Abstract
An analytical solution for the seepage field in water‐filled karst tunnel is derived based on the inversion of complex function and groundwater hydraulics theory. The solution considers the distance between the tunnel and the cavern, the size of the cavern, and the properties of the lining structure, such as the permeability coefficient as well as the radius of the grouting ring. This paper also performed numerical simulations for two cases: the application of gravity and the absence of gravity. The numerical solution was obtained to verify the analytical solution, and a good agreement was found. Then, the effect of parameters is discussed in detail, including the distance between the tunnel and the cavern, the radius of the cavern, the grouting ring, and the initial support. The results show that when the radius of the cavern is constant, the pressure head and seepage flow decrease as the distance between the tunnel and the cavern increases. When the distance is constant, the pressure head and seepage flow increase with the increase of the radius of the cavern. In addition, the pressure head and the seepage flow decrease with the increase of the thickness of the grouting ring and decrease with the decrease of the permeability coefficient. As the thickness of the initial support increases, the pressure head gradually increases and the percolation decreases. Furthermore, due to the great influence of the grouting ring and initial support on the pressure head and seepage flow, the thickness and permeability coefficient of the grouting ring and initial support should be taken into account carefully during construction.
Highlights
In recent years, with the development of the Belt and Road strategy, the construction of tunnels has developed rapidly
Some researchers used the theory of hydraulics and complex functions to solve the analytical solution of seepage field of underwater tunnel composed of surrounding rocks and lining structures [6,7,8,9]
E pore water pressures extracted from the six groups of numerical simulation data in Figure 5 with gravity and Figure 6 without gravity are compared with the theoretical solutions. e results are shown in Figure 7. e law obtained by numerical and theoretical solutions is that when the grouting ring and the initial support are completed and the secondary lining is not yet completed, H1 decreases with the increase of d
Summary
With the development of the Belt and Road strategy, the construction of tunnels has developed rapidly. Based on well mapping theory and superposition principle, Zhang [1] deduced the potential function and distribution of water head in the karst tunnel, but did not study the influence of karst water on tunnel lining structure. Wu [4] deduced the analytic solution of the complex variable function for the distribution of high water pressure seepage field according to the conformal mapping theory. Some researchers used the theory of hydraulics and complex functions to solve the analytical solution of seepage field of underwater tunnel composed of surrounding rocks and lining structures [6,7,8,9]. Based on the theory of the growth of pore pressure caused by linear waves, Xiong et al [10] developed an analytical solution of the seepage field of a tunnel affected by the wave in the semiinfinite aquifer. Huangfu et al [14] studied analytical solutions for steady groundwater flowing into a horizontal tunnel in the semiinfinite aquifer
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