Three-dimensional Stress State Research Articles

Experimental study on the deformation and failure characteristics of cement stone under true triaxial stress state

The cement stone is widely utilized to fill the gap between the formation and the casing in wells. A clear understanding of the deformation and failure mode of cement stone under true triaxial stress state is necessary to ensure the safety and stability of wells. To analyze the three-dimensional deformation and failure characteristics of cement stone, the loading paths with constant Lode angle were employed in conducting true triaxial tests on cement stone. The stress-strain curve and failure mode of cement stone are first analyzed. Then, the three-dimensional deformation characteristics are discussed in meridian and deviatoric planes. Both peak strength and deformability increase with minimum principal stress, but show a tendency to increase and then decrease with intermediate principal stress coefficient. With the increase of minimum principal stress and intermediate principal stress coefficient, the failure mode of cement stone transforms from brittle to ductile behavior. Under elastic stage, the strain path in the meridian plane is a straight line, and is under constant Lode angle within the deviatoric plane. Due to the existence of plastic strain, the strain path in the meridian plane displays a downward convex shape. The strain path in the deviatoric plane deviates from the reference of constant Lode angle for stress, directly reflecting the Lode angle dependence of deformation. Both deformation and failure characteristics of cement stone are dominated by the three-dimensional stress state. Besides, deformation of cement stone is closely related to the failure characteristics of cement stone.

On anisotropic local bifurcation based on hypoplastic model

The incipience of shear band in homogeneous granular materials is well captured by the bifurcation analysis. Most bifurcation analyses are based on isotropic plastic constitutive models. In this paper, a hypoplastic constitutive model is presented by considering a fabric tensor for inherent anisotropy. Based on this model, we carry out bifurcation analysis for the plane strain case, and then extend the analysis to consider general three-dimensional stress state. The theoretical results are compared with experiments on sand conducted using a plane strain device and a true triaxial device. It's indicated the salient features of stress-strain behaviour and shear band formation are well captured by our analyses.

Mesoscale mechanism of damage in fracture process zone of CFRP laminates simulated with triaxial stress state-dependent constitutive equation of matrix resin

The three-dimensional failure process experimentally observed by synchrotron radiation X-ray computed tomography (SR X-CT) regarding the influence of the interfiber distance is discussed on the basis of the results of numerical experiments. Triaxial stress states in the fracture process zone of carbon fiber reinforced polymers were analyzed on the mesoscale under mode I and mixed-mode (mode I + II) loading. Yield and damage models depending on stress triaxiality were used to accurately simulate three-dimensional stress states in the damage zone around the crack tip. Owing to the heterogeneity of composites, deviatoric stress is prominent in the thin resin region where the interfiber distance is small under mode I loading. On the other hand, matrix resin is triaxially stressed in the middle point between carbon fibers in the thick resin region where the interfiber distance is large. Under mode II loading, the shapes of fiber/matrix debonding depended on the interfiber distance. Areas with stress concentration were found owing to a large debonding area in the thick resin region resulting in a matrix cracking-prone stress state. These findings explain the damage and failure processes well observed by SR X-CT and provide a fundamental understanding of the damage mechanism at a mesoscale.

Small Punch Testing of a Ti6Al4V Titanium Alloy and Simulations under Different Stress Triaxialities.

The mechanical properties of local materials subjected to various stress triaxialities were investigated via self-designed small punch tests and corresponding simulations, which were tailored to the geometry and notch forms of the samples. The finite element model was developed on the basis of the actual test method. After verifying the accuracy of the simulation, the stress, strain, and void volume fraction distributions of the Ti6Al4V titanium alloy under different stress states were compared and analyzed. The results indicate that the mechanical properties of the local material significantly differ during downward pressing depending on the geometric shape. A three-dimensional tensile stress state was observed in the center area, where the void volume fraction was greater than the fracture void volume fraction. The fracture morphology of the samples further confirmed the presence of different stress states. Specifically, the fracture morphology of the globular head samples (with or without U-shaped notches) predominantly featured dimples. Modifying the specimen's geometry effectively increased stress triaxiality, facilitating the determination of the material's constitutive relationship under varying stress states.

