In the underhand cut-and-fill mining method,a sill mat(i.e.an artificial horizontal pillar)constructed by cemented backfill is essential to prevent mine workers from being directly exposed under problematic rock roofs...In the underhand cut-and-fill mining method,a sill mat(i.e.an artificial horizontal pillar)constructed by cemented backfill is essential to prevent mine workers from being directly exposed under problematic rock roofs.A critical issue is to determine the minimum required strength of the sill mat to ensure a safe and cost-effective design.Until now,Mitchell’s analytical solution is the only available option,considering two stiff and immobile rock walls.Unavoidable rock wall closure associated with stope excavation below the sill mat was neglected.This,along with other undefined parameters,explains why Mitchell’s solution is rarely used in sill mat design.A new analytical solution for determining the minimum required strength of the sill mat accounting for wall closure is necessary.In this study,a closed-form analytical solution for estimating rock wall closure generated by stope excavation below a sill mat is developed by using Salamon’s and Flamant’s models.The proposed analytical solution does not contain any coefficients of correction or calibration.Despite several assumptions(or somewhat of oversimplifications)necessary to render a simple analytical solution possible,good agreements are obtained between the rock wall closures predicted by applying the proposed analytical solution and those obtained numerically with FLAC3D for many cases with arbitrarily chosen geometrical and material parameters.The proposed analytical solution is therefore validated and can be used to evaluate the rock wall closure generated by stope excavation below a sill mat.展开更多
In the numerical study of rough surfaces in contact problem, the flexible body beneath the roughness is commonly assumed as a half-space or a half-plane. The surface displacement on the boundary, the displacement comp...In the numerical study of rough surfaces in contact problem, the flexible body beneath the roughness is commonly assumed as a half-space or a half-plane. The surface displacement on the boundary, the displacement components and state of stress inside the half-space can be determined through the convolution of the traction and the corresponding influence function in a closed-form. The influence function is often represented by the Boussinesq-Cerruti solution and the Flamant solution for three-dimensional elasticity and plane strain/stress, respectively. In this study, we rigorously show that any numerical model using the above mentioned half-space solution is a special form of the boundary element method(BEM). The boundary integral equations(BIEs) in the BEM is simplified to the Flamant solution when the domain is strictly a half-plane for the plane strain/stress condition. Similarly, the BIE is degraded to the Boussinesq-Cerruti solution if the domain is strictly a half-space. Therefore, the numerical models utilizing these closed-form influence functions are the special BEM where the domain is a half-space(or a half-plane). This analytical work sheds some light on how to accurately simulate the non-half-space contact problem using the BEM.展开更多
基金financial support from the Young Scientist Project of the National Key Research and Development Program of China(Grant No.2021YFC2900600)the Beijing Nova Program(Grant No.20220484057)+1 种基金The authors acknowledge the financial support from the Natural Sciences and Engineering Research Council of Canada(Grant No.RGPIN-2018-06902)industrial partners of the Research Institute on Mines and the Environment(RIME UQAT-Polytechnique:https://irme.ca/en/).
文摘In the underhand cut-and-fill mining method,a sill mat(i.e.an artificial horizontal pillar)constructed by cemented backfill is essential to prevent mine workers from being directly exposed under problematic rock roofs.A critical issue is to determine the minimum required strength of the sill mat to ensure a safe and cost-effective design.Until now,Mitchell’s analytical solution is the only available option,considering two stiff and immobile rock walls.Unavoidable rock wall closure associated with stope excavation below the sill mat was neglected.This,along with other undefined parameters,explains why Mitchell’s solution is rarely used in sill mat design.A new analytical solution for determining the minimum required strength of the sill mat accounting for wall closure is necessary.In this study,a closed-form analytical solution for estimating rock wall closure generated by stope excavation below a sill mat is developed by using Salamon’s and Flamant’s models.The proposed analytical solution does not contain any coefficients of correction or calibration.Despite several assumptions(or somewhat of oversimplifications)necessary to render a simple analytical solution possible,good agreements are obtained between the rock wall closures predicted by applying the proposed analytical solution and those obtained numerically with FLAC3D for many cases with arbitrarily chosen geometrical and material parameters.The proposed analytical solution is therefore validated and can be used to evaluate the rock wall closure generated by stope excavation below a sill mat.
文摘In the numerical study of rough surfaces in contact problem, the flexible body beneath the roughness is commonly assumed as a half-space or a half-plane. The surface displacement on the boundary, the displacement components and state of stress inside the half-space can be determined through the convolution of the traction and the corresponding influence function in a closed-form. The influence function is often represented by the Boussinesq-Cerruti solution and the Flamant solution for three-dimensional elasticity and plane strain/stress, respectively. In this study, we rigorously show that any numerical model using the above mentioned half-space solution is a special form of the boundary element method(BEM). The boundary integral equations(BIEs) in the BEM is simplified to the Flamant solution when the domain is strictly a half-plane for the plane strain/stress condition. Similarly, the BIE is degraded to the Boussinesq-Cerruti solution if the domain is strictly a half-space. Therefore, the numerical models utilizing these closed-form influence functions are the special BEM where the domain is a half-space(or a half-plane). This analytical work sheds some light on how to accurately simulate the non-half-space contact problem using the BEM.
