Quantifying progressive pre-peak brittle fracture damage in rock during uniaxial compression

This paper presents the findings of an extensive laboratory investigation into the identification and quantification of stress-induced brittle fracture damage in rock. By integrating the use of strain gauge measurements and acoustic emission monitoring, a rigorous methodology has been developed to aid in the identification and characterization of brittle fracture processes induced through uniaxial compressive loading. Results derived from monocyclic loading tests demonstrate that damage and the subsequent deformation characteristics of the damaged rock can be easily quantified by normalizing the stresses and strains observed in progression from one stage of crack development to another. Results of this analysis show that the crack initiation, σ_ci, and crack damage, σ_cd, thresholds for pink Lac du Bonnet granite occur at 0.39σ_UCS and 0.75σ_UCS, respectively. Acoustic emissions from these tests were found to provide a direct measure of the rapid release of energy associated with damage-related mechanisms. Simplified models describing the loss of cohesion and the subsequent development of microfractures leading up to unstable crack propagation were derived using normalized acoustic emission rates. Damage-controlled cyclic loading tests were subsequently used to examine the effects of accumulating fracture damage and its influence on altering the deformation characteristics of the rock. These tests revealed that two distinct failure processes involving the progressive development of the microfracture network, may occur depending on whether the applied cyclic loads exceed or are restrained by the crack damage stress threshold.     

Non-dilatant deformation and failure mechanism in two Long Valley Caldera rocks under true triaxial compression

We conducted laboratory rock strength experiments in two ultra-fine-grained brittle rocks, hornfels and metapelite, which together are the major constituent of the Long Valley Caldera (California, USA) basement in the 2025–2996 m depth range. Both rocks are banded, and have very low porosity. Uniaxial compression tests at different orientations with respect to banding planes reveal that while the hornfels compressive strength is nearly isotropic, the metapelite possesses distinct anisotropy. Conventional triaxial tests in these rocks reveal that their respective strengths in a specific orientation increase approximately linearly with confining pressure. True triaxial compression experiments in specimens oriented at a consistent angle to banding, in which the magnitudes of the least (σ₃) and the intermediate (σ₂) principal stresses are different but kept constant during testing while the maximum principal stress is increased until failure, exhibit a behavior unlike that previously observed in other rocks under similar testing conditions. For a given magnitude of σ₃, compressive strength σ₁ does not vary significantly in both Long Valley rock types, regardless of the applied σ₂, suggesting little or no intermediate principal stress effect. Strains measured in all three principal directions during loading were used to obtain plots of σ₁ versus volumetric strain. These are consistently linear almost to the point of rock failure, suggesting no dilatancy. The phenomenon was corroborated by SEM inspection of failed specimens that showed no microcrack development prior to the emergence of one through-going shear failure plane steeply dipping in the σ₃ direction. The strong dependency of compressive strength on the intermediate principal stress in other crystalline rocks was found to be related to microcrack initiation upon dilatancy onset, which rises with increased σ₂ and retards the failure process. We infer that strength independence of σ₂ in the Long Valley rocks derives directly from their non-dilatant deformation.     

Mechanical and hydraulic behavior of rock salt in the excavation disturbed zone around underground facilities

The mechanical and hydraulic behavior of rock salt in the excavation disturbed zone (EDZ) around sealing systems in underground repositories is relevant for the assessment of the safety function of these geotechnical barriers. It has been determined through laboratory tests that the development of the EDZ, and thus, the hydraulic pathways, is closely related to the corresponding damage boundary and the associated damage. By integrating short- and long-term strength considerations, dilatancy, damage and healing into the newly extended Hou/Lux constitutive model for rock salt, it is possible to treat the tertiary creep in order to identify the EDZ around underground facilities. This leads to prediction of the time-dependent development of the EDZ and, together with a permeability model, calculation the permeability of rock salt in the EDZ.With the Hou/Lux model, several phenomena, such as EDZ, spalling, dilatancy and radial deformation into the axial bore observed in laboratory tests on axially perforated cylinder samples are simulated qualitatively and quantitatively.Under in situ conditions, the EDZ of a 37-year-old drift at the Sondershausen mine, the prototype cavity at the Asse mine, as well as a 1,000,000 m³ salt cavity, are examined. The results are then compared with the stress and permeability measurements at the Sondershausen mine. The calculations show the various capabilities of the Hou/Lux model, including tertiary creep and creep rupture, identification and development of the EDZ, development of dilatancy, of permeability, of damage and of healing, and finally, stress rearrangements from the contour into the center of the rock mass formation.     

