True Triaxial Stress Conditions 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.

Mechanical properties and constitutive model of artificial frozen sandy soils under true triaxial stress state conditions

Triaxial compression tests were conducted on frozen sandy soils under a constant minimum principal stress (σ3 = 1.6 MPa) and various intermediate principal stresses (σ2 = 1.6, 3.4, 5.2, 7.0, 8.8, 9.8 MPa). The purpose of the research was to investigate the influence of intermediate principal stress on mechanical properties of frozen soil, and to establish a constitutive model to predict the stress-strain relationship of frozen soil under complex stress state. The test results obtained demonstrated that the crack damage stress and failure stress initially increase and then decrease with an increase in the intermediate principal stress. However, the crack initiation stress exhibits an initial increase up to a specific value, after which it stabilizes. From the perspective of crack propagation, the influence mechanism of intermediate principal stress on the strength was discussed. With the variation of stress state, the difference between intermediate principal strain and minimum principal strain gradually increases. The deformation difference was revealed using the stress superposition principle and Poisson's effect. Finally, the constitutive model based on the Weibull distribution and Drucker-Prager strength criterion can accurately represent the stress-strain relationships of frozen sandy soils under true triaxial stress states.

Experimental and numerical analysis of injection-induced permeability changes in pre-existing fractures

This paper presents a combined laboratory and numerical investigation on the injection-induced permeability changes in pre-existing fractures. The analyses conducted were primarily based on the results of an innovative laboratory experiment designed to replicate the key mechanisms that occur during hydraulic stimulation of naturally fractured rocks and/or faulted zones. The experiment involved pressure-controlled fluid injection into a laboratory-scale pre-existing fracture within a granite block, which was subjected to true triaxial stress conditions. Rough and smooth fractures are investigated, and the results are discussed. Based on the experimental results, two contributing mechanisms were considered to describe the pressure-driven permeability changes in pre-existing fractures: (1) elastic opening/closure leading to a reversible permeability change, and (2) fracture sliding in shear mode, causing dilation and hence an irreversible permeability increase. With these assumptions, an aperture-dependent permeability function was adopted to couple the hydraulic flow with the mechanical deformations along the fracture. Subsequently, a 3D coupled hydro-mechanical model was developed to replicate fluid-injection tests conducted at various conditions, including different stress conditions and fracture surface roughness. The employed modeling framework effectively captured the experimental observations. Our results indicate that the maximum permeability increases twofold.

Effect of true triaxial principal stress unloading rate on strain energy density of sandstone

Deep rock are often in a true triaxial stress state. Studying the impacts of varying unloading speeds on their strain energy (SE) density is highly significant for predicting rock stability. Through true triaxial unloading principal stress experiments and true triaxial stress equilibrium unloading experiments on sandstone, this paper proposes a method to compute the SE density in a true triaxial compressive unloading principal stress test. This method aims to analyze the SE variation in rocks under the action of true triaxial unloading principal stresses. Acoustic emission is used to verify the correctness of the SE density calculation method in this paper. This study found that: (1) Unloading in one principal stress direction causes the SE density to rise in the other principal stress directions. This rise in SE, depending on its reversibility, can be categorized into elastic and dissipated SE. (2)When unloading principal stresses, the released elastic SE density in the unloading direction is influence by the stress path and rate. (3) The higher the unloading speed will leads to greater increases in the input SE density, elastic SE density, and dissipative SE density in the other principal stress directions. (4) The dissipated SE generated under true triaxial compression by unloading the principal stress is positively correlated with the damage to the rock; with an increase in unloading rate, there is a corresponding increase in the formation of cracks after unloading. (5) Utilizing the stress balance unloading test, we propose a calculation method for SE density in true triaxial unloading principal stress tests.

