Coupled discrete element and finite volume solution of two classical soil mechanics problems

One dimensional solutions for the classic critical upward seepage gradient/quick condition and the time rate of consolidation problems are obtained using coupled routines for the finite volume method (FVM) and discrete element method (DEM), and the results compared with the analytical solutions. The two phase flow in a system composed of fluid and solid is simulated with the fluid phase modeled by solving the averaged Navier–Stokes equation using the FVM and the solid phase is modeled using the DEM. A framework is described for the coupling of two open source computer codes: YADE-OpenDEM for the discrete element method and OpenFOAM for the computational fluid dynamics. The particle–fluid interaction is quantified using a semi-empirical relationship proposed by Ergun [12]. The two classical verification problems are used to explore issues encountered when using coupled flow DEM codes, namely, the appropriate time step size for both the fluid and mechanical solution processes, the choice of the viscous damping coefficient, and the number of solid particles per finite fluid volume.     

非静水应力作用固体的化学位及其构造地球化学意义

非静水应力作用的含水岩石中的力学 -化学相互作用是构造地球化学研究的主要对象之一 ,非静水应力作用固体物质的化学位则是了解这种作用的关键。本文在总结前人有关成果的基础上 ,从理论上了提出了非静水应力作用固体岩石中固 -液界面上的固体物质的化学位的一般形式。在此基础上 ,根据 Onsager扩散方程和局部平衡假设 ,推导了固体物质在颗粒间流体中溶解浓度随固体岩石中应力场和应变能的时空变化关系的动力学方程。以此论证了在温度较低时 ,固体物质在颗粒间流体中的溶解的浓度的时间变化是受固体岩石中应力梯度和应变能梯度控制的     

Numerical modeling of two-phase binary fluid mixing using mixed finite elements

Diffusion coefficients of dense gases in liquids can be measured by considering two-phase binary nonequilibrium fluid mixing in a closed cell with a fixed volume. This process is based on convection and diffusion in each phase. Numerical simulation of the mixing often requires accurate algorithms. In this paper, we design two efficient numerical methods for simulating the mixing of two-phase binary fluids in one-dimensional, highly permeable media. Mathematical model for isothermal compositional two-phase flow in porous media is established based on Darcy’s law, material balance, local thermodynamic equilibrium for the phases, and diffusion across the phases. The time-lag and operator-splitting techniques are used to decompose each convection–diffusion equation into two steps: diffusion step and convection step. The Mixed finite element (MFE) method is used for diffusion equation because it can achieve a high-order and stable approximation of both the scalar variable and the diffusive fluxes across grid–cell interfaces. We employ the characteristic finite element method with moving mesh to track the liquid–gas interface. Based on the above schemes, we propose two methods: single-domain and two-domain methods. The main difference between two methods is that the two-domain method utilizes the assumption of sharp interface between two fluid phases, while the single-domain method allows fractional saturation level. Two-domain method treats the gas domain and the liquid domain separately. Because liquid–gas interface moves with time, the two-domain method needs work with a moving mesh. On the other hand, the single-domain method allows the use of a fixed mesh. We derive the formulas to compute the diffusive flux for MFE in both methods. The single-domain method is extended to multiple dimensions. Numerical results indicate that both methods can accurately describe the evolution of the pressure and liquid level.     

基于能量原理的露天矿边坡开挖稳定性突变研究

基于边坡系统能量的原理,借助FLAC3D有限差分法内嵌FISH语言进行了三维露天矿边坡模型在开挖过程中能量计算的二次开发。将能量与突变理论相结合,以边坡系统的总耗散能作为状态变量,构建了边坡系统的能量耗散突变判别准则。以大孤山露天矿西北帮边坡为例,通过能量耗散突变分析、塑性区演化分析、安全系数变化分析及关键点位移分析可知,以上分析得到的边坡稳定性演化规律具有一致性,验证了提出的突变判别准则的适用性,研究结果表明：能量突变特征值 是露天矿边坡在第ki步开挖后发生失稳的充要力学条件;当进行至第6～8步开挖时,边坡局部岩体系统发生了失稳,且第7、8、9三个台阶受开挖扰动的影响较为严重,与现场的实际开挖情况相符,为预防露天矿边坡在开挖扰动过程中的局部围岩系统失稳提供了一定的理论支持。     

