Effect of microstructure and weathering on the strength anisotropy of porous rhyolite

To study the effect of microstructure and weathering on the strength anisotropy of rock, unconfined compressive strength (UCS) tests were carried out on three porous rhyolites having the same original lithology, but different weathering periods of 2600, 20,000 and 40,000 years. The rock is mainly composed of glassy groundmass, with flow structure. UCS tests were undertaken on a series of samples at 15° intervals, from right angles to the flow structure (β=90°) to parallel (β=0°), where β is the angle between the direction of the applied load and the direction of the flow structure. The test results show that UCS-values are maximum when β=0–30° and minimum when β=60–90°. This differs from previous reports for layered anisotropic rocks such as sandstone, sandy shale, schist etc., for which, UCS-values are maximum at β=0 or 90°. It is also found that UCS-values for β=60–90° reduce rapidly in the initial stage of weathering (the first 20,000 years), while for β=0–30°, the reduction rate increases after 20,000 years. This shows that the effect of weathering on strength anisotropy is not uniform, but depends on the weathering processes of the microstructures of the rock.     

An anisotropic strength criterion for jointed rock masses and its application in wellbore stability analyses

In this paper, an anisotropic strength criterion is established for jointed rock masses. An orientation distribution function (ODF) of joint connectivity, is introduced to characterize the anisotropic strength of jointed rock masses related to directional distributed joint sets. Coulomb failure condition is formulated for each plane of jointed rock masses by joint connectivity, where the friction coefficient and cohesion of the jointed rock mass are related to those of the intact rock and joint and become orientation dependent. When approximating joint connectivity by its second‐order fabric tensor, an anisotropic strength criterion is derived through an approximate analytical solution to the critical plane problem. To demonstrate the effects of joint distribution on the anisotropic strength of jointed rock masses, the failure envelopes are worked out for different relative orientations of material anisotropy and principal stress axes. The anisotropic strength criterion is also applied to wellbore stability analyses. It is shown that a borehole drilled in the direction of the maximum principal in situ stress is not always the safest due to the anisotropic strength of the jointed rock mass. Copyright © 2007 John Wiley & Sons, Ltd.     

Deformability characteristics of a rock mass under true-triaxial stress compression

In this paper an experimental study was planned on rock mass model with three joint sets under triaxial and true-triaxial stress states to assess the influence of joint geometry and stress ratios on deformational behaviour of rock mass. The physical models were composed of three continuous orthogonal joint sets in which joint set-I was inclined at angle θ=0°, 20°, 40°, 60°, 80° and 90° with x-axis, joint set-II was produced at staggering s=0.5 and joint set-III was kept always vertical. Thus, rock mass models with medium interlocked smooth joints (ϕ _j =36.8°) were simulated under true triaxial compression (σ₁>σ₂>σ₃). Modulus of rock mass shows anisotropy with joint inclination θ which diminishes with increase in σ₂/σ₃ ratio. The rock mass at θ=60° shows the highest modulus enhancement (599.9%) whereas it is minimum (32.3%) at θ=90°. Further two empirical expressions for estimation of deformation modulus were suggested based on experimental results, which were developed by incorporating two basic concepts, e.g. Janbu’s coefficients and joint factor, J _f.     

Failure Characteristics of Complicated Random Jointed Rock Mass Under Compressive-Shear Loading

Most natural rock masses contain a large number of random joints and fissures, and most of the rock masses at the rock engineering are commonly in both compression and shear stress environment. However, the research on the failure characteristics of complex random jointed rock mass under compressive-shear loading is still limited. To address this gap, this paper uses the particle flow code 2D to establish a discrete fractured rock mass model and carry out a series of numerical tests with different compressive-shear angles (α) and different joint geometric parameters. The effects of compressive-shear angle and joint geometric parameters on the strength and failure characteristics of fractured rock masses are studied. The results indicate that with the increase of α, the peak strength of the specimen decreases gradually, and the failure mode changes from the composite shear failure mode (Mode-I) to a plane shear failure mode (Mode-II) and then to intact shear failure mode (Mode-III). Specifically, the three failure modes occur in the specimens with α?=?15°, 30° or 45°, 60°, respectively. The existence of joints affects stress distribution on rock mass during the loading process. Furthermore, the stress at the joint tip is relatively concentrated, while on both sides of the joint is smaller. Three kinds of crack coalescence patterns are observed: tensile, shear, and tensile-shear mixed coalescence. The inclination angle of the rock bridge between adjacent joints affects the specific type of coalescence.

