Granite rock fragmentation at percussive drilling – experimental and numerical investigation

The aim of this study is to numerically model the fracture system at percussive drilling. Because of the complex behavior of rock materials, a continuum approach is employed relying upon a plasticity model with yield surface locus as a quadratic function of the mean pressure in the principal stress space coupled with an anisotropic damage model. In particular, Bohus granite rock is investigated, and the material parameters are defined based on previous experiments. This includes different tests such as direct tension and compression, three‐point bending, and quasi‐oedometric tests to investigate the material behavior at both tension and confined compression stress states. The equation of motion is discretized using a finite element approach, and the explicit time integration method is employed. Edge‐on impact tests are performed, and the results are used to validate the numerical model. The percussive drilling problem is then modeled in 3D, and the bit‐rock interaction is considered using contact mechanics. The fracture mechanism in the rock and the bit penetration‐ resisting force response are realistically captured by the numerical model. Copyright © 2013 John Wiley & Sons, Ltd.     

A generalized rigid particle contact model for fracture analysis

Rigid particle models taking directly into consideration the physical mechanisms and the influence of the material meso‐structure have recently been developed for fracture studies of quasi‐brittle material such as concrete. The formulation of a generalized contact model for rigid particle simulations is presented in which the contact discretization is a model parameter. The contact model performance for different discretizations is evaluated for uniaxial tensile tests, for uniaxial compression tests and for a notched beam in mode I. Copyright © 2005 John Wiley & Sons, Ltd.     

A macroscopic damage‐plastic constitutive law for modeling quasi‐brittle fracture and ductile behavior of concrete

A new phenomenological macroscopic constitutive model for the numerical simulation of quasi‐brittle fracture and ductile concrete behavior, under general triaxial stress conditions, is presented. The model is particularly addressed to simulate a wide range of confinement stress states, as also, to capture the strong influence of the mean stress value in the concrete failure mechanisms. The model is based on a two‐surface damage‐plastic formulation. The mechanical behavior in different domains of the stress space is separately described by means of a quasi‐brittle or ductile material response:

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Finite element simulation of the thermoviscoplastic behaviour of bituminous concrete

The general framework of the paper deals with the finite element modelling of thermomechanical problems involving viscous materials. The study focuses on the statement of constitutive equations describing the thermoviscoplastic behaviour of bituminous concrete, as well as on their implementation in a finite element program. After stating the general equations of the space- and time-continuous problem and the constitutive relations governing the viscoplastic component of the bituminous concrete behaviour, we deal with their integration over finite time steps, considering two different schemes. Eventually, two sets of numerical results are presented. The first one, an homogeneous triaxial test, is used to compare those schemes, whereas the second one consists of numerical simulations of real-size experiments performed on a road structure subjected to thermal and mechanical loadings. By comparing the numerical results with experimental ones, it allows us to test the finite element code on a more complex and realistic problem. Copyright © 1999 John Wiley & Sons Ltd.     

不同级配颗粒材料的循环硬化行为与能量耗散

颗粒材料在循环荷载作用下呈现循环硬化行为,然而关于循环硬化行为的宏-微观相对应的机理解释的研究却不多见。本文通过3D-DEM实施了循环三轴数值模拟试验,研究了不同级配下颗粒材料在循环荷载下的循环硬化行为,并分析了(轴向)平均模量和由滑动接触造成的能量耗散的演化趋势。结果表明随着循环荷载的进行,平均模量逐渐增加并趋于渐进值。每个循环内的能量耗散随着循环数的增加不会一直衰减,存在一个阈值。不同颗粒级配下平均模量的增加指数和能量耗散衰减指数的大小相近(约为0.6),表明在描述循环荷载硬化行为时,无论是使用变形模量还是归一化能量耗散在结果上是一致的,即微观尺度上滑动接触引起的能量耗散映射出宏观尺度上平均模量的变化。颗粒平均粒径越大的颗粒体系,其平均模量越大,而且越早完成能量耗散过程,但不同的颗粒级配下对应的能量耗散阈值差异较小,基本上维持在一个常数(约为0.15)。     

