# Sensitivity Analyses of the Seepage and Stability of Layered Rock Slope Based on the Anisotropy of Hydraulic Conductivity: A Case Study in the Pulang Region of Southwestern China

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Control Differential Equation

_{x}is the hydraulic conductivity in the x-direction, the unit is m/s; k

_{y}is the hydraulic conductivity in the y-direction, the unit is m/s; Q is the applied boundary flux, m

_{w}is the slope of the storage curve, t is the time, the unit is s; γ

_{w}is the unit weight of water, the unit is N/m

^{3}.

#### 2.2. Factors of Safety for Unsaturated Layered Rock Slope

_{a}is the pore-air pressure and the unit is kPa; u

_{w}is the pore-water pressure and the unit is kPa; c

_{i}′ is the effective cohesion for every rock slice and the unit is kPa; i indicates the rock slice number; W

_{i}represents the weight of every rock slice; the unit is N/m

^{3}; P

_{i}indicates the water pressure and the unit is kPa; φ

_{b}is an angle defining the increase in shear strength for an increase in suction, β

_{i}is the angle of the bottom of the rock slice; b

_{i}denotes the length of every rock slice and the unit is m; φ

_{i}′ represents the shear strength angle for every rock slice; r

_{i}is the radius of the sliding arc; F

_{s}denotes the factors of safety.

#### 2.3. Finite Element Model and Boundary Conditions

#### 2.4. Determination of the Maximum Initial Matric Suction

#### 2.5. Van Genuchten Model Parameter Sensitivity Analysis

^{−1}; θ

_{r}is the residual volumetric water content, unit is m

^{−1}; θ

_{s}indicates the saturated volumetric water content, unit is m

^{−1}; a is the fitting parameter closely related to the air-entry value of the unsaturated rock mass, and the unit is kPa; n and m (m = 1 − 1/n and n > 1)are fitting parameters that control the slope at the inflection point in the volumetric water content function [18]. k

_{w}is the saturated hydraulic conductivity, unit is m/s; k is the adjusted hydraulic conductivity, unit is m/s.

_{r}are known to have major influences on the unsaturated flow of rock slope. For example, based on the analysis results of the seepage and stability of different slopes under the Fredlund and Xing parameters, Yu et al. [20] determined that the fitting parameters a, n, and m have major influences on the seepage characteristics of the slope. Additionally, Chen et al. [6] found that the unsaturated fitting parameters of the VG model were in the range of a = 0.2 to 100, m = 0.31 to 0.69, and n = 1.45 to 3.23 for rock masses. In a study by Jiang et al. [28], for general soil, the fitting parameters a = 100 and n = 2 were adopted in the Geostudio software, and for rock mass, the fitting parameter a = 10.

_{r}can take any value from 0.001 to 0.05, so θ

_{r}is set as 0.001 in this study.

#### 2.6. Definition of Anisotropy and the Calculation Conditions

_{11}= k

_{x}cos

^{2}α + k

_{y}sin

^{2}α, C

_{22}= k

_{x}sin

^{2}α + k

_{y}cos

^{2}α, and C

_{12}= C

_{21}= k

_{x}sinαcosα + k

_{y}sinαcosα. The k

_{x}and k

_{y}, as well as the anisotropy angle α, were defined according to Figure 2. In the present study, k

_{x}represents the horizontal hydraulic conductivity; k

_{y}is the vertical hydraulic conductivity; α is the direction between k

_{x}and x-axis. Therefore, if α = 0°, then [C] will be reduced to:

_{r}= k

_{y}/k

_{x}considered. However, for the layered rock masses, due to the dip angles of the bedding plane, the conditions under which the anisotropy angle α is not equal to 0 should also be considered. Therefore, in this study, to restore a reasonable rock formation state, a dip angle range of between 50° and 70° in the layered rock slope in the Pulang area was taken into consideration. As shown in Figure 2, the anisotropic angle of hydraulic conductivity is equivalent to the dip angle of the layered rock slope. Combining the recommendations of previous related research [6,12,18,30,31,32], it was determined that the anisotropy ratio k

_{r}was 0.01, 0.02, 0.1, and 1, and the anisotropy angle α was 50°, 55°, 60°, 65°, and 70°, respectively, neglecting the anisotropy of the moderately weathered carbonaceous slate, as detailed in Table 3. The failure criterion of the rock layered slope simulation adopted the Mohr-Coulomb Criterion, and the rock mass strength parameters were obtained from the geotechnical test results, as shown in Table 4.

