DEM study on the undrained mechanical behavior of gassy sand

Exploitation of gas hydrate requires an improved understanding of the behavior of gassy soil. In this study, a numerical simulation technique is proposed that uses the discrete element method (DEM) to evaluate the undrained mechanical behavior of gassy sand, which consists of three phases—sand particles, water, and gas. The governing equation of gassy sand under undrained condition is derived and incorporated into the DEM simulation, in which gas solution and exsolution are considered. Undrained isotropic unloading and undrained triaxial compression tests on gassy sand samples with dissolved methane and carbon dioxide are simulated. Reasonable consistency is found when the simulation results are compared with experimental observation and theoretical calculation. The simulation highlights the significant influence of the gas solubility on the undrained behavior of gassy sand. The micro-responses of the observed phenomenon are also investigated.

     

DEM analysis of the onset of flow deformation of sands: linking monotonic and cyclic undrained behaviours

This study explores the link between the monotonic and cyclic undrained behaviour of sands using the discrete element method (DEM). It is shown that DEM can effectively capture the flow deformation of sands sheared under both monotonic and cyclic undrained loading conditions. When subjected to cyclic shearing, flow-type failure is observed for a loose sample, while cyclic mobility is observed for a dense sample. A strong correlation between the monotonic and cyclic loading behaviour that has been revealed experimentally is also confirmed in DEM simulations: (a) flow deformation occurs in the compressive loading direction when the cyclic stress path intersects the monotonic compression stress path prior to the monotonic extension stress path, and vice versa; (b) the onset of flow deformation in q–\(p^{\prime }\) space is located in the zone bounded by the critical state line and the instability line determined from monotonic simulations. Hill’s condition of instability is shown to be effective to describe the onset of flow failure. Micro-mechanical analyses reveal that flow deformation is initiated when the index of redundancy excluding floating particles drops to below 1.0 under both monotonic and cyclic loading conditions. Flow deformation induced by either monotonic or cyclic loading is characterized by an abrupt change of structural fabric which is highly anisotropic. The reason why the dense sample dilated during monotonic loading but showed cyclic mobility (temporary liquefaction) during cyclic loading is attributed to the repeating reversal of loading direction, which leads to the periodic change of microstructure.     

An AI-based model for describing cyclic characteristics of granular materials

Modelling cyclic behaviour of granular soils under both drained and undrained conditions with a good performance is still a challenge. This study presents a new way of modelling the cyclic behaviour of granular materials using deep learning. To capture the continuous cyclic behaviour in time dimension, the long short-term memory (LSTM) neural network is adopted, which is characterised by the prediction of sequential data, meaning that it provides a novel means of predicting the continuous behaviour of soils under various loading paths. Synthetic datasets of cyclic loading under drained and undrained conditions generated by an advanced soil constitutive model are first employed to explore an appropriate framework for the LSTM-based model. Then the LSTM-based model is used to estimate the cyclic behaviour of real sands, ie, the Toyoura sand under the undrained condition and the Fontainebleau sand under both undrained and drained conditions. The estimates are compared with actual experimental results, which indicates that the LSTM-based model can simultaneously simulate the cyclic behaviour of sand under both drained and undrained conditions, ie, (a) the cyclic mobility mechanism, the degradation of effective stress and large deformation under the undrained condition, and (b) shear strain accumulation and densification under the drained condition.     

DEM modeling of aging or creep in sand based on the effects of microfracturing of asperities and evolution of microstructural anisotropy during triaxial creep

