Rock Strength Anisotropy Research Articles

An experimental study of tensile stress and deformation in an anisotropic rock

Anisotropy is a very common condition in rock mass; it can be due to different factors and directly affects the failure mechanisms affecting the rock mass. For example, metamorphic rocks that are foliated, sedimentary rocks that are stratified or volcanic formations with alternating layers. Despite the existence of several studies related to anisotropy those specifically addressing the tensile strength of anisotropic rocks are quite limited. The present study is focused on the determination of the deformability, compressive and tensile strength of anisotropic rocks. It must be highlighted that the mechanical behavior of the anisotropic rock mass is dependent on the angle between the inclination of planes of weakness (e.g. foliation) and the direction of the load. Assuming a vertical load, the two extremes of tensile strength are 0°(horizontal) and 90° (vertical). A series of laboratory tests has been done in anisotropic sandstone (lithic arkose), from Burgos (Spain), including uniaxial compressive strength tests, direct tensile strength tests, and diametric compression (Brazilian tests). The tests were carried out with strain gauges that allowed estimating the elastic modulus. To determine the anisotropic direction, ultrasonic pulse wave velocity tests were also performed. The variation of strength and deformability as a function of anisotropy is analyzed, as well as the variation of elastic behavior in tensile and compressive.

Theoretical and experimental investigation of a shear failure model for anisotropic rocks using direct shear test

This study proposes a theoretical model for predicting the shear strength of anisotropic rocks in which failure is dependent on the inclination of the inherent structural weak planes. For this purpose, triaxial and direct shear tests were conducted on dried and saturated shale samples. Samples were cored at different orientations (β) to the inherent structural weak planes, i.e., bedding planes. To verify the anisotropic behavior of the samples, triaxial tests were performed on samples with various inclinations of the bedding planes. The experimental results demonstrated a U-shape relationship between the compressive strengths and the inclination of the bedding planes, which is in accordance with Jaeger's model of the plane of weakness (JPW). Accordingly, apparent strength and elastic properties, such as Young's modulus, Poisson's ratio, cohesion, and internal friction angle were all observed to be dependent on β, which verified the mechanical anisotropy of the shale samples. Many of the existing failure criteria consider the impact of bedding inclination on failure strength based on uniaxial and triaxial conditions. However, it is also important that the failure modes of anisotropic rocks are evaluated during shearing. For this purpose, a theoretical model was derived to relate shear strength to β following the Coulomb-Navier criterion. The relationship between shear strength and β was plotted and illustrated in an Inverted-U shape. Direct shear tests were conducted to validate the proposed criterion. Plotted experimental data confirmed the shape of the geometry determined by theoretical analysis. From the results, the maximum shear strength occurred when β was between 30° and 60° in direct shear tests. To obtain a more comprehensive understanding, changes in the shear stress-displacement curve and dependence of the friction angle, to the bedding plane orientation, β, were evaluated and indicated shear anisotropy behavior.

Implementation of a constitutive model for anisotropic rocks based on modified Lade failure criterion

The strength anisotropy for inherent anisotropic rocks presents a challenge to simulate considering the influence of intermediate principal stress. Based on the modified Lade failure criterion, a new anisotropic modified Lade criterion combining an empirical equation is established and verified using published experimental datasets of anisotropic rocks. The incremental constitutive model for anisotropic rocks is derived by using finite difference theory. The dynamic link library (DLL) module of the model is obtained by using the VC++ program, and then the model is validated against various laboratory test results. It is concluded that the proposed criterion and derived model can describe the strength anisotropy of inherent anisotropic rocks well.

Tensile strength of anisotropic rocks from enhanced Brazilian laboratory testing and data analysis protocols

The tensile strength of rock and rock-like materials is a critical material property in rock engineering design and the prediction of rockmass behaviour to mitigate any potential failure that may affect personnel safety or damage property. This study presents new instrumentation guidelines to the Brazilian Tensile Strength (splitting tensile strength) test to enhance the data processing techniques to determine true tensile strength. For this study a total of eighteen (18) specimens of two lithologies (Pointe Du Bois tonalite gneiss and Key Anacon metabasalt) were instrumented, tested, and reviewed to determine the true tensile strength of the material. This paper also identifies three potential failure modes and presents a failure envelope based on the identified potential failure modes.

