Particle breakage evolution of coral sand using triaxial compression tests

Particle breakage continuously changes the grading of granular materials and has a significant effect on their mechanical behaviors.Revealing the evolution pattern of particle breakage is valuable for development and validation of constitutive models for crushable materials.A series of parallel triaxial compression tests along the same loading paths but stopped at different axial strains were conducted on two coral sands with different particle sizes under drained and undrained conditions.The tested specimens were carefully sieved to investigate the intermediate accumulation of particle breakage during the loading process.The test results showed that under both drained and undrained conditions,particle breakage increases continuously with increasing axial strain but exhibits different accumulating patterns,and higher confining pressures lead to greater particle breakage.Based on the test results,the correlations between particle breakage and the stress state as well as the input energy were examined.The results demonstrated that either the stress state or input energy alone is inadequate for describing the intermediate process of particle breakage evolution.Then,based on experimental observation,a path-dependent model was proposed for particle breakage evolution,which was formulated in an incremental form and reasonably considers the effects of the past breakage history and current stress state on the breakage rate.The path-dependent model successfully reproduced the development of particle breakage during undrained triaxial compression using the parameters calibrated from the drained tests,preliminarily demonstrating its effectiveness for different stress paths.     

Particle breakage in triaxial shear of a coral sand

This paper presents a laboratory experimental study to comprehensively investigate the characteristics of particle breakage using numerous triaxial tests on a coral sand. Coral is a highly crushable granular material which fills the gaps between more crushable and less crushable granular materials. The monotonic tests and cyclic tests were terminated at the designated axial strains and the designated cyclic numbers, respectively. The grain size distributions were measured by sieve analyses of the specimens after the triaxial tests were performed. The relative breakage and relative fractal dimension were used to quantify the particle breakage. The cause of particle breakage that increased with increasing isotropic consolidation stress was shown to be isotropic stress. An almost linear increase in particle breakage in relative breakage was found as axial strain increased, whereas the increase in particle breakage in relative fractal dimension showed upward convexity. More particle breakage occurred in denser samples. During consolidation to the identical mean effective stress, the anisotropic stress state played a bigger role in particle breakage than the isotropic stress state, but during shearing particle breakage occurred more sharply in the triaxial tests with the isotropic consolidation to the higher confining pressure. In the cyclic shearing, the particle breakage in relative breakage and relative fractal dimension increased in upward convexity as the cyclic number increased, but in upward concavity with increasing axial strain. A hyperbolic model was proposed to correlate the relative fractal dimension with the relative breakage for use with both monotonic and cyclic tests. In the monotonic tests, a hyperbolic model was proposed to correlate the particle breakage in relative breakage and relative fractal dimension with the plastic work per unit volume. It is proposed that the loading-mode-induced (i.e., monotonic loading and cyclic loading) different mechanism of particle breakage meant that this model could not be applicable in the cyclic tests. The results suggested that the hyperbolic correlation of the particle breakage in relative fractal dimension and the plastic work per unit volume is the most reliable method of interpreting the energy consumption characteristics of particle breakage. This approach takes the fractal nature of soil into consideration. A microscopic view of particle breakage is also effective for observing the evolution of particle breakage.     

模拟堆石料颗粒破碎对强度变形的影响

许多试验事实表明,极高压力下颗粒材料粒径极限分布并非 Hardin 所谓的以 0.074 mm 为截断粒径的均匀分布。通过拓展破碎概念提出了 Hardin 破碎指标修正定义,并用以区分剪切过程中破碎的暂时和永久终止状态。 开展了系列模拟 堆石料固结排水大型三轴试验,提出了系列非线性关系用以描述模拟堆石料的级配、破碎指标以及应力–应变–体变响应变化规律。分析表明：随着围压增加,特征粒径减小而级配指标增加,试样级配变化明显;随着围压增加,峰值（或临界）状态破碎指标增加,相应的应力比和内摩擦角则减小,两种状态下破碎指标与内摩擦角具有唯一对应关系;同一剪切过程中,破碎指标变化率、剪胀率和塑性剪切模量具有非同步变化关系,由此形成了颗粒破碎对于模拟堆石料应力变形影响的复杂性。     

Shear characteristics of calcareous gravelly soil

Because of its angularity, crushability, and high void ratio, calcareous gravelly soil has peculiar geotechnical properties. A series of large-scale direct laboratory shear tests was conducted on calcareous gravelly soil taken from coral reefs in the South China Sea. This study aimed to investigate the shear characteristics of calcareous gravelly soil under conditions of varying gradation, water content, density, and mineral composition. The experimental results revealed the extremely different mechanical properties of calcareous gravelly soil compared to common non-cohesive soil: calcareous gravelly soil has greater apparent cohesion, larger friction angle, and lower softening value than quartz sand. The friction angle increases with dry density, while the apparent cohesion increases with the median particle size (D ₅₀) of the soil. After shear failure, the apparent cohesion decreases significantly from the peak value, but friction angle decreased slightly. Grouting can be employed to reinforce foundations and enhance slopes consisting of calcareous gravelly soil at the early stage of shear failure. This study intends to provide reference information for engineering constructions on coral reefs and report new findings on coarse-grained soil.     

