Hermite spectral solution for vertical deformation of underlying tunnel induced by excavation of foundation pit
Aiming at the vertical deformation issue of the underlying tunnel induced by an excavation of the foundation pit,this paper adopts the Hermite functions to develop a novel Hermite-spectral analysis method for estimating the soil additional stress and the vertical deformation of the underlying tunnel.Based on Mindlin's solution and the theory of Euler-Bernoulli beam that lies on the Pasternak foundation,the calculation expression of soil additional stress induced by an excavation of the foundation pit and the governing equation of the underlying tunnel for its vertical deformation are successively developed.Taking advantage of the Hermite functions,both the soil additional stress and the vertical deformation of the underlying tunnel are approximated as two truncated series of Hermite functions and further the developed governing equation above is simplified into a linear algebraic system.By solving this linear algebraic system,a novel solution is developed for calculating the vertical displacement of the underlying tunnel.Then,some calculations on two typical cases are performed to verify the convergence and validity of the developed solution.Finally,the deformation behavior of the underlying tunnel due to the excavation of the foundation pit is investigated,and the influences from the tunnel depth,the horizontal distance between the tunnel and foundation pit as well as the plane sizes of the foundation pit on the induced vertical deformation behavior of underlying tunnel are discussed.The results indicate that as the increase in tunnel depth and that in the horizontal distance between the tunnel and the foundation pit,the effect from the excavation of the foundation pit decreases,and the vertical deformation of the underlying tunnel becomes smaller.The increase in plane size of the foundation pit generally enlarges the vertical deformation of the underlying tunnel,and the size changing parallel to the tunnel shows a more obvious effect.The developed Hermite-spectral solution proposes a novel approach for studying the vertical deformation behavior of the underlying tunnel due to the excavation of foundation pits.
safety engineeringunderlying tunnelvertical deformationexcavation of foundation pitHermite spectral method
万方数据
维普
