Based on the characteristic that the potential sliding surfaces of rock slope are commonly in the shape of either line or fold line,analysis thought of conventional pile foundation in the flat ground under complex loa...Based on the characteristic that the potential sliding surfaces of rock slope are commonly in the shape of either line or fold line,analysis thought of conventional pile foundation in the flat ground under complex load condition was applied and the upper-bound theorem of limit analysis was used to compute thrust of rock layers with all possible distribution shapes. The interaction of slope and pile was considered design load in terms of slope thrust,and the finite difference method was derived to calculate inner-force and displacement of bridge pile foundation in rock slope under complex load condition. The result of example shows that the distribution model of slope thrust has certain impact on displacement and inner-force of bridge pile foundation. The maximum displacement growth rate reaches 54% and the maximum moment and shear growth rates reach only 15% and 20%,respectively,but the trends of inner-force and displacement of bridge pile foundation are basically the same as those of the conventional pile foundation in the flat ground. When the piles bear the same level lateral thrust,the distribution shapes of slope thrust have different influence on inner-force of pile foundation,especially the rectangle distribution,and the triangle thrust has the smallest displacement and inner-force of pile foundation.展开更多
The natural element method (NEM) is a newly- developed numerical method based on Voronoi diagram and Delaunay triangulation of scattered points, which adopts natural neighbour interpolation to construct trial functi...The natural element method (NEM) is a newly- developed numerical method based on Voronoi diagram and Delaunay triangulation of scattered points, which adopts natural neighbour interpolation to construct trial functions in the framework of Galerkin method. Owing to its distinctive advantages, the NEM is used widely in many problems of computational mechanics. Utilizing the NEM, this paper deals with numerical limit analysis of structures made up of perfectly rigid-plastic material. According to kinematic the- orem of plastic limit analysis, a mathematical programming natural element formulation is established for determining the upper bound multiplier of plane problems, and a direct iteration algorithm is proposed accordingly to solve it. In this algorithm, the plastic incompressibility condition is handled by two different treatments, and the nonlinearity and nons- moothness of the goal function are overcome by distinguishing the rigid zones from the plastic zones at each iteration. The procedure implementation of iterative process is quite simple and effective because each iteration is equivalent to solving an associated elastic problem. The obtained limit load multiplier is proved to monotonically converge to the upper bound of true solution. Several benchmark examples are investigated to validate the significant performance of the NEM in the application field of limit analysis.展开更多
Based on the lower bound theorem of limit analysis, a solution procedure for limit analysis of three_dimensional elastoplastic structures was established using conventional boundary element method (BEM). The elastic s...Based on the lower bound theorem of limit analysis, a solution procedure for limit analysis of three_dimensional elastoplastic structures was established using conventional boundary element method (BEM). The elastic stress field for lower bound limit analysis was computed directly by three_dimensional boundary element method (3_D BEM). The self_equilibrium stress field was constructed by the linear combination of several self_equilibrium “basis vectors” which can be computed by elastic_plastic incremental iteration of 3_D BEM analysis. The lower bound limit analysis problem was finally reduced to a series of nonlinear programming sub_problems with relatively few optimal variables. The complex method was used to solve the nonlinear programming sub_problems. The numerical results show that the present solution procedure has good accuracy and high efficiency.展开更多
The analytical solutions for predicting the exact shape of collapse mechanisms in shallow tunnels with arbitrary excavation profiles were obtained by virtue of the upper bound theorem of limit analysis and variation p...The analytical solutions for predicting the exact shape of collapse mechanisms in shallow tunnels with arbitrary excavation profiles were obtained by virtue of the upper bound theorem of limit analysis and variation principle according to Hoek-Brown failure criterion. The seepage force was included in the upper bound limit analysis, and it was computed from the gradient of excess pore pressure distribution. The seepage was regarded as a work rate of external force. The numerical results of roof collapse in square and circular tunnels with different rock parameters were derived and discussed, which proves to be valid in comparison with the previous work. The influences of different parameters on the shape of collapsing blocks were also discussed.展开更多