Three-dimensional fractional plastic models for saturated sand using Caputo derivative and R-L derivative: A comparative study

The strength and dilatancy of sand are mainly influenced by the void ratio, confining pressure and stress path. In engineering, the stress-strain relationship of sand in three-dimensional stress state is complicated, where the state-dependent properties of sand are difficult to be described by traditional constitutive models. Thus, fractional plastic models based on different fractional derivatives were developed to capture such state-dependent behavior of sand. This paper attempts to make a comparative study of the fractional models based on two typical fractional derivatives, i.e., the R-L derivative and Caputo derivative. The results show that the different types of fractional derivatives are mainly reflected in the different order of differentiation and integration, which will have a significant impact on the calculation of plastic flow direction, stress-dilatancy ratio and fractional order parameter βin the constitutive model. By determining the constitutive parameters of the two models, the constitutive behaviors predicted by different models were compared with the corresponding test results of saturated sands under different initial mean pressures and different stress paths. The models can reasonably simulate the test results of saturated sands, where the dilatancy characteristic can be captured. Compared with R-L model, Caputo model can predict more volumetric strain in the dilatancy process, and has better prediction effect. Overall, the predicted effects of the two models are close, with a maximum difference of about 7 %.

Mechanical Properties of Rock Salt from the Kłodawa Salt Dome-A Statistical Analysis of Geomechanical Data.

Rock salt is a potential medium for underground storage of energy resources and radioactive substances due to its physical and mechanical properties, distinguishing it from other rock media. Designing storage facilities that ensure stability, tightness, and safety requires understanding the geomechanical properties of rock salt. Despite numerous research efforts on the behaviour of rock salt mass, many cases still show unfavourable phenomena occurring within it. Therefore, the formulation of strength criteria in a three-dimensional stress state and the prediction of deformation processes significantly impact the functionality of storage in salt caverns. This article presents rock salt's mechanical properties from the Kłodawa salt dome and a statistical analysis of the determined geomechanical data. The analysis is divided into individual mining fields (Fields 1-6). The analysis of numerical parameter values obtained in uniaxial compression tests for rock salt from mining Fields 1-6 indicates an average variation in their strength and deformation properties. Upon comparing the results of Young's modulus (E) with uniaxial compressive strength (UCS), its value was observed with a decrease in uniaxial compressive strength (E = 4.19968·UCS2, R-square = -0.61). The tensile strength of rock salt from mining Fields 1-6 also exhibits moderate variability. An increasing trend in tensile strength was observed with increased bulk density (σt = 0.0027697·ρ - 4.5892, r = 0.60). However, the results of triaxial tests indicated that within the entire range of normal stresses, the process of increasing maximum shear stresses occurs linearly ((σ1 - σ3)/2 = ((σ1 + σ3)/2)·0.610676 + 2.28335, r = 0.92). A linear relationship was also obtained for failure stresses as a function of radial stresses (σ1 = σ3·2.51861 + 32.9488, r = 0.73). Based on the results, the most homogeneous rock salt was from Field 2 and Field 6, while the most variable rock salt was from Field 3.

Seepage characteristics and mechanism of double damage basalt fiber reinforced concrete under three-dimensional variable stress states