The use of stress-density functions for lifetime predictions of brittle structures

The tools necessary to perform a lifetime analysis for a brittle structure are presented. The paper explains methods for measuring the relevant material properties, such as Weibull modulus m, normalization strength σ₀, and subcritical crack growth parameter n, and for combining them with suitable statistics, stress analysis, and linear-elastic fracture mechanics, in order to arrive at strength-probability-time (SPT) diagrams for a particular structure. Moreover, it will be shown, how mathematical difficulties arising during the statistical analysis can be overcome by making use of the so-called stress-density functions, which were recently introduced by Nadler [1].     

Models for normal fracture deformation under compressive loading

A new semi-empirical model that can be used to predict fracture deformation behavior under normal compressive loading is presented. The development of a simple exponential model is presented first after which a modified and more general exponential model, with an additional degree of freedom in the model parameters, is obtained. The simple and the modified exponential models are then compared to available fracture closure models, namely the empirical Barton–Bandis hyperbolic model, and a power-law model based on Hertzian contact theory, to determine how good they fit the results of fracture closure experiments under monotonically increasing normal compressive loading. A new parameter called the half-closure stress, σ_1/2, is introduced and is used, in addition to the maximum fracture closure, Δv_m, in the model fitting procedures for the Barton–Bandis and the simple exponential model. The half-closure stress is shown to be related to the initial normal stiffness, K_ni, used in the original Barton–Bandis model. An additional parameter, n, is used in fitting the modified exponential model to the experimental data. Of the models presented herein, the modified exponential model was found to provide the best fit to the experimental data, for the same values of σ_1/2 and Δv_m, over the entire range of compressive stresses. The power-law model based on Hertzian contact theory was found to be unsuitable for predicting normal fracture deformation behavior.     

Generalized crack initiation and crack damage stress thresholds of brittle rock masses near underground excavations

The rock mass failure process is characterized by several distinct deformation stages which include crack initiation, crack propagation and coalescence. It is important to know the stress levels associated with these deformation stages for engineering design and practice.Extensive theoretical, experimental and numerical studies on the failure process of intact rocks exist. It is generally understood that crack initiation starts at 0.3 to 0.5 times the peak uniaxial compressive stress. In confined conditions, the constant-deviatoric stress criterion was found to describe the crack initiation stress level.Here, generalized crack initiation and crack damage thresholds of rock masses are proposed. The crack initiation threshold is defined by σ₁−σ₃=A σ_cm and the crack damage threshold is defined by σ₁−σ₃=B σ_cm for jointed rock masses, where A and B are material constants and σ_cm is the uniaxial compressive strength of the rock masses. For a massive rock mass without joints, σ_cm is equal to σ_cd, the long-term uniaxial strength of intact rock. After examining data from intact rocks and jointed rock masses, it was found that for massive to moderately jointed rock masses, the material constants A and B are in the range of 0.4 to 0.5, 0.8 to 0.9, respectively, and for moderately to highly jointed rock masses, A and B are in the range of 0.5 to 0.6, 0.9 to 1.0, respectively. The generalized crack initiation and crack damage thresholds, when combined with simple linear elastic stress analysis, assist in assessing the rock mass integrity in low confinement conditions, greatly reducing the effort needed to obtain the required material constants for engineering design of underground excavations.     

