Strain Rate Dependency of Coarse Crystal Marble Under Uniaxial Compression: Strength,Deformation and Strain Energy

Strain rate during testing, uniaxial or triaxial, has important influence on the measured mechanical properties of rocks. Uniaxial compression tests were performed at nine pre-specified static-to-quasistatic strain rates (ranging from 1 × 10^?5 to 1 × 10^?1 s^?1) on coarse crystal marble. The aim is to gain deep insight into the influence of strain rate on characteristic stresses, deformation properties and conversion of strain energy of such rock. It is found that the strain rate of 5 × 10^?3 s^?1 is the threshold to delineate the failure modes the tested coarse marble behaves in. At a strain rate less than this threshold, single-plane shear and conjugate X-shaped shear are the main failure modes, while beyond this threshold, extensile and splitting failures are dominant. The stress for crack initiation, the critical stress for dilation, the peak stress, and Young’s modulus are all found to increase with strain rate, with an exception that the above stresses and modulus appear relatively low compared to the strain rate in the range of between 1 × 10^?4 and 5 × 10^?3 s^?1. The pre-peak absorbed strain energy, damage strain energy and elastic strain energy are found to increase with strain rate. In addition, the elastic strain energy stored before peak point favors brittle failure of the specimen, as the more stored elastic energy in the specimen, the stronger the fragmenting.     

Viscoelastic damage model for asphalt concrete

The strain rate-dependent mechanical behavior of asphalt concrete was characterized using unconfined compression tests carried out at different loading rates. It was shown that at high strain rates, the elastic deformation and peak axial stress are highly sensitive to strain rate. Both increase as the strain rate increases. At very low strain rates, elastic response and unconfined compressive strength are relatively independent of the loading rate. Based on the experimental observations, a simple viscoelastic damage model is proposed for the strain rate-dependent unconfined compression behavior of asphalt concrete. In the model, strain rate response is modeled by a two-component viscoelastic model consisting of a constant elastic modulus and a viscous modulus that is related by a power-law function to the axial strain rate. Failure and strain softening are modeled via a damage formulation where damage evolution in the asphalt concrete is given by a simple form of the Weibull distribution function. The model was shown to be capable of describing the strain rate-dependent deformation, compressive strength, strain-softening and creep behavior of asphalt concrete. The model is relatively simple and requires only five material parameters.     

Influence of different strain rates on hydro-mechanical behaviour of reconstituted unsaturated soil

The hydro-mechanical behaviour of a reconstituted unsaturated soil under different suctions and strain rates was studied through various rate-controlled unsaturated/undrained triaxial tests. The fully saturated reconstituted specimens were desaturated to four different initial suctions (s₀?=?0, 100 kPa, 200 kPa and 300 kPa) and then triaxially sheared (conventional triaxial compression) at three different strain rates in undrained conditions (\(\dot{\varepsilon }_{1} = 0.001\) h^?1, 0.01 h^?1, and 0.1 h^?1). The observed hydro-mechanical behaviour during shearing including the volumetric strain, deviatoric stress, degree of saturation and suction is presented and discussed in this paper. The results indicate that when the strain rate rises at the given initial suctions (or pore water pressures), the maximum deviatoric stress (q_max), critical net stress ratio (M) and critical state suction (s_c) increase but the degree of saturation (S_rc) and volumetric strain at the critical state (ε^c_v ) reduce. The critical effective stress ratio (M′) is not dependent on the strain rate for saturated and unsaturated samples. The critical state lines for unsaturated soils with the constant strain rates are parallel with each other in the e???lnp′ space.

     

Computational model coupling mode II discrete fracture propagation with continuum damage zone evolution

