Behaviour Of Intact Rock Research Articles

An improvement in the method of correcting indirect radial strain measurements during triaxial strength tests in rocks

The present article provides an improvement in the method to correct indirect strain measurements in triaxial compressive strength tests through axial displacement and hydraulic fluid volume change measurements. The improvement focused on reducing the parameters of the formula proposed for indirect volumetric strain in the original method, thereby facilitating the development of a simpler formula in which the radial strain depends on only two parameters: the initial volume of the rock specimen and the volume changes of the hydraulic fluid for each instant. The comparison between the improvement proposed, and original method resulted in a mean absolute difference of 0.003.•This improvement does not depend on the axial strain, unlike the original method, which requires correcting the indirect axial strain measurements before correcting the indirect radial strain measurements.•This improvement can be useful for research on the stress-strain behavior of intact rock under laboratory conditions, such as in the study of the post-peak state.

Nonlinear criterion for strength mobilization in brittle failure of rock and its extension to the tunnel scale

As underground excavations are getting deeper and field stresses increase, the behavior of intact rock blocks plays an increasingly important role in understanding and estimating the overall rock mass strength. To model the brittle behavior of intact rock blocks, the stress–strain curve is usually idealized considering a linear strength mobilization approach (cohesion-weakening-friction-strengthening, CWFS), however, it is well recognized that rock presents a nonlinear behavior in terms of the confining stress. This study extends the strength mobilization in brittle failure of rock using nonlinear criteria. To determine the model parameters, a standard statistical method that uses the complete laboratory stress–strain curves of the intact rock is employed. Several hypotheses of linear and nonlinear models are statistically compared for different types of rock and confining stress levels. Results demonstrate that the best approach to model the brittle failure of rock is to consider a nonlinear strength envelope, such as the Hoek-Brown criterion assuming a residual uniaxial compressive strength different from zero and a m i parameter that increases, both with simultaneous mobilization. This model helps to recreate high-confining conditions and a more realistic transition between peak and post-peak strength. The obtained parameters are discussed and compared with literature values to verify the validity and to develop guidelines for the estimation of parameters, providing an objective mobilization criterion. Finally, the nonlinear model was applied to a finite element code and extended to a tunnel scale in the brittle rock under high-stress conditions. A reasonable fit between the simulations and the in-situ overbreak measurements was found.

A gradient enhanced transversely isotropic damage plasticity model for rock ‐ formulation and comparison of different approaches

AbstractThe nonlinear mechanical behavior of intact rock and rock mass is characterized by irreversible deformation, associated with strain hardening, strain softening and degradation of stiffness. In the case of stratified rock types like shales or phyllites, the mechanical behavior additionally depends on the loading direction with respect to the orientation of the principal material directions, resulting in inherent anisotropic material behavior, or in many cases more specifically in transversely isotropic material behavior. On the basis of a critical review of several approaches for modeling nonlinear anisotropic material behavior, proposed in the literature, the linear mapping of the Cauchy stress tensor into a fictitious isotropic configuration, originally proposed by Boehler [1], was identified as the best choice for the application in 3D finite element simulations. Within this framework, an isotropic damage plasticity model for rock, proposed by Unteregger et al. [2], extended to inherent transversely isotropic behavior is presented. It is implemented into a FE‐program by means of the return mapping algorithm and it is regularized by an over‐nonlocal implicit gradient enhancement for ensuring mesh‐insensitive results. For validation, numerical simulations of triaxial compression tests on Tournemire shale, documented in Niandou et al. [3], are performed at both the integration point level and the structural level. The performance of the constitutive model is assessed by its ability to predict the complex direction‐dependent mechanical behavior of transversely isotropic rock and the failure modes observed in triaxial compression tests with different confining pressures and different inclination angles of the stratification planes with respect to the direction of axial loading.

