Stability of twin square and circular tunnels placed at relative depths in clayey deposit using adaptive lower bound – finite element limit analysis

Abstract

Owing to the space restraints, the changes in soil formations, the presence of important structures on the ground surface, the presence of a largely confined aquifer; the tunnels in the 'twin-tunnel' may be required to be placed at two different depths relative to each other. In view of this possible scenario, this study utilizes the lower bound finite element limit analysis technique to determine the stability factors of twin tunnels placed at different relative depths in a clayey deposit. The tunnels are assumed to be unsupported, straight and infinitely long; thus, modeled as a plain strain problem. The soil surrounding the tunnels in assumed to be clayey soil in undrained condition. Two categories of shapes are taken into account, namely square, and circular tunnel. The stability number is obtained by following two different approaches: (i) load multiplier method where the objective function, i.e., the collapse multiplier in the limit analysis, is the net surface surcharge, and (ii) gravity multiplier method where the acceleration due to gravity becomes the objective function of the optimization problem. The analysis conducted in this thesis utilizes the OptumG2, a finite element limit analysis software and it leverages the feature ‘adaptive meshing’ to obtain precise results within lesser computation time. The impacts of different depth ratios, spacing between the tunnels, and soil properties on the stability factors as well as the failure mechanism have been studied thoroughly. For the ease of interpretation, all the parameters have been expressed as dimensionless parameter and stability charts are obtained in terms of stability number for various combinations of these dimensionless parameters. Variation of the collapse mechanism based on state of yield for different parameters is also presented in this study. Accuracy of the adopted methodology is verified by comparing the results with that of a standard stability problem of square tunnel and circular tunnel.