The combined influence of nonlinearity and dilation on slope stability was evaluated using the upper-bound limit analysis theorem.The mechanism of slope collapse was analyzed by dividing it into arbitrary discrete soi...The combined influence of nonlinearity and dilation on slope stability was evaluated using the upper-bound limit analysis theorem.The mechanism of slope collapse was analyzed by dividing it into arbitrary discrete soil blocks with the nonlinear Mohr–Coulomb failure criterion and nonassociated flow rule.The multipoint tangent(multi-tangent) technique was used to analyze the slope stability by linearizing the nonlinear failure criterion.A general expression for the slope safety factor was derived based on the virtual work principle and the strength reduction technique,and the global slope safety factor can be obtained by the optimization method of nonlinear sequential quadratic programming.The results show better agreement with previous research result when the nonlinear failure criterion reduces to a linear failure criterion or the non-associated flow rule reduces to an associated flow rule,which demonstrates the rationality of the presented method.Slope safety factors calculated by the multi-tangent inclined-slices technique were smaller than those obtained by the traditional single-tangent inclined-slices technique.The results show that the multi-tangent inclined-slices technique is a safe and effective method of slope stability limit analysis.The combined effect of nonlinearity and dilation on slope stability was analyzed,and the parameter analysis indicates that nonlinearity and dilation have significant influence on the result of slope stability analysis.展开更多
By means of Lagrange duality of Hill's maximum plastic work principle theory of the convex program, a dual problem under Mises' yield condition has been derived and whereby a non-differentiable convex optimization m...By means of Lagrange duality of Hill's maximum plastic work principle theory of the convex program, a dual problem under Mises' yield condition has been derived and whereby a non-differentiable convex optimization model for the limit analysis is developed. With this model, it is not necessary to linearize the yield condition and its discrete form becomes a minimization problem of the sum of Euclidean norms subject to linear constraints. Aimed at resolving the non-differentiability of Euclidean norms, a smoothing algorithm for the limit analysis of perfect-plastic continuum media is proposed. Its efficiency is demonstrated by computing the limit load factor and the collapse state for some plane stress and plain strain problems.展开更多
In this paper,a novel discretization method inσ-τspace is developed to calculate the upper bound limit loads and failure modes of anisotropic Mohr-Coulomb materials.To achieve this objective,the Mohr-Coulomb yield c...In this paper,a novel discretization method inσ-τspace is developed to calculate the upper bound limit loads and failure modes of anisotropic Mohr-Coulomb materials.To achieve this objective,the Mohr-Coulomb yield criterion is linearized inσ-τspace,which allows for upper bound solution of soils whose cohesion and friction coefficient varying with direction.The finite element upper limit analysis formulation using the modified anisotropic yield criterion is then developed.Several examples are given to illustrate the capability and effectiveness of the proposed numerical procedure for computing rigorous upper bounds for anisotropic soils.展开更多
Based on the upper bound limit analysis theorem and the shear strength reduction technique,the equation for expressing critical limit-equilibrium state was employed to define the safety factor of a given slope and its...Based on the upper bound limit analysis theorem and the shear strength reduction technique,the equation for expressing critical limit-equilibrium state was employed to define the safety factor of a given slope and its corresponding critical failure mechanism by means of the kinematical approach of limit analysis theory.The nonlinear shear strength parameters were treated as variable parameters and a kinematically admissible failure mechanism was considered for calculation schemes.The iterative optimization method was adopted to obtain the safety factors.Case study and comparative analysis show that solutions presented here agree with available predictions when nonlinear criterion reduces to linear criterion,and the validity of present method could be illuminated.From the numerical results,it can also be seen that nonlinear parameter m,slope foot gradient β,height of slope H,slope top gradient α and soil bulk density γ have significant effects on the safety factor of the slope.展开更多
