Optimization Design of Cross-Section Configuration of Four-Track Tunnel Based on Toolbox of Matlab

This paper mainly discussed how to use optimize the toolbox of Matlab to optimize the cross-section configuration of four-track tunnel, which has not had standard drawing yet. Cross-section above rail level adopted three-centered arch styles. In order to minimize excavation volume, sectional area above rail level (marked S) was set for object function, and parameters describing cross-section configuration (marked R₁, R₂, φ₁, φ₁, a, b, c) were set for design variables. Object function is non-linear to design variables, and among design variables there are some restrictions. Fmincon, an inner function in optimization toolbox of Matlab was employed to derive the minimal value of object function. By the result, when R₁ = 11160mm, R₂ = 10252mm, a= 619mm, b = 1116mm, c=758mm, φ₁ =56.7°, φ₂ = 39.5°, object function was minimized to 208.51 square meters.