基于HBP本构模型的泥石流动力过程SPH数值模拟

本构模型是描述泥石流流变特性的关键,也是决定其动力过程数值模拟准确性的核心问题之一。泥石流流体属多相混合物,现有的研究已证实其存在剪切增稠或剪切变稀的现象,传统基于Bingham及Cross线性本构关系的数值模型难以准确描述泥石流流变特性。文中探讨了Bingham模型在低剪应变率下的数值发散问题,在光滑粒子流体动力学（SPH）方法框架上建立了整合Herschel-Bulkley-Papanastasiou(HBP）本构关系的稀性泥石流动力过程三维数值模型。相比传统基于浅水波假设的二维数值模型,所述方法从三维尺度建立SPH形式下的泥石流浆体纳维?斯托克斯方程并进行数值求解,可获取泥石流速度场时空分布及堆积形态,同时采用HBP本构关系描述泥石流流变特性,能在确保数值收敛的前提下反映泥石流流体在塑性屈服过渡段及大变形状态下应力?应变的非线性变化。为验证提出方法的合理性,结合小型模型槽实验观测进行了对比,结果表明数值模拟与实测结果基本吻合。     

Transient solution for a plane‐strain fracture driven by a shear‐thinning,power‐law fluid

This paper analyses the problem of a fluid‐driven fracture propagating in an impermeable, linear elastic rock with finite toughness. The fracture is driven by injection of an incompressible viscous fluid with power‐law rheology. The relation between the fracture opening and the internal fluid pressure and the fracture propagation in mobile equilibrium are described by equations of linear elastic fracture mechanics (LEFM), and the flow of fluid inside the fracture is governed by the lubrication theory. It is shown that for shear‐thinning fracturing fluids, the fracture propagation regime evolves in time from the toughness‐ to the viscosity‐dominated regime. In the former, dissipation in the viscous fluid flow is negligible compared to the dissipation in extending the fracture in the rock, and in the later, the opposite holds. Corresponding self‐similar asymptotic solutions are given by the zero‐viscosity and zero‐toughness (J. Numer. Anal. Meth. Geomech. 2002; 26 :579–604) solutions, respectively. A transient solution in terms of the crack length, the fracture opening, and the net fluid pressure, which describes the fracture evolution from the early‐time (toughness‐dominated) to the large‐time (viscosity‐dominated) asymptote is presented and some of the implications for the practical range of parameters are discussed. Copyright © 2006 John Wiley & Sons, Ltd.     

A pore-scale numerical model for flow through porous media

A pore-scale numerical model based on Smoothed Particle Hydrodynamics (SPH) is described for modelling fluid flow phenomena in porous media. Originally developed for astrophysics applications, SPH is extended to model incompressible flows of low Reynolds number as encountered in groundwater flow systems. In this paper, an overview of SPH is provided and the required modifications for modelling flow through porous media are described, including treatment of viscosity, equation of state, and no-slip boundary conditions. The performance of the model is demonstrated for two-dimensional flow through idealized porous media composed of spatially periodic square and hexagonal arrays of cylinders. The results are in close agreement with solutions obtained using the finite element method and published solutions in the literature. Copyright © 1999 John Wiley & Sons, Ltd.     

Flow analysis of liquefied soils based on smoothed particle hydrodynamics

To overcome the disadvantages of traditional flow analysis methods for liquefied soils that exhibit fluidization and large deformation characteristics, Smoothed particle hydrodynamics (SPH) is adopted in this study to analyze the flow processes of liquefied soils. Bingham model with the use of the Mohr–Coulomb yield criterion, the concepts of equivalent Newtonian viscosity, and the Verlet neighbor list method are introduced into the framework of SPH to build an algorithm for the analysis of flowing liquefied soils. This modeling involves a simulation of physical model test of flowing liquefied soils that can be compared with numerical results. In addition, a shaking table test is selected from the literature for SPH analysis to verify the validation of the SPH method and extend its applications. The SPH simulation can reproduce the flow processes of liquefied soils and constrain estimates of the horizontal displacement, vertical displacement, and velocity of soils after liquefaction. According to the dynamic behaviors of the materials involved, designs can be implemented to improve the seismic safety of structures.     

A new SPH-based approach to simulation of granular flows using viscous damping and stress regularisation

The smoothed particle hydrodynamics (SPH) method was recently extended to simulate granular materials by the authors and demonstrated to be a powerful continuum numerical method to deal with the post-flow behaviour of granular materials. However, most existing SPH simulations of granular flows suffer from significant stress oscillation during the post-failure process, despite the use of an artificial viscosity to damp out stress fluctuation. In this paper, a new SPH approach combining viscous damping with stress/strain regularisation is proposed for simulations of granular flows. It is shown that the proposed SPH algorithm can improve the overall accuracy of the SPH performance by accurately predicting the smooth stress distribution during the post-failure process. It can also effectively remove the stress oscillation issue in the standard SPH model without having to use the standard SPH artificial viscosity that requires unphysical parameters. The predictions by the proposed SPH approach show very good agreement with experimental and numerical results reported in the literature. This suggests that the proposed method could be considered as a promising continuum alternative for simulations of granular flows.     

