When the slope is in critical limit equilibrium(LE) state, the strength parameters have different contribution to each other on maintaining slope stability. That is to say that the strength parameters are not simultan...When the slope is in critical limit equilibrium(LE) state, the strength parameters have different contribution to each other on maintaining slope stability. That is to say that the strength parameters are not simultaneously reduced. Hence, the LE stress method is established to analyze the slope stability by employing the double strengthreduction(DSR) technique in this work. For calculation model of slope stability under the DSR technique, the general nonlinear Mohr–Coulomb(M–C) criterion is used to describe the shear failure of slope. Meanwhile, the average and polar diameter methods via the DSR technique are both adopted to calculate the comprehensive factor of safety(FOS) of slope. To extend the application of the polar diameter method, the original method is improved in the proposed method. After comparison and analysis on some slope examples, the proposed method's feasibility is verified. Thereafter, the stability charts of slope suitable for engineering application are drawn. Moreover, the studies show that:(1) the average method yields similar results as that of the polardiameter method;(2) compared with the traditional uniform strength-reduction(USR) technique, the slope stability obtained using the DSR techniquetends to be more unsafe; and(3) for a slope in the critical LE state, the strength parameter φ, i.e., internal friction angle, has greater contribution on the slope stability than the strength parameters c, i.e., cohesion.展开更多
Dynamic strength parameters are extensively used in mining engineering and rock mechanics.However,there are no widely accepted dynamic failure models for rocks.In this study,the dynamic punching shear strength,uniaxia...Dynamic strength parameters are extensively used in mining engineering and rock mechanics.However,there are no widely accepted dynamic failure models for rocks.In this study,the dynamic punching shear strength,uniaxial compressive strength(UCS) and tensile strength of fine-grained Fangshan marble(FM)are first measured by using a split Hopkinson pressure bar(SHPB) system.The pulse-shaping technique is then implemented to maintain the dynamic force balance in SHPB tests.Experimental results show that the dynamic punching shear strength,UCS and tensile strength increase with the loading rate.A recently developed dynamic Mohr-Coulomb theory is then used to interpret the testing data.In this model,the angle of internal friction φ is assumed to be independent of loading rate and is obtained using the static strength values.According to the dynamic Mohr-Coulomb theory,the dynamic UCS and the dynamic tensile strength are predicted from the dynamic punching shear strength.Furthermore,based on this dynamic theory,the dynamic UCS is predicted from the dynamic tensile strength.The consistency between the predicted and measured dynamic strengths demonstrates that the dynamic Mohr-Coulomb theory is applicable to FM.展开更多
In this paper, the Mohr-Coulomb shear strength criterion is modified by mobilising the cohesion and internal friction angle with normal stress, in order to capture the nonlinearity and critical state concept for intac...In this paper, the Mohr-Coulomb shear strength criterion is modified by mobilising the cohesion and internal friction angle with normal stress, in order to capture the nonlinearity and critical state concept for intact rocks reported in the literature. The mathematical expression for the strength is the same as the classical form, but the terms of cohesion and internal friction angle depend on the normal stress now,leading to a nonlinear relationship between the strength and normal stress. It covers both the tension and compression regions with different expressions for cohesion and internal friction angle. The strengths from the two regions join continuously at the transition of zero normal stress. The part in the compression region approximately satisfies the conditions of critical state, where the maximum shear strength is reached. Due to the nonlinearity, the classical simple relationship between the parameters of cohesion, internal friction angle and uniaxial compressive strength from the linear Mohr-Coulomb criterion does not hold anymore. The equation for determining one of the three parameters in terms of the other two is supplied. This equation is nonlinear and thus a nonlinear equation solver is needed. For simplicity, the classical linear relationship is used as a local approximation. The approximate modified Mohr-Coulomb criterion has been implemented in a fracture mechanics based numerical code FRACOD,and an example case of deep tunnel failure is presented to demonstrate the difference between the original and modified Mohr-Coulomb criteria. It is shown that the nonlinear modified Mohr-Coulomb criterion predicts somewhat deeper and more intensive fracturing regions in the surrounding rock mass than the original linear Mohr-Coulomb criterion. A more comprehensive piecewise nonlinear shear strength criterion is also included in Appendix B for those readers who are interested. It covers the tensile, compressive, brittle-ductile behaviour transition and the critical state, and gives smooth transitions.展开更多
The paper presents an experimental investigation on the strength behaviour of natural rock subjected to polyaxial state of stress. The polyaxial tests were conducted on cubical specimens of sandstone obtained from the...The paper presents an experimental investigation on the strength behaviour of natural rock subjected to polyaxial state of stress. The polyaxial tests were conducted on cubical specimens of sandstone obtained from the Shivpuri district in Madhya Pradesh state of India, The specimens having nominal dimensions of100 mm x 100 mm x 100 mm were tested using a polyaxial testing machine. Twenty-five combinations of intermediate and minor principal stresses were applied and the specimens were loaded till failure occurs. It was observed that the intermediate principal stress has a substantial effect on the strength of the Shivpuri sandstone. A database of rock strength under various combinations of σ_2 and σ_3 was obtained for the Shivpuri sandstone. The database was used to study the predictability of five most commonly used strength criterion. Root mean square error(RMSE), average absolute relative error percentage(AAREP) and coefficient of accordance(COA) were used as indices for the measure of goodness of fit. It was observed that the least error in the prediction was shown by modified Mohr Coulomb criterion followed by modified Weibols and Cook criterion. A probability analysis of the error in prediction was also done.展开更多
