An improved SPH method for saturated soils and its application to investigate the mechanisms of embankment failure: Case of hydrostatic pore‐water pressure

The method of smoothed particle hydrodynamics (SPH) has recently been applied to computational geomechanics and has been shown to be a powerful alternative to the standard numerical method, that is, the finite element method, for handling large deformation and post‐failure of geomaterials. However, very few studies apply the SPH method to model saturated or submerged soil problems. Our recent studies of this matter revealed that significant errors may be made if the gradient of the pore‐water pressure is handled using the standard SPH formulation. To overcome this problem and to enhance the SPH applications to computational geomechanics, this article proposes a general SPH formulation, which can be applied straightforwardly to dry and saturated soils. For simplicity, the current work assumes hydrostatic pore‐water pressure. It is shown that the proposed formulation can remove the numerical error mentioned earlier. Moreover, this formulation automatically satisfies the dynamic boundary conditions at a submerged ground surface, thereby saving computational cost. Discussions on the applications of the standard and new SPH formulations are also given through some numerical tests. Furthermore, techniques to obtain the correct SPH solution are also proposed and discussed throughout. As an application of the proposed method, the effect of the dilatancy angle on the failure mechanism of a two‐sided embankment subjected to a high groundwater table is presented and compared with that of other solutions. Finally, the proposed formulation can be considered a basic formulation for further developments of SPH for saturated soils. Copyright © 2011 John Wiley & Sons, Ltd.     

基于GIS空间数据的滑坡SPH粒子模型研究

针对光滑粒子流体动力学方法（SPH）在滑坡模拟中建立粒子模型的难题,提出了基于地理信息系统（GIS）栅格数据的粒子排列与插入方法。根据该方法,建立了滑坡SPH粒子模型及相关粒子生成程序,进一步以结合摩尔-库仑破坏准则的SPH宾汉流体模型为核心,实现了运用SPH方法模拟滑坡破坏后三维运动的过程。该SPH模型在对唐家山滑坡的模拟中得到了验证,并预测了金坪子滑坡破坏后的影响范围。结果表明：基于GIS空间数据的滑坡SPH粒子模型具有可行性与良好的适用性。以GIS数据库为基础,开展滑坡灾害的模拟研究,将大大提高对滑坡等地质灾害的仿真分析,为滑坡灾害的预测与防治提供参考。     

基于光滑粒子流体动力学的流动法则对土体滑坡大变形的影响探讨

光滑粒子流体动力学（SPH）是近年来发展起来的一种纯拉格朗日无网格法,并因其在大变形领域内的优势而受到广泛关注。在进行滑坡大变形分析时,流动法则及剪胀角的选取对于边坡失稳后的运动特性有重要的影响。采用Fortran自行编写了基于SPH的边坡稳定性及失稳后大变形分析程序,然后通过2个经典的算例,讨论了不同流动法则及剪胀角的选取对滑坡大变形分析精度的影响。结果表明：（1）剪胀角的选取对土体失稳后的滑动距离有显著影响,随着剪胀角的增大,土体的滑动速度与距离呈明显增大趋势;（2）在关联性流动法则及非关联性流动法则? =1/2? （? 为剪胀角,? 为摩擦角）条件下,土体在大变形过程中会产生过度膨胀,且运动速度与距离要大于实际情况,而采用关联性流动法? =0时,对于非膨胀土可以得到比较令人满意的结果,但对于膨胀土体会使得运动速度和运动距离过小,不符合实际情况。建议在计算膨胀土大变形时,采用非关联性流动法则且适当考虑膨胀性（? =(0.1～0.2)? ）,可以得到较好的结果。     

考虑物理性质参数变化的膨润土缓冲材料水-热耦合SPH数值解

为了研究热源温度和外界水压对缓冲层中水-热迁移规律的影响,以GMZ膨润土为例,从基于势能的非饱和土的水-热迁移控制方程出发,考虑了蒸发效应的影响,得到了水-热耦合的方程组,采用改进的光滑粒子流体动力学(SPH)算法,能够对每一处土体根据不同时刻的不同状态实时更新计算参数,得到参数变化的水-热耦合解。计算结果表明：土的物理性质参数与土体的温度和饱和度密切相关,是否考虑这些参数的变化会对计算结果产生较大影响;核废料释放的热量能够在较短的时间内扩散到外边界,水分迁移的速度则相对慢很多;缓冲层温度的升高会加快水分的迁移速度,外界水压对温度的分布则影响较小。     