A depth‐integrated,coupled SPH model for flow‐like landslides and related phenomena

In the past decades, flow‐like catastrophic landslides caused many victims and important economic damage around the world. It is therefore important to predict their path, velocity and depth in order to provide adequate mitigation and protection measures. This paper presents a model that incorporates coupling between pore pressures and the solid skeleton inside the avalanching mass. A depth‐integrated, coupled, mathematical model is derived from the velocity–pressure version of the Biot–Zienkiewicz model, which is used in soil dynamics. The equations are complemented with simple rheological equations describing soil behaviour and are discretized using the SPH method. The accuracy of the model is assessed using a series of benchmarks, and then it is applied to back‐analyse the propagation stage of some catastrophic flow‐like slope movements for which field data are available. Copyright © 2008 John Wiley & Sons, Ltd.     

The response of a deep rigid anchor due to undrained elastic deformations of the surrounding soil medium

The equations governing the undrained linear elastic behaviour of a saturated soil are formally similar to the equations governing slow of an incompressible Newtonian viscous fluid. This principle of equivalence can then be effectively employed to obtain the load-deflection reiationship for a deep rigid anchor with the shape of a solid of revolution which is embedded in bonded contact with an unbounded incompressible elastic medium. It is found that the load-deflection relationship for the deep rigid anchor can be directly recovered from the expression for the drag induced on an impermeable object with the same size and shape as the anchor, which is appropriately placed in a slow viscous flow region of uniform velocity.     

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.     

Multiphase SPH modeling of free surface flow in porous media with variable porosity

This paper presents a numerical model for simulating free surface flow in porous media with spatially varying porosity. The governing equations are based on the mixture theory. The resistance forces between solid and fluid is assumed to be nonlinear. A multiphase SPH approach is presented to solve the governing equations. In the multiphase SPH, water is modeled as a weakly compressible fluid, and solid phase is discretized by fixed solid particles carrying information of porosity. The model is validated by several numerical examples including seepage through specimen, fast flow through rockfill dam and wave interaction with porous structure. Good agreements between numerical results and experimental data are obtained in terms of flow rate and evolution of free surface. Parameter study shows that (1) the nonlinear resistance law provides more accurate results; (2) particle size and porosity have significant influence on the porous flow.     

Study of the interaction between dry granular flows and rigid barriers with an SPH model

This study uses an incompressible smoothed‐particle hydrodynamics model to investigate the interaction between dry granular material flows and rigid barriers. The primary aim is to summarise some practical guidelines for the design of debris‐resisting barriers. The granular materials are modelled as a rigid‐perfectly plastic material where the plastic flow corresponds to the critical state. The coupled continuity equation and momentum equation are solved by a semi‐implicit algorithm. Compared with flows in controlled flume experiments, the model adequately reproduces both the kinetic of the flows and the impact force under various conditions. Then the numerical simulations are used to study the detailed interaction process. It is illustrated quantitatively that the interaction force consists of two parts, ie, the earth pressure force caused by the weight of the soil and a dynamic force caused by the internal deformation (flowing mass on top of a dead zone). For the estimation of impact load, this study suggests that an increased earth pressure coefficient depending on the Froude number should be incorporated into the hydrostatic model.     

A stabilized assumed deformation gradient finite element formulation for strongly coupled poromechanical simulations at finite strain

An adaptively stabilized finite element scheme is proposed for a strongly coupled hydro‐mechanical problem in fluid‐infiltrating porous solids at finite strain. We first present the derivation of the poromechanics model via mixture theory in large deformation. By exploiting assumed deformation gradient techniques, we develop a numerical procedure capable of simultaneously curing the multiple‐locking phenomena related to shear failure, incompressibility imposed by pore fluid, and/or incompressible solid skeleton and produce solutions that satisfy the inf‐sup condition. The template‐based generic programming and automatic differentiation (AD) techniques used to implement the stabilized model are also highlighted. Finally, numerical examples are given to show the versatility and efficiency of this model. Copyright © 2013 John Wiley & Sons, Ltd.     

