Discrete numerical modelling of rockfill dams

The aim of this study is to obtain quantitative information on the behaviour of rockfill used in embankment dams, and particularly on the influence of block breakage on the displacement field, from a numerical analysis using the Distinct element method. A methodology is set up to define the resistance of the 2D particles so that the same probability of breaking blocks may be reproduced as in a 3D material. The model uses the discrete element code PFC^2D (Itasca Consulting Group Inc., PFC2D (Particle Flow Code in Two Dimensions), Version 3.0, 2002) and considers breakable clusters of 2D balls. The different parameters are determined from experimental data obtained from laboratory tests performed on rock blocks. The model is validated by comparing the results of the simulation of shearing tests with actual triaxial tests on rockfill material published in the literature. The numerical analysis of block crushing in an actual dam is proposed in the last part of this paper. Copyright © 2006 John Wiley & Sons, Ltd.     

Dynamic characteristics of multiscale longitudinal stress and particle rotation in ballast track under vertical cyclic loads

Loads transfer in ballast track through contacts among randomly distributed ballast particles and have strong heterogeneity. Since the size ratio between ballast track and ballast particles is generally small, using averaged stress to describe the internal mechanical state in ballast track faces practical difficulties. For example, particle movements and high local concentration stress tend to be ignored. The inter-particle contact stress is crucial to evaluate the particle behaviors, such as abrasion, movements, and furtherly the performance of ballast track. However, the contact stress on ballast particles is hard to predict or measure. We conduct a full size model test to investigate the dynamic characteristics of longitudinal stress on ballast particles as well as different lateral regions under vertical cyclic loads with various loading magnitudes and frequencies. An obvious seesaw effect of longitudinal contact stress is observed: the stresses at some contact areas have the same phase with applied cyclic load while at other contact areas have an opposite phase. The seesaw effect of contact stress is then used to evaluate the rotational movements of ballast particles. The variation of contact area and stress of the ballast particles with loading magnitudes demonstrates that the rigid contact assumption is appropriate when analyzing the contact behavior of ballast particles. The cumulative probability distribution of contact stress with stress level can be described by an inversely proportional function, based on which the maximum contact stress can be estimated according to the longitudinal average stress. Besides, the lateral dispersion angle of the vertical loads in the ballast track is about 35°, which is independent of the given loading magnitudes and frequencies.

     

Behaviour of Track Ballast Under Repeated Loading

Najaf-sea quarry is located in Najaf city about 160 km south west of Baghdad the capital of Iraq. It is the main source that supplies track ballast for maintenance of existing railway network and construction of new railway lines in the middle and southern parts of Iraq. Track ballast experience a complex combination of stresses during its service lifetime, primarily from repeated axial loads of the trains in addition to stresses generated from the environmental conditions. The ideal evaluation of suitability of track ballast must be carried out under real field loading conditions, however such field tests are usually costly and time consuming. On the other hand laboratory model tests simulating field loads under limited boundary conditions can provide satisfactory indication about the suitability of the material. The present paper investigates the deformation characteristics of Najaf-sea track ballast, under repeated loading using model tests simulating ballast conditions under a selected track section. A test setup was designed and manufactured capable of applying both monotonic as well as repeated loading on the track section under different conditions. The repeated model tests which simulate as close as possible the field conditions shed the light on the generated settlement, modulus of deformation and degradation of the ballast particles under different repeated loading levels. Statistical analysis in terms of breakage index and repeated applied load revealed satisfactory correlations that help in understanding the overall performance of the ballast material. The results also demonstrate that 4–5 tamping are capable of controlling both the settlement and modulus of deformation of the ballast material.     

