初始裂隙对岩溶水紊流形成的影响

焦友军; 黄奇波; 于青春

doi:10.11932/karst20220401

初始裂隙对岩溶水紊流形成的影响

doi: 10.11932/karst20220401

焦友军^{1, 2,},
黄奇波²,
于青春^1, ,

1.
中国地质大学(北京)水资源与环境学院, 北京 100083
2.
中国地质科学院岩溶地质研究所/自然资源部、广西岩溶动力学重点实验室, 广西桂林 541004

基金项目: 国家自然科学基金项目(41877196, U1612441, 41272387)；中国地质调查项目（DD20221758）

详细信息

作者简介:
焦友军（1990－），男，博士研究生，从事岩溶水资源研究。E-mail：jiaoyj@karst.ac.cn

通讯作者:
于青春（1963－），男，教授，博士研究生导师，从事岩溶水资源研究。E-mail：yuqch@cugb.edu.cn

中图分类号: P641.2
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出版历程
- 收稿日期: 2022-02-10
- 刊出日期: 2022-08-31

Influence of initial fractures on the occurrence of karst turbulent flow

JIAO Youjun^{1, 2
,},
HUANG Qibo²,
YU Qingchun^{1
, ,}

1.
School of Water Resources and Environment, China University of Geosciences (Beijing) , Beijing 100083, China
2.
Institute of Karst Geology, CAGS/ Key Laboratory of Karst Dynamics,MNR&GZAR, Guilin, Guangxi 541004, China

摘要

摘要: 岩溶地区地下发育着大量的溶洞和地下河管道，地下水流状态既有层流也有紊流，而紊流是溶洞管道形成的重要条件。紊流的形成受到岩石初始裂隙的影响，初始裂隙的张开度、分布、走向、迹长、密度等因素都影响着裂隙发育过程中水流状态的变化。通过对不同统计特征的初始裂隙网络进行水流和溶蚀的数值模拟发现，以张开度标准差反映的裂隙网络非均匀性越强，模拟紊流出现的时间就越早；主要裂隙的存在使裂隙网络的非均性增强，主要裂隙与水力梯度总方向的角度越小，紊流出现的时间就越早；当裂隙平均迹长过小时会导致裂隙连通性较差，影响裂隙水流和溶蚀作用；裂隙密度，尤其是主要裂隙密度，对岩溶发育的影响较大。相对于次要裂隙，如果主要裂隙密度偏小，紊流形成时间会大大增加，甚至很难形成紊流。当初始裂隙张开度小于0.001 cm，增大水力梯度仍没有紊流发生，岩溶几乎不发育。
- 初始裂隙 /
- 岩溶管道 /
- 紊流 /
- 溶蚀 /
- 数值模拟
Abstract: In karst areas of China, there are many karst caves and underground river conduits in the underground aquifer. The development of large cave and conduit are controlled by many factors and it is not every karst aquifer would develop into conduit system, for example, the southern karst area with ample rainfall has many underground rivers, but in the northern arid and semi-arid karst area, underground rivers are relatively rare. The flow states in conduits may be laminar or turbulent. Turbulent flow is an important condition of forming large-scale caves and conduits. In turbulent state, the water flow begin to have the ability of mechanical transportation, which would carry the solid granule and cause the impact and erosion into surrounding rock. The powerful mechanical erosion of turbulence is very important for karst aquifer to develop into large scale conduits and caves. Furthermore, the dissolution rate of carbonate rock in turbulent flow is at least one order of magnitude faster than laminar flow condition. Therefore, the mechanical erosion and chemical dissolution in turbulent flow make the development of conduit and cave more possible. However, the occurrence of turbulent flow is rigidly affected by the hydraulic condition and the initial medium of the aquifer, such as the initial rock fracture, including the aperture, direction, length and density of initial fractures. So we designed different statistic features of fractures and different hydraulic gradients to study the flow state and dissolution widening rates of fractures by numerical simulation. The cubic law and Lomize equation were used to model the laminar and turbulent flow state in fracture. The Newton-Raphson iteration is high-performance to solve the nonlinear flow equation system of laminar and turbulent flow. Then the dissolution rate equation and the Ca²⁺ concentration equation system was employed to model the widening of the fractures. The simulation results and discussions were all under given outer environment with P_CO₂ 0.8% and hydraulic gradient 0.02. The modeling results of fracture aperture showed that when the standard deviation of aperture was 0.0005 cm and the mean of aperture is 0.006, there was no turbulence in the modeling period of 5,000 thousand years. But when the standard deviation was increased to 0.001 cm, the turbulent flow emerged on 189 thousand year and the time was greatly shorten. In the 8 modeling aperture statistic situations, as the mean and the standard deviation of aperture increased and the heterogeneity of fractures was more intensive, the turbulent flow began to appear and the time of turbulence became earlier. The existence of primary fractures led to much heterogeneous aquifer and earlier turbulent time. The results of fracture direction modeling scenes showed that when the angle between the direction of primary fractures and the direction of main hydraulic gradient was smaller, the turbulence time would be shorter. If the mean of fracture length is too little, the connectivity of fracture would become poor and the karst dissolution would be heavily restricted. The fracture density, especially the primary fracture density, had much influence on the karst development. Compared with the secondary fractures, if the density of primary fractures was too smaller, the turbulence time would largely increase, and even no turbulence in the whole simulation. We also discussed the influence of hydraulic gradient on the turbulent time. The hydraulic gradient varied from 0.001 to 1 and the mean of aperture was from 0.001 to 0.005. The results showed that for each aperture, it had the corresponding smallest hydraulic gradient to the occurrence of turbulence and the greater gradient the turbulent time would become earlier. Below the smallest hydraulic gradient the turbulence would never occur. If the mean of aperture is less than 0.001cm, no matter how the hydraulic gradient is increased, the flow state in fractures remained laminar and no turbulence occurred, in which karst is nearly not developed in the aquifer. In conclusion, the occurrence time of turbulent flow reflects the possibility of forming large karst conduits and caves in present aquifer. The shorter the time is, the greater the possibility will be.
- initial fractures /
- karst conduit /
- turbulent flow /
- dissolution /
- numerical modeling