## 3. Results and Discussion

#### 3.1. Effects of The Hydraulic Conductivity Anisotropy on The Seepage Characteristics

#### 3.1.1. Analysis of the Volumetric Water Content

_{r}= 0.01 and k

_{r}= 0.1 are shown in Figure 8 to illustrate the influence of anisotropy direction α on seepage characteristics, and different k

_{r}values with α = 50° and α = 70° are also displayed in Figure 9 to show the impacts of anisotropy ratio k

_{r}.

_{r}. It is worth mentioning that k

_{r}had a great influence on the variation of water content in the shallow part of the bottom of the slope, as shown in Figure 9c,f. It can be seen in Figure 8 and Figure 9 that the turning point of the volumetric water content appeared within the shallow part of the rock slope. The moisture condition of the region above this point began to change from unsaturated to saturated, which indicated that the moist front had reached that turning point after the rain had ceased. The turning point of volumetric water content also appeared within the deep part of the rock slope. The moisture condition of the region above this point began to change from saturated to unsaturated, indicating that the groundwater line rose to this turning point after the rain had ceased.

#### 3.1.2. Analysis of the Changes in the Groundwater Levels

_{r}was constant, it was found that with the increases of α, the differences in the heights of the groundwater levels near the free face of the rock were smaller. Then, when α was constant, with the anisotropy being increased, the differences in the heights of groundwater levels near the free face of the rock slope were larger.

#### 3.1.3. Analysis of the Maximum Water Content of the Surface and the Rising Height of the Groundwater

_{r}and α conditions, the maximum water content on the surface (MWCS) and the rising heights of the groundwater (RHG) were determined [25]. Figure 11 shows the variations of the volumetric water content on the slope over time. It can be seen in the figure that as the rainfall continued, the surface volumetric water content in the slope changed and gradually become saturated. Additionally, the maximum was reached at the end of the rainfall event. Therefore, the MWCS was used to describe the maximum water content on the slope surface during the rainfall event. As the rainfall infiltrated the slope, the groundwater level increased and the saturated areas expanded. Therefore, the RHG was used to describe the maximum height of the groundwater level increase when rainfall had subsided.

_{r}and α. It can be seen in Figure 12a,c that MWCS increases gradually with the decrease of α. The reason for this is mentioned in Section 3.1.1. It is worth noting that with the change of k

_{r}, MWCS has different change rules at different positions of slope body. At the top of the slope, MWCS gradually decreases with the increase of α. At the bottom of the slope, MWCS gradually increases with the increase of α. In the middle of the slope, the variations in α have little connection with MWCS under different k

_{r}and α conditions. The variations of the MWCS at the top of the slope were found to range between 0.154 and 0.163 and the change rate was 5.8%. The variations of the MWCS at the middle of the slope ranged between 0.155 and 0.160, and the change rate was 3.2%. The variations of the MWCS at the middle of the slope ranged between 0.156–0.160, and the change rate was 2.6%, The maximum and minimum values of the MWCS both appeared at the top of the slope, and the change rate of the MWCS at the top of the slope was the largest, which indicated that the MWCS at the top was most greatly affected by the k

_{r}and α. The change rate of the MWCS at the bottom of the slope was the smallest, indicating that the MWCS at the bottom was the least affected by the k

_{r}and α.

_{r}and increases in α, since vertical penetration was enhanced and horizontal discharge was weakened, resulting in a large increase in the height of the water level. It was observed that under different k

_{r}and α conditions, the variations of the RHG at the top of the slope ranged between 11.32 and 12.47 m and the change rate was 10.16%. The variations of the RHG in the middle of the slope ranged between 12.40 and 15.05 m and the change rate was 21.37%. Also, the variations of the RHG at the bottom of the slope ranged from 3.88 to 12.22 m and the change rate was 214.95%.

_{r}and α. The RHG change rate at the top of the slope was observed to be the smallest, indicating that the RHG at the top was the least affected by the k

_{r}and α.