A hypo-plastic approach for evaluating railway ballast degradation

Repetitive or cyclic rail loading deteriorates the engineering properties of the railway ballast by particle crushing and rearrangement. Most of the classical elasto-plastic models are unable to predict such ballast degradation despite successfully predicting the overall load–deformation behavior during cyclic densification. In this context, the present study delivers a novel hypo-plastic modeling approach coupled with breakage mechanics theory to bridge the gap of the conventional models. The hypo-plastic approach enables to predict the nonlinear load–deformation response of ballast-type granular materials for both monotonic and cyclic loading conditions, while circumventing the requirement of notional yield condition to predict the inelastic behavior. Breakage mechanics theory, on the other hand, establishes the links between particle comminution and the macroscopic deformation. The novelty of the proposed approach is threefold. Firstly, unlike the conventional hypo-plastic approaches, the development of the proposed model is within the continuum thermodynamics framework. Secondly, the model requires less number of physically identifiable parameters as compared to that of earlier models employed for assessing the particle breakage under cyclic loading. Third and finally, the numerical implementation of the model as a user-defined material is simple for solving boundary value problems. Under the compressive deformation regime, the model prediction of the ballast degradation along with the cyclic densification response agrees reasonably well with the experimental results found in the literature.     

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 constitutive model for coal-fouled ballast capturing the effects of particle degradation

Rail tracks undergo degradation owing to particle breakage and fouling of ballast by various fines including coal and subgrade soil. As the ballast becomes fouled, its strength and drainage capacity are compromised, sometimes resulting in differential settlement and reduced track stability. This paper demonstrates a continuum mechanics based framework to evaluate the detrimental effect of fines on the strength, deformation and degradation of coal-fouled ballast under monotonic loading. An elastoplastic constitutive model that considers the effect of fines content and energy consumption associated with particle breakage during shearing is presented. This multiphase constitutive model is developed within a critical state framework based on a kinematic-type yield locus and a modified stress-dilatancy approach. A general formulation for the rate of ballast breakage and coal particle breakage during triaxial shearing is presented and incorporated into the plastic flow rule to accurately predict the stress–strain response of coal-fouled ballast at various confining pressures. The behaviour of ballast at various levels of fouling is analysed and validated by experimental data.     

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.     

A semi-empirical dilatancy model for ballast fouled with plastic fines

In the era of high speed trains, it is very important to ensure the stability of rail tracks under adverse conditions including the fouling of ballast. Fouling of ballast from unstable and saturated soft subgrade soil is one of the major reasons for track deterioration. The reported results of a number of large-scale laboratory experiments on the shear behaviour of ballast and fouled ballast are analysed, herein. It was observed that fines have a significant influence on the shear behaviour of ballast. Shear strength increases and dilatancy decreases with the addition of fines. In this paper, a semi-empirical mathematical model has been proposed to capture the dilatancy of ballast fouled with fines during shearing. The empirical constants a, b and c proposed in the model are a function of the fines content Void Contamination Index (VCI). The results of the model have been compared with the laboratory experiments and are found to be in good agreement.     

Improvements for the smooth joint contact model of the particle flow code and its applications

This paper deals with two shortcomings of the smooth-joint contact model (SJCM) used in the particle flow code (PFC). The first shortcoming is the increase of the shear strength of the joint when the shear displacement of the joint exceeds a specific value that is related to the particle size. This problem is named as the interlocking problem, which is caused by the interlocking particles. It occurs due to a shortcoming of the updating procedure in the PFC software related to the contact conditions of the particles that lie around the intended joint plane during high shear displacements. This problem also increases the dilation angle and creates unwanted fractures around the intended joint plane. To solve this problem two new approaches are proposed in this paper: (1) joint plane checking (JPC) approach and (2) joint sides checking (JSC) approach. These approaches and the regular approach are used to model: (a) the direct shear test using the PFC^2D and PFC^3D, (b) the biaxial test on a sample having a persistent joint with a dip angle varying from 0° to 90° at an interval of 15° using the PFC^2D and (c) the polyaxial test on two samples, one of them having a joint with a dip direction of 0° and the dip angle varying from 0° to 90° at an interval of 15°, and the other sample having a joint with a dip angle of 60° and the dip direction varying from 0° to 90° at an interval of 15° using the PFC^3D. All numerical results show that the JPC and JSC approaches can solve the interlocking problem. Also, they proved to be more consistent with the theory compared to the regular approach. However, the JPC approach leads to a slightly softer joint. Therefore, the JSC approach is suggested for jointed rock modeling using the PFC. The other shortcoming of the SJCM dealt within this paper is its inability to capture the non-linear behavior of the joint closure varying with the joint normal stress. This problem is solved in this paper by proposing a new modified smooth-joint contact model (MSJCM). MSJCM uses a linear relation between the joint normal stiffness and the normal contact stress to model the non-linear relation between the joint normal deformation and the joint normal stress observed in the compression joint normal stiffness test. A good agreement obtained between the results from the experimental test and the numerical modeling of the compression joint normal test shows the accuracy of this new model.     

