Dynamic prediction model of tunnel surrounding rock deformation based on Bayesian network
WANG Hongxing1, LI Keyao1, ZHANG Chao2*, RUAN Junhao1, WANG Liping1, LIU Wei3, WU Shangwei1
(1. School of Safety Science and Engineering, Chongqing University of Science and Technology, Chongqing 400041, China;
2. State Key Laboratory of Geomechanics and Geotechnical Engineering Safety, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, Hubei 430071, China; 3. School of Resource and Safety Engineering,
Chongqing University, Chongqing 400044, China)
Abstract：Significant limitations and hysteresis are presented in dynamic prediction methods driven by on-site monitored displacement data for tunnel surrounding rock deformation. By comprehensively utilizing the physical information contained in tunnel construction project documents and the mathematical information from displacement time-series curves, a modelling method based on the dynamic Bayesian network (DBN) was developed using the concept of physical information machine learning (PIML) to achieve dynamic predictions of surrounding rock deformation. Through discretization processing and reconstruction of displacement time-series curves, a static sample database was established by combining physical information data with ultimate displacement data, while a dynamic sample database was created by integrating physical information data with displacement time-series curve data. Based on the characteristics of the static samples, the K2-score algorithm was improved to construct a static Bayesian network (BN) model for ultimate displacement prediction. Utilizing the static BN model and the characteristics of the dynamic samples, physical-data dual-drive modelling methods for the Markov DBN were derived by incorporating prior information, including the constraints of steady-state random processes and Markov process constraints. By integrating prior information for constraint-enhanced optimization, the optimized Markov DBN model was established. Five-fold cross-validation tests revealed that the prediction capability of the Markov DBN model decreased rapidly over time and that the network transition direction significantly affected this capability. In contrast, the prediction ability of the optimized Markov DBN model remained robust over time, was unaffected by the network transition direction, and significantly exceeded that of the Markov DBN model, as the optimized model enhanced constraint connections between target nodes and influencing factor nodes throughout the entire timeframe. Through engineering case analysis, it was concluded that before and during the early stages of tunnel construction, the optimized Markov DBN model could effectively predict displacement time-series curves, overcoming the limitations and hysteresis inherent in traditional methods. Furthermore, during construction, self-updating of the optimized Markov DBN model and dynamic predictions of surrounding rock deformation could be achieved by inputting the on-site monitored displacement data.
汪洪星1，李珂瑶1，张 超2*，阮俊浩1，王丽萍1，刘 伟3，巫尚蔚1. 基于贝叶斯网络的隧道围岩变形动态预测模型[J]. 岩石力学与工程学报, 2026, 45(2): 553-577.
WANG Hongxing1, LI Keyao1, ZHANG Chao2*, RUAN Junhao1, WANG Liping1, LIU Wei3, WU Shangwei1. Dynamic prediction model of tunnel surrounding rock deformation based on Bayesian network. , 2026, 45(2): 553-577.
[1] 郑艾辰，黄 锋，林 志，等. 2008 年至 2016 年我国隧道工程施工安全事故统计与分析[J]. 施工技术，2017，46(增1)：833–836.(ZHENG Aichen，HUANG Feng，LIN Zhi，et al. The statistics and analysis of safety accident during tunnel engineering construction in China from 2008 to 2016[J]. Construction Technology，2017，46(Supp.1)：833–836.(in Chinese))
[2] 吕擎峰，李 钰，牛 荣，等. 基于深度学习的特殊岩土隧道围岩变形预测研究[J]. 应用基础与工程科学学报，2023，31(6)： 1 590–1 600.(LÜ Qingfeng，LI Yu，NIU Rong，et al. Research on deformation prediction of surrounding rock in special geotechnical tunnels based on deep learning[J]. Journal of Fundamental and Engineering Science，2023，31(6)：1 590–1 600.(in Chinese))
[3] 孙振宇，张顶立，侯艳娟，等. 基于现场实测数据统计的隧道围岩全过程变形规律及稳定性判据确定[J]. 岩土工程学报，2021，43(7)：12–20.(SUN Zhenyu，ZHANG Dingli，HOU Yanjuan，et al. Whole-process deformation laws and determination of stability criterion of surrounding rock of tunnels based on statistics of field measured data[J]. Chinese Journal of Geotechnical Engineering，2021，43(7)：12–20.(in Chinese))
[4] 王述红，董福瑞. 基于变形预测和参数反演的山岭隧道围岩稳定性分析[J]. 岩土工程学报，2023，45(5)：1 024–1 035.(WANG Shuhong，DONG Furui. Stability analysis of surrounding rock of mountain tunnels based on deformation prediction and parameter inversion[J]. Chinese Journal of Geotechnical Engineering，2023，45(5)：1 024–1 035.(in Chinese))
[5] WANG Y，LIU Y，WANG Z F，et al. Investigation on progressive failure process of tunnel lining induced by creep effect of surrounding rock：A case study[J]. Engineering Failure Analysis，2023，144：106946.
