Effect Of Intermediate Principal Stress Research Articles

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.

Effects of intermediate principal stress on the granular material behavior under partial drainage conditions

Effects of intermediate principal stress on the granular material behavior under partial drainage conditions

Intermediate Principal Stress Effects on the 3D Cracking Behavior of Flawed Rocks Under True Triaxial Compression

Abstract Crack initiation, growth, and coalescence in flawed rocks have been extensively studied for 2D (planar, penetrating) flaws under uniaxial/biaxial compression. However, little is known as to the mechanisms and processes of cracking from 3D flaws under true triaxial compression, where the intermediate principal stress ($$\sigma _2$$ σ 2 ) is distinguished from the major and minor principal stresses. In this work, we systematically investigate the effects of $$\sigma _2$$ σ 2 on the 3D cracking behavior of rock specimens with preexisting flaws, through the use of mechanistic simulations of mixed-mode fracture in rocks. We explore how two characteristics of $$\sigma _2$$ σ 2 , namely, (i) its orientation with respect to the flaw and (ii) its magnitude, affect two aspects of the cracking behavior, namely, (i) the cracking pattern and (ii) the peak stress. Results show that the orientation of $$\sigma _2$$ σ 2 exerts more control over the cracking pattern than the flaw inclination angle. The peak stress becomes highest when $$\sigma _1$$ σ 1 is parallel to the flaw, whereas it becomes lowest when $$\sigma _2$$ σ 2 is parallel to the flaw. Also, the effects of $$\sigma _2$$ σ 2 magnitude are more significant when $$\sigma _2$$ σ 2 becomes more oblique to the flaw plane. On the basis of our observations, we propose mechanisms underlying the cracking behavior of 3D flawed rocks under true triaxial compression. Highlights The effects of the intermediate principal stress ($$\sigma _2$$ σ 2 ) on the 3D cracking behavior of flawed rocks under true triaxial compression are systematically investigated. The orientation of $$\sigma _2$$ σ 2 exerts more control over the cracking pattern than the flaw inclination angle. The effects of $$\sigma _2$$ σ 2 magnitude become more significant when $$\sigma _2$$ σ 2 are more oblique to the flaw plane. Mechanisms underlying the cracking behavior of 3D flawed rocks under true triaxial compression are proposed based on the observations made.

A new three-dimensional rock strength criterion based on shape function in deviatoric plane

Rock strength criteria are the theoretical grounding of geotechnical design and stability estimation, the Mohr–Coulomb (MC) and Hoek–Brown (HB) criteria are the widely accepted criteria at present, due to their reasonability and unambiguous concept, however they overlook the effect of intermediate principal stress, and contain six singular corners in π plane. Aimed at overcoming those limitations, the MC and normal parabolic criterion (NPC) were improved to their 3D versions that lead to smooth and convex for a wide range of strength parameters. The extended 3D strength criteria coincide with corresponding original forms in the triaxial compression and triaxial extension states, which not only take intermediate principal stress into account, but also provide great convenient in numerical calculation. Multigroup of poly-axial strength datasets gathered from the references are used to check the prediction accuracy of the proposed 3D criteria by the least absolute deviation method. Research proved that the 3D NPC criterion has a relatively larger deviation on poly-axial strength data prediction, but the proposed 3D MC criterion can describe peak strength with low misfit for soft or hard rocks. Peak strength σ1 increases first and then decreases with the increase of σ2, whether increasing or decreasing σ2, both will result in rock failure. Moreover, the 3D MC can fit the poly-axial strength data well for lower or higher values of σ3, which strongly suggests the proposed 3D MC criterion is adequate. Applicability of the proposed strength criterion will be discussed in further research.

