# The Cause and Statistical Analysis of the River Valley Contractions at the Xiluodu Hydropower Station, China

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Background of the Engineering

^{2}, as shown in Figure 1b. The basin is a wide, gentle, and relatively complete tectonic synclinal basin, which has not been cut by regional faults. In this basin, the direction of the synclinal axial line is northeast, and the dip angle of the northwest wing is 10°–15°, while the southeast wing is 20°–35°.

_{2}β

_{n}), and Upper Permian sand-shale (P

_{2}x), as well as three aquifer formations, namely Lower Permian Yangxin limestone (P

_{1}y), Upper Permian Emeishan basalt (P

_{2}β), and Quaternary loose deposits (Q). The aquitard and aquifer formations are adjacent to each other from the bottom to the top, and the contact surface of each formation features disconformity. Because the burial depth of the Silurian shale (S) is more than 500 m, the effect of this layer on the hydropower station was not considered in this paper. With a total thickness of 500 m, the Lower Permian Yangxin limestone formation is continuously buried, except for some of the formation exposed on the edge of the basin and part of the upstream channel. From upstream to downstream, the burial depth of the limestone formation increases gradually to about 90 m beneath the dam foundation. The thickness of the Upper Permian mudstone (P

_{2}β

_{n}) is generally 2 m (not more than 5 m), and its burial depth is 79–163 m near the dam. The Upper Permian Emeishan basalt formation is widely distributed over the Yongsheng synclinal basin, and its rock is dense and hard. The Upper Permian sand-shale (P

_{2}x), which is continuously distributed in the region, forms the non-permeable bottom of the top pore aquifer (the Quaternary loose deposits) and plays an impermeable boundary role in groundwater movement. The geological conditions of the Xiluodu Dam area and the Q–Q’ cross-section of the Yongsheng synclinal basin are shown in Figure 1.

_{2}β

_{n}) on the top. Above the Upper Permian mudstone, there is a basalt unconfined aquifer. Between the limestone confined aquifer and the basalt unconfined aquifer, there is a hydraulic head difference of 2 m near the riverbed. Hydrogeological investigations revealed some characteristics of the limestone confined aquifer, such as a large circulation depth, a long cycle route, and high salinity and temperature. The limestone confined aquifer receives rainfall recharge in outcropping regions at elevations about 2000 m. The limestone confined aquifer discharges at the bottom of the Jinsha River and numerous small overflow springs along the valley floor (at a 370 m to 400 m elevation above sea level; Figure 1b). The basalt unconfined aquifer is recharged by rainfall at the edge of the basin and is discharged by springs in the Jinsha River. Due to the retardation of the Upper Permian sand-shale (P

_{2}x) above the Upper Permian Emeishan basalt formation, the rainfall has difficulty infiltrating into the basalt layer, so the phreatic surface in the basalt layer is minimal. Figure 1b,c illustrate regional groundwater flow in the Yongsheng basin.

## 3. RVCs of the Xiluodu Dam

## 4. Hydraulic Response of the Confined Aquifer

_{s}is the hydraulic diffusivity; K is the hydraulic conductivity; S

_{s}is the specific storage; β

_{i}is the change rate of reservoir water level in the ith time period; t

_{i}is the ith time node; and t

_{0}= 0. Zhuang et al. [19] have provided an analytical solution to the boundary value problem, as shown in Equations (1) to (4), by using the method of separating variables:

^{2}/d, respectively, and the average increase in the hydraulic head of the confined aquifer can be calculated using Equation (7), as shown in Figure 6. The calculation results reveal that (1) the average hydraulic head increases with time in the confined aquifer; (2) hydraulic diffusivity has an influence on the increased rate of the average hydraulic head. With a large hydraulic diffusivity, the average hydraulic head increases rapidly and enters a relatively stable stage quickly; and (3) a change in the reservoir water level determines the change of the hydraulic head of the confined aquifer. The average increase in the hydraulic head will approximate the mean value of the reservoir water level increase.

## 5. HST Model and GHS Model

#### 5.1. The Conventional HST Model for Dam Behavior

#### 5.2. The GHS Model for RVCs

_{1}, b

_{2}, b

_{3}, b

_{4}, and b

_{5}are the coefficients, and they will be estimated through the inversion program; $\overline{u}$ is the average change in the hydraulic head over the whole range of the confined aquifer length, which can be calculated using Equation (7), where b

_{2}= a/10,000, a is the hydraulic diffusivity; b

_{3}= l/1000; l is the length of the aquifer; and t is the number of days since the beginning of the observation; and s = 2πd/365, d is the number of days between the beginning of the year (January 1) and the date of the observation (0 ≤ d ≤ 365).

#### 5.3. Parameter Settings of the GHS Model

_{1}to b

_{5}are taken as (−1, 2, 10, 1, 1), and the parameter range is (−5, 5), (1, 10), (1, 15), (−10, 10), and (−10, 10), respectively. The coefficients b

_{2}and b

_{3}cannot be negative values, as their physical meanings relate to hydraulic diffusivity and the length of the aquifer.

