Causative Characteristics and Prediction Model of Rockburst Based on Large and Incomplete Data Set
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摘要: 为判别影响岩爆的敏感性因素并构建不完整数据条件下的岩爆预测方法，在收集到429组国内外岩爆案例的基础上建立大样本数据库，归纳总结岩爆致因分布特征及规律，选取埋深、岩石单轴抗压强度、岩石单轴抗拉强度、围岩最大切向应力、弹性应变能量指数、岩体完整性系数6个评价指标，利用贝叶斯网络建立基于大样本不完整数据集的岩爆概率预测模型，并进行敏感性分析和工程应用.分析发现围岩最大切向应力与岩体完整性系数对岩爆的影响较大，所建模型对信息缺失率为20%的岩爆案例预测吻合率达83.3%，且预测效果优于常用岩爆经验判据.结果表明所选取的预测指标能够综合考虑岩爆的影响因素，所建立模型对于深部岩爆灾害的预测具有适用性和可靠性.Abstract: In order to distinguish the sensitivity factors affecting rockburst and construct a rockburst prediction method under the condition of incomplete data cases, a large sample database is established on the basis of collecting 429 groups of rockburst cases at home and abroad, and the distribution characteristics and regulation of rockburst disaster-inducing factors were summarized. Six evaluation indexes, including buried depth, uniaxial compressive strength of rock, uniaxial tensile strength of rock, maximum tangential stress of surrounding rock, rock elastic energy index and integrity coefficient of rock mass, are selected to establish a rockburst probability prediction model based on large and incomplete data set by using Bayesian network, and the sensitivity analysis and engineering application are carried out. Through analysis, it is found that the maximum tangential stress of surrounding rock and the integrity coefficient of rock mass have a great influence on rockburst. The model has a prediction coincidence rate of 83.3% for rockburst cases with information loss rate of 20%, and the prediction effect is better than the commonly used empirical criterion of rockburst. The results show that the prediction indexes selected in this paper can comprehensively consider the influencing factors of rockburst, and the established model has applicability and reliability for the prediction of deep rockburst disasters.
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图 2 所收集的岩爆案例各指标分布直方图
Fig. 2. Index distribution histograms of rockburst cases collected
图 3 无岩爆情况下单轴抗压强度所对应的数据集剔除谱系
Fig. 3. Elimination spectrum of data set corresponding to uniaxial compressive strength in terms of none rockburst
图 4 异常值剔除后不同岩爆等级样本所对应的各评价指标分布箱型
Fig. 4. Distribution box plots of each evaluation index corresponding to samples of different rockburst grades after outlier elimination
图 5 基于BN的岩爆概率预测模型建立流程
Fig. 5. Establishment process of probabilistic prediction model of rockburst based on BN
图 6 岩爆预测的初始BN结构模型
Fig. 6. Initial Bayesian network structural model of rockburst prediction
图 7 参数学习后的岩爆概率预测模型
Fig. 7. Probabilistic prediction model of rockburst after parameter learning
图 8 岩爆BN模型回判准确率与其他方法对比结果
Fig. 8. Comparison of return discriminant accuracy of rockburst BN model with other methods
图 9 相同强岩爆案例数下BN模型与其他方法准确率对比
Fig. 9. Accuracy comparison between BN model and other methods under the same number of strong rockburst cases
图 10 BN模型与其他方法对强岩爆的误判率对比结果
Fig. 10. Comparison of misjudgement rate of BN model with other methods for strong rockburst cases
图 11 岩爆概率预测模型十折交叉验证结果
Fig. 11. Tenfold cross validation results of probabilistic prediction model of rockburst
图 12 围岩最大切向应力对岩爆各状态发生概率的影响
Fig. 12. Influence of tangential stress on the occurrence probability of rockburst grades
图 13 岩体完整性系数对岩爆各状态发生概率的影响
Fig. 13. Influence of rock mass integrity coefficient on occurrence probability of rockburst grades
图 14 岩爆BN模型预测准确率与其他方法对比结果
Fig. 14. Comparison results of prediction accuracy of rockburst BN model with other methods
