Statistical analysis of stress transmission in wet granular materials

The micromechanics of wet granular materials encompasses complex microstructural and capillary interconnects that can be readily described through a formal derivation of stress transmission in such a 3‐phase medium. In the quest for defining an appropriate stress measure, the stress tensor expression that results from homogenization [Duriez et al. J Mech Phys Solids 99 (2017): 495‐511] of such a medium provides theoretical insights necessary to extract useful information on the relationship between capillary effects and microforce interactions via several small‐scale parameters whose evaluation can be challenging. Using instead a statistical approach where microvariable distributions are described by probability density functions, the current study provides simple estimates of stress components in terms of only a few tractable microvariables such as coordination number and fabric anisotropy. In particular, the latter recognizes details of contacts such as force interactions being either mechanical or capillary, including interactions with and without mechanical contact. The developed expressions are in a good agreement with discrete element method simulation results of the triaxial loading of a wet granular assembly, notably for hydrostatic (mean) pressure. A new set of dimensionless groups is also identified to characterize the significance of mechanical and capillary physics, which facilitates a better understanding of the contribution of dominating elements to stress, while also providing the opportunity to incorporate important capillary effects in micromechanically based constitutive formulations.     

Pore‐scale modeling of surface erosion in a particle bed

A fully coupled transient two‐dimensional model was employed to study fundamentals of flood‐induced surface erosion in a particle bed. The interaction of the liquid and solid phases is the key mechanism related to surface erosion. The solid phase was idealized at a particle scale by using the discrete element method. The fluid phase was modeled at a mesoscale level and solved using the lattice Boltzmann method. The fluid forces applied on the particles were calculated on the basis of the momentum the fluid exchanges with the particle. The proposed approach was used to model both single particles and particle beds subjected to Couette flow conditions. The behavior of both the single particle and the particle bed depended on particle diameter and surface shear fluid velocity. The conducted simulations show that the fluid flow profile penetrates the bed for a small distance. This penetration initiates sheet‐flow and surface erosion as the fluid interacts with particles. The effect of suppressing particle rotation on the fluid‐induced forces on the particle was also examined. Suppressing particle spinning may lead to underestimated erosion rate. Results of fluid and particle velocities were compared against experimental results and appeared to agree with the observed trends.Copyright © 2013 John Wiley & Sons, Ltd.     

基于普通克里金外推的迭代维纳滤波法向下延拓

在利用普通克里金方法外推的基础上，通过频域径向平均功率谱估算噪声方差，采用迭代维纳滤波法获取较为稳定的重力场向下延拓结果，并分别利用模拟算例和实际数据进行实验。对于模拟算例，外推后的均方根误差由6.72 μGal下降到1.89 μGal，相对误差由9.26%下降到4.44%。对于实际数据，外推后延拓结果不仅可避免边缘失真现象，而且能更好地反映浅源高频异常特征信息。     

Simulations of realistic granular soils in oedometer tests using physics engine

Discrete element method (DEM) has become a preeminent numerical tool for investigating the mechanical behavior of granular soils. However, traditional DEM uses sphere clusters to approximate realistic particles, which is computationally demanding when simulating many particles. This paper demonstrates the potential of using a physics engine technique to simulate realistic particles. The physics engines are originally developed for video games for simulating physical and mechanical processes that occur in the real world to produce realistic game experiences. The simulation accuracy and efficiency of physics engines have been significantly improved in the last two decades allowing them to be used as a scientific tool in many disciplines. This paper introduces modeling methodologies of physics engine including realistic particle representation and the contact model. Then, oedometer tests are simulated using realistic particles scanned by X-ray computed tomography (X-ray CT). The simulation results agree well with experimental results. This paper demonstrates that physics engines can output contact parameters for geotechnical analysis and force chains for visualization.     

The effects of intermediate principle stress on the mechanical behavior of transversely isotropic rocks: Insights from DEM simulations