We propose a numerical method that couples a cohesive zone model (CZM) and a finite element‐based continuum damage mechanics (CDM) model. The CZM represents a mode II macro‐fracture, and CDM finite elements (FE) represent the damage zone of the CZM. The coupled CZM/CDM model can capture the flow of energy that takes place between the bulk material that forms the matrix and the macroscopic fracture surfaces. The CDM model, which does not account for micro‐crack interaction, is calibrated against triaxial compression tests performed on Bakken shale, so as to reproduce the stress/strain curve before the failure peak. Based on a comparison with Kachanov's micro‐mechanical model, we confirm that the critical micro‐crack density value equal to 0.3 reflects the point at which crack interaction cannot be neglected. The CZM is assigned a pure mode II cohesive law that accounts for the dependence of the shear strength and energy release rate on confining pressure. The cohesive shear strength of the CZM is calibrated by calculating the shear stress necessary to reach a CDM damage of 0.3 during a direct shear test. We find that the shear cohesive strength of the CZM depends linearly on the confining pressure. Triaxial compression tests are simulated, in which the shale sample is modeled as an FE CDM continuum that contains a predefined thin cohesive zone representing the idealized shear fracture plane. The shear energy release rate of the CZM is fitted in order to match to the post‐peak stress/strain curves obtained during experimental tests performed on Bakken shale. We find that the energy release rate depends linearly on the shear cohesive strength. We then use the calibrated shale rheology to simulate the propagation of a meter‐scale mode II fracture. Under low confining pressure, the macroscopic crack (CZM) and its damaged zone (CDM) propagate simultaneously (i.e., during the same loading increments). Under high confining pressure, the fracture propagates in slip‐friction, that is, the debonding of the cohesive zone alternates with the propagation of continuum damage. The computational method is applicable to a range of geological injection problems including hydraulic fracturing and fluid storage and should be further enhanced by the addition of mode I and mixed mode (I+II+III) propagation. Copyright © 2016 John Wiley & Sons, Ltd.     

An experimental study on deformation and failure mechanical behavior of granite containing a single fissure under different confining pressures

Fissures in natural rocks play an important role in determining the strength, deformability and failure behavior of rock mass. However in the past, triaxial compression experiments have rarely been conducted for rock materials containing three-dimensional (3-D) fissures and the failure mechanical behavior of fissured rocks is not well known due to the difficulty of conducting triaxial experiments on fissured rocks. Therefore in this research, conventional triaxial compression experiments were performed to study the strength, deformability and failure behavior of granite specimens with one preexisting open fissure. Thirty-one specimens were prepared to perform conventional triaxial compression tests for intact and fissured granite. First, based on the experimental results, the effects of the confining pressure and the fissure angle on the elastic modulus and the peak axial strain of granite specimens are analyzed. Second, the influence of the confining pressure on the crack damage threshold and the peak strength of granite with respect to various fissure angles are evaluated. For the same fissure angle, the crack damage threshold and the peak strength of granite both increase with the confining pressure, which is in good agreement with the linear Mohr–Coulomb criterion. With increasing fissure angle, the cohesion of granite first increases and later decreases, but the internal friction angle is not obviously dependent on the fissure angle. Third, nine crack types are identified to analyze the failure characteristics of granite specimens containing a single fissure under conventional triaxial compression. Finally, a series of X-ray microcomputed tomography (CT) observations were conducted to analyze the internal damage mechanism of granite specimens with respect to various fissure angles. Reconstructed 3-D CT images indicate obvious effects of confining pressure and fissure angle on the crack system of granite specimens. The study helps to elucidate the fundamental nature of rock failure under conventional triaxial compression.     

考虑应变局部化的粗粒料剪切损伤力学机制

针对粗粒料的应变软化、剪胀等力学特性,通过考虑以剪切带为标志的应变局部化现象,建立了具有广泛适用性的剪切损伤力学模型。损伤模型采用了包体理论中的剪切带数学简化,基于应变等价原理、Weibull分布,推导了粗粒料的应力-应变关系方程。从剪胀作用的机制出发,提出可以描述剪胀弱化的轴向塑性应变和体积塑性应变的非线性函数关系。结合粗粒料三轴压缩试验中的伺服过程,提出了基于遗传算法的损伤模型参数确定方法。通过开展不同围压下的粗粒料三轴压缩试验,对剪切损伤力学模型进行验证,进一步分析了参数演化对粗粒料强度和变形特征的影响。研究结果表明,考虑应变局部化特征的剪切损伤力学模型可以高精度的模拟粗粒料的应变软化和剪胀等特征,有效揭示剪切带内部变形对试样整体宏观变形的影响机制,模型中剪切带参数和围压的关系与粗粒料细观机制一致,计算得到强度组成与颗粒破碎、重组特征较为吻合。     