Development in modeling cyclic loading of sands based on kinematic hardening

In this paper, there is presented an elastoplastic constitutive model to predict sandy soils behavior under monotonic and cyclic loadings. This model is based on an existing model (Cambou‐Jafari‐Sidoroff) that takes into account deviatoric and isotropic mechanisms of plasticity. The flow rule used in the deviatoric mechanism is non‐associated and a mixed hardening law controls the evolution of the yield surface. In this research the critical state surface and history surface, which separates the virgin and cyclic states in stress space, are defined. Kinematic hardening modulus and stress–dilatancy law for monotonic and cyclic loadings are effectively modified. With taking hardening modulus as a function of deviatoric and volumetric plastic strain and with defining the history surface and stress reversal, the model has the ability to predict the sandy soils' behavior. All of the model parameters have clear physical meanings and can be determined from usual laboratory tests. In order to validate the model, the results of homogeneous tests on Hostun and Toyoura sands are used. The results of validation show a good capability of the proposed model. Copyright © 2009 John Wiley & Sons, Ltd.     

Error-controlled implicit time integration of elasto-visco-plastic constitutive models for rock salt

The mechanical behavior of rock salt is rate-dependent at different time scales. Using caverns in rock salt formations for renewable energy storage implies that the underground structures are subjected to both short-term and long-term loads, increasing robustness and flexibility requirements for numerical simulators used to assess the safety of such structures. So far, explicit time integration with model-specific heuristics for time-step size determination dominate in application studies. In this paper, the suitability of error-controlled adaptive time-integration schemes of the diagonally implicit Runge-Kutta type is investigated in comparison with the Backward Euler and Crank-Nicolson schemes when applied to the integration of typical elasto-visco-plastic constitutive models of rock salt. The comparison is made both for monotonic and for cyclic loads as well as taking account of thermo-mechanical coupling. Analyses of the time-integration errors and the time step-size evolution show the suitability of the integration scheme for these material models. The automatic adjustment of the time-step size was found to be robust across all material models and boundary conditions as well as for non-isothermal situations for a single algorithmic parameter set.     

Numerical modeling of dynamic rock fracture with a combined 3D continuum viscodamage‐embedded discontinuity model

This paper deals with numerical modeling of dynamic failure phenomena in rate‐sensitive quasi‐brittle materials, such as rocks, with initial microcrack populations. To this end, a continuum viscodamage‐embedded discontinuity model is developed and tested in full 3D setting. The model describes the pre‐peak nonlinear and rate‐sensitive hardening response of the material behavior, representing the fracture‐process zone creation, by a rate‐dependent continuum damage model. The post‐peak response, involving the macrocrack creation accompanied by exponential softening, is formulated by using an embedded displacement discontinuity model. The finite element implementation of this model relies upon the linear tetrahedral element, which seems appropriate for explicit dynamic analyses involving stress wave propagation. The problems of crack locking and spreading typical of embedded discontinuity models are addressed in this paper. A combination of two remedies, the inclusion of viscosity in the spirit of Wang's viscoplastic consistency approach and introduction of isotropic damaging into the embedded discontinuity model, is shown to be effective in the present explicit dynamics setting. The model performance is illustrated by several numerical simulations. In particular, the dynamic Brazilian disc test and the Kalthoff–Winkler experiment show that the present model provides realistic predictions with the correct failure modes and rate‐dependent tensile strengths of rock at different loading rates. The ability of initial embedded discontinuity populations to model the initial microcrack populations in rocks is also successfully tested. Copyright © 2016 John Wiley & Sons, Ltd.     

