Particle breakage and deformation of carbonate sands with wide range of densities during compression loading process

In this technical note, evolutions of the particle size distribution, particle breakage, volume deformation and input work of carbonate sands with varying relative densities were investigated through performing a series of one-dimensional compression tests. Loading stress levels ranged from 0.1 to 3.2 MPa. It was found that the initial relative density could greatly affect the magnitude of particle size distribution, particle breakage, volume deformation and input work. Particularly, it was observed that the specimen at a lower relative density underwent much more particle breakage than that at a higher relative density. This could be attributed to the change of the coordination number with the initial density. However, a unique linear relationship between the particle breakage and input work per volume could be obtained, which is independent of the initial relative density.     

循环荷载作用下斜长花岗岩弹性模量演化规律

通过MTS815岩石力学试验机开展斜长花岗岩循环荷载试验,揭示循环次数、围压、含水率对斜长花岗岩弹性模量变化规律的影响,分析饱和与天然试样应力功、弹性应变能、耗散能随循环次数的演化规律。根据能量演化规律将岩石压缩变形破坏过程划分为4个阶段,研究各阶段切线模量与耗散能之间的关系。试验结果表明:（1）同一个应力水平切线模量随循环次数呈先增大后降低的趋势,其降低幅度随循环次数与应力水平增加而增大。（2）围压抑制了裂纹扩展,随围压增加切线模量弱化幅度减小。（3）饱和试样比天然试样切线模量弱化幅度大,说明水的存在加剧饱和试样内部结构损伤。（4）耗散能增加是引起切线模量弱化的内在因素,两者的变化规律呈现出很好的相关性。     

粗粒土的破碎耗能计算及影响因素

粗粒土的颗粒破碎直接改变了土体本身结构,对粗粒土的剪胀和内摩擦角都会产生影响。在土体剪切过程中,体积应力和剪切应力在体积应变和剪切应变上做功,这部分能量在剪切过程中转化为颗粒的弹性储能、颗粒间的摩擦耗能、颗粒剪胀时对外做功和颗粒破碎耗能4部分。准确计算剪切过程中粗粒土破碎耗能的目的是：从能量角度分析颗粒破碎对土体本构关系的影响,为建立考虑颗粒破碎的粗粒土本构关系创造条件。通过分析粗粒土的常规三轴试验数据,计算得到了剪切过程中的粗粒土破碎耗能。计算结果表明,常规三轴试验条件下粗粒土破碎耗能主要受固结应力、土体摩擦系数M等因素的影响。     

加卸荷条件下灰岩能耗变化规律试验研究

对灰岩开展单轴、常规三轴与峰前卸荷试验,对比分析不同应力路径下灰岩变形过程的能量变化特征。试验分析表明,灰岩加荷破坏和卸荷破坏的能量变化规律存在明显差异。由于围压抑制了裂纹的扩展,与单轴压缩破坏相比,常规三轴压缩试验灰岩吸收的总能量 和积蓄的弹性能 更多。常规三轴试验灰岩积蓄的弹性能 在峰值强度前一直增加,而卸荷破坏的弹性能 在卸荷开始后基本不变,说明卸荷破坏释放的弹性能 主要是在加荷阶段累积完成的,岩体所处的初始地应力状态决定了其破坏的能量释放量。加荷和卸荷应力路径下,灰岩临近破坏点耗散能 都快速增加,但是卸荷破坏耗散能 增速远大于加荷破坏耗散能增速,耗散能的迅速增加表明岩石破坏的发生。随着围压升高,灰岩吸收的总能量 和储存的弹性能 逐渐升高。随着卸荷速度增加,灰岩吸收的总能量 、储存的弹性能 和耗散的应变能 逐渐减小。     

Particle breakage of uniformly graded carbonate sands in dry/wet condition subjected to compression/shear tests

