Determination of support pressure for semi-elliptical tunnels in anisotropic and nonhomogeneous soil by lower bound limit analysis

This research work examines the stability of long semi-elliptical tunnels in purely cohesive and cohesionless soils. The support pressure (σi) required to apply along the tunnel periphery by means of lining and anchorage system has been evaluated using lower bound limit analysis with finite elements and second-order conic programming technique (SOCP). The results are presented in terms of normalized support pressure as (i) σi/cv0 in purely cohesive soil for different combinations of γD/cv0 and αc and (ii) σi/γD in cohesionless soil for different combinations of ϕv and αϕ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \alpha_{\phi } $$\end{document} considering different values of 2h/D and H/D of tunnel where h, D and H are height of tunnel, width of tunnel and soil cover depth of the semi-elliptical tunnel, respectively; cv0, ϕv and γ are soil undrained shear strength of cohesive soil in vertical direction at the ground level, peak vertical friction angle of cohesionless soil and unit weight of all type of soils, respectively; αc and αϕ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \alpha_{\phi } $$\end{document} are anisotropy factors in cohesive and cohesionless soil, respectively.