非饱和土土-水特征曲线预估方法研究

在Wei等[1]基于多相孔隙介质非平衡渗流理论提出的多孔介质热动力学混合物理论模型的基础上,建立了一个能描述不考虑土骨架变形的非饱和土土-水特征曲线动态模型。依据非饱和土土-水特征曲线动态模型,推导出不考虑土骨架变形的气-水两相非饱和土的饱和度演化方程。利用饱和度演化方程并结合多步流动瞬态试验的成果,通过数值反演,提出了一种能利用多步流动瞬态试验数据快速确定非饱和土土-水特征曲线的方法。通过对低液限粉土及低液限黏土的多步流动瞬态试验研究发现,饱和度演化方程能较好地模拟非饱和土在小基质吸力步长变化下饱和度的变化规律。此外,通过对多步流动瞬态试验试样饱和度的模拟确定的非饱和土土-水特征曲线与联合测试系统测得的土-水特征曲线的结果较为一致。     

粗粒土的颗粒破碎耗能及剪胀方程研究

颗粒破碎对于粗粒土的应力变形性质有显著影响。在Rowe剪胀方程的基础上考虑颗粒破碎耗能的影响,并引入颗粒破碎的演化规律对颗粒破碎耗能进行计算,得到了一个简单实用且对粗粒土适用性较好的剪胀方程。主要结论如下：（1）通过粗粒土的三轴CD试验结果分析并证明了弹性应变对于剪胀比的影响较小,因此,可以将剪胀比 表示为 ,进而得到了剪胀方程表达式的一般形式。（2）将剪胀方程中的临界状态应力比Mc折减为摩擦系数M,并引入了颗粒破碎的演化规律,将M定量表示为广义剪应变的函数,从而使得所计算的破碎耗能在剪切过程中是递增的,且逐渐趋于稳定值,符合了颗粒破碎不可逆的规律。（3）试验表明,剪胀方程中的未知量 与摩擦系数M之间呈现显著的线性关系,将该关系代入剪胀方程即确定了方程的具体表达形式,并且利用堆石料的三轴CD试验证明了其对粗粒土的剪胀性预测效果较好。     

An elastoplastic constitutive model for rockfills incorporating energy dissipation of nonlinear friction and particle breakage

A new elastoplastic model is developed for rockfills within the general critical state framework incorporating the state parameter. Two state functions are proposed to characterize the evolution of volume dilation and strain softening of rockfills, and a modified breakage index based on the concept of Hardin's relative breakage is defined to describe the progressive crushing of rockfills. The nonassociated plastic flow rule is derived from a state dependent dilatancy equation, and it incorporates energy dissipation due to intrinsic nonlinear friction and particle breakage upon shearing. Thus, their couple effect on the plastic deviatoric and volumetric deformation of rockfills is taken into account in the current model. The numerical analyses are carried out for a series of drained triaxial tests on the modeled rockfills at various consolidation pressures and stress paths. The volume dilation/contraction and strain softening/hardening of rockfills are accurately predicted by the proposed model, and the particle breakage and nonlinear critical state shear strength of rockfills are also well captured. The research findings indicate that the current model is applicable to represent the complex stress–strain–volume change behavior of rockfills in general. Copyright © 2013 John Wiley & Sons, Ltd.     

A generalized cubic equation of state with application to pure CO<Subscript>2</Subscript> injection in aquifers

A generalized cubic equation of state is given. The Peng-Robinson and the Soave-Redlich-Kwong equations are special cases of this equation. The generalized equation of state is precisely as simple and computationally efficient as these classical equations. Through comparison with the Span-Wagner equation for CO ₂, we obtain an improved density accuracy in predefined temperature-pressure domains. The generalized equation is then verified through two relevant examples of CO ₂ injection and migration. Comparisons are made with other standard cubic EOS in order to show the range of solutions obtained with less accurate EOS.     

Error Estimates for a Time Discretization Method for the Richards' Equation

We present a numerical analysis of a time discretization method applied to Richards' equation. Written in its saturation-based form, this nonlinear parabolic equation models water flow into unsaturated porous media. Depending on the soil parameters, the diffusion coefficient may vanish or explode, leading to degeneracy in the original parabolic equation. The numerical approach is based on an implicit Euler time discretization scheme and includes a regularization step, combined with the Kirchhoff transform. Convergence is shown by obtaining error estimates in terms of the time step and of the regularization parameter.     

石油包裹体热动力学模拟古压力改进: 饱和压力预测和体积校正

除实验室测定参数(T_{h, oil}、T_{h, aqu}和F_v)外, 石油包裹体热动力学模拟古压力精度还极大地受控于石油组分模型、饱和压力预测以及气、液相摩尔体积的预测精度.在改进α-β组分模型前提下, 利用微调组分和匹配饱和压力方法改进并验证了石油流体饱和压力预测精度; 在匹配饱和压力与实验实测饱和压力前提下, 利用体积转换方法匹配22组油藏流体391个常组分膨胀实验相对体积数据, 从而改善了利用Peng-Robison状态方程计算油包裹体气泡充填度(20 ℃)和等容线的能力.最终评价了真实石油流体组分甲烷摩尔含量和等效石油流体组分甲烷摩尔含量两个组分模拟约束条件下, 改进的热动力学模拟方法和PIT软件及Vtflinc软件重构捕获压力的精度.结果表明, 改进的热动力学模拟古压力方法较其他两种方法可以有效地提高捕获压力预测的精度.考虑到石油包裹体甲烷摩尔含量难获取问题, 利用改进后的方法结合等效流体组分约束条件是重构捕获压力的理想方法组合.      

