True Triaxial Conditions Research Articles

Influences of True Triaxial Loading-Unloading Stress Paths on Mechanical Properties and Wave Velocity of Coal Samples subject to Risk of Rock Burst

To study fracture evolution and peak stress in burst risk coal samples (BRCSs) under true triaxial loading and unloading conditions, experimental and numerical research was applied to BRCSs under true triaxial stress paths entailing “x-direction displacement fixed, y-direction loading, z-direction unloading.” Both the experimental and the numerical results demonstrated that the peak stress borne by the BRCSs was not only affected by the initial stress but also had a negative exponential relationship with the ratio of the unloading rate and the loading rate (RURLR); therefore, peak stress equations of BRCSs under true triaxial loading and unloading conditions were established. The triaxial stress-time curves obtained by experiments and simulations exhibited an “elasticity-yield-destruction” phase, and the characteristics of the yield phase were determined by the RURLR. A typical BRCS was selected for velocity tomographic imaging to analyze the fracture evolution characteristics under true triaxial loading and unloading. The results showed that when the BRCS was subjected to a triaxial state of stress, the high- and low-velocity regions existed alternately due to the presence of the crack; during the elastic phase, the crack closed during loading in the previous phase was reopened upon unloading, so that the velocity of the sample decreased and a wide range of low-velocity regions could be formed; when entering the yield phase, the original crack continued to expand into a hole-through crack, leading to wider extreme values and ranges of these low- and high-velocity regions; at the breaking phase, multiple microcracks were generated around the hole-through cracks, decreasing the overall velocity, and showing point distributions characteristics of high- and low-velocity regions. Overall, many low-velocity regions with similar normal directions to the unloading direction were formed; these correlated well with macrofractures (postfailure).

A Statistical Damage Constitutive Model of Anisotropic Rock: Development and Validation

The damage constitutive model is of great significance to research the stress-strain relationship and damage evolution of rock under loading in engineering. In order to investigate the effect of anisotropic characteristic on the stress-strain relationship and damage evolution, a statistical damage constitutive model of anisotropic rock under true triaxial condition was developed. In this study, the plane which existed perpendicular to the coordinate axis was extracted from representative volume element (RVE) of rock. The extracted plane was assumed to be composed of abundant mesoscopic elements whose failure strength satisfied the Weibull distribution. According to the number of failure elements on the plane in each direction under loading, the anisotropic damage variable was established based on the proposed concept of areal damage. A statistical damage constitutive model of anisotropic rock was developed by using strain equivalent hypothesis and generalized Hooke constitutive model. Subsequently, the parameters in the anisotropic damage constitutive model were determined by the method of total differential. Thus, the damage evolution of anisotropic rock under various stress conditions can be conveniently evaluated by the anisotropic damage model. The model was validated based on the tests of rocks under the stress conditions of conventional triaxial and true triaxial, respectively. Moreover, for the purpose of studying the influence of parameters on the model, sensitivity analyses of mechanical parameters and model parameters were carried out. The results of statistical damage constitutive clearly demonstrate the stress-strain and damage evolution of anisotropic rock under various stress conditions.

Bifurcation analysis of shear band in sand under true triaxial conditions with hypoplasticity

AbstractPredicting the onset of shear band is of significance in understanding the failure of geomaterials. The prediction accuracy is dictated by the constitutive model used for the description of the pre‐bifurcation behaviour. In this study, we first modify a recently proposed hypoplastic constitutive model by incorporating a general strength criterion and a stiffness function. We proceed to consider the onset of shear band in sand under true triaxial conditions. We demonstrate that our analyses capture the pre‐bifurcation stress–strain relationship at different values of intermediate principal stress and predict fairly well the onset of shear band. The acoustic tensor criterion generally adopted in elastoplastic approaches is inadequate for hypoplastic approaches. No special non‐coaxial treatment is required for the present approach to yield a reasonable variation trend of bifurcation strain with intermediate principal stress ratio .

