Empirical and semi-analytical methods for evaluating tunnelling-induced ground movements in sands

Empirical formulas and closed-form solutions provide, in many cases, good predictions of tunnelling-induced ground movements which, when combined with their computational efficiency, make them valuable for tunnel-structure interaction analyses. For sandy soils, however, there is a shortage of available methods that can adequately describe the changes in soil deformation patterns that occur as a result of tunnel volume loss, soil relative density, and geometrical parameters. In this paper, two approaches are adopted to describe centrifuge test outcomes for tunnelling in dry silica sand of varying relative density. Firstly, empirical expressions for the prediction of settlement trough shape and magnitude are presented; additionally, a set of equations is given to describe the settlement troughs using modified Gaussian curves. Next, semi-analytical expressions (modifying an elastic analytical solution for incompressible soil and ovalized tunnel) are developed to predict both vertical and horizontal movements within the ground. Results from both methods can capture the main effects that cover-to-diameter ratio, relative density, and volume loss have on surface and subsurface ground movement profiles. The proposed expressions can be used for the calibration/verification of tunnel-structure interaction analysis methods by using outputs from comparable centrifuge tests; once verified, these methods may be more widely applied to other scenarios and used within design or risk-assessment exercises