工程科学学报，第37卷，第7期：839843,2015年7月 Chinese Journal of Engineering,Vol.37,No.7:839-843,July 2015 DOI:10.13374/j.issn2095-9389.2015.07.003:http://journals.ustb.edu.cn 考虑围岩松动圈支护体影响的深埋圆形隧道衬砌优 化设计 杨 凯2》，吴顺川)四，吴庆良”，高永涛”，王运庆》 1)北京科技大学土木与环境工程学院，北京1000832)中电建路桥集团有限公司，北京100048 ☒通信作者，E-mail:wushunchuan(@usth.cdu.cm 摘要首先考虑围岩松动圈支护体的影响，在完全接触条件下，根据弹塑性力学理论，推导出深埋圆形隧道每层衬砌切向 应力和径向应力分量的解析解：然后根据混凝土和围岩材料受力状态的不同，选用不同的破坏准则，引入功能梯度材料思想， 构建了不同弹性模量双层混凝土圆形衬砌优化设计的目标函数，即当目标函数为最小值时，I、Ⅱ和Ⅲ层结构同时接近或达 到预设破坏状态，在设计上才最为合理：最后对衬砌材料的弹性模量和衬砌厚度分别进行了优化设计.算例分析表明：(1)随 着围岩应力的增大，E,/E,和E,/E,都减小.在相同大小的围岩应力作用下，总有E,/E,<E,/E,,故而建议设计时I层衬砌 的弹性模量应大于围岩松动圈支护体的弹性模量.(2)随着围岩应力的增大，I层衬砌的厚度增大.在相同大小的围岩应力 作用下，当E2/E1>E2/E,时所求得的I层衬砌最优厚度总是小于E,/E,<E2/E3时所求得的I层衬砌厚度，故而可通过改变 I层衬砌和围岩松动圈支护体的弹性模量相对大小来调整I、Ⅱ层衬砌的厚度. 关键词隧道：支护体：村砌：弹性模量：厚度：优化设计 分类号TU312 Lining support optimization design of a deep-buried tunnel in consideration of the broken rock zone support YANG Kai,WU Shun-chuan,WU Qing-liang",GAO Yong-tao,WANG Yun-qing? 1)School of Civil and Environmental Engineering,University of Science and Technology Beijing,Beijing 100083,China 2)PowerChina Road Bridge Group Co.,Ltd.,Beijing 100048,China Corresponding author,E-mail:wushunchuan@ustb.edu.cn ABSTRACT Considering the broken rock zone support,tangential and radial stress component analytical solutions of each layer in full contact conditions are deduced in a deep circular tunnel based on the elastoplastic theory.Then an optimization objective function of circular concrete lining layers with different elastic moduli is constructed by choosing different failure criteria and different stress states of concrete and rock materials and by introducing the idea of functionally graded materials,that is,when the objective function is minimum,the most reasonable design is that the I,II and IlI layer structures destroy at the same time.Finally,the elastic modu- lus and thickness of the lining is designed separately.The analysis of examples shows the following.(1)With the increase of sur- rounding rock stress,E2/E and E2/E:both decrease.Under the same stress,there is always E2/E<E,/E3,therefore it is suggested that the elastic modulus of the I layer should be greater than the broken rock zone supporting's.(2)With the increase of surrounding rock stress,the thickness of the I layer increases.Under the same stress,when E2/E >E,/E,the thickness of the I layer is al- ways less than that obtained when E2/E<E2/E:,therefore the thicknesses of the I and II layers can be adjusted by changing the e- lastic moduli of the I layer and the broken rock zone support. KEY WORDS tunnels:supports:lining:elastic modulus:thickness:optimization design 收稿日期：201403-18 基金项目：科技北京百名领军人才培养工程(Z151100000315014):国家自然科学基金资助项目(51074014,51174014)工程科学学报，第 37 卷，第 7 期: 839--843，2015 年 7 月 Chinese Journal of Engineering，Vol． 