Depth of strong development of karst based on quantitative factors of hydrodynamic conditions
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摘要: 地下水垂向循环水动力条件是岩溶发育深度的主要控制因素。为探求川东背斜构造岩溶区多级水流系统控制下的岩溶强发育深度，采用地理信息系统（GIS）技术，选取地形指数和水动力坡降构建岩溶水动力强弱的量化因子FHQ，并结合钻孔数据推求假角山背斜构造区地下岩溶强发育深度。研究显示：水动力因子FHQ与地形指数、水动力坡降在空间上呈明显正相关关系，同时可指示岩溶水流系统向深循环的深度，以此推求背斜构造区地下岩溶的强发育深度下限。假角山背斜两翼FHQ集中在0.1~0.4之间，岩溶水动力整体偏弱，深沟FHQ值整体高于浅沟。东、西翼深沟控制下的地下岩溶强发育深度分别约40~100 m和110~180 m；浅沟控制下的地下岩溶强发育深度分别约15~60 m和10~90 m。研究成果可进一步丰富川东背斜区岩溶发育评价方法体系，为隧道工程岩溶突水灾害预测防治提供理论依据。Abstract: The hydrodynamic condition of groundwater vertical circulation is the main factor to control the development depth of karst.In order to explore the karst strong development depth under the multistage flow system in the anticline karst area of East Sichuan.The quantitative factor of karst hydrodynamic strength(FHQ) is constructed by using GIS technology and selecting topographic index and hydrodynamic gradient.Combined with drilling data, the depth of strong development of underground karst in Jiajiao Mountain anticline structure area is calculated.The results show that the hydrodynamic factor FHQ is positively correlated with topographic index and hydrodynamic gradient in space.At the same time, it can indicate the depth of deep circulation of karst water flow system, so as to calculate the lower limit of strong development depth of underground karst in anticline structural areas.The FHQ of the two wings of the Jiajiao Mountain anticline is between 0.1 and 0.4, the karst hydrodynamic force is generally weak, and the FHQ value of the deep ditch is generally higher than that of the shallow ditch.The strong development depth of underground karst under the control of deep trenches in the east and west wings of anticline is about 40-100 m and 110-180 m respectively.It is hoped that the research results will further enrich the evaluation method system of karst development in east Sichuan anticline area.It also provides a theoretical basis for the prediction and prevention of karst water inrush disaster in tunnel engineering.
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图 2 假角山背斜两翼T2b1/T2b2岩性界限处横切沟谷多级水流系统发育剖面图
Figure 2. Development profile of cross-cutting gully multistage water flow system at the lithologic boundary of T2b1/T2b2 on the two wings of Jiajiao Mountain anticline
图 3 假角山背斜多级水流系统发育平面图
Figure 3. Development plan of multi-stage flow system in Jiajiao Mountain anticline
图 5 沟谷纵剖面水动力坡降示意图
H为沟底距坡顶的高差(m)；L为沟底距坡顶的横向距离(m)；h为浅沟沟底与其深沟排泄基准面的垂向距离(m)；l为浅沟沟底与其深沟排泄基准面的横向距离(m)
Figure 5. Schematic diagram of hydrodynamic gradient of valley longitudinal section
图 6 沟谷水动力坡降计算结果对比图
Figure 6. Comparison of calculation results of valley hydrodynamic gradient