The behaviour of a granular material is primarily affected by its particle size distribution (PSD), which is not necessarily a soil constant as assumed in traditional soil mechanics. The PSD may change over time due to mechanical as well as environmental actions. In this study, a series of ring shear tests and one-dimensional compression tests were completed on carbonate sand, in both dry and saturated conditions. Samples were prepared with different initial uniform gradings, to investigate: (1) the influence of the saturation state and initial grading on mechanical and deformational behaviour of carbonate sands and (2) the evolution of the PSD as a result of breakage. The ring shear tests show that the residual friction angle remains almost constant, but dilatancy reduces with increasing saturation degree. In the one-dimensional compression test, the yield stress decreases with increasing saturation degree, but the compressibility (as defined by C_c) remains almost constant, irrespective of the saturation state. Moreover, saturated samples suffer more breakage than dry samples during ring shear tests, while there is no obvious effect of saturation state on particle breakage in one-dimensional compression. A recently proposed PSD model with only two parameters (λ_p and κ_p) is employed to model the evolution of PSD, as it can more broadly capture the whole PSD throughout the breakage process than existing breakage indices. Test results demonstrate that parameter λ_p is linearly related to Einav’s breakage index \( B_{\text{r}}^{*} \) and is dependent on initial grading, but independent of test mode. Parameter κ_p is in power relationship with \( B_{\text{r}}^{*} \) and is independent of initial grading or test mode. The evolution of parameters λ_p and κ_p is related to the input work for both ring shear and compression tests, with λ_p being hyperbolically related to input work and κ_p in power relationship with input work. Using such an evolution law provides an alternative approach to capture the effects of particle breakage in constitutive models.

     

Effects of particle size on crushing and deformation behaviors of rockfill materials

Strength and deformation behaviors of rockfill materials,key factors for determining the stability of dams,pertain strongly to the grain crushing characteristics.In this study,single-particle crushing tests were carried out on rockfill materials with nominal particle diameters of 2.5 mm,5 mm and 10 mm to investigate the particle size effect on the single-particle strength and the relationship between the characteristic stress and probability of non-failure.Test data were found to be described by the Weibull distribution with the Weibull modulus of 3.24.Assemblies with uniform nominal grains were then subjected to one-dimensional compression tests at eight levels of vertical stress with a maximum of 100 MPa.The yield stress in one-dimensional compression tests increased with decreasing the particle size,which could be estimated from the single-particle crushing tests.The void ratio-vertical stress curve could be predicted by an exponential function.The particle size distribution curve increased obviously with applied stresses less than 16 MPa and gradually reached the ultimate fractal grading.The relative breakage index became constant with stress up to 64 MPa and was obtained from the ultimate grading at the fractal dimension(a?2:7).A hyperbolical function was also found useful for describing the relationship between the relative breakage index and input work during one-dimensional compression tests.     

坝体填筑料压缩特性及影响因素分析

堆石料的压缩性直接关系工程的安全问题,对某一抽水蓄能电站坝体填筑料开展多组大型侧限压缩试验,结果表明,堆石料的压缩模量较大、压缩指数很小。只有在应力超过颗粒破碎应力以后堆石料压缩曲线才会发生较大程度的下降,且认为颗粒破碎应力是堆石料发生弹塑性变形的转折点,对于不同初始孔隙比的同一种堆石料,在极高的应力状态下它们的压缩曲线会聚到唯一的极限压缩曲线LCC。压缩曲线中堆石料的卸荷回弹量非常小,表明其是弹性变形。不论何种加载路径材料的初始级配决定了堆石料的最终压缩状态,且随着母岩强度的增加、初始孔隙比或者泥岩含量的减小堆石料的压缩性减小。     

Modeling the effect of wetting on the mechanical behavior of crushable granular materials

It is well known that the compressibility of crushable granular materials increases with the moisture content,due to the decrease of particle strength in a humid environment.An existing approach to take into account the effect of grain breakage in constitutive modeling consists in linking the evolution of the grain size distribution to the plastic work.But how the material humidity can affect this relationship is not clear,and experimental evidence is quite scarce.Based on compression tests on dry and saturated crushable sand recently reported by the present authors,a new non-linear relationship is proposed between the amount of particle breakage and the plastic work.The expression contains two parameters:(1)a material constant dependent on the grain characteristics and(2)a constant depending on the wetting condition(in this study,dry or saturated).A key finding is that the relationship does not depend on the stress path and,for a given wetting condition,only one set of parameters is necessary to reproduce the results of isotropic,oedometric,and triaxial compression tests.The relationship has been introduced into an elastoplastic constitutive model based on the critical state concept with a double yield surface for plastic sliding and compression.The breakage ratio is introduced into the expression of the elastic stiffness,the critical state line and the hardening compression pressure.Incremental stress-strain computations with the model allow the plastic work to be calculated and,therefore,the evolution of particle crushing can be predicted through the proposed non-linear relationship and reintroduced into the constitutive equations.Accurate predictions of the experimental results in terms of both stress-strain relationships and breakage ratio were obtained.     

