吴忠广等：深埋硬岩隧道围岩参数概率反演方法 ·87· sion analysis method of a CFRD based on multi-output support ings of the 47th US Rock Mechanics/Geomechanics Symposium. vector machines and the clonal selection algorithm.Comput San Francisco,2013:503 Geotech,2013,47:68 [43]Martin C D.Kaiser P K,MeCreath D R.Hoek-Brown parame- [34]Li S J,Zhao H B,Ru Z L,et al.Probabilistic back analysis ters for predicting the depth of brittle failure around tunnels.Can based on Bayesian and multi-output support vector machine for a Geotech J,1999,36(1):136 high cut rock slope.Eng Geol,2016,203:178 [44]Griffith A.The theory of rupture /Proceedings of the 1st Inter- [35]Kennedy J,Eberhart R.Particle swarm optimization//Proceed- national Congress on Applied Mechanics.Delft,1924:55 ings of ICNN'95 International Conference on Neural Netorks. [45]Murrell S A F.A criterion for brittle fracture of rocks and con- Perth,1995:1942 crete under triaxial stress and the effect of pore pressure on the [36]Feng X T,Zhou H,Li S J,et al.System of intelligent evaluation criterion//Proceedings of the 5th Rock Mechanics Symposium. and prediction in space-time for safety of rock engineering under 0fod,1963:563 hazardous environment.Chin J Rock Mech Eng,2008,27(9): [46]Cai M.Practical estimates of tensile strength and Hoek-Brown 1741 strength parameter m of brittle rocks.Rock Mech Rock Eng, (冯夏庭，周辉，李邵军，等.复杂条件下岩石工程安全性的 2010,43(2):167 智能分析评估和时空预测系统.岩石力学与工程学报， [47]Perras M A.Diederichs M S.A review of the tensile strength of 2008,27(9):1741) rock:concepts and testing.Geotech Geol Eng,2014,32(2): [37]Diederichs M S.The 2003 Canadian geotechnical colloquium: 525 mechanistic interpretation and practical application of damage and [48]Metropolis N,Rosenbluth A W.Rosenbluth M N,et al.Equa- spalling prediction criteria for deep tunnelling.Can Geotech / tions of state calculations by fast computing machines.Chem 2007,44(9):1082 Phys,1953,21(6):1087 [38]Hoek E,Carranza-Torres C T,Corkum B,et al.Hoek-Brown [49]Hastings W K.Monte Carlo sampling methods using Markov failure criterion -2002 edition /Proceedings of NARMS-Tac chains and their applications.Biometrika,1970,57(1):97 Conference.Toronto,2002:267 [50]Yu S W.Case Analysis and Application of MATLAB Optimization [39]Perras MA,Diederichs M S.Predicting excavation damage zone Algorithm.Beijing:Tsinghua University Press,2014 depths in brittle rocks.Int J Rock Mech Geotech Eng,2016,8 (余胜威.MATLAB优化算法案例分析与应用.北京：清华 (1):60 大学出版社，2014) [40]Dammyr 0.Prediction of brittle failure for TBM tunnels in aniso- [51]Wu C,Zhang P.Analysis of numerical simulation methods for tropic rock:a case study from Norther Norway.Rock Mech Rock excavation failure zone of deep underground opening in hard rocks Eng,2016,49(6):2131 with high geostress.Hydrogeol Eng Geol,2012,39(6):35 [41]Langford JC.Diederichs M S.Reliable support design for exca- (吴成，张平。高地应力硬岩洞室开挖破坏区数值模拟方法 vations in brittle rock using a global response surface method. 探讨.