A simplified analysis of interface failure under compressive normal stress and monotonic or cyclic shear loading

Interface damage and delamination is usually accompanied by frictional slip at contacting interfaces under compressive normal stress. The present work is concerned with an analysis of progressive interface failure using the cohesive crack model with the critical stress softening and frictional traction present at the contact. Both monotonic and cyclic loadings are considered for anti‐plane shear of an elastic plate bonded to a rigid substrate by means of cohesive interface. An analytical solution can be obtained by neglecting the effect of minor shear stress component. The analysis of progressive delamination process revealed three solution types, namely: short, medium and long plate solutions. The long plate solution was obtained under an assumption of quasistatic progressive growth of the delamination zone. In view of snap back response, the quasistatic deformation process cannot be executed by either traction or displacement control. The states of frictional slip accompanied by shake down or incremental failure are distinguished in the case of cyclic loading, related to load amplitude and structural dimensions. The analysis provides a reference solution for numerical treatment of more complex cases. Copyright © 2005 John Wiley & Sons, Ltd.     

Induced fabric under cyclic and rotational loads in a strain space multiple mechanism model for granular materials

The strain space multiple mechanism model idealizes the behavior of granular materials on the basis of a multitude of virtual simple shear mechanisms oriented in arbitrary directions. Within this modeling framework, the virtual simple shear stress is defined as a quantity dependent on the contact distribution function as well as the normal and tangential components of interparticle contact forces, which evolve independently during the loading process. In other terms, the virtual simple shear stress is an intermediate quantity in the upscaling process from the microscopic level (characterized by contact distribution and interparticle contact forces) to the macroscopic stress. The stress space fabric produces macroscopic stress through the tensorial average. Thus, the stress space fabric characterizes the fundamental and higher modes of anisotropy induced in granular materials. Herein, the induced fabric is associated with monotonic and cyclic loadings, loading with the rotation of the principal stress, and general loading. Upon loading with the rotation of the principal stress axis, some of the virtual simple shear mechanisms undergo loading whereas others undergo unloading. This process of fabric evolution is the primary cause of noncoaxiality between the axes of principal stresses and strains. Although cyclic behavior and behavior under the rotation of the principal stress axis seem to originate from two distinct mechanisms, the strain space multiple mechanism model demonstrates that these behaviors are closely related through the hysteretic damping factor. Copyright © 2011 John Wiley & Sons, Ltd.     

原状和重塑海洋粘土经历动载后的静强度衰减

根据海洋粉质粘土原状和重塑土样的动三轴试验结果, 比较和分析了两种土样应力、应变、孔隙水压力和不排水抗剪强度行为, 得到了土样的静不排水抗剪强度衰减与波浪荷载作用下土样产生的动应变以及平均累积孔压之间的关系。 并将波浪荷载作用使土样内孔压升高, 有效应力降低, 形成拟超固结现象的理论, 应用到土样不排水抗剪强度衰减与平均累积孔压之间关系的分析;同时与重塑土样的超固结静态剪切试验结果进行比较, 得到了土样在波浪荷载作用后的归一化不排水抗剪强度与拟超固结比之间的关系式。 建议以少量原状土样, 配合大量重塑土样的动三轴试验结果, 实现对实际海洋粘土地基在波浪荷载作用后的静不排水抗剪强度衰化规律的评估。     

An anisotropic damage–plasticity model for saturated quasi‐brittle materials

This article is devoted to numerical modeling of anisotropic damage and plasticity in saturated quasi‐brittle materials such as rocks and concrete. The damaged materials are represented by an isotropic poroelastic matrix containing a number of families of microcracks. Based on previous works, a discrete thermodynamic approach is proposed. Each family of microcracks exhibits frictional sliding along crack surfaces as well as crack propagation. The frictional sliding is described by a Coulomb–Mohr‐type plastic criterion by taking into account the effect of fluid pressure through a generalized effective stress concept. The damage evolution is entirely controlled by and coupled with the frictional sliding. The effective elastic properties as well as Biot's coefficients of cracked porous materials are determined as functions of induced damage. The inelastic deformation due to frictional sliding is also taken into account. The procedure for the identification of the model's parameters is presented. The proposed model is finally applied to study both mechanical and poromechanical responses of a typical porous brittle rock in drained and undrained compression tests as well as in interstitial pressure controlled tests. The main features of material behaviors are well reproduced by the model. Copyright © 2012 John Wiley & Sons, Ltd.     

