1. Introduction {#sec1}
===============

There are problems of leakage in mass of rivers, lakes, reservoir, and irrigation canals, which bring serious waste of water. The ground water and soil will be polluted when the industrial sewage leaks into soil. Most of the areas of earth surface are located in the arid or semiarid area, so soil in most projects is unsaturated \[[@B1]--[@B4]\]. Leakage of river is typical unsaturated seepage. Considering unsaturated seepage in seepage calculation of ground water is much more practical than just thinking of saturated seepage. The boundary of conventional seepage calculation is free water surface and unsaturated seepage is ignored. Mathematic description and parameter determination are complex for unsaturated seepage \[[@B5]--[@B7]\].

Study was focused on analytical solution of unsaturated seepage in the 1970s. With the popularization of computer technology, numerical method of unsaturated seepage appeared in the 1980s. From the 1990s, researchers realized that permeability played an important role in improving accuracy of numerical method. The permeability of unsaturated soil had become a hotspot \[[@B8], [@B9]\].

2. Mathematical Model of Ground Water Seepage {#sec2}
=============================================

In 1856, H. Darcy conducted permeability test of saturated soil and developed Darcy\'s law 1. Richards thought that Darcy\'s law was applicative for unsaturated soil but the permeability coefficient was variable, which was the function of moisture volume percentage 2 \[[@B10]--[@B12]\]. The equations of motion for unsaturated seepage are $$\begin{matrix}
{v_{i} = K\left( \theta \right)\frac{\partial H}{\partial x_{i}},\quad i = x,y,z,} \\
\end{matrix}$$ where *v* ~*i*~ is the velocity of the *x*, *y*, and *z* directions, respectively, and *H* is water head.

While ignoring the deformation of unsaturated porous medium, according to principle of mass conservation \[[@B13], [@B14]\], the equation of continuity is $$\begin{matrix}
{\frac{\partial\left( {\rho v_{ii}} \right)}{\partial x_{ii}} + \frac{\partial\rho}{\partial t} = 0,\quad{\,\,}i = x,y,z.} \\
\end{matrix}$$ By substituting ([1](#EEq1){ref-type="disp-formula"}) in ([2](#EEq2){ref-type="disp-formula"}), we obtain the fundamental equation of unsaturated seepage, which is $$\begin{matrix}
{\frac{\partial\theta}{\partial t} = \frac{\partial}{\partial x_{ii}}\left\lbrack {K\left( \theta \right)\frac{\partial H}{\partial x_{ii}}} \right\rbrack,\quad i = x,y,z,} \\
\end{matrix}$$ where *θ* is moisture volume percentage and *K*(*θ*) is permeability coefficient.

3. Numerical Model of Leakage {#sec3}
=============================

The Mengxi River is located in Chengdu Plain which is in the southwest of China. The Mengxi River is artificial river in the campus of Southwest Petroleum University, whose length is 2 kilometers. The biggest width of river is 15 meters and the smallest width is 2 meters. The water level was 5 meters at first and then leakage phenomenon was serious. The satellite imagery of Mengxi River is shown in [Figure 1](#fig1){ref-type="fig"} and red arrow points to the study area. [Figure 2](#fig2){ref-type="fig"} is true scene of Mengxi River.

In order to measure the topographical map of the Mengxi River, more than 100 points were measured. The place of measuring points and boreholes is shown in [Figure 3](#fig3){ref-type="fig"}. [Figure 4](#fig4){ref-type="fig"} is the interpolated topographic map. There are 18 boreholes, which are evenly distributed among the study area. The study area consists of miscellaneous fill, plain fill, silty clay, sandy silt, fine sand, medium sand, and gravel layer.

The three-dimensional geological model was established on the basis of topographic map and geologic examination. The numerical calculation model is shown in [Figure 5](#fig5){ref-type="fig"}. The grid number of each direction is 50, 50, and 10.

The double-ring infiltrometer is common instrument to measure permeability of unsaturated soil on the spot. The double-ring infiltrometer has a higher accuracy than single-ring infiltrometer and test hole. A new simple apparatus of double-ring infiltrometer was developed to test the permeability of soil and 24 pairs of trials were conducted. The simple apparatus is shown in [Figure 6](#fig6){ref-type="fig"}. Data in [Table 1](#tab1){ref-type="table"} is some experimental data of various trials.

The gas-water two-phase flow experiments of unsaturated hydraulic conductivity were carried out by testing instrument of state key laboratory of oil and gas reservoir geology and exploitation, and the characteristic curves of unsaturated seepage were acquired by the experiments. In numerical simulation, instead of the curve of conductivity versus matric suction and the curve volumetric water content of soil versus matric suction, we use the relative permeability curves of water and gas, which simplified the computational process and improved the speed of calculation. On the other hand, the leakage quantity was acquired accurately by integral calculation of seepage velocity. Comparing the calculation result with data of hydrologic exploration, the simulation results are very close to actual situation.

As referred to the flow of gas and water in the porous media, the velocity of each phase depends on the their relative volume, which can be described as the relative permeability curve of water and gas, through the equipment (shown in [Figure 7](#fig7){ref-type="fig"}) from State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation (Southwest Petroleum University); the results is shown in [Figure 8](#fig8){ref-type="fig"}.

4. Results and Discussion {#sec4}
=========================

The water saturation and pore pressure change with the leakage of water. The initial water saturation of model is 32% and the initial pore pressure is 55 kPa, supposing the water level of the Mengxi River is 3 meter.