水文地质工程地质，2012,39(6)：35) Rock Mech Rock Eng,2015,48(2):669 [52]Li X,Li X B,Su Y H.A hybrid approach combining uniform [42]Ghazvinian E,Perras M A,Diederichs M S,et al.The effect of design and support vector machine to probabilistic tunnel stability anisotropy on erack damage thresholds in brittle rocks/Proceed assessment.Struct Saf,2016,61:22吴忠广等: 深埋硬岩隧道围岩参数概率反演方法 sion analysis method of a CFRD based on multi鄄output support vector machines and the clonal selection algorithm. Comput Geotech, 2013, 47: 68 [34] Li S J, Zhao H B, Ru Z L, et al. Probabilistic back analysis based on Bayesian and multi鄄output support vector machine for a high cut rock slope. Eng Geol, 2016, 203: 178 [35] Kennedy J, Eberhart R. Particle swarm optimization / / Proceed鄄 ings of ICNN爷 95 International Conference on Neural Networks. Perth, 1995: 1942 [36] Feng X T, Zhou H, Li S J, et al. System of intelligent evaluation and prediction in space鄄time for safety of rock engineering under hazardous environment. Chin J Rock Mech Eng, 2008, 27(9): 1741 (冯夏庭, 周辉, 李邵军, 等. 复杂条件下岩石工程安全性的 智能分析评估和时空预测系统. 岩石力学与工程学报, 2008, 27(9): 1741) [37] Diederichs M S. The 2003 Canadian geotechnical colloquium: mechanistic interpretation and practical application of damage and spalling prediction criteria for deep tunnelling. Can Geotech J, 2007, 44(9): 1082 [38] Hoek E, Carranza鄄Torres C T, Corkum B, et al. Hoek鄄Brown failure criterion 鄄 2002 edition / / Proceedings of NARMS鄄Tac Conference. Toronto, 2002: 267 [39] Perras M A, Diederichs M S. Predicting excavation damage zone depths in brittle rocks. Int J Rock Mech Geotech Eng, 2016, 8 (1): 60 [40] Dammyr 覫. Prediction of brittle failure for TBM tunnels in aniso鄄 tropic rock: a case study from Northern Norway. Rock Mech Rock Eng, 2016, 49(6): 2131 [41] Langford J C, Diederichs M S. Reliable support design for exca鄄 vations in brittle rock using a global response surface method. Rock Mech Rock Eng, 2015, 48(2): 669 [42] Ghazvinian E, Perras M A, Diederichs M S, et al. The effect of anisotropy on crack damage thresholds in brittle rocks / / Proceed鄄 ings of the 47th US Rock Mechanics/ Geomechanics Symposium. San Francisco, 2013: 503 [43] Martin C D, Kaiser P K, McCreath D R. Hoek鄄Brown parame鄄 ters for predicting the depth of brittle failure around tunnels. Can Geotech J, 1999, 36(1): 136 [44] Griffith A. The theory of rupture / / Proceedings of the 1st Inter鄄 national Congress on Applied Mechanics. Delft, 1924: 55 [45] Murrell S A F. A criterion for brittle fracture of rocks and con鄄 crete under triaxial stress and the effect of pore pressure on the criterion / / Proceedings of the 5th Rock Mechanics Symposium. Oxford, 1963: 563 [46] Cai M. Practical estimates of tensile strength and Hoek鄄鄄 Brown strength parameter mi of brittle rocks. Rock Mech Rock Eng, 2010, 43(2): 167 [47] Perras M A, Diederichs M S. A review of the tensile strength of rock: concepts and testing. Geotech Geol Eng, 2014, 32 (2 ): 525 [48] Metropolis N, Rosenbluth A W, Rosenbluth M N, et al. Equa鄄 tions of state calculations by fast computing machines. J Chem Phys, 1953, 21(6): 1087 [49] Hastings W K. Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 1970, 57(1): 97 [50] Yu S W. Case Analysis and Application of MATLAB Optimization Algorithm. Beijing: Tsinghua University Press, 2014 (余胜威. MATLAB 优化算法案例分析与应用. 北京: 清华 大学出版社, 2014) [51] Wu C, Zhang P. Analysis of numerical simulation methods for excavation failure zone of deep underground opening in hard rocks with high geostress. Hydrogeol Eng Geol, 2012, 39(6): 35 (吴成, 张平. 高地应力硬岩洞室开挖破坏区数值模拟方法 探讨. 水文地质工程地质, 2012, 39(6): 35) [52] Li X, Li X B, Su Y H. A hybrid approach combining uniform design and support vector machine to probabilistic tunnel stability assessment. Struct Saf, 2016, 61: 22 ·87·