In practical engineering,due to the noncontinuity characteristics of joints in rock slopes,in addition to plane failure,stepped sliding failure may occur for intermittently jointed rock slopes.Especially for intermitt...In practical engineering,due to the noncontinuity characteristics of joints in rock slopes,in addition to plane failure,stepped sliding failure may occur for intermittently jointed rock slopes.Especially for intermittently bedding jointed rock slopes,the correlation and difference in strength parameters between joints and rock bridges,along with the various failure modes and intermittency of rock bridges,contribute to the complexity of stepped failure modes and the unpredictability of failure regions.Based on the upper-bound limit analysis method and multi-sliders step-path failure mode,considering the shear and tensile failure of rock bridges and the weakened relationship between the strength parameters of rock bridges and jointed surfaces,by introducing the modified M-C failure criterion and the formula for calculating the energy consumption of tensile failure of rock bridges,two failure mechanisms are constructed to obtain the safety factor(F_(s))of intermittently jointed rock slopes.The sequential quadratic programming method is used to obtain the optimal upper-bound solution for F_(s).The influence of multiple key parameters(slope height H,horizontal distance L,Slope angleβ,shear strength parameters of the rock bridgeφr and cr,Dimensionless parameter u,weakening coefficients of the internal friction angle and cohesion between the rock bridges and joint surfaces Kφand Kc)on the stability analysis of intermittently jointed rock slopes under the shear failure mode of rock bridges as well as under the tensile failure mode is also explored.The reliability of the failure mechanisms is verified by comparative analysis with theoretical results,numerical results,and landslide cases,and the variation rules of F_(s)with each key parameter are obtained.The results show that F_(s) varies linearly withφr and cr of the rock bridge and with K_(φ)and K_(c),whereas F_(s)changes nonlinearly with H and L.In particular,with the increase in Kφand Kc,Fs increases by approximately 52.78%and 171.02%on average,respectively.For rock bridge tensile failure,F_(s) shows a nonlinearly positive correlation withφr,cr,Kφand Kc.In particular,with the increase in Kφand Kc,Fs increases by approximately 13%and 61.69%on average,respectively.Fs decreases rapidly with increasing slope gradientβand decreasing dimensionless parameterμ.When Kφand Kc are both less than 1.0,the stepped sliding surface occurs more easily than the plane failure surface,especially in the case of tensile failure of the rock bridge.In addition,rock slopes with higher strength parameters,taller heights,and greater weakening coefficients are prone to rock bridge tension failure with lower Fs,and more attention should be given to the occurrence of such accidents in actual engineering.展开更多
Seismic stability of slopes has been traditionally analyzed with vertically propagated earthquake waves.However,for rock slopes,the earthquake waves might approach the outcrop still with a evidently oblique direction....Seismic stability of slopes has been traditionally analyzed with vertically propagated earthquake waves.However,for rock slopes,the earthquake waves might approach the outcrop still with a evidently oblique direction.To investigate the impact of obliquely incident earthquake excitations,the input method for SV and P waves with arbitrary incident angles is conducted,respectively,by adopting the equivalent nodal force method together with a viscous-spring boundary.Then,the input method is introduced within the framework of ABAQUS software and verified by a numerical example.Both SV and P waves input are considered herein for a 2 D jointed rock slope.For the jointed rock mass,the jointed material model in ABAQUS software is employed to simulate its behavior as a continuum.Results of the study show that the earthquake incident angles have significance on the seismic stability of jointed rock slopes.The larger the incident angle,the greater the risk of slope instability.Furthermore,the stability of the jointed rock slopes also is affected by wave types of earthquakes heavily.P waves induce weaker responses and SV waves are shown to be more critical.展开更多
Jinsha River Bridge is located along the Lijiang-Xamgyi＇nyilha railway on the southeastern Tibet plateau; it is an area with a high prevalence of earthquakes. The bridge abutments were designed to be constructed in r...Jinsha River Bridge is located along the Lijiang-Xamgyi＇nyilha railway on the southeastern Tibet plateau; it is an area with a high prevalence of earthquakes. The bridge abutments were designed to be constructed in river bank slopes, where rocks are controlled by two sets of joint planes that significantly influence the stability of the left bank slope. According to the engineering-geological conditions and the characteristics of discontinuities, strength properties of the rock mass were obtained based on Barton model and direct shear test. Numerical analyses were performed using FLAC3D software to examine the slope＇s response to seismic loading. Then in order to evaluate the damage trends of the rock mass under the different loading conditions, a calculation model based on the geological parameters and slope stability was simulated and analyzed using the discrete element numerical simulation program UDEC （Universal Dis- tinct Element Code）, and the effect of degradation of discontinuities on the slope stability was investigated. The results show that the destruction of rock mass under the gravity, bridge foundation, and seismic load are mainly concentrated within 30 m depth of slope, and the slope under loading may slide along joint planes. In addition, the dynamic analysis by amplification of the input loading indicates that instability occurs to the bank slope at a height of about 200 m, and rock blocks will fail under seismic load. Therefore, to prevent the slope from deformation under the engineering loading and strong earthquakes, the bridge foundation should be strengthened.展开更多
