Upper-bound stability analysis of a plane strain heading in non-homogeneous clay

Highlights

• We study tunnel stability in non-homogeneous soil using the multi-rigid-block method.

• The collapse pressure increases as soil gravity increases or strength decreases.

• New mechanism intermix inhomogeneous deforming region and rigid blocks translation.

• An upper bound analytical solution for the plane strain heading is obtained.

Abstract

This paper investigates the undrained stability of a plane strain tunnel heading in cohesive soil, whose undrained shear strength is assumed to increase linearly with depth. Upper bound stability solutions for a practical range of parameters of geometries and soil conditions are found using the multi-rigid-block upper bound method. The upper bound solutions obtained from the multi-rigid-block mechanisms significantly improve the classical solutions and have good agreement with those of the finite element limit analysis when C/D is small. An improved simple collapse mechanism which intermix inhomogeneous deforming region and rigid blocks translation together is proposed based on the multi-rigid-block upper-bound analysis. An upper bound analytical solution is then obtained in view of the numerical results of both the multi-rigid-block collapse mechanism and the improved simple collapse mechanism. And it predicts the plane strain heading stability relatively accurate for shallow tunnels.

Introduction

Many metropolitan cities are located on soft ground adjacent to rivers and coastlines. Underground work in such locations is classified into soft ground excavation as they are mostly constructed in shallow depth to achieve access convenience and economy. The safety assessment of shallow underground tunnel excavations in soft ground usually requires solutions to two separate predictive problems. Firstly, it is necessary to determine the stability of the excavation, for the safety of those at the surface and underground. Secondly, to prevent damage to surface or subsurface structures is also needed (Augarde et al., 2003). This paper examines the undrained face stability of a shallow tunnel heading driven by a pressurized shield in soft clay.

For tunneling in soft ground, several studies have been dedicated to the stability analysis considered a purely cohesive soil in the literature, involving experimental investigations, theoretical predictions and numerical modeling. A comprehensive experimental study on the behavior of tunnels and headings in clays has been conducted at Cambridge University during the 1970s (Cairncross, 1973; Orr, 1976; Casarin, 1977; Mollon et al., 2010; Seneviratne, 1979), and culminated in the exhaustive experimental and theoretical investigation of the work of Mair (1979), who used the centrifuge to observe the undrained collapse of two-dimensional circular tunnel sections and three-dimensional cylindrical tunnel headings in normal consolidated kaolin under different geometry and gravity regimes. Based on these experimental observations, Davis et al. (1980) conducted comprehensive analyses of the stability considering three different shapes of shallow tunnels, plane strain unlined circular tunnels, plane strain tunnel headings and three-dimensional cylindrical headings. They introduced a range of rigorous lower and upper bound solutions using the classical limit theorems for tunnel collapse in pure cohesive soil under undrained conditions. Ellstein (1986) presented an analytical expression of the stability ratio for the tunnel in homogeneous cohesive soils based on the limit equilibrium approach. Since the late 1980s, a new numerical approach was proposed by Sloan and co-workers, which involves finite element formulations of the classical limit theorems. Sloan and Assadi, 1991, Sloan and Assadi, 1993 obtained tight bounds of the collapse pressure for the square tunnel in undrained uniform soil and the circular tunnel in non-homogeneous soil separately, using the finite element limit analysis method (giving both upper and lower bounds) as well as the rigid-block upper bound method. Augarde et al. (2003) used these same approaches to investigate the stability of the plane strain tunnel heading considering the heterogeneity and self-weight of the soil. Lee et al. (2006) conducted a series of centrifuge model tests and numerical simulations of these tests were carried out to investigate the surface settlement troughs, tunnel stability and arching effects that develop during tunneling in soft clay. Mollon et al. (2010) performed the stability analysis in the framework of the kinematical approach of limit analysis theory based on a translational three-dimensional multi-block failure mechanism.

As a conclusion, the limit analysis method has been widely used in the stability analysis of the underground openings relevant to tunneling. Limit analysis has strict theory and can define scope of the true solution in geotechnical problems. But mostly the range between the upper and lower bounds need to be further improved due to the relatively simple mode adopted by the above scholars. Two main approaches have been followed in the limit analysis to improve the calculation: the finite element limit analysis and the multi-rigid-block upper-bound method. The finite element limit analysis method combines the advantages of the finite elements for handling the complex geometric and loading conditions, with the power of the plastic limit theorems for bounding the exact collapse load. More precise answers can be usually obtained by using the finite element limit analysis method (Augarde et al., 2003). However, it should be mentioned that the implementation of the finite element limit analysis method is not easy for engineering. The multi-rigid-block method is clear in concept and easy to program and solve. It has been developed to serve as simple design tools for practicing engineers in recent years. The validation of the multi-rigid-block upper-bound method has been verified in the analyses of bearing capacity of foundations (Michalowski, 2001, Huang and Qin, 2009), slope stability (Donald and Chen, 1997), basal heave stability (Qin et al., 2010), and shallow or deep strip anchors (Huang et al., 2011). It was shown by these authors that the multi-rigid-block upper bound method significantly improves the solutions given by the traditional upper bound solutions. This is due to the great freedom offered by the multi-block mechanism to move more freely with respect to the traditional mechanisms.

In this paper, the multi-rigid-block upper-bound method is used to investigate the stability of a plane strain tunnel heading in pure cohesive soil whose undrained shear strength increases linearly with depth. Least upper bound solutions are obtained by optimizing the shape of the multi-rigid-block mechanism with respect to the geometric variables and an approximation equation for estimating the collapse pressure is developed. Based on the result of the stability analysis, an improved collapse mechanism for the stability analysis of the plane strain tunnel heading is proposed and the corresponding semi-analytical solution is derived. After a short describing of the problem, the multi-rigid-block mechanism and the proposed mechanism and the corresponding numerical results are presented and discussed.