The investigation of supporting pressure is of great significance to the design of underground structures.Based on the kinematical approach of limit analysis,an improved failure mechanism is proposed,and the supportin...The investigation of supporting pressure is of great significance to the design of underground structures.Based on the kinematical approach of limit analysis,an improved failure mechanism is proposed,and the supporting pressure is investigated for deep buried cavity.Three failure mechanisms are first introduced according to the existing failure mechanisms of geotechnical structures of limit analysis.A comparison with respect to the optimal failure mechanisms and the upper bound solutions provided among these three mechanisms are then conducted in an attempt to obtain the improved failure mechanism.The results provided by the improved failure mechanism are in good agreement with those by the existing method,the numerical solution and field monitoring,which demonstrates that the proposed failure mechanism is effective for the upper bound analysis of supporting pressure.展开更多
By combining the results of laboratory model tests with relevant flow rules, the failure mode of shallow unsymmetrical loading tunnels and the corresponding velocity field were established. According to the principle ...By combining the results of laboratory model tests with relevant flow rules, the failure mode of shallow unsymmetrical loading tunnels and the corresponding velocity field were established. According to the principle of virtual power, the upper bound solution for surrounding rock pressure of shallow unsymmetrical loading tunnel was derived and verified by an example. The results indicate that the calculated results of the derived upper bound method for surrounding rock pressure of shallow unsymmetrical loading tunnels are relatively close to those of the existing "code method" and test results, which means that the proposed method is feasible. The current code method underestimates the unsymmetrical loading feature of surrounding rock pressure of shallow unsymmetrical loading tunnels, so it is unsafe; when the burial depth is less or greater than two times of the tunnel span and the unsymmetrical loading angle is less than 45°, the upper bound method or the average value of the results calculated by the upper bound method and code method respectively, is comparatively reasonable. When the burial depth is greater than two times of the tunnel span and the unsymmetrical loading angle is greater than 45°, the code method is more suitable.展开更多
At present,associated flow rule of traditional plastic theory is adopted in the slip line field theory and upper bound method of geotechnical materials. So the stress characteristic line conforms to the velocity line....At present,associated flow rule of traditional plastic theory is adopted in the slip line field theory and upper bound method of geotechnical materials. So the stress characteristic line conforms to the velocity line. It is proved that geotechnical materials do not abide by the associated flow rule. It is impossible for the stress characteristic line to conform to the velocity line. Generalized plastic mechanics theoretically proved that plastic potential surface intersects the Mohr-Coulomb yield surface with an angle,so that the velocity line must be studied by non-associated flow rule. According to limit analysis theory,the theory of slip line field is put forward in this paper,and then the ultimate bearing capacity of strip footing is obtained based on the associated flow rule and the non-associated flow rule individually. These two results are identical since the ultimate bearing capacity is independent of flow rule. On the contrary,the velocity fields of associated and non-associated flow rules are different which shows the velocity field based on the associated flow rule is incorrect.展开更多
Discontinuous lining is a special form of support in underground excavation. Based on the method of plastic limit analysis, it is found the upper and the lower bound solution of the pressure of circular discontinuous ...Discontinuous lining is a special form of support in underground excavation. Based on the method of plastic limit analysis, it is found the upper and the lower bound solution of the pressure of circular discontinuous lining and discussed support parameter of discontinuous lining and its applicable conditions , which provides theoretical basis for the design and calculation of discontinuous lining.展开更多
According to the lower-bound theorem of limit analysis the Rigid Finite Element Meth-od(RFEM)is applied to structural limit analysis and the linear programmings for limit analysis are deducedin this paper.Moreover,the...According to the lower-bound theorem of limit analysis the Rigid Finite Element Meth-od(RFEM)is applied to structural limit analysis and the linear programmings for limit analysis are deducedin this paper.Moreover,the Thermo-Parameter Method(TPM)and Parametric Variational principles(PVP)are used to reduce the computational effort while maintaining the accuracy of solutions.A better solution isalso obtained in this paper.展开更多
The stability of natural slope was analyzed on the basis of limit analysis. The sliding model of a kind of natural slope was presented. A new kinematically admissible velocity field for the new sliding model was const...The stability of natural slope was analyzed on the basis of limit analysis. The sliding model of a kind of natural slope was presented. A new kinematically admissible velocity field for the new sliding model was constructed. The stability factor formulation by the upper bound theorem leads to a classical nonlinear programming problem, when the external work rate and internal energy dissipation were solved, and the constraint condition of the programming problem was given. The upper bound optimization problem can be solved efficiently by applying a nonlinear SQP algorithm, and stability factor was obtained, which agrees well with previous achievements.展开更多
