Intermediate Principal Stress Research Articles

Influences of true 3D twin flaws on principal stress status and crack occurrence of brittle rock-like samples under uniaxial compression: Insights from experimental and DEM studies

Fracture structures commonly have negative impacts on the strength and safety of rock mass, and various combinations of 2D and 3D flaws make the destruction procedure becomes more complicated. Therefore, laboratory tests based on three types of flawed rocks (symmetric twin flaws with different 2D-3D occurrences) are finished to detect the mechanical, optical and acoustic characteristics of fractured rocks during the uniaxial compression test; PFC3D simulations are conducted for analyzing the deformation features, principal stress distributions, and detailed failure mechanism of the fractured rocks. The main results are as follows: 1) Different combinations of 2D & 3D preset flaws directly influence the results of deformation, stress distribution, and failure developments. 2) Rotation of the intermediate stress axes only appear near the flaw inclination boundary (when the monitoring position moves outwards), while the directions of intermediate principal stress axes remain stable near the flaw strike boundary. 3) Separating cracks by various occurrences helps to construct local failures along different directions, and make some local failures visible and clear; the traditional cracks (short line or thin oval shape) are induced by the uneven deformation in x-o-z planes, and the separated cracks (wide oval or standard disc shape) result from the uneven deformation in y-o-z planes. 4) Surrounding rocks at different positions suffer various modes of failures, the non-ignorable thickness of preset flaw leads to simultaneous Mode I and Mode II failure at the flaw tip, and the mixed Mode II&III failure only occurs in the rocks adjacent to the flaw strike boundary.

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 the influence of intermediate principal stress on failure characteristics of strain rock burst for granite

Experimental study on the influence of intermediate principal stress on failure characteristics of strain rock burst for granite

Scaling Microseismic Cloud Shape During Hydraulic Stimulation Using In Situ Stress and Permeability

AbstractForecasting microseismic cloud shape as a proxy of stimulated rock volume may improve the design of an energy extraction system. The microseismic cloud created during hydraulic stimulation of geothermal reservoirs is known empirically to extend in the general direction of the maximum principal stress. However, this empirical relationship is often inconsistent with reported results, and the cloud growth process remains poorly understood. This study investigates microseismic cloud growth using data obtained from a hydraulic stimulation project in Basel, Switzerland, and explores its correlation with measured in situ stress. We applied principal component analysis to a time series of microseismicity for macroscopic characterization of microseismic cloud growth in two‐ and three‐dimensional space. The microseismic cloud, in addition to extending in the general direction of maximum principal stress, expanded in the direction of intermediate principal stress. The orientation of the least microseismic cloud growth was stable and almost identical to the minimum principal stress direction. Further, microseismic cloud shape ratios showed good agreement when compared with in situ stress magnitude ratios. The permeability tensor estimated from microseismicity also provided a good correlation in terms of direction and magnitude with the microseismic cloud growth. We show that in situ stress plays a dominant role by controlling the permeability of each existing fracture in the reservoir fracture system. Consequently, microseismic cloud growth can be scaled by in situ stress as a first‐order approximation if there is sufficient variation in the orientation of existing faults.

Three-dimensional stability analysis of tunnel face based on unified strength theory

The impact of cyclic footage and intermediate principal stress on the stability of the tunnel-face area are analyzed in this study using the theory of limit analysis. The study introduces the unified strength theory and proposes three-dimensional logarithmic spiral failure modes with corresponding velocity fields. The influence of various parameters on the tunnel-face area stability is analyzed, and it is found that when the internal friction angle is less than 30°, the internal friction angle parameters should be improved first to enhance stability, while when the internal friction angle is greater than 30°, cohesion should be prioritized. When using the double shear uniform strength theory in the tunnel-face area, the intermediate principal stress can improve the stability of the tunnel face. Results show that Mohr–Coulomb criterion calculations are conservative in the good surrounding ground, but no similar conclusion has been obtained for the poor surrounding ground, and specific problems must be analyzed during construction.

Cracking property and brittleness evaluation of granite under high-temperature true triaxial compression in geothermal systems

Cracking property and brittleness are critically important to the drillability of injection and production wells of enhanced geothermal systems. This paper is devoted to evaluating the cracking property and brittleness of the Gonghe granite under high-temperature true triaxial compression conditions through a series of laboratory tests. Thermal–mechanical coupled true triaxial compression tests were conducted on Gonghe granite samples under four representative temperatures (20 °C, 120 °C, 180 °C, and 240 °C) and three different minimum (5, 10, and 30 MPa) and intermediate (40, 60, and 75 MPa) principal stresses that correspond to the in-situ conditions of Gonghe geothermal reservoir. The strength, deformation, and cracking characteristics of the Gonghe granite are quantitatively evaluated from macro- to micro-scales based on the experimental results. Meanwhile, a novel brittleness index evaluation method considering both energy and failure surface roughness is proposed to accurately assess the brittleness strength of the Gonghe granite. We found that the strength of Gonghe granite is reduced by more than 20% when the temperature increases from room temperature to 240 °C. Higher temperature contributes to a smoother fracture surface and reduced brittleness of the Gonghe granite under thermal–mechanical coupled true triaxial compression. Our findings provide new insights for brittleness evaluation of the Gonghe granite formation and assist in efficient wells drilling design of enhanced geothermal systems.

