Water Release and Consolidation Model of Aquitard Considering Moving Non-Darcy Flow Interface
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摘要: 弱透水层中渗透流速慢，不利于监测其释水过程，于是常借助固结模型来综合评价地面沉降的演化过程.然而，传统的固结模型假定弱透水层中的渗流规律满足达西定律，可能与实际不符合.为此，本研究建立了考虑移动非达西流界面的固结模型，并采用有限差分法建立了该模型的数值解.其中，假设渗透系数与孔隙比都是应力的函数.通过与现有模型和室内实验数据的对比，验证了本研究模型的可靠性.结果表明新模型能更精确地模拟水位瞬时下降诱发的弱透水层固结过程.考虑移动非达西流界面的固结模型会延缓超孔隙水压力的消散过程，但不影响孔隙水压力的总消散量和总沉降量.考虑渗透系数衰减的固结模型，其孔隙水压力的消散与沉降量达到稳定的时间明显延长，且变渗透系数延缓了移动界面达到稳定的时间、致使移动界面稳定位置上移.Abstract: The slow seepage velocity in the aquitard is not conducive to monitoring its water release process, so the consolidation model is often used to comprehensively evaluate the evolution process of land subsidence. However, the traditional consolidation model assumes that the seepage law in the aquitard meets Darcy's law, which may be inconsistent with the actual situation. Therefore, a consolidation model considering the interface of moving non-Darcy flow region is established in this study, and the numerical solution of the model is established by using the finite difference method, in which the permeability coefficient and void ratio are assumed to be functions of stress. Compared with the existing models and indoor experimental data, the reliability of this research model is verified. The results show that the new model can more accurately simulate the consolidation process of aquitard induced by the instantaneous drawdown of water level. The consolidation model considering the moving non-Darcy flow interface delays the dissipation process of excess pore water pressure, but does not affect the total dissipation and total settlement of pore water pressure. For the consolidation model considering the attenuation of permeability coefficient, the time for the dissipation of pore water pressure and the settlement to reach the stability is obviously prolonged, and the variable permeability coefficient delays the time for the moving interface to reach the stability, causing the stable position of the moving interface to move upward.
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Key words:
- land subsidence /
- aquitard /
- consolidation /
- non-Darcy flow /
- hydrogeology /
- environmental engineering
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图 1 水位降深下弱透水层固结沉降的概念模型
Fig. 1. Conceptual model of consolidation settlement of aquitard under drawdown
图 3 新模型与Liu et al. (2012)模型的超静孔隙水压力对比
Fig. 3. Comparison of excess pore water pressure between the new model and Liu et al. (2012) model
图 4 新模型和Liu et al. (2012)模型与实验数据对比
a. 新模型与实验数据的超静孔隙水头；b. Liu et al.（2012）模型与实验数据的超静孔隙水头；c. 沉降量
Fig. 4. Comparison between the new model, Liu et al. (2012) model and experimental data
图 5 移动界面对固结性状的影响
a. 超孔隙水压力；b. 沉降量
Fig. 5. Influence of moving interface on consolidation behavior
图 7 非线性渗透系数对固结性状的影响
a. 超孔隙水压力；b. 沉降量
Fig. 7. Influence of nonlinear permeability coefficient on consolidation behavior
表 1 模型参数(Liu et al., 2012)
Table 1. Parameters used in this study (Liu et al., 2012)
参数 符号 单位 取值 粘土层厚度 $ B $ $ \mathrm{c}\mathrm{m} $ 10 水位变化 $ \Delta h\left(t\right) $ $ \mathrm{c}\mathrm{m} $ 10 独立弹簧的弹性模量 $ {E}_{0} $ $ \mathrm{M}\mathrm{P}\mathrm{a} $ 2 Kelvin体弹簧的弹性模量 $ {E}_{1} $ $ \mathrm{M}\mathrm{P}\mathrm{a} $ 5 Kelvin体牛顿黏壶的粘滞系数 $ {\eta }_{1} $ $ {\mathrm{s}}^{-1} $ $ 5\times {10}^{14} $ 渗透系数 $ {k}_{\mathrm{v}} $ $ \mathrm{m}/\mathrm{s} $ $ 1\times {10}^{-8} $ 
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表 2 试样实测物理力学参数（徐海洋等，2011）
Table 2. Measured physical and mechanical parameters of sample (Xu et al., 2011)
参数 符号 单位 取值 粘土层厚度 B $ \mathrm{c}\mathrm{m} $ 20 干密度 $ {\rho }_{\mathrm{d}} $ $ \mathrm{g}/\mathrm{c}{\mathrm{m}}^{3} $ 0.883 饱和密度 $ {\rho }_{\mathrm{s}\mathrm{a}\mathrm{t}} $ $ \mathrm{g}/\mathrm{c}{\mathrm{m}}^{3} $ 1.88 相对密度 $ d $ ‒ 2.71 水位变化 $ \Delta h\left(t\right) $ $ \mathrm{c}\mathrm{m} $ 120 孔隙比 $ {e}_{0} $ ‒ 1.30 压缩指数 $ {C}_{\mathrm{c}} $ ‒ 0.308 渗透系数 $ {k}_{\mathrm{v}0} $ $ \mathrm{m}/\mathrm{s} $ $ 5.8\times {10}^{-7} $
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表 3 模型最佳拟合参数
Table 3. Model best fit parameters in this study
参数 符号 单位 新模型取值 Liu et al. (2012) 模型取值独立弹簧的弹性模量 $ {E}_{0} $ $ \mathrm{M}\mathrm{P}\mathrm{a} $ 0.193 0.193 $ \mathrm{K}\mathrm{e}\mathrm{l}\mathrm{v}\mathrm{i}\mathrm{n} $体弹簧的弹性模量 $ {E}_{1} $ $ \mathrm{M}\mathrm{P}\mathrm{a} $ 0.595 0.595 $ \mathrm{K}\mathrm{e}\mathrm{l}\mathrm{v}\mathrm{i}\mathrm{n} $体牛顿黏壶的粘滞系数 $ {\eta }_{1} $ $ {\mathrm{s}}^{-1} $ $ 7\times {10}^{9} $ $ 7\times {10}^{9} $ 临界水力梯度 $ {i}_{\mathrm{l}} $ ‒ 1.026 ‒ 低速非达西流指数 $ m $ ‒ 1.5 ‒ 渗透指数 $ {C}_{\mathrm{k}} $ ‒ 0.36 ‒
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