Aging- or creep-related phenomena in sand have been widely studied, and the discrete element method (DEM) has been frequently used to model the associated soil behavior and then to explore the associated underlying mechanisms. However, several difficulties involved in modeling still remain unsolved. To resolve these difficulties, a new approach based on the effect of the microfracturing of asperities is proposed in this study for the DEM modeling of the sand aging or creep process through several aging cycles of associated reduction in the mobilized friction resistance at particle contacts and subsequent particle rearrangement to reach a new equilibrium state. This approach can be easily incorporated into different contact models and DEM simulations of the loading, unloading, and/or reloading processes, in either drained or undrained conditions, before and/or after aging. This new approach is proven effective because the DEM simulations incorporated with this new approach can satisfactorily reproduce the experimental observations in the triaxial creep process, drained and undrained recompression after aging, and 1D secondary compression and rebound. The simulation results also indicate that, based on the stress–force–fabric relationship, the contribution from the contact normal anisotropy to the deviatoric stress q gradually increases, whereas the contribution from the tangential force anisotropy becomes less during triaxial creep under a constant q. Moreover, the contacts between particles are gradually away from the state where the frictional resistance is fully mobilized, and then become more stable. During the subsequent triaxial recompression after creep, the aged samples exhibit enhanced soil stiffness, which is also found to be associated with the evolution of the invariants of the anisotropy tensors. It is worthwhile noting that the aging or creep effects on the microstructural changes, e.g., the invariants of the anisotropy tensors, can be gradually erased upon further recompression. This explains why the stress–strain responses of the aged samples during recompression gradually rejoin the original stress–strain response obtained from the sample without being subjected to aging or creep.     

正常固结黏土中平板锚基础的吸力和抗拉力

平板锚是新近出现的一种系泊深海浮式结构的基础型式。当黏土地基中的平板锚承受上拔力时,平板上、下表面超静孔压差形成的吸力使其抗拉承载力显著增加,对于风浪等快速加载条件尤其如此。利用有限元软件ADINA建立有效应力形式的轴对称动力有限元模型,研究圆形平板锚在缓慢加载与快速加载时的超静孔压分布与地基破坏型式。快速加载时重黏土和高岭土两组典型正常固结土样所得极限承载力系数与塑性极限分析解一致。进而通过变动参数分析,讨论加载速率和埋深对吸力和总抗拉力极限值的影响,并给出排水和不排水加载条件对应的临界加载速率。结果表明,不排水加载条件的总抗拉力可能达到排水总抗拉力的3倍。     

结构性黄土一维湿陷特性的离散元数值模拟

针对结构性湿陷性黄土大孔隙和胶结特性,应用离散元生成了不同含水率结构性黄土试样,研究试样的一维湿陷特性。首先,根据已有的结构性黄土试验资料和胶结颗粒材料离散元数值试验成果,建立胶结强度和初始饱和度之间的关系。其次,采用蒋明镜等提出的分层欠压法[1]和胶结模型[2]制得不同含水率结构性黄土离散元试样,然后进行不同含水率双线法和同一含水率4个压力下单线法湿陷试验的离散元数值模拟。数值模拟结果表明,提出的离散元分析方法能模拟天然结构性湿陷性黄土的主要力学性质,随着含水率的减少,结构屈服应力和最大湿陷压力增加,湿陷系数随着压力先增加后减小,湿陷起始压力为饱和试样的结构屈服应力,单线法湿陷后压缩曲线与饱和试样的压缩曲线接近。此外,模拟结果还表明,不同含水率结构性黄土离散元试样的最大湿陷系数与天然结构性湿陷性黄土相差较远,但在最大湿陷系数与孔隙比的比值上相接近;结构屈服对应着胶结的逐步破坏,湿陷伴随着大量的胶结破坏。提出了基于胶结点数目的损伤变量,研究了其在加载和湿陷过程中的变化规律。研究成果为认识黄土复杂力学特性和建立其本构理论提供了基础。     

Micromechanics of undrained response of dilative granular media using a coupled DEM-LBM model: A case of biaxial test

