Development of Potential Slip Surface Identification Model for Active Deep-Seated Landslide Sites: A Case Study in Taiwan

Abstract

Identifying locations of landslide slip surfaces provides critical information for understanding the volume of landslides and the scale of disasters, both of which are essential for formulating disaster preparedness and mitigation strategies. Based on hydrogeological survey data from 24 deep-seated landslide-prone sites in Taiwan’s mountainous regions, this study developed the hydraulic conductivity potential index (HCPI) using principal component analysis to quantify the hydraulic properties of disturbed rock formations with six geological factors. Then, regression analysis was performed to construct a permeability estimation model for the geological environment of landslides. Finally, the established model was utilized to develop an identification method for potential slip depths in landslide-prone sites. Results indicated a strong relation between HCPI and hydraulic conductivity with a determination coefficient of 0.895. The relation equation confirmed that the data it generated concerning the depths of significant changes in hydraulic conductivity could be used to identify potential slip surfaces. Additionally, this study successfully established a rule for identifying potential slip zones by summarizing data concerning the generated hydraulic conductivity profiles, stratigraphic lithology, existing inclinometer slip depth records, and groundwater level of landslide sites. This identification method was then applied to predict potential slip depths for ten landslide sites where slip surfaces have not yet occurred. These findings offer a new alternative to having early information on potential sliding depths for timely disaster management and control implementation.

1. Introduction

Deep-seated landslides often result in severe damage due to the greater depth to slip surface and volume of soil and debris mass movement [1]. The massive falling materials cause problems such as burying houses, blocking mountain roads, and obstructing downstream flood-prone areas by clogging river channels [2]. For example, one of Taiwan’s most staggering deep-seated landslide disasters in the past decades occurred in August 2009 [3]. A rainfall event with a cumulative rainfall exceeding 2500 mm triggered a large-scale slope collapse disaster, leading to the destruction of the village of Xiaolin and the deaths of 474 people. This sudden and massive slope disaster had a slip surface depth of approximately 80 m. As a result of such a significant rainfall event, the study of deep-seated landslides has become prevalent in Taiwan.

The failure area and depth of a landslide determine the magnitude of the disaster. When the depth of the slip surface is greater, the failure surface area will also expand with depth. Therefore, the confirmation of the depth of the slip surface plays a crucial role in predicting the scale of the disaster. In terms of mitigating such landslide disasters, having early knowledge of the depth of sliding and the affected surface area allows for the timely implementation of appropriate engineering remediation and disaster preparedness efforts. To determine the location of the slip surface in engineering applications, the standard approach involves drilling a borehole and installing an inclinometer to monitor potential slip surface areas [4]. The inclinometer is an on-site tool used for monitoring displacement over time and which helps to identify the timing and location of potential cumulative slope movements. Although the inclinometer has high measurement accuracy, this technique requires labor-intensive manual observation and does not have continuous monitoring over time. To overcome this drawback, techniques with real-time monitoring have been developed, including the in-placed inclinometer (IPI) [5], ShapeAccelArray (SAA) [6], Time Domain Resistivity (TDR) [7], and Fiber Bragg Grating (FBG) [8]. Compared to the traditional sliding inclinometer, the above four types of instruments and techniques have been successfully introduced for the real-time and distributed monitoring of landslide displacement. However, there may be differences in measurement accuracy, resolution for larger shear deformations, and limitations in measurable deformations among these four methods [9].

While the previously mentioned on-site investigation methods can directly detect the depth of the sliding surface, they only provide information about the sliding surface depth once the slope has already experienced movement. Before the deformation trigger of the collapse mass, the scale of the landslide disaster cannot be determined. This scenario makes it difficult to develop proactive disaster prevention and preparedness plans to address potential future impacts and losses. Therefore, some studies have focused on the advance prediction of the disaster scale caused by landslides. The simplest method is the core drilling and visualizing method, which identifies the presence of the sliding surface by examining the lithology of the strata. Based on the comparison of previous landslide cases with actual occurrence points and lithological characteristics, the sliding surface is typically found at the soil-rock boundary or zones of sheared mud [10]. This viewpoint is supported by the notable differences in permeability between the formations above and below the sliding interface. When rainwater seeps into the slope, it gathers above the low-permeability layers, causing the soil to become heavier and decreasing its internal friction. When the sliding force exceeds the shear strength of the soil, it triggers the sliding of the formation. Therefore, determining the sliding surface location based on the concept that the permeability of rock formations plays a crucial role in groundwater seepage can allow for an early understanding of the potential depth of the sliding surface. However, the limitation of this method is that it is susceptible to errors due to subjective judgment based on experience, and visually assessing the permeability characteristics of the lithology can result in misinterpretations.