#### 3.2. Effects of the Hydraulic Conduction Anisotropy on the Stability of the Rock Slope

_{r}= 1 (for example, when the rock layers were isotropic to seepage), the FS tended to be overestimated. When analyzing the stability of the layered rock slope, only the anisotropy of the shear strength was incomplete, and the anisotropy of seepage could not be ignored for the layered rock slope.

_{r}and α conditions, the FS after the rainfall had ceased were discussed. As detailed in Figure 15, it was observed that as the k

_{r}decreased and the α increased, the FS of each sliding surface decreased. When k

_{r}= 0.01 and α = 70°, the FS was found to be minimum. The FS of sliding surface No. 284 was determined to range between 1.41 and 1.47, and the rate of change was 4.26%. The FS of sliding surface No. 112 ranged between 1.49 and 1.60, and the rate of change was 7.38%. The FS of sliding surface No. 293 was observed to range from 1.57 to 1.67, and the rate of change was 6.37%. Additionally, the No. 293 sliding surface displayed a factor of safety of 1.66 to 1.70, with a rate of change of 2.41%. It was found that the smallest factor of safety occurred in the No. 284 sliding surface.

#### 3.3. Field Investigation and Verification

## 4. Conclusions

- (1)
- The residual volumetric water content of the VG model had little effect on the hydraulic conductivity. The closer the fitting parameter a of the VG model was to 10, and the closer the fitting parameter n of the VG model was to 1.5, the closer the pore water pressure of the rock slope was to the field monitoring data.
- (2)
- The maximum initial matric suction was determined to be of major significance to the unsaturated seepage of the rock slope and the subsequent calculations. This study set the maximum initial matric suction to −75 kPa, which was determined to be consistent with the actual situation.
- (3)
- The different anisotropy ratios and dip angles of the bedding plane were found to have major impacts on the seepage in the layered rock slope.
- (4)
- The MWCS and RHG were determined to characterize the seepage characteristics of the rock slope. As the dip angles of the bedding plane decreased, the MWCS gradually increased. As the anisotropy ratios decreased and the dip angles increased, the RHG gradually increased.
- (5)
- When the seepage of layered rock slope was considered isotropic, the FS tended to be overestimated. As the anisotropy ratios decreased and the dip angles of the bedding plane increased, the FS of each sliding surface was reduced. When the dip angles of the bedding plane of the rock slope are larger, more essential protections are needed.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Zhang, Z.Y. Introduction to rock hydraulics. Geol. Hazards Environ. Prot.
**1997**, 6, 56. [Google Scholar] - Collins, B.D.; Znidarcic, D. Stability Analyses of Rainfall Induced Landslides. J. Geotech. Geoenviron. Eng.
**2004**, 130, 362–372. [Google Scholar] [CrossRef] - Dong, J.J.; Tzeng, J.H.; Wu, P.K.; Lin, M.L. Effects of anisotropic permeability on stabilization and pore water pressure distribution of poorly cemented stratified rock slopes. Int. J. Numer. Anal. Methods Geomech.
**2006**, 30, 1579–1600. [Google Scholar] [CrossRef] - Zbek, A.; Gül, M.; Karacan, E.; Alca, V. Anisotropy effect on strengths of metamorphic rocks. J. Rock Mech. Geotech. Eng.
**2018**, 10, 164–175. [Google Scholar] - Lee, C.L.; Shou, K.J.; Chen, S.S.; Zhou, W.C. Numerical analysis of tunneling in slates with anisotropic time-dependent behavior. Tunn. Undergr. Space Technol.
**2019**, 84, 281–294. [Google Scholar] [CrossRef] - Chen, Y.F.; Yu, H.; Ma, H.Z.; Li, X.; Hu, R.; Yang, Z. Inverse modeling of saturated-unsaturated flow in site-scale fractured rocks using the continuum approach: A case study at Baihetan dam site, Southwest China. J. Hydrol.
**2020**, 584, 124693. [Google Scholar] [CrossRef] - Yuan, J.P.; Lin, Y.L.; Peng, D.; Han, C.L. Influence of anisotropy induced by fissures on rainfall infiltration of slopes. Chin. J. Geotech. Eng.
**2016**, 38, 76–82. [Google Scholar] - Zhao, Y.L.; Wang, W.J.; Huang, Y.H.; Cao, P.; Wan, W. Coupling analysis of seepage-damage-fracture in fractured rock mass and engineering application. Chin. J. Geotech. Eng.
**2010**, 32, 24–32. [Google Scholar] - Gonzaga, G.G.; Leite, M.H.; Corthésy, R. Determination of anisotropic deformability parameters from a single standard rock specimen. Int. J. Rock Mech. Min. Sci.