In this paper the Discrete Element Method (DEM) is coupled with the Lattice-Boltzmann Method (LBM) to model the undrained condition of dense granular media that display significant dilation under highly confined loading. DEM-only models are commonly used to simulate the micromechanics of an undrained specimen by applying displacements at the domain boundaries so that the specimen volume remains constant. While this approach works well for uniform strain conditions found in laboratory tests, it doesn’t realistically represent non-uniform strain conditions that exist in the majority of real geotechnical problems. The LBM offers a more realistic approach to simulate the undrained condition since the fluid can locally conserve the system volume. To investigate the ability of the DEM-LBM model to effectively represent the undrained constraint while conserving volume and accurately calculating the stress path of the system, a two dimensional biaxial test is simulated using the coupled DEM-LBM model, and the results are compared with those attained from a DEM-only constant volume simulation. The compressibility of the LBM fluid was found to play an important role in the model response. The compressibility of the fluid is expressed as an apparent Skempton’s pore pressure parameter B. The biaxial test, both with and without fluid, demonstrated particle-scale instabilities associated with shear band development. The results show that the DEM-LBM model offers a promising technique for a variety of geomechanical problems that involve particle-fluid mixtures undergoing large deformation under shear loading.     

A virtual experiment technique on the elementary behaviour of granular materials with discrete element method

Multi‐scale investigations aided by the discrete element method (DEM) play a vital role for current state‐of‐the‐art research on the elementary behaviour of granular materials. Similar to laboratory tests, there are three important aspects to be considered carefully, which are the proper stress/strain definition and measurement, the application of target loading paths and the designed experiment setup, to be addressed in the present paper. Considering the volume sensitive characteristics of granular materials, in the proposed technique, the deformation of the tested specimen is controlled and measured by deformation gradient tensor involving both the undeformed configuration and the current configuration. Definitions of Biot strain and Cauchy stress are adopted. The expressions of them in terms of contact forces and particle displacements, respectively, are derived. The boundary of the tested specimen consists of rigid massless planar units. It is suggested that the representative element uses a convex polyhedral (polygonal) shape to minimize possible boundary arching effects. General loading paths are described by directly specifying the changes in the stress/strain invariants or directions. Loading can be applied in the strain‐controlled mode by specifying the translations and rotations of the boundary units, or in the stress‐controlled mode by using a servo‐control mechanism, or in the combination of the two methods to realize mixed boundary conditions. Taking the simulation results as the natural consequences originated from a complex system, virtual experiments provide particle‐scale information database to conduct multi‐scale investigations for better understanding in granular material behaviours and possible development of the constitutive theories provided the qualitative similarity between the simulation results from virtual experiments and observations on real material behaviour. Copyright © 2011 John Wiley & Sons, Ltd.     

饱和黏土不排水剪切的热破坏

试验资料表明：饱和黏土在不排水常载升温条件下会产生很大的变形并最终可发生热破坏现象,因此,升温也成为一种加载方式。基于姚仰平等提出的热UH临界状态模型,推导了受温度影响的热不排水抗剪强度表达式,对不同超固结度饱和黏土在升温下的不排水抗剪强度模拟与试验结果对比表明：所提公式能够合理反映试验资料中受温度影响的不排水抗剪强度变化规律。利用热UH模型对不排水常载-升温过程进行了模拟,模拟结果表明,热UH模型可合理地反映不排水常载-升温条件下饱和黏土的应力-应变关系以及强度变化规律。针对能影响热破坏过程的几种因素如升温初始时的偏应力比、升温幅度、超固结度以及先期固结压力等进行了讨论分析,得到了各因素对于饱和黏土不排水剪切下的应力-应变关系及强度特性的影响规律。     

A predictive deep learning framework for path-dependent mechanical behavior of granular materials

As we transition into an era of data generation and collection, empirical summaries in the classical continuum modeling of granular materials cannot take full advantage of the increasingly larger data sets. This work presents a data-driven model for modeling granular materials, with the material data being extracted from discrete element method (DEM) simulations. A long short-term memory (LSTM) network is then employed to learn the mechanical behaviors of granular materials from the material dataset. Particular emphasis is placed on three elements: modification of LSTM unit cell, phase space sampling, and material history parameterization. The LSTM unit cell is modified so that the initial hidden state can be specified as the initial states of granular materials. Massive DEM simulations are performed to consider the effects of particle size distribution, initial density, confining pressure, and loading path on the mechanical behaviors of granular materials. The history-dependency of the granular materials is well represented by the architecture of the LSTM network and internal variable-based history parameterization. We compare the model predictions against DEM simulations to assess the performance of the proposed data-driven model. The results demonstrate that the model can predict the material behaviors of granular materials with different microstructures and initial states and reproduce the material responses under complex nonmonotonic loading paths. This data-driven model exhibits good generalization ability and high prediction accuracy in various situations.