The effect of saturation on the physical and mechanical behavior of some rock samples

Different major factors control the strength of solid rocks. Moisture content is one of the most important factors, which can change the physical and mechanical behavior of intact rock as well as rock mass. Several early studies have shown that rock is weaker if tested wet rather than dry. In this paper, the density, P-wave velocity, uniaxial compressive strength, Brazilian tensile strength, and modulus of elasticity of seven different intact rock samples were measured under both dry and saturated conditions. The porosity of the samples was reported as well. Based on the obtained results, some correlations were proposed for estimating the saturated physical and mechanical properties from dry ones. The proposed correlations include different rock types and are more general than the previously reported ones. Comparing the obtained results showed that the mechanical and physical properties of weaker samples are more sensitive to the saturation process. Moreover, among the different mechanical parameters, Brazilian tensile strength exhibited more sensitivity to saturation. Comparing the results with the calculated porosities revealed that porosity is one of the key factors in the effect of saturation on physical and mechanical parameters. It seems that in the more porous rock samples, greater changes in the different measured parameters occur after saturation.

Experimental Study on Shear Mechanism of Rock-Like Material Containing a Single Non-Persistent Rough Joint

The geometrical and mechanical properties of non-persistent joints as well as the mechanical behavior of intact rock (rock bridges) are significantly effective in the shear strength of weakness planes containing non-persistent joints. Therefore, comprehensive knowledge of the shear mechanism of both joints and rock bridges is required to assess the shear strength of the planes. In this study, the shear behavior of specimens containing a single non-persistent rough joint is investigated. A novel procedure was used to prepare cast specimens embedding a non-persistent (disc-shaped) rough joint using 3D printing and casting technology, and the shear strength of the specimens was examined through an extensive direct shear testing program under constant normal load (CNL) condition. Three levels for three different variables of the joint roughness, rock bridge ratio, and normal stress were considered, and the effects of these factors on the shear behavior of prepared samples were tested. The experimental results show a clear influence of the three variables on the shear strength of the specimens. The results show that the normal stress applied to the jointed zone of weakness planes is considerable, and thus joint friction contribution should be taken into account during shear strength evaluation. Furthermore, the dilation mechanism of the specimens before and after failure was investigated through a digital image correlation analysis. Finally, a camcorder was used to analyze the location and sequence of the initiated cracks.

Development of a poly-axial platen for testing true-triaxial behavior of rocks

Mining at greater depths can lead to stress-induced failure, especially in areas of high horizontal in situ stress. The induced stresses around the opening are known to be in a poly-axial stress state where, σ1 ≠ σ2 ≠ σ3 with special case of σ3 = 0 and σ1, σ2 ≠ 0 at its boundary, where σ1, σ2, σ3 are major, intermediate, minor principal stress, respectively. The conventional triaxial testing does not represent the actual in situ strength of the rock in regions of high horizontal stress, as it ignores the influence of intermediate principal stress (σ2). The typical poly-axial testing (biaxial and true-triaxial tests) of intact rock mostly requires sophisticated and expensive loading systems. This study investigated the mechanical behavior of intact rock under a poly-axial stress state using a simple and cost-effective design. The apparatus consists of a biaxial frame and a confining device. The biaxial frame has two platens that apply equal stress in both directions (σ1 = σ2) on a 50.8 mm cubical specimen when placed inside the uniaxial loading device. The confining device performed separate biaxial tests under constant intermediate principal stress (σ2 = constant) and true-triaxial tests when used along with the biaxial frame. This study then compared the failure modes and peak strength of Berea sandstone specimens with other biaxial–triaxial devices to validate the design of the poly-axial apparatus. We also performed uniaxial tests on both standard cylindrical samples and prismatic specimens of different slenderness ratios. These tests provided a complete understanding of the failure mode transition from standard uniaxial compressive tests to triaxial stress conditions on cubical specimens. Additionally, this study determined best-fitted strength envelopes for biaxial and triaxial stress state. Based on regression analysis, we found a quadratic polynomial to be a good fit to biaxial strength envelope. For the true-triaxial strength envelope, we found the three-dimensional (3D) failure criterion to be a good fit with R2 of 0.964.

