In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,t...In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,the original Boussinesq system is transformed into an equivalent one.Then we discretize it using the second-order backward di erentiation formula(BDF2)and Crank-Nicolson(CN)to obtain two second-order time-advanced schemes.In both numerical schemes,a pressure-correction method is employed to decouple the velocity and pressure.These two schemes possess the desired property that they can be fully decoupled with satisfying unconditional stability.We rigorously prove both the unconditional stability and unique solvability of the discrete schemes.Furthermore,we provide detailed implementations of the decoupling procedures.Finally,various 2D numerical simulations are performed to verify the accuracy and energy stability of the proposed schemes.展开更多
This paper presents an integrated investigation of the ground stability of a deep gateroad with a 1 km burial depth based on a field test, case studies, and numerical modelling. In situ stress measurements and mechani...This paper presents an integrated investigation of the ground stability of a deep gateroad with a 1 km burial depth based on a field test, case studies, and numerical modelling. In situ stress measurements and mechanical properties tests were first conducted in the test site. Then, the deformation behavior, stress and yield zone distributions, as well as the bolts load of the gateroad, were simulated using FLAC3D software. The model results demonstrated that the soft rock properties and high in situ stress were the main factors for the deep gateroad instability, and the shear slip failure induced by the high stress was the primary failure model for the deep rock mass. In addition, the unsuitable support patterns, especially the relatively short bolts/cables with low pre-tensions, the lack of high-strengthen secondary supports and the unsupported floor strata, also contributed to the gateroad instability. Subsequently, a new combined supporting strategy, incorporating longer bolts/cables, yielding ring supports, and grouting measures, was proposed for the deep gateroad, and its validity was verified via field monitoring. All these could be a reference for understanding the failure mechanism of the gateroad with 1 km burial depth.展开更多
An analytical approach was presented for estimating the factor of safety(FS) for slope failure, with consideration of the impact of a confined aquifer. An upward-moving wetting front from the confined water was assume...An analytical approach was presented for estimating the factor of safety(FS) for slope failure, with consideration of the impact of a confined aquifer. An upward-moving wetting front from the confined water was assumed and the pore water pressure distribution was then estimated and used to obtain the analytical expression of FS. Then, the validation of the theoretical analysis was applied based on an actual case in Hong Kong. It is shown that the presence of a confined aquifer leads to a lower FS value, and the impact rate of hydrostatic pressure on FS increases as the confined water pressure increases, approaching to a maximum value determined by the ratio of water density to saturated soil density. It is also presented that the contribution of hydrostatic pressure and hydrodynamic pressure to the slope stability vary with the confined aquifer pressure.展开更多
基金Supported by Research Project Supported by Shanxi Scholarship Council of China(2021-029)International Cooperation Base and Platform Project of Shanxi Province(202104041101019)+2 种基金Basic Research Plan of Shanxi Province(202203021211129)Shanxi Province Natural Science Research(202203021212249)Special/Youth Foundation of Taiyuan University of Technology(2022QN101)。
文摘In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,the original Boussinesq system is transformed into an equivalent one.Then we discretize it using the second-order backward di erentiation formula(BDF2)and Crank-Nicolson(CN)to obtain two second-order time-advanced schemes.In both numerical schemes,a pressure-correction method is employed to decouple the velocity and pressure.These two schemes possess the desired property that they can be fully decoupled with satisfying unconditional stability.We rigorously prove both the unconditional stability and unique solvability of the discrete schemes.Furthermore,we provide detailed implementations of the decoupling procedures.Finally,various 2D numerical simulations are performed to verify the accuracy and energy stability of the proposed schemes.
基金Project（2017RCJJ011） supported by the Scientific Research Foundation of Shaaadong University of Science and Technology for Recruited Talents, China Projects（01CK03203, 02CK02302） supported by the Shaaadong Provincial First-Class Discipline Fundamental, China Proj ect（ZR2018QEE001） supported by the Natural Science Foundation of Shandong Province, China
文摘This paper presents an integrated investigation of the ground stability of a deep gateroad with a 1 km burial depth based on a field test, case studies, and numerical modelling. In situ stress measurements and mechanical properties tests were first conducted in the test site. Then, the deformation behavior, stress and yield zone distributions, as well as the bolts load of the gateroad, were simulated using FLAC3D software. The model results demonstrated that the soft rock properties and high in situ stress were the main factors for the deep gateroad instability, and the shear slip failure induced by the high stress was the primary failure model for the deep rock mass. In addition, the unsuitable support patterns, especially the relatively short bolts/cables with low pre-tensions, the lack of high-strengthen secondary supports and the unsupported floor strata, also contributed to the gateroad instability. Subsequently, a new combined supporting strategy, incorporating longer bolts/cables, yielding ring supports, and grouting measures, was proposed for the deep gateroad, and its validity was verified via field monitoring. All these could be a reference for understanding the failure mechanism of the gateroad with 1 km burial depth.
基金Project(R5110012)supported by Special Foundation for Distinguished Young Scholars of Zhejiang Province,ChinaProject(2009C33117)supported by The General Program of Natural Science Foundation of Zhejiang Province,China
文摘An analytical approach was presented for estimating the factor of safety(FS) for slope failure, with consideration of the impact of a confined aquifer. An upward-moving wetting front from the confined water was assumed and the pore water pressure distribution was then estimated and used to obtain the analytical expression of FS. Then, the validation of the theoretical analysis was applied based on an actual case in Hong Kong. It is shown that the presence of a confined aquifer leads to a lower FS value, and the impact rate of hydrostatic pressure on FS increases as the confined water pressure increases, approaching to a maximum value determined by the ratio of water density to saturated soil density. It is also presented that the contribution of hydrostatic pressure and hydrodynamic pressure to the slope stability vary with the confined aquifer pressure.
