Hydro-micromechanical modeling of wave propagation in saturated granular crystals

Biot theory predicts wave velocities in a saturated granular medium using the pore geometry, viscosity, densities, and elastic moduli of the solid skeleton and pore fluid, neglecting the interaction between constituent particles and local flow, which becomes essential as the wavelength decreases. Here, a hydro-micromechanical model, for direct numerical simulations of wave propagation in saturated granular media, is implemented by two-way coupling the lattice Boltzmann method (LBM) and the discrete element method (DEM), which resolve the pore-scale hydrodynamics and intergranular behavior, respectively. The coupling scheme is benchmarked with the terminal velocity of a single sphere settling in a fluid. In order to mimic a small amplitude pressure wave entering a saturated granular medium, an oscillating pressure boundary on the fluid is implemented and benchmarked with the one-dimensional wave equation. The effects of input waveforms and frequencies on the dispersion relations in 3D saturated poroelastic media are investigated with granular face-centered-cubic crystals. Finally, the pressure and shear wave velocities predicted by the numerical model at various effective confining pressures are found to be in excellent agreement with Biot analytical solutions, including his prediction for slow compressional waves.     

On the linear elastic responses of the 2D bonded discrete element model

The bonded discrete element model (DEM) is a numerical tool that is becoming widely used when studying fracturing, fragmentation, and failure of solids in various disciplines. However, its abilities to solve elastic problems are usually overlooked. In this work, the main features of the 2D bonded DEM which influence Poisson's ratio and Young's modulus, and accuracy when solving elastic boundary value problems, are investigated. Outputs of numerical simulations using the 2D bonded DEM, the finite element method, a hyper elasticity analysis, and the distinct lattice spring model (DLSM) are compared in the investigation. It is shown that a shear interaction (local) factor and a geometric (global) factor are two essential elements for the 2D bonded DEM to reproduce a full range of Poisson's ratios. It is also found that the 2D bonded DEM might be unable to reproduce the correct displacements for elastic boundary value problems when the represented Poisson's ratio is close to 0.5 or the long-range interaction is considered. In addition, an analytical relationship between the shear stiffness ratio and the Poisson's ratio, derived from a hyper elasticity analysis and applicable to discontinuum-based models, provides good agreement with outputs from the 2D bonded DEM and DLSM. Finally, it is shown that the selection of elastic parameters used the 2D bonded DEM has a significant effect on fracturing and fragment patterns of solids.     

Discrete element modeling of shear wave propagation in carbonate precipitate–cemented particles

Bioremediation is widely used to improve ground soil by introducing calcium carbonate (CaCO₃). Shear wave velocity (Vs) is usually adopted to evaluate effect but the microscopic mechanism is unclear. The discrete element method (DEM), a promising tool for simulating the behaviors of cohesive and noncohesive materials, was used in this study to simulate Vs evolution and wave propagation path of sand reinforced by calcite precipitates. Two basic calcite precipitate forms are proposed for representing individual calcite precipitation (CaCO₃-P) and calcite aggregation (CaCO₃-C). Contact cementation between adjacent sand grain pairs was the primary association pattern for calcite precipitates at a low calcite content. At a higher calcite content, the preferential shear wave propagation pathway is the clusters cemented by CaCO₃-C. With calcite content increasing from 0 to 9%, the coordination number and average contact force increased. Vs increased from 169.73 to 2132.64 m/s but had high variability due to the spatial distribution. The results suggest that the calibrated DEM model can elucidate the microscopic mechanisms and evaluate the enhancement effect of microorganism-reinforced soil.

     

Analysis of wave propagation in dry granular soils using DEM simulations

In this paper, a three-dimensional particle-based technique utilizing the discrete element method (DEM) is proposed to study wave propagation in a dry granular soil column. Computational simulations were conducted to investigate the soil response to sinusoidal motions with different amplitudes and frequencies. Three types of soil deposits with different void ratios were employed in these simulations. Different boundary conditions at the base such as rigid bedrock, elastic bedrock, and infinite medium were also considered. Analysis is done in time domain while taking into account the effects of soil nonlinear behavior. The computational approach is able to capture a number of essential characteristics of wave propagation including motion amplification and resonance. Dynamic soil properties were then extracted from conducted simulations and used to predict the response of the soil using the widely used equivalent linear method program SHAKE and compare its predictions to DEM results. Generally, there was a good agreement between SHAKE and DEM results except when the exciting frequency was close to the resonance frequency of the deposit where significant discrepancy in computed shear strains between SHAKE predictions and DEM results was observed.     