Failure Behaviour of Jointed Rock Masses with 3D Nonpenetrating Joints under Uniaxial Compression: Insights from Discrete Element Method Modelling

It is well known that joints or fissures have an important effect on the failure mechanism of natural rocks. Previously, many numerical and experimental papers have been carried out to study the strength anisotropy and failure characteristics of jointed rocks. However, few studies have been carried out on the failure mechanism of nonpersistent jointed rock masses with different persistence, especially for nonpersistent joints in three dimensions. In the present study, the failure characteristics of a 3D nonpersistent jointed rock mass with different inclinations (θ) and persistence (K) are studied by numerical simulation. For the 3D digital elevation model (DEM), the linear parallel bond model (LPBM) and smooth-joint model (S-J) were used to model the rock-like material and joint interface, respectively. The connections between the geometric parameters of joints and peak strength are revealed. For the peak strength, the joint persistence only plays a minor role in specimens with inclinations of 0° and 90°, and its influence on strength is mainly reflected in the specimens with shear failure (θ = 45°, 60°, and 75°). Based on microcrack accumulation and evolution, four typical failure processes (shear failure, split failure, mixed failure, and intact failure) are analysed from the micro perspective. The shear stress evolution process on the 3D nonpersistent joint of the specimen with different inclinations under K1 = 0.42 was monitored by the measurement circle, and it was found that the distribution of shear stress inside the rock bridge is related to the failure mode of the specimen. For the specimens with θ = 0° and 90°, the shear stress had little change, indicating that there is slight shear slip behaviour on the joint surface. When the inclination is 45°, 60°, and 75°, the shear stress changes obviously during loading, indicating that the shear action is strong in this failure mode.

Bayesian inference of rock strength anisotropy: Uncertainty analysis of the Hoek–Brown failure criterion

Strength properties of most sedimentary and metamorphic rocks are known to vary with direction. Knowledge of this so-called rock anisotropy is of utmost importance for reliability analysis and engineering design. The purpose of this paper is twofold. First, we propose a formulation of the Hoek–Brown (HB) failure criterion, which calculates strength anisotropy using a non-uniform scaling of the stress tensor. We use two scaling factors, CN and CS, to link the orientation of the anisotropy planes with the loading direction. As we assume isotropic parameters for intact rock, our HB model formulation is relatively easy to use and has the additional advantage that it does not demand any modifications to the HB failure criterion. Second, we embed our HB model formulation in a Bayesian framework and illustrate its power and usefulness using experimental data of anisotropic rock samples published in the literature. Results demonstrate that our HB model formulation predicts accurately measured peak strengths of rocks with different degrees of anisotropy, confining stresses and anisotropy orientations. The uncertainty in peak strength of anisotropic rocks can be quite large, reiterating the need for an explicit treatment of strength anisotropy uncertainty in rock mechanics studies. The Bayesian methodology is general-purpose, and, as such, can help better inform geotechnical engineers, contractors and other professionals about rock conditions and design reliability and assist decision makers in determining the overall risks of engineering structures.

Using Continuum-Discontinuum Element Method to Model the Foliation-Affected Fracturing in Rock Brazilian Test

In this study, the continuum-discontinuum element method (CDEM) was used to investigate the tensile fracture mechanism of rock materials. An isotropic rock disk model and models considering different foliation inclinations were established, and three schemes were used to simulate the rock fracturing in Brazilian test. Then, the influences of the rock matrix and foliation strengths on anisotropy rock fracturing were investigated. Furtherly, simulation results were verified, and the rock fracture mechanisms were discussed. The results show that the rock fracturing in Brazilian test can be accurately simulated by CDEM, which is in accordance with the experimental results. For isotropic and horizontal foliation rock, the stress concentration in loading positions causes a local fracture of rock sample, and application of a local strengthening scheme can simulate the integral tension fracture of sample middle. As the foliation angle varies from 15° to 45°, the rock fracturing is affected by the stress concentration and foliation distribution. In splitting simulation, a strengthening scheme should be adopted to overcome this influence. As a result, the rock sample generates the sliding and compression-shear fracture. As the foliation angle changes from 45° to 75°, the foliation, rather than the matrix, dominates the fracture behavior of rock sample. For vertical foliations’ rock, as the middle foliation thickness is appropriately broadened, the simulation results are reasonable. In general, the tensile strength of anisotropic rock entirely decreases with an increase of foliation angle, and the effect of foliation strength on the tensile strength rock sample is larger than that of the rock matrix.