Additionally, numerical analysis methods are common for predicting potential sliding surface locations in advance. Numerical methods have evolved over time and mainly include the limit equilibrium method (LEM) and numerical modeling methods (finite element, finite difference, and boundary element methods) [11,12,13,14]. These methods, however, rely on certain fundamental assumptions and necessitate the development of hydrogeological models for a landslide site, which can be time consuming and labor intensive. Furthermore, the accuracy of predicting sliding surface locations highly depends on the accuracy of the hydrogeological models built from field investigation data. Therefore, some studies [15,16,17] proposed alternative methods for predicting sliding surfaces, attempting to overcome the limitations of numerical methods.

These alternative methods were developed based on core sample record data and core testing data. Furuya and Jiang [15] integrated core-related data, including RQD (rock quality designation), Equotip hardness values, unit weight, magnetic susceptibilities, orientation of geologic discontinuities, and digital imaging of core samples, from two deep-seated landslide sites in Japan in order to determine potential slip surfaces. The investigation results indicated that most data types, except for digital imaging data and magnetic susceptibility, appeared to experience a distinct change near the observed slip surfaces for both sites. The Geological Survey and Mining Management Agency attempted to use instruments such as magnetic susceptibility meters and natural gamma ray meters to quantify the physical properties of core samples, aiming to study and evaluate their feasibility and applicability in identifying potential sliding surfaces [18]. Investigation results from a landslide site in southern Taiwan indicated that, regarding natural gamma ray measurements, there were slight variations in values depending on the composition of the rock mass, but overall, there was no significant difference. Additional data were needed to assess potential sliding surface locations if these measurements were to be used.

Regarding magnetic susceptibility measurements, variations in core susceptibility were noted due to differences in material composition. However, in this specific case, no significant changes were detected around the sliding depth. Therefore, when the lithology of landslide sites was relatively homogeneous, the sensitivity of both instruments mentioned above was limited, posing challenges in evaluating potential sliding surfaces.

Besides the newly developed methods for estimating the location of sliding surfaces, some researchers have identified a relationship between pore water pressure and the sliding surface within the strata. For instance, Vassallo et al. [19] established a three-dimensional numerical model based on long-term rainfall data, pore water pressure, and permeability investigation results. Their study results found that the permeability and pore water pressure of the sliding block were both higher than those of the stable layer beneath the sliding block. Park and Song [20] observed changes in rainfall and pore water pressure in a homogeneous sandy soil slope model, indicating that excessively high pore water pressure and hydrostatic pressure were more likely to cause slope failure. C. Di Maio et al. [21] studied the variation of pore water pressure and permeability in a mudstone landslide site using constant head tests and three-dimensional simulation methods (MODFLOW). The findings indicated that pore water pressure in the sliding zone rose significantly during rainfall, whereas the pressure below the sliding surface remained stable. On the other hand, there was a significant difference in permeability between the sliding zone and the rock formation below the sliding surface. This variation in permeability can also be found in other landslide-sliding surfaces [10,22,23]. Thus, these studies imply that if we can obtain the vertical distribution of permeability characteristics from areas where the coefficient of permeability varies, this approach may be effective in identifying the location of the sliding surface.

If the use of borehole permeability profile data to predict potential sliding surface locations is a viable approach, then the primary task is to address the method of obtaining profile data. Typically, the most direct and accurate method for obtaining such data is through dense-sampling, double-packer hydraulic tests. However, this technique is associated with high costs, lengthy testing times, and substantial workforce requirements. To obtain permeability data continuously with depth at a lower cost and with greater efficiency, some scholars have proposed influential factors related to permeability and established relationships between these factors and permeability coefficients, thereby developing empirical formulas for quickly obtaining permeability profile data. A detailed review of various empirical formulas can be found in the study by Hsu [24]. Most empirical formulas are only applicable to single lithology sites and adopt fewer factors related to permeability characteristics, rendering them unsuitable for sites with complex lithology. However, in recent years, Hsu [24] developed a rock mass permeability estimation model (HCB2 model) using composite geological indices applicable to various geological environments (sedimentary, igneous, and metamorphic rocks). Although this model can be applied to different lithology sites, the analysis data used to establish the model were not obtained from potential deep-seated landslide sites. The lithology of landslide sites mainly consists of fractured rock layers and colluvium, and the hydrogeological characteristics of these sites may differ from non-landslide sites, warranting further investigation and comparison.