Influence of intermediate principal stress on rock fracturing and strength near excavation boundaries—Insight from numerical modeling

The influence of the intermediate principal stress on rock fracturing and strength near excavation boundaries is studied using a FEM/DEM combined numerical tool. A loading condition of σ₃=0 and σ₁≠0, and σ₂≠0 exists at the tunnel boundary, where σ₁, σ₂, and σ₃, are the maximum, intermediate, and minimum principal stress components, respectively. The numerical study is based on sample loading testing that follows this type of boundary stress condition. It is seen from the simulation results that the generation of tunnel surface parallel fractures and microcracks is attributed to material heterogeneity and the existence of relatively high intermediate principal stress (σ₂), as well as zero to low minimum principal stress (σ₃) confinement. A high intermediate principal stress confines the rock in such a way that microcracks and fractures can only be developed in the direction parallel to σ₁ and σ₂. Stress-induced fracturing and microcracking in this fashion can lead to onion-skin fractures, spalling, and slabbing in shallow ground near the opening and surface parallel microcracks further away from the opening, leading to anisotropic behavior of the rock. Hence, consideration of the effect of the intermediate principal stress on rock behavior should focus on the stress-induced anisotropic strength and deformation behavior of the rocks. It is also found that the intermediate principal stress has limited influence on the peak strength of the rock near the excavation boundary.     

Variation in strength and creep life of six Japanese rocks

In this paper, variations in strength and creep life are investigated for rocks under various conditions: dry and wet, uniaxial and triaxial, and compressional and tensile. A number of parameters are introduced for this purpose; to assess the time-dependent failure under constant and monotonic loading the following parameters are used: the parameter of time dependency δ, coefficient of creep life α and coefficient of strength β. δ explains the rate dependency of strength or stress level dependency of creep life. α and β are related to each other. Variations in β have been evaluated using data from previous experiments. It is confirmed here that δ, β and variations in β determined by creep tests are in most cases identical to those determined using strength tests. Variation in β in the wet condition is almost the same as that in the dry condition; however, variation in tension increases more than in compression. Under confining pressure, variation in β is reduced for Neogene sedimentary rocks, and does not appear to change for igneous rock and welded tuff.     

Hydro-mechanical behavior of an argillaceous limestone considered as a potential host formation for radioactive waste disposal

The Canadian Nuclear Safety Commission (CNSC), Canada's nuclear regulator, conducts regulatory research in order to develop independent knowledge on safety aspects related to the deep geological disposal of radioactive wastes. In Canada, the Cobourg limestone of the Michigan Basin is currently considered as a potential host formation for geological disposal. The understanding of the hydro-mechanical behavior of such a host rock is one of the essential requirements for the assessment of its performance as a barrier against radionuclide migration. The excavation of galleries and shafts of a deep geological repository (DGR) can induce damage to the surrounding rock. The excavation damaged zone (EDZ) has higher permeability and reduced strength compared to the undisturbed rock and those factors must be considered in the design and safety assessment of the DGR. The extent and characteristics of the EDZ depend on the size of the opening, the rock type and its properties, and the in situ stresses, among other factors. In addition, the extent and characteristics of the EDZ can change with time due to rock strength degradation, evolution of fractures within the EDZ, and the redistribution of pore pressure around the excavation. In this research project initiated by the CNSC, the authors conducted experimental and theoretical research in order to assess the hydro-mechanical behavior of the Cobourg limestone under undamaged and damaged conditions, both in the short and long terms. The short-term behavior was investigated by a program of triaxial tests with the measurement of permeability evolution on specimens of Cobourg limestone. The authors formulate a coupled hydro-mechanical model to simulate the stress-strain response and evolution of the permeability during those triaxial tests. Using creep and relaxation data from a similar limestone, the model was extended to include its long-term strength degradation. The model successfully simulated both the short- and long-term hydro-mechanical behavior of the limestone during those tests. This provides confidence that the main physical processes have been adequately understood and formulated.     

