Anisotropic Rock Mass Research Articles

A revisit to the Lekhnitskii-Amadei solution for borehole stress calculation in tilted transversely isotropic media

A wellbore drilled in pre-stressed formations concentrates the far-field stresses. These concentrations often lead to borehole instability producing breakouts, drilling-induced fractures, or complete failure. In isotropic rock masses this problem has been extensively studied. However, fewer studies attempt to understand borehole failure in more realistic rocks characterized by both elastic and strength anisotropy. A program to calculate the failure pattern in elastic and strength anisotropic rocks is developed. The program combines a recent algorithm for calculating stress concentrations around a borehole within an anisotropic rock mass with anisotropic rock strength as applied through differing failure criteria. Shear failure in the rock matrix and the weak plane are examined based on Jaeger’s single plane of weakness theory. Results from test models clearly indicate that failure in the weak plane complicates the failure pattern around the wellbore, resulting in that the breakout orientation cannot correctly represent the minimum horizontal stress orientation as commonly suggested for a vertical wellbore aligned with the principal stresses. The complexity of failure patterns due to formation anisotropy suggests that additional care must be taken when borehole image logs are interpreted for stress direction indication and stress magnitude constraint.

Effect of surface void percentage (SVP) on the unconfined compressive strength (UCS) of porous rocks

In this paper, the effect of areal void size on unconfined compressive strength (UCS) depending on the core diameter is investigated and discussed in terms of obtaining more accurate and reliable strength values relating to the effect of the local increase in stress and corresponding decrease in area on the loading surface. According to the results obtained from UCS tests, the overall trend was a significant loss in the UCS with increasing surface void per cent. It can be concluded that the areal size of voids on loading surfaces is an important indicator of porosity as well as rock strengths when considering rock engineering in vuggy anisotropic rock masses.

Two Sources of Nonisotropic Radiation From Underground Explosions in Granite

AbstractSignificant tangential ground motion observed during underground explosions makes it difficult to distinguish them from natural earthquakes. Such motion can be generated by the source geometry and emplacement conditions, by the heterogeneous nature of the rock mass (mechanical properties may vary in space due to the presence of cracks, joints, faults, and various geologic layers) and also by the nonuniform in situ stress state. The last mechanism is increasingly important with depth when the difference in main principal stresses becomes significant. This paper is focused on the role of material strength of the rock mass in generation of nonradial motion during explosions in prestressed media. Numerical modeling of underground chemical explosions in granite at various depths has been conducted to compare two possible mechanisms of shear wave generation. The first, caused by rock mass anisotropy, is important at shallow depth. The second is related to elastic‐plastic relaxation around the cavity created by the explosion. Tangential motions for these two mechanisms have different signatures.

Two-phase flow pipe network method for simulation of CO2 sequestration in fractured saline aquifers

A two-phase flow unified pipe network method is developed to simulate CO2 evolution in fractured saline aquifers. Fractures are explicitly represented in the proposed method. The two-phase flow in both rock matrix and fractures is considered by using different equivalent pipe flow models respectively, namely the two-phase matrix pipe flow model and the two-phase fracture pipe flow model. The equivalent flow coefficients of the pipe flow models are derived based on flow rate equivalence. The coupling of the fracture pipe flow and matrix pipe flow is treated by applying the extended capillary pressure conditions. Brooks-Corey relative permeability model and capillary model are adopted to simulate CO2 (non-wetting phase) invasion into the brine (wetting phase) saturated formation, which is a typical drainage process. Accurate Equations of State for calculating density and viscosity of CO2 are incorporated to reflect its change in hydraulic characteristics during the injection processes. The proposed method is simple yet robust and not sensitive to the mesh quality. The complex geological and topological features of fracture networks can, therefore, be well retained in the proposed method. The anisotropy and heterogeneity characteristics of the fractured rock mass caused by the fracture networks can be accurately represented. The proposed method is verified by comparing to other numerical methods. Both 2D and 3D models with complex fracture networks are presented to demonstrate the feasibility of proposed method. Numerical examples show that fractures can significantly affect the distribution and evolution of CO2 in aquifers and the differences of entry capillary pressures for fractures and matrix rock should be accurately simulated.

Analytical Solution for a Lined Tunnel with Arbitrary Cross Sections Excavated in Orthogonal Anisotropic Rock Mass

AbstractA complete and accurate method for determining the stresses and displacements of a lined arbitrary shaped tunnel excavated in orthogonal anisotropic rock mass is proposed. The method is bas...

