Analytical solutions for discharge and hydraulic head of three-dimensional underground caverns in coastal areas

The determination of discharge and hydraulic head of underground caverns is a crucial aspect for their engineering construction. The boundary of aquifer should be bounded for the calculation of seepage field of underground caverns in coastal areas. Therefore, analytical solutions for discharge and hydraulic head of underground caverns with square arch cross-section in a three-dimensional(3D) bounded unconfined aquifer are presented in this paper. Fourier series expansion and Laplace transform are used to obtain a point sink solution. Solutions of discharge and hydraulic head caused by multiple caverns with square arch cross-section in the 3D bounded unconfined aquifer are obtained by integrating the point sink solution in cavern domain which includes cavern cavity, cavern surface and cavern outline (C-S-O integration method). The accuracy of the point sink solution and the cuboid cavern solution is verified by comparing with numerical solutions obtained by COMSOL. The comparison shows that the analytical solutions agree well with numerical solutions. The effects of vertical hydraulic conductivity and specific yield on cavern discharge and hydraulic head are investigated. Treatment methods for actual projects which usually involve the construction of multiple caverns with square arch cross-section, and the long axis of the cavern forms an angle θ with the horizontal axis are presented. A more simplified integration method (S-O), which includes only cavern surface and cavern outline, is proposed, and compared with the results of C-S-O, which indicates that the simplified approach achieves comparable accuracy. The study offers theoretical reference for the prediction of discharge and groundwater level during the excavation and operation of underground caverns.