Therefore, in order to acquire comprehensive and continuous hydrogeological data from deep-seated landslide-prone areas and to address disaster prevention management needs, this study utilized borehole cores, downhole imaging, and double-packer hydraulic test data from 24 landslide-prone locations in Taiwan. A new rock mass permeability estimation model, one specifically designed for deep-seated landslide sites, was developed. The results predicted by the new model were then compared with those from the HCB2 model. Finally, based on the above results and with displacement data monitored by inclinometer meters, a new model for confirming sliding depth was developed to rapidly predict the scale of landslide disasters.

2. Description of Study Area and Data Preparation

This study requires the establishment of models to estimate the permeability of landslide rock masses and identify sliding surface locations. To support this, it is essential to gather relevant data from investigation projects in potential deep-seated landslide areas located in Taiwan’s mountainous regions. The required data include (1) hydrogeological survey data of the strata where landslides occurred: drilling core samples, borehole imaging data, groundwater level data, and double-packer hydraulic test data, which can serve as the primary data for constructing models to assess the permeability characteristics of landslide rock masses; (2) underground displacement data: time-series monitoring data from inclinometers in landslide areas, serving as a means of investigating the relationship between the simulated distribution of hydraulic conductivity and the actual occurrence locations of sliding surfaces.

Upon reviewing the existing landslide investigation projects in Taiwan, it was found that the most extensive one was managed by the Geological Survey and Mining Management Agency (GSMMA). From 2007 to 2013 [25,26,27,28,29,30,31], the GSMMA implemented a project entitled “Investigation and Evaluation of Hydrogeological Impacts on Slope Stability in Watersheds across Taiwan”. This project mainly focused on investigating and assessing hydrogeological impacts on slope stability in major watersheds across Taiwan. It aimed to strengthen field hydrogeological investigations in order to determine the extent of hydrogeological impacts on landslide occurrence. Furthermore, it conducted research on the correlation between landslides and related factors. The project targeted deep-seated landslide areas within major northern, central, southern, and eastern Taiwan watersheds. A total of 24 landslide sites as shown in Figure 1 were selected for investigation, experimentation, monitoring, and analysis in order to determine how infiltration during rainfall alters hydrogeological conditions, leading to a potential trend of recurring rockslides. At each landslide site, three geological boreholes were drilled with depths ranging from 50 to 80 m, and geological descriptions were prepared based on core samples.

Subsequently, using the findings from borehole imaging surveys, key segments of fractured rock masses were chosen for double-packer hydraulic tests, resulting in a total of 169 test samples, each with a length of 1.5 m. Finally, an inclinometer was installed within the deepest borehole at each landslide site to monitor underground displacement, while other boreholes were set up as groundwater observation wells for monitoring groundwater levels. However, some inclinometer boreholes were constructed to monitor groundwater levels simultaneously.

The samples used to develop the specific rock mass permeability estimation model were not limited to a single rock type but included a diverse range of lithologies. The primary lithologies included sedimentary and metamorphic rocks, while sub-lithologies included sandstone, shale, alternations of sandstone and shale, sandy shale, siltstone, muddy siltstone, mudstone, argillite, slate, and phyllite. Due to the wide range of lithologies covered by the data samples, the new rock mass permeability estimation model developed in this study possesses the characteristic of adapting to different geological environments.

Finally, the primary data collected from the 24 landslide sites, including inclinometer borehole number, landslide site name, primary lithology, regolith thickness (depth to rock mass), borehole depth, and normal groundwater level, were organized as shown in

Table 1. Descriptions of collected inclinometer boreholes from the 24 landslide sites.

Inclinometer Borehole Number	Landslide Site Name ++	Main Lithology	Borehole Depth (m)	Regolith Thickness (m)	Normal Groundwater Level (m)
QH-13	Dawu	Argillite	60	7	18
OH-01	Antong	Argillaceous Siltstone	80	5	50
QH-22	Gaoshi	Sandy Shale	70	15	6.5
NH-15	Fengshan	Schists	55	1	30
NH-01	Dayuling	Slates	65	2	30
NH-21	Yanliao	Alternations of Sandstone and Mudstone	70	2	6.5
JH-27	Daguan	Argillaceous Siltstone	65	33	20
KH-01	Chaozhouhu	Alternations of Sandstone and Shale	70	20	10
KH-11	Nanshikeng	Mudstone	65	5	15
IH-23	Taipingshan	Slates	80	14	34
HH-03	Kanjiao	Sandstone interbedded with some shale	70	8	8 *
IH-13	Lantai	Argillite	80	16	10
FH-13	Tengzhi	Slates	80	12	54.4
FH-21	Jilou	Slates	70	16	41
FH-05	Baolong	Shale interbedded with some sandstone	70	12	20
EH-06	Wushe	Slates	80	10	51 *
EH-05	Hongcaiping	Shale	80	13	28.5 *
DH-05	Huayuan	Sandstone	80	19	46 *
CH-04	Caoling	Sandy Shale	80	3	50 *
CH-09	Wanda	Slates	80	15	45 *
AH-01	Yixing	Sandstone	60	4	45 *
BH-09	Xinjiayang	Slates	80	17	56 *
CH-03	Longhua	Sandy Shale	80	15	60 *
BH-03	Songmao	Slates	80	12	43 *

