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Properties and Optimization Design of a New Heteromorphic Ellipse Tunnel Cross-Section
WU Zhouhu
2021, 40(01):
87-95.
DOI: 10.3969/j.issn.1674-0696.2021.01.14
Based on the isoconcentration curve equation of two-dimensional convection-diffusion material in river, a new type of two-parameter heteromorphic ellipse inner outline equation was defined. By means of mathematics, the calculating formulas of area, perimeter, centroid coordinates, coefficient of compressibility and radius of curvature of the heteromorphic ellipse were deduced. The shape of heteromorphic ellipse was categorized: when the coefficient of compressibility θ=1, it was called the standard-type; when 0<θ<1, it was called the H-type; when θ>1, it was called the W-type. According to the construction clearance of one-way highway tunnel, the coordinate expression of control point was given. According to the principle that the construction clearance was fully included and the clearance area of tunnel chamber was minimum, the constraint conditions, objective function and optimization design method of the heteromorphic ellipse cross-section were proposed. Research shows that the heteromorphic ellipse has a high degree of conformity with the construction clearance. Compared with the three-centered circle cross-section, the heteromorphic ellipse has the advantages of less design parameters, continuous change of curvature radius, smaller clearance area of tunnel chamber, shorter support and lining perimeter, and smaller engineering quantities of inverted arch excavation and backfill.
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