_{1}, b

_{2}, b

_{3}, b

_{4,}and b

_{5}, and the 95% confidence interval of each coefficient, are shown in Table 1. The results of the estimation for the GHS model for all monitoring lines are shown in Figure 7. The mean squared error (MSE) is used to estimate the accuracy of the GHS model, which can be calculated as follows:

## 6. Results

#### 6.1. Estimation Results of the GHS Model

_{1}reveals the linear relationship between the hydraulic head of the confined aquifer and the RVCs, whose physical meaning contains, but is not limited to, the Young modulus and geometrical factors of the confined aquifer. According to the estimated values of b

_{2}and b

_{3}, the characteristics of the confined aquifer can be calculated. The hydraulic diffusivity is about 28,000 m

^{2}/d, and the extension length of the aquifer is about 8700 m, according to the inversion results of VD01–VD07. Equations (13) and (14) quantitatively describe the effect degree of the water level and the seasonality on the RVCs. Table 1 reveals that all the hydrostatic coefficients are negative. According to sign conventions, here, a negative sign indicates that increasing hydraulic head increases the RVCs.

#### 6.2. Predication of the RVCs

## 7. Discussion

## 8. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Geological overview of the dam area. (

**a**) Location of the Xiluodu Dam. (

**b**) Overview of the study area. (

**c**) Cross-section of the Yongsheng synclinal basin. ((

**a**) and (

**b**) are from OvitalMap software.)

**Figure 2.**Dynamics of the Jinsha River level and the hydraulic head of the Yangxin limestone confined aquifer.

**Figure 3.**Locations of the monitoring lines of the river valley contractions (RVCs) at the Xiluodu Dam.

**Figure 6.**Approximation of the Xiluodu reservoir level variations by piecewise linear segments and the average increment of the hydraulic head of the confined aquifer.

**Figure 9.**Prediction of RVC development. The red line represents the predicted mean value of the RVCs and the blue line represents the reservoir water level. Green circles and purple triangles represent observed RVCs.

Lines | MSE | Estimated Results | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

b_{1} | b_{2} | b_{3} | b_{4} | b_{5} | ||||||||||||

Mean | 95% CI | Mean | 95% CI | Mean | 95% CI | Mean | 95% CI | Mean | 95% CI | |||||||

VD01 | 2.045 | −0.600 | −0.601 | −0.599 | 2.961 | 2.952 | 2.971 | 9.658 | 9.650 | 9.665 | 0.136 | 0.130 | 0.142 | 0.839 | 0.831 | 0.848 |

VD02 | 3.566 | −0.599 | −0.603 | −0.596 | 2.289 | 2.279 | 2.299 | 9.658 | 9.651 | 9.666 | 0.543 | 0.539 | 0.548 | 3.109 | 3.084 | 3.134 |

VD03 | 2.513 | −0.938 | −0.942 | −0.935 | 1.919 | 1.902 | 1.937 | 10.611 | 10.542 | 10.679 | −0.247 | −0.255 | −0.240 | 0.268 | 0.262 | 0.275 |

VD04 | 3.894 | −0.511 | −0.511 | −0.510 | 3.526 | 3.513 | 3.539 | 8.855 | 8.840 | 8.870 | −0.363 | −0.375 | −0.352 | 1.755 | 1.748 | 1.763 |

VD05 | 1.460 | −0.537 | −0.538 | −0.536 | 2.986 | 2.982 | 2.991 | 7.795 | 7.787 | 7.802 | −0.704 | −0.708 | −0.700 | 0.566 | 0.558 | 0.574 |

VD06 | 2.305 | −0.560 | −0.562 | −0.558 | 1.227 | 1.222 | 1.232 | 5.227 | 5.202 | 5.252 | 0.443 | 0.437 | 0.448 | 3.091 | 3.080 | 3.103 |

VD07 | 1.423 | −0.520 | −0.521 | −0.519 | 4.961 | 4.952 | 4.969 | 9.639 | 9.627 | 9.651 | 0.221 | 0.209 | 0.233 | 1.497 | 1.491 | 1.503 |

VD08 | 0.958 | −0.483 | −0.483 | −0.482 | 8.658 | 8.630 | 8.687 | 12.784 | 12.766 | 12.801 | 0.389 | 0.385 | 0.393 | 2.154 | 2.148 | 2.160 |

VD09 | 14.015 | −1.012 | −1.015 | −1.009 | 3.385 | 3.347 | 3.422 | 11.303 | 11.251 | 11.355 | 1.181 | 1.176 | 1.186 | 4.438 | 4.418 | 4.458 |

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**MDPI and ACS Style**

Li, M.; Zhou, Z.; Zhuang, C.; Xin, Y.; Chen, M.; Wu, J.
The Cause and Statistical Analysis of the River Valley Contractions at the Xiluodu Hydropower Station, China. *Water* **2020**, *12*, 791.
https://doi.org/10.3390/w12030791

**AMA Style**

Li M, Zhou Z, Zhuang C, Xin Y, Chen M, Wu J.
The Cause and Statistical Analysis of the River Valley Contractions at the Xiluodu Hydropower Station, China. *Water*. 2020; 12(3):791.
https://doi.org/10.3390/w12030791

**Chicago/Turabian Style**

Li, Mingwei, Zhifang Zhou, Chao Zhuang, Yawen Xin, Meng Chen, and Jian Wu.
2020. "The Cause and Statistical Analysis of the River Valley Contractions at the Xiluodu Hydropower Station, China" *Water* 12, no. 3: 791.
https://doi.org/10.3390/w12030791