A simple 3D elastoplastic constitutive model for overconsolidated soils based on the improved Hvorslev envelope

Soils encountered in geotechnical engineering exhibit a certain degree of overconsolidation and are in a three-dimensional (3D) stress state. The overconsolidated ratio (OCR) and the intermediate principal stress play a significant role in the strength and deformation of overconsolidated soils. By considering the variation of the peak stress ratio with OCR, and taking the zero-tension line and the critical state line as asymptotes, a continuous and smooth Hvorslev envelope is deduced to describe the peak strength of overconsolidated soils. Based on the proposed Hvorslev envelope, a simple 3D elastoplastic constitutive model for overconsolidated soils is directly established through the characteristic stress method. The constitutive relation of the proposed model is presented by the calculation of the total strain increment. All material parameters have clear physical meanings and can be determined by conventional laboratory tests. The isotropic compression path, the triaxial drained shearing path with constant p, the triaxial undrained shearing path, and the true triaxial drained shearing path with constant p and θ are adopted to demonstrate the essential features of the proposed model. The effectiveness of the proposed model is confirmed by comparing the experimental data from Lower Cromer till, Kaolin clay, and Fujinomori clay with corresponding model predictions.

Experimental Study on the Axial Deformation Characteristics of Compacted Lanzhou Loess under Traffic Loads

It is beneficial to the sustainable development of expressway engineering to reuse excavated soil as roadbed filling material. There are a large number of filling projects using loess as a filling material in Northwest China. In this paper, the loess subgrade of an expressway in Lanzhou is taken as the research object, and a series of experimental studies are conducted using a hollow cylindrical torsion shear system to simulate the formation of a “heart-shaped” stress path and the principal stress rotation (PSR) under long-term traffic loads. The effects of the vertical cyclic dynamic stress ratio, torsion shear stress ratio, initial static shear stress, and intermediate principal stress coefficient on the axial plastic deformation and rebound deformation of compacted loess in Lanzhou were studied. The results show that the vertical cyclic stress ratio (VCSR) has a significant effect on the axial deformation of compacted loess in Lanzhou. When the VCSR is less than 0.6, all the axial strain curves develop stably with the number of cycles. With an increasing VCSR, the axial plastic deformation increases obviously, and the axial rebound deformation also increases. The vertical cyclic dynamic stress of the specimen is constant. Moreover, increasing the torsional shear stress ratio (that is, increasing the amplitude of cyclic shear stress) can greatly increase the development of axial deformation, but it has no effect on the rebound deformation curve. When the initial static shear stress exists in the specimen, the larger the initial static stress ratio (SSR) is, the larger the axial plastic deformation. The axial plastic deformation increases by approximately 33% for every 0.1 increase in the SSR. The rebound deformation of different SSRs fluctuates at the initial stage of cyclic loading, but the final stable rebound deformation is basically the same as that at the initial stage of cyclic loading. The intermediate principal stress coefficient has no effect on the development of axial strain, and the effect on axial rebound deformation is negligible. Finally, the calculation model of the axial plastic strain of Lanzhou compacted loess under traffic loads is obtained. The research results can provide a reference for the durability and settlement prediction in loess engineering.

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.

Mechanical and Energy Evolution Characteristics of Sandstone under True Triaxial Cyclic Loading

To study the mechanical and energy evolution characteristics of sandstone under true triaxial cyclic loading, a sandstone mechanical test with different intermediate principal stress under true triaxial loading was conducted using the rock true triaxial disturbance unloading test system. The influence of axial load on the deformation, energy evolution, and macroscopic failure characteristics of sandstone under different intermediate principal stress in a true triaxial test was systematically analyzed, and the damage evolution law of sandstone under true triaxial cyclic load was revealed. Results showed that the failure mode of sandstone under true triaxial compression changed from tension–shear composite failure to tension failure. Grading cyclic load σ1 greatly influenced maximum principal strain ε1 and minimum principal strain ε3 but had little influence on intermediate principal strain ε2. Under the same σ2 condition, the input energy and elastic energy in σ1, σ2, and σ3 directions increased nonlinearly. Under different σ2 conditions, the dissipated energy in σ1, σ2, and σ3 directions decreased with the increase in σ2. With the increase in σ2, graded cycles σ1, ε2, and ε3 decreased considerably, and the failure mode changed from tensile failure to shear failure. When the cyclic loading rate increased, the σ1, ε1, ε2, ε3, and volume strain εv of sandstone failure decreased, but the expansion point increased. Under true triaxial grading cyclic loading and unloading, the total dissipated energy of sandstone increased exponentially. The larger σ2 was, the smaller the damage variable was.