Concrete experiences a three-dimensional variable stress state during its service life. To explore the permeability evolution and mechanism under such conditions, a permeability test was conducted on double damage basalt fiber concrete subjected to loading and unloading of twice confining pressure. Pore structure and microstructure of specimens were analyzed before and after permeability test. The findings reveal that the reduction in permeability after primary cycle of confining pressure loading and unloading is significantly higher than that after secondary cycle, and residual deformation is also more pronounced after primary cycle. Both high temperature and salt freeze-thaw cycles induce initial damage to specimens, consequently altering internal pore structure and subsequently impacting initial permeability. Notably, initial permeability decreases in the case of 10th salt freeze-thaw cycles, while it increases under other conditions. The greater the initial extent of damage to the specimen, the higher the permeability damage coefficient and the permeability damage rate. As the confining pressure decreases, the attenuated permeability increases, with the permeability decay rate reaching a significant 88.53 %. Plastic deformation of pores during loading and unloading process cannot be fully reversed, leading to the development of macropores and mesopores into smaller pore sizes, resulting in a remarkable 87.17 % increase in the proportion of micropores. Microscopic observations reveal smaller pores within the matrix, shorter crack lengths, and narrower crack widths in the specimen. The application of confining pressure reduces permeability channels within specimens, ultimately causing a decline in permeability.

Assessing particle crushing mechanism and optimizing design for recycled aggregates in road bases via a novel particle crushing DEM method

This study introduced an innovative and effective algorithm that aims to provide a comprehensive simulation of particle crushing behavior in complex granular materials. Based on the Griffith's strength theory, the algorithm was formulated and implemented using the discrete element method (DEM). This algorithm accurately simulates the crushing behavior of real particles under arbitrary three-dimensional stress states. The robustness of the proposed method and the distribution pattern of the resulting child particles were verified through a series of single- and multi-particle crush tests. The findings demonstrate that the proposed approach exhibits exceptional generalizability, effectively describes the particle crushing behavior of granular materials, and features high efficiency and cost-effectiveness. The particle crushing simulations were conducted accordingly via DEM on a combination of natural gravel (NG), recycled mortar (RM), and recycled brick (RB) aggregates for use in road bases. The results revealed the particle crushing mechanisms in single-, binary-, and ternary-type recycled aggregate mixtures. Additionally, this study revealed the influence of recycled aggregate types on particle crushing within these different mixtures. The ternary design charts and tables were developed to determine the maximum contents of recycled aggregates in accordance with the particle crushing value requirements for different highway classes and aggregate base types. This study not only holds significant theoretical importance in developing efficient particle-crushing algorithms, but also offers valuable insights and scientific references for improving the resourceful utilization of recycled aggregates derived from construction and demolition wastes in road bases.

Derivation, characterization, and application of complete orthonormal sequences for representing general three-dimensional states of residual stress

Residual stresses are self-equilibrated stresses on unloaded bodies. Owing to their complex origins, it is useful to develop functions that can be linearly combined to represent any sufficiently regular residual stress field. In this work, we develop orthonormal sequences that span the set of all square-integrable residual stress fields on a given three-dimensional region. These sequences are obtained by extremizing the most general quadratic, positive-definite functional of the stress gradient on the set of all sufficiently regular residual stress fields subject to a prescribed normalization condition; each such functional yields a sequence. For the special case where the sixth-order coefficient tensor in the functional is homogeneous and isotropic and the fourth-order coefficient tensor in the normalization condition is proportional to the identity tensor, we obtain a three-parameter subfamily of sequences. Upon a suitable parameter normalization, we find that the viable parameter space corresponds to a semi-infinite strip. For a further specialized spherically symmetric case, we obtain analytical expressions for the sequences and the associated Lagrange multipliers. Remarkably, these sequences change little across the entire parameter strip. To illustrate the applicability of our theoretical findings, we employ three such spherically symmetric sequences to accurately approximate two standard residual stress fields. Our work opens avenues for future exploration into the implications of different sequences, achieved by altering both the spatial distribution and the material symmetry class of the coefficient tensors, toward specific objectives.

