# A New Approach to Permeability Inversion of Fractured Rock Masses and Its Engineering Application

^{1}

^{2}

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## Abstract

**:**

^{−3}cm/s. The root mean squared error and coefficient of determination of the measured and calculated values are 1.33 × 10

^{−4}m

^{3}/s and 0.9976 m

^{3}/s, respectively. The rock masses in the reservoir site area have high permeability. The groundwater level in the junction area and the mountains on both sides of Shangmo reservoir is low, and the hydraulic gradient is small. The maximum error between the calculated value of the groundwater level and the measured values is −0.41 m, and the relative error is −4.36%. The recommended anti-seepage scheme can effectively solve the problem of large leakage in the reservoir area. The results show that the innovative approach is appropriate for the seepage analysis of the field with the fractured rock masses and more meaningful from an engineering point of view.

## 1. Introduction

^{−3}cm/s, which exceeds the range of the Lugeon value measured by the test equipment. In view of this kind of rock strata with high permeability, we attempt to propose a back-analysis method to determine the equivalent permeability parameters of rock masses near the test boreholes.

## 2. Mathematical Model

^{3}/s), which indicates whether there is an external injected flow (source) or outflow flow (sink) in the seepage calculation area, $\beta $ is a constant, where $\beta $ = 0 in the unsaturated zone, and $\beta $ = 1 in the saturated zone, and ${S}_{s}$ is the elastic water storage rate (m

^{−1}), which represents the amount of water released by saturated soil per unit volume due to the compression (expansion) of soil and expansion (compression) of water when a unit head is lowered (raised). ${S}_{s}$ is a constant in the saturated zone and zero in the unsaturated zone. $C({h}_{c})$ is the specific water capacity, and C = 0 in the saturated zone, in the unsaturated zone, $C({h}_{c})$, can be solved as follows.

## 3. Back Analysis Method

#### 3.1. Objective Function of Back Analysis

#### 3.2. Procedures of Back Analysis

^{2}).

## 4. Method Verification

#### 4.1. Case Introduction

#### 4.2. Model and Parameters of the Case

^{−5}cm/s to 1.0 × 10

^{−1}cm/s.

#### 4.3. Case Analysis

^{2}) were considered as statistical performance evaluations in this study [29]. The value of RMSE is a nonnegative value, and a low RMSE indicates good consistency between the observed and simulated values. R

^{2}ranges from 0 to 1, and a larger R

^{2}value indicates a better match of the simulated and observed data.

^{2}of those are 1.33 × 10

^{−4}m

^{3}/s and 0.9976, respectively, which indicates the inversion values can match well with the measured data.

^{−3}cm/s, respectively. According to the geological conditions of the mountain and the distribution law of rock strata, the mountain fissures in the left abutment are developed and the permeability coefficient is relatively large.

## 5. Engineering Application

#### 5.1. General Description

#### 5.2. Seepage Analysis of the Reservoir Site in a Natural Period

#### 5.2.1. Model and Parameters

#### 5.2.2. Results and Discussions

#### 5.3. Seepage Analysis of Recommended Anti-Seepage Scheme for Reservoir Site

#### 5.3.1. Model and Parameters

#### 5.3.2. Results and Discussions

^{3}/s, and that is 2.801 m

^{3}/s for the recommended anti-seepage scheme. Therefore, the leakage of the reservoir under the recommended scheme is 0.007 m

^{3}/s, which is far less than the multi-year average runoff of 0.355 m

^{3}/s at the reservoir site. This shows that the recommended anti-seepage scheme can effectively solve the problem of large leakage in the reservoir area and ensures the normal storage and operation of the reservoir.