Intermittent disturbance mechanical behavior and fractional deterioration mechanical model of rock under complex true triaxial stress paths

Mechanical excavation, blasting, adjacent rockburst and fracture slip that occur during mining excavation impose dynamic loads on the rock mass, leading to further fracture of damaged surrounding rock in three-dimensional high-stress and even causing disasters. Therefore, a novel complex true triaxial static-dynamic combined loading method reflecting underground excavation damage and then frequent intermittent disturbance failure is proposed. True triaxial static compression and intermittent disturbance tests are carried out on monzogabbro. The effects of intermediate principal stress and amplitude on the strength characteristics, deformation characteristics, failure characteristics, and precursors of monzogabbro are analyzed, intermediate principal stress and amplitude increase monzogabbro strength and tensile fracture mechanism. Rapid increases in microseismic parameters during rock loading can be precursors for intermittent rock disturbance. Based on the experimental result, the new damage fractional elements and method with considering crack initiation stress and crack unstable stress as initiation and acceleration condition of intermittent disturbance irreversible deformation are proposed. A novel three-dimensional disturbance fractional deterioration model considering the intermediate principal stress effect and intermittent disturbance damage effect is established, and the model predicted results align well with the experimental results. The sensitivity of stress states and model parameters is further explored, and the intermittent disturbance behaviors at different f are predicted. This study provides valuable theoretical bases for the stability analysis of deep mining engineering under dynamic loads.

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.

The modification of Mohr-Coulomb criteria based on shape function and determination method of undetermined parameters

Rock strength criteria is a key step to estimate the stability of rock engineering, especially, the effect of intermediate principal stress on rock failure should be considered in formation at great depth. However, the mostly used Mohr-Coulomb criterion don't consider the effect of intermediate principal stress, besides, most rock mechanics laboratories do not have the ability to do true triaxial strength, the strength parameters in poly-axial strength criteria are difficult to be determined. In order to solve these problems, based on the least absolute deviation method, the square of the correlation coefficient, absolute difference and mean difference are adopted to verify the fitting effect of 10 strength criteria on 32 groups of true triaxial strength data. On this basis, the elliptical Lode angle shape function, hyperbolic Lode angle shape function, and the Lode angle shape function based on spatial slip plane are used to establish the modified MC strength criteria, which not only meets the requirements of smoothness and convexness, but also can be used widely in many geomaterials. Besides, strength parameters of the established criteria can be decided by conventional triaxial strength experiment, and the prediction accuracy of the modified MC strength criteria for the 32 groups of true triaxial strength data is better than or close to the lowest fitting error of the existing poly-axial strength criteria.

Experimental study on failure evolution mechanism of clastic rock considering cementation and intermediate principal stress

The study of clastic rock failure evolution under true triaxial stress is an important research topic; however, it is rarely studied systematically due to the limitation of monitoring technology. In this study, true triaxial compression tests were conducted on clastic rock specimens to investigate the effect of cementation and intermediate principal stress (σ2) on the failure mechanism. The complete stress–strain curves were obtained, while the acoustic emission (AE) was monitored to indirectly evaluate the evolution of tensile and shear cracks, and crack evolution under true triaxial compression was imaged in real time by a high-speed camera. The results showed that the deformation and failure characteristics of clastic rock were closely related to the cementation type and intermediate principal stress. On the basis of the distribution characteristics of the ratio of rise time to amplitude (RA) and the average frequency (AF) of AE signals, tensile cracks of the contact cementation specimen propagated preferentially. Meanwhile, the enhancement of specimen cementation promoted the evolution of shear cracks, and the increase in σ2 promoted the evolution of tensile cracks. Moreover, the mesoscale cracking mechanism of clastic rock caused by cementation and σ2 under true triaxial compression was analyzed. The failure patterns of clastic rock under true triaxial compression were divided into three modes: structure-induced, structure-stress-induced and stress-induced failures. This study confirms the feasibility of high-speed camera technology in true triaxial testing, and has important implications for elucidating the disaster mechanism of deep tunnels in weak rocks.