     

Parametric study of the smooth‐joint contact model on the mechanical behavior of jointed rock

The smooth‐joint contact model based on distinct element method has been widely used to represent discontinuity in the simulation of fractured rock mass, but there is rare efficient guidance for the selection of proper parameters of smooth‐joint contact model, which is the basement for using this model properly. In this paper, the effect of smooth joint parameters on the macroscopic properties and failure mechanism of jointed rock under triaxial compression test is investigated. The numerical results reveal that the friction coefficient of smooth joint plays a dominant role in controlling mechanical behaviors. The stiffness of smooth joint has a relative small influence on the mechanical behaviors. Poisson ratio decreases with the reduction of normal stiffness but increases with the reduction of shear stiffness. The reduction of smooth joint strength, which is determined by normal strength, cohesion, and friction angle of smooth joint, contributes to the breakage of bonded smooth joint and ultimately decreases the strength of the specimen. We proposed a detailed calibration process for smooth‐joint contact model according to the relationship between smooth‐joint parameters and mechanical properties. By following this process, the numerical results are validated against corresponding experimental results and good agreement between them can be found in stress‐strain curves and failure modes of different joint orientations. Further analyses from the microperspective are performed by looking at transmission of contact force, the nature and distribution of microcracks, and the particle displacement to show the failure process and failure modes.     

Investigation of influence of particle characteristics on the non‐coaxiality of anisotropic granular materials using DEM

As a result of deposition process and particle characteristics, granular materials can be inherently anisotropic. Many researchers have strongly suggested that the inherent anisotropy is the main reason for the deformation non‐coaxiality of granular materials. However, their relationships are not unanimous because of the limited understanding of the non‐coaxial micro‐mechanism. In this study, we investigated the influence of inherent anisotropy on the non‐coaxial angle using the discrete element method. Firstly, we developed a new discrete element method approach using rough elliptic particles and proposed a novel method to produce anisotropic specimens. Secondly, the effects of initial specimen density and particle characteristics, such as particle aspect ratio A _m, rolling resistance coefficient β , and bedding plane orientation δ , were examined by a series of biaxial tests and rotational principal axes tests. Findings from the numerical simulations are summarized as follows: (1) the peak internal friction angle ? _p and the non‐coaxial angle i both increase with the initial density, A _m and β , and they both increase initially and then decrease with δ in the range of 0–90°; (2) among the particle characteristics, the influence of A _m is the most significant; and (3) for anisotropic specimens, the non‐coaxial angle can be calculated using the double slip and rotation rate model. Then, an empirical formula was proposed based on the simulation results to depict the relationship between the non‐coaxial angle and the particle characteristics. Finally, the particle‐scale mechanism of non‐coaxiality for granular materials was discussed from the perspective of energy dissipation. Copyright © 2016 John Wiley & Sons, Ltd.     

Investigation of the anisotropy of black shale in dynamic tensile strength

Shale usually exhibits strong anisotropy due to depositional environment and pre-existed microcracks caused by geological loading for a long time. Characterizing mechanical anisotropy properties of shale, especially the tensile strength anisotropy, plays an important role in the successful exploitation of shale gas. In this work, static and dynamic tests with semi-circular bending (SCB) specimen are conducted using hydraulic servo-control machine and modified split Hopkinson pressure bar (SHPB) system, respectively. To survey the tensile strength anisotropy of shale induced by stratification, samples are cored and cut into half by diametrical cutting along different angles relative to the stratification (0°, 30°, 45°, 60°, 90°, C0°). For dynamic tests, the utilization of pulse shaping technique ensures that the samples obtain dynamic equilibrium. The tensile strength values exhibit clear anisotropy under both static and dynamic loading conditions and show typical loading rate dependence at a given angle. An anisotropic index named α_k is defined to describe the tensile strength anisotropy at a certain loading rate. The outcomes illustrate that the anisotropic index decreases as the loading rate increases. In addition, failure pattern owns different characteristic under different loading angles with respect to the stratification. These phenomena may be explained by the pre-existing microcracks, and cracks interaction during dynamic loading conditions.     

