Displacement velocity effects on rock fracture shear strengths

Triaxial shear tests are performed to assess the effects of displacement velocity and confining pressure on shear strengths and dilations of tension-induced fractures and smooth saw-cut surfaces prepared in granite, sandstone and marl specimens. A polyaxial load frame is used to apply confining pressures between 1 and 18 MPa with displacement velocities ranging from 1.15 × 10⁻⁵ to 1.15 × 10⁻² mm/s. The results indicate that the shearing resistances of smooth saw-cut surfaces tend to be independent of the displacement velocity and confining pressure. Under each confinement the peak and residual shear strengths and dilation rates of rough fractures increase with displacement velocities. The sheared-off areas increase when the confining pressure increases, and the displacement rate decreases. The velocity-dependent shear strengths tend to act more under high confining pressures for the rough fractures in strong rock (granite) than for the smoother fractures in weaker rocks (sandstone and marl). An empirical criterion that explicitly incorporates the effects of shear velocity is proposed to describe the peak and residual shear strengths. The criterion fits well to the test results for the three tested rocks.     

循环加载时围压对岩石动力特性的影响

针对砂岩岩样,探讨了在不同围压作用下和轴向循环加载时岩样的动力力学性质,研究围压对砂岩岩样的动力力学性质的影响。采用的试验设备是MTS－815岩石和混凝土试验系统,5组围压分别为10、20、30、40、50 MPa。岩样为汶川地区的干砂岩,轴向荷载施加的频率为1 Hz。结果表明,（1）随着围压的逐渐增加,试样的残余轴向应变和体变逐渐增加,且剪胀发生时的残余体变也逐渐增加;（2）动力荷载作用时岩样在高围压比低围压下的初始刚度和强度高;（3）不同围压作用下,当应力比Rs较大时,岩样在较小的循环次数下发生破坏;（4）试样的破坏模式为剪切破坏,动力荷载作用下试样形成的局部化破坏带更宽。     

冻结粉土三轴压缩变形破坏与能量特征分析

对不同温度和不同围压下的青藏冻结粉土进行了三轴压缩与加卸载试验,得到冻结粉土应力-应变关系曲线、抗压强度等力学参数随温度与围压变化的关系。结果表明,冻结粉土典型应力-应变曲线在低围压下大致可以分为线弹性、峰前塑性变形与峰后软化3个阶段。当? 3 < 3.0 MPa时,应力-应变曲线具有明显的峰后软化现象,随围压的增大,软化现象逐渐减弱,当? 3 达到14 MPa,应变软化现象重新变得明显;冻结粉土的强度与变形模量均随围压的增加先升后降;低围压作用下冻结粉土体积随轴向应变的增加先缩后胀,而高围压下体积变形只有体缩;低围压下冻结粉土体积塑性变形耗散能先是随着体积塑性变形增大而增大,之后由于剪胀而减少,高围压下体积塑性变形耗散能始终增加;剪切塑性变形耗散能与塑性剪应变之间近似成抛物线的关系。     

Predicting mechanical properties and ultimate shear strength of gypsum,limestone and sandstone rocks using Vipulanandan models

ABSTRACT

In this study, over 1000 data from the literature was used to characterize and compare the density, strengths, modulus, fracture toughness, porosity and the ultimate shear strengths of the gypsum, limestone and sandstone rocks. The compressive modulus and Mode-1 fracture toughness of the gypsum rock, limestone rock and sandstone rocks varied from 0.7 GPa to 70 GPa, and from 0.03 MPa.m^0.5 to 2.6 MPa.m^0.5  respectively. Vipulanandan correlation model was effective in relating the modulus of elasticity, fracture toughness with the relevant strengths of the rocks. A new nonlinear Vipulanandan failure criterion was developed to quantify the tensile strength, pure shear (cohesion) strength and to predict the maximum shear strength limit with applied normal stress on the gypsum, limestone and sandstone rocks. The Vipulanandan failure model predicts the maximum shear strength limit was, as the Mohr-Coulomb failure model does not have a limit on the maximum shear strength. With the Vipulanandan failure model based on the available data, the maximum shear strengths predicted for the gypsum, limestone and sandstone rocks were 64 MPa, 114 MPa and 410 MPa respectively.     