密实散粒体剪切破坏能量演化的离散元模拟

砂土等散粒体在剪切过程中的能量存储及耗散是其宏观力学响应的深层原因,但因量测难度较大而研究较少。将考虑抗转动的接触模型引入离散元软件PFC2D,基于热力学第一定律建立各种能量量测方法,并在平面应变双轴压缩试验中采用该方法统计密实散粒体在剪切过程中的能量演化规律。采取了4种耗散类型,即滑动-滚动（S-R）、滑动-非滚动（S-NR）、非滑动-滚动（NS-R）和非滑动-非滚动（NS-NR）。结果表明：密实散粒体加载时能量耗散以滑动摩擦为主;且小应变加载阶段,外力功主要转化为弹性应变能,但同时也存在均布于试样的耗散能;随着应变的增加,外力功的转化形式逐渐过渡为以耗散能为主,且集中分布在带状区域内;各个加载阶段的摩擦耗散均存在各向异性。     

Numerical Investigations of the Dynamic Shear Behavior of Rough Rock Joints

The dynamic shear behavior of rock joints is significant to both rock engineering and earthquake dynamics. With the discrete element method (DEM), the dynamic direct-shear tests on the rough rock joints with 3D (sinusoidal or random) surface morphologies are simulated and discussed. Evolution of the friction coefficient with the slip displacement shows that the 3D DEM joint model can accurately reproduce the initial strengthening, slip-weakening, and steady-sliding responses of real rock joints. Energy analyses show that the strengthening and weakening behavior of the rock joint are mainly attributed to the rapid accumulation and release of the elastic energy in the joint. Then, effects of the surface roughness and the normal stress on the friction coefficient and the micro shear deformation mechanisms, mainly volume change and asperity damage, of the rock joint are investigated. The results show that the peak friction coefficient increases logarithmically with the increasing surface roughness, but decreases exponentially with the increasing normal stress. In addition, the rougher rock joint exhibits both higher joint dilation and asperity degradation. However, high normal stress constrains the joint dilation, but promotes the degree of asperity degradation significantly. Lastly, the effects of the 3D surface morphology on the shear behavior of the rock joint are investigated with a directional roughness parameter. It is observed that the anisotropy of the surface roughness consequently results in the variation of the peak friction coefficient of the joint corresponding to different shearing directions as well as the micro shear deformation mechanisms, e.g., the extent of joint dilation.     

基于弹性波速比的岩体强度参数估算方法

针对传统的岩体强度参数估算方法考虑风化程度的研究成果较少的不足,引入弹性波速比λ,提出了岩体强度参数的估算方法。以贵州省二叠系两种典型岩体(灰岩和泥岩)为例,讨论了参数λ和正应力σ_n对岩体强度参数的影响。主要研究成果为:基于弹性波速比与Hoek-Brown强度准则,探讨了不同风化程度岩体抗剪强度参数折减系数的确定方法;研究了正应力与弹性波速比对不同风化程度灰岩与泥岩岩体瞬时抗剪强度参数的影响,结果表明,岩体所处的环境与风化程度是影响岩体剪切强度参数的主要因素;通过多项式拟合,建立了灰岩与泥岩扰动与未扰动情况下不同风化程度强度折减系数的计算公式,从理论上探讨了两种主要岩体不同风化程度对强度参数的影响。      

Numerical study of inter‐particle bond failure by 3D discrete element method

The cohesive‐frictional nature of cementitious geomaterials raises great interest in the discrete element method (DEM) simulation of their mechanical behavior, where a proper bond failure criterion is usually required. In this paper, the failure of bond material between two spheres was investigated numerically using DEM that can easily reproduce the failure process of brittle material. In the DEM simulations, a bonded‐grain system (composed of two particles and bond material in between) was discretized as a cylindrical assembly of very fine particles connecting two large end spheres. Then, the bonded‐grain system was subjected to compression/tension, shear, rolling and torsion loadings and their combinations until overall failure (peak state) was reached. Bonded‐grain systems with various sizes were employed to investigate bond geometry effects. The numerical results show that the compression strength is highly affected by bond geometry, with the tensile strength being dependent to a lesser degree. The shear, rolling and torsion strengths are all normal force dependent; i.e., with an increase in the normal force, these strengths first increase at a declining rate and then start to decrease upon the normal force exceeding a critical value. The combined actions of shear force, rolling moment and torque lead to a spherical failure envelope in a normalized loading space. The fitted bond geometry factors and bond failure envelopes obtained numerically in this three‐dimensional study are qualitatively consistent with those in previous two‐dimensional experiments. The obtained bond failure criterion can be incorporated into a future bond contact model. Copyright © 2015 John Wiley & Sons, Ltd.     