基于离散元法的真三轴应力状态下砂土破碎行为研究

基于可破碎三维离散颗粒模型模拟了一系列常规三轴试验与真三轴试验,研究了砂土在真三轴应力状态下的破碎行为。数值调查主要关注试样的应力应变特性、级配及相对破碎率的演化。随着围压增大,颗粒破碎率增大,试样应变软化特性和剪胀性逐渐减弱,而超过临界高围压后,由于固结中颗粒大量破碎,试样剪胀性反而增强。真三轴试验中,试样偏应力比峰值均随中主应力参数b值增大而减小。由于破碎随b值增加而明显增大,试样剪胀性随b值增大而逐渐减弱。试样内摩擦角φ随围压增大而减小,其演化关系基本满足对数关系;内摩擦角随b值增大先增大后减小,Lade-Duncan准则较为适合描述其变化规律。此外,试样相对破碎率增大的速率随围压和轴向应变增大而逐渐降低,暗示试样最优终极级配的存在,且相对破碎率与试验输入能量之间存在唯一的双曲线关系。     

Distinct element simulations of earthquake fault rupture through materials of varying density

Surface manifestations of earthquake fault rupture are strongly affected by the dilatant response of the soil deposit overlying the bedrock fault displacement. The granular material’s in-situ void ratio and effective confining stress affect its dilatancy, and hence, its stress-strain response and ductility. Distinct element method (DEM) assemblages of 3D, non-spherical particles are prepared with different void ratio distributions, and their dilatancy is characterized using direct shear test simulations. DEM simulations capture the response of sand in centrifuge experiments of earthquake fault rupture propagation. Macro-scale mechanisms of ground deformation and micro-scale mechanisms of shear band formation during dip-slip fault rupture propagation are analyzed through particle rotations, homogenized strains, frictional dissipation, and particle displacements. The brittle and ductile responses of granular media undergoing fault rupture are related to changes in the coordination numbers in each particle assemblage. The deformational characteristics of a metastable fabric in the loosest particle assemblages and a stable fabric in the densest particle assemblages are revealed through the accumulation of energy dissipated through friction. The normalized strong contact forces are also greater in magnitude in the loosest particle assemblages and greater in number in the densest assemblages.     

Influence of particle shape on the shear strength and dilation of sand-woven geotextile interfaces

The influence of particle shape on the mechanical behavior of sand-woven geotextile interfaces over a wide domain of soil density and normal stress is studied. A uniformly graded angular fine sand, and a blend of well rounded glass beads with identical particle size distributions, were selected as granular material. Experiments revealed the impact of particle shape on peak and residual friction angles as well as the maximum dilation angle of interfaces between both granular media and woven geotextile. It was observed that the residual friction angles of interfaces between angular sand/glass-beads and woven geotextile are very similar to the residual friction angles of angular sand and glass-beads in soil–soil direct shear test. It is understood that the peak friction angle and maximum dilation angle of angular sand-woven geotextile were slightly lower than corresponding values for angular sand in soil–soil direct shear test. While the peak friction angle and maximum dilation angle of angular sand-woven geotextile interface decrease with the increase in normal stress, experiments showed that these factors are insensitive to normal stress for glass beads-woven geotextile interfaces, at least for the range studied herein. All interfaces with woven geotextile as the contact surface exhibit an abrupt loss of shear strength in the post-peak regime of behavior. Finally, a unified stress-dilation law for the angular sand-woven geotextile, glass beads-woven geotextile, and angular sand-roughened steel interfaces is obtained.     