The effects of intermediate principle stress on the mechanical behavior of transversely isotropic rocks: Insights from DEM simulations

The discrete element method (DEM) is used to study the response of anisotropic rocks under true triaxial testing. Numerical samples of seven different bedding orientations (β = 0^o, 15^o, 30^o, 45^o, 60^o, 75^o, and 90^o) are created. Six series of test simulations (σ₃ = 0, 10, 30, 50, 70, and 100 MPa) are conducted on each sample, with five different σ₂ values, varied from σ₃ to σ₁. The effects of anisotropy and intermediate stress on the peak strength, brittle-ductile transition, and degree of anisotropy are subsequently explained through underlying micromechanics. Results show a “fan-shaped” variation of the peak strength with σ₂, displaying an ascending-then-descending trend. An increasing brittleness with σ₂ is observed at lower confining pressures for all, but medium anisotropy angles. For higher confining pressures, increasing ductility with σ₂ is seen for every anisotropy angle. A U-shaped variation of peak strength with anisotropy angles is noted that flattens under high intermediate stress. Hence, for numerical models of Posidonia shale under normalized σ₂ higher than 0.76, the anisotropy effect is found to be negligible. Micromechanical analyses reveal that the stress asymmetry, suppression of weak plane action as well as the localization and coalescence of microcracks in the intact rock matrix, due to σ₂, are the contributors towards the obtained trends. Since existing failure criteria do not weigh in these features in geotechnical assessments, this paper helps future studies by providing a deeper understanding of these effects and a comprehensive data set for the analyses of anisotropic rocks under polyaxial stress conditions.     

Assessments of Strength Anisotropy and Deformation Behavior of Banded Amphibolite Rocks

Assessment of strength anisotropy in transversely isotropic rocks has been one of the most challenging subjects in rock engineering. However, far too little attention has been paid to banded amphibolite rocks. This study aim to evaluate strength and deformation anisotropy behavior of banded amphibolite rocks. The dynamic mechanical tests including ultrasonic pulse test, uniaxial compressive strength, Brazilian test and deformability test were performed on drilled rock samples as a function of foliation plane angle (β = 0°, 30°, 60° and 90°). The results obtained have shown that the dynamic mechanical properties of amphibolite rocks have different values concerning banding plane. Compression and shear waves taken parallel to the foliation plane show highest values than those obtained in the other directions. Under uniaxial test, the banded amphibolite has a U-shaped anisotropy with maximum strength at β = 90° and minimum strength is obtained when β = 30°. Strength anisotropic index ranges between 0.96 and 1.47. It seems that the high range value of anisotropic index is mainly due to slight undulation of foliation planes, that being not perfectly straight. The results of elastic deformation test show that there is no clear dependence on microstructures characteristics of subtype-amphibolite rocks that controlling modulus “shape-anisotropy”. However, in this study, Young modulus values of amphibolite rocks with β follow both types of shape-anisotropy, “U-shape” and “decreased order-shaped”. Thus, this study recommended that further research be undertaken regarding the role of modulus “shape-anisotropy” within the same lithotype.     