利用常规测井资料基于岩石物理和多矿物分析反演横波速度

测井横波速度是测井地震联合反演的重要标定参数.为克服大量老井缺少横波速度资料和现有横波速度估算方法的不足, 基于孔隙介质岩石物理理论, 通过常规测井资料求取多矿物组分, 利用VRH模型求得地层的等效弹性模量; 最后利用纵波速度作为约束条件, 根据Biot-Gassmann方程得到地层横波速度.计算结果与实测结果对比表明, 平均相对误差限在5%左右, 与Xu-White模型相比, 该方法物理意义更为明确, 使用更简便, 计算精度提高一倍左右.      

Wave-Based Techniques for Evaluating Elastic Modulus and Poisson’s Ratio of Laboratory Compacted Lateritic Soils

A rapid, low-cost evaluation methodology using the wave-based techniques is proposed in this study in order to determine the design parameters e.g., elastic modulus and Poisson’s ratio of the laboratory compacted lateritic soils. Knowing the elastic wave velocities as measured with the wave propagation technique (i.e., a small-strain non-destructive test) and total mass density of the specimens, the elastic moduli and Poisson’s ratio of the soil specimens can be determined. In addition, the unconfined compression test (i.e., a large-strain destructive test) is also performed on the same specimens under the same unconfined testing condition in order to compare the moduli corresponding to different strain levels. The experimental results showed the potentials and limitations of using impulse signal for the determination of the elastic moduli and Poisson’s ratio for laboratory compacted soil specimens from elastic wave propagation techniques.     

Face stability analysis of shallow shield tunnels in dry sandy ground using the discrete element method

Controlling the face stability of shallow shield tunnels is difficult due to the inadequate understanding of face failure mechanism. The failure mechanism and the limit support pressure of a tunnel face in dry sandy ground were investigated by using discrete element method (DEM), which has particular advantages for revealing mechanical properties of granular materials. The contact parameters of the dry sand particles were obtained by calibrating the results of laboratory direct shear tests. A series of three-dimensional DEM models for different ratios of the cover depth to the diameter of the tunnel (C/D = 0.5, 1, and 2; i.e., relative depth) were then built to simulated the process of tunnel face failure. The limit support pressure, failure zone and soil arching were discussed and compared with other methods. The results of DEM simulations show that the process of tunnel face failure can be divided into two stages. With the increase of the horizontal displacement of the tunnel face, the support pressure decreases to the limit support pressure and then increases to the residual support pressure. The limit support pressure increases with the rise of relative depth and then tends to be constant. In the process of tunnel face failure, the failure zone is gradually enlarged in size and expands to the ground surface. The numerical results also demonstrate that soil arching occurs in the upper part of the failure zone and the soil becomes loosened in the failure zone. Consequently, the comprehensive analysis of tunnel face failure may help to guarantee safe construction during tunneling.     

Dynamic soil properties for microzonation of Delhi,India

Delhi, the capital of India, has experienced mild seismic shaking during several earthquakes in the past. The large variations of depth to bedrock and ground water table coupled with different soil types at different locations of Delhi necessitate a seismic microzonation study. Dynamic soil properties such as shear wave velocity, modulus reduction and damping characteristics of local soils are the basic and essential input parameters for conducting even a preliminary ground response analysis which is an essential input in microzonation studies. Shear wave velocity is not measured routinely due to its high cost and lack of the required expertise. Several researchers in the past developed correlations between shear wave velocity (V _s ) and routinely measured N values. In the present study, shear wave velocity profiles measured in the field at more than 80 borehole locations to a depth of about 20 to 32m using Spectral Analysis of Surface Waves (SASW) are presented and correlations between shear wave velocity and N values are also presented for use by engineers and designers. Results of strain and stress controlled cyclic triaxial tests on remoulded samples of sand-silt mixtures in the high strain range are used for generating the modulus reduction and damping curves and are compared with the well-known curves in the literature. The results presented in this article can be used for microzonation studies as well as site specific ground response analyses at Delhi.     

