Intermediate Principal Stress Research Articles

Influence of intermediate principal stress and rolling resistance on the shearing response of sand: a micromechanical investigation

Influence of intermediate principal stress and rolling resistance on the shearing response of sand: a micromechanical investigation

Study of slope stability analysis method based on equivalent Mohr‐Coulomb strength parameters of three‐dimensional stress state

AbstractMost rock slope stability analysis methods are based on the Hoke–Brown criterion under a two‐dimensional state of stress, which somewhat ignores the effect of intermediate principal stress. In this paper, by introducing the improved three‐dimensional H‐B criterion into the Meridian plane, the tangent line of a point on the H‐B strength envelope is regarded as its instantaneous equivalent M‐C parameter. Based on this, a formula for solving the equivalent M‐C strength parameters under a three‐dimensional stress state is established to describe the shear strength parameters of rock mass, considering different stress states. Taking three kinds of rocks as examples, the influence of the intermediate principal stress on their strength parameters is analyzed. On this basis, the realization scheme of the nonlinear strength reduction method is established, the stability of the slope is studied, and an example verifies the feasibility of this method. This method fully considers the nonlinear characteristics of rock slope strength parameters under a three‐dimensional stress state and provides a solid basis for slope stability analysis.

True triaxial unloading test on the mechanical behaviors of sandstone: Effects of the intermediate principal stress and structural plane

A series of true triaxial unloading tests are conducted on sandstone specimens with a single structural plane to investigate their mechanical behaviors and failure characteristics under different in situ stress states. The experimental results indicate that the dip angle of structural plane (θ) and the intermediate principal stress (σ2) have an important influence on the peak strength, cracking mode, and rockburst severity. The peak strength exhibits a first increase and then decrease as a function of σ2 for a constant θ. However, when σ2 is constant, the maximum peak strength is obtained at θ of 90°, and the minimum peak strength is obtained at θ of 30° or 45°. For the case of an inclined structural plane, the crack type at the tips of structural plane transforms from a mix of wing and anti-wing cracks to wing cracks with an increase in σ2, while the crack type around the tips of structural plane is always anti-wing cracks for the vertical structural plane, accompanied by a series of tensile cracks besides. The specimens with structural plane do not undergo slabbing failure regardless of θ, and always exhibit composite tensile-shear failure whatever the σ2 value is. With an increase in σ2 and θ, the intensity of the rockburst is consistent with the tendency of the peak strength. By analyzing the relationship between the cohesion (c), internal friction angle (φ), and θ in sandstone specimens, we incorporate θ into the true triaxial unloading strength criterion, and propose a modified linear Mogi-Coulomb criterion. Moreover, the crack propagation mechanism at the tips of structural plane, and closure degree of the structural plane under true triaxial unloading conditions are also discussed and summarized. This study provides theoretical guidance for stability assessment of surrounding rocks containing geological structures in deep complex stress environments.

Influence of Intermediate Principal Stress on Mechanical and Failure Properties of Anisotropic Sandstone

Influence of Intermediate Principal Stress on Mechanical and Failure Properties of Anisotropic Sandstone

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.

Effect of Mineral Composition and Particle Size on the Failure Characteristics and Mechanisms of Marble in the China Jinping Underground Laboratory.

In deep underground engineering, the deformation, failure characteristics, and mechanism of surrounding rock under the influence of grain sizes and mineral compositions are not clear. Based on CJPL-II variously colored marbles, the differences in grain size and mineral composition of the marble were analyzed by thin-section analysis and XRD tests, and the effect of intermediate principal stress on the mechanical properties of marble was investigated. Both SEM and microfracture analysis were coupled to reveal the failure mechanisms. The results highlight that the crack initiation strength, damage strength, peak strength, and elasticity modulus of Jinping marble exhibit an increasing trend with an increase in intermediate principal stress, while the peak strain initially increases and subsequently decreases. Moreover, this study established negative correlations between marble strength, brittleness characteristics, and fracture angle with grain size, whereas positive correlations were identified with the content of quartz, sodium feldspar, and the magnitude of the intermediate principal stress. The microcrack density in marble was found to increase with larger grain sizes and decrease with elevated quartz and sodium feldspar content, as well as with increasing intermediate principal stress. Notably, as the intermediate principal stress intensifies and grain size diminishes, the transgranular tensile failure of marble becomes more conspicuous. These research findings contribute to the effective implementation of disaster prevention and control strategies.