卸荷损伤原状膨胀土剪切力学特性试验研究

通过GDS三轴试验系统对经历3种卸荷速率损伤后的原状南阳膨胀土样进行再加荷不排水三轴伸长剪切试验,同时考虑了超固结比与固结状态的影响。试验结果表明,膨胀土再加荷剪切力学特性与初始卸荷速率有关。在相同的轴向应变下,初始卸荷速率越小,其偏应力单调越小。在主应力方向改变前后,其应力?应变关系曲线斜率显著变化。相同固结方式与超固结比状态下,孔隙水压力均表现为先增大后减小趋势,孔隙水压力峰值应变随卸荷速率增大而减小。无论是等压固结还是K0固结,初始卸荷速率越大,不排水剪切强度越大。膨胀土样经历了初始卸荷损伤后,再加荷常规三轴伸长试验所得剪切强度均低于无损伤时的强度。以膨胀土破坏强度所得损伤度SD低估了卸荷速率对膨胀土的损伤程度,建议采用孔隙水压力峰值强度进行膨胀土边坡设计计算。原状膨胀土力学性状随卸荷速率损伤的演化规律受卸荷阶段轴向应变大小及裂隙性综合影响。     

Anisotropic viscoplastic modeling of rate‐dependent behavior of clay

The objective of this study is to derive an effective stress‐based constitutive law capable of predicting rate‐dependent stress–strain, stress path and undrained shear strength and creep behavior. The flow rule used in the MIT‐E3 model and viscoplasticity theory is employed in the derivation. The model adopts the yield surface capable of representing the yield behavior of the Taipei silty clay and assumes that it is initially symmetric about the K₀‐line. A method is then developed to compute the gyration and expansion of the loading surface to simulate the anisotropic behavior due to the principal stress rotation after shear. There are 11 parameters required for the model to describe the soil behavior and six of them are exactly the same as those used in the Modified Cam‐clay model. The five additional parameters can be obtained by parametric studies or conventional soil tests, such as consolidation tests, triaxial compression and extension tests. Finally, verification of the model for the anisotropic behavior, creep behavior and the rate‐dependent undrained stress–strain and shear strength of the Taipei silty clay is conducted. Copyright © 2010 John Wiley & Sons, Ltd.     

Studying the effect of non‐spherical micro‐particles on Hoek–Brown strength parameter mi using numerical true triaxial compressive tests

The strength parameter m_i in the Hoek–Brown strength criterion is empirical and was developed by trial and error. To better understand the fundamental relationship between m_i and the physical characteristics of intact rock, this paper presents a systematic study of m_i by representing intact rock as a densely packed cemented particle material and simulating its mechanical behavior using particle flow modeling. Specifically, the three‐dimensional particle flow code (PFC3D) was used to conduct numerical true triaxial compression tests on intact rock and to investigate the effect of non‐spherical micro‐particle parameters on m_i. To generate numerical intact rock specimens containing non‐spherical micro‐particles, a new genesis process was proposed, and a specific loop algorithm was used based on the efficiency of the process and the acceptability of generated specimens. Four main parameters—number, aspect ratio, size, and shape—of non‐spherical micro‐particles were studied, and the results indicated that they all have great effect on m_i. The strength parameter m_i increases when the number, aspect ratio, or size is larger or the shape becomes more irregular, mainly as a result of the higher level of interlocking between particles. This confirms the observations from engineering experience and laboratory experiments. To simulate the right strength parameter m_i, it is important to use appropriate non‐spherical micro‐particles by controlling these four parameters. This is further demonstrated by the simulation of two widely studied rocks, Lac du Bonnet granite and Carrara marble. Copyright © 2014 John Wiley & Sons, Ltd.     

