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 new contact algorithm in the material point method for geotechnical simulations

Contact between stiff structural elements and soil is encountered in many applications in geotechnical engineering. Modelling of such contact is challenging as it often involves impact that would lead to large deformation and failure of the soil. The Material Point Method (MPM) is a mesh‐free method that has been applied to simulate such phenomena. However, the frictional contact algorithm commonly used in MPM only supports Coulomb friction and cannot model fully or partially rough contact conditions in terms of geotechnical engineering. Moreover, because of very different stiffness of contacting materials, the contact force predicted by the previous frictional contact algorithms usually suffers from severe oscillation when applied in structure–soil interaction. This paper presents a new contact algorithm, termed Geo‐contact, designed for geotechnical engineering. In Geo‐contact, a penalty function is incorporated to reduce the oscillation in contact computation, and a limited shear stress is specified along the contact interface. The proposed Geo‐contact algorithm has been implemented to simulate smooth, partially rough and rough contact in typical large deformation penetration problems. The resistance–displacement curves obtained using the Geo‐contact are compared with analytical solutions of limit analysis and large deformation finite element results to verify the accuracy and robustness of the proposed contact algorithm. Copyright © 2014 John Wiley & Sons, Ltd.     

A generic approach to modelling flexible confined boundary conditions in SPH and its application

In this paper, a new approach to applying confining stress to flexible boundaries in the smoothed particle hydrodynamics (SPH) method is developed to facilitate its applications in geomechanics. Unlike the conventional SPH methods that impose confining boundary conditions by creating extra boundary particles, the proposed approach makes use of kernel truncation properties of SPH approximations that occur naturally at free-surface boundaries. Therefore, it does not require extra boundary particles and, as a consequence, can be utilised to apply confining stresses onto any boundary with arbitrary geometry without the need for tracking the curvature change during the computation. This enables more complicated problems that involve moving confining boundaries, such as confining triaxial tests, to be simulated in SPH without difficulties. To further enhance SPH applications in elasto-plastic computations of geomaterials, a robust numerical procedure to implement Mohr-Coulomb plasticity model in SPH is presented for the first time to avoid difficulties associated with corner singularities in Mohr-Coulomb model. The proposed approach was first validated against two-dimensional finite element (FE) solutions for confining biaxial compression tests to demonstrate its predictive capability at small deformation range when FE solutions are still valid. It is then further extended to three-dimensional conditions and utilised to simulate triaxial compression experiments. Simulation results predicted by SPH show good agreement with experiments, FE solutions, and other numerical results available in the literature. This suggests that the proposed approach of imposing confining stress boundaries is promising and can handle complex problems that involve moving confining boundary conditions.     

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.     

Non-rigid disk-based DDA with a new contact model

In this paper, a new disk-based DDA formulation is presented. In the original disk-based DDA, disks are considered to be rigid and the penalty method is used to enforce disk contact constraints. In order to improve the accuracy of the disk-based DDA, new formulations of stiffness and force matrices for non-rigid disks using a new efficient contact model are presented in this paper. Blocks are considered deformable without need to do more computations for contact detection. In the proposed contact model, disk–disk and disk–boundary contacts are transformed into the form of point-to-line contacts and normal spring, shear spring and frictional force sub-matrices are derived by vector analysis. The penalty method is quite simple to implement, but has some major disadvantages. In the presented contact model, not only the simplicity of the penalty method is retained but also the limitations are overcome by using the augmented Lagrangian method. Moreover, unlike the contact model used in the original disk-based DDA, reference line can be obtained directly by using only coordinates of disk centers and their radii, and no more computations are needed. The validity and capability of the new disk-based DDA formulation are demonstrated by several illustrative examples.     