基于光滑质点流体动力学的海冰热力-动力数值模式

考虑海冰热力因素对其厚度、密集度的影响,在光滑质点流体动力学(SPH)基础上发展了一个海冰热力-动力数值模式。该模式既解决了传统欧拉有限差分法和质点网格法存在的数值扩散问题,同时弥补了光滑质点动力学海冰动力模式未考虑热力因素的不足,具有精确模拟冰缘线运动、计算精度高等优点。首先介绍了光滑质点流体动力学的基本原理,并对海冰生消的热力因素进行了分析,将影响冰厚和密集度的热力因素引入到光滑质点流体动力学的海冰动力模式中,得到该热力-动力模式的控制方程。应用该数值模式对渤海海冰进行了48 h数值模拟,得到了海冰厚度和速度矢量的分布规律;对JZ20-2海域的海冰厚度、冰内温度场分布以及热力因素的变化特性进行了讨论。数值模拟结果表明,该数值模式能够很好地适用于渤海海冰数值模拟,是一种有效的海冰数值模拟方法。     

Computational validation of the Generalized Sutherland Equation for bubble–particle encounter efficiency in flotation

Bubble–particle encounter during flotation is governed by liquid flow relative to the rising bubble, which is a function of the adsorbed frothers, collectors, and other surfactants and surface contaminants. Due to surface contamination, the bubble surface in flotation has been considered as immobile (rigid). However, surface contamination can be swept to the backside of the rising bubble due to the relative liquid flow, leaving the front surface of the rising bubble mobile with a non-zero tangential component of the liquid velocity. The bubble with a mobile surface was considered by Sutherland who applied the potential flow condition and analyzed the bubble–particle encounter using a simplified particle motion equation without inertia. The Sutherland model was found to over-predict the encounter efficiency and has been improved by incorporating inertial forces which are amplified at the mobile surface with a non-zero tangential velocity component of the liquid phase. An analytical solution was obtained for the encounter efficiency using approximate equations and is called the Generalized Sutherland Equation (GSE). In this paper, the bubble–particle encounter interaction with the potential flow condition has been analyzed by solving the full motion equation for the particle employing a numerical computational approach. The GSE model was compared with the exact numerical results for the encounter efficiency. The comparison only shows good agreement between the GSE prediction and the numerical data for ultrafine particles (< 10 μm in diameter), the inertial forces of which are vanishingly small. For non-ultrafine particles, a significant deviation of the GSE model from the numerical data has been observed. Details of the numerical methodology and solutions for the (collision) angle of tangency and encounter efficiency are described.     

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 numerical study of particle motion and two‐phase interaction in aeolian sand transport using a coupled large eddy simulation – discrete element method

Wind‐blown sand movement, considered as a particle‐laden two‐phase flow, was simulated by a new numerical code developed in the present study. The discrete element method was employed to model the contact force between sand particles. Large eddy simulation was used to solve the turbulent atmospheric boundary layer. Motions of sand particles were traced in the Lagrangian frame. Within the near‐surface region of the atmospheric boundary layer, interparticle collisions will significantly alter the velocity of sand. The sand phase is quite dense in this region, and its feedback force on fluid motion cannot be ignored. By considering the interparticle collision and two‐phase interaction, four‐way coupling was achieved in the numerical code. Profiles of sand velocity from the simulations were in good agreement with experimental measurements. The mass flux shows an exponential decay and is comparable to reported experimental and field measurements. The turbulence intensities and shear stress of sand particles were estimated from particle root‐mean‐square velocities. Distributions of slip velocity and feedback force were analysed to reveal the interactions between sand particles and the continuous fluid phase.     

Three dimensional simulation of fluid flow in X‐ray CT images of porous media

A numerical scheme is developed in order to simulate fluid flow in three dimensional (3‐D) microstructures. The governing equations for steady incompressible flow are solved using the semi‐implicit method for pressure‐linked equations (SIMPLE) finite difference scheme within a non‐staggered grid system that represents the 3‐D microstructure. This system allows solving the governing equations using only one computational cell. The numerical scheme is verified through simulating fluid flow in idealized 3‐D microstructures with known closed form solutions for permeability. The numerical factors affecting the solution in terms of convergence and accuracy are also discussed. These factors include the resolution of the analysed microstructure and the truncation criterion. Fluid flow in 2‐D X‐ray computed tomography (CT) images of real porous media microstructure is also simulated using this numerical model. These real microstructures include field cores of asphalt mixes, laboratory linear kneading compactor (LKC) specimens, and laboratory Superpave gyratory compactor (SGC) specimens. The numerical results for the permeability of the real microstructures are compared with the results from closed form solutions. Copyright © 2004 John Wiley & Sons, Ltd.     