Influence of weak interlayer thickness on mechanical response and failure behavior of rock under true triaxial stress condition

In this study, we meticulously investigate the influence of the thickness of weak interlayer on mechanical response and failure behavior of rock mass near the free surface of tunnel, with the aid of a true triaxial test system. We simulated the true triaxial stress condition of rock mass containing weak interlayer proximate to the excavation boundary, where one face remains free, while others are subjected to loading stress and increasing tangential stress. The experimental results reveal a distinct change in the fracture morphology near the free surface of rock mass as the thickness of weak interlayer increases, concomitant with a gradual decrease in the fractal dimension. With the increase of the thickness of weak interlayer, the failure characteristics of rock mass change from a “binary” to a “unitary” feature, i.e. mixed tension-shear failure near the free surface and shear failure far away from the free surface changes to mixed tension-shear failure that only occurs near the free surface. Moreover, an inverse relationship is observed between the bearing capacity of the rock mass and the thickness of weak interlayer. Conversely, the peak strain in the tangential stress direction increases with the increase of the thickness of weak interlayer, illustrating that the slip shear strain of rock block positioned above the weak interlayer is gradually formed, and governs the strain behavior of rock mass in the tangential stress direction with the increases of the thickness of weak interlayer. By employing the finite-discrete element method (FDEM), we replicated the failure process of surrounding rocks containing weak interlayers near the free surface of tunnel, demonstrating considerable congruity with our physical test results. In light of the failure characteristics of surrounding rocks containing weak interlayers, we advocated a localized area priority reinforcement support strategy, prioritizing regions with weak interlayers. Numerical simulations verified the effectiveness of this approach in controlling fracture proliferation in surrounding rocks and inhibiting the splitting failure of surrounding rocks containing weak interlayers near the free surface of tunnel.

A three-dimensional elastoplastic constitutive model incorporating Lode angle dependence

A comprehensive three-dimensional elastoplastic constitutive model is presented to characterize the stress-strain behavior of cement stone under the true triaxial stress state. This constitutive model incorporates a three-dimensional yield function and a three-dimensional potential function. The three-dimensional yield function is designed to accurately represent the true triaxial stress state during hardening. The three-dimensional potential function is devised to depict the plastic flow direction under true triaxial stress state. The yield and potential functions include parameters that control the shape of the deviatoric and meridian planes, and these parameters vary with the plastic internal variable. Consequently, the yield function can accurately describe the stress state, and the potential function can precisely capture the variations in plastic flow direction. Additionally, a detailed procedure for determining the parameters of the yield function and potential function is proposed based on the full deformation process. The constitutive model is presented in the form of analytical solution. The comparison of experimental data with the constitutive model confirms its accuracy and validity. A sensitivity analysis of the deviatoric and meridian parameters in the potential function is performed, shedding light on their impact on the model behavior. Furthermore, the significance of incorporating Lode angle dependence into the potential function is discussed, emphasizing its essential role in accurately capturing strain in the direction of the intermediate principal stress.

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.

A Test System for Microwave-Assisted Dual-Mode Mechanical Cutting of Hard Rock Under True Triaxial Compression

This paper introduces a test system for microwave-assisted dual-mode mechanical cutting of hard rock under true triaxial compression. The test system was developed by Northeastern University, China, to simulate the cutting and breaking of hard rock by a tunnel boring machine (TBM). The test system is mainly composed of a dual-mode mechanical cutting subsystem, a true triaxial loading subsystem and a high-power microwave presplitting subsystem. The system performs dual-mode cutting under true triaxial stress, applies a single sensor to monitor the three-dimensional force of the cutter head, and integrates the reduction in the vibration and resistance to torsion during the cutting process. Mechanical cutting tests of basalt under different amounts of microwave irradiation and true triaxial stress conditions were conducted in Chifeng, Inner Mongolia, China. The results showed that microwave radiation presplitting effectively improved the efficiency of mechanical rock breaking. However, after 180 s of microwave irradiation, true triaxial high stress inhibited the mechanical breaking of basalt in terms of the overall excavation depth. During the tests, each system performed stably. The test results verified the reliability of the test system.