The triaxial strength of twenty rockmass types was predicted using two non-linear triaxial strength criteria for rockmass i.e. Modified Mohr-Coulomb(MMC) criterion and Generalized Hoek-Brown(GHB)criterion. Four differ...The triaxial strength of twenty rockmass types was predicted using two non-linear triaxial strength criteria for rockmass i.e. Modified Mohr-Coulomb(MMC) criterion and Generalized Hoek-Brown(GHB)criterion. Four different rockmass classification systems were used for the calculation of MMC criterion parameters while only GSI classification system has been used for calculation of GHB parameters. The representative value of the uniaxial compressive strength and elastic modulus of rockmass have been estimated using probabilistic approach. A hypothetical case of an unsupported tunnel has been analyzed considering both MMC and GHB criteria. The analysis was done using the convergence-confinement method with two different approaches. The first approach predicts the tunnel response using GHB criterion directly. The second approach predicts the tunnel response using equivalent Mohr-Coulomb parameters obtained by linearization of triaxial data points obtained from MMC and GHB criteria. The tunnel response has been estimated in terms of radius of plastic zone, tunnel convergence and tunnel convergence strain. For very poor rockmasses the tunnel response predicted by MMC criterion is less than that predicted by GHB criterion. For poor and fair rockmass, the tunnel response estimated considering both the criteria are comparable except for few cases. Squeezing condition in rockmass has been also evaluated.展开更多
Based on the nonlinear Mohr-Coulomb failure criterion and the associated flow rules,the three-dimensional(3-D)axisymmetric failure mechanism of shallow horizontal circular plate anchors that are subjected to the ultim...Based on the nonlinear Mohr-Coulomb failure criterion and the associated flow rules,the three-dimensional(3-D)axisymmetric failure mechanism of shallow horizontal circular plate anchors that are subjected to the ultimate pullout capacity(UPC)is determined.A derivative function of the projection function for projecting the 3-D axisymmetric failure surface on plane is deduced using the variation theory.By using difference principle,the primitive function of failure surface satisfying boundary condition and numerical solution to its corresponding ultimate pullout capacity function are obtained.The influences of nonlinear Mohr-Coulomb parameters on UPC and failure mechanism are studied.The result shows that UPC decreases with dimensionless parameter m and uniaxial tensile strength increases but increases when depth and radius of plate anchor,surface overload,initial cohesion,geomaterial density and friction angle increase.The failure surface is similar to a symmetrical spatial funnel,and its shape is mainly determined by dimensionless parameter m;the surface damage range expands with the increase of radius and depth of the plate anchor as well as initial cohesion but decreases with the increase of dimensionless parameter m and uniaxial tensile strength as well as geomaterial density.As the dimensionless parameter m=2.0,the numerical solution of UPC based on the difference principle is proved to be feasible and effective through the comparison with the exact solution.In addition,the comparison between solutions of UPC computed by variation method and those computed by upper bound method indicate that variation method outperforms upper bound method.展开更多
With the increase of mining depth of mineral resources,the rock mass stress state is being more and more complex.The rock mass show different features,namely,with the increase of hydrostatic pressure,rock mass failure...With the increase of mining depth of mineral resources,the rock mass stress state is being more and more complex.The rock mass show different features,namely,with the increase of hydrostatic pressure,rock mass failure mode turns from brittle tension failure to structure ductile failure and its limit strength also increases.The restriction of minimal principal stress on the initiation and development of microcrack and the change of micro-unit stress state by the intermediate principal stress play a decisive role in the increase of rock mass limit strength.Based on the rock mass failure behavior law under complex stress state and the σ2-dependence on the rock mass strength,we proposed a Modified Mohr-Coulomb(M-MC) strength criterion which is smooth and convex.Finally,the M-MC criterion is validated by multiaxial test data of eight kinds of rock mass.We also compared the fitting results with Mohr-Coulomb criterion(MC).It shows that the new criterion fits the test data better than the Mohr-Coulomb criterion.So the M-MC strength criterion well reveals the rock mass bearing behavior and can be widely used in the rock mass strength analysis.The results can provide theoretical foundations for stability analysis and reinforcement design of complex underground engineering.展开更多
基金funded by the National Natural Science Foundation of China (Grant No. 51608541)the Postdoctoral Science Foundation of China (Grant No. 2015M580702)the Guizhou Provincial Department of Transportation of China (Grant No. 2014122006)
文摘When the slope is in critical limit equilibrium(LE) state, the strength parameters have different contribution to each other on maintaining slope stability. That is to say that the strength parameters are not simultaneously reduced. Hence, the LE stress method is established to analyze the slope stability by employing the double strengthreduction(DSR) technique in this work. For calculation model of slope stability under the DSR technique, the general nonlinear Mohr–Coulomb(M–C) criterion is used to describe the shear failure of slope. Meanwhile, the average and polar diameter methods via the DSR technique are both adopted to calculate the comprehensive factor of safety(FOS) of slope. To extend the application of the polar diameter method, the original method is improved in the proposed method. After comparison and analysis on some slope examples, the proposed method's feasibility is verified. Thereafter, the stability charts of slope suitable for engineering application are drawn. Moreover, the studies show that:(1) the average method yields similar results as that of the polardiameter method;(2) compared with the traditional uniform strength-reduction(USR) technique, the slope stability obtained using the DSR techniquetends to be more unsafe; and(3) for a slope in the critical LE state, the strength parameter φ, i.e., internal friction angle, has greater contribution on the slope stability than the strength parameters c, i.e., cohesion.