一种改进的光滑粒子动力学法在地震条件下岩质边坡中的验证与应用

开发一种改进损伤框架的粒子流算法,被称为核断裂的光滑粒子流法（kernel?broken smoothed particle hydrodynamics,KBSPH）,用于模拟地震条件下岩质边坡的裂纹扩展和变形破坏过程.在KBSPH中,提出一种改进的损伤框架,通过引入断裂标志来改进损伤粒子的核函数,使损伤粒子的虚拟应力键直接断裂,裂纹在断裂的应力键间生成,从而模拟岩石的裂纹扩展过程.在地震边界上采用了双层边界,将动力输入边界与黏滞边界分离.首先通过薄板振动实验验证KBSPH的动力特性.其次以单裂隙岩体单轴压缩试验验证KBSPH的断裂力学特性.最后模拟地震条件下多节理岩质边坡中裂纹扩展过程和动力响应.薄板振动实验验证了KBSPH的动力特性的准确性.单裂隙岩体单轴压缩试验,证明了KBSPH可以正确模拟预制裂隙尖端的翼型裂纹.通过对比以往数值模拟方法和现场案例,表明KBSPH正确揭示了加速度放大效应以及地震条件下岩质边坡的裂纹扩展过程.KBSPH避免了传统算法的网格畸变,损伤粒子应力分量重新分配的问题,降低了编程难度,提高了运行速率,可为SPH在地震条件下岩石力学中的应用和理解岩石断裂机理提供一定的参考.      

Modelling the flow of self‐compacting concrete

A Lagrangian particle‐based method, smooth particle hydrodynamics (SPH), is used in this paper to model the flow of self‐compacting concretes (SCC) with or without short steel fibres. An incompressible SPH method is presented to simulate the flow of such non‐Newtonian fluids whose behaviour is described by a Bingham‐type model, in which the kink in the shear stress vs shear strain rate diagram is first appropriately smoothed out. The viscosity of the SCC is predicted from the measured viscosity of the paste using micromechanical models in which the second phase aggregates are treated as rigid spheres and the short steel fibres as slender rigid bodies. The basic equations solved in the SPH are the incompressible mass conservation and Navier–Stokes equations. The solution procedure uses prediction–correction fractional steps with the temporal velocity field integrated forward in time without enforcing incompressibility in the prediction step. The resulting temporal velocity field is then implicitly projected on to a divergence‐free space to satisfy incompressibility through a pressure Poisson equation derived from an approximate pressure projection. The results of the numerical simulation are benchmarked against actual slump tests carried out in the laboratory. The numerical results are in excellent agreement with test results, thus demonstrating the capability of SPH and a proper rheological model to predict SCC flow and mould‐filling behaviour. Copyright © 2010 John Wiley & Sons, Ltd.     

Stable axisymmetric SPH formulation with no axis singularity

The axisymmetric formulation of the governing equations for geomechanics in the framework of smoothed particle hydrodynamics (SPH) is presented in this study. Two forms of SPH discretization for the motion equations, which are labeled as form I and form II, are proposed, and the methods to compute the hoop stress and strain terms including hoop strain rate and the acceleration introduced by the hoop stress are compared. To avoid possible singularity problem near the axis of symmetry, a perfectly smooth contact along with ghost particles are applied to prevent the real particles from overly approaching the axis of symmetry to remove this potential singularity. In addition, the Mohr–Coulomb constitutive model is implemented into the SPH formulation in describing soil behavior. Four numerical tests are carried out to validate and compare the accuracy and stability of the proposed algorithms, and their results are compared with analytical solutions and results from FEM analysis. The performance in these comparisons suggests that SPH II with hoop terms computed through direct hoop method is more stable than the others, and the adoption of contact for the symmetric axis is efficient in eliminating the singularity problem. Copyright © 2015 John Wiley & Sons, Ltd.     

Simulation of arch dam – foundation interaction with a new friction interface element

A new model for three-dimensional non-linear contact problems with irreversible friction is presented here for the interaction between the rock foundation and an arch dam structure. Based on the finite element method and load incremental theory, a constraint contact element with displacements and contact stresses as node parameters is developed. In this approach, four contact conditions are considered, i.e. fixed, slip, free and mixed. This model can simulate frictional slippage, decoupling and re-bonding of two bodies initially mating at a common interface or with any initial gaps. Furthermore boundary conditions for this element are discussed and treatment measures proposed. This method is shown to be effective and to have the advantage of being easily implemented into standard finite element programs. Solutions are obtained for a centrally loaded, simply supported composite beam and for an end-loaded elastica with initial gaps in regional contact with a rigid surface. The results obtained for these examples are compared to the plane stress solutions by contact friction analysis. As an application example, Quanshui arch dam located in Ruyuan County of Guangdong Province in southern China is simulated with the new element.     