Influence of geostress field on dynamic mechanical behavior of intact rock

The high magnitude of in situ geostress under deep underground conditions and the intermediate principal stress under complex stress conditions have a significant influence on the static or dynamic mechanical behavior and strength characteristics of intact rock material. The constitutive relationship for quasi-brittle materials (e.g., intact rock or concrete) subjected to large strains, high strain rates, high pressures, and complex stress states was investigated, but the mechanical behavior and strength characteristics for rock under high pressures and complex stress states have not yet been elucidated. This study mainly focuses on constitutive modeling and theoretical prediction of the dynamic mechanical behavior and strength characteristics for rock under high dynamic pressures and complex stress states. A damaged elastoplastic constitutive model for intact rock is established in this study by taking the influence of a high strain rate, high pressure, and complex stress state into account. The failure mechanism of deeply buried rock engineering under high in situ stress and an additional impact pressure from a high-velocity underground impact was analyzed in this paper. The influence of the high pressure and intermediate principal stress on the quasi-static or dynamic mechanical behavior and strength characteristics of the deeply buried rock was investigated under a complex stress state.

Effect of Stress Path on the Failure Envelope of Intact Crystalline Rock at Low Confining Stress

Numerical modelling is playing an increasing role in the interpretation of geological observations. A similar phenomenon is occurring with respect to the interpretation of the stress–strain response of intact rock measured in laboratory tests. In this research, the three-dimensional (3D) bonded particle model (BPM) with flat-jointed (FJ) contact was used to investigate the impact of stress paths on rock failure. The modified FJ contact model used for these studies numerically captured most of the intact rock behavior of Lac du Bonnet granite observed in the laboratory. A numerical simulation was used to track the behavior of this rock for different stress paths, starting with uniaxial tension and compression loading conditions. The migration from uniaxial tension to triaxial compression is challenging to simulate in physical laboratory tests but commonly observed around underground excavations. The numerical modelling methodology developed for this research tracks this stress path and the impact of the intermediate stress on peak strength at low confinements, commonly found around underground excavations.

Numerical Simulation of Laboratory Strength Tests Using a Stochastic Approach

Heterogeneity and discontinuity significantly affect rock strength. For accurate stability prediction, intact rock behavior is imperatively included in rock mass behavior. However, past research largely used arbitrary scaling approaches to produce rock strength. This paper considers a stochastic approach in order to determine the strength of a rock. Based on the laboratory data, a MATLAB® with extreme value stochastic model generates a database for each physico-mechanical property. Then FLAC® simulates laboratory-sized rock specimens. The grids developed in the numerical model can in turn develop random material properties in MATLAB®, which researchers then applied to the final FLAC® model. Model runs simulate the approach performed in the laboratory. The results from the model indicate that a stochastic approach produces strengths that are lower than a deterministic approach. Failure modes for each specimen are different, similar to observations in the laboratory. In addition, random density also influences the failure mode, highlighting the importance of stochastic analysis in rocks.

Experimental Determination of the Mechanical Properties and Deformation Constants of M\xf3r\xe1gy Granitic Rock Formation (Hungary)

Determination of the mechanical behaviour of intact rock is one of the most important parts of any engineering projects in the field of rock mechanics. The most important mechanical parameters required to understand the quality of intact rock are Young’s modulus (E), Poisson’s ratio (ν), the strength of rock (σc) and the ratio of Young’s modulus to the strength of rock known as modulus ratio (MR), which can be used for calculations. The particular interest of this paper is to investigate the relationship between these parameters for Hungarian granitic rock samples. To fulfil this aim, Modulus of elasticity (E), Modulus of rigidity (G), Bulk modulus (K) and the modulus ratio (MR = E/σc) of 50 granitic rock samples collected from Bátaapáti radioactive waste repository were examined. Fifty high-precision uniaxial compressive tests were conducted on strong (σc > 100 MPa) rock samples, exhibiting the wide range of elastic modulus (E = 57.425–88.937 GPa), uniaxial compressive strength (σc = 133.34–213.04 MPa) and Poisson’s ratio (ν = 0.18–0.32). The observed value (MR = 326–597) and mean value of MR = 439.4 are compared with the results of similar previous researches. Moreover, the statistical analysis for all studied rocks was performed and the relationship between MR and other mechanical parameters such as maximum axial strain (εa, max) for studied rock samples was discussed. Finally, the validity of the proposed mathematical model by Palchik (Geomech Geophys Geo-energy Geo-resour 6:1–12, 2019) for stress–strain behaviour of granitic rock samples was investigated.