基金Project(50578060) supported by the National Natural Science Foundation of China
文摘Based on the characteristic that the potential sliding surfaces of rock slope are commonly in the shape of either line or fold line,analysis thought of conventional pile foundation in the flat ground under complex load condition was applied and the upper-bound theorem of limit analysis was used to compute thrust of rock layers with all possible distribution shapes. The interaction of slope and pile was considered design load in terms of slope thrust,and the finite difference method was derived to calculate inner-force and displacement of bridge pile foundation in rock slope under complex load condition. The result of example shows that the distribution model of slope thrust has certain impact on displacement and inner-force of bridge pile foundation. The maximum displacement growth rate reaches 54% and the maximum moment and shear growth rates reach only 15% and 20%,respectively,but the trends of inner-force and displacement of bridge pile foundation are basically the same as those of the conventional pile foundation in the flat ground. When the piles bear the same level lateral thrust,the distribution shapes of slope thrust have different influence on inner-force of pile foundation,especially the rectangle distribution,and the triangle thrust has the smallest displacement and inner-force of pile foundation.
基金supported by the National Foundation for Excellent Doctoral Thesis of China (200025)the Program for New Century Excellent Talents in University (NCET-04-0075)the National Natural Science Foundation of China (19902007)
文摘The natural element method (NEM) is a newly- developed numerical method based on Voronoi diagram and Delaunay triangulation of scattered points, which adopts natural neighbour interpolation to construct trial functions in the framework of Galerkin method. Owing to its distinctive advantages, the NEM is used widely in many problems of computational mechanics. Utilizing the NEM, this paper deals with numerical limit analysis of structures made up of perfectly rigid-plastic material. According to kinematic the- orem of plastic limit analysis, a mathematical programming natural element formulation is established for determining the upper bound multiplier of plane problems, and a direct iteration algorithm is proposed accordingly to solve it. In this algorithm, the plastic incompressibility condition is handled by two different treatments, and the nonlinearity and nons- moothness of the goal function are overcome by distinguishing the rigid zones from the plastic zones at each iteration. The procedure implementation of iterative process is quite simple and effective because each iteration is equivalent to solving an associated elastic problem. The obtained limit load multiplier is proved to monotonically converge to the upper bound of true solution. Several benchmark examples are investigated to validate the significant performance of the NEM in the application field of limit analysis.
文摘Based on the lower bound theorem of limit analysis, a solution procedure for limit analysis of three_dimensional elastoplastic structures was established using conventional boundary element method (BEM). The elastic stress field for lower bound limit analysis was computed directly by three_dimensional boundary element method (3_D BEM). The self_equilibrium stress field was constructed by the linear combination of several self_equilibrium “basis vectors” which can be computed by elastic_plastic incremental iteration of 3_D BEM analysis. The lower bound limit analysis problem was finally reduced to a series of nonlinear programming sub_problems with relatively few optimal variables. The complex method was used to solve the nonlinear programming sub_problems. The numerical results show that the present solution procedure has good accuracy and high efficiency.
基金Project(2013CB036004)supported by the National Basic Research Program of ChinaProjects(51178468,51378510)supported by National Natural Science Foundation of China
文摘The analytical solutions for predicting the exact shape of collapse mechanisms in shallow tunnels with arbitrary excavation profiles were obtained by virtue of the upper bound theorem of limit analysis and variation principle according to Hoek-Brown failure criterion. The seepage force was included in the upper bound limit analysis, and it was computed from the gradient of excess pore pressure distribution. The seepage was regarded as a work rate of external force. The numerical results of roof collapse in square and circular tunnels with different rock parameters were derived and discussed, which proves to be valid in comparison with the previous work. The influences of different parameters on the shape of collapsing blocks were also discussed.