[6] SHI S，ZHAO R，LI S，et al. Intelligent prediction of surrounding rock deformation of shallow buried highway tunnel and its engineering application[J]. Tunnelling and Underground Space Technology，2019，90：1–11.
[7] AYDAN O，AKAGI T，KAWAMOTO T. The squeezing potential of rocks around tunnels：Theory and prediction[J]. Rock Mechanics and Rock Engineering，1993，26(2)：137–163.
[8] BIAN K，LIU J，LIU Z，et al. Mechanisms of large deformation in soft rock tunnels a case study of Huangjiazhai Tunnel[J]. Bulletin of Engineering Geology and the Environment，2019，78(1)：431–444.
[9] 王明年，王志龙，张 霄，等. 深埋隧道围岩形变压力计算方法研究[J]. 岩土工程学报，2020，42(1)：81–90.(WANG Mingnian，WANG Zhilong，ZHANG Xiao，et al. Method for calculating deformation pressure of surrounding rock of deep-buried tunnels[J]. Chinese Journal of Geotechnical Engineering，2020，42(1)：81–90.(in Chinese))
[10] 马鑫民，陈 攀，陈 晨，等. 基于机器学习的煤巷围岩稳定性预测与应用[J]. 矿业科学学报，2023，8(2)：156–165.(MA Xinmin，CHEN Pan，CHEN Chen，et al. Prediction of surrounding rock stability of coal roadway based on machine learning and its application[J]. Journal of Mining Science and Technology，2023，8(2)：156–165.(in Chinese))
[11] WANG L，PAN Q，WANG S. Data-driven predictions of shield attitudes using Bayesian machine learning[J]. Computers and Geotechnics，2024，166：106002.
[12] FENG X D，JIMENEZ R. Predicting tunnel squeezing with incomplete data using Bayesian networks[J]. Engineering Geology，2015，195：214–224.
[13] WU X G，JIANG Z，ZHANG L M，et al. Dynamic risk analysis for adjacent buildings in tunneling environments：a Bayesian network based approach[J]. Stochastic Environmental Research and Risk Assessment，2015，29(5)：1 447–1 461.
[14] ZHOU J，ZHU S L，QIU Y G，et al. Predicting tunnel squeezing using support vector machine optimized by whale optimization algorithm[J]. Acta Geotechnica，2022，17(4)：1 343–1 366.
[15] 梁文添，陈劲慧. 新奥法在三连拱特大断面隧道施工中的应用[J]. 岩石力学与工程学报，2017，36(11)：2 763–2 770.(LIANG Wentian，CHEN Jinhui. Application of new Austrian tunnelling method to a large span trinocular cross section tunnel[J]. Chinese Journal of Rock Mechanics and Engineering，2017，36(11)：2 763–2 770.(in Chinese))
[16] FENG T G，WANG C R，ZHANG J，et al. An improved artificial bee colony-random forest(IABC-RF) model for predicting the tunnel deformation due to an adjacent foundation pit excavation[J]. Underground Space，2022，7(4)：514–527.
[17] CHEN S，ZHU Y，HUANG L. Application of chaotic time series analysis to the prediction of tunnel surrounding rock displacement[J]. Modern Tunnelling Technology，2015，52(3)：75–81.
[18] LI Z H，MA E L，LAI J X，et al. Tunnel deformation prediction during construction：An explainable hybrid model considering temporal and static factors[J]. Computers and Structures，2024，294：107276.
[19] BAI C H，XUE Y G，QIU D H，et al. Analysis of factors affecting the deformation of soft rock tunnels by data envelopment analysis and a risk assessment model[J]. Tunnelling and Underground Space Technology，2021，116：104111.