On Applicability of Some Indirect Tests for Estimation of Tensile Strength of Anisotropic Rocks

The tensile strength of rocks plays a noteworthy role in their failure mechanism, and its determination can be beneficial in optimizing the design of the rock structures. Schistose rocks due to their inherent anisotropy in different foliation directions show a diverse strength at each direction. The purpose of this work was to compare and assess the tensile strength of phyllite, which was obtained in direct and indirect tensile tests in different foliation directions. To this end, several phyllite specimens with different foliation angles (0o, 30o, 45o, 60o, and 90o) related to the loading axis (β) were prepared. Finally, the direct tensile test, diametrical and axial point load tests, Brazilian test, and Schmidt hammer test were conducted on 188 samples. The results of the experimental tests revealed that the maximum and minimum tensile strengths in direct tensile testing tension were directly related to the angles of 0o and 90o. Also it was observed that the Brazilian tensile strength overestimated the tensile strength. Furthermore, an exponential correlation was introduced between the direct tensile strength and the Brazilian tensile strength.

Analysis of electron backscattered diffraction (EBSD) mapping of geological materials: precautions for reliably collecting and interpreting data on petro-fabric and seismic anisotropy

Automated electron backscattered diffraction (EBSD) data yield abundant information on the lattice-preferred orientations (LPOs) and deformation microstructures and mechanisms of minerals in a rock, which aid in our understanding of the tectonic conditions and history of a region. Additionally, this information allows us to interpret seismic anisotropies in the crust and mantle. However, great care must be taken in the collection and production of crystallographic orientation data via automated EBSD to more precisely interpret LPOs, deformation microstructures, and seismic anisotropies because petro-fabrics can be different depending on sampling methods such as all-points-per-grain (whole) data and one-point-per-grain (one orientation per grain) data. Here, we report a detailed comparison of the crystallographic orientation data produced using both all-points-per-grain and one-point-per-grain techniques to analyze eclogites from the Yuka terrane in the North Qaidam ultrahigh-pressure metamorphic belt of northwestern China. By comparing eclogite crystallographic orientations between different sampling methods, we found that there was no marked difference in the LPOs, fabric strengths (J-index and M-index), and seismic anisotropies for relatively small mineral grains (e.g., garnet and omphacite). However, there were large differences in the LPOs, fabric strengths, and seismic anisotropies of relatively large minerals grains (e.g., amphibole). This result can be attributed to the acquisition method of crystallographic orientation data, which can influence the LPO, fabric strength, and seismic anisotropy of minerals and rocks. Therefore, the pole figures of minerals should be constructed from one point per grain data in order to avoid the oversampling of large grains for samples with highly heterogenous grain size distributions, as well as to permit the comparison of crystallographic orientations obtained using different tools and in other studies.

Wellbore stability and failure regions analysis of shale formation accounting for weak bedding planes in ordos basin

Borehole instability problem is one of the key problems in drilling engineering, especially the shale formation with bedding planes and natural fractures, the failure of shale rock could be divided into two parts, shear failure across intact rock matrix and slippage failure in shale bedding, resulting in more serious borehole instability problem during drilling process. In this study, combining with rock strength anisotropy, a method of failure region around wellbore is developed for layered rocks on the basis of isotropic borehole stability model. The effect of shale bedding occurrence on failure region around wellbore, what was hardly conducted by former researchers, is examined systematically. The results show that, polar plot of critical lower mud weight with rock strength anisotropy considered reflects the actual situation of a shale formation; the shale bedding strength, pore pressure and intrinsic cohesion are the three most impact parameters on wellbore stability. Moreover, the maximum failure depth is no longer in the minimum principal stress, but locates in four corners at top and bottom of wellbore, which is induced by slippage failure in laminated formations; the collapse of wellbore will be aggravated due to the overlapping of failure in rock matrix and bedding. This proposed model not only can provide guiding suggestions for well constructions and cementations, but also can be used as an effective complement to provide richer ground stress inversion data.

