Optimization of anchorage location of three dimensional slopes based on improved differential evolution algorithm
YIN Zhi-kai1, LU Kun-lin1, SHI Feng1, ZHU Da-yong2
1. School of Civil and Hydraulic Engineering, Hefei University of Technology, Hefei 230009, China; 2. School of Civil and Architectural Engineering, Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China
Abstract：Based on the improved differential evolution algorithm, considering the 3D spatial distribution of anchoring force through calculation of the 3D anchoring force, the anchorage position of 3D slope is optimized reasonably to save the number of bolts. By using the stress solution of one point in the semi-infinite elastic space under the action of concentrated force, the anchoring force is superimposed on the normal stress and shear stress of the slope surface. Then the function for anchoring force about the coordinates of the anchorage position is derived, and taken as the objective function of the optimization of the anchorage position. For the improvement of the standard differential evolution algorithm (DE), the adaptive differential evolution algorithm is combined with the general constraint multiplier algorithm (PHR) to solve the problem of constraint optimization of anchoring slopes. Numerical and engineering examples show that with the same safety factor of slope reinforcement and unchanged single anchoring force, through the optimization of anchorage position, the number of anchorage points can be saved by 20% ~ 25%, and the proposed method can provide reference for engineering application.
尹志凯, 卢坤林, 石峰, 朱大勇. 基于改进差分进化算法的三维边坡锚固位置优化[J]. 岩土工程学报, 2020, 42(7): 1322-1330.
YIN Zhi-kai, LU Kun-lin, SHI Feng, ZHU Da-yong. Optimization of anchorage location of three dimensional slopes based on improved differential evolution algorithm. Chinese J. Geot. Eng., 2020, 42(7): 1322-1330.
[1] 郑颖人, 杨明成. 边坡稳定安全系数求解格式的分类统一[J]. 岩石力学与工程学报, 2004, 23(16): 2836-2841. (ZHENG Ying-ren, YANG Ming-cheng.Classification unification of calculation formulation for safety factor of slope stability[J]. Chinese Journal of Rock Mechanics and Engineering, 2004, 23(16): 2836-2841. (in Chinese)) [2] 康景文, 朱大勇. 一种边坡锚固力新的计算方法[J]. 四川建筑科学研究, 2005, 31(5): 72-74. (KANG Jing-wen, ZHU Da-yong.A new method for calculating the anchoring force of slope[J]. Sichuan Building Science, 2005, 31(5):72-74. (in Chinese)) [3] 赵洪领, 台佳佳, 朱大勇. 边坡稳定性计算中锚固力计入方式讨论[J]. 中国水利水电科学研究院学报, 2006, 4(4): 271-276. (ZHAO Hong-ling, TAI Jia-jia, ZHU Da-yong.Discussion on calculation method of anchorage force in slope stability calculation[J]. Journal of China Institute of Water Resources and Hydropower Research, 2006, 4(4): 271-276. (in Chinese)) [4] WANG Wen-jie, SONG Qian-qiang.Mechanical behavior of fully grouted GFRP rock bolts under the joint action of pre-tension load and blast dynamic load[J]. Tunneling and Underground Space Technology, 2018, 38(3): 82-91. [5] ZHANG R, ZHAO J, WANG G X.Stability analysis of anchored soil slope based on finite element limit equilibrium method[J]. Mathematical Problems in Engineering, 2016(20): 1-8. [6] 刘华丽, 李宏伟, 朱大勇. 锚固力在边坡加固中的工程应用[J]. 