Effect of lateral stress on frictional properties of a fracture in sandstone

The injection of large volumes of natural gas into geological formations, as is required for underground gas storage, leads to alterations in the effective stress exerted on adjacent faults. This increases the potential for their reactivation and subsequent earthquake triggering. Most measurements of the frictional properties of rock fractures have been conducted under normal and shear stresses. However, faults in gas storage facilities exist within a true three-dimensional (3D) stress state. A double-direct shear experiment on rock fractures under both lateral and normal stresses was conducted using a true triaxial loading system. It was observed that the friction coefficient increases with increasing lateral stress, but decreases with increasing normal stress. The impact of lateral and normal stresses on the response is primarily mediated through their influence on the initial friction coefficient. This allows for an empirical modification of the rate-state friction model that considers the influence of lateral and normal stresses. The impact of lateral and normal stresses on observed friction coefficients is related to the propensity for the production of wear products on the fracture surfaces. Lateral stresses enhance the shear strength of rock (e.g. Mogi criterion). This reduces asperity breakage and the generation of wear products, and consequently augments the friction coefficient of the surface. Conversely, increased normal stresses inhibit dilatancy on the fracture surface, increasing the breakage of asperities and the concomitant production of wear products that promote rolling deformation. This ultimately reduces the friction coefficient.

Strength characteristics and energy evolution of cement stone under true-triaxial loading conditions

Oil well cement is a commonly used cementing material in oil and gas extraction engineering. Due to the change of stress conditions, it is prone to microcracks or micro annular gaps, leading safety concerns. To study the strength characteristics and energy evolution of oil well cement stone under three-dimensional stress states, a series of true-triaxial compression tests were carried out. Based on the experimental results, the mechanical properties and energy evolution mechanisms during the true-triaxial compression process of cement stone under different stress states were explored. The research results indicate that there is an intermediate principal stress effect on the true-triaxial compressive strength of cement stone specimens. When the minimum principal stress remains constant, the strength of cement stone first increases and then decreases with the increase of intermediate principal stress. When the minimum principal stress is 5 MPa, the specimen exhibits brittle failure, with ε1 at peak stress approximately 0.015. As the minimum principal stress increases to 20 MPa, the specimen gradually transits to plastic failure, with ε1 at failure exceeding 0.04. The type of failure is determined by the energy ratio at the time of failure; when there is more elastic energy, it results in brittle failure, otherwise it leads to ductile failure. Due to the high porosity of cement stone samples, most of the input energy is converted into dissipated energy. At minimum principal stresses of 5 MPa, 10 MPa and 20 MPa, the ratio of peak dissipated energy to total input energy fluctuates around 0.55, 0.73 and 0.85, respectively. There is a strong linear relationship between the peak elastic energy, peak dissipated energy, and total input energy, with fitting correlation coefficients of 0.847 and 0.996, indicating that the cement stone sample also follows the linear energy storage law. A strength criterion for cement stone was established based on the modified Lade criterion, which is more suitable for describing the strength of high porosity materials compared to traditional strength criteria. Finally, based on the interaction mechanism between energy accumulation and energy dissipation, a nonlinear model of energy evolution in cement stone was established. The results of the theoretical model are in good agreement with the experimental data.

Dynamic stress analysis of rock joints under railway loading

The proper estimation of stresses generated by the passage of a train is fundamentally important to the serviceability and longevity of railways, and yet very limited knowledge is available where the track substructure is built on a jointed rock mass. The present study introduces an analytical solution for estimating the ground stresses arising from moving wheel loads, causing a change in the three-dimensional stress state in the track formation, in relation to the stress variation with depth and along the longitudinal track section – that is, the direction of train passage. Based on 21 case histories, an array of field measurements and numerical simulations covering a wide range of freight tonnage, train speeds and different formation conditions were considered to validate the proposed analytical solution. The proposed methodology (analytical solution) was then applied to a jointed rock subgrade to determine the normal and shear stresses acting along a specific discontinuity plane. The main analytical outcome demonstrates that the orthogonal vertical and shear stresses present different and phase-shifted history plots for homogeneous ground conditions with principal stresses rotation. However, conversely for a jointed subgrade, the normal and shear stresses along the discontinuity have the same history plot pattern and are in phase. As a practical guide, the results from this study would help to define which cyclic loads should be applied in laboratory tests to simulate realistic traffic patterns of trains travelling over a jointed rock subgrade.