Complex analysis of uniaxial compressive tests of the Mórágy granitic rock formation (Hungary)

Abstract Understanding the quality of intact rock is one of the most important parts of any engineering projects in the field of rock mechanics. The expression of correlations between the engineering properties of intact rock has always been the scope of experimental research, driven by the need to depict the actual behaviour of rock and to calculate most accurately the design parameters. To determine the behaviour of intact rock, the value of important mechanical parameters such as Young’s modulus (E), Poisson’s ratio (ν) and the strength of rock (σcd) was calculated. Recently, for modelling the behaviour of intact rock, the crack initiation stress (σci) is another important parameter, together with the strain (σ). The ratio of Young’s modulus and the strength of rock is the modulus ratio (M R), which can be used for calculations. These parameters are extensively used in rock engineering when the deformation of different structural elements of underground storage, caverns, tunnels or mining opening must be computed. The objective of this paper is to investigate the relationship between these parameters for Hungarian granitic rock samples. To achieve this goal, the modulus ratio (M R = E/σc) of 50 granitic rocks collected from Bátaapáti radioactive waste repository was examined. Fifty high-precision uniaxial compressive tests were conducted on strong (σc >100 MPa) rock samples, exhibiting the wide range of elastic modulus (E = 57.425–88.937 GPa), uniaxial compressive strength (σc = 133.34–213.04 MPa) and Poisson’s ratio (ν = 0.18–0.32). The observed value (M R = 326–597) and mean value of M R = 439.4 are compared with the results of similar previous researches. Moreover, the statistical analysis for all studied rocks was performed and the relationshipbetween M R and other mechanical parameters such as maximum axial strain ( ε a, max ) $\left( {{\varepsilon }_{\text{a,}\,\text{max}}} \right)$ for studied rocks was discussed.

Evaluation of Specimen Size-Effect in Sedimentary Rocks and Grain Size Effect in Concrete Specimens on Uniaxial Compressive Strength

Summary In rock engineering, the effect of scale on the strength and deformation properties of the rock mass is one of the most important issues. Prediction of uniaxial compressive strength in different diameters using the specimen size-effect models is valuable. To specify the application scope of the specimen size-effect models in the rock and concrete specimens, a few significant study have so far been carried out. This paper proposes a model of appropriate size-effect in sedimentary rocks and concrete specimens. Another object of this paper is discussion on the effect of specimen size and grain size on uniaxial compressive strength of rock and concrete specimens using statistical and experimental methods. The results of this study can be used for engineering designs in or on rocks and are more useful for determining of the elastic constants and compressive strength of rock. Introduction Dependence of compressive strength on the specimen size has a fundamental role in the designing of rock structures. In the rock mechanics, many experimental and analytical methods have been used to determine the specimen size-effect on the mechanical behavior of intact rock. In the area of rock mechanics and solid mechanics, the most notable proposed analytical models to predict the specimen size-effect on the uniaxial compressive strength are including the Weibull statistical theory (1951), the Hoek and Brown empirical theory (1980), the specimen size-effect model using fracture energy theory (Bazant, 1983 and 1984), the multi-fractal scaling model (Carpinteri et al., 1995), the fractal fracture size-effect model (Bazant, 1997) and the unified size-effect model for intact rock (Masoumi et al., 2015). To specify the application scope of these models in the rock and concrete specimens, few significant study have so far been carried out. Methodology and Approaches Statistical analysis of this study, were conducted in each size-effect model by means of a non-linear least-squares fitting algorithm and Levenberg-Marquardt method using SPSS software. In the experimental study, three concrete blocks of approximately 500mm×500mm×500mm in size with three different grain sizes (0-12, 0-20 and 0-25) were manufactured. After the curing time, using a laboratory drilling machine, cylindrical specimens were obtained from blocks with diameters of 56, 68, 72 and 94 mm and with a length-to-diameter ratio of 2.0 (L/D=2.0) according to the recommendation of International Society of Rock Mechanics (ISRM, 2007). ACI-211 standard and ASTM C33 standard were utilized for mixture design of samples and required grain sizes respectively. Results and Conclusions In the sedimentary rocks and concrete specimens, respectively, there was a good agreement between outputs of laboratory tests with the specimen size-effect model using fracture energy and the multifractal scaling model. In experimental study, results of uniaxial compressive strength tests for grain sizes 0-20 and 0-25 mm indicated that increase of the specimens' diameter resulted in first increase and then decrease of uniaxial compressive strength. The results of this study confirmed grain size effect on the predictions of specimen size-effect models (i.e. increase of the grain size, leads to reduction of the value of correlation coefficient for different models. These results can be used for engineering designs in rocks and concrete mixtures.