基金provided by the Natural Sciences and Engineering Research Council of Canada(NSERC)through the Discovery Grant No.72031326
文摘Dynamic strength parameters are extensively used in mining engineering and rock mechanics.However,there are no widely accepted dynamic failure models for rocks.In this study,the dynamic punching shear strength,uniaxial compressive strength(UCS) and tensile strength of fine-grained Fangshan marble(FM)are first measured by using a split Hopkinson pressure bar(SHPB) system.The pulse-shaping technique is then implemented to maintain the dynamic force balance in SHPB tests.Experimental results show that the dynamic punching shear strength,UCS and tensile strength increase with the loading rate.A recently developed dynamic Mohr-Coulomb theory is then used to interpret the testing data.In this model,the angle of internal friction φ is assumed to be independent of loading rate and is obtained using the static strength values.According to the dynamic Mohr-Coulomb theory,the dynamic UCS and the dynamic tensile strength are predicted from the dynamic punching shear strength.Furthermore,based on this dynamic theory,the dynamic UCS is predicted from the dynamic tensile strength.The consistency between the predicted and measured dynamic strengths demonstrates that the dynamic Mohr-Coulomb theory is applicable to FM.
基金the International Collaboration Project on Coupled Fracture Mechanics Modelling(project team consisting of CSIRO,SDUST,Posiva,KIGAM,KICT,CAS-IRSM,DUT/Mechsoft,SNU,LBNL,ETH,Aalto Uni.,GFZ and TYUT)Taishan Scholar Talent Team Support Plan for Advantaged&Unique Discipline Areas,Shandong Province
文摘In this paper, the Mohr-Coulomb shear strength criterion is modified by mobilising the cohesion and internal friction angle with normal stress, in order to capture the nonlinearity and critical state concept for intact rocks reported in the literature. The mathematical expression for the strength is the same as the classical form, but the terms of cohesion and internal friction angle depend on the normal stress now,leading to a nonlinear relationship between the strength and normal stress. It covers both the tension and compression regions with different expressions for cohesion and internal friction angle. The strengths from the two regions join continuously at the transition of zero normal stress. The part in the compression region approximately satisfies the conditions of critical state, where the maximum shear strength is reached. Due to the nonlinearity, the classical simple relationship between the parameters of cohesion, internal friction angle and uniaxial compressive strength from the linear Mohr-Coulomb criterion does not hold anymore. The equation for determining one of the three parameters in terms of the other two is supplied. This equation is nonlinear and thus a nonlinear equation solver is needed. For simplicity, the classical linear relationship is used as a local approximation. The approximate modified Mohr-Coulomb criterion has been implemented in a fracture mechanics based numerical code FRACOD,and an example case of deep tunnel failure is presented to demonstrate the difference between the original and modified Mohr-Coulomb criteria. It is shown that the nonlinear modified Mohr-Coulomb criterion predicts somewhat deeper and more intensive fracturing regions in the surrounding rock mass than the original linear Mohr-Coulomb criterion. A more comprehensive piecewise nonlinear shear strength criterion is also included in Appendix B for those readers who are interested. It covers the tensile, compressive, brittle-ductile behaviour transition and the critical state, and gives smooth transitions.