A Bounding Surface Plasticity Model for Intact Rock Exhibiting Size-Dependent Behaviour

A new constitutive model for intact rock is presented recognising that rock strength, stiffness and stress–strain behaviour are affected by the size of the rock being subjected to loading. The model is formulated using bounding surface plasticity theory. It is validated against a new and extensive set of unconfined compression and triaxial compression test results for Gosford sandstone. The samples tested had diameters ranging from 19 to 145 mm and length-to-diameter ratios of 2. The model captures the continuous nonlinear stress–strain behaviour from initial loading, through peak strength to large shear strains, including transition from brittle to ductile behaviour. The size dependency was accounted for through a unified size effect law applied to the unconfined compressive strength—a key model input parameter. The unconfined compressive strength increases with sample size before peaking and then decreasing with further increasing sample size. Inside the constitutive model two hardening laws act simultaneously, each driven by plastic shear strains. The elasticity is stress level dependent. Simple linear loading and bounding surfaces are adopted, defined using the Mohr–Coulomb criterion, along with a non-associated flow rule. The model simulates well the stress–strain behaviour of Gosford sandstone at confining pressures ranging from 0 to 30 MPa for the variety of sample sizes considered.     

Experimental Investigation on the Strength, Deformability, Failure Behavior and Acoustic Emission Locations of Red Sandstone Under Triaxial Compression

Conventional triaxial compression and “reducing confining pressure” experiments were carried out for red sandstone by an MTS815 Flex Test GT rock mechanics experimental system. Our results show that the post-peak axial deformation characteristics of red sandstone changed as the confining pressure was increased from 5 to 65?MPa. Young’s modulus of red sandstone increased nonlinearly with increasing confining pressure, but Poisson’s ratio remained unaffected. Using our new data, the compactive and dilatant behavior, strength and failure characteristics of sandstone under triaxial compression are further discussed. For our data, the nonlinear Hoek-Brown criterion better reflects the peak strength properties than the linear Mohr-Coulomb criterion. However, the residual strength shows a clear linear relationship with confining pressure, which can be best described using the linear Mohr-Coulomb criterion. The peak and residual strengths were not directly related to the two different loading paths. The onset of dilatancy (C′), the switch from compaction-dominated to dilatant-dominated behavior (D′) and the stress at zero volumetric strain all increased linearly with the confining pressure. In our conventional triaxial compression experiments, the failure mode changed from mixed tension and shear fracture (single shear fracture) to shear fracture with double slippage planes with increasing confining pressure. However, the failure mode in our “reducing confining pressure” experiments was more complicated and results mainly from the unstable failure characteristics of the rock during the reduction in confining pressure. Finally, based on our acoustic emission (AE) locations, at a confining pressure of 35?MPa, a detailed analysis of the evolutionary process of internal cracks is presented for the entire loading process.     

人工单节理砂岩的三轴试验研究

采用云石胶黏结岩块的方法制备人工节理面,通过直剪试验获得人工节理面的抗剪强度特性,基于完整和单节理砂岩的常规三轴试验,分析不同倾角（0°,30°,60°,90°）对单节理岩体试样力学响应的影响。结果表明:人工节理面在直剪试验中呈现脆性破坏,其抗剪强度符合M-C准则;不同围压下（2.5,5 0和7.5 MPa）完整砂岩的破坏形态和弹性模量基本相同,峰值强度随围压增大;相同围压下（2.5 MPa）不同倾角单节理岩体的破坏形态、弹性模量、峰值强度均不相同,单节理岩体试样的峰值强度-倾角曲线呈反对号“”形,节理倾角对岩体力学性质的影响明显,其中60°节理岩体试样的强度最低,仅为完整岩石强度的19.7%。推导了过圆柱体试样中心任意斜截面内力的三维计算公式,根据其理论预测所得完整岩石的破裂面角度和60°节理试样的破坏方式均与试验结果相符,其吻合度较传统的二维分析更高。     

Considerations on strength of intact sedimentary rocks

This study presents the results of laboratory testing of sedimentary rocks under point loading as well as in uniaxial and triaxial compression. From the statistical analysis of the data, different conversion factors relating uniaxial compressive and point loading strength were determined for soft to strong rocks. Additionally, the material constant m_i, an input parameter for the Hoek and Brown failure criterion, was also estimated for different limestone samples by analysing the results from a series of triaxial compression tests under different confining pressures. The uniaxial compressive strength (UCS) of intact rocks, as estimated from the point load index using conversion factors, together with the Hoek–Brown constant m_i, and the Geological Strength Index (GSI) constitute the parameters for the calculation of the strength and deformability of rock masses.     

