Influence Of Intermediate Principal Stress Research Articles

Dilation and energy evolution mechanisms of sandstone under true-triaxial mining unloading conditions

The study of sandstone dilation characteristics under actual mining and excavation conditions promotes the safe and efficient development of underground engineering. Accordingly, this study employs true-triaxial testing to reveal the influence of intermediate principal stress and unloading action in the minimum principal stress directions on rock dilation. In the stress–strain analysis, with increasing intermediate principal stress, the maximum compression of the sandstone volume in the loading and unloading tests increases, while the onset of dilation is delayed under loading conditions and initially delayed and then accelerated under unloading conditions. The energy storage limit of sandstone under the unloading test tends to decrease with increasing intermediate principal stress, contrary to the results of the loading test, and the characteristic point at which the percentage of dissipative energy is greater than that of elastic energy occurs earlier. The energy of sandstone in the unloading test in the intermediate principal stress direction was smaller than that in the minimum principal stress direction, while the loading test showed the opposite trend. Combining these two analyses can elucidate the restraining effect and tensile stress effect of the intermediate principal stress, as well as the weakening and strengthening effects of the unloading action on the two effects. By further combining the average elastic energy and dissipative energy conversion rate under different test conditions, the weakening effect was manifested by shortening the compressive deformation course, and the strengthening effect was manifested by developing the degree of plastic expansion deformation. This study provides important guidance for deep mining projects.

A generalized nonlinear three-dimensional Hoek‒Brown failure criterion

To understand the strengths of rocks under complex stress states, a generalized nonlinear three-dimensional (3D) Hoek‒Brown failure (NGHB) criterion was proposed in this study. This criterion shares the same parameters with the generalized HB (GHB) criterion and inherits the parameter advantages of GHB. Two new parameters, β, and n, were introduced into the NGHB criterion that primarily controls the deviatoric plane shape of the NGHB criterion under triaxial tension and compression, respectively. The NGHB criterion can consider the influence of intermediate principal stress (IPS), where the deviatoric plane shape satisfies the smoothness requirements, while the HB criterion not. This criterion can degenerate into the modified HB criteria under triaxial compression condition and the HB criterion under triaxial compression and tension condition. This criterion was verified using true triaxial test data for different parameters, six types of rocks, and two kinds of in situ rock masses. For comparison, three existing 3D HB criteria were selected for performance comparison research. The result showed that the NGHB criterion gave better prediction performance than other criteria. The prediction errors of the strength of six types of rocks and two kinds of in situ rock masses were in the range of 2.0724%–33.5091% and 1.0144%–3.2321%, respectively. The proposed criterion lays a preliminary theoretical foundation for prediction of engineering rock mass strength under complex in situ stress conditions.

Multivariable Regression 3D Failure Criteria for In-Situ Rock

Wellbore stability problems increase with the exploration and development of oil and gas reservoirs. A new 3D non-linear failure criterion is proposed as a trigonometric function considering the intermediate principal stress (2)  on the triaxial compression test data. Mohr-Coulomb and Hoek-Brown are well-known failure criteria, but they do not consider the influence of (2) on rock strength. This new criterion produces a concave surface on the principal stress space (1,2, 3) with the influence of intermediate principal stress. In this study, sensitivity analysis for the variable is also done to understand the significant influence of parameters on the accuracy of the proposed criterion. Further validation of this non-linear criterion on three principal stresses (1,2, 3) was done compared with linear regression and second-degree polynomial regression results. It has been observed that the new non-linear 3D criterion with five material parameters reveals a good fit compared to linear regression and second-degree polynomial regression, which have four and six material parameters, respectively. The new non-linear criterion was further validated by comparison with existing criteria like the Priest, Drucker-Prager, and Mogi-Coulomb. It has been observed that the new 3D non-linear criterion shows a more accurate result than these existing criteria as certain rock types exhibit coefficient of determination (DC) values near one, precisely 0.95 for inada granite, 0.94 for orikabe monzonite, and 0.91 for KTB amphibolite. In contrast, other rock types have DC values ranging from 0.7 to 0.9. The new 3D non-linear criterion also yields lower root means square error (RMSE) values than the Mogi-Coulomb criterion for seven rock types. Specifically, the RMSE values by the new criterion are as follows: KTB amphibolite - 40.03 MPa, Dunham dolomite - 15.16 MPa, Shirahama sandstone - 9.08 MPa, Manazuru andesite - 22.14 MPa, Inada granite - 35.47 MPa, and Coconino sandstone - 19.047 MPa. This new 3D criterion gave precise predictions of the failure of the formation under in-situ stresses and was further helpful for the simulation of the wellbore in the petroleum industry. The variable in the new 3D criterion should be calculated from triaxial compression test data for each formation rock before applying this criterion to the wellbore stability problem and the sand production problem.