Performance of multi-ribbed composite wall incorporating reactive powder concrete-filled steel tubular columns under axial compression

In this study, axial compression researches of an innovative composite shear wall, named multi-ribbed composite wall incorporating reactive powder concrete-filled steel tubular columns, were conducted using theoretical analyses as well as experimental and numerical investigations. This precast hybrid system embedded reactive powder concrete-filled steel tubular columns as boundary elements of multi-ribbed composite wall. A novel approach, namely the unified strength theory, was adopted in consideration of various materials diversity. The outcomes of unified strength theory were utilized to predict the ultimate compressive capacity of multi-ribbed composite wall equipped with reactive powder concrete-filled steel tubular columns. The proposed theoretical formulas were validated against the experimental results reported in this paper. Despite the fact that the calculated formula with b= 0 was obtained to predict the closest capacity value of the test specimen infilling ordinary concrete. The calculations with different values of b clearly indicated that the intermediate principal stress effect should be rationally considered. Experimental observations suggested that the frame column significantly contributed to improving the compressive performance throughout the entire process and maintained the wall integrity. Meanwhile, finite element models were developed using the ABAQUS program, followed by the elaboration of its numerical implementation. The numerical predictions of ten shear wall specimens infilling reactive powder concrete were found to be reasonably in agreement with the calculated results corresponding to b= 0.5. These findings revealed the characteristics of multiple defensive lines of "block-ribbed column-frame column" under axial compression. Following the successful validation of finite element models, parametric studies were carried out to evaluate the influences of the filled block compressive strength, steel tube wall thickness and height-width ratio. The results show that the axial compression capacity of multi-ribbed composite wall incorporating reactive powder concrete-filled steel tubular columns can be noticeably improved with an increase in block strength and tube thickness. The proposed composite wall demonstrates favorable cooperative working performance and desirable displacement ductility. Subsequently, the primary objective of this pilot study aimed at developing a reliable theoretical calculation formula and conducting numerical simulation verification of the innovative composite wall. The aforementioned conclusions are intended to provide insights for the guidance and optimization of engineering structures.

Experimental Study on the Response of Cracked Sandstone to the Intermediate Principal Stress Coupled with Pore Pressure

Experimental Study on the Response of Cracked Sandstone to the Intermediate Principal Stress Coupled with Pore Pressure

Anisotropic characteristics and creep model for thin-layered rock under true triaxial compression

The failure phenomenon of thin-layered rock tunnels not only exhibits asymmetric spatial characteristics, but also significant time-dependent characteristics under high in-situ stress, which is attributed to the time-dependent fracture of thin-layered rocks. This paper conducted a series of true triaxial creep compression tests on typical thin-layered rock siliceous slate with acoustic emission technique to reveal its anisotropic time-dependent fracture characteristics. The anisotropic long-term strength, creep fracturing process, and fracture orientation characteristics of thin-layered rocks under different loading angles (β, ω) and intermediate principal stress were summarized. A three-dimensional (3D) non-linear visco-plastic creep model for thin-layered rock was developed to simulate its anisotropic creep behavior. The time-dependent fracturing of rocks during true triaxial creep loading is reflected through the change of equivalent strain based on an improved Euler iteration method. By constructing the plastic potential function and overstress index related to loading angles and stress state, the anisotropic time-dependent fracturing process and propagation of thin-layered rocks under different loading angles and intermediate principal stress are expounded. The model was validated experimentally to show it can reflect the long-term strength and creep deformation characteristics of thin-layered rocks under true triaxial compression.

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.