3D modeling of stratified and irregularly jointed rock slope and its progressive failure

Little has been published on the three-dimensional (3D) simulation of the progressive failure of rock slopes, possibly because the process of failure involves a complex, nonlinear evolution from initiation, through propagation and crack. In addition, rock is typically anisotropic, which makes it difficult to identify and describe the slope constituents and failure processes accurately. Despite such difficulties, further study of the fracture process is just as important as analyzing stress fields in 3D rock slope failures. In this paper, the 3D realistic failure process analysis code using finite element programming, and an extended version of numerical centrifugal method, is used to simulate slopes failure with different dip angles. The numerical centrifugal analysis results in this paper are found that the critical failure surface develops along the weak structural surface when the slope dip angle β is below 30°; conversely, the failure surface is formed along the toe of circular sliding when β is above 30°. In addition, it is also found that whether or not including the irregularity of joint into modeling to analyze the 3D slope stability problem will lead to a significant difference in factors of safety, it can reach 8.41 % at the same slope angle. Furthermore, the acoustic emission analyzing reveals deformed location characters of rock slope during the failure processes. With such capabilities, the approach contributes significantly to the in-depth study of the mechanisms of rock slope instability process.     

Digital spatial cracking behaviors of fine-grained sandstone with precracks under uniaxial compression

X-ray computed tomography (CT) imaging and digital image correlation techniques are applied to study spatial cracking behaviors of sandstone under uniaxial compression, in which the angle between precracks is 45°, 90°, and 135° and the crack depth is 7.5 mm and 10 mm, respectively. Layered anisotropy damages and spatial cracking evolution are quantitatively analyzed by the defined digital layered anisotropy index and digital damage ratio, respectively. Three cases with different array of precracks evidence the depth effects of precracks on spatial crack propagation. Results show that the failure process of samples is first controlled by the coalescence of surface cracks in 2D space and then the samples are failed by the propagation of coalesced cracks (shear cracks with different shapes). The crack types for samples with precrack depth of 7.5 mm are all shear cracks for Cases 1‑3. Nevertheless, the crack types for samples with precrack depth of 10 mm are, respectively, the half X-shape crack for Case 1, X-shape crack for Case 2, and double shell crack for Case 3. The precrack has a significant promotion effect on the failure process when the angle between the two precracks is β = 90°, and the precrack has little to no effect on the failure process when the angle between the two precracks is β = 135°. As the depth of precrack increases to 10 mm, the crack types are changed in this study. The peak strength of sample subjected to uniaxial compression decreases with increasing depth of precracks, implying the decrease of the rock strength by the discontinuity.     

Prediction of Unconfined Compressive Strength for Jointed Rocks Using Point Load Index Based on Joint Asperity Angle

This research paper is aimed to briefly highlight the correlation between unconfined compressive strength and point load index for jointed rocks based on joint asperity & orientation. In this observe, specimens were tested to obtain their unconfined compression strength and point load index for a different joint condition. The different joint conditions considered for this study were clean joint and joint filled condition. For both clean joint and joint filled specimens were prepared by various asperity angles of 30°, 45°, 60° and 90° with different orientation angles such as 0°, 30°, 45°, 60°, 90°. Plaster of Paris was used as model material to simulate weak rock mass in the field. By testing intact model specimens for unconfined compressive strength leads to revealing of optimum moisture content for further testing. The curing period for the model specimens is 3 days at room temperature. To simulate jointed rocks, various moulds of different orientation of joint with respect to major principal stress are prepared separately. The inner diameter of the mould is 50 mm and height is 100 mm. After casting, a rough joint was created by cutting the prepared sample using the cutter. The specimens are tested for both clean joint and joint filled condition to determine the favorable joint orientation and asperity angle. After curing, the specimens are tested for unconfined compressive strength and Point load index. The new multi-linear correlation for determining unconfined compressive strength with the help of point load index is developed and cross checked with equations formed for actual rock. On comparing both results it is found that the new equation can suitable for assessing the unconfined compressive strength of limestone and serpentinite rocks through point load index value.     