To research the reinforcement effect of a rock slope with group anchorage cablesand the stress characteristics of pre-stressed anchorage cables in the fractured surface,the rock slope calculated model of a wedge block...To research the reinforcement effect of a rock slope with group anchorage cablesand the stress characteristics of pre-stressed anchorage cables in the fractured surface,the rock slope calculated model of a wedge block within the double-slide face wasestablished by using the finite difference software according to the actual slope projectcombined with indoor model test.The pre-stress loss rule of the anchorage cable andthe distribution of axial force and the force-transferring mechanism of the anchorage cablewere analyzed during simulation.Also, based on the displacement contour and thesafety factor of the calculated results, the quantitative analysis for the reinforcement effectof the rock slope with group pre-stressed anchorage cable was discovered.The resultscomputed by the software conform with the data in the experiment, which canprove the effectiveness and correctness of parameter selection and model building.展开更多
In this study,the effect of rock bridges on rock slope stability was investigated by incorporating nonpersistent joint networks in numerical models,and the critical profiles of an open pit mine were analysed.Parallel ...In this study,the effect of rock bridges on rock slope stability was investigated by incorporating nonpersistent joint networks in numerical models,and the critical profiles of an open pit mine were analysed.Parallel deterministic networks of infinite and finite lengths,ubiquitous joint network model and Veneziano joint network model were used in order to simulate the rock fractures.Materials were modelled based on the generalised Hoek-Brown and equivalent Mohr-Coulomb failure criteria.The parallel deterministic infinite and the ubiquitous joint network models produced lower safety factors.The introduction of rock bridges along discontinuity planes in the parallel deterministic network and Veneziano joint network models significantly contributed to the stability and strain distribution,which should be considered in stability analysis of rock mass in open pit by rock slope practitioners.The results show the significance of joints in hard rock behaviour and the joints should be included in order to attain practical and realistic simulations.展开更多
Cohesion(c) and friction angle(φ) of rock are important parameters required for reliability analysis of rock slope stability. There is correlation between c and φ which affects results of reliability analysis of roc...Cohesion(c) and friction angle(φ) of rock are important parameters required for reliability analysis of rock slope stability. There is correlation between c and φ which affects results of reliability analysis of rock slope stability. However, the characterization of joint probability distribution of c and φ through which their correlation can be estimated requires a large amount of rock property data, which are often not available for most rock engineering projects. As a result, the correlation between c and φ is often ignored or simply assumed during reliability studies, which may lead to bias estimation of failure probability. In probabilistic rock slope stability analysis, the influence of ignoring or simply assuming the correlation of the rock strength parameters(i.e., c and φ) on the reliability of rock slopes has not been fully investigated. In this study, a Bayesian approach is developed to characterize the correlation between c and φ, and an expanded reliability-based design(RBD) approach is developed to assess the influence of correlation between c and φ on reliability of a rock slope. The Bayesian approach characterizes the sitespecific joint probability distribution of c and φ, and quantifies the correlation between c and φ using available limited data pairs of c and φ from a rock project. The expanded RBD approach uses the joint probability distribution of c and φ obtained through the Bayesian approach as inputs, to determine the reliability of a rock slope. The approach gives insight into the propagation of the correlation between c and φ through their joint probability into the reliability analysis, and their influence on the calculated reliability of the rock slope. The approaches may be applied in practice with little additional effort from a conventional analysis. The proposed approaches are illustrated using real c and φ data pairs obtained from laboratory tests of fractured rock at Forsmark, Sweden.展开更多
基金supported by the National Natural Science Foundation of China(Nos.52208369,52309138,52209142,51978666)the Department of Science and Technology of Sichuan Province(2023NSFSC0284).
