Elastic analysis of full stress and displacement field for inclined shaft liner sub-jected to non-uniform stresses

In order to obtain the elastic analytical solution of the non circular inclined shaft wall under non-uniform load,and to learn the stressstrain distribution of the non circular shaft wall,a straight wall semi circular arch affected by the surrounding rock and soil skeleton pressure and pore water pressure was established.Firstly,the mapping function equation of the irregular wall shape was calculated.Secondly,the complex analytical method was used to derive the approximate analytical solution of the total stress and displacement field of the shaft wall,and the analytical solution was verified by numerical simulation method.Finally the influence of factors such as interface porosity np,unloading rate η,side pressure coefficient λ,and well wall thickness diameter ratio ξ were considered.The results show that the mapping function can highly map the non-circular cross section of the wall and ensure the effect of the shape of the wall on the theoretical solution.By comparing the theoretical and numerical simulation,the theoretical solution has a higher accuracy.For a straight walled semi circular arch shaft wall,the largest stress gradient occurs at the floor and the joint between the floor and the side wall.The crack control point lies on the bottom edge of shaft wall and the vault.The change in the porosity of the contact surface will ease the tensile stress of the top and bottom,but will also increase the tension at the side wall.The stress and the porosity of the contact surface can change the stress state of the vault and the side wall.After np≥0.8,the crack control point turns to upper side wall,and the inner edge of the vault turns to a compressed state.It can reduce the stress and deformation value of the borehole wall,but does not change the stress and deformation state of the borehole wall with the increase of wall thickness.Therefore,in the design of the shaft wall,it is necessary to comprehensively consider the ratio of shaft radius to the side wall height,reasonably optimize the shaft section.The unloading rate directly reflects the stress of the surrounding rock applied on the shaft wall after the excavation of the shaft.In the design and construction,the self-bearing capacity of the surrounding rock should be fully used to reduce the load on the wall