粗粒土剪胀性大型三轴试验研究

剪胀性是土体显著区别于一般弹性材料的基本特性,与土体的强度和变形特性密切相关。通过4组不同初始密度的塔城砂砾石常规大型三轴试验,研究剪胀性对粗粒土强度和变形特性的影响。试验结果表明,（1）若体变速率（体变和轴向应变均以压缩为正）先从正值减小到负值并达到最小值,随后又有所增大但仍小于0,则应力-应变曲线为软化型,在比值为最小值时土体剪胀性最大,对应于峰值强度,若体变速率从某一正值单调减小并一直大于0,则应力-应变曲线为硬化型;（2）体变变化趋势取决于剪胀性和压缩性的大小,剪切后期若剪胀速率大于压缩速率,则体变先压缩后膨胀,应力-应变曲线呈软化型,反之若剪胀速率小于压缩速率,则体变一直是压缩的,应力-应变曲线呈硬化型。研究结果对于加深认识粗粒土的强度和变形特性具有重要意义。     

Study on the strength of frozen clay at high confining pressure

An extensive test program was conducted on East China deep clay to investigate mechanical behavior in the process of axial compression and triaxial compression. In addition, the effect of negative temperature and confining pressure on the strength of frozen clay was analyzed. It is concluded that the stress-strain curves at high confining pressure belong to the strain hardening type and its strength almost corresponds to confining pressure in the range of tested confined stress. With respect to temperature, the strength increases when the temperature decreases. __________ Translated from Journal of Glaciology and Geocryology, 2007, 29(4): 636–639 [译自: 冰川冻土]     

不同围压下龙马溪组页岩能量、损伤及脆性特征

页岩气储层的力学性质是影响页岩井壁稳定性的重要因素。根据不同围压下龙马溪组页岩的单三轴试验结果,开展页岩能量演化规律、损伤演化规律和脆性特征研究。结果表明:从初始到屈服阶段,岩样的总吸收能几乎全部转化为弹性应变能;屈服阶段至峰值强度阶段期间,弹性应变能与总吸收能之比逐渐减小,耗散能逐渐增加。峰后弹性应变能骤降,耗散能迅速增加。能量的耗散与岩石损伤具有正相关性;从能量角度揭示的损伤演化规律符合"S"型曲线特征;低围压下,龙马溪组页岩脆性指数更强,高围压下,它的脆性指数更弱。本文的研究对指导储层压裂效果评价及井壁稳定性评价具有重要的意义和应用价值。     

不同应变率单轴加载条件下页岩的各向异性力学行为

基于静载条件下的常规力学试验可以证明,页岩层理面的存在是导致其力学行为各向异性的主要原因,而应变率的变化势必也影响着页岩各向异性特征的变化。为探究应变率对页岩各向异性力学行为的影响,分别在10-4 s-1、5×10-4 s-1、10-3 s-1和10-2 s-1 4种应变率条件下对不同层理角度的页岩进行单轴压缩力学试验。研究表明:（1）页岩弹性模量的各向异性程度随应变率升高而减弱,泊松比的各向异性程度受应变率的影响不明显;（2）页岩峰值强度随应变率升高而增加,其中45°~60°试样应变率敏感性最强,页岩的强度各向异性度随应变率升高而降低;（3）随着应变率升高,层理面对页岩破坏模式的控制作用得到削弱,破坏模式的各向异性程度减弱。总体而言,页岩的各向异性力学特征随应变率升高而减弱,研究结论有助于页岩力学行为的深入理解。     

Strain rates at high temporal resolution from curved inclusion trails in garnet,Passo del Sole,Central Swiss Alps

Quantitative strain rates at outcrop scale are very difficult to obtain, but they may be estimated from crystals with curved inclusion trails by calculating rotation rates from growth rates and corresponding deflections of the internal foliation. Garnet in a quartzose pelite at Passo del Sole in the central Swiss Alps is extraordinarily valuable for calculation of strain rates during Alpine orogenesis, because the unusual zoning patterns clearly define the kinetics of its nucleation and growth. Complex concentric zoning patterns can be correlated from one crystal to another in a hand sample, based on compositional and microstructural similarities; the ubiquity of these features demonstrates that all garnet crystals nucleated at nearly the same time. Compositional bands whose radial widths are proportional to crystal size provide evidence for growth governed by the kinetics of intergranular diffusion of locally sourced nutrients. Together, these constraints increase the reliability of estimates of rates of garnet growth, and the strain‐rate calculations that depend on them. To obtain growth rates, P–T conditions during garnet crystallization were modelled in a series of pseudosections, and compositional evolution was connected to rates of garnet growth by means of an independently determined heating rate. These growth rates, combined with measured amounts of curvature of inclusion trails, indicate that the time‐averaged strain rate at Passo del Sole during Alpine metamorphism was on the order of 10^?14 s^?1. Strain rates calculated using rotational v. non‐rotational models are similar in magnitude. The constraints on crystallization kinetics also allow direct calculation of strain rates during individual stages of garnet growth, revealing short‐term increases to values on the order of 10^?13 s^?1. These higher strain rates are correlated with the growth of concentric high‐Ca or high‐Mn zones in garnet, which implies that strain softening associated with the transient passage of fluids is responsible for acceleration of deformation during these intervals.     