煤岩组合体分级加卸载特性的试验研究

通过MTS 815试验机研究了煤岩组合体分级加卸载试验。分级加卸载下煤岩组合体破坏以脆性破坏机制为主,与单轴作用相比,分级加卸载作用下煤岩组合体的破坏更为破碎,且破坏强度有所提高,但轴向和环向应变却有所降低。同一循环中的加载与卸载曲线基本不重合,且多数情况不形成闭合环路;卸载曲线与下一个循环的加载曲线通常也不重合,但会形成闭合环路。第1循环结束时残余变形较大,加卸载曲线形成了类似“牛角”状的曲线;随着循环加卸载地进行,与残余变形相比第1循环有所降低,加载和卸载曲线在逐渐靠近,并且加卸载曲线类似“竹叶”状。获得了残余变形和加卸载弹性模量随循环加卸载的变化关系,并且实验表明卸载到1 MPa附近时,卸载线是曲折波动的;但在再次加载初期,加载线几乎是直线,且随着荷载的继续增加,加载线和上一个循环的卸载线逐渐分离。循环加卸载后应变相位逐渐滞后于应力相位,内因可能是因为岩石矿物颗粒间的黏滞性以及煤岩组合体界面之间的摩擦引起的,而外因可能是循环加卸载导致了煤岩体内部损伤,并由此诱发不可恢复的残余变形     

Discrete element model for quasi‐brittle rupture under tensile and compressive loading

In the absence of initial cracks, the material behavior is limited by its strength, usually defined in homogeneous conditions (of stress and strain). Beyond this limit, in quasi‐brittle case, cracks may propagate and the material behavior tends to be well described by fracture mechanics. Discrete element approaches show consistent results dealing with this transition during rupture. However, the calibration of the parameters of the numerical models (i.e., stiffness, strength, and toughness) may be quite complex and sometimes only approximative. Based on a brittle rupture criterion, we analyze the biaxial response of uncracked samples. Thus, tensile and compressive strengths are analytically identified and become direct parameters of our discrete model. Furthermore, a physically reliable crack initiation (and subsequent propagation) is shown to be induced during rupture and verified by the simulation of three‐point bending and diametral compression tests. Copyright © 2016 John Wiley & Sons, Ltd.     

周期性循环载荷作用下岩石声发射规律试验研究

声发射是岩石等脆性材料内部损伤的伴生现象。在周期性循环载荷作用下通过改变不同应力幅度和不同加载速率对细粒砂岩进行声发射试验研究,探讨了声发射在周期性载荷作用下的声发射规律。研究结果表明,改变上限应力对声发射现象的影响显著,而改变下限应力的影响主要在循环末期,提早了每个循环声发射产生时间;加载速率的增加提高了声发射率,特别是循环过程中主裂纹的形成和扩展阶段,加快了岩石破坏进程;不同应力幅度和加载速率下声发射表现出不同的发展模式,不同模式预示着不同的岩石变形破坏速率。     

任意荷载下欠固结地基的非线性一维固结

根据Gibson得到的固相坐标z下的非线性固结控制方程,运用Laplace变换求解了在任意荷载作用下的单层饱水欠固结地基一维非线性变形问题;通过Laplace逆变换,求得单层饱水欠固结地基在任意荷载作用下的一维非线性固结解。结合单层地基在几种常见荷载作用下固结变形的算例,对解进行了探讨,揭示了任意变荷载作用下单层饱和软粘土欠固结地基一维非线性固结的特性,得到了一些可用于指导工程实践的有益结论。     

Investigation and modeling on fatigue damage evolution of rock as a function of logarithmic cycle