A discrete approach for modelling the permeability evolution of granite under triaxial and true-triaxial stress conditions

In deep underground engineering, modelling the seepage characteristics of rock masses under complex stress conditions is crucial for the safe construction and stable operation of a project. The permeability of the rock mass is not only controlled by its internal pore structure but is also closely related to the deformation and fracturing of the rock. Although discrete methods offer advantages in describing the formation and development of fractures, these methods still face challenges due to the difficulties in establishing microscopic seepage models. This paper introduces a new hydro-mechanical coupled numerical model. In this model, a simple method is proposed to couple the Rigid-Body-Spring Method (RBSM) for rock deformation and fracturing simulation and the Equivalent Matrix-Fracture Network (EMFN) for seepage simulation. Subsequently, the model is employed to simulate the permeability of granite under three-dimensional stress conditions. The simulation results show that under hydrostatic stress conditions, the model accurately captures the decrease in permeability due to pore compression and collapse. Additionally, under deviatoric stress conditions, it reveals the stage-wise increase in permeability caused by granite fracturing. Finally, the model is applied to study the permeability evolution behaviour of rocks under true triaxial stress conditions. The results unveiled the significant impact of the intermediate principal stress on permeability evolution and revealing the microscopic mechanisms underpinning these effects. This paper paves a way for enhancing the application of discrete methods in forecasting the permeability evolution behaviour of intricate rock masses.

Brittle rock mass failure in deep tunnels: The role of infilled structural plane with varying dip angles

Filled rock discontinuities are commonly encountered in underground engineering excavations, and their mechanical behavior has a significant impact on the stability of surrounding rocks. However, their performance under three-dimensional stress conditions has rarely been explored in the past. In this study, we summarized the typical failure characteristics of filled structural planes in deep-buried tunnels and conducted laboratory true triaxial tests on granite specimens to investigate the effect of dip angle and infill thickness on the failure characteristics of high-stress brittle surrounding rocks. The study monitored the characteristics of vertical stress-displacement, acoustic emission, acceleration, and failure process of granite specimens during the loading process and revealed the failure mechanism of brittle rock masses under the influence of infill thickness and structural plane dip angle. The results showed that the dip angle of structural planes has a significant influence on the failure mode of rock masses in deep tunnels. There exists a critical range of dip angles, within which the rock mass undergoes shear slip failure along the pre-existing structural plane, manifested by rock spalling near the structural plane. Beyond this critical range, the rock mass experiences strain-type brittle failure, characterized by violent rock ejection. Furthermore, the filling of structural planes can change the failure mode of rock masses and lead to more severe damage when the friction coefficient of the structural plane falls below a specific threshold. Additionally, it was revealed that a perpendicular ejection force exists on the free surface of the rock mass under loading, which is approximately vertical to the normal direction and is the primary factor responsible for the formation of vertical parallel cracks within the rock mass. The findings of this work are of paramount importance for comprehending the failure characteristics of deep-buried tunnels containing infilling joints.

Adsorption–desorption characteristics of coal-bearing shale gas under three-dimensional stress state studied by low field nuclear magnetic resonance spectrum experiments

