# Study of the Scale Effect on Permeability in the Interlayer Shear Weakness Zone Using Sequential Indicator Simulation and Sequential Gaussian Simulation

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}was selected as an example, which is one of ISWZs developed in the Baihetan dam site, to describe the discrepancy between near-fault ground motion.

## 2. Materials and Methods

#### 2.1. General Description of the Interlayer Shear Weakness Zones

_{2}β) basalts of the Upper Permian. Basalt is an igneous rock, formed from the cooling of lava erupted from the upper mantle. The rock units have been folded into a monocline, which gently dips (S120–145E/15–20, dip direction/dip) towards the right bank of the upstream section [36,37]. At the Baihetan dam site, eleven lava flows (P

_{2}β

_{1}–P

_{2}β

_{11}) have been noted, each separated by a discontinuity produced by time between distinct eruptions. In general, an incompetent tuff layer composed of basaltic debris, basaltic gravel and other sediments is found between each lava flow, with a width no more than 1 m. Subsequent tectonic stress has folded the rock strata into a series of folds. During the formation of these folds, structurally complicated ISWZs were formed in the incompetent tuff layers as a result of shear dislocation. The ISWZs on the left bank of the Baihetan dam site contain C

_{2}, C

_{3}and C

_{3-1}. However, the right bank contains C

_{2}to C

_{10}. Geological surveys reveal that different ISWZs present varying degrees of dislocation, with argillisation appearing in some regimes affected by groundwater. The mud-dominated sections of individual ISWZs are impermeable, consequently fluid flow is concentrated along gravel-dominated layers. This phenomenon indicates that permeability within ISWZs is controlled by strong heterogeneity and anisotropy.

_{3}(see Figure 3) denotes that the grain size of interlayer soils has a broad distribution, ranging from 0.075 mm to 20.0 mm.

#### 2.2. Basic Principles and Methods of Modeling

_{0}might be expressed as follows:

_{i}(i = 1, 2, 3, …, n) can be obtained after observing the variable Z n times. Under such circumstances, the ratio of the number of Z

_{i}< Z

_{0}to n can show the probability of Z < Z

_{0}. During practical geological study, only one observed value is, in most cases, selected for one variable at a certain point. Moreover, a random process should be assumed to be second-order stationary. For these reasons, when the sample capacity n is quite large, the probability of Z < Z

_{0}can be calculated by the ratio of the number of Z

_{i}≤ Z

_{0}to n, namely:

_{i}(z, x) is weight.

_{i}(z, x) can be solved by the following equations:

_{k}, x|(n)} (the cumulative distribution function) be obtained. The cumulative distribution function value between [Z

_{k}, Z

_{k+}

_{1}] can be achieved by means of linear interpolation. In this way, the LCPD at all locations can be determined. When SIS is applied to conducting a conditional simulation for K discrete variables (S

_{k}(k = 1, 2, 3, …, K)), the following steps can be followed:

- (1)
- Transform the discrete variable S
_{k}into an indicator variable. Set i_{k}(u) as the indicator value of S_{k}. When u ∈ S_{k}, i_{k}(u) is 1, otherwise it is 0. For all samples, K discrete variables must be mutually exclusive. In other words, the following relations can be established:$${i}_{k}(n){i}_{k}^{\prime}(n)=0,\forall k\ne {k}^{\prime}\phantom{\rule{0ex}{0ex}}{\displaystyle \sum _{k=1}^{k}{i}_{k}(u)=1}$$ - (2)
- Calculate the indicator variation function of each indicator variable i
_{k}(u). If there is a cluster effect for the original data, the cluster effect should be eliminated first. - (3)
- The following steps should be used to conduct sequential simulation:
- (i)
- Determine the random access path for each grid point. Confirm the quantity (maximum and minimum) of the adjacent conditional data (including the original y and the y value of the grid point) at appointed grid point.
- (ii)
- Apply indicator kriging to the indicator variable i
_{k}(u) to estimate the probability that the type variable at the grid point belongs to S_{k}. For example, when simple indicator kriging is used, the probability of S_{k}at grid point u is:$${P}^{\ast}\left\{{I}_{k}(u)=1|(n)\right\}={P}_{k}+{\displaystyle \sum _{\alpha =1}^{n}{\lambda}_{\alpha}\left[{I}_{k}({u}_{\alpha})-{P}_{k}\right]}$$_{k}= E{I_{k}(u)} ∈ [0, 1] is the marginal probability which can be inferred. The weight coefficient λ_{α}can be obtained through the simple kriging equations. - (iii)
- Determine the sequence (e.g., 1, 2, 3, …, K) of k discrete variables S
_{k}. This sequence defines the distribution order of k discrete variables S_{k}within the probability range of [0, 1]. - (iv)
- Randomly formulate a value within [0, 1] and determine the type of the discrete variable corresponding to the value. This type refers to the variable type of the grid point.
- (v)
- Use a simulated value to update the k indicator data set and deal with the next grid point by following a random path until all the points have been simulated. Under such circumstances, one realization is obtained.

#### 2.3. Generation of the 3-D Numerical Models

#### 2.3.1. The Geometry Model

#### 2.3.2. The Permeability Model

## 3. Results

#### 3.1. Variation of Permeability as a Function of Sample Support

_{s})” and the corresponding size of this sample is called the “volume of the locally homogeneous region (V

_{s})”. However, it is difficult to identify whether a sample has captured local homogeneity. Corbett and Jensen [39] proposed that Cv is a persuasive parameter, which can be used to quantize the variability of permeability. The Cv, a normalized standard deviation that can be considered a normalized treatment of the deviation for a probability distribution, giving the proper estimator of the variation in permeability. The Cv can be expressed as:

_{s}and V

_{s}by only one realization, we propose a criterion based on Cv between the five realizations to estimate them. Note that a value of Cv < 0.5 may accidentally appear in a small-scale model, but only the scale in which the Cv remains below 0.5 is deemed valid. Jensen et al. [40] has a detailed discussion of Cv.

_{h}and k

_{v}of each sample were then calculated by applying the flow equivalence principle.

_{v}and k

_{h}) for each sub-sample and the Cv value between the five realizations at each scale step were then computed using the numerical method discussed above. Note that the calculated permeability applies only to a single phase flow. The variation in permeability as a function of sample scale is shown in Figure 7, Figure 8, Figure 9 and Figure 10. Each solid line represents the results of a realization and the dotted lines are the Cv curves calculated between the five realizations at each scale step. Several observations can be noted from the results, as follows:

- For all eighteen ISWZs, it is observed that each sample has a similar trend with the increase in sample scale. As for the individual realizations, the fluctuations of permeability are gradually reduced with the increase in sample scale for each realization. This means that local homogeneity is captured at a particular model scale if its permeability is not sensitive to the slight variation.
- For ISWZs with constant width, the permeability values for all five realizations remain nearly unchanged with the increase in sample scale when mud < 0.4 for k
_{h}and mud > 0.45 for k_{v}. However, this trend is found to be absent for ISWZs with varying width. In addition, note that there is a highly positive correlation between the k_{v}and sample scale, whereas the k_{h}decreases with the increase in sample scale.

_{h}, and all ISWZs meet this criterion for k

_{v}. This indicates that most ISWZs with constant width can be considered as a homogeneous medium at a larger size (meter-scale). For ISWZs with varying width, there is a big difference compared to the former case, where the same observation can be seen only when mud > 0.5 for k

_{v}and mud < 0.3 for k

_{h}. These behaviors denote that the V

_{s}of an ISWZ sometimes does not exist, especially for ISWZs with varying width.