HTML

图 1 裂隙含水层模拟500万年的水流状态和张开度分布（含水层长宽单位为m，张开度单位为cm）

绿色代表层流，初始时刻模拟图与500万年相同

Figure 1. Flow state and apertures of the fracture aquifer at 5 million year which is similar to the initial state, where the green lines represent laminar flow, the unit of the aquifer length is m, the aperture is shown with the line width, and the unit of aperture is cm

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图 2 第1组裂隙张开度增大后的含水层水流状态和张开度分布（图中含水层长度单位为m, 张开度单位为cm）

（a）为初始时刻，（b）为50万年，（c）为70万年，（d）为83.9万年出现紊流，红色代表紊流

Figure 2. Flow state and apertures of the aquifer with the first group fracture aperture increased

(a) initial time, (b) 500 thousand year, (c) 700 thousand year, (d) 839 thousand year, where the red lines represent turbulent flow

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图 3 (a)模拟情形A 在500万年的结果与初始裂隙分布相同，(b) 模拟情形C裂隙网络在18.9万年产生了紊流（图中含水层长度单位为m, 张开度单位为cm）

Figure 3. (a) Results of the simulation A at 5 million year which is the same with initial fractures, (b) Tturbulent time 189 thousand year of simulation C

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图 4 （a）模拟情形E水平裂隙逆时针旋转45度的含水层在82.3万年出现紊流；（b）在图2中将第二组裂隙扩大为主要裂隙的含水层在21.7万年出现紊流, 图中含水层长度单位为m, 张开度单位为cm

Figure 4. (a) Turbulent time 823 thousand year of the aquifer based on model E in which the plane fractures were rotated 45° counterclockwise, (b) Turbulent time 217 thousand year with the second group of fractures widen into primary fractures

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图 5 （a）裂隙迹长减小后含水层在47.1万年出现紊流；（b）主要裂隙密度减小后模拟500万年仍没有出现紊流, 图中含水层长度单位为m, 张开度单位为cm

Figure 5. (a) Turbulent time 471 thousand year of the aquifer with the length of fractures decreased, (b) No turbulent flow occurred in 5 million years with the density of primary fracture decreased

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图 6 不同水力梯度和张开度条件下紊流形成时间的三维柱状图，其中每个柱体上的数字为紊流出现的时间（万年），500万年表示没有出现紊流

Figure 6. 3D histogram of the turbulent time with different hydraulic gradients and apertures

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表 1 随机裂隙网络统计参数

Table 1. Statistic parameters of the random fracture network

裂隙组	统计参数	服从分布	均值	标准差	最小值	最大值
	走向	正态分布	30	5	15	45
第一组	迹长/m	对数正态分布	130	10	100	160
	张开度/cm	正态分布	0.005	0.001	0.002	0.008
	走向	正态分布	120	5	105	135
第二组	迹长/m	对数正态分布	130	10	100	160
	张开度/cm	正态分布	0.005	0.001	0.002	0.008

下载: 导出CSV

表 2 不同模拟情形的初始裂隙张开度统计参数和紊流出现时间

Table 2. Statistic parameters of the initial aperture and the turbulent time in different simulations

模拟情形	均值/cm	标准差/cm	99.7%置信区间/cm		紊流出现时间/万年
A	0.005	0.001	0.002	0.008	>500
B	0.006	0.000 5	0.004 5	0.007 5	>500
C	0.006	0.001	0.003	0.009	18.9
D	0.006	0.001 5	0.001 5	0.010 5	12.0
E	0.008	−	−	−	42.7
F	0.008	0.000 5	0.006 5	0.009 5	20.3
G	0.008	0.001	0.005	0.011	14.3
H	0.008	0.001 5	0.003 5	0.012 5	9.0

下载: 导出CSV

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