True triaxial energy evolution characteristics and failure mechanism of deep rock subjected to mining-induced stress

In deep rock engineering, complex stress conditions are encountered, which leads to difficulties in engineering disaster prevention and control. To investigate the failure behaviors and mechanisms of deep rock mining, a series of tests was designed for mining-induced failure at different simulated depths using a multifunctional true triaxial geophysical (TTG) apparatus. The results showed that both the simulated depth and mining disturbance affected the deformation characteristics of the sandstone specimens. With increasing depth, the strength gradually increased. The peak strength increased fastest in the single-sided unloading failure test (SUFT) and slowest in the stress loading and unloading failure test (SLUFT). The failure mode also changed significantly. In the displacement loading failure test (DLFT), the failure mode gradually changed from tensile failure to shear failure. In the SLUFTs, the failure mode of the specimens changed from layer cracking to shear failure. In the SUFTs, the failure mode of the specimen transitioned from layer cracking to tensile shear failure and then to shear failure. Scholars have previously proposed an elastic strain energy calculation method for true triaxial stress conditions. An elastic strain energy calculation method applicable to different mining disturbance was proposed under true triaxial stress conditions, and the evolution characteristics of the work done, elastic strain energy, and dissipated energy were analyzed. Additionally, a method to quantitatively characterize the relationship between macroscopic cracks and dissipated energy was proposed, and microscopic fracture analysis was performed using scanning electron microscopy (SEM). Different depths and various types of mining-induced failure were fully considered, and the specimen deformation, failure type, energy evolution (including dissipation), and failure mechanisms were analyzed. The results can provide guidance for deep underground engineering projects.

Failure behaviors and acoustic emission characteristics of flawed granite of different grain sizes: Insights from true triaxial experiments with a free face

In this study, a group of experiments using true triaxial stress conditions with free face loading are performed on granite specimens with non-penetrating double flaws. The crack development and failure characteristics of these specimens are explored by integrating video of the free face and acoustic emission technology, with the combination of the four different intermediate principal stresses and three different grain sizes of the granite chosen as variables. First, surface flaws with a depth of 50 mm are found to have limited influence on the specimen’s failure mode. The intermediate principal stress has a greater effect as it inhibits the development of surface cracks; however, surface cracks develop much more readily in coarse-grained specimens than in other specimens. Second, when the intermediate principal stress exceeds 10 MPa, the rock burst failure phenomenon occurs in the specimen. Third, irrespective of changes in the intermediate principal stress and granite specimen grain size, the specimens primarily fail by tensile-shear failure and shear failure. Extending inward from the free face in the σ3 direction, according to the failure types, the failure types can be classified into tensile failure, shear failure, and tensile-shear failure. Finally, using the stress state synthesis method, the specimen’s stress state and crack distribution mechanism on the σ2 loading plane are analyzed.

Dynamic damage mechanism of coal with high true triaxial stress level subject to water jets

Deep mineral resources are abundant, and water jet technology has been proven to be an efficient means of developing this resource. In-situ stress is one of the prominent features in deep mines. However, the dynamic damage process of rock under the in-situ stress environment subject to water jets has not been revealed. Therefore, this study aims to fill this gap. For this study, coal breaking tests were performed to reveal the macro fracture patterns of coal under different true triaxial stress conditions. The results show that the bedding angle can significantly affect the coal-breaking characteristics, and when the bedding angle is 45° combines the advantages of length and aperture for jet drilling. When there is no geostress, the width of the cracks on the wall of the fracture pit is 3 μm, with a crack width of 7.5 μm at the bottom of the hole, and no through cracks generated under triaxial stress. Subsequently, further theoretical analysis and numerical simulation showed that the in-situ stress has a hysteresis and inhibitory effect on the dynamic damage evolution of jet coal breaking, hereby affecting the final fracture mode during the period. The results of this study will provide basic theoretical support for the jet drilling of rock in deep layered rock.

