Experiment and numerical simulation of co-seismic water level response in unconsolidated confined aquifer
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摘要: 为深入理解井水位同震响应机理，本文开展了向完整井-松散含水层系统输入由不同频率和振幅（加速度）组成的正弦波荷载的振动台实验。以实验模型为物理模型，建立了振动作用下松散承压含水层中孔隙水压力响应的流固耦合模型和含水层水流与井流的相互作用模型，并运用多物理场耦合模拟软件COMSOL Multiphysics对实验过程进行了数值模拟。实验中观测到的四种典型水位变化形态与野外场地同震井水位变化形态相似。数值模拟结果显示，本研究建立的数学模型能较好地反映松散承压含水层中孔隙水压力和水位的响应情况。本文研究对解释地下水同震响应机制、岩体渗流稳定性和安全问题具有重要意义。Abstract: In order to promote understanding mechanisms of co-seismic response of water level in well shaking table experiments have been carried out with sinusoidal loading in different vibration frequencies and amplitudes （accelerations） for complete well unconsolidated confined aquifer system. The physical model has been built based on experimental model, and fluid-solid coupled model of pore pressure response in unconsolidated aquifer and mathematical model of flow interaction between aquifer well under vibrations have been established. The experimental processes have been simulated in COMSOL Multiphysics, a multi-field coupling simulation software. Four typical water level variation forms observed in experiment are similar to those of field studies, and the results of numerical simulation show that the mathematical model established in this study can well reflect the response of pore water pressure and water level in unconfined aquifer. This research is of great significance to explain the mechanism of co-seismic responses of groundwater, and stability and safety of seepage in rock and soil mass.
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图 2 实验所记录的典型井水位变化形态（以G2井为例）
（a） 振荡；（b） 上升；（c） 下降；（d） 阶变
Figure 2. Typical change forms of well water level in experiments （taking well G2 as an example）
（a） Oscillation；（b） Rise；（c） Drop；（d） Step-like change
图 3 初始平衡状态下承压含水层模型剖面图
Figure 3. Profile of confined aquifer model at initial equilibrium state
图 4 压力扰动井-含水层系统的概念模型
Figure 4. Conceptual model of the well-aquifer system disturbing by a harmonic pressure
图 5 井流运动示意图
（a） 静止状态；（b） 运动状态
Figure 5. Schematic diagram of well flow
（a） Stationary state；（b） Motion state
图 6 工况1中孔隙水压力的实测值（a）与模拟值（b）时程变化对比图
Figure 6. Comparison diagram of time history changes between measured （a） and simulated （b） pore water pressure values in working condition 1
图 7 工况2的孔隙水压力实测值（a）与模拟值（b）时程变化对比
Figure 7. Comparison diagram of time history changes between measured （a） and simulated （b） pore water pressure values in working condition 2
图 8 工况3中孔隙水压力的实测值（a）与模拟值（b）时程变化对比图
Figure 8. Comparison diagram of time history changes between measured （a） and simulated （b） pore water pressure values in working condition 3
图 9 工况4中孔隙水压力的实测值（a）与模拟值（b）时程变化对比图
Figure 9. Comparison diagram of time history changes between measured （a） and simulated （b） pore water pressure values in working condition 4
图 10 工况5中孔隙水压力的实测值（a）与模拟值（b）时程变化对比图
Figure 10. Comparison diagram of time history changes between measured （a）and simulated （b） pore water pressure values in working condition 5
图 11 工况6中孔隙水压力的实测值（a）与模拟值（b）时程变化对比图
Figure 11. Comparison diagram of time history changes between measured （a） and simulated （b） pore water pressure values in working condition 6
图 12 G2井中各工况的水位的实测值与模拟值时程变化对比图
Figure 12. Comparison diagram of time history changes between measured and simulated water levels in well G2
图 13 孔隙水压力（a）和井水位（b）的模拟值与实测值误差分析对比图
Figure 13. Comparison diagram of error analysis between simulated and experimental measured values of pore water pressure （a）and groundwater level （b）
表 1 正弦波的振动参数
Table 1. Shaking parameters of different sine waves
工况编号 频率/Hz 加速度/g 加载时间/s 工况编号 频率/Hz 加速度/g 加载时间/s 1 0.5 0.1 35 4 5 0.25 35 2 2 0.25 35 5 10 0.25 35 3 5 0.15 35 6 15 0.15 35 注：1g＝9.81 m/s2。 
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表 2 数值模拟中的参数取值
Table 2. Parameters used in numerical experiments.
参数 单位 数值 弹性模量$E$ Pa 2.63×1010 泊松比$\upsilon $ 1 0.25 渗透系数$K$ m/d 33 孔隙度$n$ 1 0.398 ${{{\rm{Biot}}'{\rm{s}}} }$系数 1 1 固相密度$\;{\rho _{\rm{s}}}$ kg/m3 2 650 液相密度$\;{\rho _{\rm{f}}}$ kg/m3 1 000 固相体积模量${E_{\rm{s}}}$ Pa 1.56×1010 液相体积模量${E_{\rm{f}}}$ Pa 1×108 储水率${S_{ {\rm{s} }} }$ 1 1×10−3 动力黏度系数$\;\mu$ Pa·s 1×10−4
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