Simulation of mixed-mode fracture using SPH particles with an embedded fracture process zone

This paper focuses on the modelling of mixed-mode fracture using the conventional smoothed particle hydrodynamics (SPH) method and a mixed-mode cohesive fracture law embedded in the particles. The combination of conventional SPH and a mixed-mode cohesive model allows capturing fracture and separation under various loading conditions efficiently. The key advantage of this framework is its capability to represent complex fracture geometries by a set of cracked SPH particles, each of which can possess its own mixed-mode cohesive fracture with arbitrary orientations. Therefore, this can naturally capture complex fracture patterns without any predefined fracture topologies. Because a characteristic length scale related to the size of the fracture process zone is incorporated in the constitutive formulation, the proposed approach is independent from the spatial discretisation of the computational domain (or mesh independent). Furthermore, the anisotropic fracture responses of materials can be naturally captured thanks to the orientation of the fracture process zone embedded at the particle level. The performance of the proposed approach demonstrates its potentials in modelling mixed-mode fracture of rocks and similar quasi-brittle materials.     

Lagrangian meshfree particles method (SPH) for large deformation and failure flows of geomaterial using elastic–plastic soil constitutive model

Simulation of large deformation and post‐failure of geomaterial in the framework of smoothed particle hydrodynamics (SPH) are presented in this study. The Drucker–Prager model with associated and non‐associated plastic flow rules is implemented into the SPH code to describe elastic–plastic soil behavior. In contrast to previous work on SPH for solids, where the hydrostatic pressure is often estimated from density by an equation of state, this study proposes to calculate the hydrostatic pressure of soil directly from constitutive models. Results obtained in this paper show that the original SPH method, which has been successfully applied to a vast range of problems, is unable to directly solve elastic–plastic flows of soil because of the so‐called SPH tensile instability. This numerical instability may result in unrealistic fracture and particles clustering in SPH simulation. For non‐cohesive soil, the instability is not serious and can be completely removed by using a tension cracking treatment from soil constitutive model and thereby give realistic soil behavior. However, the serious tensile instability that is found in SPH application for cohesive soil requires a special treatment to overcome this problem. In this paper, an artificial stress method is applied to remove the SPH numerical instability in cohesive soil. A number of numerical tests are carried out to check the capability of SPH in the current application. Numerical results are then compared with experimental and finite element method solutions. The good agreement obtained from these comparisons suggests that SPH can be extended to general geotechnical problems. Copyright © 2008 John Wiley & Sons, Ltd.     

SPH法在大坝表孔泄流数值模拟中的应用

主要对光滑粒子流体动力学(SPH)法进行研究,建立了大坝表孔泄流的光滑粒子模型。将SPH数学模型应用于拉西瓦水电站表孔泄流中,提出了采用补水边界的方法来满足库区恒定水位条件,模拟了表孔泄流的流场变化及粒子运动过程。通过与物理模型实测的压力值比较,堰表面压力变化基本一致。对模拟结果进行分析,表明光滑粒子流体动力学可用于高速水流的计算模拟研究。     

A SPH framework for dynamic interaction between soil and rigid body system with hybrid contact method

A smoothed particle hydrodynamics (SPH) framework for three-dimensional dynamic soil-multibody interaction modeling is presented, where both soils and rigid bodies are discretized using SPH particles. In the framework, soils are modeled using the Drucker-Prager model, while rigid bodies are considered with a multibody dynamics solver. A hybrid contact method suitable for three-dimensional simulations is developed to model the soil-body and body-body frictionless and frictional contacts, where contact forces are calculated based on ideal plastic collision and the unit normal/tangential vectors of the actual surface. Owing to its simplicity in contact detection and accuracy in contact force calculation, the hybrid contact method can be easily incorporated into SPH. Furthermore, graphics processing unit (GPU) parallelization is utilized to improve efficiency. The presented numerical framework and the hybrid contact method are validated using several examples. Numerical results are compared with analytical solutions and results from the literature. Furthermore, two three-dimensional simulations involving dynamic soil-multibody interaction are included to demonstrate the application.     