37，No． 7: 839--843，July 2015 DOI: 10． 13374 /j． issn2095--9389． 2015． 07． 003; http: / /journals． ustb． edu． cn 考虑围岩松动圈支护体影响的深埋圆形隧道衬砌优 化设计 杨 凯1，2) ，吴顺川1) ，吴庆良1) ，高永涛1) ，王运庆2) 1) 北京科技大学土木与环境工程学院，北京 100083 2) 中电建路桥集团有限公司，北京 100048  通信作者，E-mail: wushunchuan@ ustb． edu． cn 摘 要 首先考虑围岩松动圈支护体的影响，在完全接触条件下，根据弹塑性力学理论，推导出深埋圆形隧道每层衬砌切向 应力和径向应力分量的解析解; 然后根据混凝土和围岩材料受力状态的不同，选用不同的破坏准则，引入功能梯度材料思想， 构建了不同弹性模量双层混凝土圆形衬砌优化设计的目标函数，即当目标函数为最小值时，Ⅰ、Ⅱ和Ⅲ层结构同时接近或达 到预设破坏状态，在设计上才最为合理; 最后对衬砌材料的弹性模量和衬砌厚度分别进行了优化设计． 算例分析表明: ( 1) 随 着围岩应力的增大，E2 /E1 和 E2 /E3 都减小． 在相同大小的围岩应力作用下，总有 E2 /E1 ＜ E2 /E3，故而建议设计时Ⅰ层衬砌 的弹性模量应大于围岩松动圈支护体的弹性模量． ( 2) 随着围岩应力的增大，Ⅰ层衬砌的厚度增大． 在相同大小的围岩应力 作用下，当 E2 /E1 ＞ E2 /E3 时所求得的Ⅰ层衬砌最优厚度总是小于 E2 /E1 ＜ E2 /E3 时所求得的Ⅰ层衬砌厚度，故而可通过改变 Ⅰ层衬砌和围岩松动圈支护体的弹性模量相对大小来调整Ⅰ、Ⅱ层衬砌的厚度． 关键词 隧道; 支护体; 衬砌; 弹性模量; 厚度; 优化设计 分类号 TU312 Lining support optimization design of a deep-buried tunnel in consideration of the broken rock zone support 收稿日期: 2014--03--18 基金项目: 科技北京百名领军人才培养工程( Z151100000315014) ; 国家自然科学基金资助项目( 51074014，51174014) YANG Kai1，2) ，WU Shun-chuan1)  ，WU Qing-liang1) ，GAO Yong-tao1) ，WANG Yun-qing2) 1) School of Civil and Environmental Engineering，University of Science and Technology Beijing，Beijing 100083，China 2) PowerChina Ｒoad Bridge Group Co． ，Ltd． ，Beijing 100048，China  Corresponding author，E-mail: wushunchuan@ ustb． edu． cn ABSTＲACT Considering the broken rock zone support，tangential and radial stress component analytical solutions of each layer in full contact conditions are deduced in a deep circular tunnel based on the elastoplastic theory． Then an optimization objective function of circular concrete lining layers with different elastic moduli is constructed by choosing different failure criteria and different stress states of concrete and rock materials and by introducing the idea of functionally graded materials，that is，when the objective function is minimum，the most reasonable design is that the Ⅰ，Ⅱ and Ⅲ layer structures destroy at the same time． Finally，the elastic modu￾lus and thickness of the lining is designed separately． The analysis of examples shows the following． ( 1) With the increase of sur￾rounding rock stress，E2 /E1 and E2 /E3 both decrease． Under the same stress，there is always E2 /E1 ＜ E2 /E3，therefore it is suggested that the elastic modulus of the Ⅰ layer should be greater than the broken rock zone supporting's． ( 2) With the increase of surrounding rock stress，the thickness of the Ⅰ layer increases． Under the same stress，when E2 /E1 ＞ E2 /E3，the thickness of the Ⅰ layer is al￾ways less than that obtained when E2 /E1 ＜ E2 /E3，therefore the thicknesses of the Ⅰ and Ⅱ layers can be adjusted by changing the e￾lastic moduli of the Ⅰ layer and the broken rock zone support． KEY WOＲDS tunnels; supports; lining; elastic modulus; thickness; optimization design