Scale Effects Observed in Compression Testing of Stanstead Granite Including Post-peak Strength and Dilatancy

Scale effects refer to changes in mechanical behaviour associated with the volume of material being loaded or deformed. Scale effects in rocks and rockmasses are particularly complex, as an increased volume of interest changes not only the measured behaviour of intact rock, but also results in an increased sampling of natural fractures, which can often significantly influence rockmass mechanical behaviour. To isolate one component of these effects, laboratory tests performed using different size specimens can be used (scale effects in the absence of jointing). Previous studies on scale effects based on laboratory testing have tended to focus on changes in stiffness and peak strength, particularly under unconfined conditions. In this study, data are examined from specimens tested in uniaxial and triaxial compression considering not only stiffness and peak strength, but also strength evolution and post-peak dilatancy evolution. The crack initiation and crack damage stresses are found to be scale independent, whereas the post-yield rate of cohesion loss appears to change as a function of specimen size. Trends in the dilation angle are shown to be relatively scale independent, which is consistent with prior studies that found laboratory-based dilation angle models could be used to accurately replicate data collected from sparsely fractured in situ rockmasses.

Development of Synthetic Rock Mass Bonded Block Models to Simulate the Behaviour of Intact Veined Rock

Synthetic rock mass (SRM) modelling, based on bonded particle models (BPM), has been successfully used to model jointed and veined rock. BPM models, however, have significant limitations in simulating some key elements of the behaviour of intact rock. In particular, BPMs have difficulties in reproducing the compressive to tensile strength ratio and determining the angle of internal friction characteristic of typical hard rock specimens. Use of bonded block models (BBM), where angular blocks are used in place of spherical particles in BPM, demonstrated improvements in modelling the behaviour of intact rock. However, SRM-style models using BBM have been only used on a limited basis to model foliated and veined rock. In previous applications the BBM based models lacked use of discrete fracture networks which are key in SRM simulations. This paper reports on an original application of bonded block SRM for modelling of intact veined rock and presents the developed methodology for SRM modelling of intact veined rock based on BBM. It has been demonstrated that that BBM models of intact rock are an improvement over modelling of intact rock using BPM. Finally, this paper presents the results of BBM SRM numerical simulations of compressive experiments on intact veined rock under a series of confining pressures.

Calibration and Verification of Two Bonded-Particle Models for Simulation of Intact Rock Behavior

Abstract In this study, bonded-particle models were used to simulate the intact rock behavior of Westerly granite. Two three-dimensional models were tested: the enhanced bonded-particle model (EBPM) and the flat-joint contact model (FJCM). To calibrate both models, a new standard procedure was developed. The results of the simulations of the models were compared with the intact rock behavior determined by laboratory tests, including elastic parameters, peak and threshold envelopes, and postpeak behavior. From this study, it can be concluded that the FJCM better represents the mechanical behavior of Westerly granite rock, especially at the low to intermediate confining pressures. Based on this work, it is recommended to use the FJCM to model the behavior of brittle rock at the low to intermediate confining pressures.

Characterization of clastic rock using a biconcave bond model of DEM

SummaryThis paper presents a biconcave bond model to investigate the effect of the cementation between grains on the mechanical behavior of rock. The proposed model considers the shape of the bonds among particles that have a biconcave cement form, based on observations of microscopic rock images. The general equations of the proposed model are based on Dvorkin theory. The accuracy and efficiency of the bond model is improved in three ways. After the biconcave bond model is implemented in the discrete element method software Particle Flow Code in 2 Dimensions, a series of numerical uniaxial compression tests were performed to investigate the relationships between the micro‐ to macro‐parameters. The simulations revealed that the biconcave bond model reflects the effect of micro‐parameters, such as the elastic modulus and Poisson's ratio of the cement, on the macroscopic deformation of cemented granular material. Variations in the bond geometry caused extremely diverse macro‐mechanical behaviors. Experimental results concerning rock demonstrate that the biconcave bond model accurately captures the mechanical behavior of intact rock and supports an innovative method for investigating the relationships between the micro‐ and macro‐parameters of cemented granular material. Copyright © 2016 John Wiley & Sons, Ltd.

