Considering the factors of static buoyancy and dynamic buoyancy

time variation of grout and compression of the overburden soil

based on curved differential equation of elastic foundation beam

finite element theory

boundary conditions and the coordination equations for deformation

angle rotation

shear and bending moment

a theoretical solution for longitudinal upward movement of underwater shield tunnel is obtained. It was applied to comprehensive pipe Project of Caofeidian Industrial Zone Gallery known as ‘the 1st shield of Hebei. The computation example of engineering shows that the maximum error of theoretical solution and numerical solution is within 2.5%. Furthermore

the result obtained by the proposed theoretical solution is well consistent with the monitoring result of normal excavation section and can be used to analyze the longitudinal upward movement of shield tunnel. Moreover

the theoretical solution has got rid of the tedious process when numerical model established and unit refined

so it will be accepted more easily by constructers or designers

so as to provide some reference to perfect the related design specifications.