表 1 假角山背斜地下水循环模式
Table 1. Groundwater circulation model in Jiajiao Mountain anticline
构造部位 区段 地下水流系统 地下水循环模式 西翼 Ⅰ-1 中间水流系统 双侧浅切沟谷控制的地下水浅循环 Ⅰ-2 中间水流系统 单侧深切沟谷控制的地下水浅循环 Ⅰ-3 中间水流系统 双侧深切沟谷控制的地下水浅循环 东翼 Ⅱ-1 中间水流系统 双侧浅切沟谷控制的地下水浅循环 Ⅱ-2 局部水流系统 单侧深切沟谷控制的地下水浅循环 Ⅱ-3 局部水流系统 双侧深切沟谷控制的地下水浅循环 
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表 2 判断矩阵及一致性检验
Table 2. Matrix judgment and consistency detection
指标 TWI j J TWI 1 4 2 j 1/4 1 1 J 1/2 1 1 一致性检验λmax=3.053 6，CI=0.026 8，RI=0.52，CR=0.051 6 < 0.1，W=(0.584 2, 0.184 0, 0.231 8)T
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表 3 水动力因子指标权重分配
Table 3. Weight distribution of hydrodynamic index
目标层 指标层 权重 水动力因子 TWI 0.584 2 J 0.231 8 j 0.184 0
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表 4 FHQ指示下的岩溶强发育深度计算结果
Table 4. Calculation results of karst strong development depth under FHQ instruction
沟谷编号(对应钻孔) FHQ 钻孔深度/m 计算深度/m 沟谷编号(对应钻孔) FHQ 钻孔深度/m 计算深度/m 沟谷编号(对应钻孔) FHQ 钻孔深度/m 计算深度/m X-25(Z1) 0.24 64 52~64 D-17(Z3) 0.21 46 46~57 D-15(Z5) 0.27 60 59~73 D-18(Z2) 0.21 49 46~57 D-13(Z4) 0.28 64 60~74 沟谷编号 FHQ 计算深度/m 沟谷编号 FHQ 计算深度/m 沟谷编号 FHQ 计算深度/m 最小值 最大值 最小值 最大值 最小值 最大值 X-1 0.07 15 19 X-22 0.20 44 54 D-3 0.31 68 84 X-2 0.26 58 71 X-23 0.14 31 38 D-4 0.36 78 96 X-3 0.13 28 34 X-24 0.24 53 65 D-5 0.30 65 80 X-4 0.04 10 12 X-26 0.16 35 43 D-6 0.16 35 44 X-5 0.32 69 85 X-27 0.15 32 39 D-7 0.21 45 56 X-6 0.27 58 71 X-28 0.16 34 42 D-8 0.12 26 32 X-7 0.21 46 56 X-29 0.33 71 87 D-9 0.21 46 56 X-8 0.10 22 27 X-30 0.21 46 56 D-10 0.17 36 45 X-9 0.14 31 38 X-31 0.18 39 48 D-11 0.28 60 74 X-10 0.11 25 31 X-32 0.50 109 134 D-12 0.28 61 75 X-11 0.32 69 85 X-33 0.56 121 150 D-14 0.26 58 71 X-12 0.16 35 43 X-34 0.50 109 134 D-16 0.28 61 75 X-13 0.14 31 39 X-35 0.66 144 178 D-19 0.21 45 55 X-14 0.19 42 52 X-36 0.22 48 59 D-20 0.27 59 73 X-15 0.21 46 57 X-37 0.24 52 64 D-21 0.13 29 36 X-16 0.18 40 49 X-38 0.22 47 58 D-22 0.23 51 62 X-17 0.21 45 55 X-39 0.22 49 60 D-23 0.16 34 42 X-18 0.25 54 66 X-40 0.27 59 72 D-24 0.11 23 29 X-19 0.21 46 56 X-41 0.31 68 84 D-25 0.08 18 22 X-20 0.14 30 37 D-1 0.13 27 34 D-26 0.16 34 42 X-21 0.14 32 39 D-2 0.10 23 28 构造部位 FHQ 深度统计/m 构造部位 FHQ 深度统计/m 最小值 最大值 最小值 最大值 西翼 深沟 0.50~0.66 109 178 东翼 深沟 0.21~0.36 45 96 浅沟 0.04~0.33 10 87 浅沟 0.08~0.21 18 56
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表 5 钻孔揭露值与推测值对比
Table 5. Comparison between exposed value and inferred value of borehole
钻孔编号 构造部位(对应沟谷编号) 钻孔揭露的强弱界限/m 计算值/m 误差范围/% Z1 西翼柏法村(X-25) 标高778 深度52~64，对应标高772~783 0.64~0.77 Z2 东翼凤仙村(D-18) 标高571 深度46~57，对应标高536~547 4.20~6.10 Z3 东翼南草-凤仙(D-17) 标高544 深度46~57，对应标高534~545 0.18~1.80 Z4 东翼善字小学(D-13) 标高502 深度60~74，对应标高491~505 0.59~2.19 Z5 东翼双碾村(附近)(D-15) 深度60 深度59~73 1.60~21.6
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