Triaxial compression experiments on intact veined andesite

A comprehensive experimental program was instigated to test intact veined andesite from the El Teniente Mine (Chile) under triaxial compression with confining pressure ranging from 2 to 60MPa. The experimental program established that the veins acted as weak mechanical components in the specimens, promoting rock fracture under stress. The experimental results indicated that the stress thresholds identifying the onset of dilatancy and the transition from the stable to unstable fracturing were higher in intact veined rock than in intact rock. The observed behaviour illustrated a significant departure from intact rock where the onset of Acoustic Emissions (AE) correlates with the onset of specimen dilatancy. The experimental results from intact veined rock indicated that the onset of AE correlated with the crack damage stress. The departure from the behaviour of intact rock is attributed to the presence of veins.

Bayesian prediction of elastic modulus of intact rocks using their uniaxial compressive strength

The uniaxial compressive strength (UCS) and the Young's modulus (E) are two important aspects of intact rock behavior. Although they can be measured in the laboratory, testing requirements increase the difficulty and cost of such tests. For that reason, faster and less costly methods have been proposed to indirectly estimate UCS, and many models have been proposed to estimate E of intact rock based on UCS. We present a novel approach, based on the Bayesian framework for model assessment, to estimate the Young's moduli of intact rocks based on their uniaxial compressive strengths. We work with Deere's proportionality rule (E=MRUCS); and we develop an extensive database, available as “Supplementary material”, of testing data compiled from the literature. Our approach provides uncertainty estimates of parameters and predictions, and can differentiate among the sources of error. We develop ‘rock-specific’ models for common rock types. In some cases, our MR results are significantly different from Deere's traditional values. We also illustrate that such ‘initial’ models can be ‘updated’ to incorporate new project-specific information as it becomes available, reducing model uncertainties and improving their predictive capabilities.

Anisotropic Deformation of a Circular Tunnel Excavated in a Rock Mass Containing Sets of Ubiquitous Joints: Theory Analysis and Numerical Modeling

Determining anisotropic deformation surrounding underground excavations for tunnels is an intuitional task that involves many difficulties due to the inherent anisotropies in the strength and deformability of natural rocks. This study investigates joint-induced anisotropic deformation surrounding a tunnel via a numerical simulation that accounts for the mechanical behavior of intact rock, the orientations of joint sets, and the mechanical behavior of joint planes; this numerical simulation can model the complete stress–strain relationship with anisotropic rock mass characteristics. Simulation results demonstrate that the well-known excavation-induced stress variation–decrease in the radial component and increase in the tangential component–decrease shear strength and increase shear stress for the joint plane tangential to the tunnel wall, resulting in joint sliding failure and considerable shear deformation. This joint sliding failure and significant shear deformation account for the joint-induced anisotropic deformation surrounding a tunnel. When a rock mass has two joint sets with unfavorable joint orientations, the area with joint sliding failure can deteriorate mutually, resulting in large anisotropic deformation. Additionally, for a rock mass containing three joint sets with well-distributed orientations, joint sliding in various joint sets and associated stress variations can counter balance each other, resulting in less anisotropic deformation than those of rock masses containing one or two joint sets.

Application of equivalent continuum and discontinuum stress analyses in three-dimensions to investigate stability of a rock tunnel in a dam site in China

Deformation and stability around a tunnel in a limestone rock mass is investigated using both (a) an equivalent continuum/discontinuum model and (b) a fully discontinuum model through three-dimensional stress analyses. In model (a), the Representative Elementary Volume (REV) mechanical properties estimated in a previous paper are used to represent the combined behavior of intact rock and 4 of the five fracture sets that had significantly smaller sizes compared to the fifth fracture set (bedding planes). To this system the bedding plane fractures were added according to its statistical geometric properties. In model (b), all five fracture sets were generated according to the obtained fracture geometry statistical models. Using model (a), effect of several factors, such as REV property values, bedding plane modeling method, the average horizontal stress to the vertical stress and tunnel depth, on the geotechnical behavior around the tunnel was studied in detail. A comparison is made between the stress analyses results obtained through the aforementioned two models.