Analytical solution for consolidation of saturated viscoelastic soils around tunnels with general Voigt model

Abstract

This paper presents a novel analytical solution for the consolidation behavior of viscoelastic saturated soft soil subjected to large-scale ground loading. The rheological properties of clay are described using the general Voigt model. Based on the Terzaghi-Rendulic theory, the governing equations for the dissipation of excess pore water pressure in the surrounding soil mass of a tunnel are established under the first and second boundary conditions. The governing equations are solved using the complex variable method. The obtained solutions are verified by reducing them to the forms of three traditional rheological models, demonstrating the reliability of the proposed approach. Finally, based on the established solutions, the dissipation characteristics of excess pore water pressure around the tunnel are analyzed. The case results indicate that the soil permeability coefficient (k), the independent Newtonian viscosity coefficient (K0) and Hooke’s spring modulus (E0) in the general Voigt model have significant influences on the dissipation of excess pore water pressure and the degree of consolidation. A larger k, K0, and E0 lead to faster dissipation and consolidation development, while a greater tunnel buried depth (b) results in slower consolidation process. The influence of k on excess pore water pressure dissipation is more significant than that of K0 and E0. For the first boundary type, consolidation is instantaneous when k > 0.1 m/d. For the second type, when k < 0.0001 m/d, excess pore pressure remains unchanged within 100 d. The permeability condition of the tunnel has a considerable impact on the distribution of excess pore water pressure in the soil layer directly above the crown. When the tunnel is fully permeable, the effects of k, K0, and E0 on the dissipation of excess pore water pressure are more pronounced in the early stage, with almost complete dissipation of excess pore pressure above the tunnel before 100 d. However, when the tunnel is completely impermeable, their effects are more prominent in the later stage, and by 100 d, the maximum excess pore pressure within the depth range is 25 % of the initial.