DEM simulation of the behaviour of geogrid stabilised ballast fouled with coal

Geogrids are commonly used in railway construction for reinforcement and stabilisation. When railway ballast becomes fouled due to ballast breakage, infiltration of coal fines, dust and subgrade soil pumping, the reinforcement effect of geogrids decreases significantly. This paper presents results obtained from Discrete Element Method (DEM) to study the interface behaviour of coal-fouled ballast reinforced by geogrid subjected to direct shear testing. In this study, irregularly-shaped aggregates (ballast) were modelled by clumping together 10–20 spheres in appropriate sizes and positions. The geogrid was modelled by bonding a large number of small spheres together to form the desired grid geometry and apertures. Fouled ballast with 40% Void Contaminant Index (VCI) was modelled by injecting a predetermined number of miniature spheres into the voids of fresh ballast. A series of direct shear tests for fresh and fouled ballast reinforced by the geogrid subjected to normal shear stresses varying from 15 kPa to 75 kPa were then simulated in the DEM. The numerical results showed a good agreement the laboratory data, indicating that the DEM model is able to capture the behaviour of both fresh and coal-fouled ballast reinforced by the geogrid. The advantages of the proposed DEM model in terms of capturing the correct stress–displacement and volumetric behaviour of ballast, as well as the contact forces and strains developed in the geogrids are discussed.     

Discrete modeling of strain accumulation in granular soils under low amplitude cyclic loading

An advanced understanding of the strain accumulation phenomenon in granular soils subjected to low amplitude cyclic loading with relatively high frequency is needed to enhance the ability to predict the settlement of granular soils induced by vibrations. In the current study, the discrete element method is used to study this phenomenon. A loose and a medium dense sample composed of a relatively large number of spheres are considered. A series of stress controlled cyclic triaxial tests with different excitation amplitudes and frequencies is performed on these samples at different static stress states. The response of these samples at the macroscopic and microscopic scales is analyzed. The sample density, the cyclic stress amplitude and the static stress state importantly affect strain accumulation. However, the cyclic excitation frequency has a small effect on strain accumulation. At the microscopic scale, frictional sliding occurring at a few contacts continuously dissipates energy and the fraction of these contacts varies periodically during cyclic loading. The coordination number of these samples increases slightly as strain accumulates. However, the anisotropy remains almost constant during low amplitude cyclic excitation. A qualitatively good agreement between numerical and experimental results is found.     

Discrete element modeling of dynamic behaviors of railway ballast under cyclic loading with dilated polyhedra

The dynamic behaviors of railway ballast under cyclic loading are simulated with discrete element method (DEM). Dilated polyhedra are constructed based on the Minkowski sum operator in order to resemble the irregular shapes of ballast particles. The polyhedral particle generation, contact detection between particles and contact laws are presented. Ballast box tests with periodic lateral boundaries are conducted to simulate the dynamics of the sleeper and ballast particles. The settlement and effective stiffness of ballast bed are investigated under cyclic loadings with five distinct frequencies. The settlement of ballast bed is significant in the first several cycles and increases with the number of cycles gradually. The higher frequency loading generates larger displacement in the same simulation time. The effective stiffness of ballast bed increases gradually. To study the effect of particles' sharpness, dilated polyhedra with different dilating radii and spherical particles are also developed. Simulation results show the sharper the ballast particles are, the smaller the produced settlement. Copyright © 2016 John Wiley & Sons, Ltd.     

A numerical model for the transient analysis of offshore foundations under cyclic loading

A comprehensive numerical model for the analysis of offshore foundations under a general transient loading is presented here. The theoretical basis of the model lies on the Swansea formulation of Biot’s equations of dynamic poroelasticity combined with a constitutive model that reproduces key aspects of cyclic soil behaviour in the frame of the theory of generalised plasticity. On the practical side, the adoption of appropriate finite element formulations may prevent the appearance of spurious numerical instabilities of the pore pressure field. In this respect, the use of a coupled enhanced-strain element is here proposed. On the other hand, the practicality of the presented model depends ultimately on its computational efficiency. Some practical recommendations concerning the solution strategies, the matrix storage/handling procedures and the parallel multi-processor computation are here provided. Finally, the performance of the model with a benchmark study case and its practical application to analyse the soil–structure interaction of an offshore monopile under a realistic transient storm loading are discussed.     