The flattened Brazilian disc specimen used for testing elastic modulus, tensile strength and fracture toughness of brittle rocks: analytical and numerical results

The flattened Brazilian disc specimen is proposed for determination of the elastic modulus E, tensile strength σ_t and opening mode fracture toughness K_IC for brittle rocks in just one test. This paper is concerned with the theoretical analysis as well as analytical and numerical results for the formulas. According to the results of stress analysis and Griffith's strength criteria, in order to guarantee crack initiation at the centre of the specimen, which is considered to be crucial for the test validity, the loading angle corresponding to the flat end width must be greater than a critical value (2α20°). The analysis shows that, based on the recorded complete load–displacement curve of the specimen (the curve should include the ‘fluctuation’ section after the maximum load), E can be determined by the slope of the section before the maximum load, σ_t by the maximum load, and K_IC by the local minimum load immediately subsequent to the maximum load. The relevant formulas for the calculation of E, σ_t, K_IC are obtained, and the key coefficients in these formulas are calibrated by finite-element analysis. In addition, some approximate closed-form formulas based on elasticity are provided, and their accuracy is shown to be adequate by comparison with the finite-element results.     

An experimental study on creep of welded tuff

This paper presents results of five creep tests conducted in uniaxial compression at room temperature. The test specimens were from the welded Topopah Spring tuff formation at Yucca Mountain, Nevada. The specimens exhibited brittle failure. Multiple stress levels were applied in steps to each specimen. Each stress level was maintained for 3 days or longer. The transient creep for all the stress levels can be well described by power functions. The transient creep is caused by an elastic aftereffect. The tuff does not show real steady-state creep. The so-called steady-state creep rate decreases with time. In general it is very low, typically in the range of 10⁻⁷ h⁻¹. For the first 50 h, the so-called steady-state creep rate may be described as a power function of stress. The specimen failed shortly after it entered into the accelerating creep phase.     

Fracture toughness study for a brittle rock subjected to mixed mode I/II loading

A semi-disk specimen containing an angled edge crack has been used in the past for conducting fracture tests on a brittle rock named Johnstone [Fracture testing of a soft rock with semi-circular specimens under three-point bending. Part 2—mixed mode. Int J Rock Mech Min Sci Geomech Abstr 1994b;31(3):199–212]. The test specimen is appropriate for investigating brittle fracture when the rock samples are subjected to the combined effects of tension and shear along the crack line. However, the experimental results reported in Lim, Johnston, Choi, Boland [Fracture testing of a soft rock with semi-circular specimens under three-point bending. Part 2—mixed mode. Int J Rock Mech Min Sci Geomech Abstr 1994b;31(3):199–212.] are inconsistent with all of the well-known theoretical criteria available for predicting mixed mode brittle fracture. In this paper, a modified criterion is used to provide accurate predictions for the reported experimental results. The modified criterion makes use of a three-parameter model (based on K_I, K_II and T) for describing the crack tip stresses. It is shown that the non-singular stress term T has a significant role when the rock fracture tests are conducted on the semi-disk specimens.     

Coupled evolutions of fracture toughness and elastic wave velocities at high crack density in thermally treated Westerly granite

A series of 20 chevron cracked notched Brazilian disc (CCNBD) samples of Westerly granite were failed in a standard Mode I tensile test at room temperature in order to evaluate the effect of thermal damage on fracture toughness. The heat treatment involved slowly heating four sets of four samples to 250, 450, 650 and 850 °C. The fifth set of samples was not thermally treated. Thermal cracking not only induced a substantial decrease of the mechanical strength, but also of the dynamic elastic properties of Westerly granite. In particular, normalized P-wave compressional velocities matched remarkably well the decreasing trend of normalized fracture toughness (K_IC). Above 450 °C, grain boundary opening and cracking, intragranular cracking and mineral grain dissection linked to the quartz α–β phase transition induced a significant increase in the total crack density. Fracture path interaction with various mineral–mineral contact types showed that fracture branching and total fracture length increased with the amount of temperature of heat treatment.Using non-interactive crack theories, dimensionless crack densities were obtained from wave velocity inversion, up to unusually high values of 10 at 850 °C. This geophysical analysis showed to be in close agreement with crack parameters determined optically, such as optical crack density determination, crack aspect ratio evolutions, and the measured sample porosity with temperature. Our results also show that only the non-interactive crack theory can predict K_IC relatively well at high crack density, by simply using dimensionless crack densities inverted from velocities. A decrease of 50% for crack densities larger than 1, 80% for crack densities larger than 5 is predicted, in close agreement with our observed experimental variation of K_IC. At the microscale, this can be interpreted by the fact that the main fracture is strongly interacting with the pre-existing microcrack fabric. These combined experimental and modeling results illustrate the importance of understanding the details of how the rock microstructure is changing in response to an external stimulus, in order to predict the simultaneous evolution of physical and mechanical properties of rock.     