Damage characteristics of rock induced by unloading in hole under true triaxial boundary stresses: Experimental study

In order to study the effect of unloading of underground rock excavation on the stability of surrounding rock, the true triaxial compression (TTC) and coupled true triaxial compression and in-hole loading-unloading tests (TTC-HU) were conducted on hollow cubic rock (100mm × 100mm × 100mm). The experimental results indicate that the compressive strengths of the specimens increase as confining pressure increases in the equal biaxial stressand increase with increasing intermediate principal stresses in the unequal biaxial stress. At low confining pressure (σ < 30 MPa), the internal stress at unloading damage in the hole of hollow cubic specimen increases with the increase of the three-directional boundary stresses. At high confining pressure (σ ⩾ 30 MPa), the specimen will not be damaged during the entire unloading process in the hole. The damage mode of the specimen is dominated by tensile damage. The shape of the holes in the specimens did not significant change, and hole wall of specimen have layered destruction along the circumference in low confining pressure. In high confining pressure, the hole area of the specimen undergoes significant deformation damage, forming a V-groove along the direction of the minimum principal stress, and the wall of the hole is completely peeled off. This study can reasonably predict the actual engineering damage patterns and guide the optimization of surrounding rock support.

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.

Study on the Damage Mechanism of Coal under Hydraulic Load

Hydraulic fracturing is extensively utilized for the prevention and control of gas outbursts and rockbursts in the deep sections of coal mines. The determination of fracturing construction parameters based on the coal seam conditions and stress environments merits further investigation. This paper constructs a damage analysis model for coal under hydraulic loads, factoring in the influence of the intermediate principal stress, grounded in the unified strength theory analysis approach. It deduces the theoretical analytical equation for the damage distribution of a coal medium subjected to small-flow-rate hydraulic fracturing in underground coal mines. Laboratory experiments yielded the mechanical parameters of coal in the study area and facilitated the fitting of the intermediate principal stress coefficient. Leveraging these datasets, the study probes into the interaction between hydraulic loads and damage radius under assorted influence ranges, porosity, far-field crustal stresses, and brittle damage coefficients. The findings underscore that hydraulic load escalates exponentially with the damage radius. Within the variable range of geological conditions in the test area, the effects of varying influence range, porosity level, far-field stress, and brittle damage coefficient on the outcomes intensify one by one; a larger hydraulic load diminishes the impact of far-field stress variations on the damage radius, inversely to the influence range, porosity, and brittle damage. The damage radius derived through the gas pressure reduction method in field applications corroborates the theoretical calculations, affirming the precision of the theoretical model. These findings render pivotal guidance for the design and efficacy assessment of small-scale hydraulic fracturing in underground coal mines.

Elastic–plastic criterion solution of deep roadway surrounding rock based on intermediate principal stress and Drucker–Prager criterion

AbstractExcavation‐induced rock failure and deformation near an underground opening boundary is closely associated with the intermediate principal stress, strain softening and rock mass dilation. By combining theoretical analysis and numerical simulation to explore the mechanical evolution of the roadway surrounding rock during excavation. The elastic–plastic criterion solutions for surrounding rock stress, displacement, and the plastic zone of a circular roadway were deduced by including the intermediate principal stress, strain softening and rock mass dilation, based on the Drucker–Prager criterion and the nonassociated flow rule. Furthermore, ABAQUS finite element software was utilized for numerical simulations to scrutinize the influence of mechanical parameters on stress redistribution, surface displacement, and plastic range. The results of the numerical simulations verify the reliability of the theoretical analysis and affirm the high consistency of the results with the theoretical solution. The research findings indicate that the strength of surrounding rock is significantly influenced by the intermediate principal stress, and the deformation and failure of rock mass are primarily impacted by rock mass dilation, while strain softening mainly affects the thickness of the fractured zone. Moreover, the study reveals that enhancing the residual strength of the surrounding rock can improve its resistance to deformation and failure. Furthermore, the excavation of the roadway is observed to increase the original rock stress in the surrounding rock, but increasing the ground support strength effectively controls the deformation and failure of surrounding rock. Ultimately, the research outcomes offer valuable references for engineering calculations and ground support design of surrounding rock in deep roadways.