* Groundwater levels were estimated from data collected at nearby groundwater monitoring stations. ⁺⁺ The order of the landslide sites is presented based on the investigation timeline, from the most recent to the oldest.

. Among them, normal groundwater levels were primarily collected from monitoring wells after the completion of inclinometer borehole installation and a few days of settling without any occurrence of heavy rain. If the inclinometer boreholes did not present groundwater monitoring capabilities, groundwater levels were estimated from the data collected at nearby groundwater monitoring stations. Previous studies have suggested a correlation between groundwater levels and slope stability [32,33]. Therefore, this study also used the collected groundwater level data as one of the key factors for developing landslide slip surface identification models.

3. Methodology

This study targeted mountainous areas of Taiwan with deep-seated landslide potential. Utilizing past hydrogeological survey data, a model for estimating rock mass permeability was constructed. The aim was to reveal the distribution of permeability characteristics in the vertical direction of rock formations and attempt to explain the mechanism of landslide occurrence from the perspective of permeability distribution patterns. The research findings were expected to provide rapid feedback on disaster scale information for landslide-prone areas with deep-seated landslide potential, contributing to disaster prevention efforts. The associated approaches and procedures—including (1) selecting influential factors for characterizing the hydraulic properties of fractured rocks in active landslide sites; (2) multicollinearity analysis for the selected influential factors; (3) principal component analysis (PCA) for determining the weight of each factor; (4) model establishment and evaluations; and (5) developing a rule for identifying potential slip surface—are provided as follows.

3.1. Selection of Influential Factors

Prior to developing a rock mass permeability estimation model for landslide sites, influential factors that may affect the permeability of disturbed rock mass must be considered. Based on the material composition and structural characteristics of fractured rock masses in landslide areas, this study referred to previous research [34,35,36,37,38,39,40,41,42,43] to select potential factors related to rock mass permeability characteristics. The most commonly considered factors include depth index (DI), rock quality designation (RQD), fracture aperture (FA), and fracture density (FD). Earlier models were developed based solely on individual influencing factors. However, subsequent research has considered multiple factors in model development [38,41,44], and the research results have demonstrated that predictive models using multiple factors outperform those using single factors. However, the models established above were often limited to application in single lithology sites. In recent years, Hsu [24] attempted to develop predictive models applicable to various geological environments, considering up to eight influencing factors. Eventually, six different combinations of factors were used to build predictive models. Although Hsu [24] has improved the accuracy and limitations of predictive models, the models were built using data collected from non-collapsible strata in the mountainous areas of Taiwan. However, hydrogeological characteristics are significantly more complex for sites with high collapsibility potential compared to non-disturbed strata conditions. Currently, there is no systematic construction of similar predictive models. As a result, this study utilized survey data from locations in Taiwan with a high potential for collapsibility. Drawing from Hsu’s [24] six-factor model, it identified six influencing factors—RQD, DI, FA, FD, gouge content designation (GCD), and lithology permeability index (LPI)—to develop a predictive model for the permeability of disturbed strata.

In brief, RQD assesses the quality of rock formations, where lower values signify increased fracturing, which is associated with greater permeability. DI represents the influence of in situ stress on rock mass permeability, theoretically leading to decreased permeability with depth. GCD calculates the content of shear mud in a specific section of the rock mass, aiming to correct the drawback of RQD in neglecting shear mud, thereby identifying a critical factor in determining whether fractures have groundwater-conducting properties. LPI represents the overall permeability of the intact rock mass and is related to the rock’s pore characteristics, excluding the influence of fracture characteristics on permeability. Finally, FA and FD describe the structural features of the rock mass and are crucial indicators of rock mass permeability, indirectly influencing the groundwater flow. Detailed scoring definitions and criteria in response to permeability for each influencing factor can be found in Hsu [24] and will not be repeated in this paper.