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

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

Influence of Intermediate Principal Stress on Shear Strength of Natural Granite Residual Soil

As a result of weathering, the mechanical behavior of granite residual soil differs from that of sedimentary soil. Although the mechanical properties of granite residual soil have been studied extensively, its strength anisotropy is yet to be established. Previous work has revealed the association between the principal stress direction α and soil shear strength, but little is known about how the intermediate principal stress affects the soil strength. This paper presents the shear-strength parameters under various combinations of α and the intermediate principal stress factor b as obtained through undrained hollow-cylinder torsional shear tests performed on samples of natural granite residual soil. The test results confirmed the considerable effect of b on the shear strength and highlighted the differences between the soil studied here and those studied previously. It was found that b affects the undrained strength and mobilized frictional angle (or ultimate stress ratio) differently, with increasing b leading to lower undrained strength but higher frictional angle. In addition, the degrees to which b affects undrained strength and frictional angle are not the same and depend on the α value at which the soil is sheared. Therefore, two parameters are proposed to quantify that difference. This study extends the understanding of the strength anisotropy of granite residual soil and provides data for soil behavior under various values of b.

Implementation of a constitutive model for anisotropic rocks based on modified Lade failure criterion

The strength anisotropy for inherent anisotropic rocks presents a challenge to simulate considering the influence of intermediate principal stress. Based on the modified Lade failure criterion, a new anisotropic modified Lade criterion combining an empirical equation is established and verified using published experimental datasets of anisotropic rocks. The incremental constitutive model for anisotropic rocks is derived by using finite difference theory. The dynamic link library (DLL) module of the model is obtained by using the VC++ program, and then the model is validated against various laboratory test results. It is concluded that the proposed criterion and derived model can describe the strength anisotropy of inherent anisotropic rocks well.

Experimental study on nonlinear seepage characteristics of coal under true triaxial stress loading

The characteristics of coalbed methane flow are jointly determined by the fracture and stress environment. Previous studies conducted under conventional triaxial or uniaxial stress conditions cannot truly reflect the in situ stress environment and neglected the influence of intermediate principal stress on the nonlinear seepage characteristics of coal. For this study, coal seepage tests were performed under true triaxial stress, allowing the nonlinear seepage characteristics of coal to be analyzed under different principal stresses. This enables the applicability of nonlinear seepage characterization equations and the change laws of relevant parameters to be clarified. The results show that the nonlinear seepage characteristics of coal under true triaxial stress increase as the principal stresses and gas pressure gradient increase. Using the Forchheimer equation for characterization, the nonlinear effect factor, viscous permeability, and inertial permeability gradually decrease with increasing principal stress in all directions. Intermediate principal stress σ2 has the most significant effect on nonlinear effects and inertial permeability, whereas principal stress σ3 has the greatest effect on viscous permeability. Using the Izbash equation for characterization, the fitting coefficients λ, m increase with increasing principal stress. Principal stress σ2 has the most significant effect on m, whereas principal stress σ3 has the greatest influence on λ. Comparative analysis shows that both Forchheimer and Izbash equations accurately characterize the nonlinear seepage characteristics of coal under real triaxial stress. The Forchheimer equation requires more theoretical parameters to measure the degree of nonlinear seepage and thus better describes the evolution process of linear to nonlinear seepage.

Mechanical Analysis of Frozen Wall with Trapezoidal Temperature Field Distribution Based on Unified Strength Theory

In order to study the elastic–plastic stress field distribution of a double-row-pipe frozen wall, the temperature field of the double-row-pipe frozen wall is equivalent to a trapezoidal distribution, and the frozen wall is regarded as an elastic–plastic thick-walled cylinder with functionally gradient material (FGM) characteristics in the radial direction. Considering that the elastic modulus and cohesion of the frozen wall material change linearly with the radius, the elastic–plastic analysis of the frozen wall is carried out based on unified strength theory. The analytical solutions of the elastic–plastic stress field distribution, the elastic ultimate bearing capacity, the plastic ultimate bearing capacity, and the relative radius of the plastic zone of the frozen wall are derived. The analytical solution is calculated based on the engineering case and compared with the numerical solution obtained based on COMSOL. At the same time, the influence of strength theory parameters on the mechanical properties of heterogeneous and homogeneous frozen walls is analyzed. The results show that the analytical solution and the numerical solution are in good agreement, and their accuracy is mutually verified. The external load on the frozen wall of the selected layer is greater than its elastic ultimate bearing capacity and less than its plastic ultimate bearing capacity, which indicates that the frozen wall is in a safe state of stress. The radial stress increases with the increase in the strength theoretical parameter b and the relative radius r, the tangential stress increases with the increase in the strength theoretical parameter b, and first increases and then decreases with the increase in the relative radius r. The larger the strength theoretical parameter b, the smaller the relative radius of the plastic zone of the frozen wall. The strength theoretical parameter b increases from 0 to 1, the elastic ultimate bearing capacity and plastic ultimate bearing capacity of the heterogeneous frozen wall increase by 33.3% and 40.8%, respectively, and the elastic ultimate bearing capacity and plastic ultimate bearing capacity of the homogeneous frozen wall increase by 33.3% and 41.0%, respectively. Therefore, considering the influence of intermediate principal stress, the potential of materials can be fully exerted and the ultimate bearing capacity of frozen walls can be improved. This study can provide theoretical reference for the design and construction of frozen wall.

A Chemical Damage Creep Model of Rock Considering the Influence of Triaxial Stress.

In order to accurately describe the characteristics of each stage of rock creep behavior under the combined action of acid environment and true triaxial stress, based on damage mechanics, chemical damage is connected with elastic modulus; thus, the damage relations considering creep stress damage and chemical damage are obtained. The elastic body, nonlinear Kelvin body, linear Kelvin body, and viscoelastic-plastic body (Mogi-Coulomb) are connected in series, and the actual situation under the action of true triaxial stress is considered at the same time. Therefore, a damage creep constitutive model considering the coupling of rock acid corrosion and true triaxial stress is established. The parameters of the deduced model are identified and verified with the existing experimental research results. The yield surface equation of rock under true triaxial stress is obtained by data fitting, and the influence of intermediate principal stress on the creep model is discussed. The derived constitutive model can accurately describe the characteristics of each stage of true triaxial creep behavior of rock under acid environment.

A Proposed Algorithm to Compute the Stress-Strain Plastic Region and Displacement of a Deep-Lying Tunnel Considering Intermediate Stress and Strain-Softening Behavior

Past studies on deep-lying tunnels under the assumption of plane strain have generally neglected the influence of intermediate principal stress even though this affects the surrounding rocks in the plastic zone. This study proposes a finite difference method to compute the stress strain plastic region and displacement of a tunnel based on the Drucker–Prager (D–P) yield criterion and non-associated flow rule and considering the influences of intermediate principal stress and the strain-softening behavior of surrounding rock. The computed results were compared with those of other well-known solutions and the accuracy and validity of the method were confirmed through some examples. Parameter analysis was conducted to investigate the effects of intermediate principal stress on stress-strain, the plastic region, the ground response curve, and the dilatability of surrounding rock. The results showed that the plastic radius Rp, the residual radius Rd, and radial displacement of surrounding rock first decreased and then increased with increasing intermediate principal stress coefficient b from 0 to 1, with the minimums occurring at b = 0.75. On the contrary, the peak and rate of variation of the dilatancy coefficient first increased and then decreased with increasing b and the dilatancy coefficient Kψ gradually transitioned from nonlinear to linear variation. Meanwhile, the inhibition of the plastic radius and radial displacement gradually weakened with increasing support pressure, whereas the dilatancy coefficient of the tunnel opening gradually increased.

Influence of intermediate principal stress on the strength and deformation behavior of artificial frozen sand

Influence of intermediate principal stress on the strength and deformation behavior of artificial frozen sand

Investigation of the influence of intermediate principal stress on the dynamic responses of rocks subjected to true triaxial stress state

Precisely understanding the dynamic mechanical properties and failure modes of rocks subjected to true triaxial stress state (σ1 > σ2 > σ3, where σ1, σ2, and σ3 are the major principal stress, intermediate principal stress, and minor principal stress, respectively) is essential to the safety of underground engineering. However, in the laboratory, it is difficult to maintain the constant true triaxial stress state of rocks during the dynamic testing process. Herein, a numerical servo triaxial Hopkinson bar (NSTHB) was developed to study the dynamic responses of rocks confronted with a true triaxial stress state, in which lateral stresses can maintain constant. The results indicate that the dynamic strength and elastic modulus of rocks increase with the rise of intermediate principal stress σ2, while the dynamic elastic modulus is independent of the dynamic strain rate. Simulated acoustic emission distributions indicate that the intermediate principal stress σ2 dramatically affects dynamic failure modes of triaxial confined rocks. As σ2 increases, the failure pattern switches from a single diagonal shear zone into two parallel shear zones with a small slant. Moreover, a recent triaxial Hopkinson bar experimental system using three bar pairs is also numerically established, and the measuring discrepancies are identified between the two numerical bar systems. The proposed NSTHB system provides a controllable tool for studying the dynamic triaxial behavior of rocks.

Axial Compression Behavior of Circular Concrete-Filled High-Strength Thin-Walled Steel Tubular Columns with Out-of-Code D/t Ratios

This paper systematically investigated the axial compression behavior of circular concrete-filled high-strength thin-walled steel tubular (CFHTST) columns with out-of-code diameter-to-thickness (D/t) ratios. The axial compression test was first conducted to examine the failure mode, load-displacement curves, and composite mechanism effect. The finite element (FE) model was thereafter established to perform full-range analysis on the load versus displacement curve as well as the interaction behavior, where the parametric study was performed to investigate the influences of the material strengths and geometric sizes. Subsequently, the applicability of typical design methods was evaluated, and a revised equation for determining strain εscy corresponding to ultimate strength was established to assess the plastic deformation capacity of CFHTST columns. Finally, a theoretical model for calculating axial bearing capacity was derived based on unified twin-shear strength theory by considering the influence of intermediate principal stress. The research results indicate that a relatively high confine effect can be guaranteed for CFHTST columns under out-of-code D/t ratios, given that the ratio Nu/Nnom between the measured capacity (Nu) and nominal cross-sectional capacity (Nnom) mainly distributes within 1.179∼1.292; the full-range analysis reflects that the axial load-deformation curve can be distinguished by four various loading stages; the scope b = 0.3∼0.55 of intermediate stress coefficient is generally suggested for predicting axial strength of circular CFST columns within an error of ±5%. The abovementioned study can provide the meaningful design reference for the analysis and application of CFHTST columns.

Influence of Intermediate Principal Stress on the Strainburst Characteristics of Beishan Granite with Consideration of End Effect

Influence of Intermediate Principal Stress on the Strainburst Characteristics of Beishan Granite with Consideration of End Effect

The Analysis of Anchoring Mechanism of Rock Slope in Two Layers Based on the Nonlinear Twin-Shear Strength Criterion

The nonlinear strength criterion is introduced into the paper firstly, and then the geometric anchoring characteristic model of rock slope separated from two layers according to rock type with the fracture surface of log-spiral curve considering nonlinear twin-shear criterion subjected to seismic loads is established. Finally, some correlated influential parameters are analyzed, and the conclusions are drawn, showing that the intermediate principal stress has great influence on the total anchoring force of bolt P, so when different criteria are selected, the influence of intermediate principal stress should not be omitted. The effects of thickness ratio h1/h2 on total anchoring force increase gradually with the increase of inclination angle ϕ . The total anchoring force P decreases gradually with the increase of inclination angle ϕ and surcharge load q. The total anchoring force increases gradually with the increase of horizontal seismic acceleration coefficients kh and geometric coefficients mi and GSI.

Development of a poly-axial platen for testing true-triaxial behavior of rocks

Mining at greater depths can lead to stress-induced failure, especially in areas of high horizontal in situ stress. The induced stresses around the opening are known to be in a poly-axial stress state where, σ1 ≠ σ2 ≠ σ3 with special case of σ3 = 0 and σ1, σ2 ≠ 0 at its boundary, where σ1, σ2, σ3 are major, intermediate, minor principal stress, respectively. The conventional triaxial testing does not represent the actual in situ strength of the rock in regions of high horizontal stress, as it ignores the influence of intermediate principal stress (σ2). The typical poly-axial testing (biaxial and true-triaxial tests) of intact rock mostly requires sophisticated and expensive loading systems. This study investigated the mechanical behavior of intact rock under a poly-axial stress state using a simple and cost-effective design. The apparatus consists of a biaxial frame and a confining device. The biaxial frame has two platens that apply equal stress in both directions (σ1 = σ2) on a 50.8 mm cubical specimen when placed inside the uniaxial loading device. The confining device performed separate biaxial tests under constant intermediate principal stress (σ2 = constant) and true-triaxial tests when used along with the biaxial frame. This study then compared the failure modes and peak strength of Berea sandstone specimens with other biaxial–triaxial devices to validate the design of the poly-axial apparatus. We also performed uniaxial tests on both standard cylindrical samples and prismatic specimens of different slenderness ratios. These tests provided a complete understanding of the failure mode transition from standard uniaxial compressive tests to triaxial stress conditions on cubical specimens. Additionally, this study determined best-fitted strength envelopes for biaxial and triaxial stress state. Based on regression analysis, we found a quadratic polynomial to be a good fit to biaxial strength envelope. For the true-triaxial strength envelope, we found the three-dimensional (3D) failure criterion to be a good fit with R2 of 0.964.