考虑颗粒破碎效应的堆石料静动力本构模型

为合理反映颗粒破碎对堆石料力学特性的影响,基于试验结果分析,得出了堆石料在压缩和剪切作用下的颗粒破碎特性规律。通过引入压缩破碎和剪切破碎的相关参数,借鉴已有本构模型的合理定义,吸收临界状态理论和边界面理论的优点,发展了考虑颗粒破碎和状态相关的堆石料静动力统一弹塑性本构模型,并阐述了模型参数的确定方法。该模型不仅能够反映堆石料在静力荷载作用下的低压剪胀、高压剪缩、应变软化和硬化等特性,还能够反映在循环荷载作用下应力-应变的滞回特性和残余变形的累积效应。最后为验证模型的合理性,分别对堆石料的静力三轴和循环三轴试验进行了数值模拟预测,结果表明：模型预测与试验数据吻合良好,所提出的本构模型能够合理地描述颗粒破碎对堆石料静动力变形特性的影响。     

Effects of Frequency on the Dynamic Properties of Intact Rock Samples Subjected to Cyclic Loading under Confining Pressure Conditions

A series of laboratory tests was performed to assess the effects of frequency on the dynamic properties of sandstone samples subjected to cyclic loading in the confining stress state. Three levels of confining pressure (2.0, 10.0, and 40.0 MPa) and three sets of frequencies (0.1, 1.0, and 3.0 Hz) were applied for the axial cyclic loading tests by the MTS-815 Rock and Concrete Test System. The results from the cyclic loading tests indicate that frequency has a strong influence on the dynamic deformation, the dynamic stiffness, and the failure mode at the same confining pressure. With an increase in the frequency, the axial strain and the number of cycles at failure increased at the same confining pressure, the residual volumetric strain increased when dilatancy occurred at the same confining pressure, and the number of cycles at failure increased. A new damage variable D was defined that describes the degradation process of sandstone samples upon dynamic cyclic loading. The larger the frequency, the wider the localized band. Sandstone samples subjected to dynamic cyclic loading responded with a significantly higher initial stiffness. The higher the initial stiffness, the greater the frequency.     

Bonding degradation and stress–dilatancy response of weakly cemented sands

The progressive bond breakage of artificially cemented sands induced by shear straining was investigated through conventional isotropically consolidated drained triaxial compression tests. Sand specimens were prepared with a low degree of cementation by adopting a chemical grout. Test results were interpreted in terms of two stress–dilatancy theories for cohesive-frictional materials proposed in literature. The influence of debonding on the stress–dilatancy behaviour of cemented sands was analysed with particular emphasis on the ‘delayed dilatancy’ phenomenon. A bonding degradation curve was determined for each test relating the interparticle cohesion (c) to the magnitude of the total plastic strain vector (ε_d) and a bond degradation rate factor (D_c) was assessed from each curve. The maximum value of interparticle cohesion (c₀) before the onset of bond degradation under shearing was found to correspond with a sharp decrease in the soil stiffness of the specimens. The influence of the effective confining stress (p^′_c) on both c₀ and D_c parameters gathered from each test was also ascertained.     