表 1 岩爆数据库部分案例信息
Table 1. The information of part cases from the constructed rockburst database
序号 隧道名称 埋深H(m) 岩石单轴抗压强度σc(MPa) 岩石单轴抗拉强度σt(MPa) 围岩最大切向应力σθ(MPa) 弹性应变能量指数Wet 岩体完整性系数Kv 岩爆等级 1 终南山隧道竖井工程 119 122.00 5.38 43.10 3.31 0.63 轻微岩爆 2 283 121.00 8.73 87.50 9.05 0.91 强烈岩爆 3 316 124.00 8.64 79.10 7.74 0.96 强烈岩爆 4 467 119.00 7.21 56.20 5.52 0.84 中等岩爆 5 659 120.00 6.45 62.80 4.16 0.87 中等岩爆 6 程潮铁矿 428 81.20 10.60 18.70 1.50 N/A 无岩爆 7 580 120.50 14.90 72.00 2.50 N/A 中等岩爆 8 650 155.80 11.77 109.80 5.20 N/A 强烈岩爆 9 560 126.80 6.56 55.90 8.10 N/A 轻微岩爆 … … … … … … … … … 423 大相岭隧道 362 59.70 1.30 25.70 1.70 N/A 无岩爆 424 981 80.60 2.50 57.20 5.50 N/A 强烈岩爆 425 金伯利岩石矿山 768 132.00 2.40 62.10 5.00 N/A 中等岩爆 426 N/A 60.00 3.17 21.00 1.70 N/A 中等岩爆 427 N/A 82.00 3.87 31.16 2.30 N/A 中等岩爆 428 N/A 74.80 2.98 46.38 3.20 N/A 中等岩爆 429 N/A 76.00 4.09 48.64 2.50 N/A 中等岩爆 注：岩爆数据来源于许梦国等(2008)；Zhang et al. (2011)；张乐文等(2012)；Zhou et al.(2012)；Pu et al.(2019)；Wu et al.(2019)；Li et al.(2020)；田睿等(2020)；吴枋胤等(2020)；谢学斌等(2020)；周航等(2020)等. 
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表 2 各指标中各岩爆等级异常值剔除情况
Table 2. The elimination of abnormal values of each rockburst grade in each index
剔除比（%） σc σt σθ Wet Kv 无岩爆 3.13 1.56 1.56 4.68 0.00 轻微岩爆 1.39 1.08 1.74 0.68 3.64 中等岩爆 3.95 1.16 2.82 2.82 0.00 强烈岩爆 3.90 1.30 2.60 2.70 0.00
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表 3 岩爆评价指标双变量相关性分析
Table 3. Analysis on the bivariate correlation of rockburst evaluation indexes
H σc σt σθ Wet Kv 岩爆等级 H 1 0.204** -0.089 0.463** -0.065 0.132 0.324** σc 0.204** 1 0.420** 0.355** 0.347** 0.155 0.232** σt -0.089 0.402** 1 0.243** 0.282** 0.406** 0.241** σθ 0.463** 0.355** 0.243** 1 0.239** 0.481** 0.593** Wet -0.065 0.347** 0.282** 0.239** 1 0.256** 0.458** Kv 0.132 0.155 0.406** 0.481** 0.256** 1 0.751** 岩爆等级 0.324** 0.232** 0.241** 0.593** 0.458** 0.751** 1 注：0.6~0.8为强相关性，0.4~0.6为中等程度相关，0.2~0.4为弱相关性，0.0~0.2为极弱相关性或无相关性，**相关性在0.01水平（双尾）上显著相关.
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表 4 岩爆样本各指标离散等级分类区间划分
Table 4. Division of discrete classification intervals for each index of rockburst samples
指标 离散等级区间 极低水平 低水平 中等水平 高水平 极高水平 H(m) ≤370 (370, 600] (600, 775] (775, 1 000] > 1 000 低水平 中等水平 高水平 极高水平 σc(MPa) ≤94 (94, 124] (124, 156.73] > 156.73 σt(MPa) ≤3.85 (3.85, 5.38] (5.38, 8.30] > 8.30 σθ(MPa) ≤32.8 (32.8, 53] (53, 75] > 75 Wet ≤2.96 (2.96, 4.6] (4.6, 6.11] > 6.11 Kv ≤0.64 (0.64, 0.72] (0.72, 0.8] > 0.8
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表 5 前人提出的4种判据方法
Table 5. Four criterion methods proposed by predecessors
预测方法与指标 岩爆等级划分 无岩爆 弱岩爆 强岩爆 Russense（σθ/σc） < 0.2 [0.20, 0.55) ≥0.55 强度脆性系数（σc/σt） > 40 [14.5, 40] < 14.5 Kidybinski（Wet） < 2 [2, 5) ≥5 王元汉（σθ/σc） < 0.3 [0.3, 0.7) ≥0.7
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表 6 BN模型中岩爆等级节点敏感性分析结果
Table 6. Sensitivity results of rockburst grade nodes in BN model
节点 互信息 百分比 岩爆等级 1.325 51 100 围岩最大切向应力 0.291 95 25 岩体完整性系数 0.100 99 6.03 岩石单轴抗压强度 0.015 31 1.35 埋深 0.011 22 0.583 岩石单轴抗拉强度 0.006 21 0.334 弹性应变能量指数 0.001 50 0.14
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表 7 工程应用预测案例工程概况
Table 7. Project overview of engineering application prediction cases
工程名称 巴玉隧道 桑珠岭隧道 秦岭隧道 锦屏二级水电站 江边水电站 双江口水电站 地理位置 西藏自治区山南市 西藏自治区山南市 陕西省长安县与柞水县交界 四川省凉山彝族自治州 四川省甘孜州九龙县 四川省境内 最大埋深 2 080 m 1 347 m 1 600 m 2 525 m 1 678 m / 岩性 以花岗岩为主 闪长岩、花岗岩 混合岩类 以大理岩为主 黑云母石英、片岩 花岗岩杂岩体 现场岩爆照片 
注：巴玉隧道、桑珠岭隧道、秦岭隧道据宫凤强等(2010); 江边水电站据张德永等(2015); 锦屏二级水电站据邱士利等(2014)；严健等(2019).