Experimental investigations on the elastic parameters and uniaxial compressive strength of slate under freeze–thaw cycles

ABSTRACT

In this study, uniaxial compression experiments with seven different bedding angles and six numbers of freeze–thaw cycles were conducted to investigate the influences of freeze–thaw cycles on the elastic parameters and the uniaxial compressive strength of slate. The laws of the elastic parameters, uniaxial compressive strength and failure characteristics were analysed, and a new uniaxial compressive strength prediction model that considers the bedding angle and the number of freeze–thaw cycles as control variables was established and verified using the experimental data. The results showed that the uniaxial compressive strength, elastic modulus and shear modulus decreased exponentially with an increasing number of freeze–thaw cycles. However, the Poisson’s ratio increased linearly with an increasing number of freeze–thaw cycles. The uniaxial compressive strength initially decreased and then increased with increasing bedding angle. There are three forms of failure occurred during the tests: when the bedding angle was 0°≤β ≤ 26.6°, the splitting failure and shear failure occurred at the same time; when the bedding angle was 26.6°≤β ≤ 83.0°, sliding failure occurred along the bedding plane; and when the bedding angle was 83.0°≤β ≤ 90°, splitting failure occurred along the axial direction of sample.     

Influence of inclination angles and confining pressures on mechanical behavior of rock materials containing a preexisting crack

To deeply understand the cracking mechanical behavior of brittle rock materials, numerical simulations of a rock specimen containing a single preexisting crack were carried out by the expanded distinct element method (EDEM). Based on the analysis of crack tips and a comparison between stress- and strain-based methods, the strain strength criterion was adopted in the numerical models to simulate the crack initiation and propagation processes under uniaxial and biaxial compression. The simulation results indicated that the crack inclination angle and confining pressure had a great influence on the tensile and shear properties, peak strength, and failure behaviors, which also showed a good agreement with the experimental results. If the specimen was under uniaxial compression, it was found that the initiation stress and peak strength first decreased and then increased with an increasing inclination angle α. Regardless of the size of α, tensile cracks initiated prior to shear cracks. If α was small (such as α ≤ 30°), the tensile cracks dominated the specimen failure, the wing cracks propagated towards the direction of uniaxial compression, and the propagation of shear cracks was inhibited by the high concentration of tensile stress. In contrast, if α was large (such as α ≥ 45°), mixed cracks dominated the specimen failure, and the external loading favored the further propagation of shear cracks. Analyzing the numerical results of the specimen with a 45° inclination angle under biaxial compression, it was revealed that lateral confinement had a significant influence on the initiation sequence and the mechanical properties of new cracks.     

Modeling crack propagation path of anisotropic rocks using boundary element method

In a cracked material, the stress intensity factors (SIFs) at the crack tips, which govern the crack propagation and are associated with the strength of the material, are strongly affected by the crack inclination angle and the orientation with respect to the principal direction of anisotropy. In this paper, a formulation of the boundary element method (BEM), based on the relative displacements of the crack tip, is used to determine the mixed‐mode SIFs of isotropic and anisotropic rocks. Numerical examples of the application of the formulation for different crack inclination angles, crack lengths, and degree of material anisotropy are presented. Furthermore, the BEM formulation combined with the maximum circumferential stress criterion is adopted to predict the crack initiation angles and simulate the crack propagation paths. The propagation path in cracked straight through Brazilian disc specimen is numerically predicted and the results of numerical and experimental data compared with the actual laboratory observations. Good agreement is found between the two approaches. The proposed BEM formulation is therefore suitable to simulate the process of crack propagation. Copyright © 2008 John Wiley & Sons, Ltd.     

Effects of Cyclic Loading on the Shear Behaviour of Infilled Rock Joints Under Constant Normal Stiffness Conditions

The variation of the shear strength of infilled rock joints under cyclic loading and constant normal stiffness conditions is studied. To simulate the joints, triangular asperities inclined at angles of 9.5° and 18.5° to the shear movement were cast using high-strength gypsum plaster and infilled with clayey sand. These joints were sheared cyclically under constant normal stiffness conditions. It was found that, for a particular normal stiffness, the shear strength is a function of the initial normal stress, initial asperity angle, joint surface friction angle, infill thickness, infill friction angle, loading direction and number of loading cycles. Based on the experimental results, a mathematical model is proposed to evaluate the shear strength of infilled rock joints in cyclic loading conditions. The proposed model takes into consideration different initial asperity angles, initial normal stresses and ratios of infill thickness to asperity height.     