高温静水应力状态花岗岩中钻孔围岩的 流变实验研究

 采用自主研制的“20 MN伺服控制高温高压岩体三轴试验机”对f 200 mm×400 mm的内含f 40 mm钻孔的花岗岩体高温三维静水应力状态的流变特性进行了深入的研究。研究结果表明：(1) 花岗岩是由多种晶体胶结而成的脆性坚硬岩石,5 000 m静水应力以内及600 ℃以内的恒温恒压状态下,花岗岩中钻孔围岩主要表现为稳态蠕变;当应力达到5 000 m静水应力,温度为600 ℃时的蠕变为非稳态蠕变。(2) 高温静水应力状态下花岗岩中钻孔围岩蠕变过程存在应力阈值和温度阈值。(3) 热力耦合作用下钻孔围岩内部晶间胶结物及晶粒内部产生的位错及微破裂过程,是高温高压下钻孔围岩蠕变存在温度阈值和应力阈值的主要原因。(4) 高温静水应力状态下,含有钻孔的花岗岩体流变破坏的应力为5 000～6 000 m的静水应力(125～150 MPa),温度为500 ℃～600 ℃,破坏形式为压裂破坏、压剪破坏或两者相结合。同时,获得了600 ℃以内及埋深6 000 m以内静水应力条件下,不同温度不同埋深静水应力状态下花岗岩中钻孔围岩的蠕变率参数,为高温岩体地热开发钻井井壁稳定性研究提供了重要的力学参数依据。     

Experimental and numerical evaluation of stress redistribution in thick-walled rocksalt cylinders

Whenever an opening is excavated in soft rocks showing elastic–visco-plastic behaviour, like rocksalt and potash, the stress state prevailing soon after the excavation will not remain constant in time but will eventually evolve from the initial state, σ^o, generally considered to be elastic, to a state of stress that can be considered to be stationary for all practical purposes, σ^ss. The knowledge of the stress state prevailing around the excavation some time after its completion is essential for many short-term applications such as the interpretation of in situ tests based on the cavity expansion principle and of stress measurements based on overcoring techniques. Since no analytical solutions are available for the evaluation of this stress redistribution process, numerical analyses are often used to study this problem. The results obtained from such analyses depend on many factors but mainly, the kind of creep law formulation and related parameters. This paper presents an experimental methodology to quantify the amount of stress redistribution occurring in a thick-walled cylinder under a given set of conditions. This experimental methodology does not require any assumption regarding the creep behaviour of the material. As a consequence, it allows the validation of numerical analyses by comparing the amount of stress redistribution obtained experimentally and that obtained from these numerical analyses.     

Damage-induced permeability changes in granite: a case example at the URL in Canada

This paper concerns both in situ measurements of permeability and numerical modelling of changes in permeability induced by microcrack growth. Hydraulic experiments including pulse tests with the SEPPI probe are in progress. These tests are a part of the tunnel sealing experiment (TSX) at the 420 m level of Canada's Underground Research Laboratory, whose aim is to estimate the in situ hydraulic properties of Lac du Bonnet granite. Based on laboratory investigations, the anisotropic damage model developed by Homand et al. (Comput. Geotech. 22 (1998) 135) and recently reviewed by Shao et al. (Int. J. Rock Mech. Min. Sci. 36 (1999) 1001) has been extended in order to account for changes in permeability induced by microcrack growth. We have implemented this extension in the three-dimensional code (FLAC^3D). Triaxial compression tests, with permeability measurements carried out on two different granites, provide a verification of the numerical implementation with a good agreement between experiments and predictions. Comparison between in situ measurements of permeability and predictions indicates that both the results of numerical modelling and observations are globally in agreement. Finally, numerical modelling as well as the in situ measurements indicate that a depth of 50–70 cm is a good estimation of the extent of excavation disturbed zone in the TSX tunnel.     