A Symmetrical Streamline Stabilization scheme for high advective transport

An overview of numerical techniques and previous investigations related to the solution of advection‐dominated transport processes is presented. In addition a new Symmetrical Streamline Stabilization (S³) scheme is introduced. The basis of the technique is to treat the transport equation in two steps. In the first step the dispersion part is approximated by a standard Galerkin approach, while in the second step the advection is approximated by a least‐squares method. The two parts are reassembled, resulting in one system of equations. The resulting coefficients' matrix is symmetric. Only half of a sparse matrix needs to be stored. Robust iterative algorithms for symmetrical systems of equations such as the preconditioned conjugate gradient method (PCG) can be successfully used. The new method leads to an implicit introduction of an ‘artificial diffusion’ term. Solute transport with high Peclet and Courant numbers does not lead to oscillations due to an inherent upwind damping. The upwind effect acts only in flow direction. The efficiency of the new formulation in terms of accuracy and computation time is shown in comparison with the Galerkin approach for mesh parallel and mesh oblique high advective solute transport. Copyright © 2000 John Wiley & Sons, Ltd.     

基于能量变化率法自动拾取场地剪切波速

提出了一种提高单孔法剪切波速测量精度的新方法--能量变化率的自回归曲线法。首先把剪切波的时程曲线变换为能量变化率时程曲线;然后对能量变化率时程曲线进行长短平均处理,拾取各测点P波和S波的大致初至;最后提出采用一种二次方自回归模型对初至附近的能量变化率曲线进行二次方自回归处理,精确拾取出各测点P波和S波的精确到时。采用此方法、互相关函数法和人工拾取法对某场地的剪切波速进行了对比分析。分析结果表明：此方法相比互相关函数法,具有更好的噪声抑制能力,不仅能精确地自动拾取出各测点的S波的到时差,也能更准确地自动拾取出各测点的P波的到时差。以人工拾取结果为参考,此方法在实际测试中具有很高的准确率和稳定性。此方法丰富了场地剪切波速分析方法。基于此方法、互相关函数法和人工拾取法,设计了一套剪切波波速的测试系统,此系统能自动分析出各测点的剪切波速和形成完整的报告。     

对MPS法在溃坝模拟中数值压力振荡问题的改进

为探索模拟大变形自由面流体运动的高精度数值计算方法,以溃坝水流运动为例,基于MPS法(Moving Particle Semi-implicit method,移动粒子半隐式法)建立了一个垂向二维改良MPS法数值计算模型。首先,为了改善传统MPS法中存在的自由表面粒子误判以及数值能量耗散问题,提出新的自由表面粒子识别方法和高精度的压力梯度模型。在此基础上,以Lobovsky'等的溃坝物理模型实验为例,探讨不同形式压力泊松方程源项对溃坝冲击压计算精度的影响,提出一个新的源项形式。数值结果分析表明,新自由表面粒子识别方法和高精度压力梯度模型可以有效地减少自由面粒子的误判概率,抑制水流运动计算中的数值能量耗散。而压力计算结果与实验结果的对比表明,所提出的压力泊松方程源项可以有效地减少数值压力震荡的幅度。     

Identification of diffusion parameters in a nonlinear convection–diffusion equation using the augmented Lagrangian method

Numerical identification of diffusion parameters in a nonlinear convection–diffusion equation is studied. This partial differential equation arises as the saturation equation in the fractional flow formulation of the two-phase porous media flow equations. The forward problem is discretized with the finite difference method, and the identification problem is formulated as a constrained minimization problem. We utilize the augmented Lagrangian method and transform the minimization problem into a coupled system of nonlinear algebraic equations, which is solved efficiently with the nonlinear conjugate gradient method. Numerical experiments are presented and discussed. This work was partially supported by the Research Council of Norway (NFR), under grant 128224/431.     

