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.

     

Testing and modeling of the state-dependent behaviors of rockfill material

Dense Tacheng rockfill material (TRM) exhibits strain softening and dilation during drained triaxial tests, and therefore, an adapted Rowe’s stress–dilatancy equation was proposed for TRM. This equation incorporates an internal state index related to the density and pressure, as well as the coefficient of particle breakage and rotation. The adapted Rowe’s stress–dilatancy equation indicates that the relationship between stress and dilatancy is not constant, but varies with density and pressure. This result is in agreement with TRM test data. A state-dependent model was established for TRM using generalized plasticity theory combined with the adapted Rowe’s stress–dilatancy equation. The model includes twelve constants calibrated using TRM test data from Group A, and this model was used to predict the strain softening and dilatancy behaviors of dense TRM. Furthermore, the model predictions were validated using test data from Group B. In summary, the model accurately represented the stress–strain and dilatancy behaviors of TRM over a wide range of densities and pressures.     

考虑颗粒破碎的冻结砂土非线性本构模型研究

颗粒破碎是粒状材料在高应力状态下的一种基本现象。为了研究冻结砂土中颗粒破碎对应力应变关系的影响,将冻结砂土视为复合颗粒材料,忽略冰的压融,考虑内摩擦角随应力状态的变化,构建一个适用于冻结砂土的考虑颗粒破碎的非线性本构模型。构建过程分为三步,首先是基于三轴剪切前后颗粒分析对冻结砂土颗粒破碎模式和产生机理进行探讨;其次是基于考虑颗粒破碎的能量平衡方程,对冻土在三轴剪切试验过程中的颗粒破碎耗能进行分析,结果表明颗粒破碎耗能随轴向应变呈双曲线变化趋势;最后应用考虑颗粒破碎的剪胀方程修正沈珠江三参数非线性模型中的体积切线模量ν_t,得到一个考虑颗粒破碎的非线性本构模型,模型参数可以通过单轴压缩试验和常规三轴试验确定。将原模型和修正后模型的计算结果与控制温度为-6℃,围压为1 MPa、4 MPa、6 MPa、8 MPa和10 MPa时冻结砂土的试验结果进行对比,结果表明该模型能够较好的模拟冻结砂土从低围压到高围压的应变软化特征与剪胀特征。      

粗粒土的颗粒破碎耗能及剪胀方程研究

颗粒破碎对于粗粒土的应力变形性质有显著影响。在Rowe剪胀方程的基础上考虑颗粒破碎耗能的影响,并引入颗粒破碎的演化规律对颗粒破碎耗能进行计算,得到了一个简单实用且对粗粒土适用性较好的剪胀方程。主要结论如下：（1）通过粗粒土的三轴CD试验结果分析并证明了弹性应变对于剪胀比的影响较小,因此,可以将剪胀比 表示为 ,进而得到了剪胀方程表达式的一般形式。（2）将剪胀方程中的临界状态应力比Mc折减为摩擦系数M,并引入了颗粒破碎的演化规律,将M定量表示为广义剪应变的函数,从而使得所计算的破碎耗能在剪切过程中是递增的,且逐渐趋于稳定值,符合了颗粒破碎不可逆的规律。（3）试验表明,剪胀方程中的未知量 与摩擦系数M之间呈现显著的线性关系,将该关系代入剪胀方程即确定了方程的具体表达形式,并且利用堆石料的三轴CD试验证明了其对粗粒土的剪胀性预测效果较好。     

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.     

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。     

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.     

Experimental characterization and 3D DEM simulation of bond breakages in artificially cemented sands with different bond strengths when subjected to triaxial shearing

This paper describes the mechanical behavior of artificially cemented sands with strong, intermediate, and weak bond strengths, using experimentation and 3D discrete element method (DEM) simulation. The focus is on the features of bond breakage and the associated influences on the stress–strain responses. Under triaxial shearing, the acoustic emission rate captured in the experiment and the bond breakage rate recorded in the simulations show resemblance to the stress–strain response, especially for strongly and intermediately cemented samples, where a strain softening response is observed. The simulations further reveal the shear band formation coincides with the development of bond breakage locations due to the local weakness caused by the bond breakages. Strain softening and volumetric dilation are observed inside the shear band, while the region outside the shear band undergoes elastic unloading. The weakly cemented sample exhibits a strain hardening response instead; bond breakages and the associated local weaknesses are always randomly formed such that no persistent shear band is observed. Note that in the DEM simulation, the flexible membrane boundary is established by a network of bonded membrane particles; the membrane particle network is further partitioned into finite triangular elements. The associated algorithm can accurately distribute the applied confining pressure onto the membrane particles and determine the sample volume.     