Influence of radial stress on strainbursts under true triaxial conditions: Insights from a distinct element modelling

The radial (minimum) stress of the near-boundary rockmass in deep excavations plays a key role in inducing rock failures such as spalling and strainbursts. In this study, a strainburst is treated as a structural failure of the near-boundary rockmass. The influence of the radial stress acting asymmetrically on one boundary surface of the burst volume on strainbursts is numerically investigated using a 3D bonded block distinct element method (DEM). The 3D DEM model for simulating the overall process of strainbursts is introduced and its effectiveness is verified by comparing with the analogous true triaxial experiments. Then based on the simulation results, the influence of radial stress on strainbursts is studied from the perspectives of deformation and strength characteristics, fracturing process, crack development, failure mode and energy balance. In addition, discussions of the mechanisms of the influence of radial stress on strainbursts are presented from the perspectives of fracture mechanics and a graphical explanation. Results show that, as the radial stress increases, the strength of the strainburst sample exhibits a quadratic law that increases first and then decreases, the number of shear cracks increases remarkably, the degree of accumulated rock damage precedes burst is getting higher and higher, the failure mode of strainbursts transforms gradually from a tensile-type to a shear-type, and the kinetic energy is getting higher and higher. The fundamental influence of radial stress on strainbursts is concluded as its suppression effect on the tensile failure mechanism of brittle rocks.

Strength and Deformation Characteristics of Reconstituted Sand under Different Stress Paths in True Triaxial Tests

To improve the geotechnical stress–strain analysis, the stress–strain behavior of geomaterial under general three-dimensional stress conditions prevailing in the field need to be captured. The true triaxial apparatus is an enhanced version of the conventional triaxial apparatus, which allows to simulate stresses by applying loadings independently in 3 orthogonal directions. This study evaluated the strength and deformation behavior of Bangka sand under true triaxial test conditions. The test specimens were prepared by means of the multi-sieve sand pluviation method. Various true triaxial test stress paths were applied under axial compression, lateral extension, axial extension, and lateral compression with the objective of understanding and developing the empirical correlation of coarse-grained soil strength parameters in axial compression stress paths related to other stress paths. The test results showed that an increase in the value of b, the parameter used to quantify the relative magnitude of the intermediate principal stress to the other principal stresses, resulted in an increase of the internal friction angle and a decrease of the peak stress ratio. In addition it was observed that the Lade-Duncan failure criterion fitted the results of this study better than other failure criteria, namely the extended von Mises, Mohr-Coulomb, and Matsuoka-Nakai failure criteria.

A stress-path-independent damage variable for concrete under multiaxial stress conditions

The damage rule of concrete is theoretically analyzed and discussed from the aspects of the stiffness degradation and the cohesive strength degradation. Further, the multiaxial damage rules of concrete are studied by 25 groups of tests under true triaxial and conventional triaxial compressive cyclic conditions. The analysis of the test results shows that the relationship between the damage variable and the axial plastic strain depends on the loading path. This dependence of the damage variable on the stress paths can be normalized by the equivalent plastic shear strain. A partial differential equation of the damage variable, driven by the equivalent plastic shear strain, is constructed based on two characteristic boundary conditions of the damage gradient. Then, a stress-path-independent isotropic damage variable is proposed by the integral of the partial differential equation. The proposed damage variable can reasonably capture the multiaxial damage behavior of the concrete. The stress path independence of the proposed damage variable is analyzed and further verified by the test results under multiaxial stress conditions.

Fractal characteristics of acoustic emission of gas-bearing coal subjected to true triaxial loading

As coal mining proceeds deeper, coal and rock are subjected to growing stresses and gas pressures. Consequently, coal and rock gas dynamic disasters pose more and more considerable threats and hazards which should be warned in advance. Coal and rock in the field is actually in the true triaxial stress state. Study on deformation characteristics and precursory information of coal and rock under this state is meaningful for disaster warning. In this paper, experiments on the deformation, failure and acoustic emission (AE) characteristics of gas-bearing coal under true triaxial loading conditions were carried out. Besides, the variation law and fractal characteristics of AE under different gas pressures and confining stresses were analyzed. Furthermore, the effects of gas pressure and confining stress on the deformation, failure and fractal characteristics of coal were discussed. The results show that the process of AE variation under true triaxial loading conditions can be divided into two stages, namely the slow growth stage and the accelerated growth stage. A higher gas pressure corresponds to a shorter duration of slow growth stage, while a higher confining stress corresponds to a longer duration of slow growth stage. AE time series has fractal characteristics, and the correlation dimension can characterize the damage degree of a loaded coal sample. The dynamic changes, i.e., fluctuation-increase-decrease, in correlation dimension can accurately reflect the damage evolution process of a coal sample. In addition, the gradual reduction of correlation dimension can be used as the precursor information of coal sample instability and damage. The research results boast instructive significance for preventing the occurrence of coal and rock gas dynamic disasters and for reducing casualties and property loss in coal mines.