A novel computational approach for large deformation and post‐failure analyses of segmental retaining wall systems

Segmental retaining wall (SRW) systems are commonly used in geotechnical practice to stabilize cut and fill slopes. Because of their flexibility, these systems can tolerate minor movements and settlements without incurring damage or crack. Despite these advantages, very few numerical studies of large deformations and post‐failure behavior of SRW systems are found in the current literature. Traditional numerical methods, such as the finite element method, suffer from mesh entanglement, thus are unable to simulate large deformations and flexible behavior of retaining wall blocks in SRW systems. To overcome the above limitations, a novel computational framework based on the smoothed particle hydrodynamics (SPH) method was developed to simulate large deformations and post‐failure behavior of soils and retaining wall blocks in SRW systems. The proposed numerical framework is a hybrid continuum/discontinuum approach that can model soil as an elasto‐plastic material and retaining wall blocks as independent rigid bodies associated with both translational and rotational degrees of freedom. A new contact model is proposed within the SPH framework to simulate the interaction between the soil and the blocks and between the blocks. As an application of the proposed numerical method, a two‐dimensional simulation of an SRW collapse was simulated and compared to experimental results conducted under the same conditions. The results showed that the proposed computational approach provided satisfactory agreement with the experiment. This suggests that the new framework is a promising numerical approach to model SRW systems. Copyright © 2014 John Wiley & Sons, Ltd.     

A novel coupled FDM-DEM modelling method for flexible membrane boundary in laboratory tests

Difficulties are involved in discrete element method (DEM) modelling of the flexible boundary, that is, the membranes covering the soil sample, which can be commonly found in contemporary laboratory soil tests. In this paper, a novel method is proposed wherein the finite difference method (FDM) and DEM are coupled to simulate the rubber membrane and soil body, respectively. Numerical plane strain and triaxial tests, served by the flexible membrane, are implemented and analysed later. The effect of the membrane modulus on the measurement accuracy is considered, with analytical formulae derived to judge the significance of this effect. Based on an analysis of stress-strain responses and the grain rotation field, the mechanical performances produced by the flexible and rigid lateral boundaries are compared for the plane strain test. The results show that (1) the effect of the membrane on the test result becomes more significant at larger strain level because the membrane applies additional lateral confining pressure to the soil body; (2) the tested models reproduce typical stress and volumetric paths for specimens with shear bands; (3) for the plane strain test, the rigid lateral boundary derives a much higher peak strength and larger bulk dilatation, but a similar residual strength, compared with the flexible boundary. The latter produces a more uniform (or ‘diffuse') rotation field and more mobilised local kinematics than does the former. All simulations show that the proposed FDM-DEM coupling method is able to simulate laboratory tests with a flexible boundary membrane.     

A comprehensive study on the parameters setting in smoothed particle hydrodynamics (SPH) method applied to hydrodynamics problems

Smoothed particle hydrodynamics (SPH) is a meshfree, Lagrangian particle method which has advantages in handling solids with extremely large deformation. Like any other numerical methods, cares must be taken to ensure its desirable accuracy and stability through considering several correction techniques in calculation. The selection of values for parameters in those correction approaches is a key step in SPH simulation, which is always difficult for new beginners to deal well with effectively. This paper examines the common inconsistency and instability problems in SPH method and studies its computational efficiency when applied to hydrodynamics problems with material strength like soil column collapse. We analyzed in detail how the correction techniques mitigate these inconsistency and instability problems. Also, the numerical testing results associate with different values for the parameters used in the correction techniques are provided for better understanding the influence of these parameters and for finding out the desirable values. It is found that (1) the SPH method is easily subjected to an inconsistency problem in the boundary area due to the boundary deficiency, and it can be treated well by adopting “virtual particles” contributing to the particle summations. (2) The numerical oscillation in SPH simulation can be mitigated effectively by artificial viscosity with the suggested parameter values. (3) The tension cracking treatment, artificial viscosity and artificial stress work well in removing the tensile instability problem in SPH method. In addition, the nearest neighboring particle searching (NNPS) algorithm, spacing ratio, smoothing length and time step influence the efficiency and accuracy of SPH method significantly. It is shown that SPH method with suggested parameters values can produce a very good result compared with the experimental result.     

A novel nonlinear solution for the polygon scaled boundary finite element method and its application to geotechnical structures

The polygon scaled boundary finite element method is semi-analytical and known for its high precision. However, the material nonlinearity cannot be maintained because this method uses an analytical solution in the radial direction. In this paper, a novel nonlinear algorithm is developed by introducing internal Gaussian points over a subdomain. The response of nonlinearity for a concrete-faced rockfill dam is modeled. The results correspond well with the results from finite element modelling, which demonstrates the method can be used to describe the nonlinear characteristics of geomaterials. Furthermore, this method offers promising flexibility for analyzing complex geometries without decreasing the precision.     