[20] 张 振，苏欣荣，袁 新. 基于物理信息神经网络的气膜冷却湍流模型反演学习[J]. 动力工程学报，2024，44(9)：1 459–1 465. (ZHANG Zhen，SU Xinrong，YUAN Xin. PINN-based inversion learning of turbulence model for film cooling[J]. Journal of Chinese Society of Power Engineering，2024，44(9)：1 459–1 465.(in Chinese))
[21] 卢鑫月，许成顺，侯本伟，等. 基于动态贝叶斯网络的地铁隧道施工风险评估[J]. 岩土工程学报，2022，44(3)：492–501.(LU Xinyue，XU Chengshun，HOU Benwei，et al. Risk assessment of metro construction based on dynamic Bayesian network[J]. Chinese Journal of Geotechnical Engineering，2022，44(3)：492–501.(in Chinese))
[22] CHING W K，程伟琪，黄曦敏，等. 马尔可夫链：模型、算法与应用[M]. 北京：清华大学出版社，2015：13–27.(CHING W K，CHENG Weiqi，HUANG Ximin，et al. Markov Chains：models，algorithms and applications second edition[M]. Beijing：Tsinghua University Press，2015：13–27.(in Chinese))
[23] SMITH J Q，ANDERSON P E. Conditional independence and chain event graphs[J]. Artificial Intelligence，2008，172(1)：42–68.
[24] 杨 悦，陈孝国，高 霞，等. 基于神经网络–蒙特卡罗法的隧道初衬可靠度研究[J]. 齐齐哈尔大学学报：自然科学版，2017，33(1)：5–9.(YANG Yue，CHEN Xiaoguo，GAO Xia，et al. Study on reliability of tunneling initial lining based on radial basis function neural network-Monte Carlo method[J]. Journal of Qiqihar University：Natural Science，2017，33(1)：5–9.(in Chinese))
[25] 张广泽，邓建辉，王 栋，等. 隧道围岩构造软岩大变形发生机理及分级方法[J]. 工程科学与技术，2021，53(1)：1–12.(ZHANG Guangze，DENG Jianhui，WANG Dong，et al. Mechanism and classification of tectonic-induced large deformation of soft rock tunnels[J]. Engineering Science and Technology，2021，53(1)：1–12.(in Chinese))
[26] 中华人民共和国国家标准编写组. GB/T 10003—2016 铁路隧道设计规范[S]. 北京：中国铁道出版社，2016.(The National Standards Compilation Group of People?s Republic of China. GB/T 10003—2016 Code for design of railway tunnel[S]. Beijing：China Railway Publishing House，2016.(in Chinese))
[27] 中华人民共和国行业标准编写组. JTG 3370.1—2018 公路隧道设计规范[S]. 北京：人民交通出版社，2018.(The Professional Standards Compilation Group of People?s Republic of China. JTG 3370.1—2018 Specification for design of highway tunnel[S]. Beijing：China Communications Press，2018.(in Chinese))
[28] COOPER G，HERSKOVITS E. A Bayesian method for the induction of probabilistic networks from data[J]. Machine Learning，1992，9(4)：309–347.
[29] 朱永全，宋玉香. 隧道工程[M]. 北京：中国铁道出版社，2018：21–30.(ZHU Yongquan，SONG Yuxiang. Tunnel engineering[M]. Beijing：China Railway Publishing House，2018：21–30.(in Chinese))
[30] 孙景来，刘保国，储昭飞，等. 隧道坍塌事故类型划分及其主要特征[J]. 中国铁道科学，2018，39(6)：44–51.(SUN Jinglai，LIU Baoguo，CHU Zhaofei，et al. Type classification and main characteristics of tunnel collapses[J]. China Railway Science，2018，39(6)：44–51.(in Chinese))
[31] 陈子全，何 川，吴 迪，等. 高地应力层状软岩隧道大变形预测分级研究[J]. 西南交通大学学报，2018，53(6)：1 237–1 244. (CHEN Ziquan，HE Chuan，WU Di，et al. Study of large deformation classification criterion for layered soft rock tunnels under high geostress[J]. Journal of Southwest Jiaotong University，2018，53(6)：1 237–1 244.(in Chinese))
[32] 任德惠，张 平. 不同倾角结构面对巷道稳定性的影响[J]. 煤炭学报，1988，13(3)：13–19.(REN Dehui，ZHANG Ping. Influence of structural planes with different dip angles on roadway stability[J]. Journal of China Coal Society，1988，13(3)：13–19.(in Chinese))
[33] 吴秋军. 铁路隧道围岩变形机理与分级方法研究[博士学位论文][D]. 成都：西南交通大学，2017.(WU Qiujun. Deformation mechanism and classification methods for surrounding rock of railway tunnels[Ph. D. Thesis][D]. Chengdu：Southwest Jiaotong University，2017.(in Chinese))
[34] 王冠勇. 分析影响隧道围岩稳定性因素[J]. 交通世界(建养?机械)，2012，(13)：234–235.(WANG Guanyong. Analysis of factors affecting the stability of tunnel surrounding rock[J]. Traffic World (Construction and Maintenance?Machinery)，2012，(13)：234–235.(in Chinese))
[35] 吉小明. 隧道开挖的围岩损伤扰动带分析[J]. 岩石力学与工程学报，2005，24(10)：1 697–1 702.(JI Xiaoming. Study on mechanical and hydraulic behavior of tunnel surrounding rock masses in excavation-disturbed zone[J]. Chinese Journal of Rock Mechanics and Engineering，2005，24(10)：1 697–1 702.(in Chinese))
[36] 来弘鹏，林永贵，谢永利，等. 支护时机对软弱围岩公路隧道力学特征影响的试验研究[J]. 岩土工程学报，2009，31(3)：390–395.(LAI Hongpeng，LIN Yonggui，XIE Yongli，et al. Influence of supporting opportunity on stress characteristics of soft-weak surrounding rocks in highway tunnels[J]. Chinese Journal of Geotechnical Engineering，2009，31(3)：390–395.(in Chinese))
[37] ŠPA?KOVÁ O，STRAUB D. Dynamic Bayesian network for probabilistic modeling of tunnel excavation processes[J]. Computer-Aided Civil and Infrastructure Engineering，2013，28(1)：1–21.
