马蹄形隧洞断面收缩水深迭代公式推求及程序实现

摘要

In order to solve the difficulty of calculating the contraction depth for tunnels with horseshoe cross-sections ,a set of proper dimensionless parameters were introduced to unify a variety of calculating formulas ,and then an iterative for-mula of contraction depth for tunnels with horseshoe cross-sections were derived theoretically .By the calculation of MAT-LAB language on an actual example ,it is demonstrated that programming can solve the complexity of calculating formula of contraction depth for horseshoe cross-section well .It is simple and universal with accurate calculation results ,moreover it can provide a comparatively simple calculation method for engineering design .%为了解决马蹄形隧洞收缩水深不易计算的问题，本文首先引入恰当的无量纲参数，使各种马蹄形断面收缩水深的计算公式统一化，从理论上推求得到了马蹄形断面收缩水深的迭代计算公式，然后针对实例采用 MATLAB 语言进行编程计算，通过应用实例可证明，编程方式能很好的解决马蹄形断面收缩水深计算公式复杂的问题，该方法简单、准确、通用，能为工程设计提供较为简便的计算方法。