The micro-scale gas adsorption–desorption characteristics determine the macro-scale gas transport and production behavior. To reveal the three-dimensional stress state-induced gas adsorption–desorption characteristics in coal-bearing shale reservoirs from a micro-scale perspective, the coal-bearing shale samples from the Dongbaowei Coal Mine in the Shuangyashan Basin were chosen as the research subject. Isothermal adsorption–desorption experiments under three-dimensional stress state were conducted using the low field nuclear magnetic resonance (L-NMR) T2 spectrum method to simulate the in-situ coal-bearing shale gas adsorption–desorption process. The average effective stress was used as the equivalent stress indicator for coal-bearing shale, and the integral of nuclear magnetic resonance T2 spectrum amplitude was employed as the gas characterization indicator for coal-bearing shale. A quantitative analysis was performed to examine the relationship between gas adsorption in coal-bearing shale and the average effective stress. And a quantitative analysis was performed to examine the relationship between the macroscopic and microscopic gas quantities of coal-bearing shale. Experimental findings: (1) The adsorption–desorption process of coal-bearing shale gas follows the L-F function model and the D-A-d function model respectively with respect to the amount of gas and the average effective stress. (2) There is a logarithmic relationship between the macroscopic and microscopic gas quantities of coal-bearing shale during the adsorption–desorption process. This quantitatively characterizes the differences in the curves, which may be related to the elastic–plastic deformation, damage and fracture of the micropores in coal-bearing shale, as well as the hysteresis of gas desorption and the stress field of the gas occurrence state.

A Multiscale Method to Develop Three-Dimensional Anisotropic Constitutive Model for Soils

A multiscale method is presented to develop a constitutive model for anisotropic soils in a three-dimensional (3D) stress state. A fabric tensor and its evolution, which quantify the particle arrangement at the microscale, are adopted to describe the effects of the inherent and induced anisotropy on the mechanical behaviors at the macroscale. Using two steps of stress mapping, the deformation and failure of anisotropic soil under the 3D stress state are equivalent to those of isotropic soil under the triaxial compression stress state. A series of discrete element method (DEM) simulations are conducted to preliminarily verify this equivalence. Based on the above method, the obtained anisotropic yield surface is continuous and smooth. Then, a fabric evolution law is established according to the DEM simulation results. Compared with the rotational hardening law, the fabric evolution law can also make the yield surface rotate during the loading process, and it can grasp the microscopic mechanism of soil deformation. As an example, an anisotropic modified Cam-clay model is developed, and its performance validates the ability of the proposed method to account for the effect of soil anisotropy.

Finite Element for the Analysis of Massive Reinforced Concrete Structures with Cracking

The solid finite element has been developed for the calculation of massive reinforced concrete structures with cracks. When constructing a finite element in the compression-compression-compression mode, the Willam Warnke failure criterion was used. The tensile behavior of concrete was assumed to be linear before the crack initiation. Modern building codes require non-linear calculations of concrete and reinforced concrete structures, taking into account the real properties of concrete and reinforcement. In this regard, a technique has been developed and a solid finite element has been built, adapted to the PRINS software, which makes it possible to perform calculations of massive reinforced concrete structures, taking into account their actual work. Development of a method for calculating reinforced concrete structures under conditions of a three-dimensional stress state, taking into account the brittle fracture of compressed concrete and cracking in tensile concrete. Based on this technique, the implementation of a solid finite element in the PRINS software. To verify the developed finite element, a series of test calculations of a beam under three-point bending conditions was carried out. Comparison of the calculation results with the data of experiments by the authors confirmed the high accuracy and reliability of the results obtained. The developed solid finite element included in the PRINS software can be effectively used by engineers of design and scientific organizations to solve a wide class of engineering problems related to the calculations of massive reinforced concrete structures.

Establishment and engineering application of viscoelastic-plastic constitutive laws for creep modeling in interbedded rock masses

