Non-linear description of ground settlement over twin tunnels in soil

• We propose a new model which describes ground settlement trough over twin tunnels.
• We demonstrate that the settlement trough model fits the settlement data well.
• We suggest a new method for calculating ground loss over twin tunnels.
• Levenberg–Marquardt method is suitable to fit non-linear settlement trough model.

Tunneling inevitably leads to ground settlement. The ground settlement trough over a single tunnel is well described by the generally accepted Peck’s formula. A new model of settlement trough is proposed by extending Peck’s formula to the case of horizontally aligned twin tunnels, which is a widely used tunnel configuration in urban metro projects. The feasibility of the new model is demonstrated through exploration of a large amount of ground settlement data accumulated from a metro tunnel project in China. Two numerical methods are implemented in the data exploration process to solve the problem of non-linear curve-fitting and estimation of model parameters. The Levenberg–Marquardt method is shown to be more suitable than the Nelder–Mead method. Based on the new model of settlement trough, a new method for calculating ground loss over twin tunnels is also proposed. The concluded empirical value of the ratio of ground loss is considered to provide an excellent reference for similar urban railway projects in the future.