A Simple Solution and Dilatancy Characterization for a Circular Tunnel Excavated in the Nonlinear Strain-Softening and Nonlinear Dilatancy Rock Mass

Tunnel opening or excavation in the strain-softening rock masses primarily leads to initial stress release and rock deformation. The increasing plastic shear strain induces a nonlinear variation of dilatancy in rock masses. Therefore, tunnel stability is strongly dependent on the stress state and the strain-softening and dilatancy behaviors of rock masses. In view of this, this paper proposes an elastoplastic finite difference solution based on the triple-shear element (TS) unified strength criterion (USC) and the nonassociative flow law; thereafter, some typical examples are referred to verify its validity. This solution allows for the description of the intermediate principal stress effect, the nonlinear strain-softening and dilatancy behaviors of the rock mass. Parametric analysis finally determines the influence characteristics of the intermediate principal stress effect (b), the critical softening parameter ( η ∗ ), softening factor (δ), and support force (pi) on the dilation angle (ψ) of the rock mass in the plastic zone. The findings confirm that the intermediate principal stress mainly affects peak values of ψ, which increases as b grows. The rate of change of ψ mainly depends on η ∗ , which tends to be slower with increasing η ∗ . The variation pattern of ψ in the residual zone under different δ is generally consistent, while the variability of ψ in the softening zone is significant. For a given intermediate principal stress state and strain-softening behavior of the rock mass, the values and the developed form of ψ in the plastic zone is independent of pi.

A novel elastoplastic model for Yunnan sandstone under poly-axial loading

The lack of understanding of plastic hardening (softening) laws, especially under anisotropic stress conditions, results in inappropriate geotechnical management. Most of the yielding envelopes do not consider the effect of intermediate principal stress and the influence of Lode’s angle. In addition, the application of plastic flow rules regarding yielding surfaces compromises the softening of rock internal friction as well as the influence of Lode’s angle on the plastic potential. Moreover, the ductility to brittleness transition in the intermediate principal stress direction still requires a theoretical foundation. In this study, based on poly-axial testing results of Yunnan sandstone, we adopted a failure criterion with the intermediate principal stress proposed by Menétrey and Willam. The proposed new failure envelope was applied to capture the plastic evolution of rock samples. A plastic hardening-softening model is constructed, based on the framework of the plastic theory. The softening envelope is modified to better present the stress drop and considers the deterioration of rock internal friction in the post-peak stage of poly-axial loading. The differential of plastic potential according to the principal stresses is also modified, considering the rotation of Lode’s angle in the poly-axial loading tests. The model results were compared with laboratory testing results, which showed great consistency across 9 different loading tests (5 under triaxial stress and 4 under poly-axial stress with 22 stress-strain curves in total). The induced brittleness by the intermediate principal stress is also well captured by the proposed model.

Influence of stress state on dynamic behaviors of concrete under true triaxial confinements

The strain rate sensitivity and stress state are two important factors affecting the mechanical behavior of concrete under dynamic load. However, few studies involved high strain rates and different stress states. Herein, the strain rate effect and intermediate principal stress effect of concrete are studied by using the true triaxial Hopkinson test system, and the influence of heterogeneity under dynamic load is also discussed. A series of experiments, including the static biaxial and static triaxial confinements, are conducted to investigate the intermediate principal stress effects by a dynamic testing system for cubic concrete specimens under static triaxial confinements. The results show that the triaxial experimental data show good consistency with the dynamic M-C strength, but the biaxial experimental data deviate greatly from the dynamic M-C strength, which indicates evident the intermediate principal stress effect. The Drucker-Prager (D-P) model is then modified to describe the intermediate principal stress dependence and loading rate effect by introducing the Lode angle (θ) and the strain rate, and better simulation results are obtained. The meso finite element model (meso‑FEM) is employed to further explain the effects of non-uniformity in concrete specimens, and a Weibull-type modification is introduced to describe the transversal inertia effect due to concrete heterogeneity. Although the relative dynamic stress (η=(σx−σe)/σx) in the x-axis is rate-dependent, hydrostatic pressure-dependent, and size-dependent, the relation of η to the stress triaxiality is insensitive to these effects. This work would provide experimental and theoretical guidance for the effect of stress state on the mechanical behavior of concrete under dynamic load.