基金Projects(51208522,51478477)supported by the National Natural Science Foundation of ChinaProject(2012122033)supported by the Guizhou Provincial Department of Transportation Foundation,ChinaProject(CX2015B049)supported by the Scientific Research Innovation Project of Hunan Province,China
文摘The combined influence of nonlinearity and dilation on slope stability was evaluated using the upper-bound limit analysis theorem.The mechanism of slope collapse was analyzed by dividing it into arbitrary discrete soil blocks with the nonlinear Mohr–Coulomb failure criterion and nonassociated flow rule.The multipoint tangent(multi-tangent) technique was used to analyze the slope stability by linearizing the nonlinear failure criterion.A general expression for the slope safety factor was derived based on the virtual work principle and the strength reduction technique,and the global slope safety factor can be obtained by the optimization method of nonlinear sequential quadratic programming.The results show better agreement with previous research result when the nonlinear failure criterion reduces to a linear failure criterion or the non-associated flow rule reduces to an associated flow rule,which demonstrates the rationality of the presented method.Slope safety factors calculated by the multi-tangent inclined-slices technique were smaller than those obtained by the traditional single-tangent inclined-slices technique.The results show that the multi-tangent inclined-slices technique is a safe and effective method of slope stability limit analysis.The combined effect of nonlinearity and dilation on slope stability was analyzed,and the parameter analysis indicates that nonlinearity and dilation have significant influence on the result of slope stability analysis.
基金Project supported by the National Natural Science Foundation of China (Nos.10572031, 10332010)
文摘By means of Lagrange duality of Hill's maximum plastic work principle theory of the convex program, a dual problem under Mises' yield condition has been derived and whereby a non-differentiable convex optimization model for the limit analysis is developed. With this model, it is not necessary to linearize the yield condition and its discrete form becomes a minimization problem of the sum of Euclidean norms subject to linear constraints. Aimed at resolving the non-differentiability of Euclidean norms, a smoothing algorithm for the limit analysis of perfect-plastic continuum media is proposed. Its efficiency is demonstrated by computing the limit load factor and the collapse state for some plane stress and plain strain problems.
文摘In this paper,a novel discretization method inσ-τspace is developed to calculate the upper bound limit loads and failure modes of anisotropic Mohr-Coulomb materials.To achieve this objective,the Mohr-Coulomb yield criterion is linearized inσ-τspace,which allows for upper bound solution of soils whose cohesion and friction coefficient varying with direction.The finite element upper limit analysis formulation using the modified anisotropic yield criterion is then developed.Several examples are given to illustrate the capability and effectiveness of the proposed numerical procedure for computing rigorous upper bounds for anisotropic soils.
基金Project(2006318802111) supported by West Traffic Construction Science and Technology of ChinaProject(2008yb004) supported by Excellent Doctorate Dissertations of Central South University, China Project(2008G032-3) supported by Key Item of Science and Technology Research of Railway Ministry of China
文摘Based on the upper bound limit analysis theorem and the shear strength reduction technique,the equation for expressing critical limit-equilibrium state was employed to define the safety factor of a given slope and its corresponding critical failure mechanism by means of the kinematical approach of limit analysis theory.The nonlinear shear strength parameters were treated as variable parameters and a kinematically admissible failure mechanism was considered for calculation schemes.The iterative optimization method was adopted to obtain the safety factors.Case study and comparative analysis show that solutions presented here agree with available predictions when nonlinear criterion reduces to linear criterion,and the validity of present method could be illuminated.From the numerical results,it can also be seen that nonlinear parameter m,slope foot gradient β,height of slope H,slope top gradient α and soil bulk density γ have significant effects on the safety factor of the slope.