基金financial assistance obtained from NRDMS Division,Department of Science and Technology,New Delhi(No.NRDMS/11/3067/014(G)
文摘The paper presents an experimental investigation on the strength behaviour of natural rock subjected to polyaxial state of stress. The polyaxial tests were conducted on cubical specimens of sandstone obtained from the Shivpuri district in Madhya Pradesh state of India, The specimens having nominal dimensions of100 mm x 100 mm x 100 mm were tested using a polyaxial testing machine. Twenty-five combinations of intermediate and minor principal stresses were applied and the specimens were loaded till failure occurs. It was observed that the intermediate principal stress has a substantial effect on the strength of the Shivpuri sandstone. A database of rock strength under various combinations of σ_2 and σ_3 was obtained for the Shivpuri sandstone. The database was used to study the predictability of five most commonly used strength criterion. Root mean square error(RMSE), average absolute relative error percentage(AAREP) and coefficient of accordance(COA) were used as indices for the measure of goodness of fit. It was observed that the least error in the prediction was shown by modified Mohr Coulomb criterion followed by modified Weibols and Cook criterion. A probability analysis of the error in prediction was also done.
文摘The triaxial strength of twenty rockmass types was predicted using two non-linear triaxial strength criteria for rockmass i.e. Modified Mohr-Coulomb(MMC) criterion and Generalized Hoek-Brown(GHB)criterion. Four different rockmass classification systems were used for the calculation of MMC criterion parameters while only GSI classification system has been used for calculation of GHB parameters. The representative value of the uniaxial compressive strength and elastic modulus of rockmass have been estimated using probabilistic approach. A hypothetical case of an unsupported tunnel has been analyzed considering both MMC and GHB criteria. The analysis was done using the convergence-confinement method with two different approaches. The first approach predicts the tunnel response using GHB criterion directly. The second approach predicts the tunnel response using equivalent Mohr-Coulomb parameters obtained by linearization of triaxial data points obtained from MMC and GHB criteria. The tunnel response has been estimated in terms of radius of plastic zone, tunnel convergence and tunnel convergence strain. For very poor rockmasses the tunnel response predicted by MMC criterion is less than that predicted by GHB criterion. For poor and fair rockmass, the tunnel response estimated considering both the criteria are comparable except for few cases. Squeezing condition in rockmass has been also evaluated.
基金Project(51478477)supported by the National Natural Science Foundation of ChinaProject(2016CX012)supported by the Innovation-driven Project of Central South University,ChinaProject(2014122006)supported by the Guizhou Provincial Department of Transportation Foundation,China
文摘Based on the nonlinear Mohr-Coulomb failure criterion and the associated flow rules,the three-dimensional(3-D)axisymmetric failure mechanism of shallow horizontal circular plate anchors that are subjected to the ultimate pullout capacity(UPC)is determined.A derivative function of the projection function for projecting the 3-D axisymmetric failure surface on plane is deduced using the variation theory.By using difference principle,the primitive function of failure surface satisfying boundary condition and numerical solution to its corresponding ultimate pullout capacity function are obtained.The influences of nonlinear Mohr-Coulomb parameters on UPC and failure mechanism are studied.The result shows that UPC decreases with dimensionless parameter m and uniaxial tensile strength increases but increases when depth and radius of plate anchor,surface overload,initial cohesion,geomaterial density and friction angle increase.The failure surface is similar to a symmetrical spatial funnel,and its shape is mainly determined by dimensionless parameter m;the surface damage range expands with the increase of radius and depth of the plate anchor as well as initial cohesion but decreases with the increase of dimensionless parameter m and uniaxial tensile strength as well as geomaterial density.As the dimensionless parameter m=2.0,the numerical solution of UPC based on the difference principle is proved to be feasible and effective through the comparison with the exact solution.In addition,the comparison between solutions of UPC computed by variation method and those computed by upper bound method indicate that variation method outperforms upper bound method.
基金supported by the National Natural Science Foundation of China (Nos.50774082 and 50804046)
文摘With the increase of mining depth of mineral resources,the rock mass stress state is being more and more complex.The rock mass show different features,namely,with the increase of hydrostatic pressure,rock mass failure mode turns from brittle tension failure to structure ductile failure and its limit strength also increases.The restriction of minimal principal stress on the initiation and development of microcrack and the change of micro-unit stress state by the intermediate principal stress play a decisive role in the increase of rock mass limit strength.Based on the rock mass failure behavior law under complex stress state and the σ2-dependence on the rock mass strength,we proposed a Modified Mohr-Coulomb(M-MC) strength criterion which is smooth and convex.Finally,the M-MC criterion is validated by multiaxial test data of eight kinds of rock mass.We also compared the fitting results with Mohr-Coulomb criterion(MC).It shows that the new criterion fits the test data better than the Mohr-Coulomb criterion.So the M-MC strength criterion well reveals the rock mass bearing behavior and can be widely used in the rock mass strength analysis.The results can provide theoretical foundations for stability analysis and reinforcement design of complex underground engineering.