粗粒料颗粒破碎数值模拟研究

粗粒料在外力作用下存在明显的颗粒破碎特性,研究颗粒破碎过程是当前研究的热点问题之一。基于粗粒料单颗粒破碎机制,考虑单颗粒破碎强度与直径的变化规律,采用非线性接触H-Z模型和密度控制法建立了粗粒料颗粒破碎数值模型。开展粗粒料双轴剪切试验数值模拟研究,并与室内试验结果进行对比分析。研究表明：建立的粗粒料颗粒破碎数值模型能够较好地模拟粗粒料偏应力与轴向应变和体积应变与轴向应变的关系;数值模拟获得的粗粒料颗粒破碎率与室内试验结果基本一致;去除试样制备过程和固结过程引起的颗粒破碎,不同围压条件下的颗粒破碎率归一化后基本重合,且可以近似地采用双曲线函数进行拟合。颗粒破碎率随着围压的增大,逐渐增大,试验级配趋于Einav提出的颗粒破碎的最终级配（分维数等于2.6）     

适用于堆石料的分数阶下加载面模型

堆石料的应力-应变曲线具有应变硬化和软化的特性,并且体积变形会伴随着剪缩和剪胀现象的发生;此外,应力水平、应力路径和密度等因素均会对堆石料的力学特性产生显著的影响。基于临界状态土力学的理论框架,建立了适用于堆石料的分数阶下加载面模型,该模型为典型的双屈服模型。在平均主应力p-剪应力q平面,剪切过程中堆石料当前应力状态点和参考应力点分别位于下加载面和参考屈服面上,两者之间的相对位置与孔隙比之差ρ相关。相比于状态参量Ψ,ρ能够额外考虑应力路径对堆石料剪胀特性的影响。新模型的另一个显著特点在于能够考虑堆石料塑性流动方向与加载方向之间的差异性。在不引入塑性势函数的情况下,新模型对屈服函数进行Caputo微分并得到分数阶塑性流动法则,进而统一描述相关联和非相关联的塑性流动法则。新模型具有形式简单且参数较少等优点,所包含的7个材料参数均具有明确的物理意义,并且可以采用常规的室内试验结果进行标定。通过将模型计算结果与Tacheng堆石料在不同初始孔隙比和围压条件下的三轴压缩排水试验结果进行对比分析,结果表明新模型能够准确地描述堆石料的应力-应变曲线和体积变形特点;同时,新模型也能够合理地描述初始孔隙比对堆石料在e-lnp平面(e为孔隙比)临界状态线的影响。     

Constitutive description of interface behavior including cyclic loading and particle breakage within the framework of critical state soil mechanics

The cyclic behavior of soil–structure interface can be very important in dynamic problems. The cyclic behavior of soil–structure interface may be nonlinear, which includes hysteresis, hardening, degradation, and particle breakage. The breakage of granular soil particles during shearing of granular soil–structure interface is associated with cyclic degradation and can be critical to the dynamic behavior of soil–structure system. The critical state soil mechanics concept formerly used to simulate the nonlinear monotonic behavior of granular soil–structure interface was modified and extended to describe the cyclic behavior, especially soil‐particle breakage and degradation during cyclic shearing. Soil‐particle breakage was assumed to relate to the energy consumption during cyclic shearing and the critical state line of the soil–structure interface was assumed to translate with the consumption of shearing energy during cyclic shearing as the threshold value is attained. The model was formulated in the framework of generalized plasticity and is capable of describing the salient features of granular soil–structure interface under cyclic loading. Most of the model parameters have straightforward physical meanings and are calibrated using monotonic or cyclic interface test results. The proposed model was calibrated and validated against published test results. The dependency of interface behavior on stress path and cyclic degradation can be successfully described by the proposed model. Copyright © 2008 John Wiley & Sons, Ltd.     

A critical state model for sands dependent on stress and density

An elastoplastic model for sands is presented in this paper, which can describe stress–strain behaviour dependent on mean effective stress level and void ratio. The main features of the proposed model are: (a) a new state parameter, which is dependent on the initial void ratio and initial mean stress, is proposed and applied to the yield function in order to predict the plastic deformation for very loose sands; and (b) another new state parameter, which is used to determine the peak strength and describe the critical state behaviour of sands during shearing, is proposed in order to predict simply negative/positive dilatancy and the hardening/softening behaviour of medium or dense sands. In addition, the proposed model can also predict the stress–strain behaviour of sands under three-dimensional stress conditions by using a transformed stress tensor instead of ordinary stress tensor. Copyright © 2004 John Wiley & Sons, Ltd.     

