Development and Application of a New Exponential Model for Hydraulic Conductivity with Depth of Rock Mass
Abstract
:1. Introduction
2. Methodology
2.1. Model Analysis
2.2. Source and Classification of Database
2.3. Geological Setting of Qinghai Engineering Project
3. Results and Discussions
3.1. Performance of the Two Models
3.2. Lithology Influence on the Hydraulic Conductivity with the Exponential Model
3.3. Geological Region’s Stableness, Faults’ Influence on the Hydraulic Conductivity with the Exponential Model
3.4. Exponential Model Application in Qinghai Engineering Project
4. Conclusions
- The proposed exponential model overcame the two main limitations of the power-like model: First, it can effectively represent residual hydraulic conductivity in specific engineering conditions. Second, it captured the fast stabilization effects of the datasets well.
- Igneous rocks, metamorphic rocks, and mudstones have a similar distribution range for Log K within a range of (−13 to −2), while the sandstone is (−7 to −3). In addition, the hydraulic conductivity decays to stability from fast to slow in the order of metamorphic rocks, sandstones, igneous rocks, and mudstones.
- Hydraulic conductivity in stable regions is approximately one-tenth of unstable regions. Faults can limit and promote seepage, with hydraulic conductivity declining through fault cores and increasing through fault damage zones.
- In the application of the exponential model to the Qinghai engineering project, the model provides an accurate prediction of hydraulic conductivities in engineering projects.
Supplementary Materials
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Model Name | Model Formula | Parameter Significance |
---|---|---|
The linear model [21,22,23,24] | Ks refers to the hydraulic conductivity at the depth of 0 (refer to surface hydraulic conductivity), α is the decay coefficient, and z is the depth. | |
The logarithmic model [26,27,28,29,30] | Ks refers to the hydraulic conductivity at a depth of 1 km (refer to surface hydraulic conductivity), α is the decay coefficient, and z is the depth. | |
The power-like model [33] | Ks refers to the hydraulic conductivity at the depth of 0 (referring to surface hydraulic conductivity), Kr is the residual hydraulic conductivity at depths exceeding the study area, α is the decay coefficient, and z is the depth. | |
Other models [31,32] | Ks is the surface hydraulic conductivity and z is the depth. The remaining parameters do not have physical meaning that can be directly correlated to hydrological properties. |
Groups | Sub-Dataset | Description | Source | |
---|---|---|---|---|
Lithology | 1. Igneous | Granite, granodiorite, and diorite Location: Europe, Asia, North America Z (0, 1600 m) | Snow [38]; Stevenson [39] Li Wan [23]; Yi Feng Chen [28]; Achtziger [26] | |
2. Metamorphic | Quartzite, marble, gneiss, and amphibolite Location: Europe, Asia, North America Z (0, 1600 m) | P. Snowdon [37]; Burger [41]; Achtziger [26] | ||
Sedimentary | 3. Sandstone | Location: Norway, Australia, China Z (0, 5000 m) | Pouyan [34]; Geoprovider [35]; Geoscience Australia [36] | |
4. Mudstone | Location: Alpine Basin, China, Japan Z (0, 7000 m) | Saffer [49]; Fisher [43]; Pouyan [34] | ||
Geological | 1. Stable | Cratons, Shields, located in Europe, Asia, North America Z (0, 1600 m) | Gale [45]; Macdonald [51]; Achtziger [26,48] | |
2. Unstable | Volcanic arcs, Rift Valleys, Ophiolite mafic belts, located in Europe, Asia, North America Z (0, 1600 m) | Pfister [46]; Zhao [47]; Achtziger [26,53] | ||
Fault Presence | 1. Faulted | A fault passes through or near a rock mass, located in Europe, Asia, North America Z (0, 1200 m) | Winkler [50]; Zhao [47]; Achtziger [26,53] | |
2. Non-Faulted | A complete rock mass that has not been crossed by a fault, located in Europe, Asia, North America Z (0, 1400 m) | Macdonald [51]; Vandenberg [52]; Achtziger [26] |
Dataset | True Log Kr | Log Kre | Log Krp | Ie | Ip |
---|---|---|---|---|---|
1 | −8.51 | −8.60 | −9.05 | 0.09 | 0.54 |
2 | −8.73 | −8.66 | −8.85 | 0.07 | 0.12 |
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Dou, Z.; Huang, X.; Wan, W.; Zeng, F.; Wang, C. Development and Application of a New Exponential Model for Hydraulic Conductivity with Depth of Rock Mass. Water 2024, 16, 778. https://doi.org/10.3390/w16050778
Dou Z, Huang X, Wan W, Zeng F, Wang C. Development and Application of a New Exponential Model for Hydraulic Conductivity with Depth of Rock Mass. Water. 2024; 16(5):778. https://doi.org/10.3390/w16050778
Chicago/Turabian StyleDou, Zhi, Xin Huang, Weifeng Wan, Feng Zeng, and Chaoqi Wang. 2024. "Development and Application of a New Exponential Model for Hydraulic Conductivity with Depth of Rock Mass" Water 16, no. 5: 778. https://doi.org/10.3390/w16050778