弹性地基条件下狭窄煤柱岩爆的突变理论分析

将未采煤层视为弹性地基条件下,运用maple9.5符号运算软件解得岩梁的挠曲线方程。根据能量守恒原理得到的功、能增量平衡关系式,求得岩梁–煤柱系统作准静态形变时的平衡方程--折迭突变模型平衡方程;用折迭突变总势能函数所作的稳定性判别表明,岩爆前兆阶段岩梁–煤柱系统处于不稳定平衡状态;煤柱岩爆的条件是Cook刚度准则,该准则可以动态地用煤柱形变增大时所需外界的能量输入率趋于0来表示;计算了煤柱岩爆地震能释放量,阐明煤柱岩爆机制是由于岩梁弹性能释放量超过峰后软化煤柱形变所耗的能量。通过岩梁弹性势能变化率曲线和煤柱耗能曲线,以几何形式描述了所得研究结果。计算表明,未开采煤层刚度变化对岩梁的等效刚度影响微弱。工作面开挖和采空区增大,将显著减小岩梁刚度Ke,对煤柱岩爆有重要影响。     

南海钙质砂宏细观破碎力学特性

针对取自我国南部某海域的钙质砂样本,做了以下两方面工作：一是通过电子显微镜获取了钙质砂颗粒的几何投影图像,利用图像处理技术对图形进行黑白二值化处理,获取单元颗粒形状轮廓边界,使用圆度和粗糙度2个参数对钙质砂的颗粒形状进行定义和量化。二是通过不同围压下的三轴固结排水剪切试验及试验前后的颗分测量对比,研究了颗粒破碎对钙质砂的变形、强度、能量耗散等特性的影响。研究表明,大粒径钙质砂（粒径大于2.0 mm）和小粒径钙质砂（粒径小于0.5 mm）形态比较接近圆形、颗粒表面相对光滑;相比而言,中间粒径（粒径介于0.5～2.0 mm之间）钙质砂形状较不规则,表面棱角较多。钙质砂在三轴排水剪切过程中发生颗粒破碎,试样向着级配均匀的方向发展。随着初始围压的增大,颗粒破碎程度加大,土样整体剪胀趋势减小,而破碎引起的能量耗散增加。而在高围压（初始围压为600 kPa）剪切过程中,仅考虑摩擦耗散,以及同时考虑摩擦、体积耗散两种情况下,计算得到的最大颗粒破碎耗散分别可达土样总输入塑性功的25%和18%。     

页岩单轴压缩应力-应变特征及能量各向异性

层理对页岩力学性质和应变能的积聚和耗散具有重要影响,以不同层理面角度下龙马溪组页岩为研究对象,开展电镜扫描试验和单轴压缩试验,研究起裂、扩容和峰值特征点的应力-应变、弹性模量和泊松比的各向异性特征,分析其页岩变形破坏过程中输入应变能、可释放弹性应变能和耗散应变能的变化规律,揭示输入应变能与层理面角度和抗压强度的关系。结果表明：龙马溪组页岩脆性矿物含量达到72.58%,微观结构各向异性明显;随层理面角度增加,起裂、扩容和峰值特征点的应力和应变都先减少后增大,在 30°时均达到一个最低值,总体上呈现两边高、中间低的U型变化规律;随层理面角度增加,起裂、扩容和峰值特征点的输入应变能、可释放弹性应变能和耗散应变能也先减少后增大,在 30°时均达到一个最低值;各特征点的应力、应变和应变能各向异性敏感性明显,0°≤ ≤30°和30°≤ ≤60°内各向异性的敏感性大于60°≤ ≤90°;起裂应力和扩容应力均与峰值应力呈线性相关,同时峰值应变能与抗压强度存在相应的二次非线性关系,这为页岩气钻井、储层压裂改造和井壁稳定性预测预警提供了根据和参考。     

考虑颗粒破碎影响的粗粒土本构关系

粗粒土在较大的应力条件下容易产生颗粒破碎现象,而现有的大多数模型都没有考虑剪切过程中的颗粒破碎。模型将塑性功引入土体受力变形过程的能量方程中,推导得到土体流动法则。采用直线型屈服轨迹和非相关联流动法则,利用不排水应力路径计算得到硬化函数,建立了一个考虑颗粒破碎的粗粒土本构模型。对比分析表明：该模型对粗粒土在各种围压下的应力-应变和体应变计算结果与试验曲线吻合较好。     