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。     

钙质砂剪切特性的围压效应和粒径效应研究

为研究钙质砂剪切特性的围压效应和粒径效应,开展了在不同粒径、不同相对密实度以及不同围压条件下的三轴剪切试验,并引入应力相对软化系数和剪胀系数对应变软化特征及剪胀特征进行了定量表征。试验研究表明,随围压的增大,不同粒径钙质砂试样应变软化特征及剪胀特征逐渐减弱,且围压与应力相对软化系数和剪胀系数均呈半对数线性相关。不同粒径钙质砂试样存在一强度临界围压和体变临界围压分别使得应变软化特征和剪胀特征消失。在粒径为5～0.075 mm范围内,对松样而言,围压对软化特征和剪胀特征存在显著影响,但与粒径不存在显著相关性;对密样而言,随粒径逐渐减小,围压对试样软化特征的影响逐渐增强,而对试样剪胀特征的影响逐渐减弱。在低围压（50 kPa）条件下,0.5～0.25 mm粒径组试样破碎最显著。     

堆石料强度变形特性与非线性弹性本构模型研究

在大型三轴试验研究的基础上,提出了堆石料应力-应变关系、侧向应变与轴向应变关系的指数函数表达式,以及抗剪强度包线在q-p平面上的幂函数表达式。继而推导得到了一个反映堆石料强度与变形特性的非线性弹性本构模型。通过对实体工程的数值模拟,将Duncan E-B模型与新建模型进行了对比分析,验证了该模型的可行性。     

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。     

Numerical simulation of the shear behavior of rockfills

A strain hardening model is proposed for simulation of the shear behavior of rockfills, including the non-linear stress–strain relationship, stress-dependence of stiffness, non-linear strength envelope, and particularly the shearing contraction and dilatancy. This model utilizes the Mohr–Coulomb yield criterion, which is defined by the mobilized friction angle varying with plastic octahedral shear strain. The development of Rowe’s stress dilatancy theory is reviewed, with its limitation for rockfills highlighted. A modified solution is then proposed to derive the mobilized dilatancy angle of rockfills. Compared with large-scale triaxial testing results, it has been demonstrated that this simple model is capable of predicting the shear behavior of rockfills with fair accuracy.     

Modified Structured Cam Clay: A generalised critical state model for destructured,naturally structured and artificially structured clays

This paper presents a generalised constitutive model for destructured, naturally structured and artificially structured clays that extends the Structured Cam Clay (SCC) model. This model is designated as “Modified Structured Cam Clay (MSCC) model”. The influence of structure and destructuring on the mechanical behaviour of clay can be explained by the change in the modified effective stress, which is the sum of the current mean effective stress and the additional mean effective stress due to structure (structure strength). The presence of structure increases the modified mean effective stress and yield surface, enhancing the cohesion, peak strength and stiffness. The destructuring begins when the stress state is on the virgin yield surface. After the failure (peak strength) state, the abrupt destructuring occurs as the soil–cementation structure is crushed; hence the strain softening. The soil structure is completely removed at the critical state when the yield surface becomes identical to the destructured surface. The destructuring law is proposed based on this premise. In the MSCC model, the yield function is the same shape as that of the Modified Cam Clay (MCC) model. A plastic potential is introduced so as to account for the influence of structure on the plastic strain direction for both hardening and softening behaviours. The required model parameters are divided into those describing destructured properties and those describing structured properties. All the parameters have physical meaning and can be simply determined from the conventional triaxial tests. Thus, the MSCC model is a useful tool for geotechnical practitioners. The capability of the model is verified by the test results of destructured, natural structured and artificially structured clays.     

弹塑性软化模型下隧洞围岩变形与支护压力分析

为深入探究岩体非线性软化应变特性对隧洞围岩力学行为的影响,提出了一种考虑软化系数的岩体弹塑性软化模型,并推导了圆形隧洞围岩应力-应变的求解方法。然后,通过将本文方法与Brown方法、换算后的Mohr-Coulomb屈服准则方法进行对比,验证了本文方法的合理性。最后,探究了软化系数对围岩变形及支护压力影响规律。结果表明：软化系数较大时,采用弹塑性软化模型与弹脆塑性模型算得结果基本相同;对围岩变形及稳定性起主要控制作用的是松动区域范围;控制塑性区域出现时的临界支护压力在数值上与弹塑性区域交界处径向应力是相等的。     

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...