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.     

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.     

Flexible membranes anchored to the ground for slope stabilisation: Numerical modelling of soil slopes using SPH

An alternative modelling for flexible membranes anchored to the ground for soil slope stabilisation is presented using Smoothed-Particle Hydrodynamics to model the unstable ground mass in a soil slope, employing a dynamic solve engine. A regression model of pressure normal to the ground, q_sim, and also membrane deflection, f_sim, have been developed using Design of Experiment. Finally, a comparison between the pressure obtained from numerical simulation and from a limit equilibrium analysis considering infinite slope has been carried out, showing differences in the results, mainly due to the membrane stiffness.     

砾石单元法与SPH耦合模型在数值波浪水槽中的应用研究

为研究以流体粒子描述波浪运动,以固体单元描述砾石运动的两相介质大变形运动,在港口、海岸工程科学研究中具有重要意义。本文提出砾石单元法（GEM）,介绍了光滑粒子动力学方法（SPH）和GEM的基本原理,阐述了GEM与离散单元法（DEM）的异同之处,说明了采用SPH方法与GEM构建波浪砾石耦合运动数学模型的方法和过程。应用SPH方法建立数值波浪水槽,用GEM模拟波浪作用下堆积砾石的滚落、坍塌变形,构建了SPH方法与GEM耦合数学模型。模拟了水槽造波和波浪生成过程和波浪作用下砾石的滚落、坍塌变形,并与物理模型试验成果进行了比较,结果基本吻合。本文提出的GEM法具有模拟单相堆积砾石运动和堆积砾石与流体粒子耦合多相介质运动的功能,是对DEM法的补充和改善。本文提出的堆积力学球概念和拟序排列求解方法是砾石单元法的重要组成部分。     

BZ19—4海底混输管网优化算法探讨

以海洋油气开发工程为实例,利用HYSYS和PIPEFLOW软件,分析了影响海底混输管网计算的若干因素,指出了HYSYS和PIPEFLOW的适用条件,最终确立了海底混输管网优化算法,提高计算效率。     

Green water overtopping analyzed with a SPH model

Wave overtopping on the decks of offshore platforms and ships can cause severe damage due to the high forces generated by the water. This phenomenon is analyzed within the framework of the Smoothed Particle Hydrodynamics (SPH) method. The presence of a fixed horizontal deck above the mean water level modifies strongly the wave kinematics. In particular, the flow in the wave crest is split into two, showing a different behavior above and below the deck. Numerical results generated by the SPH method are compared to laboratory experiments. The formation of a jet in the rear of the deck after overtopping is observed under extreme conditions.     

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.     

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.