Non-linear anisotropic damage rheology model: Theory and experimental verification

We extend the isotropic non-linear damage rheology model with a scalar damage parameter to a more complex formulation that accounts for anisotropic damage growth under true triaxial loading. The model takes account of both the anisotropy of elastic properties (associated with textural rock structure) and the stress- and damage-induced anisotropy (associated with loading). The scalar, isotropic model is modified by assuming orthotropic symmetry and introducing a second-order damage tensor, the principal values of which describe damage in three orthogonal directions associated with the orientations of the principal loading axes. Different damage components, accumulated under true triaxial loading conditions, allows us to reproduce both stress-strain curves and damage- and stress-induced seismic wave velocity anisotropy. The suggested model generalization includes a non-classical energy term similar to the isotropic non-linear scalar damage model, which allows accounting for the abrupt change in the effective elastic moduli upon stress reversal.For calibration and verification of the model parameters, we use experimental stress-strain curves from deformation of dry sandstone under both conventional and true triaxial stress conditions. Cubic samples were deformed in three orthogonal directions with independently controlled stress paths. To characterize crack damage, changes in ultrasonic P-wave velocities in the three principal directions were measured, together with the bulk acoustic emission output. The parameters of the developed model were constrained using the conventional triaxial test data, and provided good fits to the stress-strain curves and P-wave velocity variations in the three orthogonal directions. Numerical simulation of the true triaxial test data demonstrates that the anisotropic damage rheology model adequately describes both non-linear stress-strain behavior and P-wave velocity variations in the tested Darley Dale sandstone.

Experimental Study on the Mechanical Behaviour of Natural Loess Based on Suction-Controlled True Triaxial Tests

Loess is mostly distributed in an unsaturated state in nature, and the complexity of the engineering properties of unsaturated soil is mainly due to the existence of matric suction. Therefore, matric suction must be considered in investigating the mechanical properties of unsaturated loess. However, soils are most often subjected to three principal stresses with different magnitudes in practical engineering. For the sake of examining and discussing the mechanical behaviour of unsaturated natural loess under a complex stress path, a suction-controlled true triaxial apparatus with a rigid-flexible boundary is used to test unsaturated natural loess under a complicated stress path. Four trials of isotropic consolidation tests are conducted on natural loess under suction-controlled conditions via the true triaxial apparatus. The consolidation yield characteristics of the natural loess under different matric suctions are investigated. Forty-eight trials of consolidated drained true triaxial tests under suction-controlled conditions are conducted on unsaturated natural loess to examine and discuss the influence of the matric suction and intermediate principal stress parameter (b-value). The consolidated drained trials are performed under a constant net mean stress and a constant matric suction with different intermediate principal stress parameters (b-values). Stress-strain curves and failure envelopes of the natural loess are also presented. The results indicate that the stress-strain-strength response of unsaturated natural loess depends on the matric suction and intermediate principal stress parameter under true triaxial conditions.

Effects of prior cyclic loading damage on failure characteristics of sandstone under true-triaxial unloading conditions

To investigate the effects of prior cyclic loading damage in rocks on subsequent unloading failure characteristics under true-triaxial conditions, a series of complicated unloading tests incorporating the damage-controlled cyclic loading path and stress σ3 unloading path was conducted using a true-triaxial test system. The experimental results reveal that the prior cyclic loading damage has an impact on the strength and deformation characteristics, energy conversion and failure mode. As the number of prior cyclic loads increases, the unloading strength and Young's modulus increase firstly and then decrease, while the peak unloading strain, as well as the ratio (η) of crack damage stress to peak unloading stress, exhibits a descending trend. The energy storage capacity of rock samples is dramatically reduced as cycle number increases to 10 and enlarged slightly with a further increase in cycle number. Both shear fracture and tensile fracture appear in each rock sample under this unloading condition, as the prior cyclic loading number increases, the dominant failure mode of rock samples changes from tensile failure to mixed tensile-shear failure, then to shear failure, while the failure angle ranging from 65° to 80° deceases firstly and then turns to rise.