一种解岩土工程变形体-刚体接触问题的有限元法

大多数的岩土工程问题都会涉及到岩土体-结构之间的相互作用,它们之间界面的合理模拟对计算结果有重要的影响。目前常用的Goodman节理单元、Desai薄层单元等虽然简单好用,但也存在着明显的缺陷。相比之下,作为接触问题计算,可更为合理地模拟接触面的力学行为。针对变形体-刚体这种特殊的接触问题,应用变形体的虚功原理建立了相应的虚功方程,在此基础上得出有限元计算公式,并建立了弹塑性接触问题有限元计算的实现方法。通过对刚性条形基础基底压力分布和刚性挡墙土压力分布等算例的计算,验证了该法的正确性和求解工程问题的有效性。     

SPH-DEM coupling method based on GPU and its application to the landslide tsunami. Part I: method and validation

Landslide-induced tsunami is a complex fluid–solid coupling process that plays a crucial role in the study of a disaster chain. To simulate the coupling behaviors between the fluid and solid, a graphics processing unit-based coupled smoothed particle hydrodynamics (SPH)-discrete element method (DEM) code is developed. A series of numerical tests, which are based on the laboratory test by Koshizuka et al. (Particle method for calculating splashing of incompressible viscous fluid, 1995) and Kleefsman et al. (J Comput Phys 206:363–393, 2005), are carried out to study the influence of the parameters, and to verify the accuracy of the developed SPH code. To ensure accurate results of the SPH simulation, the values for the diffusion term, particle resolution (1/25 characteristic length), and smoothing length (1.2 times of particle interval) are suggested. The ratio of the SPH particle size and the DEM particle’s diameter influences the accuracy of the coupling simulation between solid particles and water. For the coupling simulation of a single particle or a loose particle assembly (not contact each other) with fluid, this ratio should be smaller than 1/20; for a dense particle assembly, a ratio of smaller than 1/6 will be good.

     

Finite element modelling of frictional instability between deformable rocks

Earthquakes are recognized as resulting from a stick–slip frictional instability along faults. Based on the node‐to‐point contact element strategy (an arbitrarily shaped contact element strategy applied with the static‐explicit algorithm for modelling non‐linear frictional contact problems proposed by authors), a finite element code for modelling the 3‐D non‐linear friction contact between deformable bodies has been developed and extended here to analyse the non‐linear stick–slip frictional instability between deformable rocks with a rate‐ and state‐dependent friction law. A typical fault bend model is taken as an application example to be analysed here. The variations of the normal contact force, the frictional force, the transition of stick–slip instable state and the related relative slip velocity along the fault between the deformable rocks and the stress evolution in the total bodies during the different stages are investigated, respectively. The calculated results demonstrate the usefulness of this code for simulating the non‐linear frictional instability between deformable rocks. Copyright © 2003 John Wiley & Sons, Ltd.     

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.     

An improved discrete element method based on a variational formulation of the frictional contact law

An improved algorithm based on the contact dynamics approach is proposed. Like previous developed algorithms it involves two stages. In the first one (local stage) for each particle, forces are computed from the relative displacement using an interaction law, which models frictional contact and shock. In the second stage (global stage) Newton's second law is used to determine, for each particle, the resulting acceleration which is then time-integrated to find the new particle positions. This process is repeated for each time step until convergence is achieved. The two distinguishing features of the present algorithm are the local integration of the frictional contact law and the convergence criterion. By adopting a variational statement of the frictional contact law based on the bi-potential concept, the integration procedure is reduced to a single predictor-corrector step and a new convergence criterion is introduced. Both aspects significantly reduce the computing time and enhance the convergence. Numerical applications show the robustness of the algorithm.     