[Figure 9](#fig9){ref-type="fig"} shows the initial distribution of water saturation. Figures [10](#fig10){ref-type="fig"} and [11](#fig11){ref-type="fig"} show the distribution of water saturation after 100 days and 245 days, respectively. By Figures [9](#fig9){ref-type="fig"}, [10](#fig10){ref-type="fig"}, and [11](#fig11){ref-type="fig"}, it is obvious that the water saturation increases. The water saturation of area increases from 32% to 65%. The water saturation of area above water level decreases slightly. Reason for this phenomenon is that water in the river and surface soil leaks continuously and the water of lower soil get recharged.

[Figure 12](#fig12){ref-type="fig"} shows the pore pressure after 100 days and [Figure 13](#fig13){ref-type="fig"} shows the pore pressure after 245 days. With reference to Figures [12](#fig12){ref-type="fig"} and [13](#fig13){ref-type="fig"} we can see that pore pressure increases along with depth direction. Another conclusion is that the farther away from the river is, the smaller the pore pressure is. The biggest pore pressure is in the bottom and it runs up to as much as 59 kPa.

[Figure 14](#fig14){ref-type="fig"} shows the velocity vector diagram. The water leaks around from river. The seepage velocity decreases with the increase of distance. Leakage leads to the change of water saturation and pore pressure.

In order to harness the leakage and decrease seepage, the performance of seepage prevention of asphalt and antiseepage film was compared in the study. The biggest water saturation is 51% when the river bed and bank have a superstratum of asphalt shown in [Figure 15](#fig15){ref-type="fig"}. The biggest water saturation is 37.4% when the river bed and bank have a superstratum of antiseepage film shown in [Figure 15](#fig15){ref-type="fig"}. [Figure 16](#fig16){ref-type="fig"} shows the curve of monthly drawdown after antiseepage measure. [Figure 17](#fig17){ref-type="fig"} shows the reduction of water level under different conditions.

5. Conclusion {#sec5}
=============

The hydraulic conductivity of the soil in Mengxi River was tested by double-ring infiltrometer. The total station was applied to measure the topography of the ground surface surrounding the river. The geological model of Mengxi River was set up by the combination of strata data.Based on seepage mechanics, fluid mechanics, and soil mechanics, the model considering unsaturated seepage of the ground water was established, combined with the hydrological and geological conditions of Mengxi River; the numerical model was built.The leakage of water from Mengxi River was simulated and the results indicate that the leakage was serious. After 245 days, the saturation of the soil under the river increased by 33%, from 32% to 65%; the saturation of soil in the riverbed and slope goes up obviously.The asphalt and impermeable membrane were paved, respectively, to prevent the leakage of water; both of them can reduce the water loss in river, but the effect of the latter is better than the former; when the impermeable membrane was used as waterproof material, the maximal value of soil\'s saturation under the river only reached 37.4% which is far below the saturation of soil on condition of asphalt as waterproof material.

This work was financially supported by the Open Foundation Project from State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation of Southwest Petroleum University (Grant no. PLN1131), reconstruction method of pore scaled model for coal bed rock (Grant no. KSZ1211), effective development technology of ultralow permeability reservoir (Grant no. 2011ZX05013004), the Key Project (Grant no. 13ZA0189) from Education Department of Sichuan Province, the Open Experiment Project Leakage Analysis and Prevention Methods of the MENGXI River Located in Southwest Petroleum University (Grant no. KSZ1128) from Southwest Petroleum University, Natural Science Foundation of China (Grant no. 51074137 and no. 51174170), major projects (09ZA139, 12ZA197) from the Education Department of Sichuan Province, the key project (Grant no. 2012XJZ027) from Science and Technology Fund of Southwest Petroleum University, and the SWPU Geotechnical Mechanics and Engineering Science & Technology Innovation (Cultivation) Youth Team (no. 2013XJZT006).

Conflict of Interests
=====================

The authors declare that there is no conflict of interests regarding the publication of this paper.

![Satellite imagery.](TSWJ2014-270939.001){#fig1}

![Satellite imagery of study area.](TSWJ2014-270939.002){#fig2}

![Arrangement plan of measuring points and boreholes.](TSWJ2014-270939.003){#fig3}

![Interpolated topographic map.](TSWJ2014-270939.004){#fig4}

![Numerical calculation model.](TSWJ2014-270939.005){#fig5}

![Simple apparatus of double-ring infiltrometer.](TSWJ2014-270939.006){#fig6}

![The sketch of equipment.](TSWJ2014-270939.007){#fig7}

![The relative permeability of water versus gas.](TSWJ2014-270939.008){#fig8}

![Initial water saturation distribution.](TSWJ2014-270939.009){#fig9}

![The water saturation after 100 days.](TSWJ2014-270939.010){#fig10}

![The water saturation after 245 days.](TSWJ2014-270939.011){#fig11}

![The pore pressure after 100 days.](TSWJ2014-270939.012){#fig12}

![The pore pressure after 245 days.](TSWJ2014-270939.013){#fig13}

![The flow vector of water under river.](TSWJ2014-270939.014){#fig14}

![Water saturation with asphalt superstratum.](TSWJ2014-270939.015){#fig15}

![Water saturation with antiseepage film superstratum.](TSWJ2014-270939.016){#fig16}

![The reduction of water level.](TSWJ2014-270939.017){#fig17}

###### 

Experimental data.

  Volume of inject water/mL   Time/min                                                   
  --------------------------- ---------- ----- ----- ----- ----- ----- ----- ----- ----- -----
  Number 1 hole               235        250   180   200   220   250   220   225   200   190
  Number 2 hole               180        260   275   270   265   275   270   280   270   270
  Number 3 hole               170        260   270   260   245   300   290   150   200   225
  Number 4 hole               155        205   215   210   190   185   190   175   180   170

[^1]: Academic Editors: C. W. Chang-Jian, A. Esmaeily, and A. Rodríguez-Castellanos
