We propose a computational method for assessing bolt reinforcement of the tunnel face in cohesive frictional soils and weak rocks under seepage flow conditions. The method is based on limit equilibrium factors and can be applied to reinforcement layouts that are arbitrary in terms of the spacing, length, longitudinal overlapping and installation sequence of the bolts. An investigation is made into the influence of water table height on the stability of a reinforced face. In particular, we show that, if the gradient of the hydraulic head is high, then tensile failure of the ground ahead of the face may be more critical than shear failure. For an approximate hydraulic head distribution in the ground around the tunnel face and assuming uniform face reinforcement, we derive a closed-form solution for the necessary bolting density.
Ground reinforcement using bolts is a very efficient measure for stabilizing the face in conventional tunneling. It was applied for the first time in around 1980 in Italian tunnels (cf. [1, 2]). Over the years, considerable research has been conducted by numerous authors into the conditions for and the assessment of face stability. A recent review of the state of the art can be found in .
Seepage flow may occur in the case of highly permeable ground or very slow excavation and results in hydraulic head gradients in the ground ahead of the excavation face. The hydraulic head gradient acts as a body force, the so-called "seepage force", which is directed towards the face and is therefore unfavorable with respect to its stability.
Although tunneling in water bearing grounds is common in practice and many publications address the stability of the excavation face under such conditions (a recent review can be found in ), few studies (e.g. ) deal specifically with the stability of tunnel faces reinforced by bolts under seepage flow conditions.
The present paper investigates the face stability of a reinforced tunnel face beneath the water table and under drained conditions using the wedge and prism mechanism of Figure 1a and analyses the equilibrium of the wedge based upon the method of slices ().
It extends research works  and , which used the same approach to investigate the stability of reinforced tunnel faces located above the water table and the stability of tunnel faces in water bearing grounds, respectively, under conditions of uniform support pressure and partial compensation of the hydraulic head at the tunnel face.
Section 2 outlines the seepage-flow analysis and presents a simplified distribution of the hydraulic head, which will be introduced in the limit equilibrium analysis. Section 3 describes the limit equilibrium analysis of the mechanism considered. Section 4 shows some comparative computations.