DEM modeling of pullout behavior of geogrid reinforced ballast: The effect of particle shape

The performance of a geogrid reinforced system depends heavily on the properties of interface between the interacting components (i.e., backfill soil and geogrid inclusion). The comprehensive understanding of soil-geogrid interaction requires proper consideration of the true aperture geometry and the discontinuous nature of backfill soil. Based on the calibrated parameters, this paper presents a simulation procedure using PFC3D to reproduce the realistic pull-out behaviors of a triaxial geogrid embedded in various ballast aggregates with diverse particle shapes. The load transfer behaviors across the interacting components have been visualized in terms of the evolution of bond forces along the geogrid and the evolution of contact forces across the particle assembly. Meanwhile, the inherent microscopic changes accounting for the regression of macroscopic strength and the correlation between macro pull-out force and micro anisotropy parameters have been addressed. In addition, the differences in macro performance and the particle responses produced by different shapes of particles are also systematically discussed to justify the significant role of particle geometry. The findings obtained in this study are expected to provide better understanding of soil-geogrid interaction and the improved interlocking caused by irregular ballast geometry.     

Discrete element analysis of breakage of irregularly shaped railway ballast

In order to reduce the maintenance costs of ballasted railway track and improve passenger comfort, the railway ballast particle breakage and its effect on track settlement need to be better understood. The failure process of individual railway ballast loaded between flat platens is simulated using the discrete element method, considering its irregular shape with the incorporation of parallel bonds. The tensile strength, the stress of a survival probability of 37% of samples, is obtained and compared with laboratory results from published literature for the verification of DEM simulations. The evolution to failure of the particle is understood from the stress-strain curve and progressive failure modes. The internal breakage mechanisms are analysed by tracking the accumulation of bond breakage number and the contact force distributions.     

水平荷载作用下根式基础受力特性分析

根式基础是一种新型的结构式基础,利用自身的结构性,可以在增加少量成本的情况下大幅度提高基础的承载力。但是,目前还没有关于根式基础的理论研究成果,有必要对根式基础的受力特性进行分析。采用弹塑性有限元法,对淮河特大桥1#桥的根式基础原位试验进行数值模拟,验证了数值模拟方法和参数选取的合理性。在此基础上,通过无根键沉井基础和有根键沉井基础的受力特性对比,分析了根式基础的受力特性,对根键上的弯矩分布型式进行了研究,并探讨了根键沿深度位置分布对根式基础承载力的影响。研究证明,根键分布在合理的位置可以有效地提高沉井基础的水平承载力。     

DEM investigation of the effect of intermediate principle stress on particle breakage of granular materials

This study investigates the influence of the intermediate principle stress on the particle breakage of granular materials. The crushable agglomerate method is applied to model soil particles and numerical true triaxial tests were carried out. The results show that particle breakage increases with increasing b value, the relationship of which follows an exponential function and agrees well with previous experimental results. More importantly, the study found that the relationship between particle breakage and total energy input is independent of the intermediate principle stress, which provides a good basis for the constitutive modeling of granular materials.     

Implementation of DSC model and application for analysis of field pile tests under cyclic loading

The disturbed state concept (DSC) model, and a new and simplified procedure for unloading and reloading behavior are implemented in a nonlinear finite element procedure for dynamic analysis for coupled response of saturated porous materials. The DSC model is used to characterize the cyclic behavior of saturated clays and clay–steel interfaces. In the DSC, the relative intact (RI) behavior is characterized by using the hierarchical single surface (HISS) plasticity model; and the fully adjusted (FA) behavior is modeled by using the critical state concept. The DSC model is validated with respect to laboratory triaxial tests for clay and shear tests for clay‐steel interfaces. The computer procedure is used to predict field behavior of an instrumented pile subjected to cyclic loading. The predictions provide very good correlation with the field data. They also yield improved results compared to those from a HISS model with anisotropic hardening, partly because the DSC model allows for degradation or softening and interface response. Copyright © 2000 John Wiley & Sons, Ltd.     

DEM study on the effect of particle breakage on the macro- and micro-behavior of rockfill sheared along different stress paths

The behavior of crushable rockfill sheared along different stress paths is studied using the discrete element method. Rockfill particles are modeled as breakable agglomerates, and reasonable consistency is found between the predicted and experimental results. The simulation highlights the influence of agglomerate breakage on both the macro- and micro-behavior of the assembly. The evolution of both the number and mode of agglomerate breakage during shearing is significantly influenced by the confining pressure, deviator stress ratio, and loading direction. The relationship between the deviator stress ratio on the macro-scale and the deviator fabric on the micro-scale along different stress paths is explored.     