Experimental Study on Energy Release Mechanism and Crack Propagation Evolution of Sandstone under True Triaxial Loading

The instability of hard and brittle rock often leads to disastrous consequences in underground engineering. Under various surrounding rock pressure conditions, in situ stress induces corresponding deformation and damage to the floor post-mining. Therefore, it is crucial to examine the effects of mining under different confining pressures on rock disturbance, damage characteristics, and their distribution. Consequently, triaxial loading experiments under varying intermediate principal stress conditions were conducted on red sandstone specimens, using an acoustic emission monitoring system to track energy changes during rock damage and failure. This approach aids in studying crack generation, propagation, and fracture damage evolution. The results indicate that rock deformation results in axial compression and dilatancy, aligned with the direction of minimum and intermediate principal stresses. Ductility in rock failure becomes more pronounced with increased stress, primarily manifesting as shear failure. Internal cracks in the specimen lead to stress concentration and marked plastic deformation under compression, yet do not result in macroscopic surface cracks. The fracture angle θ of specimens post-failure generally exceeds 45° and varies with stress changes; at consistent burial depths, the angle of the sandstone failure surface increases with intermediate principal stress. This paper preliminarily establishes the informational linkage between rock failure and energy release, analyzing the rock samples over time and space. This research offers insights for analyzing and mitigating sudden rock instability.

Investigation of the dense granular soil behaviour inside and outside the shear band: a three-dimensional DEM-FDM study

The present paper aims to compare the behaviour of dense granular soils inside and outside the Shear Band (SB) during the Plane Strain Compression (PSC) test using the Discrete Element Method (DEM). The flexible membrane in the PSC test was modelled by adopting a discrete element–finite difference (DEM-FDM) hybrid approach. In contrast with previous 2D studies, the present study employed 3D simulations to consider the effects of out-of-plane characteristics such as the intermediate principal stress. According to the findings, the minimum and intermediate principal stresses outside the SB were twice as high as those inside at the residual state. It was also found that mechanical coordination numbers and redundancy indexes both inside and outside the SB decreased up to the onset of the residual phase, with a higher reduction rate inside the SB. As far as fabric anisotropy is concerned, the degree of anisotropy increased both in and out the SB until the peak state, with a somewhat higher rate inside the SB. A further finding was that the distribution of normal contact forces outside the SB remained symmetrical around the vertical axis after shear banding, however, it became asymmetrical inside the SB.

Three-dimensional numerical simulation on failure mechanical characteristics of fissured sandstone specimens under true triaxial conditions

Understanding intermediate principal stress influences on deformation characteristics and failure mechanism of fractured rock from deep engineering often necessitates long term on-site detection and complex experimental research, although very limited efficacy can be obtained. With presently available experimental data on conventional triaxial cuboid noncoplanar fissured sandstones, this study further investigated the effects of differential stress (σ2 − σ3) and rock bridge inclination angle (β30°, β60°, β90°, β120°, and β150°) on their damage evolution processes and failure modes based on 3D discrete element methods (PFC3D). Numerical simulation results indicated that the peak strength of the fissured sandstone under the same state of horizontal principal stress shows an overall increasing pattern with the increase of the inclination angle of the rock bridge, while its peak strain displays a decreasing and then increasing trend. Besides, in this work, five failure modes, nine crack types and two kinds of stress–strain curves are summarized which are significantly affected by the horizontal principal stress, rock bridge inclinations or cooperative interaction. Differential stress value of 15 MPa is an important threshold for determining the residual strength of the stress–strain curve from present to absent. The cracking and force chain evolution processes of five failure modes were analyzed in order to discover the corresponding failure mechanisms. Finally, differential stress and flaw inclination influences on rock mechanical parameters and failure behavior have significant implications for strategies of the design, operation, and maintenance of rock engineering under severe conditions in the underground.

A quantitative tunnel support design method considering the safety factor of the surrounding rock

The quantitative support design plays a vital role in tunnel design, while the conventional quantitative framework of tunnel support design through convergence-confinement method (CCM) generally focuses on the safety of the support structure element. Herein, a quantitative tunnel support design method considering the safety factor of the surrounding rock is proposed. First, the solution for the safety factor of surrounding rock element is derived under the CCM framework considering influences of the intermediate principal stress (IPS) and the dilatancy on rock-mass yielding. Second, the allowable safety factor of surrounding rock element is obtained based on the critical support line in the widely used rock quality (Q) system. Then, the framework and procedure of the quantitative tunnel support design method are outlined. Verification of the proposed method is conducted through comparisons with the analytical solution, laboratory model experiment and field monitoring data. Furthermore, a case study is employed to illustrate the proposed method, results indicate that the failure of the whole underground system is caused by the insufficient safety reserve of surrounding rock element. In general, the proposed method provides theoretical guidance for quantitative stability analysis and design optimization of tunnels.