Influence of moisture content and intermediate principal stress on cracking behavior of sandstone subjected to true triaxial unloading conditions

The presence of water has been confirmed to play an important role in affecting the failure properties of underground surrounding rock when subjected to complicated stress circumstances. In the current study, the crack propagation behavior of red sandstone affected by various moisture contents and intermediate principal stresses were investigated by using the QKX-YB200 true triaxial test system with unloading minimum principal stress. The experimental results demonstrate that the failure mode can be divided into shear, tension with shear, and slabbing. A clear observation of the fractured specimen shows that the extensional cracks tend to increase while shear cracks gradually diminish with the increase of moisture content and intermediate principal stress. For natural sandstone (with lower moisture content), the transition of failure mode from shear to slabbing requires higher intermediate principal stress. However, with the increase of moisture content, the occurrence of slabbing failure requires lower intermediate principal stress. The analysis of failure process indicates that the presence of water may restrain the possibility of rockburst, and the intermediate principal stress exhibits distinct functions in the failure behavior of natural and saturated sandstone. The surface microscopic morphological characteristics and acoustic emission signal feature were also analyzed to validate the transformation of the cracking mode. The current research indicated that the water-induced micro defect and damage effect, “water wedge” effect, intermediate principal stress effect are the key factors that contribute to the final slabbing failure in immersed hard rocks under true‑triaxial unloading conditions.

Rock Slope Stability Analysis Incorporating the Effects of Intermediate Principal Stress

Rock Slope Stability Analysis Incorporating the Effects of Intermediate Principal Stress

A generalized nonlinear three-dimensional failure criterion based on fracture mechanics

Based on fracture mechanics theory and wing crack model, a three-dimensional strength criterion for hard rock was developed in detail in this paper. Although the basic expression is derived from initiation and propagation of a single crack, it can be extended to microcrack cluster so as to reflect the macroscopic failure characteristic. Besides, it can be derived as Hoek–Brown criterion when the intermediate principal stress σ2 is equal to the minimum principal stress σ3. In addition, the opening direction of the microcrack cluster decreases with the increase of the intermediate principal stress coefficient, which could be described by an empirical function and verified by 10 kinds of hard rocks. Rock strength is influenced by the coupled effect of stress level and the opening direction of the microcrack clusters related to the stress level. As the effects of these two factors on the strength are opposite, the intermediate principal stress effect is induced.

Upper bound analysis of the anti-seismic stability of slopes considering the effect of the intermediate principal stress

Considering the intermediate principal stress effect of soils, the unified strength theory was applied to correct the shear strength index of soils. Based on a mechanical model of the anti-seismic stability of slopes, the analytical formula of the stability coefficient was deduced by the upper bound method and the quasi-static method. Then the optimal solution of the stability coefficient was figured out via the Matlab software. The result shows that, if the intermediate principal stress is ignored, the shear strength of soils would obviously be underestimated; this is also the case with the slope stability coefficient, the relative error of which could reach 39.87%. The horizontal and vertical seismic forces significantly affect slope stability. When the horizontal seismic force is considered, the slope stability coefficient Ns is reduced by 79.82%. Similarly, if the seismic effect is not neglected, the stability of the slope would be seriously overestimated. Slope cutting can significantly improve slope stability. When the slope angle is reduced from 90° to 50°, the stability factor increases by 279.82%. The suitable design angle of the slope is between 50° and 60° without taking into account additional elements like groundwater level and stratum structure.

Convergence-confinement analysis for tunnels with combined bolt–cable system considering the effects of intermediate principal stress

Convergence-confinement analysis for tunnels with combined bolt–cable system considering the effects of intermediate principal stress

Effect of intermediate principal stress on the failure characteristics of an underground powerhouse

