Tunnel Face Stability & New CPT Applications - Geo-Engineering

12 2. Stability Analysis of the Tunnel FaceOγOγOγτττ(a)(b)(c)Figure 2.9: Circular and spherical failure mechanisms [98]zx yCDFigure 2.10: Wedge and silo modelure 2.9) have been calculated by Krause [98] in 1987 in a limit-equilibrium analysis usingthe shear stresses on the sliding planes. Of the three mechanisms proposed, the quarter circle(Figure 2.9b) will always yield the highest minimal support pressures min = 1tan ϕ( 13 D γ ′ − 1 2 π c ). (2.14)As Krause already indicates this may not always be a realistic representation of the actual failurebody. In many cases the half-spherical body (Figure 2.9c) will be a better representation. In thatcase the minimal support pressure can be found froms min = 1tan ϕ( 19 D γ ′ − 1 2 π c ). (2.15)An often encountered limit equilibrium model is the wedge model, which assumes a slidingwedge loaded by a soil silo. As it is central to the new stability model developed in this thesis,the theoretical background of the wedge model will be covered in more detail in section 2.2. Anumber of slightly different implementations has been described in literature.Murayama [92, 98] calculated the minimal support pressure using a two-dimensional logspiralshaped sliding plane in 1966 (Figure 2.11). Five years before, a three-dimensional model