固体颗粒破碎的分维演化规律

固体颗粒破碎后的粒径分布符合分形模型,颗粒破碎程度采用粒径分布的分维表示。本文采用垃圾炉渣的颗粒破碎试验,统计计算炉渣颗粒破碎的分维。收集总结了岩石颗粒破碎分维随破碎应力和破碎能量的变化规律,颗粒破碎的分维是变化的,随着破碎应力和破碎能量增加而增加,颗粒完全破碎后的粒径分布的分维趋于定值,为2.6左右。将颗粒破碎过程中变化的分维称为颗粒破碎的“似分维”,简称分维;分维的极限值称为“真分维”。结合颗粒破碎概率的Weibull统计理论,建立了颗粒破碎“似分维”与破碎应力和破碎能量的相关关系。     

钙质砂一维压缩回弹过程中声发射特征试验研究

为了揭示钙质砂在一维压缩回弹作用下的压缩变形、颗粒破碎特性以及声发射规律,对钙质砂进行了3种相对密实度下不同粒组的一维压缩回弹实验和声发射实验。通过对不同粒组、不同相对密实度的钙质砂进行一维压缩实验和同步的声发射实时监测,获得其压缩、回弹和声发射特性,最后通过筛分获得实验后的颗粒粒径分布,得出相对破碎势B_r。实验结果表明:钙质砂的压缩变形由颗粒位置调整和破碎两部分组成,其中颗粒破碎是产生压缩变形的主要因素,回弹曲线近似一条直线,表明压缩变形为不可恢复的塑形变形;压力相同时颗粒粒径越大,相对破碎势B_r越大。颗粒形状不同致使颗粒间填充作用与嵌合作用不同,影响颗粒的滑移与重排列,进而影响颗粒的压缩变形。两种砂的声发射计数率随粒径增大而增大,且都集中出现在800~3200 kPa的压缩阶段,钙质砂的压缩变形及破碎特性与其声发射特征具有一致性,钙质砂声发射计数率与时间关系曲线和应力与时间关系曲线吻合较好,可通过声发射计数率与时间关系曲线来反映钙质砂的力学特性。钙质砂存在一个声发射事件最少的“临界孔隙比”,本次实验中1~2 mm钙质砂临界孔隙比为1.33~1.41,试样的初始孔隙比偏离该临界值时,声发射活动会有不同程度提高。     

颗粒破碎对钙质砂压缩特性影响的试验研究

利用南海钙质砂和阿拉伯湾钙质砂,进行侧限压缩试验,对其压缩特性进行分析,得到了相应的压缩指数;采用相对破碎率为度量指标,评价了钙质砂在压缩试验过程中的颗粒破碎情况。同时根据试验数据得到了不同初始相对密实度的砂样的塑性功,通过建立塑性功与相对破碎率以及塑性功与压缩指数之间的关系,探讨了颗粒破碎对钙质砂压缩特性的影响。研究显示,在本次试验条件下,颗粒破碎是导致钙质砂压缩变形的主要因素,钙质砂的中值粒径以及碳酸钙含量等因素对其颗粒破碎程度有明显影响;钙质砂的相对破碎率与其输入的塑性功有关,并且受到初始相对密实度的影响,采用相对密实度进行归一化后,两者呈现较好的幂函数关系;通过建立钙质砂压缩指数与塑性功之间的关系,进一步建立了钙质砂的压缩指数与相对破碎率之间的关系,经相对密实度归一化后,两者也呈现幂函数规律,此规律可以用于评价颗粒破碎对钙质砂压缩特性的影响。     

An elastoplastic constitutive model for frozen saline coarse sandy soil undergoing particle breakage

The mechanical property of frozen saline sandy soil is complicated due to its complex components and sensitivity to salt content and confining pressure. Thus, a series of triaxial compression tests were carried out on sandy samples with different Na₂SO₄ contents under different confining pressures to explore the effects of particle breakage, pressure melting, shear dilation and strain softening or hardening. The test results indicate that the stress–strain curves exhibit strain softening/hardening phenomena when the confining pressures are below or above 6 MPa, respectively. A shear dilation phenomenon was observed in the loading process. With increasing confining pressure, the strength firstly increases and then decreases. By taking into consideration the changes between the grain size distributions before and after triaxial compression tests, a failure strength line incorporating the influences of both particle breakage and pressure melting is proposed. In order to describe the deformation characteristics of frozen saline sandy soil, an elastoplastic incremental constitutive model is established based on the test results. The proposed model considers the plastic compressive, plastic shear and breakage mechanisms by adopting the non-associated flow rule. The breakage mechanism can be reflected by an index related to the initial, current and ultimate grain size distributions. The hardening parameters corresponding to compressive and shear mechanisms consider the influence of particle breakage. Then the effect of particle breakage on both the stress–strain and volumetric strain curves is analyzed. The calculated results fit well with the test results, indicating that the developed constitutive model can well describe the mechanical and deformation features of frozen saline sandy soil under various stress levels and stress paths. In addition, the strain softening/hardening, contraction, high dilation and particle breakage can be well captured.