岩土力学, 2015, 36(2): 509-514. (LIU Hua-li, Li Hong-wei, ZHU Da-yong.A method for calculation of anchor force in slope reinforcement[J]. Rock and Soil Mechanics, 2015, 36(2): 509-514. (in Chinese)) [7] HARIYADI S M, YOSHIMI S.Experimental analysis of anchor bolt in concrete under the pull-out loading[J]. Procedia Engineering, 2017, 171: 926-933. [8] LAURA B M, TIJANI M, HADJ-HASSEN F.A new analytical solution to the mechanical behaviour of fully grouted rock bolts subjected to pull-out tests[J]. Construction & Building Materials, 2011, 25(2): 749-755. [9] 雷军, 肖世国. 考虑滑体中锚拉力扩散效应的锚固边坡稳定性分析方法[J]. 岩土工程学报, 2019, 41(9): 1724-1730. (LEI Jun, XIAO Shi-guo.Stability analysis method for anchored slopes considering stress dispersion effect in sliding mass due to anchor tensile forces[J]. Chinese Journal of Geotechnical Engineering, 2019, 41(9): 1724-1730. (in Chinese)) [10] 卢坤林, 王运敏, 朱大勇. 三维滑体锚固力计算方法及工程应用[J]. 岩土力学, 2017, 38(2): 501-506, 516. (LU Kun-lin, WANG Yun-min, ZHU Da-yong.A method for calculating reinforcing forces of 3D sliding mass and its engineering applications[J]. Rock and Soil Mechanics, 2017, 38(2): 501-506, 516. (in Chinese)) [11] LI Z, WEI J, YANG J.Stability calculation method of slope reinforced by prestressed anchor in process of excavation[J]. The Scientific World Journal, 2014(10): 1-7. [12] 曹国金, 姜弘道, 熊红梅. 一种确定拉力型锚杆支护长度的方法[J]. 岩石力学与工程学报, 2003, 22(7): 1141-1145. (CAO Guo-jin, JIANG Hong-dao, XIONG Hong-mei.Calculation method of support length for stretched bolts[J]. Chinese Journal of Rock Mechanics and Engineering, 2003, 22(7): 1141-1145. (in Chinese)) [13] YANG G, ZHONG Z, ZHANG Y, et al.Optimal design of anchor cables for slope reinforcement based on stress and displacement fields[J]. Journal of Rock Mechanics and Geotechnical Engineering, 2015, 7(4): 411-420. [14] LI C, WU J, WANG J, et al.Layout and length optimization of anchor cables for reinforcing rock wedges[J]. Bulletin of Engineering Geology and the Environment, 2016, 75(4): 1399-1412. [15] 石露, 李小春, 任伟, 等. 蚁群算法与遗传算法融合及其在边坡临界滑动面搜索中的应用[J].岩土力学, 2009, 30(11): 3486-3492. (SHI Lu, LI Xiao-chun, REN Wei, et al.Hybrid of ant colony algorithm and genetic algorithm and its application to searching critical slope slip surface[J]. Rock and Soil Mechanics, 2009, 30(11): 3486-3492. (in Chinese)) [16] HUANG Q J, ZHANG K, SONG J C, et al.Adaptive differential evolution with a Lagrange interpolation argument algorithm[J]. Information Sciences, 2018, 9(4): 180-202. [17] 徐东方, 郭战伟, 侯春娟. 约束尺度和算子自适应变化的差分进化算法[J]. 数学的实践与认识, 2017(16): 151-158. (XU Dong-fang, GUO Zhan-wei, HOU Chun-juan.Differential evolutionary algorithm of constraint scale and operator adaptive change[J]. Mathematics in Practice and Theory, 2017(16): 151-158. (in Chinese)) [18] 王凯. 层状弹性体系的力学分析与计算[M]. 北京: 科学出版社, 2009. (WANG Kai.Mechanical Analysis and Calculation of Layered Elastic System[M]. Beijing: Science Press, 2009. (in Chinese)) [19] 卢坤林, 朱大勇, 甘文宁, 等. 一种边坡稳定性分析的三维极限平衡法及应用[J]. 岩土工程学报, 2013, 35(12): 2276-2282. (LU Kun-lin, ZHU Da-yong, GAN Wen-ning, et al.3D limit equilibrium method for slope stability analysis and its application[J].Chinese Journal of Geotechnical Engineering, 2013, 35(12): 2276-2282. (in Chinese)) [20] 岩土锚杆与喷射混凝土支护工程技术规范:GB 50086—2015[S]. 2015. (Technical code for engineering of ground anchoranges and shotcrete support:GB 50086—2015[S]. 2015. (in Chinese)) [21] 基于分片光滑技术三维边坡安全系数计算软件V2.0(登记号: 2019SR0071874)[CP]. (3D slope safety factor calculation software based on piecewise smoothing technique V2.0 registration. No. 2019SR0071874 [CP].(in Chinese))