Time‐dependent modelling for soils and its application in tunnelling

Monitoring of the progressive convergence of a tunnel shows that deformations occurring in the soil surrounding a tunnel exhibit a strong evolution with time. This time‐dependent behaviour can be linked to three essential factors: the distance from the point of interest to the working face over time, the distance of unsupported tunnel to the working face and the viscous properties of the soil. The objective of this paper is to propose a constitutive model of the time‐dependent behaviour of soil which has been developed within the framework of elastoplasticity–viscoplasticity and critical state soil mechanics. The consideration of viscoplastic characteristic sets the current model apart from the CJS (Cambou, Jafari and Sidoroff) model as the basic elastoplastic model, and introduces an additional viscous mechanism. The evolution of the viscous yield surface is governed by a particular hardening called ‘viscous hardening’ with a bounding surface. The proposed constitutive model has been applied in the analysis of tunnelling. Two kinds of numerical calculations have been used in the analysis, axisymmetric analysis and plane strain analysis. Monitoring of the progressive convergence of a tunnel conducted in the railway tunnel of Tartaiguille (France), has been used to describe the calculation procedure proposed and the capability of the model. The finite difference software, fast Lagrangian analysis of continua (FLAC), has been used for the numerical simulation of the problems. The comparison of results shows that the observed deformations could have been reasonably predicted by using the constitutive model and calculation strategy proposed. Copyright © 2004 John Wiley & Sons, Ltd.     

One-dimensional self-weight consolidation with continuous drainage boundary conditions: Solution and application to clay-drain reclamation

Traditional consolidation theories cannot provide good predictions of consolidation settlement in land reclamation because of their assumptions that the influence of soil's self-weight is often neglected, and the drainage boundary is considered as fully pervious/impervious. In view of these limitations, an analytical solution is derived for one-dimensional self-weight consolidation problems with a continuous drainage boundary using the finite Fourier sine transform method. Following the classical Terzaghi's small strain theory, the soil's self-weight is considered to produce consolidation settlement in dredged materials with a constant coefficient of consolidation. The continuous drainage boundary can essentially describe the time-dependent variation of drainage capacity at the interface between two adjacent soil layers. By reducing the interface parameters, the effectiveness of the calculation is demonstrated against the Terzaghi's solution. The influence of interface parameters and soil's self-weight stress coefficient on self-weight consolidation is discussed. As expected, the rate of consolidation considering the self-weight stress is faster, although the dependency of consolidation rate on the material property of void ratio is neglected. Moreover, the plane of maximum excess pore-water pressure is estimated as a function of time factor, based on which a design chart is developed to optimize the layout of horizontal drains in land reclamation.     

Cross-bedding related anisotropy and its interplay with various boundary conditions in the formation and orientation of joints in an aeolian sandstone

Previous research revealed that the cross-bedding related anisotropy in Jurassic aeolian Aztec Sandstone cropping out in the Valley of Fire State Park, Nevada, affects the orientation of compaction bands, also known as anti-cracks or closing mode structures. We hypothesize that cross-bedding should have a similar influence on the orientation of the opening mode joints within the same rock at the same location. To test this hypothesis, we investigated the relationship between the orientation of cross-beds and the orientation of different categories of joint sets including cross-bed package confined joints and joint zones in the Aztec Sandstone. The field data show that the cross-bed package confined joints occur at high-angle to bedding and trend roughly parallel to the dip direction of the cross-beds. In comparison, the roughly N–S trending joint zones appear not to be influenced by the cross-beds in any significant way but frequently truncate against the dune boundaries.To characterize the anisotropy due to cross-bedding in the Aztec Sandstone, we measured the P-wave velocities parallel and perpendicular to bedding from 11 samples and determined an average P-wave anisotropy to be slightly larger than 13%. From these results, a model based on the generalized Hooke's law for anisotropic materials is used to analyze deformation of cross-bedded sandstone as a transversely isotropic material. In the analysis, the dip angle of cross-beds is assumed to be constant and the strike orientation varying from 0° to 359° in the east (x), north (y), and up (z) coordinate system. We find qualitative agreement between most of the model results and the observed field relations between cross-beds and the corresponding joint sets. The results also suggest that uniaxial extension (ε_zz > ε_xx = ε_yy = 0) and axisymmetric extension (ε_xx = ε_yy < ε_zz and ε_xx = ε_yy > ε_zz) would amplify the influence of cross-bedding associated anisotropy on the joint orientation whereas a triaxial extension (ε_xx > ε_yy > ε_zz) would mitigate this influence. We suggest that the potential implication of different categories of joint sets (i.e., cross-bed package confined joints and joint zones) forming in response to the variation of the boundary conditions (axisymmetric extension and triaxial extension, respectively) and the interplay with the rock anisotropy is significant. These results have important implications for fluid flow through aeolian sandstones in reservoirs and aquifers.     