干砂弹性参数测定的弯曲-伸展元试验

利用安装在共振柱测试系统中的弯曲-伸展元,开展了干砂中P波（压缩波）和S波（剪切波）的室内试验,详细地分析了干砂中P波和S波的信号特征,研究了输入频率、土体密实度和有效围压对输出信号的影响。对比各种信号分析方法,并参考共振柱试验结果确定了S波的传播时间。根据实测波速和波动理论,确定了土体的弹性参数,包括剪切模量,侧限模量和泊松比。研究结果表明,P波和S波的输出信号频率在一定程度上随输入信号频率、土体密实度和有效围压的增加而增加,且P波信号比S波信号更容易确定波的传播时间;土体的弹性模量随土体密实度和有效围压的增加而增加,但剪切模量增长比侧限模量快;土体的泊松比并非一个常数,随着土体密实度和有效围压的增加而下降。初步探讨了利用剪切模量估算泊松比,以方便实际工程应用。     

Application of MASW in road failure investigation

Multichannel analysis of surface waves (MASW) survey was conducted to measure shear wave velocities in order to ascertain the likely causes of road failure along LASU-IBA expressway in Alimosho local government area, Lagos, Nigeria. MASW data were acquired along the express road. The acquired dataset was processed and transformed into two-dimensional structure reflective of depth and surface wave velocity distribution within a depth of investigation using SurfSeis software. The MASW shear wave velocity data were compared to geophysical data that was acquired along the same profile. The comparison was also done with geotechnical data that had been acquired prior to the study some meters away from the study area. The correlation between N values to measured shear wave velocity using MASW was generated. The comparison illustrates the accuracy and consistency of MASW-derived shear wave velocity profiles. We concluded that (1) the low-velocity region that varies between 100 and 250 m/s at surface down to 4 m beneath the surface is characterized by loose/peat materials and may have been responsible for the road failure within the study area; this region depicts a very loose compaction area. (2) The MASW technique is a time–cost-effective tool for obtaining reliable shear wave velocity profiles, and (3) the MASW is particularly attractive in areas that cannot be readily assessed by other geophysical and geotechnical tools.     

水合物沉积物力学性质的三维离散元分析

水合物沉积物力学特性研究是天然气水合物开采领域中的热点问题。为深入了解水合物对沉积物力学特性的影响,在提出一个新的水合物沉积物离散元数值试样制备方法的基础上,模拟了不同水合物饱和度沉积物试样的三轴排水试验,并从其应力-应变关系、体变特性、弹性模量及峰值强度等方面对模拟结果及已有室内三轴试验结果进行了对比,然后利用该方法对具有不同微观胶结参数的水合物沉积物样进行了三轴离散元数值试验。研究结果表明：所提出的离散元模拟方法能较好地反映水合物沉积物的主要力学特性;天然气水合物与土颗粒间胶结性能的改变会对水合物沉积物的力学响应产生一定的影响;水合物沉积物强度和模量的增加是孔隙填充水合物和粒间胶结水合物共同作用的结果。     

基于SEM的可变形块体离散元法研究

针对边坡工程中岩土体连续-非连续渐进破坏的特点,提出一种新的变形体离散元方法（DEM）。与传统有限单元法（FEM）不同,弹簧元法（SEM）通过构建一组广义弹簧系统描述单元的力学行为。弹簧元法中的一个广义弹簧可以具有多个方向的刚度系数,确定广义弹簧系统的构造形式及其各刚度系数表达式是弹簧元法的核心。以三角形单元为例,介绍平面弹簧元的基本理论。对任何二维正交广义弹簧系统,通过定义广义弹簧变形与单元应变之间的关系,直接对比单元的应变能与弹簧系统的弹性势能即可得到广义弹簧刚度系数的表达形式。定义泊松刚度系数和纯剪刚度系数两个系统参数,描述正交广义弹簧之间的联系。对任意泊松比的材料,该方法都可准确地描述泊松效应的影响,计算结果与传统有限元法一致。该方法不需要求得有限元单元刚度矩阵的具体形式,具有直接方便、物理意义明确的优点,应用该方法给出任意4节点单元弹簧系统的构造形式及其各刚度系数的表达式。基于SEM的可变形块体离散元法,用弹簧元中的广义弹簧求解块体变形,用离散元中的接触弹簧计算块体间作用力,在单元节点的控制方程中实现弹簧元-离散元耦合计算,通过接触弹簧的状态实现材料由连续到非连续的破坏过程。在基于连续介质离散元法（CDEM）程序的基础上实现弹簧元-离散元耦合程序,应用耦合程序计算均质土坡在重力作用下的弹塑性变形和基覆边坡在重力作用下的破坏,初步证明该方法用于边坡变形渐进破坏分析的可行性。     

