Mathematical Problems in Engineering

Volume 2016 (2016), Article ID 1656738, 11 pages

http://dx.doi.org/10.1155/2016/1656738

## Seepage Monitoring Models Study of Earth-Rock Dams Influenced by Rainstorms

^{1}State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing 210098, China^{2}National Engineering Research Center of Water Resources Efficient Utilization and Engineering Safety, Hohai University, Nanjing 210098, China^{3}College of Water-Conservancy and Hydropower, Hohai University, Nanjing 210098, China

Received 20 November 2015; Revised 2 March 2016; Accepted 10 March 2016

Academic Editor: Sajid Hussain

Copyright © 2016 Jianchun Qiu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

For earth-rock dams influenced by rainstorms, seepage status monitoring is very important and provides the basis for the safe and effective operation of earth-rock dams. The most influential factors concerning the seepage of earth-rock dams are the reservoir water level, precipitation, temperature, and timeliness, and the influence of the reservoir water level and precipitation on the seepage of an earth-rock dam exhibits hysteretic effects. The reservoir water level of an earth-rock dam abruptly increases and may exceed the historically highest water level, therein causing new deformations of the earth-rock dam or even plastic deformation. Thus, the permeability coefficient for parts of an earth-rock dam changes, and we present the exceeded water level factor. Considering the complexity of the seepage monitoring of earth-rock dams, based on the hysteretic reservoir water level and precipitation, temperature, timeliness, and the exceeded water level factor, a statistical model based on an explicit function and an artificial wavelet neural network model based on an implicit function are established. Based on these two models, an integrated monitoring model based on maximum entropy theory is established. At the end of this paper, three monitoring models are used for the seepage monitoring of a measuring point of an earth-rock dam influenced by rainstorms, and the results show that the three monitoring models obtain satisfactory predication accuracy.

#### 1. Introduction

Due to the characteristics of low cost, fine environmental adaptability, and lower construction difficulty, earth-rock dams have been widely used and rapidly developed in the world, which make up over 80 percent of all dams [1]. During the construction and running period of earth-rock dams, safety problems such as seepage [2], cracks [3], and landslide [4] may happen. Seepage has considerable influence on earth-rock dams and often increases from small range to large range, which may cause dam settlement, collapse, and concentrated leakage passage for earth-rock dams. The structural damage may be a single form or multiple forms of damage in one part or different parts of the earth-rock dams. For the earth-rock dams in coastal areas suffer from rainstorms, the rapidly increased reservoir water lever and large amount of rain within a short time may cause threatened structural problems. Therefore, it is of great significance to study the seepage status of earth-rock dams influenced by rainstorms. Because earth-rock dams and the surrounding environment are rather complex and fickle, the potential seepage diseases are difficult to find out. Seepage monitoring analysis [5] of earth-rock dams could help to judge the existence of seepage damage and grasp the running status of earth-rock dams, which provides basis for the safety running of earth-rock dams.

To monitor and analyze the seepage status of earth-rock dams influenced by rainstorms accurately and timely, seepage monitoring models should be built up to help to find out seepage diseases conveniently and ensure the stable operation of the dams [5, 6]. The influence factors concerning earth-rock dam seepage are the reservoir water level, precipitation, temperature, timeliness, and so forth. In fact, the influence of the reservoir water level and precipitation on earth-rock dam seepage exhibits hysteretic effect. Moreover, rainstorms may lead the reservoir water level to exceed the historical highest water level, which causes new deformation or even plastic deformation of earth-rock dams. Then, the permeability property of earth-rock material would change, which influences the seepage state of earth-rock dams. The exceeded reservoir water level factor is put forward to consider the abrupt increased reservoir water level.

Therefore, the seepage statistical model considering the hysteretic effect of reservoir water level and precipitation and the exceeded water level factor is established. Meanwhile, the influence factors on seepage monitoring indexes are rather complex, which make it difficult to simulate with explicit function. Artificial wavelet neural network [7–9] is the implicit function, which has the advantage to explain complex relationship. Thus, earth-rock dam seepage monitoring model based on artificial wavelet neural network is established. Based on the two monitoring models and maximum entropy theory [10–12], an integrated seepage monitoring model is set up to optimize the earth-rock dam seepage monitoring further. Finally, the three seepage monitoring models are applied to analyze the seepage status of an earth-rock dam influenced by rainstorms. The results show the three models with fine precision successfully used in earth-rock dam seepage monitoring, which provide technical support for seepage monitoring of other earth-rock dams.

#### 2. Earth-Rock Dam Seepage Statistical Model considering the Hysteretic Effect of Reservoir Water Level and Precipitation and the Exceeded Water Level Factor

The most influential factors concerning earth-rock dam seepage include reservoir water level, precipitation, temperature, and timeliness. Given that the effect of reservoir water level and precipitation on seepage has the hysteretic effect, in the traditional seepage statistical model, the previous reservoir water level and precipitation are categorized based on averages over a number of previous days [5], for example, the previous two days, the previous five days, and the previous ten days. Practice has proven that the influences of reservoir water level and precipitation on seepage rise in the first stage and then decrease, which are presented as normal distribution [5]. The normal distribution curve is used to simulate the hysteretic effect, and the hysteretic days and influence days of reservoir water level and precipitation influence on earth-rock dam seepage are hard to determine. Considering the efficiency of general calculation methods is low, quantum genetic algorithm [13, 14] is used to calculate the hysteretic days and influence days to obtain the optimal earth-rock dam seepage statistical model. Moreover, due to the influence of rainstorms, the reservoir water level may exceed the historical highest water level. As a result, the abrupt increased reservoir water level is difficult to simulate. Hence, the exceeded water level factor is added.

##### 2.1. Reservoir Water Level Component

For the seepage index, we take the piezometric tube level as an example. The piezometric tube level is hysteretic influenced by the reservoir water level, and the seepage index at the time is given as follows:where is the retardation time, , , and and are the reservoir water level at the corresponding time.

Equation (1) reflects the hysteretic relationship between the reservoir water level and the piezometric tube level, and the piezometric tube level at the time is continuously influenced by the previous reservoir water level. Because the hysteretic time is difficult to determine, the previous reservoir water level is often categorized based on averages over a number of previous days, for example, the previous two days, the previous five days, and the previous ten days. However, these factors are fuzzy and are unable to accurately reflect the hysteretic effect of reservoir water levels. Moreover, the influence of the reservoir water level on the piezometric tube level may be from the previous two days, the previous ten days, or longer.

Suppose that the seepage index is influenced by the reservoir water level from the previous days , and the equivalent water level is expressed as follows:where , is the weight of the th water level’s influence on the equivalent water level and is the function reflecting the hysteretic influence of the reservoir water level on the seepage index.

Considering the characteristic of the weight vector , the following equation is then obtained:

Therefore, the equivalent water level is obtained as follows:

Numerous studies have shown that presents a normal distribution [5]. Combined with the characteristics of normal distributions, the hysteretic days and influenced days are set as and . The process that describes the influence of the reservoir water level on the seepage index is shown in Figure 1, and the hysteretic influence function is given as follows: