The convergence confinement methods are solutions employed to estimate convergence in circular tunnels. They are mostly based on constitutive equations governed by the Mohr-Coulomb and Hoek-Brown yield criteria. Howev...The convergence confinement methods are solutions employed to estimate convergence in circular tunnels. They are mostly based on constitutive equations governed by the Mohr-Coulomb and Hoek-Brown yield criteria. However, the solutions based on these criteria neglect the intermediate principal stress confining effect on the ground reaction estimation. Therefore, in this paper, a Drucker-Prager yield criterion governed solution integrated with the Lode angle parameter is employed. It considers the intermediate principal stress influence and the critical effect of the parameter on failure characterization.Subsequently, it is verified with results attained from numerical simulations which consider an elasticperfectly plastic constitutive law with a non-associative flow rule within FLAC3D. It was drawn from the results that the ground reaction and plastic evolution are influenced by the confining stress.Furthermore, considering a suitable yield criterion leads to realistic convergence and plastic evolution estimation. The circumscribed DP criterion governed solution with Lode angle parameter value(0.8) is considered appropriate for the realistic ground reaction estimation in the three-dimensional(3D) stress state rock mass. It estimates approximately 3.4% of tunnel convergence as compared to the classic solutions(5%) and plastic radius estimated to be approximately 2.45 m compared to 2.84 m.展开更多
To investigate the deformation mechanisms of rock under hydrostatic stress, destructive experiments were conducted on sandstone under different levels of hydrostatic stress and stress Lode angles. The results reveal t...To investigate the deformation mechanisms of rock under hydrostatic stress, destructive experiments were conducted on sandstone under different levels of hydrostatic stress and stress Lode angles. The results reveal that the shape of the strength envelope on the π plane gradually changes from the shape of the Lade criterion to the shape of the Drucker-Prage criterion with an increase in hydrostatic stress.Normally, there exists a deviation between the strain and stress paths for porous rocks on the π plane,and the deviation decreases with an increase in stress Lode angle and hydrostatic stress. A rock failure hypothesis based on the rock porous structure was proposed to investigate the reasons for the abovementioned phenomena. It was found that the shear expansion in the minimum principal stress direction is the dominant factor affecting the Lode angle effect(LAE);the magnitude of the hydrostatic stress induces the variation of the porous structure and influences the shear expansion. Therefore, the hydrostatic stress state affects the LAE. The failure hypothesis proposed in this paper can clarify the hydrostatic stress effect, LAE, and the variation of the rock strength envelope shape.展开更多
A novel fractional elastoplastic constitutive model is proposed to accurately characterize the deformation of sandstone under true-triaxial stress states.This model is founded on the yield function and the fractional ...A novel fractional elastoplastic constitutive model is proposed to accurately characterize the deformation of sandstone under true-triaxial stress states.This model is founded on the yield function and the fractional flow rule.The yield function includes parameters that govern the evolution of yield surface,enabling an accurate description of three-dimensional stress states.The direction of plastic flow is governed by the two different fractional orders,which are functions of the plastic internal variable.Additionally,a detailed process is proposed for identifying the yield function parameters and fractional orders.Subsequently,the relationship between the fractional order and the direction of plastic flow in the meridian and deviatoric planes is examined,characterized by the dilation angle and the plastic deflection angle,respectively.The non-orthogonal flow rule,also referred to as the fractional flow rule,allows for a border range of plastic deflection and dilation angles compared to the orthogonal flow rule,thereby significantly enhancing its applicability.The validity and accuracy of proposed model are verified by comparing the analytical solution of the constitutive model with the experimental data.A comparison between the non-orthogonal flow rule and orthogonal flow rule is conducted in both the deviatoric and meridian planes.The further comparison of the stress-strain curves for the non-orthogonal and orthogonal flow rules demonstrates the superiority of the fractional constitutive model.展开更多
Lightweight aggregate concrete cube specimens (100 mm×100 mm×100 mm) and plate specimens (100 mm×100 mm×50 mm) were tested under biaxial compression-compression (CC) and compression-tension (CT) lo...Lightweight aggregate concrete cube specimens (100 mm×100 mm×100 mm) and plate specimens (100 mm×100 mm×50 mm) were tested under biaxial compression-compression (CC) and compression-tension (CT) load combinations. For comparison, normal concrete plate specimens (100 mm×100 mm×50 mm) were tested under the same load combinations. Based on the test results, a two-level strength criterion of lightweight aggregate concrete in both octahedral stress coordinate and principal stress coordinate was suggested. The lightweight aggregate concrete cube specimens (100 mm×100 mm×100 mm) were then tested under triaxial compression-compression-compression (CCC) load combination with corresponding tests on normal concrete cube specimens (100 mm×100 mm×100 mm). The effect of intermediate principal stress on triaxial compressive strength is further examined. A "plastic flow plateau" area was apparent in principal compressive stress-strain relationships of lightweight aggregate concrete but not in normal concrete. A quadratic formula was suggested for the expression of strength criterion under triaxial compression.展开更多
A reasonable strength criterion should reflect the hydrostatic pressure effect, minimum principal stress effect,and intermediate principal stress effect. The former two effects can be described by the meridian curves,...A reasonable strength criterion should reflect the hydrostatic pressure effect, minimum principal stress effect,and intermediate principal stress effect. The former two effects can be described by the meridian curves, and the last one mainly depends on the Lode angle dependence function. Among three conventional strength criteria, i.e.Mohr–Coulomb(MC), Hoek–Brown(HB), and Exponent(EP) criteria, the difference between generalized compression and extension strength of EP criterion experience a firstly increase then decrease process, and tends to be zero when hydrostatic pressure is big enough. This is in accordance with intrinsic rock strength characterization. Moreover, the critical hydrostatic pressure Icorresponding to the maximum difference of between generalized compression and extension strength can be easily adjusted by minimum principal stress influence parameter K. So, the exponent function is a more reasonable meridian curves, which well reflects the hydrostatic pressure effect and is employed to describe the generalized compression and extension strength.Meanwhile, three Lode angle dependence functions of L,L, and L, which unconditionally satisfy the convexity and differential requirements, are employed to represent the intermediate principal stress effect. Realizing the actual strength surface should be located between the generalized compression and extension surface, new true-triaxial criteria are proposed by combining the two states of EP criterion by Lode angle dependence function with a same lode angle. The proposed new true-triaxial criteria have the same strength parameters as EP criterion. Finally, 14 groups of triaxial test data are employed to validate the proposed criteria. The results show that the three new true-triaxial exponent criteria,especially the Exponent Willam-Warnke criterion(EPWW)criterion, give much lower misfits, which illustrates that the EP criterion and Lhave more reasonable meridian and deviatoric function form, respectively. The proposed new true-triaxial strength criteria can provide theoretical foundation for stability analysis and optimization of support design of rock engineering.展开更多
Deep rocks are typically under a true-triaxial stress state. The strength of deep rock is thus dictated by both the direction and magnitude of principal stresses. The formulation of three-dimensional strength criterio...Deep rocks are typically under a true-triaxial stress state. The strength of deep rock is thus dictated by both the direction and magnitude of principal stresses. The formulation of three-dimensional strength criterion for rocks is thus essential for evaluating the stability of deep-buried rock structures. With advancements in true-triaxial experimental instrumentation, several three-dimensional strength criteria have been proposed, necessitating a systematic review and consolidation of these criteria. This review first introduces the concept of three-dimensional stress state. Subsequently, classical strength criteria such as the Mohr-Coulomb Criterion, the Hoek-Brown criterion, and the Drucker-Prager criterion are reiterated. However, these traditional strength criteria inadequately describe rock strength under true-triaxial stress conditions. To better capture the influence of intermediate principal stress, hydrostatic pressure, and Lode angle on rock strength, researchers have revised classical strength criteria. Modified strength criteria and unified strength criteria based on classical formulations are also introduced. Notably, the unified strength criterion incorporates multiple single criteria and demonstrates wider applicability. Furthermore, beyond macroscopic strength criteria, this review also discusses micromechanical strength criteria, where the stress state and crack propagation govern rock mechanical behaviors. This comprehensive review may serve as a valuable source for addressing the problem of deep rock strength in energy extraction and other rock engineering applications.展开更多
基金The author gratefully acknowledges the financial support and affiliation from the University of Adelaide.