In order to study the creep behavior of the surrounding rock of the interbedded rock mass tunnel considering the time-dependent deformation, this paper proposes a viscoelastic-plastic seven-element model considering the stress threshold, and derives and establishes its creep equation under three-dimensional stress state. At the same time, the UMAT (User-defined Material) subroutine of the model is developed based on the ABAQUS software. The rationality of the seven-element model and the effectiveness of the subprogram are verified by rheological test results. Finally, the UMAT subroutine is applied to the numerical simulation of the creep behavior of soft and hard interbedded rock tunnels with different rock inclinations (α). The results show that the different rock inclination angles have different effects on the horizontal displacement of the ground above the tunnel, settlement deformation, and the convergence of the tunnel section. With the increase of the rock inclination (0 ≤ α ≤ 90°), the horizontal displacement of the surface on both sides is antisymmetric. When α is 0°, 45° and 90°, the horizontal displacement on both sides is equivalent. Surface subsidence decreases and then increases slowly. When α is 0° and 45°, the surface subsidence is the largest (12.4 mm) and the smallest (11.1 mm), respectively. The convergence values of the tunnel section change according to different parts of the tunnel. The convergence values of the arch top and arch bottom decrease continuously, and their maximum convergence values are 23.4 mm and 17.3 mm, respectively. The change trend of the arch waist and arch shoulder convergence values is the opposite. When α is 0°, the convergence value of the arch waist is maximum (3.5 mm). When α is 15°, the convergence value of the arch shoulder is the maximum (2.0 mm).

Failure characterization of fully grouted rock bolts under triaxial testing

Confining stresses serve as a pivotal determinant in shaping the behavior of grouted rock bolts. Nonetheless, prior investigations have oversimplified the three-dimensional stress state, primarily assuming hydrostatic stress conditions. Under these conditions, it is assumed that the intermediate principal stress (σ2) equals the minimum principal stress (σ3). This assumption overlooks the potential variations in magnitudes of in situ stress conditions along all three directions near an underground opening where a rock bolt is installed. In this study, a series of push tests was meticulously conducted under triaxial conditions. These tests involved applying non-uniform confining stresses (σ2 ≠ σ3) to cubic specimens, aiming to unveil the previously overlooked influence of intermediate principal stresses on the strength properties of rock bolts. The results show that as the confining stresses increase from zero to higher levels, the pre-failure behavior changes from linear to nonlinear forms, resulting in an increase in initial stiffness from 2.08 kN/mm to 32.51 kN/mm. The load-displacement curves further illuminate distinct post-failure behavior at elevated levels of confining stresses, characterized by enhanced stiffness. Notably, the peak load capacity ranged from 27.9 kN to 46.5 kN as confining stresses advanced from σ2 = σ3 = 0 to σ2 = 20 MPa and σ3 = 10 MPa. Additionally, the outcomes highlight an influence of confining stress on the lateral deformation of samples. Lower levels of confinement prompt overall dilation in lateral deformation, while higher confinements maintain a state of shrinkage. Furthermore, diverse failure modes have been identified, intricately tied to the arrangement of confining stresses. Lower confinements tend to induce a splitting mode of failure, whereas higher loads bring about a shift towards a pure interfacial shear-off and shear-crushed failure mechanism.

True-triaxial simulation of sandstone with full range of σ2 based on the Rigid-Body-Spring method

Accurately simulating the mechanical properties of rock under true-triaxial stress conditions (σ1 > σ2 > σ3) is crucial for understanding deep underground rock masses. Although discrete approaches have advantages in describing rock fracturing behavior, further development seems necessary for quantitatively simulating the intermediate principal stress σ2 effects on rock strength. In this paper, we study the failure mechanisms of microscopic contacts of a discrete approach, the modified Rigid-Body-Spring Method (mRBSM), in response to σ2. Numerical results indicate that the model calibrated by axisymmetric-triaxial tests underestimates the strength of Yunnan sandstone when the stress state approaches σ2 = σ1. To address this discrepancy, we propose a new microscopic contact failure criterion that takes into consideration not only the normal and shear stresses on the contact but also the average Cauchy stress tensor around the contact. Results show that the mRBSM with the new failure criterion is able to reproduce the true-triaxial strength of Yunnan sandstone more accurately than the original model, especially under high σ2 and σ3 conditions. In addition, the corresponding stress–strain curves and failure modes under the influence of σ2 still show reasonable trends under true-triaxial stress conditions. This study indicates that when simulating rock failure under three-dimensional stress conditions using the rigid-body-spring system, the contact failure criterion might be influenced by the local stress state.