Tunnel Face Stability & New CPT Applications - Geo-Engineering

18 2. Stability Analysis of the Tunnel FaceτGτs(z t )DFigure 2.16: Blow-out model including friction at boundariesits surroundings can be neglected and the blow-out pressure equals the vertical total stresss max = σ v . (2.16)Other models do take the shear stresses between the moving soil body and its surroundingsinto account. These shear stresses can be included directly as a shear force along the vertical sidesof a two-dimensional rectangular body, as sketched in figure 2.16, which leads to an allowablepressures max = C[γ + 2c + C K y γ ′ tan ϕD]. (2.17)Another approach is to include a wedge shaped body which is lifted together with the soilcolumn and calculate the allowable support pressure assuming that this entire body must belifted. Balthaus [24] for example models an inverted truncated pyramid with angles 45 ◦ + ϕ/2(see figure 2.17) and holds that the safety against blow-out η is given byη = G S > η 1 = 6 ( B ′ + C cot (45 ◦ + ϕ/2) )B ′ > η 2 = γ C(2.18)s(z t )s(z t )and further that it is sufficient to determine η 1 as a conservative estimate of the safety againstblow-out. It should of course be ensured that the shear force between the central soil columnand the outer wedges is sufficient to lift the wedges. An assumption made in this model is thatthe support pressure can find no weakened flow channels to the surface, for example due to boreholes [9].When the face is supported by air, the same estimates of the maximal allowable supportpressure hold but another effect has also be taken into account. When the face is not completelysealed, air will leak out of the working chamber and flow into the soil. An air bubble maythen form in front of the face, as sketched in figure 2.18. If the assumption is made that the airpressure must be lower than the weight of the overlying layers [62], a critical height h a abovethe tunnel can be determined asγγh a = wC − D1 + γ (2.19)γ wwith γ w the unit weight of water, while the stand-up time before blow-out is given byt = n [ ((D + C) ln 1 + h ) ]a− h a . (2.20)kD