Role of equal-strain assumption in unit-cell theory for consolidation with vertical drains

In the development of unit-cell theory for the analytical analysis of consolidation with vertical drains, the equal-strain assumption is often made with the intention of modelling consolidation under uniform settlement conditions. In contrast, the free-strain assumption for modelling consolidation under uniform load conditions is seldom employed, mainly because of the complexities involved in the analysis. This study derives a rigorous analytical solution to the generalised governing equations of free-strain consolidation with a vertical drain subjected to an instantaneous load. Calculated results from the newly proposed solution are compared with those from three available solutions derived based on the equal-strain assumption. Surprisingly good agreement is obtained in terms of excess pore-water pressure, degree of consolidation, and settlement. Horizontal profiles of settlement were not uniform before the end of consolidation. This indicates that the uniform settlement condition is not actually reproduced by the analytical solutions derived based on the equal-strain assumption. The equal-strain assumption is a sufficient but not necessary condition for deriving an analytical solution to unit-cell consolidation theory. The assumption plays no role in modelling consolidation under uniform settlement conditions but simplifies the analytical analysis of free-strain consolidation and results in an approximate solution of high accuracy for consolidation under uniform load conditions. Moreover, drain resistance and smear effects not only retard the consolidation rate, but also importantly shape the vertical and horizontal profiles of excess pore-water pressure, respectively.

Centrifuge modeling of tunneling-induced ground surface settlement in sand

Stress changes in the soil induced by tunnel excavation may cause excessive ground settlement.However,high-quality experimental data on ground settlement due to tunnel excavation are limited.In this study,centrifuge tests are conducted to investigate the threedimensional ground surface settlement,considering different intersection angles and cover-to-tunnel diameter ratios.The results indicate that the major influence zone along the longitudinal direction on the ground surface settlement is±1.25D,where D is the tunnel diameter.When the monitoring section is perpendicular to the tunneling direction,the transverse ground settlement due to the tunnel excavation is symmetrical with respect to the tunnel centerline.In contrast,an asymmetric ground settlement profile is observed when the monitoring section intersects the tunneling direction at an angle of 60
.Applying a Gaussian curve to fit the ground surface settlement curve,the width parameter,K(i.e.,the distance between the tunnel centerline and the inflection point of the settlement trough to the tunnel burial depth),varies from 0.33 to 0.39.The ground surface settlement induced by twin tunnel excavation can be captured reasonably by superimposing two identical Gaussian curves.When the cover to tunnel diameter ratios(C/D)are 1.5 and 2.7,the maximum ground surface settlements are 0.67%of D and 0.35%of D,respectively.It is clear that the maximum ground surface settlement decreases with an increase in the C/D ratio.