DEM Investigation on the Evolution of Fabric under True Triaxial Conditions in Granular Materials

Abstract The evolution of fabric under loading plays an important role in the micromechanical analysis of granular materials. This paper addressed this issue from the perspective of the discrete el...

Effects of high differential stress and mineral properties on deformation and failure mechanism of hard rocks

To study the deformation and failure mechanism of hard rocks, true triaxial compression tests were conducted on four types of hard rocks to obtain the complete stress–strain curves and failure modes. Under true triaxial compression conditions, the shapes of the complete stress–strain curves can be divided into three types: elastic–brittle (EB), elastic–plastic–brittle (EPB), and elastic–plastic–ductile (EPD) types. According to the different post-peak deformation behaviours, the stress–strain curves of EPB type can be subdivided into three sub-categories: post-peak instantaneous brittle (EPB-I), post-peak multi-stage brittle (EPB-M), and post-peak delayed brittle (EPB-D). The stress–strain curves change from EPD to EPB-D, EPB-M, EPB-I, and finally EB with increasing differential stress (σ2– σ3). The deformation characteristics are dependent on intermediate principal stress σ2, minimum principal stress σ3, mineral compositions, and mineral textures of rock samples. An increase in σ3leads to an increased ductility, while an increase in σ2leads to an increased brittleness. Moreover, rocks with regular mineral textures and low mineral hardness are more prone to ductility. When the deformation curve is transformed from EPD to EPB and then to EB, the tensile crack gradually predominates, and the macroscopic failure angle gradually becomes steeper.

Experimental and theoretical analysis of hydraulic fracturing and gas fracturing of rock under true triaxial compressions

A test system was developed for true triaxial hydraulic fracturing (HF) and gas fracturing (GF) combined with acoustic emission (AE) monitoring and 3D computerized tomography (CT) scanning reconstruction to carry out a series of HF and GF tests under different true triaxial loading conditions. The critical breakdown pressure characteristics, the AE activities, and the fracture propagation and spatial morphologies were obtained during the fracturing process. The test results showed that the GF breakdown pressure was approximately 29.0–31.3% less than the HF breakdown pressure. Moreover, for the GF specimen, the gas pore pressure induced a large number of new microfractures before critical fracture. However, both HF and GF under true axial compression can only produce simple main longitudinal fractures (LFs, along the borehole) and transverse fractures (TFs, across the borehole) that are strictly dependent on the initial true triaxial stress field. Based on the experimental observations, a hypothesis for the initiation of the HF and GF under true triaxial compression was proposed by using the maximum tangential stress on the borehole wall and the maximum axial stress along the borehole. Accordingly, analytical solutions of the critical breakdown pressure for the HF (impermeable) and GF (permeable) specimens were derived. The theoretical predictions agree well with the observations from the 3D numerical simulations and tests. Lastly, a novel pulsed GF method (dynamic loading fracturing) was proposed to overcome the dependence of the in-situ crustal stress field associated with traditional HF and GF methods (static loading fracturing). Laboratory test results showed that the dynamic pulsed GF at moderate pressure can generate a complex and random fracture network independent of the in-situ stress field in rock.

Undrained true triaxial response of initially anisotropic particulate assemblies using CFM-DEM

Abstract While simulation of the drained true triaxial response of particulate assemblies using discrete element method (DEM) has caught the attention of researchers in the recent years, simulation of the undrained condition under generalized stress condition has not yet been well addressed in the literature. This treatment suggests an applicable coupled fluid-discrete element scheme to simulate the undrained response of initially anisotropic particulate assemblies under true triaxial condition. Coupled fluid-discrete element simulations highlight the combined impact of Lode angle and anisotropic microstructure of the assemblies on the effective stress paths, mobilization of shear strength, and accumulation of pore-water pressure under undrained condition. For loose assemblies suffering from flow instability, it is shown that stress ratio, mobilized friction angle, and pore-water pressure at the onset of instability depend on Lode angle.

