Upper and lower bound solutions for the face stability of shallow circular tunnels in frictional material

Abstract

With the recent increase in underground urban development as well as for transportation, tunnels need to he driven in increasingly dif&ult soil conditions. In most cases the ground itself is not stable and face stability is achieved by applying fluid pressure to the tunnel front. The question of determining the retaining pressure to he used has received special consideration in the past hecause of the concern for safety during construction, and also hecause of the damage that could he caused to surface structures by the failure of a shallow tunnel. The problem is three-dimensional and can he studied by using the limit state design method. Solutions are available for the case of a circular tunnel in purely cohesive ground, but very little is known of the face stability of a tunnel driven in sandy soils. This Paper approaches this latter problem from the point of view of limit analysis. Both safety against face collapse and blow-out are considered. Three upper hound solutions are derived from the consideration of mechanisms based on the motion of rigid conical blocks. The results are compared with lower hound solutions published in a previous article. A failure criterion is proposed for the tunnel face in the general case of a cohesive and frictional soil, and charts are provided to allow a bracketed estimate of the required retaining pressure. A comparison with centrifuge laboratory tests shows close agreement between the theoretical upper hound solutions and the face pressures at collapse measured experimentally.

Centrifuge model test on the face stability of shallow tunnel

“…However, the range of required support pressure is in good agreement with other experimental investigations [5,11,25] and some proposed theoretical approaches [2,15,35] (Table 2). Some other models predict a pressure about twice as high [12,14].…”

“…Measured pressure at tunnel face was close to the upper bound solution for frictional material proposed by Léca and Dormieux [15], as well as to other experimental and analytical examinations. Since the minimum support pressure required for face stability was sought after, this finding is quite reasonable.…”

“…Tables 2 and 3. Amongst others, the support pressure was compared with the kinematical approach proposed by Léca and Dermieux [15], where the first value corresponds to the upper bound and the second to the lower bound value of face collapse ( Table 2). Some key information on the DIC is given in Table 3.…”

“…Among others, Leca and Dormieux [15] proposed a failure criterion for the tunnel face in cohesive and frictional soil. Chambon and Corte [5,6] reported on centrifuge model tests where the support pressure for face stability was measured.…”

“…Chambon and Corte [5,6] reported on centrifuge model tests where the support pressure for face stability was measured. Despite the wide choice of proposed models, only a few of them have been applied in tunnel projects (e.g., Horn [9], Leca and Dormieux [15], Anagnostou and Kovári [1,2]). Only limited evidence for their quality exists.…”