文摘In practical engineering,due to the noncontinuity characteristics of joints in rock slopes,in addition to plane failure,stepped sliding failure may occur for intermittently jointed rock slopes.Especially for intermittently bedding jointed rock slopes,the correlation and difference in strength parameters between joints and rock bridges,along with the various failure modes and intermittency of rock bridges,contribute to the complexity of stepped failure modes and the unpredictability of failure regions.Based on the upper-bound limit analysis method and multi-sliders step-path failure mode,considering the shear and tensile failure of rock bridges and the weakened relationship between the strength parameters of rock bridges and jointed surfaces,by introducing the modified M-C failure criterion and the formula for calculating the energy consumption of tensile failure of rock bridges,two failure mechanisms are constructed to obtain the safety factor(F_(s))of intermittently jointed rock slopes.The sequential quadratic programming method is used to obtain the optimal upper-bound solution for F_(s).The influence of multiple key parameters(slope height H,horizontal distance L,Slope angleβ,shear strength parameters of the rock bridgeφr and cr,Dimensionless parameter u,weakening coefficients of the internal friction angle and cohesion between the rock bridges and joint surfaces Kφand Kc)on the stability analysis of intermittently jointed rock slopes under the shear failure mode of rock bridges as well as under the tensile failure mode is also explored.The reliability of the failure mechanisms is verified by comparative analysis with theoretical results,numerical results,and landslide cases,and the variation rules of F_(s)with each key parameter are obtained.The results show that F_(s) varies linearly withφr and cr of the rock bridge and with K_(φ)and K_(c),whereas F_(s)changes nonlinearly with H and L.In particular,with the increase in Kφand Kc,Fs increases by approximately 52.78%and 171.02%on average,respectively.For rock bridge tensile failure,F_(s) shows a nonlinearly positive correlation withφr,cr,Kφand Kc.In particular,with the increase in Kφand Kc,Fs increases by approximately 13%and 61.69%on average,respectively.Fs decreases rapidly with increasing slope gradientβand decreasing dimensionless parameterμ.When Kφand Kc are both less than 1.0,the stepped sliding surface occurs more easily than the plane failure surface,especially in the case of tensile failure of the rock bridge.In addition,rock slopes with higher strength parameters,taller heights,and greater weakening coefficients are prone to rock bridge tension failure with lower Fs,and more attention should be given to the occurrence of such accidents in actual engineering.
基金National Basic Research Program of China under Grant No.2015CB057902Beijing Municipal Natural Science Foundation under Grant No.8164049Young Foundation of the National Science of China under Grant No.51608015
文摘Seismic stability of slopes has been traditionally analyzed with vertically propagated earthquake waves.However,for rock slopes,the earthquake waves might approach the outcrop still with a evidently oblique direction.To investigate the impact of obliquely incident earthquake excitations,the input method for SV and P waves with arbitrary incident angles is conducted,respectively,by adopting the equivalent nodal force method together with a viscous-spring boundary.Then,the input method is introduced within the framework of ABAQUS software and verified by a numerical example.Both SV and P waves input are considered herein for a 2 D jointed rock slope.For the jointed rock mass,the jointed material model in ABAQUS software is employed to simulate its behavior as a continuum.Results of the study show that the earthquake incident angles have significance on the seismic stability of jointed rock slopes.The larger the incident angle,the greater the risk of slope instability.Furthermore,the stability of the jointed rock slopes also is affected by wave types of earthquakes heavily.P waves induce weaker responses and SV waves are shown to be more critical.