Elastoplastic Model and Three-Dimensional Method for Unsaturated Soils

This paper proposed a new elastoplastic constitutive model to predict the deformation and strength behaviour of unsaturated soils. Applying the modified Cambridge model as a generalization, the degree of saturation is introduced into the elastoplastic model of unsaturated soil. Under the condition of ensuring that the model parameters are unchanged, the model is transformed into three dimensions based on the SMP criterion transformation stress method. Enhanced modified van Genuchten model under true triaxial conditions is also proposed in this paper to describe hydromechanical behaviours of unsaturated soils. The proposed constitutive model can capture the observed mechanical and hydraulic behaviours. Then, the model is validated via equal p and equal b value true triaxial tests, and the results show that a reasonable agreement can be obtained.

Failure properties of cubic granite, marble, and sandstone specimens under true triaxial stress

Cubic specimens of granite, marble, and sandstone, with side lengths of 50 mm, were prepared in the laboratory. True triaxial compression tests were conducted on each rock type with minor principal stress (σ3) magnitudes of 10, 20, 30, 50, and 100 MPa and the intermediate principal stress (σ2) varying from σ2 = σ3 to σ2 = σ1 (where σ1 represents the major principal stress). The experimental results demonstrated that the failure strength, fracture dip angle, non-linear behavior and failure mode of these rocks under true triaxial conditions were affected by both σ2 and σ3, as well as by the rock lithology. When σ3 was kept constant and σ2 increased, failure strength showed an initial increase followed by a decrease, whereas the fracture dip angle increased monotonically. The non-linear behavior before the peak strength point of granite became more apparent by the increase of σ3, whereas σ2 had an opposite effect on the non-linear behavior of granite under high σ3 (e.g. 100 MPa). The non-linear behavior before the peak strength point was always found in marble and sandstone for all of the stress state conditions. Analyses of fracture dip angle and failure mode showed that when σ3 = 10, 20, and 30 MPa and σ2/σ3 ≥ 5, 7.5, and 10, respectively, the failure mode of granite changed from shear to slabbing, whereas marble and sandstone always fractured in the shear direction. This study confirms that rocks may experience slabbing failure under true triaxial stress, and slabbing failure mode is likely to be induced in high-strength and brittle rocks under low σ3 with the stress ratio of σ2/σ3 exceeding a particular threshold value.

Influence of Loading and Unloading Stress Paths on the Deformation and Failure Features of Jinping Marble Under True Triaxial Compression

To study the difference in the failures of laboratories #7 and #8 of the China Jinping Underground Laboratory Phase II (CJPL-II), different loading and unloading stress path tests were carried out under a true triaxial compression condition based on the measured in situ stress of CJPL-II. The strength, deformation and failure mechanisms of Jinping marble under different stress paths were thoroughly investigated. The results showed that under the same stress state as that at sample failure, the bearing capacity and deformation of the unloading stress path were greater than those of the loading stress path. The bearing capacity and deformation in the σ2 and σ3 directions of stress path II and stress path III were similar, and the others decreased from stress path IV to stress path V under unloading conditions. The failure mode results reflect the violence of the unloading failure. The failure features and mechanisms of different stress paths were analysed though the acoustic emission (AE) ring, cumulative energy and strain energy trend. This research may provide a reference for the excavation and support of deep underground works.