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表 8 开展岩爆BN模型应用的工程案例信息
Table 8. Information of rockburst cases for engineering application of BN model
序号 工程名称 H(m) σc(MPa) σt(MPa) σθ(MPa) Wet Kv BN模型预测结果 实际岩爆等级 1 巴玉隧道 1 533 160.00 7.60 128.00 N/A 0.82 弱岩爆 弱岩爆 2 1 872 160.00 7.60 155.20 N/A 0.69 弱岩爆 弱岩爆 3 2 080 160.00 7.60 176.00 N/A 0.50 弱岩爆 强岩爆 4 2 080 190.00 8.90 74.20 N/A N/A 强岩爆 强岩爆 5 桑珠岭隧道 240 141.00 7.22 47.80 4.30 0.71 弱岩爆 弱岩爆 6 300 141.00 6.59 48.90 4.30 0.71 弱岩爆 弱岩爆 7 680 N/A N/A 41.90 4.00 0.62 弱岩爆 弱岩爆 8 800 147.00 6.87 58.40 4.60 0.71 弱岩爆 弱岩爆 9 1 050 N/A N/A 61.10 4.60 0.62 弱岩爆 弱岩爆 10 江边水电站 N/A 96.41 2.01 18.32 1.87 N/A 无岩爆 无岩爆 11 N/A 107.52 2.98 21.50 2.29 N/A 无岩爆 无岩爆 12 N/A 126.88 N/A 40.60 4.15 0.59 弱岩爆 无岩爆 13 174 114.07 N/A 15.97 2.40 0.61 无岩爆 无岩爆 14 275 106.31 N/A 19.14 2.07 0.54 无岩爆 无岩爆 15 186 117.81 N/A 12.96 2.49 0.60 无岩爆 无岩爆 16 214 138.50 N/A 29.09 2.77 0.69 无岩爆 无岩爆 17 289 106.32 2.92 23.39 1.75 0.46 无岩爆 无岩爆 18 N/A 164.05 N/A 104.99 8.41 0.88 强岩爆 强岩爆 19 锦屏二级水电站 970 160.83 11.06 30.56 3.63 N/A 强岩爆 强岩爆 20 N/A 85.00 4.80 91.80 3.20 0.70 弱岩爆 弱岩爆 21 N/A 62.00 3.88 38.44 3.00 0.37 弱岩爆 弱岩爆 22 N/A 70.00 4.70 21.70 2.50 0.40 无岩爆 无岩爆 23 秦岭隧道 1 600 133.99 9.09 54.20 7.08 N/A 弱岩爆 弱岩爆 24 1 600 128.52 8.73 70.30 6.43 N/A 弱岩爆 弱岩爆 25 双江口水电站 115 71.96 7.14 44.80 N/A 0.65 弱岩爆 弱岩爆 26 400 86.80 8.23 105.25 N/A 0.65 强岩爆 弱岩爆 27 其他工程 N/A 140.00 8.00 108.00 N/A N/A 强岩爆 强岩爆 28 N/A 225.60 17.20 91.30 N/A N/A 弱岩爆 强岩爆 29 N/A 78.70 2.65 32.27 3.30 0.64 弱岩爆 无岩爆 30 N/A 167.20 12.67 110.35 6.80 0.82 强岩爆 强岩爆 注：岩爆数据来源于宫凤强和李夕兵(2007); 李航(2020); Xue et al. (2020); 杨小彬等(2021); 张翔宇(2021); 周航等(2022).
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