Analytical theory for one‐dimensional consolidation of clayey soils exhibiting rheological characteristics under time‐dependent loading

This paper presents analytical solutions to the one‐dimensional consolidation problem taking into consideration the rheological properties of clayey soil under variable loadings. A four‐element rheological model is introduced, and different loading types are involved, i.e. constant loading, one‐step loading, triangular loading, rectangular loading, and isosceles–trapezoidal cyclic loading. The differential equations governing consolidation are solved by the Laplace transform. Based on the solutions obtained, the influences of the rheological parameters and loading conditions on the consolidation process are investigated. It has been shown that the consolidation behavior is mainly governed by four dimensionless parameters, a₁, a₂, b, and T_v0. Load shape has a great influence on the rate of consolidation. A decrease either in the modulus of the spring in the Kelvin body or in the viscosity coefficient of independent dashpot will slow down the rate of consolidation. An increase in the viscosity coefficient of the dashpot in the Kelvin body will make the rate of consolidation increase at an early stage but decrease at a later stage. For isosceles–trapezoidal cyclic loading, the consolidation rate in each cycle reaches a maximum at the end of the constant loading phase and the minimum at the end of this cycle. Copyright © 2008 John Wiley & Sons, Ltd.     

Experimental investigation of the effect of grading characteristics on the liquefaction resistance of various graded sands

The liquefaction susceptibility of various graded fine to medium saturated sands are evaluated by stress controlled cyclic triaxial laboratory tests. Cyclic triaxial tests are performed on reconstituted specimens having global relative density of 60%. In all cyclic triaxial tests; loading pattern is selected as a sinusoidal wave form with 1.0 Hz frequency, and effective consolidation pressure is chosen to be 100 kPa. Liquefaction resistance is defined as the required cyclic stress ratio which caused initial liquefaction in 10 cycles during the cyclic triaxial test. The results are used to draw relationship between grading characteristics (e.g. coefficient of uniformity and coefficient of curvature) and the liquefaction resistance of various graded sands. It is found that a relationship between cyclic resistance and any of the size (i.e. D₁₀, D₃₀ or D₆₀) would be more realistic than to build a relation between grading characteristics and the cyclic resistance.     

Tensile Fracture Strength of Brisbane Tuff by Static and Cyclic Loading Tests

This research presents the results of laboratory experiments during the investigation of tensile strength–strain characteristics of Brisbane tuff disc specimens under static and diametral cyclic loading. Three different cyclic loading methods were used; namely, sinusoidal cyclic loading, type I and II increasing cyclic loading with various amplitude values. The first method applied the stress amplitude?cycle number (s–n) curve approach to the measurement of the indirect tensile strength (ITS) and fracture toughness (K _IC) values of rocks for the first time in the literature. The type I and II methods investigated the effect of increasing cyclic loading on the ITS and K _IC of rocks. For Brisbane tuff, the reduction in ITS was found to be 30 % under sinusoidal loading, whereas type I and II increasing cyclic loading caused a maximum reduction in ITS of 36 %. The maximum reduction of the static K _IC of 46 % was obtained for the highest amplitude type I cyclic loading tested. For sinusoidal cyclic loading, a maximum reduction of the static K _IC of 30 % was obtained. A continuous irreversible accumulation of damage was observed in dynamic cyclic tests conducted at different amplitudes and mean stress levels. Scanning electron microscope images showed that fatigue damage in Brisbane tuff is strongly influenced by the failure of the matrix because of both inter-granular fracturing and trans-granular fracturing. The main characteristic was grain breakage under cyclic loading, which probably starts at points of contact between grains and is accompanied by the production of very small fragments, probably due to frictional sliding within the weak matrix.     

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.     

