堆石料的临界状态与考虑颗粒破碎的本构模型

高应力水平时堆石料的颗粒破碎对其强度和变形机制有重要影响。临界状态土力学理论对重塑土的应力-应变关系的描述较为成功,但目前颗粒破碎对堆石料的临界状态的影响及其数学描述鲜有研究。对堆石料进行了固结应力从0.4 MPa到4 MPa的18组固结排水和固结不排水常规三轴压缩试验,以及6组等向压缩试验。试验结果表明：在排水条件和不排水条件下,不同的固结应力试样都趋于临界状态;堆石料的临界状态在q-p′平面和e-lgp′平面均为非线性变化。基于此试验结果,通过引入状态参数,在广义塑性力学的理论框架下,建立了考虑颗粒破碎的堆石料本构模型,并给出了模型参数的确定方法。与长河坝料的试验进行了对比,结果表明所建议的本构模型可以较好地模拟堆石料从低围压0.4 MPa到高围压 3.5 MPa下的应力-应变特性     

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.     

循环荷载作用下考虑颗粒破碎的堆石体本构模型

中国西部兴建的很多200～300 m高的堆石坝处于高烈度地震区。应力水平高时堆石体的颗粒破碎对其在循环荷载作用下的应力、应变特性有重要的影响。基于广义塑性理论,通过引入状态参数,建立了循环荷载作用下考虑颗粒破碎的堆石体的本构模型,并给出了模型参数的确定方法。与堆石体在400、800、1 500、2 200 kPa围压作用时的试验结果对比,表明所提出的本构模型可以较好地模拟循环荷载作用下颗粒破碎时堆石体的动应力和动应变响应。     

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。     

堆石料单粒强度尺寸效应的颗粒流模拟方法研究

围绕堆石料单粒强度尺寸效应的颗粒流模拟方法展开研究。首先,基于FISH二次开发建立了堆石料的随机不规则单粒模型,充分考虑堆石料的形状特征和破碎现象;然后,建立了堆石料单粒强度尺寸效应的等效模拟方法,以单粒强度随其粒径的变化规律为基础,推导了堆石料模型中细观黏结强度与堆石料等效粒径的负指数经验公式;其次,基于建立的数值模型对堆石料的室内单粒压缩试验进行仿真模拟,验证数值模型的正确性和合理性,并对较大粒径堆石料的单粒强度进行模拟预测,突出数值试验的优势;最后,基于建立的数值模型对相同粒径不同形状特征堆石料的单粒强度分布特征进行模拟研究。研究结果表明：（1）堆石料内部缺陷含量和尺寸随粒径增加对其单粒强度所产生的尺寸效应,可通过堆石料模型中细观强度参数随粒径折减进行等效模拟;（2）形状特征对堆石料的破裂机制具有重要影响,方形颗粒为压剪破裂,单粒强度较高,而随机不规则颗粒和圆形颗粒为拉剪或劈裂,单粒强度相对较低;（3）拉剪或劈裂条件下,堆石料形状越不规则,其单粒强度的离散程度越高,反之则离散程度越低。相关研究成果可为进一步研究荷载作用下堆石体内各粒径段堆石料的破碎量奠定基础,从而更加真实地反映堆石体的级配演化规律。     

Modeling for critical state line of granular soil with evolution of grain size distribution due to particle breakage

Determination of the critical state line(CSL)is important to characterize engineering properties of granular soils.Grain size distribution(GSD)has a significant influence on the location of CSL.The influence of particle breakage on the CSL is mainly attributed to the change in GSD due to particle breakage.However,GSD has not been properly considered in modeling the CSL with influence of particle breakage.This study aims to propose a quantitative model to determine the CSL considering the effect of GSD.We hypothesize that the change of critical state void ratio with respect to GSD is caused by the same mechanism that influences of the change of minimum void ratio with respect to GSD.Consequently,the particle packing model for minimum void ratio proposed by Chang et al.(2017)is extended to predict critical state void ratio.The developed model is validated by experimental results of CSLs for several types of granular materials.Then the evolution of GSD due to particle breakage is incorporated into the model.The model is further evaluated using the experimental results on rockfill material,which illustrates the applicability of the model in predicting CSL for granular material with particle breakage.     

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.     

堆石料的剪胀特性与广义塑性本构模型

以三轴试验成果为基础,考虑颗粒破碎引起堆石料剪胀比与应力比之间的非线性关系,提出了能够反映堆石料低围压剪胀、高围压剪缩特性的剪胀方程。在广义塑性理论框架内构造堆石料的塑性流动方向向量和加载方向向量,引入依赖于密实度与平均应力的压缩参数,构造随平均应力、剪应力比和密实度变化的塑性模量,建立了一个考虑颗粒破碎的堆石料弹塑性本构模型。阐述了该模型10个参数的确定方法,并通过模拟不同围压和不同应力路径下堆石料的三轴压缩试验资料验证了模型与参数的合理性。     