Influence of advance direction on surrounding rock stability of main ramp under deep high ground stress

Due to the widespread use of trackless equipment in metal mines, the main ramp has become a major development roadway in large mines. Under deep high ground stress condition, the stability of the surrounding rock of the main ramp is subject to significant variability due to the change in the advance direction, leading to structural failure in different areas of the roadway. Because the support design scheme of surrounding rock of main ramp will not pay attention to the advance direction of roadway, leading to the key support area of the surrounding rock is not clear, resulting failure of the local supporting form occur frequently. Therefore, this paper adopts the combination of on-site investigation and numerical simulation to carry out the stability analysis of the surrounding rock under different advance directions of the roadway. Through on-site investigation, various failure modes of surrounding rock induced by the change of the advance direction of the roadway are summarized, and the key supporting area of surrounding rock of main ramp is determined according to the angle change between the roadway advance direction and the intermediate principal stress. The extent of the risk zone of the roadway surrounding rock is defined based on the Drucker-Prager criterion, which can be used as the new basis for the design of roadway support parameters. The results show that: As the angle between the advance direction and the intermediate principal stress increases, the degree of deformation of the surrounding rock decreases linearly, and the volume of the plastic and risk zones of the surrounding rock decreases nonlinearly. Based on the distribution of the strain energy density of the roadway surrounding rock, when the angle between the advance direction and the intermediate principal stress is small, the roadway surrounding rock is more prone to the floor heave phenomenon. When the angle between the advance direction and the intermediate principal stress is larger, the roadway surrounding rock is prone to the full-section failure phenomenon. Based on the block theory, when the advance direction is changed, the location and production of key blocks have significant variability, leading to the need for reasonable adjustment of the support parameters for the surrounding rock. The research results of this paper are of guiding significance for the optimization of the surrounding rock support scheme of the main ramp.

Influence of orientation of the intermediate principal stress on fracture reactivation in granite

Fracture (fault) reactivation can lead to dynamic geological hazards including earthquakes, rock collapses, landslides, and rock bursts. True triaxial compression tests were conducted to analyze the fracture reactivation process under two different orientations of σ2, i.e. σ2 parallel to the fracture plane (Scheme 2) and σ2 cutting through the fracture plane (Scheme 3), under varying σ3 from 10 MPa to 40 MPa. The peak or fracture reactivation strength, deformation, failure mode, and post-peak mechanical behavior of intact (Scheme 1) and pre-fractured (Schemes 2 and 3) specimens were also compared. Results show that for intact specimens, the stress remains nearly constant in the residual sliding stage with no stick-slip, and the newly formed fracture surface only propagates along the σ2 direction when σ3 ranges from 10 MPa to 30 MPa, while it extends along both σ2 and σ3 directions when σ3 increases to 40 MPa; for the pre-fractured specimens, the fractures are usually reactivated under all the σ3 levels in Scheme 2, but fracture reactivation only occurs when σ3 is greater than 25 MPa in Scheme 3, below which new faulting traversing the original macro fracture occurs. In all the test schemes, both ε2 and ε3 experience an accumulative process of elongation, after which an abrupt change occurs at the point of the final failure; the degree of this change is dependent on the orientation of the new faulting or the slip direction of the original fracture, and it is generally more than 10 times larger in the slip direction of the original fracture than in the non-slip direction. Besides, the differential stress (peak stress) required for reactivation and the post-peak stress drop increase with increasing σ3. Post-peak stress drop and residual strength in Scheme 3 are generally greater than those in Scheme 2 at the same σ3 value. Our study clearly shows that intermediate principal stress orientation not only affects the fracture reactivation strength but also influences the slip deformation and failure modes. These new findings facilitate the mitigation of dynamic geological hazards associated with fracture and fault slip.