**2008**, 45, 1420–1438. [Google Scholar] [CrossRef] - Yeh, P.T.; Lee, K.Z.Z.; Chang, K.T. 3D Effects of permeability and strength anisotropy on the stability of weakly cemented rock slopes subjected to rainfall infiltration. Eng. Geol.
**2020**, 266, 105459. [Google Scholar] [CrossRef] - Dong, J.J.; Tu, C.H.; Lee, W.R.; Jheng, Y.J. Effects of hydraulic conductivity/strength anisotropy on the stability of stratified, poorly cemented rock slopes. Comput. Geotech.
**2012**, 40, 147–159. [Google Scholar] [CrossRef] - Yu, S.; Ren, X.; Zhang, J.; Wang, H.; Wang, J.; Zhu, W. Seepage, Deformation, and Stability Analysis of Sandy and Clay Slopes with Different Permeability Anisotropy Characteristics Affected by Reservoir Water Level Fluctuations. Water
**2020**, 12, 201. [Google Scholar] [CrossRef] [Green Version] - Mandal, A.K.; Li, X.; Shrestha, R. Influence of Water Level Rise on the Bank of Reservoir on Slope Stability: A Case Study of Dagangshan Hydropower Project. Geotech. Geol. Eng.
**2019**, 37, 5187–5198. [Google Scholar] [CrossRef] - Illman, W.A.; Hughson, D.L. Stochastic simulations of steady-state unsaturated flow in a three-layer, heterogeneous, dual continuum model of fractured rock. J. Hydrol.
**2005**, 307, 37. [Google Scholar] [CrossRef] - Li, X.; Li, D. A numerical procedure for unsaturated seepage analysis in rock mass containing fracture networks and drainage holes. J. Hydrol.
**2019**, 574, 23–34. [Google Scholar] [CrossRef] - Brooks, R.H.; Corey, A.T. Hydraulic Properties of Porous Media; Colorado State University, Hydrology and Water Resources Program: Fort Collins, CO, USA, 1964; pp. 1–27. [Google Scholar]
- Fredlund, D.G.; Xing, A. Equations for the soil-water characteristic curve. Can. Geotech. J.
**1994**, 31, 521–532. [Google Scholar] [CrossRef] - Genuchten, V.T.M. A Closed-form Equation for Predicting the Hydraulic Conductivity of Unsaturated Soils1. Soil Sci. Soc. Am. J.
**1980**, 44, 892–898. [Google Scholar] [CrossRef] [Green Version] - Mualem, Y. A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resour. Res.
**1976**, 12, 513–522. [Google Scholar] [CrossRef] [Green Version] - Yu, S.; Zhang, J.; Wang, J.; Wang, T.; Zhu, W.; Hu, N. Seepage and Slope Stability Analysis under Different Rainfall Patterns Based on Fredlund&Xing Parameters. J. China Three Gorges Univ.
**2017**, 39, 46–51. (In Chinese) [Google Scholar] [CrossRef] - GEO-SLOPE International Ltd. Seepage Modeling with SEEP/W 2007; Geo-Slope International Ltd.: Calgary, AB, Canada, 2010; pp. 1–207. [Google Scholar]
- Morgenstern, N.R.; Price, V.E. The Analysis of the Stability of General Slip Surfaces. Géotechnique
**1965**, 15, 79–93. [Google Scholar] [CrossRef] - Johansson, J.M.A.; Edeskr, T. Effects of external water-level fluctuations on slope stability. Electron. J. Geotech. Eng.
**2014**, 19, 2437–2463. [Google Scholar] - Oo, H.Z.; Ai, L.; Qiu, Z. Numerical Analysis of River Bank Slope Stability During Rapid Drawdown of Water Level. Study Civ. Eng. Archit.
**2013**, 2, 98–103. [Google Scholar] - Yu, S.; Ren, X.; Zhang, J.; Wang, H.; Zhang, Z. Sensibility Analysis of the Hydraulic Conductivity Anisotropy on Seepage and Stability of Sandy and Clayey Slope. Water
**2020**, 12, 277. [Google Scholar] [CrossRef] [Green Version] - Tang, D.; Li, D.; Zhou, C. Slope stability analysis considering the antecedent rainfall process. Rock Soil Mech.
**2013**, 34, 3239–3248. [Google Scholar] - Fredlund, D.G.; Morgenstern, N.R.; Widger, R.A. The shear strength of unsaturated soils. Can. Geotech. J.
**1978**, 15, 313–321. [Google Scholar] [CrossRef] - Jiang, Z.; Xiong, X.; Zeng, L. Unsaturated seepage analysis of slope under rainfall condition based on FLAC3D. Geotech. Mech.
**2014**, 35, 855–861. (In Chinese) [Google Scholar] [CrossRef] - Yeh, H.F.; Tsai, Y.J. Analyzing the Effect of Soil Hydraulic Conductivity Anisotropy on Slope Stability Using a Coupled Hydromechanical Framework. Water
**2018**, 10, 905. [Google Scholar] [CrossRef] [Green Version] - Wang, Z.H.; Li, L.; Zhang, Y.X.; Zheng, S.S. Reinforcement model considering slip effect. Eng. Struc.
**2019**, 198, 109493. [Google Scholar] [CrossRef] - Zhang, Y.; Zhang, Z.; Xue, S.; Wang, R.; Xiao, M. Stability analysis of a typical landslide mass in the Three Gorges Reservoir under varying reservoir water levels. Environ. Earth Sci.
**2020**, 79, 42. [Google Scholar] [CrossRef] - Zhou, W.; Shi, X.; Lu, X.; Qi, C.; Luan, B.; Liu, F. The mechanical and microstructural properties of refuse mudstone-GGBS-red mud based geopolymer composites made with sand. Constr. Build. Mater.
**2020**, 253. [Google Scholar] [CrossRef]