Dynamic failure analysis on granite under uniaxial impact compressive load

High strain-rate uniaxial compressive loading tests were produced in the modified split Hopkinson pressure bar (SHPB) with pulse shaper on granite samples. It was shown that the failure of the granite cylinder was typical tensile splitting failuremode by sudden splitting parallel to the direction of uniaxial compressive loading at different strain rates. Besides, it was concluded that not only the strength of granite increased, but also the fragment size decreased and the fragment numbers increased with the increasing strain rate. To quantitatively analyze the failure phenomena, the numerical calculation based on a dynamic interacting sliding microcrack model was adopted to investigate the influence of microcrack with the different initial crack length, crack angle, crack space and friction coefficient on the macro-mechanical properties of granite under different strain rates. Accordingly, the strain-dependency of the compression strength and the fragmentation degree of granite was explained reasonably. __________ Translated from Chinese Journal of Geotechnical Engineering, 2007, 29(3): 385–390 [译自: 岩土工程学报]     

Circumferential strain behavior during creep tests of brittle rocks

Creep tests were carried out on Inada granite under confining pressure and on dry and wet specimens of Kamisunagawa sandstone. Distinctive points Q_A (the point where the axial strain rate reaches a minimum), Q_C (the point where the magnitude of circumferential strain rate reaches a minimum) and R_C (the point where the magnitude of circumferential strain acceleration begins to increase) were defined. Dependency of the strain values at the distinctive points on creep stress, confining pressure and water presence was examined. Circumferential strain at Q_C or R_C was not affected by creep stress for both rocks. Peak load points were observed in reloading stress–strain curves when reloading was carried out before Q_C for Kamisunagawa sandstone. Circumferential strain values at peak load during reloading coincided with critical extensile strain, which is defined as circumferential strain value at peak load during constant strain rate tests and is insensitive to confining pressure, water presence, and anisotropy, although slightly affected by strain rate. Load increased slightly or did not increase when reloading was carried out after R_C for both rocks. R_C in creep tests scattered around unloading stress–strain curves from peak load during constant strain rate tests for Kamisunagawa sandstone. These observations suggest that Q_C and R_C in creep tests are closely related to the peak load points during constant strain rate tests. Circumferential strain would be used as a condition-insensitive damage indicator of rock in creep tests as well as in constant strain rate tests.     

脆性岩石渐进及蠕变失效特性宏细观力学模型研究

压应力作用脆性岩石渐进及蠕变失效特性是其力学性质研究的两个主要研究方向。其对于深部地下开挖围岩稳定性的判断有着重要的指导意义。岩石内部微裂纹扩展对脆性岩石的渐进及蠕变特性有着重要的影响。因此,基于岩石的应力与裂纹扩展关系及裂纹扩张演化法则,并结合宏细观损伤定义之间的关系,提出了一个新的宏细观力学模型,推出了岩石完整的应力–应变关系与蠕变理论表达式。分析了围压对岩石的应力–应变关系的影响。研究了岩石内部初始微裂纹尺寸及裂纹间摩擦系数对应力应变关系及岩石强度的影响。并给出了不同围压下岩石裂纹初始应力与峰值应力,其对蠕变实验中的施加应力初始值选取提供了一定参考。然后,研究了恒定围压、轴压分级加载应力路径下的岩石蠕变应变及应变率变化趋势。通过试验结果验证了理论模型的合理性。进而,对压应力作用下细观裂纹扩展对岩石力学特性影响的理解提供了一定的理论参考。