Estimating Tunnelling-Induced Ground Deformation in Sandy Cobble Stratum Considering Rock Content Variation

Abstract

In sandy cobble stratum, the contents of rock blocks along the tunnel line present to be different. The tunneling-induced ground deformation under different rock contents is perceived as a main concern. Considering the heterogeneity of ground material, the meso-scale numerical models of sandy cobble strata were used to simulate tunnel excavation, in which the rock blocks and soil matrix were treated as separated constituents. By comparing the ground stress of simulation results with that of theoretical values, the applicability of meso-scale models was verified. The simulation results show that the rock content has a significant effect on the ground deformation performance. With the increase of rock content from 0 to 50%, the maximum ground settlement and the expansion of plastic zone gradually decreases, and the variation rule of the maximum ground settlement with rock content can be described by a normal distribution function. Meanwhile, the tunnel deformation pattern changes from non-uniform convergence to uniform convergence. It is also found that the relationship between the maximum subsurface settlement or the width coefficient of subsurface settlement trough and subsurface depth can be described by a power function, respectively.

Appendix: Gaussian Function for Predicting Ground Settlement

Through analyzing the surface settlement data monitored from lots of tunnels, Peck (1969) proposed that in the case of a single tunnel, the Gaussian function curve can be used to describe the ground surface settlement profile. The ground surface settlement S is defined as:

$$ S(x) = S_{\max } \exp \left({ - }\frac{{x^{2} }}{{2i^{2} }}\right) $$

(8)

where S_max is the maximum ground surface settlement, x is the horizontal distance from the tunnel centerline, i is the trough width parameter which represents the horizontal distance from the tunnel centerline to the inflection point of the Gaussian curve (see Fig. 19. 

Fig. 19

Schematic diagram of the ground settlement trough in transverse section

After analyzing the field and centrifuge model test measurements of subsurface settlements above tunnels, Mair et al. (1993) found that the shapes of subsurface settlement profiles also could be characterized by the Gaussian distribution curve, as shown in Fig. 19. Then, Eq. (A1) is extended to be the following form

$$ S(x,z) = S_{\max } (z)\exp \left[{ - }\frac{{x^{2} }}{{2i(z)^{2} }}\right] $$

(9)

where S_max(z) is the maximum subsurface settlement at depth z, i(z) is the width coefficient of the settlement trough at depth z, z is the vertical distance from the ground surface to investigated subsurface location.