中文摘要：

利用近年来发展的渐进结构优化方法（ESO）的概念，发展了适用于支护拓扑优化问题的双向渐进结构优化方法（BESO）。本文方法能在优化过程中控制开孔数，有效地避免了棋盘格式的出现，提出了两个解决振荡问题的技巧。将加固后的岩体看成人工支护材料，可以把加固优化的问题转化为人工支护材料在原岩中的分布的拓扑优化问题。建立了防治底臌帮臌的准则及其敏感度，研究了均匀地基不同地应力条件给定加固量时使得底臌帮臌最小的洞室开挖支护的最优拓扑。最优设计的底臌量明显小于经验设计的底臌量，证明了方法的有效性。

英文摘要：

A bi-direction evolutionary structural optimization （BESO） method for topology optimization of tunnel support based on a newly developed evolutionary structural optimization （ESO） method is presented. The proposed method can control the number of cavities during the optimization process to avoid the so-called chessboard pattern, and provides two techniques that can overcome oscillate phenomenon. Reinforced rock is considered as artificial reinforcement material, and optimization of tunnel support is transformed into locating the optimal distribution of the reinforcing material. The criteria and sensitivity to prevent floor or sidewall heaves are established, and the optimal support topology of tunnel in homogeneous rock with different situ stresses and with the same reinforcement material are sought for minimum floor or sidewall heaves. The results shows that the floor heaves under optimal designs are much smaller than those under empirical designs and validate the method＇s efficiency.