A macro-mesoscopic constitutive model for porous and cracked rock under true triaxial conditions

The complex mechanical and damage mechanisms of rocks are intricately tied to their diverse mineral compositions and the formation of pores and cracks under external loads. Numerous rock tests reveal a complex interplay between the closure of porous defects and the propagation of induced cracks, presenting challenges in accurately representing their mechanical properties, especially under true triaxial stress conditions. This paper proposes a conceptualization of rock at the mesoscopic level as a two-phase composite, consisting of a bonded medium matrix and frictional medium inclusions. The bonded medium is characterized as a mesoscopic elastic material, encompassing various minerals surrounding porous defects. Its mechanical properties are determined using the mixed multi-inclusion method. Transformation of the bonded medium into the frictional medium occurs through crack extension, with its elastoplastic properties defined by the Drucker–Prager yield criterion, accounting for hardening, softening, and extension. Mori–Tanaka and Eshelby’s equivalent inclusion methods are applied to the bonded and frictional media, respectively. The macroscopic mechanical properties of the rock are derived from these mesoscopic media. Consequently, a True Triaxial Macro-Mesoscopic (TTMM) constitutive model is developed. This model effectively captures the competitive effect and accurately describes the stress-deformation characteristics of granite. Utilizing the TTMM model, the strains resulting from porous defect closure and induced crack extension are differentiated, enabling quantitative determination of the associated damage evolution.

Hydraulic fracturing behavior of shale–sandstone interbedded structure under true triaxial stress conditions: A comprehensive experimental analysis

AbstractReservoirs characterized by shale–sandstone interbedded structures are extensively dispersed throughout China, and understanding the propagation mode of hydraulic fractures is a prerequisite for shale gas exploitation engineering. In this study, hydraulic fracturing tests were conducted using horizontal wells subjected to true triaxial compression conditions to elucidate the mechanism by which the initiated layer lithology and stress state influence the fracture morphology. Furthermore, the propagation mode of the fractures and the consequential effects on fracture network formation were investigated. The findings demonstrate four distinct interaction modes between the shale–sandstone interfaces and hydraulic fractures. The lithology of the initiated layer influences the fracture propagation trajectory, thereby affecting the propagation modes at the shale–sandstone interface and resulting in varying effects on layer penetration. The stress difference exerts a significant controlling influence on the fracturing behavior, enhancing the possibility of interconnecting multiple rock layers characterized by substantial stress differences.

Permeability enhancement by CO2 injection and chelating agent stimulation for creating geothermal reservoirs in granite

Existing research indicates that to create geothermal reservoirs using CO2 injection, additional stimulation methods are necessary. N, N-bis(carboxymethyl)-L-glutamic acid (GLDA) injection has been predicted to increase the permeability of CO2 injection-induced cloud-fracture networks (CFNs) and could serve as an additional stimulation method. Nevertheless, the influence of differential stress, flow geometry, and scale on the characteristics of permeability enhancement by GLDA injection is yet to be clarified. Accordingly, this study experimentally elucidated the permeability enhancement characteristics of injecting a chelating agent in fractured granite under differential stress conditions as an additional method for creating geothermal reservoirs using CO2 injection. GLDA injection experiments were conducted on fractured-granite samples under conventional- and true-triaxial stress states under varying differential stress and pH conditions. Regardless of the differential stress and pH conditions, rock deformation and acoustic emission (AE) were negligible during the chelating agent flow-through experiments on the fractured samples, whereas similar permeability enhancement factors were achieved within the same duration. Thus, stress did not affect the permeability enhancement by chelating agent injections. The permeability enhancement factors were inferred to be high near the injection borehole because of the high viscosity of the solution. Therefore, reservoir stimulation should be conducted using low-concentration chelating agent solutions at constant injection pressures. The study provides insights into the stimulation strategies for creating geothermal reservoirs using CO2 injection.