文摘The convergence confinement methods are solutions employed to estimate convergence in circular tunnels. They are mostly based on constitutive equations governed by the Mohr-Coulomb and Hoek-Brown yield criteria. However, the solutions based on these criteria neglect the intermediate principal stress confining effect on the ground reaction estimation. Therefore, in this paper, a Drucker-Prager yield criterion governed solution integrated with the Lode angle parameter is employed. It considers the intermediate principal stress influence and the critical effect of the parameter on failure characterization.Subsequently, it is verified with results attained from numerical simulations which consider an elasticperfectly plastic constitutive law with a non-associative flow rule within FLAC3D. It was drawn from the results that the ground reaction and plastic evolution are influenced by the confining stress.Furthermore, considering a suitable yield criterion leads to realistic convergence and plastic evolution estimation. The circumscribed DP criterion governed solution with Lode angle parameter value(0.8) is considered appropriate for the realistic ground reaction estimation in the three-dimensional(3D) stress state rock mass. It estimates approximately 3.4% of tunnel convergence as compared to the classic solutions(5%) and plastic radius estimated to be approximately 2.45 m compared to 2.84 m.
文摘To investigate the deformation mechanisms of rock under hydrostatic stress, destructive experiments were conducted on sandstone under different levels of hydrostatic stress and stress Lode angles. The results reveal that the shape of the strength envelope on the π plane gradually changes from the shape of the Lade criterion to the shape of the Drucker-Prage criterion with an increase in hydrostatic stress.Normally, there exists a deviation between the strain and stress paths for porous rocks on the π plane,and the deviation decreases with an increase in stress Lode angle and hydrostatic stress. A rock failure hypothesis based on the rock porous structure was proposed to investigate the reasons for the abovementioned phenomena. It was found that the shear expansion in the minimum principal stress direction is the dominant factor affecting the Lode angle effect(LAE);the magnitude of the hydrostatic stress induces the variation of the porous structure and influences the shear expansion. Therefore, the hydrostatic stress state affects the LAE. The failure hypothesis proposed in this paper can clarify the hydrostatic stress effect, LAE, and the variation of the rock strength envelope shape.
基金sponsored by the National Natural Science Foundation of China(Grant No.42141010).
文摘A novel fractional elastoplastic constitutive model is proposed to accurately characterize the deformation of sandstone under true-triaxial stress states.This model is founded on the yield function and the fractional flow rule.The yield function includes parameters that govern the evolution of yield surface,enabling an accurate description of three-dimensional stress states.The direction of plastic flow is governed by the two different fractional orders,which are functions of the plastic internal variable.Additionally,a detailed process is proposed for identifying the yield function parameters and fractional orders.Subsequently,the relationship between the fractional order and the direction of plastic flow in the meridian and deviatoric planes is examined,characterized by the dilation angle and the plastic deflection angle,respectively.The non-orthogonal flow rule,also referred to as the fractional flow rule,allows for a border range of plastic deflection and dilation angles compared to the orthogonal flow rule,thereby significantly enhancing its applicability.The validity and accuracy of proposed model are verified by comparing the analytical solution of the constitutive model with the experimental data.A comparison between the non-orthogonal flow rule and orthogonal flow rule is conducted in both the deviatoric and meridian planes.The further comparison of the stress-strain curves for the non-orthogonal and orthogonal flow rules demonstrates the superiority of the fractional constitutive model.
