Preliminary Study of Assessment System for Subsurface Karst Development Degree
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摘要: 为了对下岩溶液发育状况进行初步的判断，从而为岩溶区地下工程的规划与施工提供指导，采用定量与定性相结合的方法建立一套地下岩溶发育程度的评价体系，其评价结果可以用来对下岩溶发育状况进行初步的判断.首先，选取了6个影响岩溶发育的主要因素作为地下岩溶发育程度的评价指标，并对地下岩溶的不同发育程度等级进行定义；其次，采用基于模糊层次分析法与贝叶斯网络法的综合赋权法确定了各个因素对于岩溶发育影响的权重，并基于层次分析法确定了评价指标各状态的统一评分标准；最后，采用对比分析的方法确立了各个岩溶发育程度等级所对应的定量评价值的范围.为了检验该评价系统的实用性，该系统被应用于某岩溶区的铁路隧道工程当中.通过地预测评价结果与实际记录结果的对比分析可得：占隧道总长度97.1%的区域的地下岩溶发育程度的评价结果与实际岩溶发育状况相一致，只有2.9%的区域的评价结果产生了误差；在评价结果产生误差的这一区域，岩溶发育程度的定量评价值为0.69，岩溶发育程度被评价为"发育"，十分接近实际发育状况"强烈发育"所属的定量值范围0.70~1.00，验证了该地下岩溶发育程度评价系统的的可靠性.Abstract: An attempt was made to establish an assessment system for subsurface karst development by combining quantitative and qualitative methods. The assessment results can assist the preliminary determination of the extent of underground karst development and guide the planning and construction of underground engineering projects. Firstly, the major factors influencing the karst development were selected as the assessment indices in the system, and the varying degrees of subsurface karst development are defined. Then, the weights of these assessment indices were determined using a synthetic weighting method, in which the fuzzy hierarchy analytic process determines the qualitative weights, while the quantitative weights were determined by a sensitivity analysis of the Bayesian belief network. The Fuzzy Analytic Hierarchy Process was used to determine the ratings of the karst development states in the assessment indices. Moreover, based on the statistical data, the quantitative assessment results belonging to each degree of karst development were determined by comparing the calculated assessment results with the real karst development status. The proposed assessment system was applied to a railway tunnelling project in China to evaluate the degree of surface karst development before tunnel construction. A comparative analysis of the assessment results with the recorded results shows that the assessment of the tunnel zone, accounting for 97.1% of the total tunnel length, is consistent with the recorded results. Assessment errors only occur in 2.9% of the tunnel zone, where the degree of karst development was assigned as "developed", while the records indicated it was "extremely developed". However, the quantitative assessment result of the karst development degree is 0.69, which is close to the value range of "extremely developed", 0.70-1.00. As this minor error is acceptable in the preliminary assessment of the degree of karst development, the proposed assessment system is verifiably reliable.
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图 2 各岩溶发育程度对应的评价值落在各个区间的比例
Figure 2. Proportions of assessment results belonging to each karst development degree within each interval
表 1 地下岩溶发育程度及其指标
Table 1. Underground karst development and its index
地下岩溶发育程度 描述 强烈发育 大型溶洞或暗河; 或n≥15 发育 中等溶洞, 较小的暗河或连通的岩溶管道; 或5≤n＜15; 中等发育 小型溶洞、溶槽或独立的岩溶管道; 或1≤n＜5 轻微发育或不发育 主要以溶隙或溶孔为主; 或n＜1 注: n为沿隧道每千米长度上发育规模为中等及以上的溶洞的个数. 