Evaluation of the anisotropy and directionality of a jointed rock mass under numerical direct shear tests

The characteristics of the anisotropy and directionality of jointed rock masses are the key to simplifying it as a transversely anisotropic material. Experimental direct shear tests were performed on stratified rocks cored from granulite rocks. The influence of normal stresses and joint orientations was tested and the anisotropy and directionality of the shear strength were evaluated. Numerical shearing tests on stratified rock models and discrete fractures network (DFN) models were subsequently conducted. In addition, the shear anisotropy and directionality in the DFN models were tested and discussed. The results demonstrate that the peak shear stress was more sensitive to the inclination angles than the normal stress. The stratified rocks in the experimental test showed apparent shear anisotropy and directionality. The maximum value of directionality coincided with the direction of the strike of the bedding plane. The more apparent the anisotropy was, the higher the directionality became. The failure patterns of stratified rocks exhibited more complex characteristics under higher normal stress. Significant variation of the shear strength distribution occurred due to the different orientations of fractures relative to the directions of the shear load. The failure patterns of DFN models of varied scales differed, and no apparent convergence was discovered. The shear strength of the DFN model showed an apparent principal direction. The numerical results presented in this paper are valuable for evaluating the prediction of the failure behaviour of rock masses, and can be further applied to the study of the failure mechanism of surrounding rock in engineering.

Practical Use of the Ubiquitous-Joint Constitutive Model for the Simulation of Anisotropic Rock Masses

Anisotropic rock masses, the behavior of which is dominated by closely spaced planes of weakness, present particular difficulties in rock engineering analyses. The orientation of discontinuities relative to an excavation face has a significant influence on the behavioral response. At the present time, discontinuum modeling techniques provide the most rigorous analyses of the deformation and failure processes of anisotropic rock masses. However, due to their computational efficiency continuum analyses are routinely used to represent laminated materials through the implementation of a Ubiquitous-Joint model. The problem with Ubiquitous-Joint models is that they do not consider the effects of joint spacing, length and stiffness. As such, without an understanding of the limitations of the modeling approach and detailed calibration of the material response, simulation results can be misleading. This paper provides a framework to select and validate ubiquitous-joint constitutive properties.

국내에 분포하는 암반의 물리·역학적 특성 분석

본 연구에서는 국내의 107개 터널 설계 과정에서 수행한 현장 및 실내시험 자료 4,280개를 이용하여 암반 및 무결암의 역학적 특성을 암종 및 강도별로 분석하였다. 분석된 물리 및 역학적 특성은 단위중량, 점착력, 내부마찰각, 변형계수, 탄성계수, 포아송비, 일축압축강도, 인장강도, 투수계수, 비중이다. 평균값의 분석 결과에 의하면 편마암은 비중, 화강암은 투수계수, 퇴적암은 단위중량과 점착력, 내부마찰각, 화산암은 변형계수와 탄성계수, 일축압축강도, 인장강도, 변성암은 포아송비에서 가장 높은 값을 보인다. 역학적 특성의 분포 범위는 암종 및 강도를 고려한 분석에도 불구하고 넓게 분포하며, 이는 암반의 불균질성과 이방성에 기인하는 것으로 판단된다. To understand the mechanical properties of rock masses and intact rock in Korea, data from 4,280 in situ and laboratory tests from 107 tunnels on general national roads were analyzed. The mechanical properties (unit weight, cohesion, friction angle, modulus of deformation, Young's modulus, Poisson's ratio, uniaxial compressive strength, tensile strength, coefficient of permeability, and specific gravity) were analyzed by rock types and strength of rock in each rock type. The results of analysis, the mean specific gravity was highest in gneiss. The coefficient of permeability and Poisson's ratio show the highest mean values in granite and metamorphic rock, respectively. In addition, the unit weight, cohesion and friction angle in sedimentary rock, modulus of deformation, Young's modulus, uniaxial compressive strength and tensile strength in volcanic rock have the highest mean values. The values for each mechanical property showed wide ranges by the heterogeneity and anisotropy of rock masses in spite of detailed analysis by rock type and classification of rocks according to the strength.