However, regarding the scoring system for the LPI factor across various lithologies, Hsu [24] initially designed it based on core samples obtained from relatively undisturbed rock mass sites. However, the sites examined in this study mainly consist of disturbed geological strata. According to the core investigation data from the collapse sites, lithologies such as weathered slate, weathered shale, weathered argillite, and argillite frequently appear, which were not accounted for in the original LPI scoring system. Therefore, this study made partial modifications to the LPI scoring system. In

Table 2. Description and ratings for lithology permeability index (LPI).

Lithology	Hydraulic Conductivity k (m/s)				Range of Rating	Suggested Rating
	Reference 1	Reference 2	Reference 3	Kaverage 4
Sandstone	10−6~10−9	10−7~10−9	10−7~10−9	10−7.5	0.9~1.0	0.92~1.0
Silty Sandstone					0.8~0.9	0.9
Argillaceous Sandstone					0.8~0.9	0.85
Sandstone interbedded with some Shale					0.7~0.8	0.75
Alternations of Sandstone & Shale					0.6~0.7	0.65
Shale interbedded with some Sandstone					0.5~0.7	0.6
Alternations of Shandstone & Mudstone					0.5~0.6	0.55
Dolomite	10−6~10−10.5	10−7~10−10.5	10−9~10−10	10−8	0.6~0.8	0.7
Limestone	10−6~10−10.5	10−7~10−9	10−9~10−10	10−8	0.6~0.8	0.7
Shale	10−10~10−12	10−10~10−13		10−10.5	0.4~0.6	0.5
Sandy Shale					0.5~0.6	0.6
Siltstone	10−10~10−12			10−11	0.2~0.4	0.4
Sandy Siltstone					0.3~0.5	0.45
Argillaceous Siltstone					0.3~0.4	0.35
Claystone		10−9~10−13		10−11	0.2~0.3	0.2
Mudstone					0.2~0.4	0.3
Sandy Mudstone					0.3~0.4	0.4
Silty Mudstone					0.2~0.4	0.35
Granite			10−11~10−12	10−11.5	0.1~0.2	0.15
Basalt	10−6~10−10.5	10−10~10−13		10−11.5	0.1~0.2	0.15
Schists						0.25
Slates						0.35
Quartzite						0.3~1.0
Argillite (a)					0.4~0.5	0.4
Weathered Argillite (a)					0.45~0.5	0.5
Weathered Slates (a)					0.35~0.6	0.5
Weathered Schists (a)					0.5~0.75	0.6

¹ B.B.S. Singhal and R.P. Gupta (1999) [43]; ² Karlheinz Spitz and Joanna Moreno (1996) [43]; ³ http://en.wikipedia.org/wiki/Hydraulic_conductivity (accessed on 15 October 2024) (modified from Bear, 1972) [43]; ⁴ Hsu (2021) [24]; ^(a) Modified from Hsu (2021) [24].

, in addition to the LPI score table developed by Hsu [24], additional rock mass scoring values specific to collapse sites were added (as shown in the last four rows of Table 2). The scoring ranges from 0 to 1, where a higher score indicates a higher permeability. Finally, due to the complexity of lithologies in collapse areas, the calculation of LPI values in double-packer test sections may involve different lithological proportions, and therefore, the calculation was performed by combining various lithological ratios.

3.2. Multicollinearity Analysis for Selected Influencing Factors

Since this study employs multiple-factor statistical analysis, it is necessary to conduct multicollinearity tests on the selected influencing factors to examine whether there are multicollinearity issues among them. Multicollinearity can be assessed using one commonly used indicator—tolerance and variance inflation factor (VIF). Tolerance refers to the percentage of variance in a predictor variable that is not explained by other predictor variables, with values ranging from 0 to 1. A tolerance value close to 1 indicates the absence of multicollinearity, while values closer to 0 suggest multicollinearity issues. However, there is no formal threshold to determine the presence of multicollinearity among factors [45]. Although no universally accepted standards exist, some studies have explored the relationship between tolerance values and multicollinearity. For instance, Myers [46] suggested that tolerance values below 0.1 indicate severe multicollinearity issues, while Menard [47] proposed that values below 0.2 indicate potential multicollinearity problems.

