltd.     

Spatial distribution and influencing factors of interprovincial terrestrial physical geographical names in China

The interprovincial terrestrial physical geographical entities are the key areas of regional integrated management. In this paper, we analyzed the spatial patterns of the interprovincial terrestrial physical geographical names (ITPGN) from three aspects: numerical features, spatial variance and spatial agglomeration. The influencing factors of the distribution of ITPGN and the implications for the regional management were further discussed. GIS technology was used to visualize the distribution of ITPGN, analyze the spatial agglomeration and the influencing factors of ITPGN. A total of 11,325 ITPGN, including 4243 water ITPGN and 7082 terrain ITPGN, were extracted from the database of “China’s Second National Survey of Geographical Names (2014-2018)”, and the mountain geographical names were the largest type in ITPGN. Hunan Province had the largest number of the names in China, and Shanghai had the smallest number of the names. The spatial variance of the terrain ITPGN was larger than that of the water ITPGN, and the ITPGN showed a significant agglomeration phenomenon in the southern part of China. In addition, the relative elevation and the population had an impact on the distribution of the ITPGN. The largest number of the geographical names occurred in the regions where the relative elevation was between 1000-2000 meters, and where the population was between 40-50 million. Based on the analysis, it was suggested that the government should take the ITPGN as management units, optimize management strategies based on the characteristics of different types of ITPGN, strengthen the naming of unnamed interprovincial terrestrial physical geographical entities and balance the interests in the controversial ITPGN. This study demonstrated that GIS and spatial analysis techniques were useful for the research of ITPGN and the results could provide targeted management suggestions to realize coordinated development in the interprovincial regions.     

Accelerated initial stiffness schemes for elastoplasticity

Iterative methods for the solution of non‐linear finite element equations are generally based on variants of the Newton–Raphson method. When they are stable, full Newton–Raphson schemes usually converge rapidly but may be expensive for some types of problems (for example, when the tangent stiffness matrix is unsymmetric). Initial stiffness schemes, on the other hand, are extremely robust but may require large numbers of iterations for cases where the plastic zone is extensive. In most geomechanics applications it is generally preferable to use a tangent stiffness scheme, but there are situations in which initial stiffness schemes are very useful. These situations include problems where a nonassociated flow rule is used or where the zone of plastic yielding is highly localized. This paper surveys the performance of several single‐parameter techniques for accelerating the convergence of the initial stiffness scheme. Some simple but effective modifications to these procedures are also proposed. In particular, a modified version of Thomas' acceleration scheme is developed which has a good rate of convergence. Previously published results on the performance of various acceleration algorithms for initial stiffness iteration are rare and have been restricted to relatively simple yield criteria and simple problems. In this study, detailed numerical results are presented for the expansion of a thick cylinder, the collapse of a rigid strip footing, and the failure of a vertical cut. These analyses use the Mohr–Coulomb and Tresca yield criteria which are popular in soil mechanics. Copyright © 2000 John Wiley & Sons, Ltd.     

Genetic algorithms in probabilistic finite element analysis of geotechnical problems

In application to numerical analysis of geotechnical problems, the limit-state surface is usually not known in any closed form. The probability of failure can be assessed via the so-called reliability index. A minimization problem can naturally be formed with an implicit equality constraint defined as the limit-state function and optimization methods can be used for such problems. In this paper, a genetic algorithm is proposed and incorporated into a displacement finite element method to find the Hasofer–Lind reliability index. The probabilistic finite element method is then used to analyse the reliability of classical geotechnical systems. The performance of the genetic algorithm (GA) is compared with simpler probability methods such as the first-order-second-moment Taylor series method. The comparison shows that the GA can produce the results fairly quickly and is applicable to evaluation of the failure performance of geotechnical problems involving a large number of decision variables.     

Arbitrary Lagrangian–Eulerian method for large‐strain consolidation problems

In this paper, an arbitrary Lagrangian–Eulerian (ALE) method is generalized to solve consolidation problems involving large deformation. Special issues such as pore‐water pressure convection, permeability and void ratio updates due to rotation and convection, mesh refinement and equilibrium checks are discussed. A simple and effective mesh refinement scheme is presented for the ALE method. The ALE method as well as an updated‐Lagrangian method is then used to solve some classical consolidation problems involving large deformations with different constitutive laws. The results clearly show the advantage and efficiency of the ALE method for these examples. Copyright © 2007 John Wiley & Sons, Ltd.     

水稻种植环境综合适宜性评价方法研究

开展特定区域水稻种植产业布局是科学制定区域农业种植产业规划的重要内容,而水稻种植适宜性评价是水稻种植产业布局的前提。本文以中国好粮油示范县——福建省浦城县为研究区,基于层次分析模型构建土壤条件、立地条件、灌排条件、气候条件和机械耕作条件5大类共21个指标的水稻种植适宜性评价体系,利用地学模型、回归模型和空间插值等方法计算、模拟评价指标空间分布数据,形成5 m×5 m分辨率的评价指标栅格数据集,基于经验指数法建立适宜度指数模型,开展精细尺度下的水稻种植环境综合适宜性评价。利用实测样点水稻产量与水稻种植环境综合适宜度指数进行分析,发现二者呈显著正相关,验证了本研究评价工作的正确性和可行性。最后利用K-means属性聚类法识别研究区水稻种植多维环境适宜性的空间模式。结果表明：① 研究区水稻种植高度适宜、较适宜、中度适宜耕地面积占全县耕地面积的84.4%,次适宜耕地仅占15.6%,耕地整体适宜性较高;② Ⅰ类集聚区水稻种植综合适宜性和各类指标适宜性均较高;Ⅱ类集聚区水稻种植综合适宜性较高,但灌排条件适宜性很低;Ⅲ类集聚区水稻种植综合适宜性较高,但立地、土壤条件适宜性较低;Ⅳ类集聚区水稻种植综合适宜性较低,灌排条件适宜性最低。本研究可为水稻种植适宜性评价提供方法借鉴,并为浦城县更合理科学地开展农业种植规划提供依据。     

Simulation of yielding and stress–stain behavior of shanghai soft clay

In this paper, a simple bounding surface plasticity model is used to reproduce the yielding and stress–strain behavior of the structured soft clay found at Shanghai of China. A series of undrained triaxial tests and drained stress probe tests under isotropic and anisotropic consolidation modes were performed on undisturbed samples of Shanghai soft clay to study the yielding characteristics. The degradation of the clay structure is modeled with an internal variable that allows the size of the bounding surface to decay with accumulated plastic strain. An anisotropic tensor and rotational hardening law are introduced to reflect the initial anisotropy and the evolution of anisotropy. Combined with the isotropic hardening rule, the rotational hardening rule and the degradation law are incorporated into the bounding surface formulation with an associated flow rule. Validity of the model is verified by the undrained isotropic and anisotropic triaxial test and drained stress probe test results for Shanghai soft clay. The effects of stress anisotropy and loss of structure are well captured by the model.