Investigation of hydraulic parameters of a weathered mylonite fault from field pumping tests: A case study

This paper presents a case history where the hydraulic parameters of a weathered mylonite fault located in the way of shield tunneling for the Xie-Zhong section on Metro Line No. 7 in Guangzhou City were determined using a series of field pumping tests. The weathered mylonite fault contains fissure groundwater, which would result in a high potential of water ingress during shield tunneling within the weathered mylonite strata. Therefore, the first stage of pumping tests involving five pumping wells was initially carried out. To verify the validity of the hydraulic parameters derived, the second stage of pumping tests involving four pumping wells was carried out. In addition, both an analytical method that involves a well-flow calculation for a fissure-confined aquifer for non-orthogonal anisotropic rock mass and a numerical simulation based on the theory of the equivalent continuum porous media were used to derive the hydraulic parameters based on the field pumping test data. The analytical method can provide the values of hydraulic conductivity only in the horizontal plane and is not able to capture the hydraulic characteristics of standalone stratum of the multi-aquifer system. In the numerical model, the weathered mylonite fault due to the nature of non-uniform mylonite strata distribution is further divided into four sub-regions with different hydraulic conductivities, according to the calculated influence radius of groundwater drawdown or geological formation. This leads to estimates of hydraulic parameters that are closer to real values, and enhances our understanding of non-uniform fissure development.

Mechanical conditions and modes of paraglacial deep-seated gravitational spreading in Valles Marineris, Mars

Deep-seated gravitational spreading (DSGS) affects the slopes of formerly glaciated mountain ridges. On Mars, DSGS has played a key role in shaping the landforms of the giant Valles Marineris troughs. Though less spectacular, DSGS is common in terrestrial orogens, where understanding its mechanics is critical in the light of the ongoing climate change because it is a potential source of catastrophic landslides in deglaciated valleys. We conducted parametric numerical studies in order to identify important factors responsible for DSGS initiation. DSGS models are computed using an elastoviscoplastic finite element code. Using ADELI's software, we reproduce topographic ridge spreading under the effect of valley unloading. Two types of spreading topographic ridges are investigated, homogeneous or with horizontal rheological layering. We find that gravitational instabilities are enhanced by high slopes, which increase gravitational stress, and low friction and cohesion, which decrease yield stress. In the unlayered ridge, instability is triggered by glacial unloading with plastic strain concentration inside the ridge and at the base of the high slopes. Vertical fractures develop in the upper part of the slope, potentially leading to fault scarps. Ridge homogeneity promotes a deformation mode controlled by uphill-facing normal faulting and basal bulging. In the second case, the ridge encompasses horizontal geological discontinuities that induce rock mass anisotropy. Discontinuity located at the base of the slope accumulates plastic strain, leading to the formation of a sliding plane evolving into a landslide. The presence of a weak layer at ridge base therefore promotes another slope deformation mode ending up with catastrophic failure. Mechanical conditions and slope height being equal, these conclusions can probably be extrapolated to Earth. Compared with Mars, DSGS on Earth is inhibited because terrestrial topographic gradients are lower than in Valles Marineris, an effect counterbalanced by increased gravitational stress, where the intensity of deformation is enhanced because of the Earth gravity potential.

A Study on Effect of Seepage Direction on Permeability Stress Test

Due to different pore or layer structures in different directions, reservoir rocks are often anisotropic in permeability, causing permeability tests to differ between vertical and radial permeability. Except for the anisotropy of rock mass, the seepage test direction may also have an impact on the connection between stress and permeability tests. In order to illustrate the reasons for the difference between vertical and horizontal permeability test results, this article comparatively analyses the simulation results between the vertical and horizontal direction, using the discrete element method with an isotropic model. A further permeability stress test experiment was carried out in a different direction with an improved multi-functional outburst research rig. The results show that the horizontal contact hydraulic aperture had a higher sensitivity to axial stress than the vertical contact, which made the axial permeability more sensitive to the confining stress than radial permeability. In contrast to the axial stress, as the confining stress increased, the vertical contact hydraulic aperture gradually decreased, while the horizontal contact hydraulic aperture only changed a small amount. This meant that the radial permeability was more sensitive to axial stress than axial permeability. Additionally, the reducing speed of the axial permeability was very slow or even zero, with the axial stress increasing when the axial stress was less than the confining stress. In general, the seepage test direction was a very important factor, and it should be considered in the study of the relationship between stress and permeability.

Three-dimensional analysis of complex anisotropic slope instability at MMG’s Century Mine

Anisotropic and foliated rock masses present particular difficulties in the assessment of pit slope stability. Although many attempts have been made to describe the strength of rock masses that exhibit a preferred orientation of weakness, no general methodology has emerged throughout the literature to simulate anisotropic behaviour in a three-dimensional numerical model of pit slope stability. In order to simulate the effect of the anisotropic shale rock mass on pit slope stability at MMG Limited’s (MMG) Century Mine, the Ubiquitous Joint Rock Mass (UJRM) method has been applied. This paper outlines the methodology that was used to assist mine personnel in the management of complex anisotropic slope instability that jeopardised the recovery of 1.8 million tonnes of zinc ore.