考虑超固结比和应力速率影响的膨胀土卸荷力学特性研究

利用GDS应力路径三轴试验系统对南阳膨胀土进行3种应力速率下、4种超固结比（OCR）的被动压缩三轴试验及3种超固结比的被动挤伸三轴试验,分析了不同超固结比和应力速率下其应力（孔隙水压力）-应变关系、有效应力路径及变形模量的演化规律,对膨胀土变形模量各向异性特性进行了初步探讨。结果表明,应力速率、超固结比及卸荷路径均对膨胀土力学特性有一定影响。在被动压缩路径和被动挤伸路径下,随着应力速率和超固结比的增加,相同轴向应变时的偏应力值单调增加;不同超固结比和应力速率时膨胀土的孔隙水压力始终为负值,且其降幅总体上随超固结比的增加而增大,但其降幅随应力速率的变化规律与剪切路径有关。在被动压缩路径下,相同应变时不同应力速率下的孔压降幅基本相同;而在被动挤伸路径下,其降幅随应力速率的增加而增大。边坡开挖路径的选择对于边坡变形影响显著,被动挤伸路径下达到设定极限偏应力时的轴向应变明显大于被动压缩路径。膨胀土变形模量E100随着超固结比和应力速率的增加而增加,但各应力速率下变形模量的各向异性特性则随着超固结比的增加而变弱。     

Physical and numerical investigation of a cemented granular assembly of steel spheres

In this paper, steel spheres embedded in a cement matrix were studied using numerical and physical ISRM testing procedures. A challenge in discrete element simulations is to select appropriate micro‐mechanical models and parameters, to recover the observed macro‐mechanical behavior. An ideal experiment on cohesive granular assemblies constructed identical to numerical ones would validate these micro models for a set of measured micro‐parameters. The first part of the paper summarizes the previous studies in this area, outlines such experimental methodology and depicts the steps followed for the preparation and the testing of cemented granular assemblies together with the derivation of micro‐parameters. The second part discusses the results of numerical and physical ISRM standard tests including uniaxial and triaxial compression, Brazilian tensile and shear box tests. Physical samples were prepared using steel balls bonded with Portland cement, cured under controlled laboratory conditions and tested in compression, tension and shearing. Acoustic emissions were monitored in uniaxial tests to characterize the damage thresholds relative to volumetric strains. Numerical simulations were conducted with PFC 3D using micro‐mechanical parameters derived from physical testing. Parametric sensitivity studies were carried out to look into the dependency of macroscopic responses on the parameters. The results from both numerical and physical tests showed good correspondence in macroscopic behavior i.e. peak strength, stages of damage, mode of failures. However, the numerical simulations reflected a stiffer mechanical response than physical assemblies. Copyright © 2010 John Wiley & Sons, Ltd.     

Experimental study and constitutive modelling of elasto‐plastic damage in heat‐treated mortar

This study investigates the effect of a heat‐treatment upon the thermo‐mechanical behaviour of a model cement‐based material, i.e. a normalized mortar, with a (w/c) ratio of 0.5. First, a whole set of varied experimental results is provided, in order to either identify or validate a thermo‐mechanical constitutive model, presented in the second paper part. Experimental responses of both hydraulic and mechanical behaviour are given after different heating/cooling cycling levels (105, 200, 300, 400^°C). The reference state, used for comparison purposes, is taken after mass stabilization at 60^°C. Typical uniaxial compression tests are provided, and original triaxial deviatoric compressive test responses are also given. Hydraulic behaviour is identified simultaneously to triaxial deviatoric compressive loading through gas permeability K_gas assessment. K_gas is well correlated with volumetric strain evolution: gas permeability increases hugely when ε_v testifies of a dilatant material behaviour, instead of contractile from the test start. Finally, the thermo‐mechanical model, based on a thermodynamics approach, is identified using the experimental results on uniaxial and triaxial deviatoric compression. It is also positively validated at residual state for triaxial deviatoric compression, but also by using a different stress path in lateral extension, which is at the origin of noticeable plasticity. Copyright © 2009 John Wiley & Sons, Ltd.     