Dynamic properties of dredger fill involved coupling action of initial stress and principal stress rotation

GCTS hollow cylinder apparatus was used to perform a series of tests on dredger fill from Tianjin under different initial stress states. This cyclic loading mode can simulate the rotation of the principal stress direction induced by wave loading. The effects of the initial intermediate principal stress parameter, initial shear stress and initial orientation angle of principal stress on softening index of dredger fill were investigated. A stiffness softening model which can consider different initial stress states was established. The test results show that when two of the three initial stress parameters remain unchanged, the softening index decreased with the increase of any other parameter. Among them, the initial orientation angle of principal stress has a great influence on stiffness softening. Based on the regression analysis of the test data, the relationship between the generalized shear strain ratio and the number of cycles under different cyclic shear stress amplitudes is proposed. Subsequently, the dynamic strength characteristics of the dredger fill were studied. It is found that the dynamic strength decreased significantly with the increasing initial angle of the principal stress, which can be accurately described by the model proposed in this article.

A New Close-Form Solution for Elastoplastic Seepage-Induced Stresses to Circular Tunnel with Considering Intermediate Principal Stress

A New Close-Form Solution for Elastoplastic Seepage-Induced Stresses to Circular Tunnel with Considering Intermediate Principal Stress

Triaxial stress and failure modes in hydrothermal mineral systems

Rock mechanics experiments show that the magnitude of the intermediate principal stress significantly affects rock failure. Since triaxial stress states (no principal stress is zero) are ubiquitous in the crust, and polyaxial axial states (all three principal stresses are different) are general, the magnitude of the intermediate principal stress should have an important effect on hydrothermal mineralisation. For example, extensional veins or dykes in vein-hosted gold or porphyry deposits may have multiple orientations when the intermediate and least principal stresses have similar magnitudes, or single orientations when the intermediate and maximum principal stresses are similar. The Griffith-Murrell triaxial fracture criterion with a tensile cutoff can be used to illustrate the effects of the intermediate principal stress on failure. At the lowest values of mean stress, the criterion suggests that only extensional failure can occur. At low–intermediate values of mean stress, either extensional or shear failure may occur: extensional failure is favoured when the intermediate and maximum principal stresses have similar magnitudes. At higher mean stresses, shear failure will occur at lower values of pore fluid pressure and differential stress when the magnitudes of the intermediate and minimum principal stresses are similar.

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.

Experimental study on sand anisotropy using hollow cylinder apparatus

This study investigated sand anisotropy experimentally using a hollow cylinder apparatus. The effect of the initial anisotropy on the shear behavior of sand was illustrated by conducting experiments on specimens with bedding planes and systematically varying the density, principal stress direction, and intermediate principal stress. The change in induced anisotropy during shearing was experimentally captured by re-shearing the specimens subjected to prior shear history. The experimental results revealed the following: (a) Anisotropy in sand, whether initial anisotropy developing during specimen preparation or induced anisotropy developing due to shear history, causes pseudo-density changes in the mechanical behavior, in which sand of the same density behaves as if it has a different density depending on the direction of shear. (b) The changes in induced anisotropy, due to shearing in the same direction as that of the prior shear, make the soil behave similarly to dense sand, whereas shearing in a direction perpendicular to the prior shear makes the soil behave similarly to loose sand. (c) The larger the prior shear, the more pronounced the pseudo-density changes that appear in the subsequent behavior. Moreover, the significance of induced anisotropy in liquefaction and compaction phenomena was experimentally demonstrated through single and double swing cyclic shear tests. The results obtained from the study will be useful for validating models that incorporate induced anisotropy.

Both Longitudinal and Transverse Extension Controlling Gas Migration Through Submarine Anticlinal Ridges, New Zealand's Southern Hikurangi Margin

AbstractSub‐seabed fluid flow, gas hydrate accumulation and seafloor methane seepage are tightly interwoven processes with implications for marine biodiversity, ocean chemistry and seafloor stability. We combine long‐offset seismic reflection data with high‐resolution seismic data to investigate shallow structural deformation and its relationship to focused gas migration and hydrate accumulation in the southern Hikurangi subduction wedge. Anticlines, effective traps for focusing free gas, are characterized by both normal faults and vertical zones of hydraulic fracturing within the hydrate stability zone. The normal faults form as a result of sediment layer folding and gravitational collapse of ridges during uplift. We document both longitudinal (ridge‐parallel) and transverse (ridge‐perpendicular) extensional structures (normal faults and elongated hydraulic fracture zones) in the sub‐seafloor of anticlinal ridges. Intriguingly, gas flow through ridges close to the deformation front of the wedge exploits longitudinal structures, while ridges further inboard are characterized by gas flow along transverse structures. This highlights pronounced changes in the shallow deformation of ridges in different parts of the wedge, associated with a switching of the least and intermediate principal stress directions. It is critical to understand these shallow stress fields because they control fluid flow patterns and methane seepage out of the seafloor.