**Figure 1.**Geographic location of the study area: (

**a**) Study area location [6]; (

**b**) Rock slope location.

**Figure 5.**Water retention curves and hydraulic conductivity curves: (

**a**) Condition 1 of the water retention curve; (

**b**) Condition 2 of the water retention curve; (

**c**) Condition 3 of the water retention curve; (

**d**) Condition 1 of the hydraulic conductivity curve; (

**e**) Condition 2 of the hydraulic conductivity curve; (

**f**) Condition 3 of the hydraulic conductivity curve.

**Figure 6.**Variations in pore water pressure at the different positions under different a and n: (

**a**) Top of the slope; (

**b**) Middle of the slope; (

**c**) Bottom of the slope; (

**d**) Top of the slope; (

**e**) Middle of the slope; (

**f**) Bottom of the slope.

**Figure 8.**Volumetric water content at different positions on the layered rock slope under different α values with k

_{r}= 0.01 and k

_{r}= 0.1: (

**a**) Top of the slope with k

_{r}= 0.01; (

**b**) Middle of the slope with k

_{r}= 0.01; (

**c**) Bottom of the slope with k

_{r}= 0.01; (

**d**) Top of the slope with k

_{r}= 0.1; (

**e**) Middle of the slope with k

_{r}= 0.1; (

**f**) Bottom of the slope with k

_{r}= 0.1.

**Figure 9.**Volumetric water content levels at different positions on the layered rock slope under different k

_{r}values with α = 50° and α = 70°: (

**a**) Top of the slope with α = 50°; (

**b**) Middle of the slope with α = 50°; (

**c**) Bottom of the slope with α = 50°(

**d**) Top of the slope with α = 70°; (

**e**) Middle of the slope with α = 70°; (

**f**) Bottom of the slope with α = 70°.

**Figure 10.**Variations in the groundwater levels: (

**a**) k

_{r}= 0.01, α = 50° during rainfall; (

**b**) k

_{r}= 0.01, α = 70° during rainfall; (

**c**) k

_{r}= 1 during rainfall; (

**d**) different α values with k

_{r}= 0.01 after rain had ceased; (

**e**) different k

_{r}values with α = 70° after rain had ceased.