Analysis on Loose Circle of Surrounding Rock of Large Deformation Soft-Rock Tunnel

With the rapid development of tunnel construction in China, deep buried and long tunnel projects are emerging in areas with complex engineering geological conditions and harsh environment, and thus large deformation of tunnels under conditions of high in situ stress and soft rock becomes increasingly prominent and endangers engineering safety. Therefore, it is of great significance to control the deformation and improve the stability of surrounding rock by analyzing the thickness and distribution law of loose circle according to the unique mechanical properties and failure mechanism of surrounding rock of large deformation soft-rock tunnel. Based on unified strength theory, this paper deduces the radius calculation formula of the loose circle by considering the influence of intermediate principal stress. Furthermore, the theoretical calculations and field tests of the loose circle in the typical sections of grade II and III deformation of Yuntunbao tunnel are carried out, and the thickness and distribution law of loose circle of surrounding rock of large deformation soft-rock tunnel is revealed. The results show that the formula based on the unified strength criterion is applicable for a large deformation tunnel in soft rock.

Experimental Study on Influence of Intermediate Principal Stress on the Permeability of Sandstone

In engineering, it is considerably important to understand the evolution process of sandstone deformation and permeability under complex stress conditions. Although numerous scholars have reported on sandstone permeability, many of their studies are only based on uniaxial or conventional triaxial stress conditions. In practical engineering, in situ stress evidently indicates three-dimensional anisotropy. In recent years, many scholars have performed experimental studies on rock permeability under true triaxial stress. There are, however, few investigations related to the influence of intermediate principal stress and intermediate principal stress coefficient on sandstone permeability; moreover, the mechanism is unclear. In this study, the permeability of sandstone under true triaxial stress conditions is measured using a true triaxial apparatus. The results show that the intermediate principal stress has significant effects on permeability and deformation of sandstone sample. Under different principal stress conditions, the permeability is observed to decrease with the increase of the principal stress. With increasing intermediate principal stress coefficient b (from 0 to 1), the major principal strain and the minor principal strain always compressed and finally decreased by 27.31 and 36.96%, while the intermediate principal strain finally changes from expansion to compression (from − 0.045 to 0.255%). Also the normalized permeability loss increased from 9.57 to 16.59%. In addition, by fitting the experimental data with several permeability models, it was found that a true triaxial permeability model can well describe the changes in sandstone permeability. Based on the fitting parameters, the influence of intermediate principal stress and its coefficient on the stress sensitivity of sandstone was analyzed.

Analysis of Three-Dimensional Damage Constitutive Model of Frozen Sand Based on the Influence of Intermediate Principal Stress and Temperature

To study the mechanical properties of frozen soil, it is necessary to understand the damage characteristics of frozen soil. Four types of three-dimensional indoor tests of frozen sand were carried out at −5°C, −10°C, and −15°C to study the mechanical damage properties. These include different stress path tests with the principal stress coefficients of 0, 0.25, 0.5, and 0.75 while analyzing the entire failure process. First, the three-dimensional compression test of frozen sand was studied to analyze the influence of temperature and intermediate principal stress coefficient on the large principal stress of frozen soil. The damage cost of frozen sand under the influence of different temperatures and intermediate principal stress coefficients was also established. Second, using the characteristics of discreteness and randomness of the distribution of the microelements inside the frozen soil and assuming that the failure of the microelement of the frozen soil obeys the Weibull distribution, the Drucker–Prager strength criterion was used as the statistical distribution variable of the microelement of the frozen soil based on the strain equivalence hypothesis, statistical theory, and continuous damage mechanics. This allows for a constitutive model of frozen sand damage under the three-dimensional stress state to be established. Finally, the model parameter values through low-temperature three-dimensional test data were able to be determined. This model allows for the physical meaning of Weibull distribution parameters F0 and m to be analyzed, and the distribution parameters with temperature and intermediate principal stress coefficient can be modified to obtain a modified frozen sand damage constitutive model. The results show that the modified damage constitutive model can simulate the entire process curve of the large principal stress-strain of frozen sand. It shows that the large principal stress of frozen sand increases with the increase of temperature and intermediate principal stress coefficient. Concurrently, the frozen sand damage constitutive model proposed in this paper can describe the deformation behavior of frozen soil under different temperature and stress paths and can be adapted to various other sediment types.