循环荷载下砂土液化特性颗粒流数值模拟

利用PFC2D常体积循环双轴试验条件,对砂土在不排水循环荷载作用下的液化特性进行了颗粒流数值模拟,数值模拟按等应力幅加荷方式进行。颗粒流数值模拟的优点在于得到试样液化宏观力学表现的同时,通过不同循环加荷时刻试样内细观组构参量（包括配位数、接触法向分布、粒间法向接触力、粒间切向接触力）的演化规律,分析砂土液化过程中细观组构变化与宏观力学响应之间的内在联系,从而可进一步探讨砂土液化的细观力学机制。数值模拟研究结果表明,砂土液化现象在宏观力学表现上反映为超静孔隙水压力的累积上升和平均有效主应力的不断减小,在细观组构上对应于配位数的累积损失和粒间接触力的不断减小。砂土液化细观机制分析表明,试样配位数的减少与循环加荷过程中组构各向异性滞后于应力各向异性有关。     

Study on the particle breakage of ballast based on a GPU accelerated discrete element method

Breakage of particles will have greatly influence on mechanical behavior of granular material(GM)under external loads,such as ballast,rockfill and sand.The discrete element method(DEM)is one of the most popular methods for simulating GM as each particle is represented on its own.To study breakage mechanism of particle breakage,a cohesive contact mode is developed based on the GPU accelerated DEM code-Blaze-DEM.A database of the 3D geometry model of rock blocks is established based on the 3D scanning method.And an agglomerate describing the rock block with a series of non-overlapping spherical particles is used to build the DEM numerical model of a railway ballast sample,which is used to the DEM oedometric test to study the particles’breakage characteristics of the sample under external load.Furthermore,to obtain the meso-mechanical parameters used in DEM,a black-analysis method is used based on the laboratory tests of the rock sample.Based on the DEM numerical tests,the particle breakage process and mechanisms of the railway ballast are studied.All results show that the developed code can better used for large scale simulation of the particle breakage analysis of granular material.     

Modelling the settlement behaviour of a strip footing on sloping sandy fill under cyclic loading conditions

This paper investigates the settlement behaviour of a strip footing seating on the crest of an embankment and subjected to cyclic loading. The embankment fill is a dense sand and the issue is the gradual accumulation of settlement over a large number of load repetitions. Cyclic triaxial tests were first conducted to develop a consistent but simple material model for numerical implementation. Particular emphasis was placed on linking the stress-strain behaviour of an unload-reload cycle to the accumulation of permanent strain, with only five input parameters required to model the cyclic behaviour. The material model was implemented in a numerical analysis to compute the settlement behaviour obtained from model tests conducted by another researcher. It is pertinent to highlight that the same soil, compacted to same density at same moisture content, was used for both the cyclic triaxial tests and model tests. Reasonable to good agreement between the experimental and numerical results was achieved.     

循环荷载作用下土工格栅拉伸试验研究

为了了解土工格栅在动力荷载作用下的软化特性,采用应力控制的循环拉伸试验对土工格栅进行研究。试验中研究了在不同循环拉力、预拉力、加载频率下土工格栅的力学性能,着重研究了各个因素对土工格栅动应变及循环软化特性的影响。试验结果表明,随着循环次数、循环拉力、预拉力的增加,动应变增大;随着加载频率的增大,在相同循环次数下,动应变减小。随着循环次数、循环拉力、预拉力的增加,软化指数减小;随着加载频率的增大,相同循环软化指数逐渐减少。     

基于循环加卸载的矿物定向排列致各向异性岩石损伤演化规律——以黑云母石英片岩为例

黑云母石英片岩是一种典型的各向异性岩石,为研究其损伤演化规律及各向异性表现特征,针对含0°,45°,90°3种片理角度的试样,开展了等塑性应变循环加卸载试验。结果表明：不同片理面角度试样的破坏模式有所不同,0°片理面试样中的张拉破裂现象与45°片理面中的剪切破坏现象尤为明显。随着塑性应变增加,黑云母石英片岩的弹性模量表现出先强化、后弱化的现象,这一现象在高围压下更为明显。在弱化阶段中,弹性模量演化的转折点与裂纹起裂强度σ_ci稳定时对应塑性应变一致。弹性模量作为岩石损伤劣化过程的评价指标较完整性系数受片理面角度的影响更小。在岩石内部能量演化过程中,耗散能大小与片理面角度的关系为0°>90°>45°,耗散能、弹性能下降的速率大小关系为45°>90°>0°,其降至稳定时与岩石损伤强度σ_cd稳定时对应塑性应变一致。该研究借助弹性模量和能量演化规律分析,探究了黑云母石英片岩的损伤演化力学行为。

     