**Figure 12.**Variations in the MWCS and RHG with different k

_{r}and α.: (

**a**) MWCS of top of the slope; (

**b**) MWCS of the middle of the slope; (

**c**) MWCS of the bottom of the slope; (

**d**) RHG of top of the slope; (

**e**) RHG of middle of the slope; (

**f**) RHG of the bottom of the slope.

**Figure 14.**Variations in the safety factors during rainfall: (

**a**) 284 sliding surfaces; (

**b**) 293 sliding surfaces; (

**c**) 313 sliding surfaces; (

**d**) 112 sliding surfaces.

**Figure 15.**Variations in the safety factors of the different slip surfaces when rainfall ceased: (

**a**) 284 slip surfaces; (

**b**) 293 slip surfaces; (

**c**) 313 slip surfaces; (

**d**) 112 slip surfaces.

**Figure 16.**Rock landslides and stereographic projections of rock slopes in the Pulang Region: (

**a**) Landslide point No. 1; (

**b**) Landslide point No. 2; (

**c**) Landslide point No. 3; (

**d**) Landslide point No. 4.

Conditions | Fitting Parameter a (kPa) | Fitting Parameter n (m = 1 − 1/n) | Residual Volumetric Water Content θ_{r} (m^{−1}) |
---|---|---|---|

Condition 1 | 10 | [1.2, 1.5, 2, 2.5, 3, 3.5, 5, 10] | 0.001 |

Condition 2 | [0.1, 0.5, 1, 5, 10, 20, 50, 100] | 1.5 | 0.001 |

Condition 3 | 10 | 1.5 | [0.001, 0.005, 0.01, 0.02, 0.05] |

Layer | Materials | Fitting Parameters | Hydraulic Conduction Coefficient | ||||
---|---|---|---|---|---|---|---|

A (kPa) | m | n | θ_{s} | θ_{r} | k (m/s) | ||

I | Strongly weathered carbonaceous slate | 10 | 0.33 | 1.5 | 0.242 | 0.001 | 8.08 × 10^{−5} |

II | Moderately weathered carbonaceous slate | 10 | 0.33 | 1.5 | 0.021 | 0.001 | 2.47 × 10^{−6} |

Rock Types | Anisotropy Ratio k_{r} = k_{y}/k_{x} | Anisotropic Angle α (°) |
---|---|---|

Strongly weathered carbonaceous slate | $\left[\begin{array}{cccc}0.01& 0.02& 0.1& 1\end{array}\right]$ | $\left[\begin{array}{ccccc}50& 55& 60& 65& 70\end{array}\right]$ |

Rock Types | Elastic Modulus (MPa) | Poisson Ratio | Unit Weight (kN/m^{3}) | Cohesion (kPa) | Friction Angle (°) |
---|---|---|---|---|---|

Strongly weathered carbonaceous slate | 2644.9 | 0.38 | 22.4 | 93.6 | 33.3 |

Moderately weathered carbonaceous slate | 5561 | 0.35 | 26.5 | 120 | 35 |

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## Share and Cite

**MDPI and ACS Style**

Xia, C.; Lu, G.; Bai, D.; Zhu, Z.; Luo, S.; Zhang, G.
Sensitivity Analyses of the Seepage and Stability of Layered Rock Slope Based on the Anisotropy of Hydraulic Conductivity: A Case Study in the Pulang Region of Southwestern China. *Water* **2020**, *12*, 2314.
https://doi.org/10.3390/w12082314

**AMA Style**

Xia C, Lu G, Bai D, Zhu Z, Luo S, Zhang G.
Sensitivity Analyses of the Seepage and Stability of Layered Rock Slope Based on the Anisotropy of Hydraulic Conductivity: A Case Study in the Pulang Region of Southwestern China. *Water*. 2020; 12(8):2314.
https://doi.org/10.3390/w12082314

**Chicago/Turabian Style**

Xia, Chengzhi, Guangyin Lu, Dongxin Bai, Ziqiang Zhu, Shuai Luo, and Guangkeng Zhang.
2020. "Sensitivity Analyses of the Seepage and Stability of Layered Rock Slope Based on the Anisotropy of Hydraulic Conductivity: A Case Study in the Pulang Region of Southwestern China" *Water* 12, no. 8: 2314.
https://doi.org/10.3390/w12082314