Additionally, the reciprocal of tolerance, known as the variance inflation factor (VIF), is used to indicate the extent to which the variance of coefficient estimates is influenced by multicollinearity. Like tolerance, there is no formal cutoff value for VIF. However, VIF values exceeding ten indicate multicollinearity issues, although this criterion may require smaller values for weaker regression models. For example, Midi et al. [45] recommended that VIF values exceeding 2.5 in logistic regression analyses warrant attention to multicollinearity issues. Finally, this study conducted multicollinearity tests on the six influencing factors mentioned in Section 3.1 using the aforementioned diagnostic metrics to guide model construction.

3.3. Weights of Influential Factors Through Principal Component Analysis

Theoretically, the permeability characteristics of rock masses are controlled by various influencing factors, and these factors may have different impacts on the permeability characteristics of fractured rock masses. By assigning appropriate weights to the influential factors and then combining the factors, better correlations with permeability characteristics may be obtained. To extract the weight values of each influential factor, this study adopted the principal component analysis (PCA) method, a multivariate analysis technique.

PCA can be conducted using either an unstandardized covariance matrix or a standardized correlation matrix. When the units of the analyzed variables differ, using the correlation matrix is generally preferable. The eigenvalues and eigenvectors are then calculated from this matrix. The variance of each principal component is equal to its corresponding eigenvalue, with the first principal component having the most considerable variance, followed by the second principal component, and so on. The eigenvalues can also be used to compute the contribution proportion of each principal component (the percentage of total variance accounted for by that principal component), which reflects the explanatory power of the entire set of variables and serves as a basis for selecting principal components. The eigenvectors are the coefficients in the linear combinations of the principal components, and the coefficients can be derived from the loadings. Loadings are the correlation coefficients between the variables and the principal components and are calculated using the eigenvalues, eigenvectors, and standard deviations. The loading formula is shown in Equation (1).

$$r_{y_j{x}_i}={\displaystyle \frac{a_{ji}\sqrt{{\lambda }_j}}{s_i}}$$

(1)

where the loading $r_{y_j{x}_i}$ is the correlation coefficient between the j-th principal component and the i-th variable. A larger loading value indicates a greater influence of the principal components on the variables; ${\lambda }_j$ is the eigenvalue of the j-th principal component; $s_i$ is the standard deviation of the i-th variable; and $a_{ji}$ is the eigenvector coefficient.

Therefore, the eigenvector coefficient $a_{ji}$ can be derived from Equation (1) as follows:

$$a_{ji}={\displaystyle \frac{r_{y_j{x}_i}}{\sqrt{{\lambda }_j}}}{s}_i$$

(2)

After obtaining the eigenvector coefficients, the linear combination coefficients of each principal component can be derived. The next step is to combine the linear combination coefficients of each principal component with their variance contribution ratios. Using the variance contribution ratio of each principal component as a weight, the eigenvectors and variance contribution ratios of the more explanatory principal components are integrated to calculate the new coefficients of each variable in the new linear combination model.

The selection rule for the more explanatory principal components involves selecting the first n principal components with the most significant variance contribution ratios among all j principal components. The cumulative variance contribution rate of these n principal components must exceed 80%. Assuming that the first n principal components represent the original variable indicators, the new coefficients of the variables can be considered a weighted average of the old coefficients. The linear combination of these n principal components uses their variance contribution ratios as weights. Therefore, the coefficient matrix b of all variables in the composite score model is given as follows:

$$\mathrm{b}=\left[\begin{array}{c}{b}_1\\ b_2\\ \begin{array}{c}⋮\\ b_i\end{array}\end{array}\right]={\displaystyle \frac{a_1\times c_1+a_2\times c_2+\dots +a_n\times c_n}{c_1+c_2+\dots +c_n}}$$

(3)

where $a_n$ represents the eigenvector matrix of the n-th principal component; $c_n$ represents the contribution ratio of the n-th principal component.

Finally, since the sum of the coefficients (weights) for all variables i must equal one, all variable weights need to be normalized based on the variable coefficients in the composite score model. This results in the final weight score $w_i$ for each variable given as follows:

$$w_i={\displaystyle \frac{b_i}{b_1+b_2+\dots +b_i}}$$

(4)

By using the above analysis process with the available hydrogeological investigation data, the number of principal components with significant contributions can be selected and combined with the contribution proportions to calculate the weight value for each influencing factor. The determined weights can be utilized to establish the rock mass permeability index and further construct a rock mass permeability estimation model.

