A variational method for calculating the longitudinal deformation of a shield tunnel in soft soil caused by grouting under tunnel

The paper aims to predict longitudinal deformation of a tunnel caused by grouting under the tunnel bottom in advance according to the grouting parameters, which can ensure the safety of the tunnel structure during the grouting process and also help to design the grouting parameters.,The paper adopted the analytical approach for calculating the longitudinal deformation of a shield tunnel caused by grouting under a tunnel, including usage of the Mindlin’s solution, the minimum potential energy principle and case validation.,The paper provides a variational method for calculating the longitudinal deformation of a shield tunnel in soft soil caused by grouting under the tunnel, which has high computational efficiency and accuracy.,This paper fulfils an identified need to study how the longitudinal deformation of a shield tunnel in soft soil caused by grouting under the tunnel can be calculated.