工程科学学报，第41卷，第1期：78-87,2019年1月 Chinese Journal of Engineering,Vol.41,No.I:78-87,January 2019 D0L:10.13374/j.issn2095-9389.2019.01.008;htp:/journals.ustb.edu.cm 深埋硬岩隧道围岩参数概率反演方法 吴忠广12)四，吴顺川13) 1)北京科技大学土木与资源工程学院，北京1000832)交通运输部科学研究院标准与计量研究中心，北京100029 3)昆明理工大学国土资源学院，昆明650093 ☒通信作者，E-mail:kinliwu@163.com 摘要在贝叶斯理论框架下，提出了一种基于多源数据融合的深埋硬岩隧道围岩参数概率反演方法.首先，分析硬岩隧道 常用的启裂一剥落界限本构模型中围岩单轴抗压强度、启裂强度与抗压强度比及抗拉强度三个参数不确定性来源，确定其概 率统计特征；其次，利用粒子群算法优化多输出支持向量机，建立反映反演参数与隧道监测数据间非线性映射关系的智能响 应面：最后，结合贝叶斯分析方法构建概率反演模型，运用马尔科夫链蒙特卡洛模拟算法实现了围岩参数的动态更新.将该方 法应用到某深埋硬岩隧道中，利用反演的围岩参数计算隧道拱顶下沉点、周边收敛点变化值及开挖损伤区深度，与监测数据 吻合较好.结果表明，该方法可以实现围岩多参数快速概率反演，更新后的参数可用于硬岩隧道施工安全风险评估与结构可 靠性设计. 关键词硬岩隧道：概率反演：多源数据融合：贝叶斯理论：多输出支持向量机 分类号TU452 Probabilistic back analysis method for determining surrounding rock parameters of deep hard rock tunnel WU Zhong-guang.2)回，WU Shun-chuan',3) 1)School of Civil and Resource Engineering,University of Science and Technology Beijing,Beijing 100083.China 2)Research Center for Standards and Metrology,China Academy of Transportation Sciences,Beijing 100029,China 3)Faculty of Land Resource Engineering,Kunming University of Science and Technology,Kunming 650093.China Corresponding author,E-mail:kinliwu@163.com ABSTRACT A large number of tunnel projects are being constructed or will be constructed in the mountainous areas of western Chi- na.However,they are several safety challenges in the construction of deep hard rock tunnels because of the complex topographic and geological conditions,strong geological tectonic activities,large burial depth,and high in situ stress level.Uncertainty of tunnel wall parameters is one of main factors that contribute to tunnel construction risk.The traditional deterministic back analysis method cannot reflect the uncertainty characteristics of tunnel wall parameters;therefore,within the framework of Bayesian theory,a probabilistic back analysis method based on integrating multi-source monitoring information was proposed for determining the surrounding rock parameters of deep hard rock tunnel.First,the uncertainty sources of three parameters-uniaxial compressive strength(UCS),crack initiation stress to UCS ratio,and tensile strength for the widely used damage initiation and spalling limit approach-were analyzed,and their probabilistic statistical characteristics were determined.Second,a multi-output support vector machine(MSVM)was optimized by par- ticle swarm optimization (PSO)algorithm,and an intelligent response surface model was established to reflect the nonlinear mapping relationship between back-analyzed parameters and field monitoring data.Last,by combination with the Bayesian (B)analysis meth- od,the B-PSO-MSVM model was established,and surrounding rock parameters were dynamically updated by applying the Markov 收稿日期：2018-05-29 基金项目：国家重点研发计划专项资助项目(2017YF008053003):国家自然科学基金资助项目(51174020)工程科学学报,第 41 卷,第 1 期:78鄄鄄87,2019 年 1 月 Chinese Journal of Engineering, Vol. 41, No. 1: 78鄄鄄87, January 2019 DOI: 10. 13374 / j. issn2095鄄鄄9389. 2019. 01. 008; http: / / journals. ustb. edu. cn 深埋硬岩隧道围岩参数概率反演方法 吴忠广1,2) 苣 , 吴顺川1,3) 1) 北京科技大学土木与资源工程学院, 北京 100083 2) 交通运输部科学研究院标准与计量研究中心, 北京 100029 3) 昆明理工大学国土资源学院, 昆明 650093 苣 通信作者, E鄄mail:kinliwu@ 163. com 摘 要 在贝叶斯理论框架下,提出了一种基于多源数据融合的深埋硬岩隧道围岩参数概率反演方法. 首先,分析硬岩隧道 常用的启裂—剥落界限本构模型中围岩单轴抗压强度、启裂强度与抗压强度比及抗拉强度三个参数不确定性来源,确定其概 率统计特征;其次,利用粒子群算法优化多输出支持向量机,建立反映反演参数与隧道监测数据间非线性映射关系的智能响 应面;最后,结合贝叶斯分析方法构建概率反演模型,运用马尔科夫链蒙特卡洛模拟算法实现了围岩参数的动态更新. 将该方 法应用到某深埋硬岩隧道中,利用反演的围岩参数计算隧道拱顶下沉点、周边收敛点变化值及开挖损伤区深度,与监测数据 吻合较好. 结果表明,该方法可以实现围岩多参数快速概率反演,更新后的参数可用于硬岩隧道施工安全风险评估与结构可 靠性设计. 关键词 硬岩隧道; 概率反演; 多源数据融合; 贝叶斯理论; 多输出支持向量机 分类号 TU452 收稿日期: 2018鄄鄄05鄄鄄29 基金项目: 国家重点研发计划专项资助项目(2017YFC08053003);国家自然科学基金资助项目(51174020) Probabilistic back analysis method for determining surrounding rock parameters of deep hard rock tunnel WU Zhong鄄guang 1,2) 苣 , WU Shun鄄chuan 1,3) 1) School of Civil and Resource Engineering, University of Science and Technology Beijing, Beijing 100083, China 2) Research Center for Standards and Metrology, China Academy of Transportation Sciences, Beijing 100029, China 3) Faculty of Land Resource Engineering, Kunming University of Science and Technology, Kunming 650093, China 苣 Corresponding author, E鄄mail: kinliwu@ 163. com ABSTRACT A large number of tunnel projects are being constructed or will be constructed in the mountainous areas of western Chi鄄 na. However, they are several safety challenges in the construction of deep hard rock tunnels because of the complex topographic and geological conditions, strong geological tectonic activities, large burial depth, and high in situ stress level. Uncertainty of tunnel wall parameters is one of main factors that contribute to tunnel construction risk. The traditional deterministic back analysis method cannot reflect the uncertainty characteristics of tunnel wall parameters; therefore, within the framework of Bayesian theory, a probabilistic back analysis method based on integrating multi鄄source monitoring information was proposed for determining the surrounding rock parameters of deep hard rock tunnel. First, the uncertainty sources of three parameters———uniaxial compressive strength (UCS), crack initiation stress to UCS ratio, and tensile strength for the widely used damage initiation and spalling limit approach———were analyzed, and their probabilistic statistical characteristics were determined. Second, a multi鄄output support vector machine (MSVM) was optimized by par鄄 ticle swarm optimization (PSO) algorithm, and an intelligent response surface model was established to reflect the nonlinear mapping relationship between back鄄analyzed parameters and field monitoring data. Last, by combination with the Bayesian (B) analysis meth鄄 od, the B鄄PSO鄄MSVM model was established, and surrounding rock parameters were dynamically updated by applying the Markov