基金Project (No. 50679007) supported by the National Natural Science Foundation of China
文摘Lightweight aggregate concrete cube specimens (100 mm×100 mm×100 mm) and plate specimens (100 mm×100 mm×50 mm) were tested under biaxial compression-compression (CC) and compression-tension (CT) load combinations. For comparison, normal concrete plate specimens (100 mm×100 mm×50 mm) were tested under the same load combinations. Based on the test results, a two-level strength criterion of lightweight aggregate concrete in both octahedral stress coordinate and principal stress coordinate was suggested. The lightweight aggregate concrete cube specimens (100 mm×100 mm×100 mm) were then tested under triaxial compression-compression-compression (CCC) load combination with corresponding tests on normal concrete cube specimens (100 mm×100 mm×100 mm). The effect of intermediate principal stress on triaxial compressive strength is further examined. A "plastic flow plateau" area was apparent in principal compressive stress-strain relationships of lightweight aggregate concrete but not in normal concrete. A quadratic formula was suggested for the expression of strength criterion under triaxial compression.
基金supported by the National Natural Science Foundation of China (Grants 51204168, 51579239)the China Postdoctoral Science Foundation funded project (Grants 2013M531424, 2015M580493)+1 种基金the National Basic Research 973 Program of China (Grants 2013CB036003, 2014CB046306)the Fundamental Research Funds for the Central Universities (Grant 2012QNB23)
文摘A reasonable strength criterion should reflect the hydrostatic pressure effect, minimum principal stress effect,and intermediate principal stress effect. The former two effects can be described by the meridian curves, and the last one mainly depends on the Lode angle dependence function. Among three conventional strength criteria, i.e.Mohr–Coulomb(MC), Hoek–Brown(HB), and Exponent(EP) criteria, the difference between generalized compression and extension strength of EP criterion experience a firstly increase then decrease process, and tends to be zero when hydrostatic pressure is big enough. This is in accordance with intrinsic rock strength characterization. Moreover, the critical hydrostatic pressure Icorresponding to the maximum difference of between generalized compression and extension strength can be easily adjusted by minimum principal stress influence parameter K. So, the exponent function is a more reasonable meridian curves, which well reflects the hydrostatic pressure effect and is employed to describe the generalized compression and extension strength.Meanwhile, three Lode angle dependence functions of L,L, and L, which unconditionally satisfy the convexity and differential requirements, are employed to represent the intermediate principal stress effect. Realizing the actual strength surface should be located between the generalized compression and extension surface, new true-triaxial criteria are proposed by combining the two states of EP criterion by Lode angle dependence function with a same lode angle. The proposed new true-triaxial criteria have the same strength parameters as EP criterion. Finally, 14 groups of triaxial test data are employed to validate the proposed criteria. The results show that the three new true-triaxial exponent criteria,especially the Exponent Willam-Warnke criterion(EPWW)criterion, give much lower misfits, which illustrates that the EP criterion and Lhave more reasonable meridian and deviatoric function form, respectively. The proposed new true-triaxial strength criteria can provide theoretical foundation for stability analysis and optimization of support design of rock engineering.
基金sponsored by the National Natural Science Foundation of China under Grants#42141010 and CNPC Innovation Fund(#2022DQ02-0610)support by the Fundamental Research Funds for the Central Universities(CUGB 2-9-2022-011).
文摘Deep rocks are typically under a true-triaxial stress state. The strength of deep rock is thus dictated by both the direction and magnitude of principal stresses. The formulation of three-dimensional strength criterion for rocks is thus essential for evaluating the stability of deep-buried rock structures. With advancements in true-triaxial experimental instrumentation, several three-dimensional strength criteria have been proposed, necessitating a systematic review and consolidation of these criteria. This review first introduces the concept of three-dimensional stress state. Subsequently, classical strength criteria such as the Mohr-Coulomb Criterion, the Hoek-Brown criterion, and the Drucker-Prager criterion are reiterated. However, these traditional strength criteria inadequately describe rock strength under true-triaxial stress conditions. To better capture the influence of intermediate principal stress, hydrostatic pressure, and Lode angle on rock strength, researchers have revised classical strength criteria. Modified strength criteria and unified strength criteria based on classical formulations are also introduced. Notably, the unified strength criterion incorporates multiple single criteria and demonstrates wider applicability. Furthermore, beyond macroscopic strength criteria, this review also discusses micromechanical strength criteria, where the stress state and crack propagation govern rock mechanical behaviors. This comprehensive review may serve as a valuable source for addressing the problem of deep rock strength in energy extraction and other rock engineering applications.