## 6. Conclusions

^{−3}cm/s. The maximum error of the measured leakage and calculated values in each period are 3.43% and 4.67%. Moreover, the RMSE and R

^{2}of the measured and calculated values are 1.33 × 10

^{−4}m

^{3}/s and 0.9976, respectively, which indicates the inversion values can match well with the measured data.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 7.**Water head distribution of the borehole profile at different time periods (unit: m): (

**a**) t = 0 s, (

**b**) t = 72 s, and (

**c**) t = 144 s.

**Figure 11.**Measured and calculated values of a natural groundwater level in the dam axis section (unit: m).

**Figure 13.**Water head distribution of typical sections (unit: m): (

**a**) Cross section of upstream channel (x = −500 m), (

**b**) river profile (y = −150 m), and (

**c**) profile of the maximum dam height (y = 100 m).

**Figure 15.**Groundwater level contours of the reservoir site for a recommended anti-seepage scheme (unit: m).

**Figure 16.**Water head distribution of typical sections under the recommended anti-seepage scheme (unit: m): (

**a**) Cross section of dam axis (x = 0 m). (

**b**) Profile of the maximum dam height (y = 100 m).

Time Interval (-) | Time (s) | Measured Value (m ^{3}/s) |
---|---|---|

1 | 0–18 | 4.67 × 10^{−3} |

2 | 18–34 | 4.50 × 10^{−3} |

3 | 34–52 | 4.00 × 10^{−4} |

4 | 52–72 | 3.60 × 10^{−4} |

5 | 72–102 | 3.20 × 10^{−4} |

6 | 102–144 | 2.57 × 10^{−4} |

Code | Borehole Depth (m) | Rock Permeability (cm/s) |
---|---|---|

ZK2 | h = 0–12 | 2.3 × 10^{−1} |

h = 12–24 | 4.7 × 10^{−2} | |

ZK3 | h = 0–14 | 4.1 × 10^{−1} |

h = 14–26 | 7.4 × 10^{−2} | |

ZK4 | h = 0–13 | 3.1 × 10^{−1} |

h = 13–25 | 5.7 × 10^{−2} | |

ZK5 | h = 0–10 | 7.5 × 10^{−1} |

ZK6 | h = 0–16 | 5.8 × 10^{−2} |

h = 16–34 | 7.4 × 10^{−2} | |

ZK7 | h = 0–14 | 4.7 × 10^{−1} |

h = 14–30 | 6.1 × 10^{−2} | |

ZK8 | h = 0–12 | 3.3 × 10^{−1} |

h = 12–28 | 5.7 × 10^{−2} |

Rock Classification | Rock Permeability (cm/s) |
---|---|

strong permeable layer, q ≥ 100 Lu | 2.0 × 10^{−3} |

medium permeable layer, 10 Lu ≤ q < 100 Lu | 3.0 × 10^{−4} |

weak permeable layer, 5 Lu ≤ q < 10 Lu | 5.0 × 10^{−5} |

relatively impermeable layer, q < 5 Lu | 2.0 × 10^{−5} |

fault fracture zone, q ≥ 100 Lu | 1.5 × 10^{−2} |

Zone | Permeability Coefficient (cm/s) |
---|---|

dam gravel | 2.0 × 10^{−1} |

inverted filter | 1.0 × 10^{−5} |

core material | 1.0 × 10^{−5} |

concrete panel | 1.0 × 10^{−7} |

drainage | 1.0 × 10^{−1} |

geomembrane | 1.0 × 10^{−9} |

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**MDPI and ACS Style**

Gan, L.; Chen, G.; Shen, Z. A New Approach to Permeability Inversion of Fractured Rock Masses and Its Engineering Application. *Water* **2020**, *12*, 734.
https://doi.org/10.3390/w12030734

**AMA Style**

Gan L, Chen G, Shen Z. A New Approach to Permeability Inversion of Fractured Rock Masses and Its Engineering Application. *Water*. 2020; 12(3):734.
https://doi.org/10.3390/w12030734

**Chicago/Turabian Style**

Gan, Lei, Guanyun Chen, and Zhenzhong Shen. 2020. "A New Approach to Permeability Inversion of Fractured Rock Masses and Its Engineering Application" *Water* 12, no. 3: 734.
https://doi.org/10.3390/w12030734