3.4. Model Establishment and Hypothesis Testing

As discussed in Section 3.1, six geological factors may influence the hydraulic properties of rock mass. Each factor impacts the permeability values differently. For example, if the RQD value of the rock core shows poor rock mass quality, theoretically, the permeability should be higher. However, if there is gouge filling in the fractures, the permeability of the rock mass may decrease. Likewise, if two core sections exhibit identical RQD values but are located at different depths, the deeper section might experience decreased permeability due to heightened stress that compresses the joints or reduces the porosity of the rock matrix. Therefore, a comprehensive permeability index for fractured rock masses may need to integrate various geological indicators. The six geological indicators (RQD, DI, GCD, LPI, FA, and FD) were integrated into this study. In light of the principal component analysis presented in Section 3.3, the weight of each geological factor was determined. Subsequently, the factors were combined linearly by multiplying each by its associated weight value, w_i. Equation (5) defines the hydraulic conductivity potential index (HCPI) for landslide-prone bedrock. The formula for HCPI is given as follows:

$$\mathrm{H}\mathrm{C}\mathrm{P}\mathrm{I}=[(1-{\displaystyle \frac{RQD}{100}})\times w_1]+(\mathrm{D}\mathrm{I}\times w_2)+[(1-\mathrm{G}\mathrm{C}\mathrm{D})\times w_3]+(\mathrm{L}\mathrm{P}\mathrm{I}\times w_4)+(\mathrm{F}\mathrm{D}\times w_5)+(\mathrm{F}\mathrm{A}\times w_6)$$

(5)

HCPI can quantify the permeability of the rock mass with the scores of the given six factors, except for FA, ranging between 0 and 1. Higher values indicate a greater contribution of the corresponding parameter to increasing the rock mass permeability. A higher HCPI value represents permeable rock masses in the test section. Subsequently, different mathematical models (such as simple linear, logarithmic, exponential, or power law) can be selected, and regression analysis techniques can be applied to establish an estimation model for the permeability of fractured rock masses in landslide formations. The goodness of fit for each model can be determined by the R² value, indicating the degree of correlation between permeability and HCPI.

Additionally, two statistical analyses were conducted to ensure a reliable regression result for the best model. The first statistical analysis inspected the regression model’s assumptions for residuals (independence using the Durbin–Watson statistic, constant variance using Spearman’s rank correlation, and normality using the Kolmogorov–Smirnov test). In contrast, the second statistical analysis investigated the statistical significance of the regression analysis model using the F test statistic and p values. Based on the regression analysis outcomes, the best model for predicting the permeability of fractured rock masses was decided. The regression and statistical analyses mentioned above were carried out using the commercial software SigmaPlot 14.0.

3.5. Developing a Rule for Identifying Potential Slip Surface

To summarize and clarify whether the distribution pattern of permeability in a landslide area is related to the location of the sliding surface, this study utilized the landslide-specific rock mass permeability estimation model established in Section 3.4. The model was used to create continuous hydraulic conductivity profiles for the 24 landslide sites, showing the variation with borehole depth meter by meter. Next, the observed inclinometer data from the 24 landslide sites, which had clear records of sliding, were superimposed onto the hydraulic conductivity bar charts (as illustrated in Figure 2). This work helped observe whether there were significant changes or other trends in hydraulic conductivity values near the monitored sliding depths. This process explored the feasibility of identifying sliding surface locations using information on the hydraulic conductivity profile. Subsequently, a more comprehensive method for estimating the potential sliding depth was established by combining borehole core data, groundwater level data, and the relationship between these data and the sliding surface locations. This method was then validated by applying it to sites with known sliding depths to check if it could correctly identify the sliding surface locations. Finally, the identification rule developed in this study can be applied when inclinometers have not yet detected significant displacement. This application can assist disaster prevention decision-making agencies in estimating the potential scale of deep-seated landslides in advance.

4. Results and Discussion

4.1. Descriptive Statistics for Six Influential Factors

Establishing the permeability estimation model first requires integrating the hydraulic conductivity of existing double-packer test sections. Then, the scores of the influential factors for each test section are calculated for subsequent principal component analysis and regression modeling. This study compiled 169 double-packer test section data from 48 boreholes in the 24 landslide areas. It sequentially calculated the RQD, DI, GCD, LPI, FA, and FD values for each double-packer section according to the method described in Section 3.2. The descriptive statistical results of the calculated factor scores are shown in

Table 3. Descriptive statistical results of indicative factors for both overall rock types and specific rock types.

