Second lining stability, which is the last protection in tunnel engineering, is critically important. The theological properties of the surrounding rock heavily affect second lining stability. In this work, we used la...Second lining stability, which is the last protection in tunnel engineering, is critically important. The theological properties of the surrounding rock heavily affect second lining stability. In this work, we used laboratory triaxial compressive rheological limestone tests to study nonlinear creep damage characteristics of surrounding rock mass in construction projects. We established a nonlinear creep damage constitutive model for the rock mass, as well as a constitutive model numerical implementation made by programming. Second, we introduced a new foam concrete with higher compression performance and good ductility and studied its mechanical properties through uniaxial and triaxial tests. This concrete was used as the filling material for the reserved deformation layer between the primary support and second lining. Finally, we proposed a high efficiency and accuracy staged optimization method. The minimum reserved deformation layer thickness was established as the optimization goal, and the presence of plastic strain in the second lining after 100 years of surrounding rock creep was used as an evaluation index. Reserved deformation layer thickness optimization analysis reveals no plastic strain in the second lining when the reserved deformation minimum thickness layer is 28.50 cm. The results show that the new foam concrete used as a reserved deformation layer filling material can absorb creep deformation of surrounding rock mass, reduce second lining deformation that leads to plastic strain, and ensure long-term second lining stability.展开更多
Let M be an n dimensional complete Riemannian manifold satisfying the doublingvolume property and an on-diagonal heat kernel estimate. The necessary-sufficientcondition for the Sobolev inequality ‖f‖q ≤ Cn,,v,p,q(...Let M be an n dimensional complete Riemannian manifold satisfying the doublingvolume property and an on-diagonal heat kernel estimate. The necessary-sufficientcondition for the Sobolev inequality ‖f‖q ≤ Cn,,v,p,q(‖▽f‖p+‖fp) (2≤p＜q＜∞) is given.展开更多
Under investigation in this paper is a （3 q- 1）-dimensional variable-coefficient Kadomtsev-Petviashvili equation, which describes the propagation of surface and internal water waves. By virtue of the binary Bell pol...Under investigation in this paper is a （3 q- 1）-dimensional variable-coefficient Kadomtsev-Petviashvili equation, which describes the propagation of surface and internal water waves. By virtue of the binary Bell polynomials, symbolic computation and auxiliary independent variable, the bilinear forms, soliton solutions, Backlund transformations and Lax pair are obtained. Variable coefficients of the equation can affect the solitonic structure, when they are specially chosen, while curved and linear solitons are illustrated. Elastic collisions between/among two and three solitons are discussed, through which the solitons keep their original shapes invariant except for some phase shifts.展开更多
基金Projects(51409154,41372289)supported by the National Natural Science Foundation of ChinaProjects(2015JQJH106,2014TDJH103)supported by Research Fund of Shandong University of Science and Technology,China
文摘Second lining stability, which is the last protection in tunnel engineering, is critically important. The theological properties of the surrounding rock heavily affect second lining stability. In this work, we used laboratory triaxial compressive rheological limestone tests to study nonlinear creep damage characteristics of surrounding rock mass in construction projects. We established a nonlinear creep damage constitutive model for the rock mass, as well as a constitutive model numerical implementation made by programming. Second, we introduced a new foam concrete with higher compression performance and good ductility and studied its mechanical properties through uniaxial and triaxial tests. This concrete was used as the filling material for the reserved deformation layer between the primary support and second lining. Finally, we proposed a high efficiency and accuracy staged optimization method. The minimum reserved deformation layer thickness was established as the optimization goal, and the presence of plastic strain in the second lining after 100 years of surrounding rock creep was used as an evaluation index. Reserved deformation layer thickness optimization analysis reveals no plastic strain in the second lining when the reserved deformation minimum thickness layer is 28.50 cm. The results show that the new foam concrete used as a reserved deformation layer filling material can absorb creep deformation of surrounding rock mass, reduce second lining deformation that leads to plastic strain, and ensure long-term second lining stability.
基金Project supported by the National Natural Science Foundation of China (No.10271107) the 973 Project of the Ministry of Science and Technology of China (No.G1999075105) the Zhejiang Provincial Natural Science Foundation of China (No.RC97017).
文摘Let M be an n dimensional complete Riemannian manifold satisfying the doublingvolume property and an on-diagonal heat kernel estimate. The necessary-sufficientcondition for the Sobolev inequality ‖f‖q ≤ Cn,,v,p,q(‖▽f‖p+‖fp) (2≤p＜q＜∞) is given.
基金Supported by the National Natural Science Foundation of China under Grant No.11272023the Open Fund of State Key Laboratory of Information Photonics and Optical Communications(Beijing University of Posts and Telecommunications)under Grant No.IPOC2013B008the Fundamental Research Funds for the Central Universities of China under Grant No.2011BUPTYB02
文摘Under investigation in this paper is a （3 q- 1）-dimensional variable-coefficient Kadomtsev-Petviashvili equation, which describes the propagation of surface and internal water waves. By virtue of the binary Bell polynomials, symbolic computation and auxiliary independent variable, the bilinear forms, soliton solutions, Backlund transformations and Lax pair are obtained. Variable coefficients of the equation can affect the solitonic structure, when they are specially chosen, while curved and linear solitons are illustrated. Elastic collisions between/among two and three solitons are discussed, through which the solitons keep their original shapes invariant except for some phase shifts.