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表 2 地下岩溶发育程度的评价指标及分级
Table 2. Evaluation indices of subsurface karst development and grades
因素 评价指标 指标级别 极有利于岩溶发育(Ⅰ) 有利于岩溶发育(Ⅱ) 相对有利于岩溶发育(Ⅲ) 轻微有利岩溶发育(Ⅳ) 岩层的可溶性[6] 状态等级 极度可溶 可溶 相对可溶 轻微可溶 岩层组成 均匀状灰岩类 均匀状的除灰岩以外的碳酸岩 间互状纯碳酸岩 均匀状、间互状不纯碳酸岩或变质碳酸岩 可溶岩层厚度[10] 状态等级 极厚 厚 中厚 薄 厚度/m >100 20~100 5~20 0~5 地下水的溶蚀性 状态等级 极强 强 中等 弱 游离CO2浓度/(mg·L-1) ＞60 15~60 3~15 ＜3 岩溶的富水性 状态等级 极强富水 强富水 中等富水 弱富水 单位钻孔涌水量/(L·(s·m)-1) ＞5.0 1.0~5.0 0.1~1.0 0~0.1 水的动力循环条件 状态等级 极有利 有利 相对有利 轻微有利 岩溶水动力分带 季节变动带 饱水带 包气带 深部循环带 地质构造条件 状态等级 极断裂或褶皱的 断裂或褶皱的 相对断裂或褶皱的 轻微断裂或褶皱的 构造类型或位置 张扭断层; 或向斜轴部; 或任何断层与褶皱同时出现 张性断层; 或背斜轴部、褶皱转折端 压扭断层; 或褶皱翼部 压型10.断层; 或无任何断层或褶皱构造
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表 3 由三角形模糊数定义的相对重要性规模
Table 3. Relative importance scale based on triangular fuzzy numbers
相对重要性 模糊数 三角形模糊数 倒模糊数 三角形模糊数的倒数 同等重要 ${\tilde 1} $ (1, 1, 1) ${\tilde 1} $ -1(1, 1, 1) 稍微重要 ${\tilde 3} $ (1, 3, 5) ${\tilde 3} $ -1(1/5, 1/3, 1) 强烈重要 ${\tilde 5} $ (3, 5, 7) ${\tilde 5} $ -1(1/7, 1/5, 1/3) 非常强烈重要 ${\tilde 7} $ (5, 7, 9) ${\tilde 7} $ -1(1/9, 1/7, 1/5) 极端重要 ${\tilde 9} $ (7, 9, 11) ${\tilde 9} $ -1(1/11, 1/9, 1/7) 上述相邻判断的中间值 ${\tilde 2} $ (1, 2, 4) ${\tilde 2} $ -1(1/4, 1/2, 1) ${\tilde 4} $ (2, 4, 6) ${\tilde 4} $ -1(1/6, 1/4, 1/2) ${\tilde 6} $ (4, 6, 8) ${\tilde 6} $ -1(1/8, 1/6, 1/4) ${\tilde 8} $ (6, 8, 10) ${\tilde 8} $ -1(1/10, 1/8, 1/6)
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表 4 各影响因素关于岩溶发育的两两比较矩阵及其权重
Table 4. Pairwise comparison matrix of factors to karst development and weights
因素 I1 I2 I3 I4 I5 I6 $ \sum\limits_{j = 1}^p {{\mathit{\boldsymbol{M}}_{{g_i}j}}} $ 未归一化权重 归一化权重 I1 (1, 1, 1) (1, 3, 5) (1, 2, 4) (1, 3, 5) (1, 2, 4) (1, 2, 4) (6, 12, 23) 1 0.214 I2 (1/5, 1/3, 1) (1, 1, 1) (1/5, 1/3, 1) (1, 2, 4) (1/4, 1/2, 1) (1/4, 1/2, 1) (2.9, 4.67, 9) 0.625 0.134 I3 (1/4, 1/2, 1) (1, 3, 5) (1, 1, 1) (1, 3, 5) (1, 2, 4) (1, 2, 4) (5.25, 11.5, 20) 0.959 0.205 I4 (1/5, 1/3, 1) (1/4, 1/2, 1) (1/5, 1/3, 1) (1, 1, 1) (1/4, 1/5, 1) (1/4, 1/2, 1) (2.15, 3.17, 6) 0.453 0.108 I5 (1/4, 1/2, 1) (1, 2, 4) (1/4, 1/2, 1) (1, 2, 4) (1, 1, 1) (1/4, 1/2, 1) (3.75, 6.5, 12) 0.751 0.161 I6 (1/4, 1/2, 1) (1, 2, 4) (1/4, 1/2, 1) (1, 2, 4) (1, 2, 4) (1, 1, 1) (4.5, 8, 15) 0.835 0.179
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表 5 敏感性分析结果及各因素归一化权重
Table 5. Sensitivity to findings and normalized weights of factors
节点 互信息 百分比/% 归一化权重 岩溶发育程度 1.987 02 1.00 — 岩层可溶性 0.007 54 37.90 0.285 可溶性岩层厚度 0.004 55 22.90 0.172 地下水溶蚀性 0.004 90 24.70 0.185 岩层富水性 0.004 76 24.00 0.180 水动力分带 0.003 27 16.50 0.124 地质构造条件 0.001 42 7.13 0.054