     

Slope stability analysis for undrained loading conditions

The current state of art for limit equilibrium analysis of slope stability problems lacks a satisfactory procedure for stability evaluation under general, rapid (undrained) loading conditions. Some procedures are available for the analysis of rapid drawdown, but these suffer from several shortcomings and, furthermore, are not applicable to other types of rapid loading. An approach is presented which overcomes these limitations. The approach integrates four components-establishment of soil behaviour on the basis of laboratory testing, estimation of steady-state conditions in the slope using a boundary value analysis, estimation of distribution of undrained strength in the slope using undrained stress paths, and identification of the critical slip surface followed by calculation of its factor of safety. The approach is illustrated through its application to the stability analysis of an earth dam under rapid drawdown and earthquake conditions.     

Setting up virgin stress conditions in discrete element models

In the present work, a methodology for setting up virgin stress conditions in discrete element models is proposed. The developed algorithm is applicable to discrete or coupled discrete/continuum modeling of underground excavation employing the discrete element method (DEM). Since the DEM works with contact forces rather than stresses there is a need for the conversion of pre-excavation stresses to contact forces for the DEM model. Different possibilities of setting up virgin stress conditions in the DEM model are reviewed and critically assessed. Finally, a new method to obtain a discrete element model with contact forces equivalent to given macroscopic virgin stresses is proposed. The test examples presented show that good results may be obtained regardless of the shape of the DEM domain.     

DEM study of fabric features governing undrained post-liquefaction shear deformation of sand

In an effort to study undrained post-liquefaction shear deformation of sand, the discrete element method (DEM) is adopted to conduct undrained cyclic biaxial compression simulations on granular assemblies consisting of 2D circular particles. The simulations are able to successfully reproduce the generation and eventual saturation of shear strain through the series of liquefaction states that the material experiences during cyclic loading after the initial liquefaction. DEM simulations with different deviatoric stress amplitudes and initial mean effective stresses on samples with different void ratios and loading histories are carried out to investigate the relationship between various mechanics- or fabric-related variables and post-liquefaction shear strain development. It is found that well-known metrics such as deviatoric stress amplitude, initial mean effective stress, void ratio, contact normal fabric anisotropy intensity, and coordination number, are not adequately correlated to the observed shear strain development and, therefore, could not possibly be used for its prediction. A new fabric entity, namely the Mean Neighboring Particle Distance (MNPD), is introduced to reflect the space arrangement of particles. It is found that the MNPD has an extremely strong and definitive relationship with the post-liquefaction shear strain development, showing MNPD’s potential role as a parameter governing post-liquefaction behavior of sand.     

A unified CFD‐DEM approach for modeling of debris flow impacts on flexible barriers

This paper presents a unified modeling framework to investigate the impacts of debris flow on flexible barriers, based on coupled computational fluid dynamics and discrete element method (CFD‐DEM). We consider a debris flow as a mixture of fluid and particles where the fluid and particle phases are modeled by the CFD and the DEM, respectively. The fluid‐particle coupling is considered by the exchange of interaction forces between CFD and DEM calculations. The flexible barrier is simulated by the DEM as a network of bonded particles with remote interactions. The proposed coupled CFD‐DEM approach enables us to conveniently handle the complicated three‐way interactions among the fluid, the particles, and the flexible barrier structure for debris flow impact simulations. The proposed approach is first used to investigate the influences of channel inclination and the volumetric solid fraction in a debris mixture on the impact force, the resultant deformation, and the retained mass in a flexible barrier. The predictions agree well with existing experimental and numerical studies. We further examine the possible failure modes of a flexible barrier under debris flow impact and their underlying mechanisms. The performance of different components in a flexible barrier system, including single wires, double twists and cables, and their load sharing mechanisms, are carefully evaluated. The proposed unified framework offers a novel, promising pathway towards physically based, quantitative analysis and design of flexible barriers for debris flow mitigation.     