Subcritical compaction and yielding of granular quartz sand

Cylindrical samples of water-saturated, initially loose, St. Peter quartz sand were consolidated using triaxial deformation apparatus at room temperature, constant fluid pressure (12.5 MPa), and elevated confining pressures (up to 262.5 MPa). The samples were deformed along four loading paths: (1) hydrostatic stressing tests in which confining pressure was monotonically increased; (2) hydrostatic stress cycling similar to (1) except that effective pressure was periodically decreased to initial conditions; (3) triaxial deformation at constant effective pressure in which differential stress was applied after raising effective pressure to an elevated level; and (4) triaxial stress cycling similar to (3) except that the axial differential stress was periodically decreased to zero. Hydrostatic stressing at a constant rate results in a complex nonlinear consolidation response. At low pressures, large strains occur without significant acoustic emission (AE) activity. With increased pressure, the stress versus strain curve becomes quasi-linear with a corresponding nonlinear increase in AE rates. At elevated pressures, macroscopic yielding is marked by the onset of large strains, high AE rates, and significant grain failure. Stress cycling experiments show that measurable inelastic strain occurs at all stages of hydrostatic loading. The reload portions of stress cycles are characterized by a poro-elastic response and lower AE rates than during constant rate hydrostatic stressing. As the stress nears and exceeds the level that was applied during previous loading cycles, strain and AE rates increase in a manner consistent with yielding. Triaxial stressing cycles achieve greater consolidation and AE rates than hydrostatic loading at similar mean stress levels. By comparing our results with previously published studies, we construct a three-component model to describe elastic and inelastic compaction of granular sand. This model involves acoustically silent grain rearrangement that contributes significant inelastic strain at low pressures, poro-elastic (Hertzian) deformation at all pressures, and inelastic strain related to granular cracking and particle failure which increases in significance at greater pressures.     

Mechanical Behavior of Methane Infiltrated Coal: the Roles of Gas Desorption, Stress Level and Loading Rate

We report laboratory experiments to investigate the role of gas desorption, stress level and loading rate on the mechanical behavior of methane infiltrated coal. Two suites of experiments are carried out. The first suite of experiments is conducted on coal (Lower Kittanning seam, West Virginia) at a confining stress of 2 MPa and methane pore pressures in the fracture of 1 MPa to examine the role of gas desorption. These include three undrained (hydraulically closed) experiments with different pore pressure distributions in the coal, namely, overpressured, normally pressured and underpressured, and one specimen under drained condition. Based on the experimental results, we find quantitative evidence that gas desorption weakens coal through two mechanisms: (1) reducing effective stress controlled by the ratio of gas desorption rate over the drainage rate, and (2) crushing coal due to the internal gas energy release controlled by gas composition, pressure and content. The second suite of experiments is conducted on coal (Upper B seam, Colorado) at confining stresses of 2 and 4 MPa, with pore pressures of 1 and 3 MPa, under underpressured and drained condition with three different loading rates to study the role of stress level and loading rate. We find that the Biot coefficient of coal specimens is <1. Reducing effective confining stress decreases the elastic modulus and strength of coal. This study has important implications for the stability of underground coal seams.     

硬石膏常规三轴压缩下强度和变形特性的试验研究

采用伺服刚性试验机对硬石膏进行了不同围压下的常规三轴试验,研究了硬石膏的强度和变形特性。结果表明,在低围压下硬石膏破坏方式为剪切破坏;在围压超过10 MPa时,硬石膏表现出明显的塑性流动特性。观察试验后试样发现,在围压为18 MPa时,硬石膏已经没有明显的破坏面,而是表现出明显的膨胀现象。硬石膏的峰值强度与围压近似成正比例关系。分析了峰值应变、弹性模量随围压的变化规律,其结果表明：随着围压的升高,硬石膏的的峰值应变与弹性模量均逐渐增加。根据三轴试验结果绘制了摩尔包络线,采用回归分析得到了强度准则和抗剪强度参数c、? 值,其研究结果可为地下工程提供参考与借鉴。     

人造多晶冰三轴压缩强度特性试验研究

为研究冰的三轴强度特性,对人造宏观各向同性冰进行了不同温度和不同围压下的恒定加载速率三轴压缩试验,得到多晶冰三轴压缩的应力-应变曲线、抗压强度与温度之间的关系,利用莫尔-库仑强度准则分析了温度和围压对强度参数的影响.结果表明：轴向应变加载速率为1.67×10-4 s-1时,不同温度、不同围压下冰的应力-应变曲线均为应变...     