The failure modes of deep excavation absolutely relate to three-dimensional stresses. The effect of the intermediate principal stress (σ2) on the failure of the granite surrounding an underground powerhouse was examined using true triaxial compression tests. As the initial major principal stress (σ1o) is parallel to the axis of the Shuangjiangkou Underground Powerhouse, for the cross-section the tangential stress around the excavation depends on the initial intermediate (σ2o) and minor (σ3o) principal stress components. Once the excavation is created, the radial stress becomes zero, and the tangential stress increases dramatically. The axial stress in the excavating direction remains almost unchanged. Slabbing will develop towards the excavation space that is parallel to the excavation axis. The stress σ2 after excavation can help to improve the failure brittleness, crack initiation strength, crack damage strength, and peak strength of the rock when it falls within the range of stresses encountered in engineering practice. The ratio of the crack damage strength to crack initiation strength is approximately constant as σ2 varies. More specifically, the crack damage strength is about three quarters of the value of the peak strength, and the crack initiation strength is about half the value of the peak strength. As σ2 increases, the microcracks coalesce to form a major through-going crack. Meanwhile, the Poisson's ratio in the direction of strain ε2 declines steadily and that in the direction of strain ε3 increases moderately, so that the rock exhibits anisotropy. The fracture angle (the angle between the fracture plane and the plane normal to σ1) is proportional to σ2. The results of the true triaxial compression tests allow the brittle failure events in the Shuangjiangkou Underground Powerhouse to be adequately explained. It could help facilitate an optimization of the direction of the excavation axis and efficient supporting measures for deep underground powerhouse.

A new statistical damage model for true triaxial pre-and post-peak behaviors of rock considering intermediate principal stress and initial compaction effects

Deep underground engineering excavation will induce complex change in the true three-dimensional stress state of the surrounding rock, causing rock damage and then leading to a change in mechanical properties. In this research, the true triaxial compression tests are conducted to study the influence of σ2 and σ3 on the mechanical properties of marble, such as the characteristic strength (crack initiation stress σci, damage stress σcd, peak strength σp, and residual strength σr), post-peak deformation, ductility and brittleness. The peak strength σp, crack initiation stress σci and damage stress σcd of rock increase with the increase in σ2, while the variation of residual strength σr with σ2 is different from that of peak strength. As σ2 increases or σ3 decreases, the pre-peak plasticity of the rock decreases, the post-peak curve shape of the rock changes significantly, and the overall shape of the post-peak curve transforms from Class I to Class II. The Mogi-Coulomb strength criterion with intermediate principal stress effect was used to characterize the rock microelement strength, and then the new statistical damage constitutive model considering the initial compaction effect and damage threshold was proposed, and the model validation was carried out based on the experimental results and the effects of the proposed model parameters m and F0 on the rock strength and post-peak curve morphology were further explored.

Analysis of Surrounding Rock Pressure of Deep Buried Tunnel considering the Influence of Seepage

This paper takes the surrounding rock of deep tunnel as the research object and considers the action mechanism under the influence of seepage. Based on the Mohr-Coulomb criterion, the stress mechanism of surrounding rock of deep buried tunnel is analyzed by a convergence constraint method. Based on the elastic-plastic solution, the nonlinear elastic-plastic solution of the interaction between surrounding rock and lining structure considering the effect of seepage force is proposed, and the radius of surrounding rock plastic zone is obtained. The relationship between surrounding rock stress and displacement, radial deformation of lining, and support reaction force was observed. At the same time, considering the effects of seepage, strain softening, and intermediate principal stress, the surrounding rock is divided into a plastic residual zone, plastic softening zone, and elastic zone, and the stress distribution expressions of the plastic zone and each zone of surrounding rock of circular tunnel are derived. The results show that with the change of nonuniform permeability coefficient, the seepage shows anisotropy in different directions, and the closer to the horizontal or vertical direction, the more obvious the influence of nonuniform permeability coefficient on pore water pressure distribution. Seepage and material softening have different effects on the distribution of surrounding rock stress field and the size of plastic zone. Material softening is more unfavorable to the stability of surrounding rock than seepage. The intermediate principal stress coefficient has a significant impact on the tangential stress and plastic zone of surrounding rock. When the intermediate principal stress effect is not considered, the calculation results are relatively conservative and cannot give full play to the strength of surrounding rock effectively. The research conclusion can provide a theoretical reference for studying the stability of surrounding rock in tunnel excavation under water-bearing rock.