软土地基上路堤填筑的破坏性状分析

在软土地区建设高速公路、铁路等的填筑路堤越来越多,由于软土的不排水抗剪强度较低,软土地区路堤的填筑十分困难,而软土地基的渗透性很低,通常认为路堤的填筑是在不排水条件下进行。经典的设计方法是基于极限平衡法,无法考虑变形等因素,因此,能综合考虑稳定及变形等因素的有限元方法成为分析此类问题的一种有效手段。依据连云港铁路路堤在软土地基上的填筑试验资料,采用大变形有限元方法及Mohr-Coulomb模型,采用现场试验得到的土体强度值,对平面应变条件下路堤填筑的破坏性状及极限填筑高度等进行了分析,并对比了有限元分析结果及现场试验结果,结果表明,采用大变形有限元方法能够较准确的得到填筑路堤的极限高度,并有效地分析填筑路堤的破坏性状。     

Three dimensional steady-state locus for dry monodisperse granular materials: DEM numerical results and theoretical modelling

In this paper, steady-state conditions for ideal monodisperse dry granular materials are both theoretically and numerically analysed. A series of discrete element (DEM) numerical simulations have been performed on a periodic cell by imposing stress paths characterized by different Lode angles, pressures, and deviatoric strain rates. The dependence of the material response on both inertial number and loading path has been discussed in terms of void ratio, fabric, and granular temperature. DEM numerical results have been finally compared with the prediction of an already conceived model based on both kinetic and critical state theories, here suitably modified to account for three-dimensional conditions.     

粒状介质三维复杂应力加载离散元数值试验方法

实际荷载条件下（如交通、地震荷载）,粒状岩土材料常受到三维复杂应力路径作用。目前,多数粒状岩土材料的本构理论和模型都基于简单应力路径加载条件下的物理试验提出,在更加复杂应力路径下的适用性则需要进一步验证。但受机械控制的限制,物理试验中无法实现很多客观存在的三维复杂应力路径加载。为了能够再现并分析三维复杂应力路径下粒状介质的力学响应,提出了一种离散元数值试验方法,该方法采用球形数值试样,通过直接控制试样边界应力达到对3个主应力大小和方向的任意控制,从而可以实现诸多物理试验中无法实现的复杂应力路径。通过与目前常见的一些物理试验进行定性对比,论证了该数值试验方法通过高精度的加载控制和测量能够再现已有物理试验现象。在此基础上,进一步开展了应力主轴的三维旋转,分析了在这种实际存在却无法通过物理试验再现的加载条件下粒状介质的变形规律,初步显示了提出的数值试验方法在深入研究三维复杂应力路径下粒状介质力学响应方面所拥有的能力和优势。     

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。     

颗粒离散单元法动力人工边界设置方法

采用颗粒离散单元法进行动力计算时,人工截断边界上需设置吸收边界条件,以防止波的反射。鉴于颗粒离散单元数值计算模型的人工边界上颗粒单元半径大小不一、边界面凸凹不平,在连续介质的黏性、黏弹性、自由场边界条件方程基础之上,推导出适用于离散介质的等效方程。在离散介质的黏性边界条件等效方程中引入微调系数,提出比值迭代法以快速确定其最优值,以实现对波的最佳吸收。采用二维颗粒离散单元计算软件PFC2D,分别建立黏性、黏弹性、自由场边界条件相关数值分析模型,探讨颗粒分布模式对黏性边界上颗粒单元半径、速度分布及比值迭代过程的影响;采用外源波动算例及经典Lamb问题算例验证黏弹性边界设置方法的正确性;通过隧洞算例检验提出的自由场边界条件设置方法的正确性。