A mathematical optimization model of insulation layer's parameters in seasonally frozen tunnel engineering

• We build a mathematical optimization model of the insulation layer.
• We find a way to solve the mathematical optimization model.
• The model is verified by an example.
• The relationships between the cost and some important parameters are discussed.

The insulation layer is often used in seasonally frozen tunnel to prevent from frost damages caused by the freeze–thaw cycles. In order to investigate the rationality and economic benefits of insulation layer's parameters when it is used in seasonally frozen tunnel, based on the characteristics of seasonally frozen soils and optimization theory, a mathematical optimization model of insulation layer's parameters is constructed by taking Daban mountain tunnel for an example. The example shows that the mathematical optimization model is reasonable and the solution method is feasible. And then the relationships between the cost and the insulation layer's parameters, depth of tunnel, boundary conditions and phase transition are discussed and they show that all these parameters could affect the optimization results. Therefore, the mathematical optimization model could contribute to choosing the best insulation layer's parameters for the designers when they design seasonally frozen tunnel because it contains all these important parameters and the enormous economic benefits could be obtained.