Micromechanical correlation between elasticity and strength characteristics of anisotropic rocks

The study sets forth a method upon which the strength anisotropy of rocks can be estimated from particular characteristics of the elasticity tensor. By depicting rocks as assemblies of bonded particles, micromechanical formulation of force distribution and contact deformation in conjunction with a local strength criterion eventually lead to macroscopic elasticity and strength properties with fabric tensor as a mutual microstructural descriptor. As such, knowing the elastic properties of rock, the proposed analytical procedure computes the associated fabric anisotropy, which is in turn used to estimate rock strength anisotropy, thus avoiding its costly experimental determination. The accuracy of the procedure is verified against two available experimental datasets (sandstone and slate rock samples) for which both elasticity and strength characteristics are reported. Comparisons between analytical and experimental results indicate that rock strength anisotropy can be captured realistically only when in addition to contact normal-based fabric, microscopic strength parameters are also directional in character.

The Effect of Thermochemical Factors on Fracturing Pressure in Shale Rock Characterized by Tensisle Strength Anisotropy

Drilling mud characteristics affect the stress distribution around the borehole, while anisotropic tensile strength determines the fracture behavior of the formation, but the combined effect of these factors is rarely considered in the prediction of fracture pressure. In this work, tensile strength anisotropy of shale rock was analyzed based on the Brazilian disc test (BDT), and the corresponding anisotropic tensile criteria were reviewed and contrasted with experimental results. The N-Z (Nova – Zaninetti) criterion is adopted to describe tensile strength anisotropy of shale rock. Based on the stress distribution model and the N-Z criterion, a model of shale rock fracture under the combined action of thermal and chemical factors was constructed. The solution of the model shows that chemical and thermal factors have a different effect on pore pressure distribution around the borehole. The effect of sedimentary layers, tensile strength anisotropy, in-situ stress and pore pressure on equivalent density of fracture pressure (EDFP) was also investigated. It is shown that the EDFP decreases with increasing dip angle at a given strike of the bedding plane and reaches a minimum value when the strike of the bedding plane is along the direction of the minimum horizontal stress. The decrease in EDFP caused by tensile strength anisotropy reaches or exceeds 10% of the value calculated for isotropic conditions. The more pronounced the anisotropy of strength, the smaller the possible value of EDFP. The higher the ratio of horizontal stresses and pore pressure, the more significant the effect of anisotropy on EDFP. It is also notable that increasing the temperature of the wellbore can improve EDFP parameters and enlarge the SMDW.

Strength Anisotropy of Rock with Crossing Joints: Results of Physical and Numerical Modeling with Gypsum Models

The geometric and mechanical characteristics of multiple intersecting joints can govern the strength anisotropy behavior of a rock mass. Laboratory uniaxial compression tests with artificial rock-like material (gypsum) were conducted to investigate the strength anisotropy behavior of jointed specimens. Three special kinds of gypsum were used to ensure that the handmade joints have a user-defined-strength for all samples. Specimens with one or two crossing joints covering more than 20 angle configurations and two different property sets were prepared and tested. The strength anisotropy behaviors of specimens with constant joint angles (90°, 80°, 60°, 45°, and 30°) were investigated, and the failure mechanisms were assessed through the damage pattern of the colored gypsum. The details of the design scheme and figures of the evaluated experimental results are presented in this paper. A new equivalent continuum model, called the multi-joint model, is developed for jointed rock masses that contain up to three arbitrary persistent joint sets. The Mohr–Coulomb yield criterion is used to check failure of the intact rock and the joints. The multi-joint model is implemented into the finite difference method code FLAC and compared with the distinct element method code UDEC. The experimental results are used to verify the developed multi-joint constitutive model and to investigate the behavior of jointed specimen. Experimental observations agree well with the simulation results and analytical solutions.

Assessing borehole stability in bedding-parallel strata: Validity of three models

Bedding planes have crucial influence on borehole stability and there have been several models accounting for this kind of effect. However, few articles have assessed the difference or validity of these models, especially for the common-used elastic models that consider anisotropic strength of bedding rocks. Three models (including an empirical one), named Model A, Model B and Model C, are illustrated and compared here. With simplification and modification, calculation programs are developed to figure out the similarities and differences of collapse area and collapse pressure that determined by different models. Then, according to the field data, the applicability and validity of each model are carefully analyzed. It reveals that the results predicted by Model A are relatively reasonable compared to the other two models; the predictions of Model B can explain the collapse area extends perpendicularly to the beddings around a borehole, but cannot give the accurate collapse pressure in many cases because of the exchange of principal stresses on the borehole wall; the predictions of Model C are also not precise enough for its only taking the effects of beddings into account without the in-situ stress. Besides, the fracture pressure for boreholes of arbitrary orientations considering strength anisotropy of rocks is further studied, which is incorporated to gain a recommended model for the calculating of the safe mud weight window.