The discrete element method (DEM) is used to study the response of anisotropic rocks under true triaxial testing. Numerical samples of seven different bedding orientations (β = 0^o, 15^o, 30^o, 45^o, 60^o, 75^o, and 90^o) are created. Six series of test simulations (σ₃ = 0, 10, 30, 50, 70, and 100 MPa) are conducted on each sample, with five different σ₂ values, varied from σ₃ to σ₁. The effects of anisotropy and intermediate stress on the peak strength, brittle-ductile transition, and degree of anisotropy are subsequently explained through underlying micromechanics. Results show a “fan-shaped” variation of the peak strength with σ₂, displaying an ascending-then-descending trend. An increasing brittleness with σ₂ is observed at lower confining pressures for all, but medium anisotropy angles. For higher confining pressures, increasing ductility with σ₂ is seen for every anisotropy angle. A U-shaped variation of peak strength with anisotropy angles is noted that flattens under high intermediate stress. Hence, for numerical models of Posidonia shale under normalized σ₂ higher than 0.76, the anisotropy effect is found to be negligible. Micromechanical analyses reveal that the stress asymmetry, suppression of weak plane action as well as the localization and coalescence of microcracks in the intact rock matrix, due to σ₂, are the contributors towards the obtained trends. Since existing failure criteria do not weigh in these features in geotechnical assessments, this paper helps future studies by providing a deeper understanding of these effects and a comprehensive data set for the analyses of anisotropic rocks under polyaxial stress conditions.     

A coupled 3‐dimensional bonded discrete element and lattice Boltzmann method for fluid‐solid coupling in cohesive geomaterials

This paper presents a 3D bonded discrete element and lattice Boltzmann method for resolving the fluid‐solid interaction involving complicated fluid‐particle coupling in geomaterials. In the coupled technique, the solid material is treated as an assembly of bonded and/or granular particles. A bond model accounting for strain softening in normal contact is incorporated into the discrete element method to simulate the mechanical behaviour of geomaterials, whilst the fluid flow is solved by the lattice Boltzmann method based on kinetic theory and statistical mechanics. To provide a bridge between theory and application, a 3D algorithm of immersed moving boundary scheme was proposed for resolving fluid‐particle interaction. To demonstrate the applicability and accuracy of this coupled method, a benchmark called quicksand, in which particles become fluidised under the driving of upward fluid flow, is first carried out. The critical hydraulic gradient obtained from the numerical results matches the theoretical value. Then, numerical investigation of the performance of granular filters generated according to the well‐acknowledged design criteria is given. It is found that the proposed 3D technique is promising, and the instantaneous migration of the protected soils can be readily observed. Numerical results prove that the filters which comply with the design criteria can effectively alleviate or eliminate the appearance of particle erosion in dams.     

Unified displacement boundary constraint formulation for discontinuous deformation analysis (DDA)

Displacement boundary constraints in discontinuous deformation analysis (DDA) are applied using stiff penalty springs. A co‐ordinate‐free formulation for displacement boundary constraints is presented here for DDA, which unifies previous derivations for points of fixity, and for points constrained to induce or prohibit block motion in specified directions as a function of location or time. Examples for each type of constraint are used to illustrate the behaviour of the algorithm and provide a link with previous formulations for each case. The new, unified formulation has five benefits: (1) simple to express algorithmically; (2) easy to program and verify; (3) penalty values in different directions may be chosen to allow fixed points, lines, curves or planes; (4) formulation works for 2D and 3D; (5) displacement constraint may be a function of time or location or both. Feedback in the algorithm may induce internal resonance in homogeneously deformable discrete elements used in DDA, and resonance in block‐to‐block contact interactions. Consequently, high mass problems with insufficient damping may suffer from excessive ‘vibrational hammering’, inducing physically implausible behaviour such as elastic rebound. Copyright © 2005 John Wiley & Sons, Ltd.     

Multi-scale Incremental Analysis Update Scheme and Its Application to Typhoon Mangkhut (2018) Prediction

In the traditional incremental analysis update(IAU) process, all analysis increments are treated as constant forcing in a model’s prognostic equations over a certain time window. This approach effectively reduces high-frequency oscillations introduced by data assimilation. However, as different scales of increments have unique evolutionary speeds and life histories in a numerical model, the traditional IAU scheme cannot fully meet the requirements of short-term forecasting for the damping of hig...     

Numerical Procedure for Dynamic Simulation of Discrete Fractures Due to Blasting

Summary  This paper describes development of a generic nonlinear, dynamic modelling technique to simulate discrete rock fractures due to blasting using the finite element method. The element elimination technique together with a brittle, Rankine failure-type material model are used as a means to simulate the initiation and growth of fractures in the rock under the effect of blast-induced dynamic pressure pulse. Dynamic loads representing ideal and non-ideal detonations are simulated and a new method, termed as optimised pressure profile, is proposed to approximate the pressure-time profile of the blast load to model the dynamic load. Comparison of numerical model results with previously reported observations from the literature reveals the ability of the model as a predictive tool and supports the validity of the developed modelling procedure. Author’s address: Hani S. Mitri, Department of Mining, Metals and Materials Engineering, McGill University, 3450 University Street, Montreal, Canada H3A 2A7