Influence of Freeze-Thaw Action on Deformation-Strength Characteristics and Particle Crushability of Volcanic Coarse-Grained Soils

The objective of this study is to evaluate the effect of freeze-thaw action on the deformation-strength characteristics of crushable volcanic coarse-grained soils, wherein significant particle breakage occurs even under relatively low stress levels and saturated conditions. A series of monotonic triaxial compression tests was performed for volcanic coarse-grained soils under various freeze-thaw histories. On the basis of the test results, we examined the above-mentioned effect and the relationship between the degree of particle breakage and the freeze-thaw history. The results indicate that the degree of particle breakage under consolidation and shear increased with freeze-thaw action; and consequently, the strength and the stiffness of the soils decreased with an increase in the number of freeze-thaw cycles. Moreover, to examine the influence of freeze-thaw action on the single-particle hardness of volcanic coarse-grained soils, single-particle crushing tests were conducted. The test results revealed that volcanic soil particles become more fragile after being exposed to freeze-thaw action, and as a result, the degree of particle breakage increases. These results indicate that the freeze-thaw action has a strong influence on the deformation-strength characteristics of crushable volcanic soils in terms of an increase in particle breakage, even if the soils lack frost-heave characteristics.     

考虑颗粒破碎影响的粗粒土的剪切强度理论

由于粗粒土的粒径相差很大,通过剪切试验测量粗粒土的剪切强度很麻烦,且剪切试验费时费力、试验数据离散性大;另外,已有剪切强度经验公式中的参数没有明确的物理含义,工程应用中难以确定。本文根据颗粒破碎的分形模型,揭示单颗粒破碎强度的尺寸效应,假设剪切强度是颗粒接触面上的摩擦力,导出用正应力幂函数表示的粗粒土剪切强度公式,幂函数的指数是颗粒破碎分维的函数,并采用垃圾炉渣的颗粒破碎分维和剪切强度试验结果进行验证。     

石英砂砾破碎过程中粒径分布的分形行为研究

荷载作用下粒状土的颗粒破碎改变土的粒径分布,从而影响其力学特性。试验证据显示随着颗粒破碎的增加,任何初始分布的土粒都将趋向一种自相似的分形分布。为了揭示土的粒径分布的分形转变机制,利用侧限压缩试验研究高压应力下石英砂砾的粒径分布演化规律和颗粒破碎特性,基于分形模型和粒径分布实测数据研究破碎过程中粒径分布的分形行为。研究发现:颗粒破碎增长导致粒状土趋向分形分布的过程与颗粒破碎量密切相关,并可以通过增大的分形维数来描述。尽管石英砂砾的初始分布和粒径有所不同,分形维数大于2.2的粒径分布实测数据均展示了较为严格的自相似性,因而该数值可作为分形分布的分形维数下限值。研究还发现:相同破碎状态下Hardin相对破碎率小于Einav相对破碎率,但二者对应力和体应变的响应规律是一致的。颗粒破碎发展至粒径分布成为分形分布时,体应变与相对破碎率的比值将保持恒定,并且受初始分布的均匀性和颗粒大小的影响很小。这一特点可用于分形分布的识别,并意味着试验中如果粒径分布是分形的,则无须为了粒径分析而终止试验,只需测量到体应变就可估计相对破碎率。     

Bearing capacity of surface circular footings on granular material under low gravity fields

Low gravity fields have been simulated through magnetic acceleration to conduct experimental study on bearing capacity of circular footings on a type of crushable planetary regolith simulant,which has comparable density and particle size distribution of lunar soil.The load-settlement responses of surface spread footings are obtained by investigating the relative density,footing size and gravity effects.Applying the hyperbolic asymptote method,normalised foundation stiffness and ultimate bearing capacity are obtained by curve fitting and predicted by power functions using multivariate nonlinear regression.The results show that the nonlinear gravity effect is not negligible,related to stress condition,soil dilatancy and mobilised friction angle.A cone penetration test(CPT)-based method for prediction of bearing capacity is proposed with correlations between ultimate bearing capacity of footings and shallow penetration stiffness of CPTs,avoiding the uncertainties of soil property estimations.Analyses of allowable bearing capacity and footing influence zone in consideration of footing size and gravity effects could therefore improve the design of shallow foundations on the Moon and Mars,and provide new understandings and potential implications to the bearing capacity of shallow foundations on crushable granular material in both terrestrial and extraterrestrial geotechnical engineering.     

On the Relationship between Particle Breakage and the Critical State of Sands

Ring shear and shear box tests were used to investigate the relationship between volume change and particle breakage during the shearing of two sands. One sand was a carbonate sand which was sheared under a high confining stress to examine whether, in the region of compressive shearing behaviour due to particle breakage, the breakage would ever cease and the soil reach a stable grading. The other sand tested was a quartz sand that was sheared at low confining stresses, to investigate whether a dilatant sand would also be subject to particle breakage. In both cases breakage was found to continue to very large strains, with no evidence of a stable grading being reached within the range of strains used. While the breakage was very small for the quartz sand it was large for the carbonate, emphasising that any definition of a critical state by means of conventional triaxial or shear box testing would be approximate only, because of the limited strains that they allow.     