Ultimate bearing capacity of an anisotropic discontinuous rock mass based on the modified Hoek–Brown criterion

Ultimate bearing capacity of an anisotropic discontinuous rock mass based on the modified Hoek–Brown criterion

Optimized Mamdani fuzzy models for predicting the strength of intact rocks and anisotropic rock masses

Development of accurate and reliable models for predicting the strength of rocks and rock masses is one of the most common interests of geologists, civil and mining engineers and many others. Due to uncertainties in evaluation of effective parameters and also complicated nature of geological materials, it is difficult to estimate the strength precisely using theoretical approaches. On the other hand, intelligent approaches have attracted much attention as novel and effective tools of solving complicated problems in engineering practice over the past decades. In this paper, a new method is proposed for mining descriptive Mamdani fuzzy inference systems to predict the strength of intact rocks and anisotropic rock masses containing well-defined through-going joint. The proposed method initially employs a genetic algorithm (GA) to pick important rules from a preliminary rule base produced by grid partitioning and, subsequently, selected rules are given weights using the GA. Moreover, an information criterion is used during the first phase to optimize the models in terms of accuracy and complexity. The proposed hybrid method can be considered as a robust optimization task which produces promising results compared with previous approaches.

Research on unloading nonlinear mechanical characteristics of jointed rock masses

Geological environments of rock mass projects are always very complicated, and further investigations on rock mechanical characteristics are needed. There are considerable distinctions in rock mechanical characteristics under unloading and loading conditions. A series of tests are conducted to study the stress-strain relationship of rock masses under loading and unloading conditions. Also, the anisotropy, the size effect, and the rheological property of unloading rock mass are investigated. The tests presented in the paper include model test and granite rheological test, which are conducted considering geological condition, rock mass structure, in-situ stress field of the permanent shiplock of the Three Gorges Project. The main differences between loading and unloading rock masses are stress paths, yield criteria, deformation and strength parameters, etc.. Different structural plane directions affect unloading rock mass evidently. With increasing size, the tensile strength, the compressive strength, the deformation modulus, the Poisson’s ratio and the anisotropy of rock mass all decrease. For sandstone samples with parallel bedding planes, the cohesion c increases but the internal friction angle φ decreases under unloading condition when compared with the values under loading condition. While for samples with vertical bedding planes, the trend is adverse. The rheological property of rocks has close relationship with the tensile stresses of rock masses. When the sandstone samples are tested under high stress condition, their rheological properties are very obvious with the unloading of confining pressure, and three typical rheological stages are shown. Rheological rate changes with the variations in axial stress and confining pressure.

Hydro‐mechanical response of Opalinus Clay during excavation works – a synopsis from the Mont Terri URL

AbstractIndurated clay formations are under consideration as potential host rock formations for the disposal of radioactive waste in several countries. The favourable features of such formations for deep geological repositories include an excellent hydraulic barrier function, high capacity for dissolved radionuclide retention and considerable self‐sealing potential. The development of a brittle fracture network (excavation‐induced damage zone, EDZ) around underground structures during construction and operation cannot however be avoided. To assess the impact of the EDZ on long‐term safety of the repository, a detailed structural inventory of the fracture network and the relevant hydro‐mechanical phenomena and processes during excavation and the subsequent operation phase is required. This then forms the geomechanical basis for the development of conceptual and numerical models of the EDZ. Here we present some empirical and experimental evidence from the Mont Terri Underground Research Laboratory (URL), summarizing the key phenomena and processes associated with the creation and evolution of an EDZ in the Opalinus Clay. In particular, the significance of rock mass anisotropy is highlighted, both as a likely origin for far‐reaching pore fluid pressure changes and as a controlling factor in EDZ development during the excavation process.

Stresses and Displacements in Steel-Lined Pressure Tunnels and Shafts in Anisotropic Rock Under Quasi-Static Internal Water Pressure

Steel-lined pressure tunnels and shafts are constructed to convey water from reservoirs to hydroelectric power plants. They are multilayer structures made of a steel liner, a cracked backfill concrete layer, a cracked or loosened near-field rock zone and a sound far-field rock zone. Designers often assume isotropic behavior of the far-field rock, considering the most unfavorable rock mass elastic modulus measured in situ, and a quasi-static internal water pressure. Such a conventional model is thus axisymmetrical and has an analytical solution for stresses and displacements. However, rock masses often have an anisotropic behavior and such isotropic assumption is usually conservative in terms of quasi-static maximum stresses in the steel liner. In this work, the stresses and displacements in steel-lined pressure tunnels and shafts in anisotropic rock mass are studied by means of the finite element method. A quasi-static internal water pressure is considered. The materials are considered linear elastic, and tied contact is assumed between the layers. The constitutive models used for the rock mass and the cracked layers are presented and the practical ranges of variation of the parameters are discussed. An extensive systematic parametric study is performed and stresses and displacements in the steel liner and in the far-field rock mass are presented. Finally, correction factors are derived to be included in the axisymmetrical solution which allow a rapid estimate of the maximum stresses in the steel liners of pressure tunnels and shafts in anisotropic rock.

