应力路径和干湿状态对堆石料颗粒破碎的影响研究

堆石料颗粒破碎是引起高土石坝变形的重要因素。在大坝填筑、蓄水期,堆石料的应力路径和干湿状态均是变化的。通过大型三轴试验,系统地研究了应力路径和干湿状态对堆石料颗粒破碎规律的影响。试验结果表明：（1）相同初始条件下,按不同应力路径达到同一轴向应变停机时测定的颗粒破碎率是不同的,等围压?3试验产生的颗粒破碎最大,等平均主应力p试验的次之,等最大主应力?1试验的最小,但不同应力路径下的颗粒级配演化规律是一致的。（2）相同初始条件下,湿样的颗粒破碎率明显高于干样,且二者的差距随着围压的增大而增大,不同干湿条件下的颗粒级配演化规律同样是一致的。（3）建立的考虑母岩强度的颗粒破碎率与塑性功的关系可以较好地统一描述不同应力路径及干湿状态下的颗粒破碎。该研究成果可为建立复杂应力路径及干湿变化条件下考虑颗粒破碎的堆石料弹塑性本构模型提供依据。     

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.     

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。     

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.

     

A state-dependent hyperelastic-plastic constitutive model considering shear-induced particle breakage in granular soils

Acta Geotechnica - An elastic–plastic constitutive model considering particle breakage for simulation of crushable granular soils behavior is proposed. In the model, elastic strain rates are...     

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.     

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。     

考虑颗粒破碎影响的粗粒土本构模型

颗粒破碎直接改变了粗粒土本身结构,对粗粒土的剪胀、内摩擦角、峰值强度、渗透系数都会产生影响。为了能够准确地描述粗粒土的应力-应变关系,特别是高应力条件下出现显著颗粒破碎时的应力-应变关系,亟待建立考虑颗粒破碎的粗粒土本构模型。根据三轴试验数据,建立考虑颗粒破碎耗能的应力-应变关系,采用相关联流动法则导出考虑颗粒破碎的粗粒土本构模型。所建立的本构模型考虑了颗粒破碎对粗粒土剪胀、内摩擦角的影响。通过变异粒子群优化算法确定模型参数,拟合试验曲线。模型计算结果与试验曲线拟合较好,能够很好地描述粗粒土在不同围压下的体积剪胀、剪缩和应力硬化、软化现象。     

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。     

Effect of grain crushing on shear localization in granular bodies during plane strain compression

This article deals with the effect of grain crushing on shear localization in granular materials during plane strain monotonic compression tests under constant lateral pressure. The grain diameter and the initial void ratio were stochastically distributed using a spatial correlation. To describe the mechanical behavior of cohesionless granular materials during a monotonic deformation path in plane strain compression, we used a micropolar hypoplastic constitutive model that is able to describe the salient properties of granular bodies including shear localization. The model was extended by introducing changes to the grain diameter with varying pressure using formulae from breakage mechanics proposed for crushable granulates. The initial void ratios and grain diameters took the form of correlated random spatial fields described by both symmetric and nonsymmetric random distributions using a homogeneous correlation function. The field realizations were generated with the help of an original conditional rejection method. A few representative samples of the random fields selected from the generated set were taken into account in numerical calculations. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

考虑颗粒破碎的粗粒土剪胀性统一本构模型

粗粒土作为无黏性散粒状材料具有状态依赖特性,土体的剪切特性受密度和应力水平影响。易破碎是粗粒土的另一个特点,颗粒破碎影响粗粒土的剪胀、内摩擦角、峰值强度和渗透系数。为了能够准确地描述粗粒土的应力-应变关系,采用初始状态参量描述粗粒土的内部状态,根据三轴试验数据建立考虑颗粒破碎耗能的应力-应变关系,采用相关联流动法则推导考虑颗粒破碎的粗粒土剪胀性“统一本构模型”,并建立初始状态参量与模型参数之间的关系。所建立的统一本构模型既考虑了颗粒破碎对剪胀、内摩擦角的影响,又考虑了剪切特性对土体初始状态的依赖。采用变异粒子群算法拟合试验曲线,确定模型参数。模型计算结果能够很好地拟合试验曲线。采用同一组参数对假定的初始状态进行模拟计算,计算结果表明,模型能够模拟不同初始密度和应力水平下粗粒土变形的一般规律。     