#### 3.2. Representative Effective Permeability of the ISWZs

_{v}and k

_{h}of individual realizations of each ISWZ calculated at full model size are respectively called the “k

_{v-f}” and “k

_{h-f}” in this article. All the k

_{v}(circles) and k

_{h}(diamonds) for all ninety realizations are shown in Figure 13 and Figure 14.

_{s}, especially for ISWZs with varying width, which denotes that the V

_{s}does not always exist. For all ISWZs, the k

_{v-f}and k

_{h-f}obviously follow a functional relationship with the ISWZ mud content (see Figure 13 and Figure 14). For ISWZs with constant width, k

_{h-f}of an ISWZ linearly decreases as the mud content increases and is close to the upper solid line (the arithmetic average of the input permeability values of the fillings) when mud is below 0.25; then it deviates from this line and declines rapidly. However, the trend for k

_{v-f}is different from that of k

_{h-f}; although permeability also decreases linearly with the increase in mud content, k

_{v-f}have a larger slope compared to k

_{h-f}and deviate from the lower solid line (the harmonic average) until mud > 0.45. This behavior is consistent with the percolation threshold theory which holds that permeability is related to the dominant component (gravel for k

_{h-f}, mud for k

_{v-f}) as gravel provides a main flow path across the ISWZ, but mud is a barrier. These results are different from the two-components system proposed by Nordahl et al. [41]. For ISWZs with variable width, there is a similar behavior for k

_{h-f}when the mud content is below 0.25. However, the results are clearly different for k

_{v-f}, which decreases linearly with the increase in mud content and deviates from the harmonic average all the time. We assume that the width change of an ISWZ may significantly increases its permeability heterogeneity degree.

_{s}for different ISWZs is significantly different, requiring various methods for calculation. Ringrose et al. [42] proposed flow upscaling regimes to determine the V

_{s}in a two-component heterogeneous porous medium. Nordahl et al. [41] extended their findings, which are different from some observations obtained by this study. Here, a series of three components of highly heterogeneous ISWZs considering variable width are developed and the results above further extend their findings. Table 5 gives the estimated results of V

_{s}for all eighteen ISWZs, where the Cv values remain below 0.5 are regarded as valid. The V

_{s}values of an ISWZ calculated in the vertical and horizontal directions are called the “V

_{s-v}” and “V

_{s-h}” in this article, respectively.

_{s}values of ISWZs with constant width are one order of magnitude larger than those of ISWZs with constant width. For ISWZs with constant width, the V

_{s-v}can be found in most ISWZs. However, the absence of the V

_{s-h}occurs when mud >0.55. For ISWZs with varying width, the V

_{s}for most of them cannot be found for either horizontal direction or vertical direction, and this behavior occurs for V

_{s-v}and V

_{s-h}when mud <0.5 and >0.3, respectively. Although the calculated V

_{s}data are scarce, several trends can be clearly seen from the ISWZs with constant width: V

_{s-v}decreases linearly to a mud share of 0.35; after the V

_{s-v}declines rapidly and closes to the size of about 0.5 m. For V

_{s-h}, a similar relationship can be observed, although it is not obvious. In addition, note that V

_{s-h}and V

_{s-v}cannot be found when mud >35 and <45, respectively. For ISWZs with varying width, it is not clear whether the V

_{s}is beyond the full model size or indeed does not exist; further work to confirm this hypothesis is needed.

_{s}of an ISWZ exist only when its V

_{s}can be found. However, for ISWZs with varying width, V

_{s}cannot be found in most ISWZs. Considering that each ISWZ will attempt to determine the only k

_{s}, here we regard the arithmetic mean permeability between the five realizations computed at the full model size as a good approximation of k

_{s}of an ISWZ since the permeability variability at the full model size is the smallest among all scales. The k

_{s}values of an ISWZ calculated in the vertical and horizontal directions are called the “k

_{s-v}” and “k

_{s-h}” in this article, respectively. Table 6 gives the calculated k

_{s}for all eighteen ISWZs.