[38] 李海斌，翟秋柱，张 优，等. PSO-BP神经网络在隧道围岩变形预测中的应用[J]. 路基工程，2017，(5)：164–169.(LI Haibin，ZHAI Qiuzhu，ZHANG You，et al. Application of PSO-BP neural network in prediction of tunnel rock deformation[J]. Subgrade Engineering，2017，(5)：164–169.(in Chinese))
[39] 王树栋，刘开云. 长大隧道软弱围岩施工大变形智能预测方法[J]. 中国铁道科学，2008，29(2)：82–87.(WANG Shudong，LIU Kaiyun. Intelligence method for large deformation prediction of weak surrounding rock construction in long and large tunnel[J]. China Railway Science，2008，29(2)：82–87.(in Chinese))
[40] 解志刚. 隧道围岩变形预测及其在工程中的应用[硕士学位论文][D]. 兰州：兰州交通大学，2012.(XIE Zhigang. Tunnel surrounding rock deformation and prediction and its application in engineering[M. S. Thesis][D]. Lanzhou：Lanzhou Jiaotong University，2012.(in Chinese))
[41] NIU Z L，WANG Y Q，FAN S Y. Research on the deformation control of surrounding rock about large-section tunnel in strong-medium weathered slate[J]. Frontiers in Earth Science，2023，10：1–15.
[42] 汪学清，刘 爽，李秋燕，等. 基于K折交叉验证的SVM隧道围岩分级判别[J]. 矿冶工程，2021，41(6)：126–128.(WANG Xueqing，LIU Shuang，LI Qiuyan，et al. Classification and discrimination of surrounding rock of tunnel based on SVM of K-Fold cross validation[J]. Mining and Metallurgical Engineering，2021，41(6)：126–128.(in Chinese))
[43] 毛奕喆，龚国芳，周星海，等. 基于马尔可夫过程和深度神经网络的TBM围岩识别[J]. 浙江大学学报：工学版，2021，55(3)：458–466.(MAO Yizhe，GONG Guofang，ZHOU Xinghai，et al. Identification of TBM surrounding rock based on Markov process and deep neural network[J]. Journal of Zhejiang University：Engineering Science，2021，55(3)：458–466.(in Chinese))
[44] GHAHRAMANI Z. An introduction to hidden Markov models and Bayesian Networks[J]. International Journal of Pattern Recognition and Artificial Intelligence，2001，15(1)：9–42.
[45] 刘次华. 随机过程及其应用[M]. 北京：清华大学出版社，2004：1–2.(LIU Cihua. Stochastic processes and their applications[M]. Beijing：Tsinghua University Press，2004：1–2.(in Chinese))
[46] YE X W，ZHANG X L，ZHANG H Q，et al. Prediction of lining upward movement during shield tunneling using machine learning algorithms and field monitoring data[J]. Transportation Geotechnics，2023，41：101002.
[47] 杨背背，殷坤龙，杜 娟. 基于时间序列与长短时记忆网络的滑坡位移动态预测模型[J]. 岩石力学与工程学报，2018，37(10)： 2 010–2 018.(YANG Beibei，YIN Kunlong，DU Juan. A model for predicting landslide displacement based on time series and long and short term memory neural network[J]. Chinese Journal of Rock Mechanics and Engineering，2018，37(10)：2 010–2 018.(in Chinese))
2026, Vol. 45 
