In order to study the stability control mechanism of a concave slope with circular landslide, and remove the influence of differences in shape on slope stability, the limit analysis method of a simplified Bishop metho...In order to study the stability control mechanism of a concave slope with circular landslide, and remove the influence of differences in shape on slope stability, the limit analysis method of a simplified Bishop method was employed. The sliding body was divided into strips in a three-dimensional model, and the lateral earth pressure was put into mechanical analysis and the three-dimensional stability analysis methods applicable for circular sliding in concave slope were deduced. Based on geometric structure and the geological parameters of a concave slope, the influence rule of curvature radius and the top and bottom arch height on the concave slope stability were analyzed. The results show that the stability coefficient decreases after growth, first in the transition stage of slope shape from flat to concave, and it has been confirmed that there is a best size to make the slope stability factor reach a maximum. By contrast with average slope, the stability of a concave slope features a smaller range of ascension with slope height increase, which indicates that the enhancing effect of a concave slope is apparent only with lower slope heights.展开更多
Let X and Y be Banach spaces.For A∈L(X),B∈L(Y),C∈L(Y,X),let MCbe the operator matrix defined on X⊕Y by M_(C)=(AC0B)∈L(X⊕Y).In this paper we investigate the decomposability for MC.We consider Bishop’s property(...Let X and Y be Banach spaces.For A∈L(X),B∈L(Y),C∈L(Y,X),let MCbe the operator matrix defined on X⊕Y by M_(C)=(AC0B)∈L(X⊕Y).In this paper we investigate the decomposability for MC.We consider Bishop’s property(β),decomposition property(δ)and Dunford’s property(C)and obtain the relationship of these properties between M_(C) and its entries.We explore how σ_(*)(M_(C))shrinks from σ_(*)(A)∪σ_(*)(B),where σ_(*)denotes σ_(β),σ_(δ),σ_(C),σ_(dec).In particular,we develop some sufficient conditions for equality σ_(*)(MC)=σ_(*)(A)∪σ_(*)(B).Besides,we consider the perturbation of these properties for MCand show that in perturbing with certain operators C the properties for MCkeeps with A,B.Some examples are given to illustrate our results.Furthermore,we study the decomposability for(0AB0).Finally,we give applications of decomposability for operator matrices.展开更多
Based on Bishop's model and by applying the first and second order mean deviations method, an approximative solution method for the first and second order partial derivatives of functional function was deduced acc...Based on Bishop's model and by applying the first and second order mean deviations method, an approximative solution method for the first and second order partial derivatives of functional function was deduced according to numerical analysis theory. After complicated multi-independent variables implicit functional function was simplified to be a single independent variable implicit function and rule of calculating derivative for composite function was combined with principle of the mean deviations method, an approximative solution format of implicit functional function was established through Taylor expansion series and iterative solution approach of reliability degree index was given synchronously. An engineering example was analyzed by the method. The result shows its absolute error is only 0.78% as compared with accurate solution.展开更多
The stability of earthworks (cuttings, embankments, dikes) and natural slopes is a?problem that is of concern to geotechnicians, both practitioners and researchers. The disorders generated by breaking the slopes are u...The stability of earthworks (cuttings, embankments, dikes) and natural slopes is a?problem that is of concern to geotechnicians, both practitioners and researchers. The disorders generated by breaking the slopes are usually spectacular, often destructive and sometimes murderers. Many methods of calculating stability have been proposed. These are differentiated?by the assumptions accepted by their authors (methods of calculation in equilibrium limit, methods of calculation at break, deformation calculation methods) and the ease of their implementation (calculations using charts, automatic calculations using software), but they all agree to define an overall factor of safety according to which the stability?of?the studied slope is considered to be insured or compromised, or by safety factor spartial effects on the one hand, applied stresses and, on the other hand, the mechanical properties soil. Various embankment strengthening techniques have been developed. They are differentiated by the process of their realization, their cost and their durability. The main objective of this study is to present the problems of both natural and artificial slope stability on construction projects. In this regard, special emphasis?is given to the sensitivity of the calculation model input parameters (soil, load),?which should contribute to raising awareness about this issue, as a prerequisite to make the right decisions and optimal technical solutions in this area.展开更多
基金financially supported by the China Postdoctoral Science Foundation(No.2015M580491)the National Natural Science Foundation of China(No.51404262)+1 种基金the Natural Science Foundation of Jiangsu Province(No.BK20140213)the National High Technology Research and Development Program of China(No.2012AA062004)
文摘In order to study the stability control mechanism of a concave slope with circular landslide, and remove the influence of differences in shape on slope stability, the limit analysis method of a simplified Bishop method was employed. The sliding body was divided into strips in a three-dimensional model, and the lateral earth pressure was put into mechanical analysis and the three-dimensional stability analysis methods applicable for circular sliding in concave slope were deduced. Based on geometric structure and the geological parameters of a concave slope, the influence rule of curvature radius and the top and bottom arch height on the concave slope stability were analyzed. The results show that the stability coefficient decreases after growth, first in the transition stage of slope shape from flat to concave, and it has been confirmed that there is a best size to make the slope stability factor reach a maximum. By contrast with average slope, the stability of a concave slope features a smaller range of ascension with slope height increase, which indicates that the enhancing effect of a concave slope is apparent only with lower slope heights.
