Additional stress transfer model of double layer dielectric foundation on thin topsoil covered area

When constructing some buildings on the surface of mine goaf, the additional foundation stress may cause the activation of the stable structure in goaf, and in turn the residual movement and deformation of surface may affect the safety of buildings. In view of the few and imperfect models for calculating the additional stress and the depth of load effect on thin topsoil layer area, it is necessary to further investigate the additional stress transfer model of double layer elastic medium foundation from the perspective of simple calculation process, fewer parameters and easy access. Firstly, the foundation of thin topsoil area is regarded as the upper layer with thin thickness and weak mechanical strength, and the lower layer is the rock layer with larger thickness and high mechanical strength. Secondly, based on the Boussinesp elastic solution, it is assumed that each layer of the double-layered foundation is a transversely isotropic elastomer and there is no change of kinetic energy during the propagation of additional stress in the foundation. Thirdly, based on the conservation of elastic strain energy and the balance condition of vertical additional stress between the micro cell topsoil layer and bedrock layer on the interface of rock and soil layer, the balance equation is established, and each component of the balance equation is solved and simplified in its integral domain with help of MATLAB. The equation for solving the additional stress under the center point of foundation with rectangular uniform load and circular uniform load in thin surface soil layer is derived. Then, according to the stability analysis method of goaf under the influence of additional stress of building foundation, an analysis software of the influence of proposed construction project on the stability of goaf is written using the C# language, which realizes the scientific and efficient calculation of the additional stress of foundation and the stability evaluation of goaf. The model for solving additional stress of double layer medium foundation is verified and the calculation results are compared with those of the widely used homogeneous medium model. Finally, the effect of parameters E₁, μ₁ and E₂, μ₂ on additional stress and depth of foundation are analyzed. Results show that the additional stress transfer model of double layer medium foundation with thin topsoil area is simple to be solved and can be used to guide the comprehensive utilization of mining subsidence area. For the coal mining subsidence area with thin topsoil layer, the vertical additional stress of foundation attenuates to a certain extent in the process of propagation in topsoil layer. Compared with homogeneous medium, the depth of additional stress on the foundation of double layer medium decreases by 5.3%−10.3%. The higher ratio of elastic modulus E₂/E₁ between bedrock and topsoil layer is, the more obvious attenuation of additional stress along the depth direction in bedrock is, and the smaller transfer depth is. Additional stress is less sensitive to the Poisson's ratio of topsoil and bedrock, but the smaller μ₁/μ₂ ratio, the smaller additional stress and the smaller the transfer depth in bedrock.