Numerical simulation of flow processes in liquefied soils using a soil–water-coupled smoothed particle hydrodynamics method

Liquefaction can result in the damage or collapse of structures during an earthquake and can therefore be a great threat to life and property. Many site investigations of liquefaction disasters are needed to study the large-scale deformation and flow mechanisms of liquefied soils that can be used for performance assessments and infrastructure improvement. To overcome the disadvantages of traditional flow analysis methods for liquefied soils, a soil–water-coupled smoothed particle hydrodynamics (SPH) modeling method was developed to analyze flow in liquefied soils. In the proposed SPH method, water and soil were simulated as different layers, while permeability, porosity, and interaction forces could be combined to model water-saturated porous media. A simple shear test was simulated using the SPH method with an elastic model to verify its application to solid phase materials. Subsequently, the applicability of the proposed SPH modeling method to the simulation of interaction forces between water and soil was verified by a falling-head permeability test. The coupled SPH method produced good simulations for both the simple shear and falling-head permeability tests. Using a fit-for-purpose experimental apparatus, a physical flow model test of liquefied sand has been designed and conducted. To complement the physical test, a numerical simulation has been undertaken based on the soil–water-coupled SPH method. The numerical results correspond well with the physical model test results in observed configurations and velocity vectors. An embankment failure in northern Sweden was selected so that the application of the soil–water-coupled SPH method could be extended to an actual example of liquefaction. The coupled SPH method simulated the embankment failure with the site investigation well. They have also estimated horizontal displacements and velocities, which can be used to greatly improve the seismic safety of structures.     

A coupled chemo‐thermo‐hygro‐mechanical model of concrete at high temperature and failure analysis

A hierarchical mathematical model for analyses of coupled chemo‐thermo‐hygro‐mechanical behaviour in concretes at high temperature is presented. The concretes are modelled as unsaturated deforming reactive porous media filled with two immiscible pore fluids, i.e. the gas mixture and the liquid mixture, in immiscible–miscible levels. The thermo‐induced desalination process is particularly integrated into the model. The chemical effects of both the desalination and the dehydration processes on the material damage and the degradation of the material strength are taken into account. The mathematical model consists of a set of coupled, partial differential equations governing the mass balance of the dry air, the mass balance of the water species, the mass balance of the matrix components dissolved in the liquid phases, the enthalpy (energy) balance and momentum balance of the whole medium mixture. The governing equations, the state equations for the model and the constitutive laws used in the model are given. A mixed weak form for the finite element solution procedure is formulated for the numerical simulation of chemo‐thermo‐hygro‐mechanical behaviours. Special considerations are given to spatial discretization of hyperbolic equation with non‐self‐adjoint operator nature. Numerical results demonstrate the performance and the effectiveness of the proposed model and its numerical procedure in reproducing coupled chemo‐thermo‐hygro‐mechanical behaviour in concretes subjected to fire and thermal radiation. Copyright © 2005 John Wiley & Sons, Ltd.     

Propagation of Rayleigh waves in fluid‐saturated non‐homogeneous soils with the graded solid skeleton distribution

The propagation characteristic of Rayleigh waves in a fluid‐saturated non‐homogeneous poroelastic half‐plane is addressed. Based on Biot's theory for fluid‐saturated media, which takes the inertia, fluid viscosity, mechanical coupling, compressibility of solid grains, and fluid into account, the dispersion equations of Rayleigh waves in fluid‐saturated non‐homogeneous soils/rocks are established. By considering the shear modulus of solid skeleton variation with depth exponentially, a small parameter, which reflects the relative change of shear modulus, is introduced. The asymptotic solution of the dispersion equation expressing the relationship between the phase velocity and wave number is obtained by using the perturbation method. In order to analyze the effects of non‐homogeneity on the propagation characteristic of Rayleigh waves, the variation of the phase velocity with the wave number is presented graphically and discussed through numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.     

Frictional contact algorithms in SPH for the simulation of soil–structure interaction

Simulation of frictional contact between soils and rigid or deformable structure in the framework of smoothed particle hydrodynamics (SPH) is presented in this study. Two algorithms are implemented into the SPH code to describe contact behavior, where the contact forces are calculated using the law of conservation of momentum based on ideal plastic collision or using the criteria of partial penetrating. In both algorithms, the problem of boundary deficiency inherited from SPH is properly handled so that the particles located at contact boundary can have precise acceleration, which is critical for contact detection. And the movement and rotation of the rigid structure are taken into account so that it is easy to simulate the process of pile driving or movement of a retaining wall in geotechnical engineering analysis. Furthermore, the capability of modeling deformability of a structure during frictional contact simulations broadens the fields of SPH application. In contrast to previous work dealing with contact in SPH, which usually use particle‐to‐particle contact or ignoring sliding between particles and solid structure, the method proposed here is more efficient and accurate, and it is suitable to simulate interaction between soft materials and rigid or deformable structures, which are very common in geotechnical engineering. A number of numerical tests are carried out to verify the accuracy and stability of the proposed algorithms, and their results are compared with analytical solutions or results from finite element method analysis. Good agreement obtained from these comparisons suggests that the proposed algorithms are robust and can be applied to extend the capability of SPH in solving geotechnical problems. Copyright © 2013 John Wiley & Sons, Ltd.