A 3D model of hydraulic fracturing and microseismicity in anisotropic stress fields

We present a 3D numerical model for hydraulic fracturing and damage of low permeable rock in an anisotropic stress field. The model computes the intermittent damage propagation, microseismic event-locations, microseismic event-distribution, damaged rock volume and injection pressure. The model builds on concepts from invasion percolation theory, where cells in a regular grid are connected by transmissibilities, also called bonds. An intact bond breaks when the fluid pressure exceeds the least compressive stress and random uniformly distributed bond strength. Analytical expressions are obtained for the fractions of the weakest bonds in the x-, y- and z-directions as a function of the stress anisotropy and the rock strength anisotropy. A strategy is suggested for a fast solution of the pressure equation when the fluid pressure is restricted to the damaged rock volume. An expression for the volume of damaged rock is obtained in the cases where it has a high permeability. The model is demonstrated on a published case from the Barnett Shale and it reproduces the observed main features, such as the spatial and temporal distribution of the events, the magnitude–frequency distribution and the injection pressure. The microseismic event-distribution and the b-value depend on the permeability of the damaged rock volume. The b-value increases with decreasing permeability from a little < 0.6 to a value above 2 for the maximum possible permeabilities. The damaged rock volume is non-compact and similar to a percolation cluster for “high” damaged rock permeabilities, and it becomes increasingly compact with decreasing permeabilities. The resulting loop-less fracture network is found to have similar characteristics for different damaged rock permeabilities.

A coupled thermo-poroelastic analysis of wellbore stability for formations with anisotropic strengths

The temperature difference between the drilling fluid and formation will lead to an apparent temperature change around the borehole and tend to cause borehole instability problems in oil and gas drilling process. The wellbore stability models used in thinly laminated rock formations integrate the in situ stresses, pore pressure, well trajectory, and rock strength parameters to improve the wellbore stability; however, a limited amount of research has focused on the factor of formation temperature and its difference between drilling mud. Hence, a wellbore stability model is introduced based on the stress transformations and the Mohr-Coulomb failure criteria, which incorporate the rock strength anisotropy and the temperature difference between formation and drilling mud. The wellbore instability problems of anisotropic strength formation are analyzed using this model. The results show that the shear failure of rock matrix mainly occurs at two symmetric locations around the borehole and the size of failure region decreases with the inclination angle, in contrast, the shear slip failure of weak plane occurs at four locations around the borehole. The mud density required for isotropic strength should be selected as the required mud density to keep the wellbore stable if the inclination angle less than a certain value, and it almost keeps a constant with the inclination angle changes. On the contrary, the mud density required for slippage along the plane of weakness should be selected when the inclination angle larger than this value, and it is increasing with the inclination angle. Positive temperature difference will aggravate the wellbore instability, the larger the temperature difference the bigger the mud density is required.

Effect of rock strength variation on the estimated borehole breakout using shear failure criteria

One of the primary goals of wellbore stability analysis is the estimation of the shear failure onset or borehole breakout. Estimation of borehole shear failure requires selecting an appropriate failure criterion. Numerous failure criteria have been used for rock failure analysis, but there is no common agreement of which criterion to select for wellbore stability analysis. In general, rock failure criteria mainly depend on rock mechanical properties and in situ stresses. This paper investigates the effect of rock strength variation and strength anisotropy on the estimated borehole shear failure using thirteen different criteria. A rock strength database was created from different US unconventional shale plays. Rock failure criteria were ranked based on the estimated borehole breakout for different shales. According to the results for different level of rock strength, there are some failure criteria that are highly responsive to variation in rock mechanical properties. Circumscribed Drucker–Prager, Modified Griffith, Inscribed Drucker–Prager criteria have shown great response to the change in the internal angle of friction. Murrell, Stassi D’Alia, Hoek–Brown, and Griffith are sensitive to variation of uniaxial compressive strength. Mogi-Coulomb, Modified Wiebols–Cook, Modified Lade, and Mohr-Coulomb failure criteria did not show any significant response to the variation of rock mechanical properties and strength anisotropy.