_{s}, shown in Figure 15, also reveals that all the calculated k

_{s}go between the harmonic averages and arithmetic averages on the one hand, and a monotonic decrease with the mud content on the other hand.

_{s}

_{-h}values of ISWZs with constant width are always greater than those of ISWZs with varying width. However, the opposite conclusion can be drawn for k

_{s-v}. Based on the above results, a few rules have been discovered to confirm k

_{s}of an ISWZ. First, the effective continuum media theory will be the most suitable method for estimating k

_{s}of an ISWZ when its V

_{s}follows a linear trend with a relatively low mud fraction. Secondly, for ISWZs for which the content of mud is close to the percolation threshold, where the effective continuum media theory breaks down, a percolation threshold theory would be ideal for determining k

_{s}. Thirdly, for ISWZs that behave as a stratified medium, the traditional average of permeability gives the best estimation for k

_{s}(arithmetic average and harmonic average for k

_{s}

_{-h}and k

_{s-v}, respectively).

#### 3.3. Verification of The Proposed Numerical Model

_{3}which is one of the ISWZs developed on both sides of the Baihetan mountains (see Figure 1). The permeability data of C3 are all derived from the water-pressure tests in 30 boreholes (see Table 7). Field scanline surveys for C

_{3}(data collected more than 140-m-long outcrop) indicate the minimum, maximum, mean and standard deviation of width are, respectively, 14 cm, 108 cm, 44 cm and 15.6 (see Table 2), and its mud, gravel and fractured surrounding rock content are 8.3, 30.2 and 61.5, respectively. One point worth noting is that the permeability data obtained from our water-pressure tests can only represent the horizontal permeability estimated for a small-scale ISWZ whose size is about 4 m.

_{s}of C

_{3}; the test data can only represent the permeability of the test region. As shown in Figure 16, all field-test data are within the predicted permeability domain, which suggests that the proposed method and numerical ISWZs are valid and realistic. Additionally, the V

_{s}of C

_{3}have not found, and the predicted k

_{s-h}and k

_{s-v}are 1012.4 mD and 96.4 mD, respectively.

## 4. Discussion

_{h}and k

_{v}) as a function of sample scale is still useful. Results indicate that, for all ISWZs, the variation of permeability decreases with an increase in sample scale. However, the permeability value usually displays an upward trend. When comparing different types of ISWZs, it is observed that the scale effect on horizontal permeability shows a minimum, whereas the vertical permeability displays the highest variation at the lowest mud content considered (10%). Furthermore, for ISWZs with a constant width, both horizontal and vertical permeabilities display greater variation for ISWZs with changing width. In conclusion, the width distribution and filling content are the main factors affecting the permeability properties of an ISWZ.

_{s}) and the size of a statistically homogeneous region (V

_{s}) for each realization. The variability of permeability between the five realizations (Cv) is used to quantify the variation at any sample size between the five realizations. When Cv remains below 0.5 (a homogeneous range), k

_{s}and V

_{s}can be found, which is more reliable than the use of one realization. In general, the trend of Cv has a negative linear gradient as scale increases as expected. However, the calculation results of Cv in this article demonstrate that the Cv always fluctuates with increasing scale for some ISWZs. It is assumed that this abnormal trend is due to the lack of realizations for these ISWZs. Further work, that incorporates more realizations, may identify a more precise definition of flow properties of ISWZs.

## 5. Conclusions

- A set of eighteen realistic numerical models of ISWZs were developed by geostatistical modeling, each with five stochastic realizations. The models represent common ISWZs that have variable effective permeability on their horizontal and vertical axes and on different scales. Additionally, the permeability variation displays a downward trend as the sample scale increases for all types of ISWZs.
- The width distributions and filling content are the main factors affecting the permeability properties of an ISWZ. The ISWZ that has a higher mud content will lead to a larger scale effect on ISWZ horizontal permeability, while the opposite is true for its vertical permeability. Furthermore, the ISWZs with changing width would have greater permeability variation than that of ISWZs with constant width.
- The permeability variation between the five realizations at each scale step is expressed by the Cv. When Cv remains below 0.5, this can be used as an indication that local homogeneity has been achieved at a particular sample scale (V
_{s}). The estimated V_{s}varies as a function of ISWZ type, and varies for horizontal and vertical permeability. - The modeling and simulation methods introduced here could be adopted to other types of ISWZs and can be applied to develop accurate relationships for ISWZ permeability as a function of sample scale and other ISWZ petrophysical parameters.