Laboratory validation of a new hydro-mechanical energy-based brittleness index model for hydraulic fracturing

Brittleness Index (BI) is a critical parameter characterising the deformation regime of geo-materials, covering the range from purely brittle (fractures) to ductile (plastic flow). A variety of BI models have been developed based on rock properties such as mineralogy, elastic parameters, or constitutive law. However, very few of them are based on the hydro-mechanical interactions emerging in underground engineering applications. In this study, we propose a BI model based on the partitioning of the injection energy EI into non-seismic deformation energy Ed associated with hydraulic fracture propagation. To calculate the Ed, we apply a model for temporal fracturing area (Ad) within the penny-shaped fracture; and we also correlate the wellbore pressure and the three-dimensional strain induced by hydraulic fracturing of the different types of rock samples subjected to true triaxial stress conditions (TTSC), either σv = 6.5 MPa, σH = 3 MPa, σh = 1.5 MPa or σv = 15 MPa, σH = 10 MPa, σh = 5 MPa. As a comparison, the BI is also quantified based on the existing models: (i) acoustic measurement from Rickman et al. (2008), and (ii) the Mohr-Coulomb’s criteria from Papanastasiou et al. (2016). The Ed ranges between 32.4% and 90.6% of the total injection energy EI, which is slightly higher than the value reported from field-scale data (15% to 80%), but comparable to laboratory-derived data (18% to 94%) from literature. The results show that the predictions based on our proposed energy-based BI model are qualitatively consistent with Papanastasiou et al.’s, but less so with Rickman et al.’s. Our BI model is shown to be stress-dependent and capable of capturing the brittle-to-ductile behaviour of geomaterials subjected to hydraulic fracturing. This study demonstrates that our BI model opens a new way for quantifying the brittleness index regarding to realistic fracture propagation scenarios in field.

A multifunctional shear apparatus for rocks subjected to true triaxial stress and high temperature in real-time

Deep engineering disasters, such as rockbursts and collapses, are more related to the shear slip of rock joints. A novel multifunctional device was developed to study the shear failure mechanism in rocks. Using this device, the complete shear–deformation process and long-term shear creep tests could be performed on rocks under constant normal stiffness (CNS) or constant normal loading (CNL) conditions in real-time at high temperature and true-triaxial stress. During the research and development process, five key technologies were successfully broken through: (1) the ability to perform true-triaxial compression–shear loading tests on rock samples with high stiffness; (2) a shear box with ultra-low friction throughout the entire stress space of the rock sample during loading; (3) a control system capable of maintaining high stress for a long time and responding rapidly to the brittle fracture of a rock sample as well; (4) a refined ability to measure the volumetric deformation of rock samples subjected to true triaxial shearing; and (5) a heating system capable of maintaining uniform heating of the rock sample over a long time. By developing these technologies, loading under high true triaxial stress conditions was realized. The apparatus has a maximum normal stiffness of 1000 GPa/m and a maximum operating temperature of 300 °C. The differences in the surface temperature of the sample are constant to within ±5 °C. Five types of true triaxial shear tests were conducted on homogeneous sandstone to verify that the apparatus has good performance and reliability. The results show that temperature, lateral stress, normal stress and time influence the shear deformation, failure mode and strength of the sandstone. The novel apparatus can be reliably used to conduct true-triaxial shear tests on rocks subjected to high temperatures and stress.

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.

Frictional and poromechanical properties of the Delaware Mountain Group: Insights into induced seismicity in the Delaware Basin

The Delaware Basin in West Texas and Southeast New Mexico has experienced a proliferation in seismic activity since 2016. The seismic activity is primarily due to subsurface injection of wastewater into shallow and deep reservoirs. However, the precise mechanisms connecting fluid injection to seismic activity are not well understood. To shed light on these processes, we measured rate-state friction and poromechanical properties of rocks sampled from the Delaware Mountain Group (DMG) at pressures and stresses representative of in-situ conditions. Experiments were conducted inside a pressure vessel and loaded at a true-triaxial stress state. The samples exhibit velocity-strengthening behavior and transition to velocity-neutral behavior with increasing slip. We also measure frictional healing and demonstrate that the healing rates are consistent with those measured from quartz-feldspathic-rich rocks. Experiments were conducted under a constant pore-pressure boundary condition where transient changes in pore-volume were compensated by modulating the fluid volume within the fault. Our data show that a step increase in sliding velocity leads to dilatancy and causes an influx of fluid into the fault. In contrast, a step decrease in sliding velocity causes the fault zone to compact and reduces fluid flow into the fault. Data show that changes in flow rate scale systematically with fault slip velocity. Broadly speaking, the frictional and poromechanical data indicate that shallow faults within the DMG should favor aseismic creep as opposed to unstable slip. Our data are consistent with elastic dislocation models of fault slip and InSAR data, indicating that faulting in the DMG is predominantly aseismic. The lack of velocity weakening behavior observed in our samples indicates that heterogenous frictional properties are needed to explain the co-existence of both aseismic and seismic slip in the DMG.