Effects of hydraulic conductivity/strength anisotropy on the stability of stratified,poorly cemented rock slopes

This paper presents a numerical procedure to explore how hydraulic conductivity anisotropy and strength anisotropy affect the stability of stratified, poorly cemented rock slopes. The results provide information about the anisotropic characteristics of the medium, including the orientation of bedding planes, the anisotropic ratios of the hydraulic conductivity and the geological significance of the hydraulic conductivity anisotropy on the pore water pressure (PWP) estimation of finite slopes. Neglecting the hydraulic conductivity anisotropy of a slope with horizontal layers leads to a 40% overestimation of the safety factor. For a dip slope with inclined layers with θ = 30°, including the strength anisotropy caused a 25% reduction of the safety factor compared to the cases which isotropic strength is assumed. This paper highlights the importance of the hydraulic-conductivity anisotropy and the strength anisotropy on the stability of stratified, poorly cemented rock slopes.     

迭加断裂形成机制及其与构造应力场演化关系

地质体是在地壳演化中形成的,它是建造和构造形变的综合体。断裂化的地质体在较晚期构造力或工程载荷作用下沿已存在的断裂发生形变和位移的现象被称为迭加断裂,其形成过程即是迭加断裂作用。 本文以莫尔-库仑理论为基楚,探讨断裂发育与迭加断裂作用、构造应力场的关系,并对地质构造研究中的“断裂继承”,“断裂复活”进行定量的探讨。研究过程中承谷德振老师指导和鼓励,于此表示衷心的感谢。     

Surface displacements due to batter piles driven in cross‐anisotropic media

This article derives the closed‐form solutions for estimating the vertical surface displacements of cross‐anisotropic media due to various loading types of batter piles. The loading types include an embedded point load for an end‐bearing pile, uniform skin friction, and linear variation of skin friction for a friction pile. The planes of cross‐anisotropy are assumed to be parallel to the horizontal ground surface. The proposed solutions are never mentioned in literature and can be developed from Wang and Liao's solutions for a horizontal and vertical point load embedded in the cross‐anisotropic half‐space. The present solutions are identical with Wang's solutions when batter angle equals to 0^°. In addition, the solutions indicate that the surface displacements in cross‐anisotropic media are influenced by the type and degree of material anisotropy, angle of inclination, and loading types. An illustrative example is given at the end of this article to investigate the effect of the type and degree of soil anisotropy (E/E′, G′/E′, and ν/ν′), pile inclination (α), and different loading types (a point load, a uniform skin friction, and a linear variation of skin friction) on vertical surface displacements. Results show that the displacements accounted for pile batter are quite different from those estimated from plumb piles, both driven in cross‐anisotropic media. Copyright © 2007 John Wiley & Sons, Ltd.     

层理面特性对砂岩断裂力学行为的影响研究

层理弱面对层状岩石的力学特性影响较显著，为了研究层理面特性对岩石断裂力学特性的影响，开展了具有不同层理方向的砂岩试样三点弯试验，探讨了砂岩断裂韧度及断裂模式的各向异性。之后基于有限元中的黏聚单元建立了数值模型，采用数值模拟方法研究了层理面强度对各层理角度试样断裂力学行为的影响规律。结果表明：层理方向影响下砂岩的断裂韧度及模式存在各向异性；同一层理方向试样的断裂韧度随层理面强度的增大而增大，且试样的层理面与加载方向夹角越小，断裂韧度受层理面强度变化影响越明显；试样的断裂模式不仅与层理面强度有关，还受层理倾角的控制，层理面与加载方向夹角θ = 0o试样断裂模式基本不受层理面强度影响，θ = 30o试样主要沿层理面张拉或剪切破坏，且沿层理面的破裂长度随层理面强度的降低逐渐增大；层理面强度较大时，θ = 45o试样主要沿层理面张拉破坏，θ = 60o～90o试样主要以贯穿层理的张拉破坏为主；层理面强度较小时，θ = 45o～90o试样均以沿层理面的剪切破坏为主，其中θ = 45o试样沿层理剪切长度最大。另外，通过数值模拟结果分析了层理面强度及方向对试样的起裂角及裂纹扩展路径产生的影响。该研究成果可作为层状岩石断裂力学理论的有益补充。