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## Nomenclature

ISWZ | interlayer shear weakness zone |

SIS | sequential indicator simulation |

SGS | sequential Gaussian simulation |

IK | indicator kriging |

MC | monte Carlo |

LCPD | local conditional probability distribution |

Cv | the normalized standard deviation |

k | effective permeability |

k_{h} | effective horizontal permeability of samples |

k_{v} | effective vertical permeability of samples |

k_{s} | a representative effective permeability |

V_{s} | size of a statistically homogeneous region |

k_{v-f} | k_{v} calculated at the full-size models |

k_{h-f} | k_{h} calculated at the full-size models |

k_{s-h} | k_{s} in the horizontal direction |

k_{s-v} | k_{s} in the vertical direction |

V_{s-h} | V_{s} in the horizontal direction |

V_{s-v} | V_{s} in the vertical direction |

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**Figure 1.**Several maps of the Baihetan dam site. (

**a**) Geographical location map; (

**b**) Geological section map; (

**c**) Distribution diagram for the main structural planes; (

**d**) Simplified diagram of spatial distribution of some main hydrogeological structures.

**Figure 2.**Massive rock containing an ISWZ (C

_{3}) which is located at the right bank of the Baihetan dam site area with the buried depth of about 500 m: (

**a**) The picture of C

_{3}taken at the scene; (

**b**) The corresponding structure diagram.

**Figure 3.**Grain size distribution curve of the fillings (grains from the interlayer soil of ISWZs, which are developed on both sides of the mountains of the Baihetan dam site).

**Figure 4.**One realization of the numerical model of an ISWZ at the 40 m scale with a mud share of 30%. (

**a**) The geometric model with three components represent mud (red), gravel (blue) and fractured surrounding rock (yellow), respectively; (

**b**) The corresponding permeability model. The model size in (

**a**,

**b**) is 40 × 40 m.

**Figure 6.**Sketch illustrating the sub-samples with different scales regularly extracted from a realization.

**Figure 7.**How the horizontal permeability (k

_{h}) varies with the increase in sample size for ISWZs with constant width. Each solid line is the result of one of the realizations for a certain ISWZ type, and the dotted line represents the Cv value calculated from the five realizations at each scale step.

**Figure 8.**How the vertical permeability (k

_{v}) varies with the increase in sample size for ISWZs with constant width.

**Figure 9.**How the horizontal permeability (k

_{h}) varies with the increase in sample size for ISWZs with varying width.

**Figure 10.**How the vertical permeability (k

_{v}) varies with the increase in sample size for ISWZs with varying width.

**Figure 11.**Cv curves for ISWZs with constant width: vertical permeability (

**right**) and horizontal permeability (

**left**).

**Figure 12.**Cv curves for ISWZs with varying width: vertical permeability (

**right**) and horizontal permeability (

**left**).

**Figure 13.**Permeability calculation results of each realization at the full model size (for ISWZs with constant width-10 m). The lines represent the harmonic and arithmetic means of the input permeability values of the fillings.

**Figure 14.**Permeability calculation results of each realization at the full model size (for ISWZs with varying width-100 m).