砂土中等截面桩的上拔机制分析

桩的上拔承载性能的宏观力学现象与桩周土细观结构变化相关,应用细观力学的颗粒流（PFC2D）数值模拟方法对承受上拔荷载作用的桩基进行了分析,数值模拟了上拔荷载作用的桩及桩周土的细观力学特征,研究了桩侧摩阻力的分布、桩周土剪切带的形成过程,较好的再现了桩的荷载－位移关系的实验结果,并与宏观物理实物试验的位移实测结果作了对比分析。分析了土体中剪切带形成过程中的颗粒间的细观变化及其形成过程,当上拔荷载达到极限时,上拔桩的剪切带形成原因是密砂的应变软化效应;颗粒流数值模拟的颗粒接触力与实物物理试验桩侧摩阻力是同一的,数值模拟的荷载-位移曲线与实物物理试验的荷载-位移曲线一致;桩侧摩阻力、桩上拔过程中剪切带的形成过程、桩上拔荷载-位移关系与颗粒流数值模拟的颗粒分布、速度、接触力的细观参数的变化密切相关。桩承受荷载过程中土颗粒细观结构变化的颗粒流仿真,是关于细观力学特征与宏观力学响应的初步研究。     

A smoothed particle hydrodynamics modelling of soil–water mixing and resulting changes in average strength

Soil–water interaction is a pivotal process in many underwater geohazards such as underwater landslides where soil sediments gradually evolve into turbidity currents after interactions with ambient water. Due to the large deformations, multiphase interactions and phase changes this involves, investigations from numerical modelling of the transition process have been limited so far. This study explores a simple numerical replication of such soil–water mixing with respect to changes in average strength using smoothed particle hydrodynamics (SPH). A uniform viscoplastic model is used for both the solid-like and fluid-like SPH particles. The proposed numerical solution scheme is verified by single-phase dam break tests and multiphase simple shear tests. SPH combinations of solid-like and fluid-like particles can replicate the clay–water mixture as long as the liquidity index of the solid-like particles is larger than unity. The proposed numerical scheme is shown to capture key features of an underwater landslide such as hydroplaning, water entrainment and wave generation and thus shows promise as a tool to simulate the whole process of subaquatic geohazards involving solid–fluid transition during mass transport.     

Simulation of earthquake‐induced slope deformation using SPH method

This paper presents the development, calibration, and validation of a smoothed particle hydrodynamics (SPH) model for the simulation of seismically induced slope deformation under undrained condition. A constitutive model that combines the isotropic strain softening viscoplasticity and the modified Kondner and Zelasko rule is developed and implemented into SPH formulations. The developed SPH model accounts for the effects of wave propagation in the sliding mass, cyclic nonlinear behavior of soil, and progressive reduction in shear strength during sliding, which are not explicitly considered in various Newmark‐type analyses widely used in the current research and practice in geotechnical earthquake engineering. Soil parameters needed for the developed model can be calibrated using typical laboratory shear strength tests, and experimental or empirical shear modulus reduction curve and damping curve. The strain‐rate effects on soil strength are considered. The developed SPH model is validated against a readily available and well‐documented model slope test on a shaking table. The model simulated slope failure mode, acceleration response spectra, and slope deformations are in excellent agreement with the experimental data. It is thus suggested that the developed SPH model may be utilized to reliably simulate earthquake‐induced slope deformations. This paper also indicates that if implemented with appropriate constitutive models, SPH method can be used to model large‐deformation problems with high fidelity. Copyright © 2013 John Wiley & Sons, Ltd.     

摩擦型岩土材料土拱效应微观机制颗粒流模拟分析

利用离散单元计算软件模拟太沙基活动门试验,从散粒体和微观角度研究在摩擦型岩土材料中产生土拱效应时颗粒位移、荷载传递的特点,并进一步研究了颗粒粒径、土体孔隙率、颗粒摩擦系数、活动门宽度以及活动门位移对土拱效应的影响。结果表明：由于土拱的作用,从拱脚往上一定范围内会将拱顶上方的竖向荷载转化成水平荷载并向两侧传递,同时伴随着两侧土体的侧向挤出。伴随活动门的下移,土拱效应在不断调整,增大颗粒粒径、减小孔隙率、增大颗粒摩擦系数、减小活动门宽度,不但可加强土拱效应,而且还能减小土拱效应的影响范围。     

Particle finite element analysis of large deformation and granular flow problems

A version of the Particle Finite Element Method applicable to geomechanics applications is presented. A simple rigid-plastic material model is adopted and the governing equations are cast in terms of a variational principle which facilitates a straightforward solution via mathematical programming techniques. In addition, frictional contact between rigid and deformable solids is accounted for using an approach previously developed for discrete element simulations. The capabilities of the scheme is demonstrated on a range of quasi-static and dynamic problems involving very large deformations.