珊瑚砂高压力下一维蠕变分形破碎及颗粒形状分析

珊瑚砂是一种含钙极高的海洋生物成因材料,具有高棱角性、形状不规则、易破碎等特点。通过珊瑚砂的高压一维蠕变试验,研究颗粒破碎引起颗粒分布曲线和形状因子的演化规律。借助于高速动态图像的激光粒度粒形仪器,从统计学的角度分析试验前后颗粒形状随压力演化的关系,发现颗粒的形状因子,如长宽比、球形度和凹凸度等,随压力增加而逐渐增加。不同粒径的颗粒形状因子均向一个窄幅范围趋近,说明颗粒破碎具有无尺度性和自相似性的分形特性,分形维数随压力增加而逐渐增大,且趋近分形破碎极限。采用Hardin和Einav的方法计算相对破碎量,发现在两种计算方法下相对破碎量与压力呈幂函数关系,且幂指数相同。相对破碎量随时间增加的现象并不明显,说明在高压力下颗粒破碎主要为压缩破碎,且颗粒细化滑移填充孔隙引起的变形是造成蠕变的主要原因。     

Micromechanical modeling of particle breakage of granular materials in the framework of thermomechanics

The particle breakage of granular materials under compression is a phenomenon of great importance. In this paper, a micromechanically based model for the compression of crushable granular materials is developed in the framework of thermomechanics. Both the internal and dissipative energies in the model are derived using the micro–macro volume averaging approach to ensure that all parameters involved have concrete physical meanings. The particle breakage is quantified by the change of the maximum particle size, the size polydispersity and the fractal dimension of the gradation. Compared to other breakage models, there is a major difference that highlights the novelty of the proposed model: neither the ultimate particle size distribution, nor the evolution path of the gradation is predefined in the model. The initiation, evolution and the attenuation of the breakage can be determined by the maximum dissipation principle using thermomechanics and micromechanics. Finally, it is demonstrated that the proposed model can predict the stress dependence of the elastic bulk modulus, the size dependence of the yielding stress and the elastic–plastic-pseudoelastic phase transition of granular materials.

     

颗粒形状对粒状材料破碎演化规律及强度准则影响

为探讨颗粒形状对粒状材料的颗粒破碎演化规律及强度特征的影响,提出了一个新的粒状材料颗粒形状量化参数,设计了一种考虑三维颗粒形状的人工试样制备方法,随即进行了常规三轴压缩试验,并分析了颗粒破碎和强度特征,最终建立了一个二元介质强度准则,具体的研究成果为：建立颗粒形状量化参数——球形模量GM,在此基础上制备了5种不同形状的可破碎粒状材料三轴试样,并发现球形模量影响着粒状材料的三轴压缩强度特征;通过筛分确定试样的颗粒破碎情况,对试样的颗粒破碎演化规律和临界状态进行探讨,发现颗粒形状通过影响颗粒破碎规律而控制着宏观强度的非线性演化特征;以二元介质理论为基础,建立了考虑颗粒形状的可破碎粒状材料强度准则,并通过试验对其适用性进行了验证。     

基于Cosserat连续体的颗粒破碎影响研究

颗粒破碎对颗粒材料宏观力学行为有重要影响。 结合Hardin的破碎经验公式,将表征破碎程度的破碎参量与Cosserat连续体的内部长度参数相关联,形成一个基于Cosserat连续体且能考虑颗粒破碎的弹塑性模型。数值算例主要考察了颗粒破碎对颗粒材料承载能力、塑性应变及局部化行为的影响,数值结果表明,颗粒破碎主要发生在剪切带内,颗粒破碎使得剪切带明显变窄且剪切带内外等效塑性应变梯度明显增大。     

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。     

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%。     

Numerical Method for Modeling the Constitutive Relationship of Sand under Different Stress Paths

Overonehundredconstitutivemodelsforsand havebeenproposed,howeveronlyafewmodelsare widelyappliedinengineering.Therearetwochief reasonsforthis.(1)Sandiscomposedofgeological materialsandsituatedinaneutralenvironmentthat hassufferedvariousactions.Therefore,itisdifficult todescribethecomplexbehaviorofsoilsbyusinga simplemathematicalmodelwithonlyafewparame ters.(2)Therealsoexistsabasicparadoxintradi tionalmodelingmethods.Oneaspectofthemodelsis neededtodescribetheconstitutiverelationofsoilac curatel…