基金Supported by National Natural Science Foundation of China(Grant No.11761029)Inner Mongolia Higher Education Science and Technology Research Project(Grant Nos.NJZY22323 and NJZY22324)Inner Mongolia Natural Science Foundation(Grant No.2018MS07020)。
文摘Let X and Y be Banach spaces.For A∈L(X),B∈L(Y),C∈L(Y,X),let MCbe the operator matrix defined on X⊕Y by M_(C)=(AC0B)∈L(X⊕Y).In this paper we investigate the decomposability for MC.We consider Bishop’s property(β),decomposition property(δ)and Dunford’s property(C)and obtain the relationship of these properties between M_(C) and its entries.We explore how σ_(*)(M_(C))shrinks from σ_(*)(A)∪σ_(*)(B),where σ_(*)denotes σ_(β),σ_(δ),σ_(C),σ_(dec).In particular,we develop some sufficient conditions for equality σ_(*)(MC)=σ_(*)(A)∪σ_(*)(B).Besides,we consider the perturbation of these properties for MCand show that in perturbing with certain operators C the properties for MCkeeps with A,B.Some examples are given to illustrate our results.Furthermore,we study the decomposability for(0AB0).Finally,we give applications of decomposability for operator matrices.
基金Project(50378036) supported by the National Natural Science Foundation of ChinaProject(200503) supported by Foundation of Communications Department of Hunan Province, China
文摘Based on Bishop's model and by applying the first and second order mean deviations method, an approximative solution method for the first and second order partial derivatives of functional function was deduced according to numerical analysis theory. After complicated multi-independent variables implicit functional function was simplified to be a single independent variable implicit function and rule of calculating derivative for composite function was combined with principle of the mean deviations method, an approximative solution format of implicit functional function was established through Taylor expansion series and iterative solution approach of reliability degree index was given synchronously. An engineering example was analyzed by the method. The result shows its absolute error is only 0.78% as compared with accurate solution.
文摘The stability of earthworks (cuttings, embankments, dikes) and natural slopes is a?problem that is of concern to geotechnicians, both practitioners and researchers. The disorders generated by breaking the slopes are usually spectacular, often destructive and sometimes murderers. Many methods of calculating stability have been proposed. These are differentiated?by the assumptions accepted by their authors (methods of calculation in equilibrium limit, methods of calculation at break, deformation calculation methods) and the ease of their implementation (calculations using charts, automatic calculations using software), but they all agree to define an overall factor of safety according to which the stability?of?the studied slope is considered to be insured or compromised, or by safety factor spartial effects on the one hand, applied stresses and, on the other hand, the mechanical properties soil. Various embankment strengthening techniques have been developed. They are differentiated by the process of their realization, their cost and their durability. The main objective of this study is to present the problems of both natural and artificial slope stability on construction projects. In this regard, special emphasis?is given to the sensitivity of the calculation model input parameters (soil, load),?which should contribute to raising awareness about this issue, as a prerequisite to make the right decisions and optimal technical solutions in this area.