钙质砂颗粒破碎对临界状态影响的试验研究

钙质砂的颗粒易碎性是造成其变形和强度特性不同于石英砂的重要性质。本文基于临界状态理论,通过一系列试验定量地描述钙质砂临界状态线随颗粒破碎的演化规律。本文试验分两个阶段进行:第1阶段研究了60~2000 kPa围压条件下钙质砂的力学特性和颗粒破碎特征;第2阶段以不同破碎率的试样为母本重塑制样,在100~300 kPa围压条件下,剪切至破碎临界状态线。试验结果表明:在较小围压(<300 kPa)条件下,松砂和密砂均表现出明显的剪胀和应变软化特性;而高围压(>1 MPa)条件下,显著的颗粒破碎会造成试样的持续剪缩;颗粒破碎存在明显围压阈值,对于松砂而言,在围压小于300 kPa条件下,颗粒基本不发生破碎;在e-lg p'平面内,破碎临界状态线的截距Δe_Γ和斜率λ_c均会随着修正相对破碎率B_r*的增大而减小,即颗粒破碎会使临界状态线发生下移和逆时针转动;而在q-p'平面内,钙质砂的临界状态点落在同一条直线上,即存在唯一的临界状态应力比M_cr和临界摩擦角φ_cr。     

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。     

Grain crushing in geoscience materials-Key issues on crushing response,measurement and modeling:Review and preface

Grain crushing is commonly encountered in deep foundation engineering,high rockfill dam engineering,railway engineering,mining engineering,coastal engineering,petroleum engineering,and other geoscience application.Grain crushing is affected by fundamental soil characteristics,such as their mineral strength,grain size and distribution,grain shape,density and specimen size,and also by external factors including stress magnitude and path,loading rate and duration,degree of saturation,temperature and geochemical environment.Crushable material becomes a series of different materials with the change in its grading during grain crushing,resulting in a decrease in strength and dilatancy and an increase in compressibility.Effects of grain crushing on strength,dilatancy,deformation and failure mechanisms have been extensively investigated through laboratory testing,discrete element method(DEM)modelling,Weibull statistics,and constitutive modelling within the framework of the extended crushing-dependent critical state theory or the energy-based theory.Eleven papers summarized in this review article for this special issue addressed the above issues in grain crushing through the advanced testing and modelling.     

堆石料颗粒破碎特性试验研究

颗粒破碎是堆石料的一项基本特性,它对堆石体的变形和强度特性具有明显的影响。对于高堆石坝而言,在高应力场作用下堆石颗粒发生明显破碎,可导致坝体变形率增加。为了正确认识堆石体及堆石坝的变形特性和机理,研究了堆石颗粒破碎特性以及颗粒破碎的影响因素。采用大型三轴试验研究了堆石料的颗粒破碎特性,分析了堆石体干密度、级配特征、堆石颗粒强度等对颗粒破碎的影响,研究了应力状态对颗粒破碎率的影响,建立了颗粒破碎率的计算模型以及颗粒破碎引起的堆石体应变增量与颗粒破碎率的关系。     

A random virtual crack DEM model for creep behavior of rockfill based on the subcritical crack propagation theory

The post-construction settlement of rockfill dams and high filled ground of airport, which is a phenomenon of much significance, is mainly caused by the time-dependent breakage of the rockfill material. In this paper, a random virtual crack DEM model is proposed for creep behavior of rockfill in PFC2D according to the theory of subcritical crack propagation induced by stress corrosion mechanisms. The bonded clusters are adopted to represent the rockfill particles so as to simulate their irregular shapes. Virtual cracks are set at the bonds of the clusters, and the length of the crack is considered as a random value, which leads the crushing strength of a single particle to follow the Weibull’s statistical model and the corresponding size rules. Oedometric creep tests for rockfill are simulated by using this proposed model. The results show that the model, validated preliminarily by some test data, can reflect qualitatively the creep mechanism as well as the size effects reasonably. Particles can develop various breakage patterns during creep, including global breakage, local breakage and even complex mixed breakage. The increase in stress levels and particle size will lead to an obvious growth of the creep strain and creep rate of the rockfill. The scale effects on the creep behavior of rockfill are analyzed through 35 specimens, and formulas including the effects of scales and stress levels are tentatively proposed.     

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。     

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.     

A kinematic hardening constitutive model for sands: the multiaxial formulation

This paper explores the possibility of using well-accepted concepts—Mohr-Coulomb-like strength criterion, critical state, existence of a small strain elastic region, hyperbolic relationship for representing global plastic stress–strain behaviour, dependence of strength on state parameter and flow rules derived from the Cam-Clay Model—to represent the general multiaxial stress–strain behaviour of granular materials over the full range of void ratios and stress level (neglecting grain crushing). The result is a simple model based on bounding surface and kinematic hardening plasticity, which is based on a single set of constitutive parameters, namely two for the elastic behaviour plus eight for the plastic behaviour, which all have a clear and easily understandable physical meaning. In order to assist the convenience of the numerical implementation, the model is defined in a ‘normalized’ stress space in which the stress–strain behaviour does not undergo any strain softening and so certain potential numerical difficulties are avoided. In the first part the multiaxial formulation of the model is described in detail, using appropriate mixed invariants, which rationally combine stress history and stress. The model simulations are compared with some experimental results for tests on granular soils along stress paths lying outside the triaxial plane over a wide range of densities and mean stresses, using constitutive parameters calibrated using triaxial tests. Furthermore, the study is extended to the analysis of the effects induced by the different shapes of the yield and bounding surfaces, revealing the different role played by the size and the curvature of the bounding surface on the simulated behaviour of completely stress- and partly strain-driven tests. Copyright © 1999 John Wiley & Sons, Ltd.     