Thermal Infrared Precursor Information of Rock Surface during Failure Considering Different Intermediate Principal Stresses

Rock failure generally leads to serious consequences, and it is significant to obtain the precursor information prior to failure using associated techniques. Thus, it is essential to acquire and probe the relevant precursor information. In this study, true triaxial tests are performed on red sandstone specimens under varying intermediate principal stress conditions. The thermal infrared image evolution and the temperature-induced change characteristics of rock failure are also analyzed using infrared thermal imaging technology. In addition, with the assistance of a high-speed photography technique, these characteristics during the true triaxial compression and unloading processes are systematically investigated to determine how the intermediate principal impacts on thermal image, temperature, and fracture propagation. Finally, the evolution mechanism of the specimens is summarized, and a non-contact thermal infrared rock failure precursor indicator is proposed, which can give significant advance notice of rock collapse before the abnormal temperature change. The results show that there exist thermal infrared temperature precursors, thermal image precursors, and rapid development of rock macroscopic cracks before rock failure. Abnormal thermal images are prior to the abnormal temperature changes. As the intermediate principal stress increases, thermal abnormalities will change accordingly. Both temperature changes and thermal image anomalous patches can be utilized as precursor information of rock collapse, and the mechanism and specific information of thermal infrared failure precursors can be preliminarily determined in time and space. Our results can function as a significant frame of reference for the analysis and prevention of rock failure due to sudden instability.

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 intermediate principal stress ratio on strength and deformation characteristics of frozen sandy soil under different moisture contents

Frozen ground often contain non-uniform moisture content and are under true triaxial stress state and their practical engineering application are still explored. The present study is carried out to investigate the strength and deformation characteristics of frozen soil with different moisture contents under true triaxial stress state conditions. A series of true triaxial tests were conducted on frozen soil specimens having constant minimum principal stress (σ3) and constant intermediate principal stress ratio (b). The experimental test results showed that the stress-strain curves represent the strain-hardening characteristics under different test conditions. The intermediate principal stress ratio (b) has a dual effect of strengthening and weakening on the strength of frozen sandy soil. When 0 ≤ b ≤ 0.5, the strengthening effect was found to be dominant in the frozen soil specimen, whereas, the weakening effect was dominant when 0.5 < b ≤ 1. The strength of frozen soil under true triaxial stress state is 8.18% to 36.33% higher under different water content conditions, compared to that under generalized triaxial compression stress state. The difference in deformation between the direction of the intermediate principal stress and the minimum principal stress increased with the increment in the intermediate principal stress ratio value. The volumetric strain in the soil sample initially exhibited the characteristics of shear contraction and then shear dilation.

A new hydro-mechanical coupling constitutive model for brittle rocks considering initial compaction, hardening and softening behaviors under complex stress states

After the excavation of underground engineering, the failure and instability of surrounding rock under hydro-mechanical coupling conditions is a common type of engineering disaster. However, the hydro-mechanical coupling mechanical characteristics of rock have not been fully revealed, and suitable models for the stability analysis of surrounding rock under hydro-mechanical coupling conditions are very scarce. Therefore, a series of triaxial compression and cyclic loading and unloading hydro-mechanical coupling tests were carried out to study the mechanical characteristics, deformation and mechanical parameters of rock under different confining pressures and pore pressures. Then, based on Biot’s effective stress principle, a hydro-mechanical coupling damage constitutive model within the framework of irreversible thermodynamics was proposed to describe the initial compaction effect, pre-peak hardening and post-peak softening behaviors. The functional relationships between the proposed model key parameters (η and ζ) and the effective stress were established to characterize the pre- and post-peak nonlinear behaviors of rock. A compaction function Ck for the evolution of the undamaged Young’s modulus in initial compaction stage was introduced to characterize the pre-peak compaction effect. A user-defined material subroutine (UMAT) was compiled in ABAQUS to numerically implemented the proposed model. The numerical simulation results are highly consistent with the test results, the proposed model can also predict the hydro-mechanical coupling characteristics of rock under untested stress levels. In addition, the yield function of the proposed model considers the influence of intermediate principal stress, which is also suitable for the simulation of hydro-mechanical coupling characteristics under true triaxial stress states.Graphical abstract