基金Project(51674115)supported by the National Natural Science Foundation of ChinaProject(51434006)supported by the Key Program of the National Natural Science Foundation of ChinaProject(2015JJ4024)supported by the Natural Science Foundation of Hunan Province,China
文摘The investigation of supporting pressure is of great significance to the design of underground structures.Based on the kinematical approach of limit analysis,an improved failure mechanism is proposed,and the supporting pressure is investigated for deep buried cavity.Three failure mechanisms are first introduced according to the existing failure mechanisms of geotechnical structures of limit analysis.A comparison with respect to the optimal failure mechanisms and the upper bound solutions provided among these three mechanisms are then conducted in an attempt to obtain the improved failure mechanism.The results provided by the improved failure mechanism are in good agreement with those by the existing method,the numerical solution and field monitoring,which demonstrates that the proposed failure mechanism is effective for the upper bound analysis of supporting pressure.
基金Project(2014M560652)supported by China Postdoctoral Science FoundationProjects(2011CB013802,2013CB036004)supported by the National Basic Research Program of China
文摘By combining the results of laboratory model tests with relevant flow rules, the failure mode of shallow unsymmetrical loading tunnels and the corresponding velocity field were established. According to the principle of virtual power, the upper bound solution for surrounding rock pressure of shallow unsymmetrical loading tunnel was derived and verified by an example. The results indicate that the calculated results of the derived upper bound method for surrounding rock pressure of shallow unsymmetrical loading tunnels are relatively close to those of the existing "code method" and test results, which means that the proposed method is feasible. The current code method underestimates the unsymmetrical loading feature of surrounding rock pressure of shallow unsymmetrical loading tunnels, so it is unsafe; when the burial depth is less or greater than two times of the tunnel span and the unsymmetrical loading angle is less than 45°, the upper bound method or the average value of the results calculated by the upper bound method and code method respectively, is comparatively reasonable. When the burial depth is greater than two times of the tunnel span and the unsymmetrical loading angle is greater than 45°, the code method is more suitable.
文摘At present,associated flow rule of traditional plastic theory is adopted in the slip line field theory and upper bound method of geotechnical materials. So the stress characteristic line conforms to the velocity line. It is proved that geotechnical materials do not abide by the associated flow rule. It is impossible for the stress characteristic line to conform to the velocity line. Generalized plastic mechanics theoretically proved that plastic potential surface intersects the Mohr-Coulomb yield surface with an angle,so that the velocity line must be studied by non-associated flow rule. According to limit analysis theory,the theory of slip line field is put forward in this paper,and then the ultimate bearing capacity of strip footing is obtained based on the associated flow rule and the non-associated flow rule individually. These two results are identical since the ultimate bearing capacity is independent of flow rule. On the contrary,the velocity fields of associated and non-associated flow rules are different which shows the velocity field based on the associated flow rule is incorrect.
文摘Discontinuous lining is a special form of support in underground excavation. Based on the method of plastic limit analysis, it is found the upper and the lower bound solution of the pressure of circular discontinuous lining and discussed support parameter of discontinuous lining and its applicable conditions , which provides theoretical basis for the design and calculation of discontinuous lining.
基金The project supported by National Natural Science Foundation of China
文摘According to the lower-bound theorem of limit analysis the Rigid Finite Element Meth-od(RFEM)is applied to structural limit analysis and the linear programmings for limit analysis are deducedin this paper.Moreover,the Thermo-Parameter Method(TPM)and Parametric Variational principles(PVP)are used to reduce the computational effort while maintaining the accuracy of solutions.A better solution isalso obtained in this paper.
基金Project(2013CB036004)supported by the National Basic Research Program of ChinaProject(51178468)supported by the National Natural Science Foundation of China
文摘The stability of natural slope was analyzed on the basis of limit analysis. The sliding model of a kind of natural slope was presented. A new kinematically admissible velocity field for the new sliding model was constructed. The stability factor formulation by the upper bound theorem leads to a classical nonlinear programming problem, when the external work rate and internal energy dissipation were solved, and the constraint condition of the programming problem was given. The upper bound optimization problem can be solved efficiently by applying a nonlinear SQP algorithm, and stability factor was obtained, which agrees well with previous achievements.