An enhanced constitutive model for crushable granular materials

Studies in the past have tried to reproduce the mechanical behaviour of granular materials by proposing constitutive relations based on a common assumption that model parameters and parameters describing the properties, including gradation of individual grains are inevitably linked. However successful these models have proved to be, they cannot account for the changes in granular assembly behaviour if the grains start to break during mechanical loading. This paper proposes to analyse the relation between grading change and the mechanical behaviour of granular assembly. A way to model the influence of grain breakage is to use a critical state‐based model. The influence of the amount of grain breakage during loading, depending on the individual grain strength and size distribution, can be introduced into constitutive relations by means of a new parameter that controls the evolution of critical state with changes in grain size distribution. Experimental data from a calcareous sand, a quartz sand, and a rockfill material were compared with numerical results and good‐quality simulations were obtained. The main consequences of grain breakage are increased compressibility and a gradual dilatancy disappearance in the granular material. The critical state concept is also enriched by considering its overall relation to the evolution of the granular material. Copyright © 2009 John Wiley & Sons, Ltd.     

A numerical investigation of the incremental behavior of crushable granular soils

The mechanical behavior of granular materials is characterized by strong nonlinearity and irreversibility. These properties have been differently described by a variety of constitutive models. To test any constitutive model, experimental data relative to the nature of the incremental stress–strain response of the material is desirable. However, this type of laboratory data is scarce because of being expensive and difficult to obtain. The discrete element method has been used several times as an alternative to obtain incremental responses of granular materials. Crushable grains add one extra source of irreversibility to granular materials. Crushability has been variously incorporated into different constitutive models. Again, it will be helpful to obtain incremental responses of crushable granular materials to test these models, but the experimental difficulties are increased. Making use of a recently introduced crushing model for discrete element simulation, this paper presents a new procedure to obtain incremental responses in discrete analogs of granular crushable materials. The parallel probe approach, previously used for uncrushable discrete analogs, is here extended to account for the presence of crushable grains. The contribution of grain crushing to the incremental irreversible strain is identified and separately measured. Robustness of the proposed method is examined in detail, paying particular attention to aspects such as dynamic instability or crushing localization. The proposed procedure is later applied to map incremental responses of a discrete analog of Fontainebleau sand on the triaxial plane. The effect of stress ratio and granular state on plastic flow characteristics is highlighted. Copyright © 2016 John Wiley & Sons, Ltd.     

An elastoplastic constitutive model for rockfills incorporating energy dissipation of nonlinear friction and particle breakage

A new elastoplastic model is developed for rockfills within the general critical state framework incorporating the state parameter. Two state functions are proposed to characterize the evolution of volume dilation and strain softening of rockfills, and a modified breakage index based on the concept of Hardin's relative breakage is defined to describe the progressive crushing of rockfills. The nonassociated plastic flow rule is derived from a state dependent dilatancy equation, and it incorporates energy dissipation due to intrinsic nonlinear friction and particle breakage upon shearing. Thus, their couple effect on the plastic deviatoric and volumetric deformation of rockfills is taken into account in the current model. The numerical analyses are carried out for a series of drained triaxial tests on the modeled rockfills at various consolidation pressures and stress paths. The volume dilation/contraction and strain softening/hardening of rockfills are accurately predicted by the proposed model, and the particle breakage and nonlinear critical state shear strength of rockfills are also well captured. The research findings indicate that the current model is applicable to represent the complex stress–strain–volume change behavior of rockfills in general. Copyright © 2013 John Wiley & Sons, Ltd.     

Cavity expansion analyses of crushable granular materials with state‐dependent dilatancy

Crushability is one of the important behaviors of granular materials particularly under high stress states, and affects both the deformability and strength of the materials that are in essence associated with state‐dependent dilatancy. In this presentation, first, a new critical state model is proposed to take into account the three different modes of compressive deformation of crushable granular materials, i.e. particle rearrangement, particle crushing and pseudo‐elastic deformation. Second, the governing equations for cavity expansion in crushable granulates are introduced, in which the state‐dependent dilatancy as well as the bounding surface plasticity model are used. Then, the procedure to obtain semi‐analytical solutions to cavity expansion in the material is described in detail, in which a commercial differential equation solver is employed. Finally, cavity expansion analyses are carried out on Toyoura sand, a well‐documented granular material, to demonstrate the effects of crushability and state‐dependent dilatancy. The study shows that particle crushing does occur at both high stress and critical states and affects the stress fields and the deformation behavior of the material surrounding the cavity in association with state‐dependent dilatancy. This leads to conclusion that particle crushing and state‐dependent dilatancy have to be taken into account when cavity expansion theory is used to interpret cone penetration tests and pressuremeter tests. Copyright © 2011 John Wiley & Sons, Ltd.