复合加载下软基上半圆堤结构稳定性分析

半圆堤是适用于软土地基的一种轻型重力式的新型防波堤结构,复合加载模式下软基上半圆堤的稳定性计算和结构破坏模式尚需建立合理的分析和计算方法。将加载模式与软基上大型海岸结构稳定性分析的有限元模拟方法相结合,同时考虑半圆堤在不同荷载组合时可能发生沿底板或抛石基床底部的滑动破坏及地基竖向承载力破坏,建立了复合加载模式下软基上半圆堤的稳定性分析方法,得出了结构的稳定性破坏模式和破坏包络线（面）,并分析了箱内填砂量、抛石基床宽度及地基加固深度对半圆堤稳定性的影响。计算结果表明：半圆堤结构在复合荷载作用的破坏包络线（面）均由一定区域的结构滑移破坏面和地基承载力破坏线（面）组成,并将整个荷载组合区分成4个区域：稳定区、只发生滑移破坏区、只发生地基承载力破坏区和同时发生滑移和地基承载力破坏区;荷载与位移组合加载模式得到的地基承载力破坏包络线位于Swipe加载方式得到的破坏包络线之外,但对每种加载方式得到的地基承载力破坏包络线变化趋势基本一致;随着箱内填砂高度的增加沿沉箱底部和抛石基床底部的抗滑安全系数均增加,但地基承载力安全系数减小;随着抛石基床宽度或地基加固深度的增加,地基承载力安全系数明显增大。     

循环荷载下低填方桩承式路堤动力响应分析

低填方桩承式路堤在交通荷载下的动力响应特性与路堤的承载能力及其稳定性密切相关。基于前人的室内模型试验,采用PFC2D软件建立了桩承式路堤离散元数值分析模型;采用数值双轴试验、数值单向压缩试验分别对路堤填料和桩间土的细观参数进行了标定;同时,根据路堤荷载传递效率对模拟结果与试验数据进行了对比分析,验证了离散元数值模型的正确性及适用性。在此基础上,在低填方路堤表面施加正弦波循环荷载,并对路堤荷载传递效率、接触力分布及路堤沉降等的变化规律进行了分析。模拟结果表明：在循环荷载作用下,低填方路堤中土拱结构的承载力先逐渐弱化并最终趋于稳定;该弱化作用在宏观上表现为路堤荷载传递效率的逐渐降低,而在细观上则表现为桩顶及桩间土上方接触力差异程度的逐渐减小;同时,土拱结构的弱化将不断加剧路堤表面的不均匀沉降。     

Analytical solution for 1D consolidation under haversine cyclic loading

Presented and discussed in this paper is an exact analytical solution of the nonhomogeneous partial differential equation governing the conventional one‐dimensional consolidation under haversine repeated loading. The derived analytical solution to the 1D consolidation equation is compared with the numerical solution of the same consolidation problem via FEM. The series solution takes into account the frequency of repeated loading through a dimensionless time factor T₀. The paper reveals that an increase in the frequency of imposed repeated haversine loading (a decrease in period of repeated loading) causes an increase in the number of cycles required to achieve the steady state, whereas the effect of frequency on the maximum excess pore water pressure at the bottom of a clay layer with permeable top and impermeable bottom for the range of frequencies studied is generally insignificant. The effective stress at the bottom of the clay deposit with permeable top and impermeable bottom increases with time but with some fluctuations without changing the sign. These fluctuations become more pronounced for increasing values of T₀. An increase in T₀ also causes an increase in maximum effective stress. Copyright © 2013 John Wiley & Sons, Ltd.     

考虑非Darcy渗流时循环荷载下饱和黏土一维固结分析

考虑到土体处于超固结状态下的压缩性一般要比正常固结状态下的低,引入描述非Darcy渗流的Hansbo方程,修正了Terzaghi饱和黏土一维固结方程,并将其推广到低频循环荷载作用的情况。采用有限体积法对该方程进行了求解,并讨论了非Darcy渗流参数、循环荷载周期以及超固结状态下土体压缩性对固结进程的影响。计算结果表明,在矩形波载作用下,按孔压定义和按变形定义的固结度都随时间增长而震荡增加,且按孔压定义的固结度的震荡幅度明显大于按变形定义的固结度。另外,非Darcy渗流减缓了地基的沉降速率,且循环荷载周期越短,或超固结状态下压缩性越高,地基的沉降速率就越慢。     

Fluctuation responses of saturated porous media subjected to cyclic thermal loading

Normalized, coupled governing equations for one-dimensional thermal consolidation problems are established. The non-dimensional coefficients of thermal consolidation and thermal diffusivity are defined accordingly. An analytical solution is deduced by using the Laplace transform and the Gauss–Legendre method of Laplace transform inversion. The responses of saturated porous media subjected to cyclic thermal loading are studied. The evolution of temperature, pore pressure and displacement from instantaneous state to quasi-steady state, with elapsed time, are analysed. The characteristics of cyclic fluctuation and the attenuation of the field variables with increased depth are also analysed. The influences of the permeability of media on thermal responses are discussed.