Insight on bulk shear strength parameters of clay using discrete element approach incorporating physics-based interparticle force model

This paper aims to provide insight on factors affecting the bulk shear strength parameters of clay, i.e., the cohesion and internal friction as well as the effects of memory of preconsolidation pressure. A unique Discrete Element Method (DEM) model is built on platy particles with customized particle interaction force model. The particle interaction force model considers non-contact forces (such as the long-range electrostatic repulsion, short-range van der Waals attraction) as well as the direct contact force. The long-range electrostatic forces are calibrated by measurement with Atomic Force Microscope (AFM). Parameters for direct particle contacts of the regular DEM contact model, such as the contact stiffness and the friction coefficient, are calibrated by use of experimental consolidation and direct shear testing data. Computational simulations are conducted on digital clay specimen subjected to virtual direct shear tests. The predicted experimental responses of the digital specimens are consistent with typically observed in experiments including the shear stress-shear strain relationship, volumetric contraction and dilation, shear band formation, etc. From the stress–strain curves, the soil strength parameters are obtained with common experimental criteria. The DEM simulation results show that higher preconsolidation pressure drives more particles to overcome non-contact force into direct contacts and consequently bonding by van der Waals force. Consequently, the bulk cohesion of clay increases with increasing preconsolidation pressure. The results show that bulk cohesion strength is mainly attributed to the attractive interparticle force as well as the interlocking of platy particle, while the bulk internal friction angle is affected by the particle friction coefficient and particle fabric. Overall, the simulation results indicate the experimentally observed macroscopic shear strength parameters c and φ are linked to the microscope characteristics of soil particles and their mutual interactions. The results offer insight on the microscopic properties of particles on the bulk macroscopic strength behaviors. Besides, this work demonstrates a new strategy for simulation-based prediction of bulk soil strength parameters, by incorporating microscale characterization of the interparticle interactions and particle fabric into the particle-based DEM model.     

A critical state based viscoplastic model for crushable granular materials

?Experimental studies have confirmed that the critical state of a granular material varies with alteration in granular fabric, particle shape and grain size. On the other hand, granular materials demonstrate significant strain rate dependency in the presence of particle crushing. While the first feature is well explored, the strain rate effects on the crushability of granular material and consequent critical state alteration are less ventured. This study highlights the strain rate dependence of the critical state of crushable granular materials like sand. A rate-dependent model is proposed bridging the macro and microscopic understanding. The model follows a consistent viscoplastic formulation without using any overstress function. The proposed model considers various loading rate effects at different porosities, confinements and pore water drainage conditions. Further, it can predict the strain rate-dependent particle crushing and dilation features that affect the critical state of granular materials. The model has been validated by comparing its responses with both the experimental and discrete particle simulations for drained and undrained triaxial conditions. An implicit stress return integration scheme is devised to enable accurate numerical response from the model. ? Finally, a parametric study is presented that envisages the evolution of critical state due to coupled strain rate and particle crushing effect.     

土的动力Hardin-Drnevich模型小应变特性及其阈值应变研究

以Hardin-Drnevich模型的双曲骨架曲线为基础,采用Masing准则构造其滞回圈,形成小应变土体动力耗散函数。然后从热力学基本定律出发,分析其对应的屈服面及能量耗散特性。发现筑坝堆石类无黏性材料的动力特性存在2个阈值应变,定义为第一和第二阈值应变。两个阈值应变将土体动力特性分成3段。当土体的动应变小于第一阈值应变时,土体屈服为常摩擦系数的摩擦耗散控制;当土体动应变介于第一、第二阈值应变之间时,土体屈服为变摩擦系数的摩擦耗散控制;当土体动应变大于第二阈值应变时,土体屈服除摩擦机制外还存在剪胀等土体结构改变的效应。土体的2个阈值应变主要受最大动剪切模量系数及指数控制,无黏性土的摩擦角对其也有一定影响。两个阈值应变均随最大动剪切模量系数及指数的增大而减小。     

锚杆加固散粒体的作用机制研究

采用细观数值模拟的方法研究岩土工程中散粒体锚杆加固的作用机制,基于随机模拟技术建立加锚散粒体的三维随机颗粒模型,采用颗粒形状系数控制颗粒表面的不均匀起伏程度,基于修正的增广Lagrangian算法的非线性接触算法模拟颗粒之间、颗粒与锚固体、颗粒与承托结构的相互接触,颗粒的物理力学性质服从Weibull概率分布,采用细观损伤软化模型描述颗粒的变形和破碎。分别建立散粒体和加锚散粒体的三轴数字试样,采用位移加载来进行不同围压下的常规三轴剪切试验,研究不同加锚密度对散粒体工程力学特性的影响。数值模拟结果表明:锚杆加固的作用机制为锚固体与颗粒紧密接触、相互咬合形成摩擦阻力,承托结构形成对颗粒体的径向助力,锚杆与其附近的颗粒形成锚固区;锚杆加固能显著提高散粒体的抗剪强度和整体性,峰值主应力差提高37.8%～88.8%,初始模量提高37.4%～93.2%,内摩擦角提高13.3%～24.2%。     