     

炭质页岩的颗粒破碎及其路用性能试验研究

为综合评估炭质页岩的路用性能,充分认识炭质页岩的颗粒破碎行为,测试了炭质页岩块在循环压实过程中各粒组含量的演化规律,结合室内击实试验阐述了颗粒破碎对炭质页岩击实性能的影响,确定了最佳填筑级配,并依据最佳级配进行三轴湿化变形试验,从颗粒破碎角度分析了炭质页岩填料湿化变形的变化规律,最后对炭质页岩现场填筑效果进行了验证。结果表明：炭质页岩压实过程经历结构调整、颗粒破碎、压缩变形3个阶段,形成的相对稳定级配结构为其用作路堤填料提供了基础;填料最大干密度形成机制受颗粒破碎过程中粒径为20～40 mm与粒径小于2 mm颗粒含量变化的影响较大,随粗料含量增加,试样相对破碎率线性增大,最大干密度呈先增大后减小变化,最优粗料含量约为70%;湿化变形是混合料颗粒破碎的外在表现,浸水湿化后混合料强度降低约40%,可采用相对破碎率 B_r 预估混合料遇水产生的湿化变形量,并建立了相对破碎率与围压、应力水平间的数学关系式;现场填筑过程中路堤压实度检测与沉降观测表明,炭质页岩路堤的最佳铺松厚度约为40 cm。     

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.     

考虑颗粒强度尺寸效应的原型堆石料破碎特性研究

高土石坝中,堆石体颗粒破碎是导致坝体变形的主要因素之一。但是由于原型坝料的颗粒尺寸较大,其破碎程度难以直接通过室内试验度量,因此通常要将原型级配缩尺为60 mm以下的小粒径级配堆石料,然后才能进行室内试验。而由于原型和试验级配差异较大,导致试验测得的参数往往和原型坝料实际参数有较大差异,因而影响了原型坝料力学特性的深入研究。这里提出了一种新的实时预测原型坝料破碎的方法。首先在颗粒尺度上,基于单粒强度的Weibull分布理论和颗粒分形破碎理论,阐述了原型堆石料级配演化的推求过程;然后通过单粒强度试验测得了相关参数,并与三轴试验测得的试样级配曲线对比,验证了参数选取的合理性;之后分析了颗粒强度离散程度对于原型坝料级配曲线形状的影响;最后,讨论了加载过程中原型级配和试验级配堆石体的相对破碎参量和受力状态的关系。     

On the role of particle breakage in the shear failure behavior of granular soils by DEM

This article presents a fundamental study on the role of particle breakage on the shear behavior of granular soils using the three‐dimensional (3‐D) discrete element method. The effects of particle breakage on the stress ratio, volumetric strain, plastic deformation, and shear failure behavior of dense crushable specimens undergoing plane strain shearing conditions are thoroughly investigated through a variety of micromechanical analyses and mechanism demonstrations. The simulation of a granular specimen is based on the effective modeling of realistic fracture behavior of single soil particles, which is demonstrated by the qualitative agreement between the results from platen compression simulations and those from physical laboratory tests. The simulation results show that the major effects of particle breakage include the reduction of volumetric dilation and peak stress ratio and more importantly the plastic deformation mechanisms and the shear failure modes vary as a function of soil crushability. Consistent macro‐ and micromechanical evidence demonstrates that shear banding and massive volumetric contraction depict the two end failure modes of a dense specimen, which is dominated by particle rearrangement–induced dilation and particle crushing–induced compression, respectively, with a more general case being the combination and competition of the two failure modes in the medium range of soil crushability and confining stress. However, it is further shown that a highly crushable specimen will eventually develop a shear band at a large strain because of the continuous decay of particle breakage. Copyright © 2011 John Wiley & Sons, Ltd.