A novel meso-damage constitutive model of rock under true triaxial stress with three-dimensional cracking strength, threshold and closure effect

Deep underground engineering is in a true three-dimensional stress state, and the adjustment of the three-dimensional stress state caused by engineering excavation will induce the fracture or even instability of the surrounding rock. However, three-dimensional mechanical model research suitable for the stability analysis of deep surrounding rock is very scarce. Therefore, a series of tests under different true triaxial stresses on two rocks (rhyodacite and marble) were conducted, and the characteristic strength (crack stable propagation initiation stress, crack unstable propagation initiation stress and peak strength) and deformation characteristics were further analyzed. After that, using the Lemaitre strain equivalence hypothesis and rock statistical damage theory, a new statistical damage constitutive model at true triaxial stress states was proposed, which introduced the three-dimensional strength criterion Modified Wiebols Cook to characterize the three-dimensional strength of the rock microelement. Therefore, the intermediate principal stress can be reasonably considered. The damage threshold, initial compaction effect and residual strength of the rock microelement at different true triaxial stress conditions were also considered. Then the relationships between the proposed model parameters and σ2 and σ3 were analyzed. Furthermore, sensitivity analysis of the influence of parameters m and F0 in proposed model on the shape of rock stress–strain curve and peak strength was also investigated. The comparison between the results predicted by proposed model and the experimental data shows that the new model established in this study can well simulate the prepeak and postpeak deformation characteristics of rock and the intermediate principal stress effect under true triaxial stress conditions.

Mechanical parameter evolutions and deterioration constitutive model for ductile–brittle failure of surrounding rock in high-stress underground engineering

The deep surrounding rock is usually in the true triaxial stress state, and previous constitutive models based on the understanding of uniaxial and conventional triaxial test results have difficulty characterizing the degradation and fracture process of rock ductile–brittle failure under true triaxial stress state. Therefore, this study conducted a series of true triaxial tests to obtain the understanding of the ductile–brittle behaviour of rock, and then combined the test results and the Mogi–Coulomb strength criterion, and proposed calculation methods for the elastic modulus E, cohesion c and internal friction angle φ and the evolution functions of E, c and φ of rock under true triaxial stresses. With the decreasing of the minimum principal stress σ3 or increasing of the intermediate principal stress σ2, the marble post-peak stress drop rate gradually increases, the ductility gradually weakens, and the brittleness significantly strengthens. The calculation method and evolution function of rock E, c and φ under true triaxial stress were proposed. E decreased at first and then tended to remain stable with the increasing of equivalent plastic strain increment dεp. c and φ slowly increased at first and then rapidly decreased. With a method of parameter degradation rate to realize post-peak stress drop rate to reflect the ductile–brittle characteristics, a new three-dimensional ductile–brittle deterioration mechanical model (3DBDM) was established. The proposed model can accurately characterize the influence of σ2 and σ3 on mechanical parameters, the ductile–brittle behaviour of rock under true triaxial stresses, and the asymmetric failure characteristics of surrounding rock after excavation of deep underground engineering. The proposed model can be reduced to elastic–perfectly plastic, elastic–brittle, cohesion weakening friction strengthening (CWFS), Mohr–Coulomb, and Drucker–Prager models.