基金China Railway EryuanEngineering Group CO.LTD (2009-LiXiang Railway-13)the Fundamental Research for the Central Uni-versities (SWJTU09BR033)
文摘Jinsha River Bridge is located along the Lijiang-Xamgyi＇nyilha railway on the southeastern Tibet plateau; it is an area with a high prevalence of earthquakes. The bridge abutments were designed to be constructed in river bank slopes, where rocks are controlled by two sets of joint planes that significantly influence the stability of the left bank slope. According to the engineering-geological conditions and the characteristics of discontinuities, strength properties of the rock mass were obtained based on Barton model and direct shear test. Numerical analyses were performed using FLAC3D software to examine the slope＇s response to seismic loading. Then in order to evaluate the damage trends of the rock mass under the different loading conditions, a calculation model based on the geological parameters and slope stability was simulated and analyzed using the discrete element numerical simulation program UDEC （Universal Dis- tinct Element Code）, and the effect of degradation of discontinuities on the slope stability was investigated. The results show that the destruction of rock mass under the gravity, bridge foundation, and seismic load are mainly concentrated within 30 m depth of slope, and the slope under loading may slide along joint planes. In addition, the dynamic analysis by amplification of the input loading indicates that instability occurs to the bank slope at a height of about 200 m, and rock blocks will fail under seismic load. Therefore, to prevent the slope from deformation under the engineering loading and strong earthquakes, the bridge foundation should be strengthened.
基金Supported by the National Natural Science Foundation of China(50874085)
文摘To research the reinforcement effect of a rock slope with group anchorage cablesand the stress characteristics of pre-stressed anchorage cables in the fractured surface,the rock slope calculated model of a wedge block within the double-slide face wasestablished by using the finite difference software according to the actual slope projectcombined with indoor model test.The pre-stress loss rule of the anchorage cable andthe distribution of axial force and the force-transferring mechanism of the anchorage cablewere analyzed during simulation.Also, based on the displacement contour and thesafety factor of the calculated results, the quantitative analysis for the reinforcement effectof the rock slope with group pre-stressed anchorage cable was discovered.The resultscomputed by the software conform with the data in the experiment, which canprove the effectiveness and correctness of parameter selection and model building.
文摘In this study,the effect of rock bridges on rock slope stability was investigated by incorporating nonpersistent joint networks in numerical models,and the critical profiles of an open pit mine were analysed.Parallel deterministic networks of infinite and finite lengths,ubiquitous joint network model and Veneziano joint network model were used in order to simulate the rock fractures.Materials were modelled based on the generalised Hoek-Brown and equivalent Mohr-Coulomb failure criteria.The parallel deterministic infinite and the ubiquitous joint network models produced lower safety factors.The introduction of rock bridges along discontinuity planes in the parallel deterministic network and Veneziano joint network models significantly contributed to the stability and strain distribution,which should be considered in stability analysis of rock mass in open pit by rock slope practitioners.The results show the significance of joints in hard rock behaviour and the joints should be included in order to attain practical and realistic simulations.
基金supported by grants from the Research Grants Council of the Hong Kong,Special Administrative Region,China [Project No.9042172 (CityU11200115)and Project No.8779012(T22-603/15N)]
文摘Cohesion(c) and friction angle(φ) of rock are important parameters required for reliability analysis of rock slope stability. There is correlation between c and φ which affects results of reliability analysis of rock slope stability. However, the characterization of joint probability distribution of c and φ through which their correlation can be estimated requires a large amount of rock property data, which are often not available for most rock engineering projects. As a result, the correlation between c and φ is often ignored or simply assumed during reliability studies, which may lead to bias estimation of failure probability. In probabilistic rock slope stability analysis, the influence of ignoring or simply assuming the correlation of the rock strength parameters(i.e., c and φ) on the reliability of rock slopes has not been fully investigated. In this study, a Bayesian approach is developed to characterize the correlation between c and φ, and an expanded reliability-based design(RBD) approach is developed to assess the influence of correlation between c and φ on reliability of a rock slope. The Bayesian approach characterizes the sitespecific joint probability distribution of c and φ, and quantifies the correlation between c and φ using available limited data pairs of c and φ from a rock project. The expanded RBD approach uses the joint probability distribution of c and φ obtained through the Bayesian approach as inputs, to determine the reliability of a rock slope. The approach gives insight into the propagation of the correlation between c and φ through their joint probability into the reliability analysis, and their influence on the calculated reliability of the rock slope. The approaches may be applied in practice with little additional effort from a conventional analysis. The proposed approaches are illustrated using real c and φ data pairs obtained from laboratory tests of fractured rock at Forsmark, Sweden.