Investigation of the permeability anisotropy of 2D fractured rock masses

A hydro-geometric anisotropy factor is derived for better correlation with the permeability anisotropy of field-scale fractured rock masses. The hydro-geometric anisotropy factor considers the orientation, length, spacing and hydraulic aperture properties of a discrete fracture network. Numerical simulations are carried out by using a pipe network method which simulates the fractures as connected and directed pipes obeying Darcy's law to validate the correlation between the hydro-geometric anisotropy factor and the permeability anisotropy of fracture networks. Fracture patterns from simple to complex with a scale of 10m by 10m are generated to study the effects of different fracture distributions on the hydro-geometric anisotropy of fracture networks and thus on the permeability anisotropy. It is found that the aperture size and distribution have a significant effect on the permeability anisotropy that affects the main permeable direction of the fracture networks. The permeability anisotropy varies following a power relation with the change of the intersection angle between two fracture sets. Varying the number and length ratio of the fracture sets also alters the permeability anisotropy. In all fracture patterns, the hydro-geometric anisotropy factor gives an accurate correlation with the permeability anisotropy. An anisotropic conductivity index is further defined to evaluate the directional hydraulic connectivity of the fracture system. Based on this approach, the permeability anisotropy of a fracture network system can be quickly assessed through the correlation with the hydro-geometric anisotropy factor and the anisotropic conductivity index.

Experimental study on the mechanical properties of simulated columnar jointed rock masses

Columnar jointed rock mass is a kind of structural rock mass commonly encountered in igneous rocks. Due to the effects of columnar joint networks, anisotropy is the typical mechanical property of columnar jointed rock mass, i.e. deformation and strength varying with loading direction. Correct understanding of the mechanical anisotropy of columnar jointed rock mass is a key problem that should be solved for demonstration and design of large scale rock mass projects such as dams and underground cavern excavations constructed in it. Plaster simulated columnar jointed rock mass specimens at dip angles varying from 0° to 90° with respect to the axial stress were tested under uniaxial compression conditions to investigate the mechanical anisotropy and failure modes. Based on analyses of experimental results, it was found that the strength and deformation of columnar jointed rock masses had pronounced 'U-shaped' anisotropy. In the anisotropic curves, the maximum and minimum values occurred at β = 90° and β = 45°, respectively. It was also shown that the lateral strain ratio was relatively high, especially when the dip angle was close to (45° − j/2), where j was the joint friction angle. An empirical expression was adopted to predict the 'U-shaped' anisotropy of deformation and strength and the predicted anisotropic curves agreed reasonably well with experimental data. Furthermore, four types of failure modes were summarized based on experimental results and corresponding mechanisms were also discussed.

Tunnel reinforcement in columnar jointed basalts: The role of rock mass anisotropy

The extent of the loosening zone in tunnels excavated through columnar jointed basalts is studied with the numerical discontinuous deformation analysis (DDA) method. The structure of the rock mass and tunnel geometry are modeled on the basis of a real field case study of deep tunneling performed in such a rock mass in south west China. Slender prismatic keyblocks formed by the intersection of broadly-spaced, gently-dipping breccia layers and closely-spaced, orthogonally oriented, steeply dipping columnar joints result in a highly anisotropic rock mass structure and give rise to sliding and toppling failure modes in the sidewalls and to an excessive height of loosening zone in the roof, the geometry of which is shown to be controlled by the orientation of the steeply inclined columnar joints. Results of displacement monitoring performed during tunnel excavation in a similar rock mass with multiple point borehole extensometers confirm the numerically obtained depth of the loosening zone both in the sidewalls and the roof. We find that the height of the loosening zone in the roof as obtained with DDA is greater than would have been predicted by Terzaghi’s empirical rock load classification for “blocky” rock masses, and show that its shape and orientation are controlled by the anisotropy of the rock mass structure. Moreover, we demonstrate that dimensioning rock bolt reinforcement using well-established empirical criteria without consideration of the anisotropic nature of the rock mass may lead to un-conservative design.