Failure Criteria for Isotropic Rocks Using a Smooth Approximation of Modified Mohr–Coulomb Failure Function

It is reported that strength of rocks is a function of three-dimensional (3D) stress state as observed from the large sets of experimental results under the true-triaxial condition. Triaxial compression test data in general is readily available for rocks, but in practice true-triaxial facilities are seldom used. This creates a requirement for 3D failure criterion, which can be used to predict the true-triaxial strength using simple triaxial compression test data. We have proposed three criteria by altering the deviatoric function of modified Mohr–Coulomb criterion (Singh et al. in Int J Rock Mech Min Sci 48(4):546–555, 2011). The proposed criteria represent the behaviour of rock from lower to very high confining pressures. The criteria have unique yield surfaces. The yield surface changes its shape with the change in the mean stress. It is observed beyond certain value of the mean stress; the yield surfaces converge to von-Mises yield surface which means the shape of the yield surface is independent of pressure beyond the certain value of mean normal stress. The criteria require three parameters that can be easily calculated from the triaxial compression test results. The proposed criteria also satisfy the Drucker stability postulate, hence could be adopted as a plastic potential function. For the assessment of the criteria, true-triaxial data from twelve rocks are considered. Results of the criteria are compared with the modified Mohr–Coulomb criteria both 2D and 3D proposed by Singh et al. (Int J Rock Mech Min Sci 48(4):546–555, 2011). Performance of the new failure criteria for the considered rocks are observed to be better than the modified Mohr–Coulomb criteria (2D and 3D).

Rockburst characteristics of several hard brittle rocks: A true triaxial experimental study

Abstract Rockburst is a typical rock failure which frequently threatens both human life and construction equipment during highly stressed underground excavation. Rock lithology is a control factor of rockburst. In this paper, rockburst tests were conducted on rectangular prismatic specimens of six types of intact hard brittle rocks, i.e. granodiorite, granite, marble, basalt, sandstone and limestone, under one-free-face true triaxial loading conditions. With the use of high-speed cameras, an acoustic emission (AE) system and a scanning electron microscope (SEM), rockburst of different rocks was investigated. The results show that the strainbursts of granodiorite, granite and marble were accompanied by tensile splitting near the free face, and consequently were relatively strong with a large amount of fragment ejection and kinetic energy release. For basalt, sandstone and limestone, failure was primarily dominated by shear rupture. The strainbursts of basalt and sandstone were relatively small with minor fragment ejection and kinetic energy release; while no burst failure occurred on limestone due to its relatively low peak strength. Rock strength, fracturing and fragmentation characteristics, and failure modes of different rocks can significantly affect rockburst proneness and magnitude. The AE evolution coupled with SEM analysis reveals that the differences in the inherent microstructures and fracture evolution under loading are the primary factors accounting for different rockbursts in various rock types.

Strength and deformability of a low-porosity sandstone under true triaxial compression conditions

True triaxial tests (σ1≥σ2≥σ3) were conducted on the Zigong sandstone with a relatively low porosity of ~6.5% with the aim of assessing the influence of the intermediate principal stress σ2 on the strength and deformability. Three series of true triaxial tests (σ3= 0, 20, and 60 MPa) were performed. Within each series, σ2 was planned to be varied from σ2=σ3 to σ2=σ1 from test to test. For each test, σ1 was raised monotonically to failure while σ2 and σ3 were kept constant and the post-peak behavior has been captured. It is found that the strain in the σ3-direction is always larger than that in the σ2-direction under true triaxial stresses, which is attributed to the stress-induced tensile microcracks aligned with the σ1-σ2 plane. For a constant σ3, the dilatant strain in the σ2-direction is progressively suppressed and becomes compactive as σ2 raises from σ2=σ3 to σ2=σ1. Based on a modified Hoek-Brown failure criterion with three stress invariants, the best fitting brittle strength envelope reveals that the σ2 effect on rock strength, i.e., the ascending-then-descending trend for a given σ3, is the combined effect of mean stress and Lode angle. In the series of biaxial tests (σ3=0 MPa), macro tensile fractures that parallel to the σ1-σ2 plane develop regardless of σ2, displaying a failure plane angle of approximately 90°. As σ3 is raised, failure plane angle generally decreases. When σ3 = 20 MPa, the failure plane angle generally increases with σ2 while there is no evident dependence on σ2 when σ3 = 60 MPa. Comparisons with the other two sandstones with higher porosity reveal that porosity exerts critical control on the brittle strength and that the σ2 effect on deformability is also the result of two competing effects induced by mean stress and Lode angle. It is also found that the residual strength data facilitate the prediction of brittle-ductile transition pressure when σ2=σ3 in spite of relatively low σ3 level, which matches well with the empirical relation proposed by Mogi.1