不同围压下砂岩的变形力学特性与损伤机制

开展不同围压下砂岩的强度、变形和损伤演化研究,对岩体工程的结构设计和稳定性评价具有重要意义。对赵固一矿二1煤层顶板砂岩进行试验获得其力学参数,并采用颗粒流程序获得砂岩细观力学参数,结合编制的fish语言程序进行试验,研究砂岩在不同围压的强度、变形和损伤演化机制,得到如下结论:随着围压增加砂岩的屈服段变长,围压小于40 MPa时峰值强度随围压变化敏感,大于40 MPa时敏感性降低,随着围压增加砂岩由脆性破坏逐步转变为延性破坏;砂岩的扩容经历线性体缩、线性扩容和非线性扩容3个阶段,围压增大线性扩容阶段缩短而非线性扩容阶段增加,扩容指数和扩容起始点轴向应变与围压存在指数变化规律;砂岩的损伤破坏经历损伤弥散分布、聚集成核、形成局部裂隙和主控破裂面形成4个阶段,低围压下砂岩沿单一主控破裂面发生压剪破坏,高围压下主控破裂面呈X型交叉破坏岩体,为X型共轭斜面剪切破坏形式。      

Bearing of structural anisotropy on deformation and mechanical response of rocks: An experimental example of rocksalt deformation under variable compression rates

The deformation and mechanical responses of rocks are prime concern in development of varieties of civil and mining engineering structures. The deformation and mechanical properties of both natural and artificial materials are strongly depend on mineral constituents and their arrangements, temperatures and pressures, stress rates and structural anisotropy. This study elaborates an understanding of structural anisotropy, compression rates and mechanical attributes relationship in rocks with specific examples of deformed rocksalt. The cubical samples (5X5X5 cm³) with three kinds of structural anisotropy were subjected to quasistatic compressive stress at rates 0.00035 MPa/min, 0.0035 MPa/min, 0.035 MPa/min, 0.35 MPa/min, 3.5MPa/min, 5 MPa/ min, 7MPa/min and 9 MPa/min on servo-controlled Material Testing System (MTS). The stress-strain curves prepared from deformation of rocksalt’s samples under different rates of compressions are used to determine major mechanical parameters viz., strengths, strains, and modulus of elasticity. A micromechanical en-echelon crack array model is proposed to explain the influence of structural anisotropy on deformation patterns and mechanical properties of rocksalt.According to the proposed model the deformation progresses due to different proportional contributions of tensile and shear crack arrays under the influence of structural anisotropy. The control of structural anisotropy loses with respect to increment in rate of compression with enhance contribution of shear crack arrays in comparison to tensile crack arrays and ultimately fails in shear where the structurally anisotropic rock show isotropic behaviour.     

The Mechanical Behaviour of a Pyroclastic Rock: Yield Strength and “Destructuration” Effects

Summary   A research programme on the mechanical behaviour of a homogenous volcanic tuff found in the centre of the city of Naples (Italy) was carried out at the University of Naples a few years ago. Isotropic and drained triaxial tests were performed in a very wide range of confining pressures (up to 60 MPa). After presenting the stress-strain curve pattern and the mean stress influence on the shear behaviour, the paper focuses on the definition of a strength criterion and of the yield surface for this material. Some tuff samples were subjected to isotropic compression tests up to a confining pressure approximately twice as high as the isotropic yield stress; they were subsequently unloaded and subjected to drained triaxial tests. Partial loosening of the interparticle bonds (“destructuration”) was observed. The paper also compares the mechanical behaviour of intact and “destructured” samples, emphasising the effects of the structure on strength and yield.     

