Preliminary modeling investigation on changes in Karst fractures and seepage field in rockmass between streams with equal water levels
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摘要:
经典地下水动力学根据Dupuit假设得到了河渠间潜水含水层水位分布的解析解，常用于实际工程。该解析模型是否适用于具有裂隙网络的河间地块岩溶含水层，这个问题远未得到充分论证。考虑降雨入渗强度为100～800 mm/a的情形，建立剖面二维离散裂隙网络渗流模型，对等水位河间地块开展数值模拟研究。裂隙网络包含陡倾角和缓倾角2组裂隙，具有随机分布特征，隙宽均值为0.01 cm。根据稳定流场模拟结果划分包气带和饱水带裂隙界面，分析水位分布特征，计算饱水带裂隙网络的等效渗透系数，并与经典解析模型反算的等效渗透系数进行了对比，发现采用解析模型的误差小于25％。进一步模拟岩溶作用下裂隙演变的情景，对10 ka内河间地块裂隙状态和准稳态渗流进行了预测，发现隙宽最大值达到0.07 cm，经典解析模型仍然能够通过水位反算出数量级相符的等效渗透系数。模拟结果表明潜水面具有不规则形状，而且在河岸会出现明显的渗出面泉点，裂隙泉点数量在岩溶演变过程中逐渐减少。经典解析模型虽然能够估算河间地块裂隙网络的等效渗透系数，但不能刻画潜水面的不规则形态，也不能预测岩溶裂隙渗流场的演变趋势。
Abstract:The analytical solution of distributed water table in an unconfined aquifer between streams has been obtained in classic groundwater hydraulics based on Dupuit’s assumption, and it is frequently used in engineering practice. However, the applicability of this analytical model to groundwater in karst fractures needs a further verification. A 2D profile model of discrete fractures in rockmass between streams with equal water levels was simulated, considering a rainfall infiltration rate of 100−800 mm/a. The random fracture network includes two fracture groups, steeply or slightly inclining with the same statistic average aperture of 0.01 cm. Phreatic surface were identified by checking the interface between saturated and unsaturated fractures. The equivalent hydraulic conductivity of saturated fractures was obtained from seepage simulations and compared to the inversely estimated result from the classical analytical solution. It indicates that the relative error of inverse estimation is smaller than 25%. Further, the change in fractures aperture due to dissolution of Karst rocks was simulated with predictions on the state of fractures and quasi-steady state seepage in a 10 ka period. It finds that the maximum of the fracture aperture reaches 0.07 cm, and the classical model can yield an equivalent hydraulic conductivity from water table distribution with the same order of magnitude as the real hydraulic conductivity. The simulation shows an irregular shape of water table and seepage springs on river sides, where the number of springs reduced gradually following the karstification process. Though the classical analytical model can be used to estimate the equivalent hydraulic conductivity of the fractured aquifer between streams, it is unable to reveal the irregular water table shape and predict the change in seepage in Karst fractures.
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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 第一组 倾角/（ °） 正态分布 10 1 9 12 迹长/m 对数正态分布 250 5 230 270 隙宽/cm 均匀分布 0.01 0.008 0.012 第二组 倾角/（ °） 正态分布 85 2 82 88 迹长/m 对数正态分布 250 5 230 270 隙宽/cm 均匀分布 0.01 0.008 0.012 
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表 2 不同模拟情形的最高湿节点水头及其坐标
Table 2. Hydraulic head and coordinates of the highest wet fracture node in different scenarios
模拟情形 河水位
/m降水入渗强度
/（mm·a−1）最高湿节点 水头/m 坐标x/m 坐标 z/m A1 100 300 262.17 512.14 257.83 A2 500 340.18 551.75 339.03 A3 700 382.23 692.13 376.77 B1 200 300 307.90 548.53 304.75 B2 500 378.74 587.27 368.79 B3 700 429.67 538.41 420.88
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表 3 中心线最高水位在不同情形的模拟结果
Table 3. Modeling results of the highest water level on the middle line in different scenarios
降水入渗强度
/（mm·a−1）河水位100 m情景 河水位200 m情景 水位/m 情景编号 水位/m 情景编号 100 160.41 241.74 200 204.16 280.85 300 261.58 A1 307.21 B1 400 291.37 336.79 500 326.79 A2 367.97 B2 600 346.4 390.51 700 364.43 A3 420.88 B3 800 405.34 435.55
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