**Figure 16.**Comparison between the calculated permeability of C

_{3}and its field-test results (the ISWZ scale is about 4 m): horizontal permeability (

**left**) and vertical permeability (

**right**).

Geometrical Input Parameters | Permeability Input Parameters |
---|---|

ISWZ width (range, mean and standard deviation) | Mud permeability (range, mean and standard deviation) |

Fillings percentage | Gravel permeability (range, mean and standard deviation) |

Variogram parameters (major and minor range, search radius, etc.) | Fractured surrounding rock permeability (range, mean and standard deviation) |

SIS parameters (distribution type and distribution parameters) | SGS parameters (distribution type and log-normal distribution parameters) |

**Table 2.**The width distribution laws for partial ISWZs which are developed in the Baihetan dam site.

Type | Normal Distribution Parameters of the Width (cm) | |||
---|---|---|---|---|

Minimum | Maximum | Mean | Standard Deviation | |

C_{2} | 12.9 | 58.3 | 31.49 | 7.5 |

C_{3} | 14.3 | 108.8 | 44.12 | 15.6 |

C_{4} | 14.1 | 102.1 | 61.86 | 14.6 |

C_{5} | 27.3 | 65.4 | 46.8 | 6.3 |

ISWZ Type | Mud Content (%) | Distribution Parameters of the Width (cm) | |||
---|---|---|---|---|---|

Range | Mean | Standard Deviation | |||

Constant width | Type1 | 10 | 100 | 100 | 0 |

Type2 | 20 | 100 | 100 | 0 | |

Type3 | 25 | 100 | 100 | 0 | |

Type4 | 30 | 100 | 100 | 0 | |

Type5 | 35 | 100 | 100 | 0 | |

Type6 | 40 | 100 | 100 | 0 | |

Type7 | 45 | 100 | 100 | 0 | |

Type8 | 50 | 100 | 100 | 0 | |

Type9 | 60 | 100 | 100 | 0 | |

Varying width | Type10 | 10 | 10–100 | 55 | 15 |

Type11 | 20 | 10–100 | 55 | 15 | |

Type12 | 25 | 10–100 | 55 | 15 | |

Type13 | 30 | 10–100 | 55 | 15 | |

Type14 | 35 | 10–100 | 55 | 15 | |

Type15 | 40 | 10–100 | 55 | 15 | |

Type16 | 45 | 10–100 | 55 | 15 | |

Type17 | 50 | 10–100 | 55 | 15 | |

Type18 | 60 | 10–100 | 55 | 15 |

Fillings | Log-Normal Distribution Parameters of Permeability (mD) | |||
---|---|---|---|---|