Brazilian Tensile Strength of Anisotropic Rocks: Review and New Insights

Strength anisotropy is one of the most distinct features of anisotropic rocks, and it also normally reveals strong anisotropy in Brazilian test Strength (“BtS”). Theoretical research on the “BtS” of anisotropic rocks is seldom performed, and in particular some significant factors, such as the anisotropic tensile strength of anisotropic rocks, the initial Brazilian disc fracture points, and the stress distribution on the Brazilian disc, are often ignored. The aim of the present paper is to review the state of the art in the experimental studies on the “BtS” of anisotropic rocks since the pioneering work was introduced in 1964, and to propose a novel theoretical method to underpin the failure mechanisms and predict the “BtS” of anisotropic rocks under Brazilian test conditions. The experimental data of Longmaxi Shale-I and Jixi Coal were utilized to verify the proposed method. The results show the predicted “BtS” results show strong agreement with experimental data, the maximum error is only ~6.55% for Longmaxi Shale-I and ~7.50% for Jixi Coal, and the simulated failure patterns of the Longmaxi Shale-I are also consistent with the test results. For the Longmaxi Shale-I, the Brazilian disc experiences tensile failure of the intact rock when 0° ≤ βw ≤ 24°, shear failure along the weakness planes when 24° ≤ βw ≤ 76°, and tensile failure along the weakness planes when 76° ≤ βw ≤ 90°. For the Jixi Coal, the Brazilian disc experiences tensile failure when 0° ≤ βw ≤ 23° or 76° ≤ βw ≤ 90°, shear failure along the butt cleats when 23° ≤ βw ≤ 32°, and shear failure along the face cleats when 32° ≤ βw ≤ 76°. The proposed method can not only be used to predict the “BtS” and underpin the failure mechanisms of anisotropic rocks containing a single group of weakness planes, but can also be generalized for fractured rocks containing multi-groups of weakness planes.

The relationship between magnetic anisotropy, rock-strength anisotropy and vein emplacement in gold-bearing metabasalts of Gadag (South India)

In this study the importance of rock strength and its anisotropy in controlling vein emplacement is evaluated by integrating anisotropy of magnetic susceptibility (AMS) with rock mechanics data from massive (visibly isotropic) metabasalts of Gadag region (Dharwar Craton, South India). Orientation of magnetic foliation (MF) is first recognized from AMS. Subsequently, rock mechanics tests viz. ultrasonic P-wave velocity (Vp), uniaxial compressive strength (UCS) and point load strength (Is(50)) are done in cores extracted parallel and perpendicular to MF. Vp is found to be higher in direction parallel to MF than perpendicular to it. In contrast rock strength (UCS and Is(50)) is greater in direction perpendicular to MF, than parallel to it. This proves that rocks from the gold mineralized belt of Gadag have rock strength anisotropy. Orientation of MF in Gadag region is NW-SE, which is also the mean orientation of quartz veins. Previous studies indicate that emplacement of veins in the region took place during regional D3 (NW-SE shortening). Based on the present study, it is concluded that vein emplacement took place in NW-SE orientation because the rocks have strength anisotropy and are weaker in this direction (orientation of MF), which dilated to accommodate fluid flow. In addition, vein intensities are measured along three traverses and found to be variable. It is argued that since mineralization is favoured when the system gets saturated with fluid, variation in fluid flow could not have been responsible for variation in vein intensities in the study area. Since the rock strength of the different blocks investigated here is not uniform, it is envisaged that variation in rock strength played an important role in controlling the vein intensities. It is concluded that rock strength variation controlled strain partitioning and channelized fluid flow thus influencing vein emplacement and mineralization and formation of lodes.

Investigation of Strength of Anisotropic Rocks under Axial Compression and Lateral Pressure

The article describes the theoretical and experimental research into the strength of cylindrical specimens made of layered and anisotropic geomaterials exposed to axial compression and lateral pressure. The tests used INSTRON 8802 versatile servohydraulic fatigue testing system. The experimental results are the relationships between the ultimate strength and bedding angle in specimens of an artificial material, meta-siltstone and shale. The experimental data agree well with the theoretical calculations.