紫坪铺面板坝堆石料颗粒破碎试验研究

采用大型三轴仪对紫坪铺面板坝堆石料进行了单调和循环荷载下的固结排水剪切试验,研究了不同孔隙比情况下颗粒破碎及剪胀的变化规律。试验表明：（1）单调和循环荷载条件下,堆石料颗粒破碎率与塑性功之间存在一致的双曲线关系;（2）峰值应力处剪胀率与颗粒破碎率在半对数坐标中呈近似线性关系;（3）峰值应力处主应力比与相应的剪胀率呈近似线性关系,且上述结果受初始孔隙比的影响不大。研究成果有助于进一步了解堆石料的颗粒破碎特点,对建立复杂应力条件下考虑颗粒破碎和状态相关性的弹塑性本构模型,分析紫坪铺面板堆石坝汶川地震破损机制是十分有益的。     

Influence of Relative Pile-Soil Stiffness and Load Eccentricity on Single Pile Response in Sand Under Lateral Cyclic Loading

The environment prevalent in ocean necessitates the piles supporting offshore structures to be designed against lateral cyclic loading initiated by wave action, which induces deterioration in the strength and stiffness of the pile-soil system introducing progressive reduction in the bearing capacity associated with increased settlement of the pile foundation. A thorough and detailed review of literature indicates that significant works have already been carried out in the relevant field of investigation. It is a well established phenomenon that the variation of relative pile-soil stiffness (K _rs ) and load eccentricity (e/D) significantly affect the response of piles subjected to lateral static load. However, the influence of lateral cyclic load on axial response of single pile in sand, more specifically the effect of K _rs and e/D on the cyclic behavior, is yet to be investigated. The present work has aimed to bridge up this gap. To carry out numerical analysis (boundary element method), the conventional elastic approach has been used as a guideline with relevant modifications. The model developed has been validated by comparing with available experimental (laboratory model and field tests) results, which indicate the accuracy of the solutions formulated. Thereafter, the methodology is applied successfully to selected parametric studies for understanding the magnitude and pattern of degradation of axial pile capacity induced due to lateral cyclic loading, as well as the influence of K _rs and e/D on such degradation.     

Evaluation of Indirect Tensile Strength of Track Ballast Using Weibull Statistics

Iraq is planning to expand and rehabilitate its current railway network, thus demanding huge amounts of proper ballast material. There are three common quarries in Iraq, Sinjaar in the northern sector, Al-Qaim in western desert and Najaf-sea in the middle and southern parts of Iraq. The selection of proper track ballast material is of prime importance in design and construction of railway projects. The single particle-crushing test is a simple indirect tensile test that provides useful data for the selection of the material. Two types of railway ballast materials from (Najaf-sea and Al-Qaim) quarries are commonly used in the construction of railway in Iraq. The single particle-crushing test was performed for various ballast sizes, and the obtained data were analyzed using Weibull analysis. Najaf-sea crushed stones indicate higher tensile strength for all particle sizes compared to corresponding particle sizes of Al-Qaim crushed stone. In addition, an inverse linear relationship had obtained, between tensile strength and particle size with R ² (0.837 and 0.979) for Al-Qaim and Najaf-sea crushed stone, respectively, such relationships are important in evaluating the suitability of the materials in terms of the survival probability     

Experimental study about the influence of cyclic load on the hydraulic conductivity of clay

The hydraulic conductivity k, one of the most important engineering properties of soft clay, plays a great role during the whole life cycle of underwater tunnel. Therefore, it is necessary to systematically study the responses of k to the dynamic load under the background of the great development of geotechnical engineering in the world. In this study, a series of seepage tests after cyclic loading were conducted on reconstituted kaolin clay using a modified hollow cylinder apparatus. The influence of cyclic load on the permeability characteristics of soft clay was illustrated in two aspects. The cumulative axial deformation of clay induced by cyclic loading resulted in the smaller hydraulic conductivity of the specimens, and also, the dynamic load reconstructed the microstructure of clay and made the number of large pores getting decreased and the small pores increased. There was a positive correlation between the deformation of soil and the change of hydraulic conductivity, but the reconstruction effect was irregular with the frequency of dynamic load. The measured k values got affected at the beginning, this phenomenon appropriately explains the positive correlation between the number of cycles of dynamic load and the change of hydraulic conductivity.