Relating discrete element method parameters to rock properties using classical and micropolar elasticity theories

Micro–macro relations for discrete element method (DEM) media are derived using both classical and micropolar elasticity theories. The DEM media are classified into two main categories: dense packing, and loose packing. For both categories, relations for Young modulus (E), Poisson's ratio (ν) to represent static behaviors, and wave velocities (P‐wave and S‐wave) to represent dynamic behaviors are derived using the internal DEM parameters (k_n, k_s) and compared with values obtained from static and dynamic numerical tests. Whereas the dynamic behaviors for the two categories and the static behaviors for the dense packing match the analytical relations, the static behavior for the loose packing does not. Micropolar elasticity theory is also used to study the behaviors of the DEM media, where it is shown that if element rotation is included, DEM media behave according to linear elasticity theory. However, if element rotation is constrained, asymmetrical stresses arise in the DEM media, and a new expression is derived for the S‐wave, which allows it, under certain conditions, to travel faster than the P‐wave. Copyright © 2011 John Wiley & Sons, Ltd.     

Three-dimensional DEM analysis of single geogrid-encased stone columns under unconfined compression: a parametric study

Three-dimensional discrete element method (DEM) was employed in this study to analyze the behavior of single geogrid-encased stone columns under unconfined compression. Four important parameters were investigated to understand and evaluate their effects on the behavior of the encased columns by seven DEM models. The biaxial geogrid used as an encasement material for stone columns was simulated using parallel-bonded particles, and the aggregate in the stone column was simulated using graded particles. Both the macroscopic responses (e.g., vertical pressure–strain curves) and the microscopic interactions (e.g., contact force, coordination number, and sliding fraction) of the columns under unconfined compression were analyzed and are presented in this paper. The numerical results show that the geogrid encasement with high tensile stiffness could provide high confining stresses and then effectively increased the bearing capacity of the column. The short column yielded quickly even though its column modulus at a small deformation was relatively high. The modulus of the column slightly decreased with an increase in the column diameter due to high circumferential strains mobilized in the geogrid encasement. The column with large aggregate was stiffer and deformed less than the column with small aggregate. Selecting aggregate with a size larger than the geogrid aperture size was an effective way to achieve better interlocking between the aggregate and the geogrid and to minimize mass loss for the geogrid-encased stone column under loading. Due to limited deformation allowed by the geogrid encasement, a coefficient of radial stress equal to half of the coefficient of passive earth pressure was suggested to estimate the ultimate bearing capacity of the geosynthetic-encased stone column.     

Discrete element simulation of mine tailings stabilized with biopolymer

This paper presents a series of numerical simulations using discrete element method (DEM) to study the behavior of biopolymer-stabilized mine tailings (MT). Validation is conducted by comparing the DEM results with the experimental data. The macro-behavior comparison shows that the DEM simulations are in good agreement with experimental results. Analysis of the micro-parameters indicates more biopolymer induces larger tensile and shear strengths, confirming the experimental results which show that the strength of MT increases with higher biopolymer concentration. Analysis of the bond breakage pattern suggests that at the same strain level MT stabilized with higher biopolymer concentration show less bond breakage percentage. MT specimen under greater confining pressure develops larger shear band than that under lower confining pressure. Higher biopolymer concentration induces the increase in larger inter-particle bonding strength and thus larger cracking resistance and greater macro-strength.     

Discrete element method simulations of bio-cemented sands

Microbially induced calcite precipitation (MICP) has emerged as a novel soil improvement method. In this paper, 3-D discrete element method (DEM) simulations are used to explore the behavior of MICP-cemented sands. Comparisons of the macro-scale response of numerical and physical specimens are made. Microstructure analyses indicate a shear band formed in the numerical specimens, consistent with physical experiments. The bond breakage pattern in numerical specimens is explored and compared to observed measurements from physical specimens. The relationship between dilatancy and stress-strain behavior is evaluated. The results indicate DEM is an effective technique to capture the mechanical behavior of MICP-cemented sand.