Model-independent strength-reduction factor for effect of spatial variability on tunnel with improved soil surrounds

Spatially variable cement-treated ground can be considered, in design, as a uniform medium with appropriately reduced strength. Various strength reduction factors have been proposed for cement-treated ground under different loading conditions. However, the Tresca and Mohr–Coulomb models, which are widely used to represent the behaviour of the improved soil in geotechnical design, do not replicate the strain-softening behaviour and therefore may not lead to sufficiently cautious reduction factors. This study examines the effect of constitutive models on the strength reduction factor to account for spatial variability for tunnels with improved soil surrounds. The improved ground was simulated using three different constitutive models. The results show that the Mohr–Coulomb model gives the lowest critical stress release ratio, as the yield stress decreases much faster with effective stress than with the Tresca and cohesive Cam Clay (C3) models. However, the most conservative values of strength reduction factor needed to account for spatial variability are generally taken by either the C3 or Mohr–Coulomb model, depending on the drainage condition and geometric configuration. Hence using the highest strength reduction factor for each case allows spatial variability to be conservatively considered for cases where the Tresca or Mohr–Coulomb model is used.