Minimum | Maximum | Mean | Standard Deviation | |

Mud | 0.7 | 5.6 | 2.1 | 0.8 |

Gravel | 276.7 | 28,913.2 | 3818.5 | 3464 |

Fractured surrounding rock | 16.5 | 605.3 | 119.8 | 78.9 |

ISWZ Type | V_{s} (m) | ||
---|---|---|---|

For Horizontal Direction | For Vertical Direction | ||

Constant width (100 cm) | Type1 (mud = 0.1) | <0.5 | 3 |

Type2 (mud = 0.2) | <0.5 | 2.5 | |

Type3 (mud = 0.25) | <0.5 | 3.5 | |

Type4 (mud = 0.3) | <0.5 | 2.5 | |

Type5 (mud = 0.35) | <0.5 | 1 | |

Type6 (mud = 0.4) | <0.5 | <0.5 | |

Type7 (mud = 0.45) | <0.5 | <0.5 | |

Type8 (mud = 0.5) | 2.5 | <0.5 | |

Type9 (mud = 0.6) | N/A | <0.5 | |

Varying width (10–100 cm) | Type10 (mud = 0.1) | 40 | N/A |

Type11 (mud = 0.2) | 65 | N/A | |

Type12 (mud = 0.25) | 75 | N/A | |

Type13 (mud = 0.3) | 70 | N/A | |

Type14 (mud = 0.35) | N/A | N/A | |

Type15 (mud = 0.4) | N/A | N/A | |

Type16 (mud = 0.45) | N/A | N/A | |

Type17 (mud = 0.5) | N/A | 60 | |

Type18 (mud = 0.6) | N/A | 65 |

ISWZ Type | k_{s} (mD) | ||
---|---|---|---|

For Horizontal Direction | For Vertical Direction | ||

Constant width (100 cm) | Type1 (mud = 0.1) | 2074.8 | 482 |

Type2 (mud = 0.2) | 1707.4 | 101.6 | |

Type3 (mud = 0.25) | 1416.6 | 85.8 | |

Type4 (mud = 0.3) | 941.8 | 54 | |

Type5 (mud = 0.35) | 826 | 27.2 | |

Type6 (mud = 0.4) | 645.2 | 10.4 | |

Type7 (mud = 0.45) | 405.4 | 5.12 | |

Type8 (mud = 0.5) | 291.8 | 3.98 | |

Type9 (mud = 0.6) | 81 | 3.178 | |

Varying width (10–100 cm) | Type10 (mud = 0.1) | 1044 | 378.8 |

Type11 (mud = 0.2) | 1072 | 199.2 | |

Type12 (mud = 0.25) | 834.8 | 126 | |

Type13 (mud = 0.3) | 584 | 94.6 | |

Type14 (mud = 0.35) | 330.4 | 72.4 | |

Type15 (mud = 0.4) | 270.2 | 32.6 | |

Type16 (mud = 0.45) | 232.8 | 34.2 | |

Type17 (mud = 0.5) | 154.2 | 19.8 | |

Type18 (mud = 0.6) | 105.6 | 13.2 |

Test Method | Number | k (mD) | Sample Number | k (mD) | Sample Number | k (mD) |
---|---|---|---|---|---|---|

Water-pressure test by Hohai University (boost) | No. 1 | 11.5 | No. 2 | 213.3 | No. 3 | 825.7 |

Water-pressure test by Hohai University (depressurization) | No. 4 | 328.7 | No. 5 | 222.6 | No. 6 | 365.1 |

Laboratory test | No. 7 | 108.2 | No. 8 | 149.8 | No. 9 | 24.9 |

Water-pressure test by ECIDI | No. 10 | 32.4 | No. 11 | 317.6 | No. 12 | 70.3 |

No. 13 | 17.6 | No. 14 | 625.7 | No. 15 | 175.8 | |

No. 16 | 574.4 | No. 17 | 912.3 | No. 18 | 912.3 | |

No. 19 | 10.1 | No. 20 | 736.5 | No. 21 | 617.6 | |

No. 22 | 116.5 | No. 23 | 211.8 | No. 24 | 133.8 | |

No. 25 | 29.7 | No. 26 | 39.2 | No. 27 | 623.2 | |

No. 28 | 1154.8 | No. 29 | 458.7 | No. 30 | 1287.3 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Chen, M.; Zhou, Z.; Zhao, L.; Lin, M.; Guo, Q.; Li, M.
Study of the Scale Effect on Permeability in the Interlayer Shear Weakness Zone Using Sequential Indicator Simulation and Sequential Gaussian Simulation. *Water* **2018**, *10*, 779.
https://doi.org/10.3390/w10060779

**AMA Style**

Chen M, Zhou Z, Zhao L, Lin M, Guo Q, Li M.
Study of the Scale Effect on Permeability in the Interlayer Shear Weakness Zone Using Sequential Indicator Simulation and Sequential Gaussian Simulation. *Water*. 2018; 10(6):779.
https://doi.org/10.3390/w10060779

**Chicago/Turabian Style**

Chen, Meng, Zhifang Zhou, Lei Zhao, Mu Lin, Qiaona Guo, and Mingwei Li.
2018. "Study of the Scale Effect on Permeability in the Interlayer Shear Weakness Zone Using Sequential Indicator Simulation and Sequential Gaussian Simulation" *Water* 10, no. 6: 779.
https://doi.org/10.3390/w10060779