Modeling H,Na, and K diffusion in plagioclase feldspar by relating point defect parameters to bulk properties

Hydrogen and alkali ion diffusion in plagioclase feldspars is important to study the evolution of the crust and the kinetics of exsolution and ion-exchange reactions in feldspars. Using the available PVT equation of state of feldspars, we show that the diffusivities of H and alkali in plagioclase feldspars as a function of temperature can be successfully reproduced in terms of the bulk elastic and expansivity data through a thermodynamic model that interconnects point defect parameters with bulk properties. Our calculated diffusion coefficients of H, Na, and K well agree with experimental ones when uncertainties are considered. Additional point defect parameters such as activation enthalpy, activation entropy, and activation volume are also predicted. Furthermore, the electrical conductivity of feldspars inferred from our predicted diffusivities of H, Na, and K through the Nernst–Einstein equation is compared with previous experimental data.     

Solving stiff mass transfers in compositional multiphase flow models: Numerical stability and spurious solutions

This paper points out two numerical problems linked to the resolution of compositional multiphase flow models for porous media with the finite‐volume technique. In particular, we consider fluid mixtures featuring fast mass transfers between the phases, hence stiff. In this context, we show how the computation of mass exchange kinetics can be expensive and that erroneous saturation front locations arise. A numerical splitting method is developed which is proven to be stable with advection‐type time steps, whatever the stiffness of the mass transfer. The erroneous front location problem is illustrated and shown to be intrinsically linked to the numerical diffusion. If we assume that the fluids are in thermodynamical equilibrium, we find that spurious solutions can be avoided by deriving and solving a new uncoupled hyperbolic equation for the saturation. This revised version was published online in July 2006 with corrections to the Cover Date.     

基于动态多步流动原理的快速测定SWCC方法及压力板仪改装研究

对以轴平移技术为原理的压力板测试系统进行改进,增加了数据自动采集系统,储水冲刷系统和气泡体积测量系统。解决了陶土板底部气泡体积测量问题。本次试验与常规平衡态测试非饱和土土-水特征曲线方法不同,在改进的压力板仪测试系统上对粉土试样开展动态多步流动实验。根据在Origin建立的非饱和土饱和度时间演化模型方程,对实测数据进行非线性拟合得出未知参数容水率C和特征时间τ,最终得到平衡状态下的土-水特征曲线的脱湿曲线。与常规平衡状态下测得的土-水特征曲线进行对比后能较好地重合。此方法在改进的压力板仪测试系统上测得一条脱湿曲线的时间为5d左右,具有较高准确性,与常规平衡态测试方法相比可以大大节省时间,方便快捷。     

成油环境中的流体包裹体：分析步骤与PTX重建

摘要石油盆地内的古流体以流体包裹体的形式保存在成岩矿物中，它们代表了初始石油或气相的组成并记录了流体捕获时的温度和压力条件。在储集层中卤水通常以不混溶相的形式与石油共存。一般利用单个包裹体分析法对水溶液和石油包裹体进行研究，利用显微测温法来确定相转变的温度，利用拉曼光谱定量来分析水溶液包裹体中溶解甲烷的含量，石油包裹体中CH4和CO2的含量可以利用傅立叶变换红外光谱分析来估算，通过共聚焦扫描激光显微镜来重建石油包裹体的体积。利用Duan和Peng-Robinson方程可进行热力学模拟，并分别应用于水溶液和石油包裹体体系。两类流体体系等容线的交点可用来确定流体捕获时的实际温度和压力条件，从而利用流体压力对具有不同地球动力学背景的源区流体动力学演化进行重建。     

Modelling Rock Blasting Considering Explosion Gas Penetration Using Discontinuous Deformation Analysis

Explosion gas plays an important role in rock mass fragmentation and cast in rock blasting. In this technical note, the discontinuous deformation analysis method is extended for bench rock blasting by coupling the rock mass failure process and the penetration effect of the explosion gas based on a generalized artificial joint concept to model rock mass fracturing. By tracking the blast chamber evolution dynamically, instant explosion gas pressure is derived from the blast chamber volume using a simple polytropic gas pressure equation of state and loaded on the blast chamber wall. A bench blasting example is carried out. The blast chamber volume and pressure time histories are obtained. The rock failure and movement process in bench rock blasting is reproduced and analysed.     

基于状态曲面的非饱和土强度准则及其验证

考虑体变对非饱和土土-水状态的影响,将状态曲面函数引入传统的Vanapalli强度公式得到与孔隙比相关的抗剪强度准则,新准则使用饱和土的强度参数和两条不同孔隙比对应的土-水特征曲线。选择一种尾矿砂和高岭土的混合土料为研究对象,进行一系列的土-水特征曲线试验、吸力控制的等向压缩和三轴剪切试验。试验结果表明,新准则能更准确地预测非饱和土的强度,证明了传统强度预测的误差主要来源于忽略了体变导致的土-水状态变化,并提出在不同应力空间内精确地获得抗剪强度包线的方法,合理地解释了强度包线斜率在净应力-强度平面内随吸力增大、强度包线形状在吸力-强度平面内随净应力发生变化的特性。