Design of micropiles for tunnel face reinforcement: undrained upper bound solution

Abstract

The stability of tunnel faces supported by an umbrella of subhorizontal micropiles is analyzed by means of the upper bound theorem of plasticity. The micropiles are considered beams subjected to the kinematic motion imposed by the assumed failure mechanism. The limiting resistance of the supporting beams is first addressed. The failure mechanism imposes a displacement pattern on the beam, which is similar to the response of vertical piles subjected to horizontal load. The mechanism of beam deformation was included into the overall instability mechanism for the tunnel face stability. Limiting conditions of the beam under undrained conditions are used. A general minimization process associated with the upper bound formulation is developed. Stability conditions are described in dimensionless parameters and plotted in ready-to-use design charts. In particular, a dimensionless micropile coefficient, which includes all the relevant design parameters of the umbrella, could be isolated and plotted in undrained soil strength and tunnel geometry. A real face failure is finally described, and the required supporting umbrella is designed on the basis of the developed procedure.