The fatigue damage behavior of granite under constant and variable amplitude loadings is studied. The experimental analysis reveals that there is a three‐stage law for the fatigue damage evolution as a function of absolute or relative cycle and the inverted‐S damage model proposed by the author, in this case, is capable of representing the damage behavior of rock. However, when the logarithmic cycle is considered, there are only two stages, i.e. steady and accelerated stages and the fatigue damage evolution greatly depends on the properties of rock and stress level. Accordingly, the fatigue damage evolution curves have been categorized into three types. Then, the effect of maximum stress, amplitude and fatigue initial damage on the damage evolution of rock is investigated. The analysis reveals that the damage evolution greatly depends on these influencing factors. The fatigue life decreases with the increase in the maximum stress, amplitude and fatigue initial damage due to the decrease in the proportion of the first stage to the whole fatigue process and the increase in the damage rate in the first stage. Meanwhile, a linear‐exponential formula is used to model the fatigue damage behavior of rock subjected to cyclic loading. This damage model is superior to the inverted‐S damage model in the convenience of establishment of critical instability point. The physical meanings of its constants have been illuminated and the applicability of this model to constant and variable amplitude cyclic loading explored. The fitting results for the test data show that this damage model can properly represent the fatigue damage behavior of rock. Copyright © 2010 John Wiley & Sons, Ltd.     

Implicit and explicit integration schemes in the anisotropic bounding surface plasticity model for cyclic behaviours of saturated clay

Two integration algorithms, namely the implicit return mapping and explicit sub-stepping schemes, are adopted in the anisotropic bounding surface plasticity model for cyclic behaviours of saturated clay and are implemented into finite element code. The model is a representative of a series of bounding surface models that have typical characteristics, including isotropic and kinematic hardening rules and a rotational bounding surface to capture complex but important cyclic behaviours of soils, such as cyclic shakedown and degradation. However, there is no explicit current yield surface in the model to which the conventional implicit algorithm returns the stress state back or the sub-stepping integration corrects the drift of the stress state. Hence, necessary modifications have been made for both of the integration schemes. First, the image stress point is mapped or corrected to the bounding surface instead of mapping back or correcting the stress state to the yield surface. Second, the unloading–loading criterion is checked to determine the image stress point rather than checking the yield criterion after giving the trial stress state in a conventional way. Comparative studies on the accuracy, stability and efficiency of the two integration schemes are conducted not only at the element level but also in solving boundary value problems of monotonic and cyclic bearing behaviours of rigid footings on saturated clay. For smaller strain increments, there is no significant difference in the accuracy between the two integration schemes, but the explicit integration shows a higher efficiency and accuracy. For relatively larger increments, the implicit return mapping algorithm presents good accuracy and more robustness, while the sub-stepping algorithm shows deteriorating accuracy and suffers the convergence problem. With the tolerance used in the present model, the bearing capacity of the rigid footing predicted by the return mapping algorithm is closer to the available analytical and numerical solutions, while the bearing capacity predicted by the sub-stepping algorithm shows a marginal increase.     

Calibration of a constitutive model using genetic algorithms

Before any constitutive model can be used in a numerical procedure, the model needs to be calibrated using laboratory test results. The traditional calibration techniques use stress and strain levels at certain states that a material undergoes during certain types of laboratory tests. Sometimes this method of calibrating a constitutive model fails to capture the overall behavior of a material, i.e. behavior at every point in stress/strain path. In this paper, we have shown how a random search technique, genetic algorithm (GA), can be used to calibrate constitutive models. The advantages of using GA are that it considers the overall behavior of a material, not the behavior at some specific states as the traditional method does, and it can work with many types of laboratory tests. The concept is applied to calibrate the hierarchical single surface (HiSS) δ_l model for geologic materials. Three cases have been studied where the difference is in the type of test data used to calibrate the model. These three different test data are: (1) simulated conventional test data, (2) simulated cyclic test data, and (3) real test data. A comparison of two different cross-over schemes, one-point and six-point, has been made.