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表 6 影响因素各状态关于岩溶发育的判断矩阵
Table 6. Judgment matrix of states of factors influencing karst development
状态等级 Ⅰ Ⅱ Ⅲ Ⅳ 优先级 归一化优先级 Ⅰ 1 3 5 7 0.504 1.000 Ⅱ 1/3 1 3 5 0.274 0.544 Ⅲ 1/5 1/3 1 3 0.144 0.286 Ⅳ 1/7 1/5 1/3 1 0.078 0.155
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表 7 一致性指标取值
Table 7. Value of resistency index
q 2 3 4 5 6 7 8 9 β 0 0.52 0.89 1.12 1.26 1.36 1.41 1.46
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表 8 岩溶发育程度各影响因素的因素及状态评分表
Table 8. Weights and ratings of factors affecting the degree of karst development
因素 权重 状态等级 Ⅰ Ⅱ Ⅲ Ⅳ 岩层的可溶性 0.249 极度可溶 可溶 相对可溶 轻微可溶 可溶性岩层厚度 0.153 极厚 厚 中厚 薄 地下水的溶蚀性 0.195 极强溶蚀性 强溶蚀性 中等溶蚀性 弱溶蚀性 岩层的富水性 0.144 极强富水 强富水 中等富水 弱富水 地下水动力分带 0.142 饱水带 季节变动带 包气带 深部循环带 地质构造条件 0.116 极度褶皱或断裂的 褶皱或断裂的 相对褶皱或断裂的 轻微褶皱或断裂的 状态等级的定量评分 1.000 0.544 0.286 0.155
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表 9 岩溶发育程度各等级所对应的计算结果范围
Table 9. Ranges of assessment results corresponding to different karst development degrees
岩溶发育程度 轻微发育或不发育 中等发育 发育 强烈发育 计算结果范围 0~0.2 0.2~0.4 0.4~0.7 0.7~1.0
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表 10 岩溶发育影响因素的状态
Table 10. States of factors influencing karst development
里程 岩层类型 可溶岩层厚度 地下水溶蚀性 岩层富水性 水动力分带 地质构造条件 z 岩溶发育程度预测 DK98+844~DK98+922 白云岩夹泥质灰岩 厚层 中等溶蚀性 极强富水 饱水带 褶皱或断裂 0.495 发育 DK98+922~DK99+400 白云岩夹泥质灰岩 厚层 中等溶蚀性 富水 饱水带 褶皱或断裂 0.429 DK99+400~DK99+770 白云岩 极厚层 中等溶蚀性 富水 饱水带 褶皱或断裂 0.563 DK99+770~DK99+850 白云岩 厚层 中等溶蚀性 富水 饱水带 极褶皱或断裂 0.546 DK99+850~DK100+820 白云岩 厚层 中等溶蚀性 极强富水 饱水带 褶皱或断裂 0.559 DK100+820~DK101+835 泥质灰岩夹页岩 中厚层 中等溶蚀性 富水 饱水带 相对褶皱或断裂 0.327 中等发育 DK101+835~DK102+900 钙质粉砂岩 非可溶岩 无溶蚀性 富水 无动力分带 相对褶皱或断裂 0.112 轻微发育或不发育 DK102+900~DK103+450 页岩 非可溶岩 无溶蚀性 富水 无动力分带 褶皱或断裂 0.194 DK103+450~DK106+000 石英砂岩夹页岩 非可溶岩 无溶蚀性 富水 无动力分带 褶皱或断裂 0.194 DK106+000~DK106+210 灰岩 厚层 中等溶蚀性 极强富水 饱水带 褶皱或断裂的 0.692 发育
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表 11 实际记录的岩溶发育状况
Table 11. Records of karst development status
隧道里程 实际记录的岩溶发育情况 DK98+844~DK98+922 出现一大型的封闭岩溶洼地, 洼地底部出现两个竖直溶洞.开挖过程中总共遇到中型及以上的岩溶现象12处, 且多段出现溶蚀破碎带 DK98+922~DK99+400 DK99+400~DK99+770 DK99+770~DK99+850 DK99+850~DK100+820 DK100+820~DK101+835 开挖过程中未见有较大的溶蚀现象, 偶见溶槽或溶管 DK101+835~DK102+900 基本未见溶洞等岩溶现象, 也极少出现溶蚀破碎带; 但部分地段岩层扭曲严重, 岩体破碎 DK102+900~DK103+450 DK103+450~DK106+000 DK106+000~DK106+210 DK106+075~DK106+110段靠洞壁左侧溶洞发育, 走向大致为S60°W, 宽4~6 m, 长35 m左右; 溶洞地板黏土夹碎石充填, 岩体溶蚀破碎, 局部有溶蚀空腔.其他多段出现溶蚀破碎带
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