珊瑚礁砂砾料力学行为与颗粒破碎的试验研究

珊瑚礁砂砾石是中国南海岛礁建设的主要填料,因为特殊的生物成因和多孔隙的颗粒结构,极易产生颗粒破碎。对取自南海某岛礁的珊瑚礁砂砾石填料开展了大型压缩试验、三轴排水剪切试验和三轴不排水剪切试验,研究了压缩指数、杨氏模量、剪胀和强度等基本工程力学指标与颗粒破碎的变化规律。在相同的压缩作用下,疏松试样比密实试样的颗粒破碎程度更大。颗粒破碎程度随着压力的增大而显著增大,导致珊瑚礁砂砾料的压缩模量和杨氏模量随压力的增大增幅不明显,峰值摩擦角和临界状态摩擦角随压力的增高而显著降低。颗粒破碎过程具有明显的应力路径和应力历史依赖性,有无预压作用的相同密度的试样表现出显著不同的压缩特性,相同密度和初始压力的试样在排水和不排水剪切下也表现出明显不同的剪胀和强度特性。峰值摩擦角依赖于应力路径和颗粒破碎的演化过程;临界状态摩擦角与最终的颗粒破碎指标值有较好的相关性,与颗粒破碎的产生过程无关。     

基于微观图像处理技术的土体三轴试验颗粒流模型

以扫描电子显微镜拍摄获取的粉土图片为研究对象,把数字图像处理技术引入土体的细观结构观察和定量分析中,求解土颗粒孔隙度、颗粒粒径及颗粒形状等微观颗粒组成参数,为建立颗粒流离散元细观模型提供物理参数。在此基础上,对土样的三轴试验进行模拟,并研究细观力学参数(包括:摩擦系数、平行连接强度及刚度比)对宏观性质的影响。研究表明:通过颗粒簇模型和颗粒排斥法可以实现土体微观颗粒形状和粒径组成模拟。所建立的颗粒流模型能够很好地拟合土体的应力-应变关系和模拟试验中的剪缩-剪胀现象;摩擦系数、平行连接强度和刚度比对土体的初始模量和残余强度的影响规律有所不同;通过监测孔隙率的变化,可以反映土体剪切带发展的过程。     

Particle breakage of granular materials during sample preparation

Particle breakage is commonly observed in granular materials when subjected to external loads. It was found that particle breakage would occur during both sample preparation and loading stages. However, main attention was usually paid to the particle breakage behaviour of samples during loading stage. This study attempts to explore the breakage behaviour of granular materials during sample preparation. Triaxial samples of rockfill aggregates are prepared by layered compaction method to achieve different relative densities. Extents of particle breakage based on the gradings before and after test are presented and analysed. It is found that particle breakage during sample preparation cannot be ignored. Gradings after test are observed to shift away from the initial grading. Aggregates with larger size that appear to break are more than the smaller-sized ones. Irrespective of the initial gradings, an increase in the extent of particle breakage with the increasing relative density is observed during sample preparation.     

基于弯剪分离的塑性铰支墙抗震性能试验研究

钢筋混凝土剪力墙是框架-剪力墙结构体系重要的抗震构件,可以为结构提供较大的抗侧刚度,但是在实际震害中发现墙体底部易发生不可修复的损伤。针对这一问题,提出一种基于弯剪分离的剪力墙,旨在分别设计其抗弯与抗剪构件的基础上有效控制墙体的损伤,并通过选择合适的消能器作为其抗弯构件以增强耗能能力,进一步提高抗震性能。设计并制作了3个1/3缩尺剪力墙,进行拟静力试验,其中1个为普通钢筋混凝土剪力墙,另外2个分别为采用金属型消能器和摩擦型消能器作为抗弯构件的塑性铰支墙。试验结果表明：以不同消能器作为抗弯构件的塑性铰支墙的受力性能主要由消能器控制,具有明确简单的力学模型;消能器屈服后集中产生塑性变形,拥有良好的损伤控制能力和滞回耗能能力,且震后易于对消能器进行快速修复和更换,实现“震后可恢复”的目的。