A hybrid finite element-spectral boundary integral approach: Applications to dynamic rupture modeling in unbounded domains

The finite element method (FEM) and the spectral boundary integral method (SBI) have both been widely used in the study of dynamic rupture simulations along a weak interface. In this paper, we present a hybrid method that combines FEM and SBI through the consistent exchange of displacement and traction boundary conditions, thereby benefiting from the flexibility of FEM in handling problems with nonlinearities or small-scale heterogeneities and from the superior performance and accuracy of SBI. We validate the hybrid method using a benchmark problem from the Southern California Earthquake Center's dynamic rupture simulation validation exercises.We further demonstrate the capability and computational efficiency of the hybrid scheme for resolving off-fault heterogeneities by studying a 2D in-plane shear crack in two different settings: one where the crack is embedded in a high-velocity zone and another where it is embedded in a low-velocity zone. Finally, we discuss the potential of the hybrid method for addressing a wide range of problems in geophysics and engineering.     

三维质点追踪模型及其在胶南海域的应用

在已建立的变边界河口、陆架、海洋模型(ECOM)的基础上添加一个变边界质点追踪模块,研究胶东半岛南海域的物质输运特征,讨论了三维空间中,水质点在潮流作用下的迁移特点.该模型在近海海洋环境管理上具有实用价值.     

中国风成黄土及其形成下限研究

“中国岩漠·砾漠·沙漠·黄土分布与主风向关系图”显示西北地区的第四纪黄土堆积是以风力为主的综合因素所形成，即就地起沙，近沙成土，一定地域的黄土在物源上隶属于一定地区的沙漠。黄土高原及新疆天山、昆仑山北麓的黄土地层结构的综合对比研究表明，典型风成黄土在不同地域和不同地貌单元上最早开始堆积的层位基本上是一致的，即均始于所有黄土剖面中的下粉砂层（Ｌ＿（１５））。该层以下的第四纪沉积类型因地而异，为非黄土沉积（湖相、冲洪积相及火山岩相等）。由黄土高原各代表性剖面的磁性地层学研究及新疆于田黄土下伏的安山玄武岩的同位素年龄测定获得黄土层开始堆积的时代为早更新世晚期，约１．２ＭａＢ．Ｐ。风成黄土的开始堆积是与黄土南缘各造山带（昆仑山、天山、祁连山及秦岭等）强烈的新构造隆升并产生区域环境效应有成因联系。这一更新世早期的事件层位得到了古生物学、新构造学、地貌学及地外物体高速撞击地球表面所产生的玻璃陨石等事件的佐证。     

Evaluation of excavation‐induced relaxation and its application to an arch dam foundation

Based on the damage mechanism of rock during excavation, the maximum tensile strain criterion for pinpointing relaxation region or excavation‐disturbed (damage) zone (EDZ) is introduced. To simulate the deformation and stress redistribution caused by the deterioration of the deformation and strength parameters in the EDZ, the ‘restraint‐relaxation’ finite element algorithm is formulated using the deformation and strength parameters of pre‐and post‐relaxation. The Xiaowan arch dam project (292 m high) is studied by the proposed method, in which the permissible tensile strain and fluidity parameter are evaluated using back analysis. The computation results have good agreement with the field monitoring. An important inference from the study is the necessity of considering the relaxation effects on the dam/foundation system during the construction and operation period. Copyright © 2011 John Wiley & Sons, Ltd.     

基于粒子迁徙的粒群优化算法及其在岩土工程中的应用

受自然界物种迁徙的启发,提出了一种新的改进的粒群优化算法(MPSO)。算法初始化时,将粒子随机地划分为若干个子粒群,每个子粒群按照给定的策略独立演化,在演化中的指定时段进行粒子的随机迁徙和自适应变异,以保持整个种群的多样性,避免早熟收敛。基准测试函数的计算结果表明,MPSO算法的性能优于其他几种改进算法。堆石体幂函数流变模型,参数较多,具有很强的非线性,将MPSO算法应用到堆石体幂函数流变模型的参数反演中。计算结果表明,利用反演的流变模型参数计算的坝体流变变形与实测变形在发展规律和数值上均比较吻合,证明MPSO算法在多参数、强非线性的复杂模型参数反演中的优越性。