Effects of size and strain rate on the mechanical behaviors of rock specimens under uniaxial compression

Size and strain rate are two key factors that dramatically influence the estimation of rock mechanical behaviors. To better understand the effects of size and strain rate on measured rocks, rock specimens with six different sizes were tested at six different strain rates under uniaxial compression using the MTS 815 Rock Mechanics Test System. Having determined that the size and strain rate significantly affect the peak strain, peak stress, elastic modulus, acoustic emission (AE), and failure pattern of the rock specimens, the relation was established between the strength and the size and strain rate of red sandstone. And the variation was revealed among the size and strain rate, the AE, and the failure pattern. It turned out that the peak stress was negatively correlated with the rock size and was positively correlated with the strain rate. When the length to diameter ratio (L/D) of the rock specimen was less than 2.0, the AE appeared mildly. The AE quantities gradually increased before the peak stress, and then sharply decreased after the peak stress. The failure pattern of the rock specimen was relatively complicated, with a fracture plane appearing along the axial direction. Conical failure type was also presented. When the L/D ratio of the specimen was greater than 2.0, the AE characteristics of red sandstone showed the radical model. There were relatively few AE rings before the peak stress. But the AE rings increased suddenly and dramatically during the peak stress. The rock specimens primarily failed with a single shear plane. Moreover, with an increase in the strain rate, the AE activities were enhanced and the AE quantities increased. When the strain rate of the rock specimen was less than 5.0?×?10^?4/s, the rock specimen failed with a shear or tensile-shear pattern. And when the strain rate was greater than 5.0?×?10^?4/s, the rock specimen tended to fail in a conical pattern.     

一个深海能源土弹塑性本构模型

天然气水合物赋存在低温高压环境中,会在土颗粒间形成胶结从而增大深海能源土抗剪强度。基于损伤力学理论,将结构性砂土本构模型推广应用于深海能源土分析中,模拟计算了三轴固结排水剪切试验,再根据应力-应变曲线关系定量反演初始屈服系数与水合物饱和度之间的函数关系,并修正了原有的结构性砂土破损规律,建立了深海能源土弹塑性本构模型。另外,根据该模型模拟了另外一组深海能源土三轴剪切试验和等向固结压缩试验。计算结果表明：新建立的深海能源土本构模型可以有效模拟深海能源土剪切强度随水合物饱和度之间的增长关系;随着水合物饱和度的增加,三轴压缩试验中深海能源土峰值强度及割线模量(E50)逐渐增加,等向固结压缩试验中屈服强度增加,与试验结果有较好的一致性,表明了该模型的合理性。     

Experimental Study of Brittle Behavior of Clay Shale in Rapid Triaxial Compression

The brittle failure behavior of an over-consolidated clay shale (Opalinus Clay) in undrained rapid triaxial compression was studied. The confining stress levels were chosen to simulate the range of confining stresses relevant for underground excavations at the Mont Terri Underground Research Laboratory, and to investigate the transition from axial splitting failure to macroscopic shear failure. Micro-crack initiation was observed throughout the confining stress range utilized in this study at a differential stress of 2.1 MPa on average, which indicates that friction was not mobilized at this stage of brittle failure. The rupture stress was dependent on confinement indicating friction mobilization during the brittle failure process. With increasing confinement net volumetric strain decreased suggesting that dilation was suppressed, which is possibly related to a change in the failure mode. At confining stress levels ≤0.5 MPa specimen rupture was associated with axial splitting. With increasing confinement, transition to a macroscopic shearing mode was observed. Multi-stage triaxial tests consistently showed lower strengths than single-stage tests, demonstrating cumulative damage in the specimens. Both the Mohr–Coulomb and Hoek–Brown failure criteria could not satisfactorily fit the data over the entire confining stress range. A bi-linear or S-shaped failure criterion was found to satisfactorily fit the test data over the entire confinement range studied.