重塑黄土的加载速率效应研究

为了揭示不同加载速率条件下重塑土的变形与强度特性对工程实践的影响,通过不同围压、含水率条件下重塑土样在4种加载速率条件下的三轴CU试验,对重塑土在不同状态下的加载速率效应进行分析,并从土的结构性入手对其与原状土加载速率效应的差异进行讨论。基于重塑土样的三轴试验成果,得到了加载速率对重塑土变形与力学特性的影响规律:重塑土的应力-应变曲线在不同加载速率条件下均表现出应变硬化特性;破坏强度随着加载速率的增大而表现出先增大后减小的特性,存在临界加载速率;随着加载速率的增大,黏聚力c先增大后减小,也存在临界加载速率,而内摩擦角φ则保持了小幅减小的趋势。     

三种红层岩石常规三轴压缩下的强度与变形特性研究

利用MTS815Teststar程控伺服岩石力学试验系统研究了川东地区一红层边坡中的砂岩、粉砂岩和泥岩围压为03MPa的应力-应变全过程曲线,建立了峰值强度、峰值强度前弹性模量以及峰值强度后的弹性模量和围压的关系。将低围压下红层的全应力-应变曲线概化成5个阶段,分别为压密段、弹性段、屈服段、应变软化段和塑性流动阶段。试验结果得出,红层弹性模量随围压的增加而提高且变化明显,砂岩和粉砂岩在此围压内为脆性破坏,泥岩为塑性破坏的规律。     

The Effects of Temperature and Pressure on the Porosity Evolution of Flechtinger Sandstone

A porosity change influences the transport properties and the elastic moduli of rock while circulating water in a geothermal reservoir. The static and dynamic elastic moduli can be derived from the slope of stress–strain curves and velocity measurements, respectively. Consequently, the acoustic velocities were measured while performing hydrostatic drained tests. The effect of temperature on static and dynamic elastic moduli and porosity variations of Flechtinger sandstone was investigated in a wide range of confining pressure from 2 to 55 MPa. The experiments were carried out in a conventional triaxial system whereas the pore pressure remained constant, confining pressure was cycled, and temperature was increased step wise (25, 60, 90, 120, and 140 °C). The porosity variation was calculated by employing two different theories: poroelasticity and crack closure. The porosity variation and crack porosity were determined by the first derivative of stress–strain curves and the integral of the second derivative of stress–strain curves, respectively. The crack porosity analysis confirms the creation of new cracks at high temperatures. The porosity variation was increasing with an increase in temperature at low effective pressures and was decreasing with a rise in temperature at high effective pressures. Both compressional and shear wave velocities were increasing with increasing pressure due to progressive crack closure. Furthermore, the thermomechanical behavior of Flechtinger sandstone was characterized by an inversion effect where the sign of the temperature derivative of the drained bulk modulus changes.     

不同风化程度花岗岩动力特性实验研究

采用6种不同风化程度的花岗岩试样,在相同围压下进行了不同加载速率（1～105 MPa/s）的动三轴压缩实验。研究发现,不同风化程度花岗岩试件的抗压强度、弹性模量均随加载速率的增加而增加,泊松比随加载速率的增加而减小。抗压强度的增加幅度随风化程度的增加而增加,弹性模量的增加幅度基本保持不变     

Numerical studies on the failure process and associated microseismicity in rock under triaxial compression

In this paper, firstly the mesoscopic elemental mechanical model for elastic damage is developed and implemented into the rock and tool interaction code (R-T^2D). Then the failure processes of a heterogeneous rock specimen subjected to a wide variety of confining pressures (0–80 MPa) are numerically investigated using the R-T^2D code. According to the simulated results, on the one hand, the numerical simulation reproduced some of the well-known phenomena observed by previous researchers in triaxial tests. Under uniaxial compression, rock failure is caused by a combination of axial splitting and shearing. Dilatancy and a post-failure stage with a descending load bearing capacity are the prominent characteristics of the failure. As the confining pressure increases, the extension of the failed sites is suppressed, but the individual failure sites become dense and link with each other to form a shear fracture plane. Correspondingly, the peak strength, the residual strength and the shear fracture plane angle increase, but the brittleness decreases. When the confining pressure is high enough, the specimen behaves in a plastic manner and a narrow shear fracture plane leads to its failure. The prominent characteristics are volume condensation, ductile cataclastic failure, and a constant load bearing capacity with increasing strain. On the other hand, the numerical simulation revealed some new phenomena. The highest microseismicity events occur in the post-failure stage instead of the maximal stress, and most of the microseismicity energies are released in the failure localization process. As the confining pressure increases, the microseismicity events in the non-linear deformation stage increase dramatically and the ratio between the energies dissipated at the non-linear deformation stage and those dissipated in the whole loading process increases correspondingly. Therefore, it is concluded that the developed mesoscopic elemental mechanical model for elastic damage is able to reproduce accurately the failure characteristics in loading rock specimens under triaxial conditions, and the numerical modelling can furthermore obtain some new clarifications of the rock fracture process.