	Factors	RQD	DI	GCD	LPI	FF	FW
All lithologies	quantity	169	169	169	169	169	169
	average	0.479	0.362	0.088	0.508	0.571	1.110
	Standard deviation	0.300	0.226	0.146	0.176	0.275	0.742
Sedimentary rocks	quantity	87	87	87	87	87	87
	average	0.656	0.470	0.088	0.595	0.444	0.955
	Standard deviation	0.238	0.243	0.154	0.180	0.232	0.773
Metamorphic rocks	quantity	82	82	82	82	82	82
	average	0.291	0.349	0.088	0.415	0.706	1.276
	Standard deviation	0.239	0.219	0.138	0.113	0.252	0.673

. The overall average RQD value for all lithologies is approximately 0.479, with sedimentary rocks averaging 0.656 and metamorphic rocks averaging 0.291. According to Bieniawski’s [48] rock core quality determination method, the overall rock core quality is poor, with fragmented metamorphic rock formations. Although the rock core quality of sedimentary rock formations is better than that of metamorphic rocks, it only reaches a fair level according to Bieniawski’s [48] criteria. These results indicate that the overall rock core quality in landslide areas is generally poor, as expected.

A closer look at the statistical analysis of FD and FA reveals that the average values for both parameters are higher in metamorphic rock formations than in sedimentary ones. This suggests a more extensive fracture network in metamorphic rocks, aligning with the RQD findings. Moreover, the descriptive statistics concerning GCD indicate that the gouge content in sedimentary and metamorphic rocks is comparable. Since DI and LPI represent the relative depth and lithology of the sampling section, their mean values and standard deviations have less physical significance and are not discussed here.

Finally, examining the six geological characteristic indicators selected for this study reveals that higher RQD and GCD values indicate better core quality and higher gouge content in the rock core section. Both higher values lead to lower hydraulic conductivity K, meaning RQD and GCD are negatively correlated with K. Conversely, the remaining four indicators are positively correlated with K. To ensure that all indicator factors have a positive correlation with K, this study transformed the RQD and GCD values to (1-RQD) and (1-GCD). This transformation changes the correlation to positive without affecting the order and spacing of the values. After the transformation, all factors show a positive correlation with K. This enhances the convenience of interpreting the results of subsequent multicollinearity analysis and principal component analysis.

4.2. Multicollinearity Analysis Results of the Selected Factors

When establishing regression models using possible geological factors, checking for multicollinearity among them is vital to prevent redundancy in the independent variables. This could artificially enhance the explanatory and predictive power of certain variables, leading to inaccurate regression model predictions. Therefore, the tolerance or variance inflation factor (VIF) can be used to assess multicollinearity. Actually, the reciprocal of tolerance is VIF. Therefore, this study only used VIF to assess multicollinearity. The criteria for VIF are as follows: When VIF is greater than ten, it indicates a strong multicollinearity problem. The smaller the VIF value, the smaller the issue of multicollinearity. The results of the multicollinearity analysis are shown in

Table 4. Multicollinearity analysis of the chosen controlling variables (dependent variable: K).

Controlling Variables	Tolerance	VIF
1-RQD	0.242	4.136
DI	0.906	1.104
1-GCD	0.740	1.351
LPI	0.660	1.514
FA	0.322	3.103
FD	0.285	3.514

. Upon examining the VIF column in Table 4, it is evident that the VIF values for all factors are less than ten, indicating no strong multicollinearity among the indicator factors. Therefore, the regression model can directly include the six geological factors—RQD, DI, GCD, LPI, FA, and FD. However, the VIF values of the six factors show slight differences and can generally be divided into two groups. FA, FD, and RQD form one group, with VIF values higher than those of the other parameter group (DI, GCD, and LPI). The higher values in the first group are likely due to the commonality among RQD, FA, and FD, as they are mainly related to the fractured rock characteristics. The smaller VIF values of the second group are attributed to the lack of commonality among them. DI represents the influence of geostress on permeability, GCD reflects the permeability of gouge, and LPI represents the permeability of intact rock cores from different lithologies.

4.3. Results of PCA

This section presents the analysis results of calculating the weight values for each factor using PCA. First, the varimax method was used for axis rotation, and more influential factors were extracted based on principal components with eigenvalues greater than 1, aided by a scree plot to determine the number of components to extract (as shown in Figure 3). The analysis was performed with a cumulative contribution ratio of over 80%.

Table 5. Results of each component in the principal component analysis.

Component Number	Eigenvalue	Proportion of Variance (%)	Cumulative Proportion of Variance (%)
1	2.539	42.316	42.316
2	1.312	21.868	64.184
3	1.041	17.344	81.528
4	0.722	12.041	93.569
5	0.239	3.986	97.555
6	0.147	2.445	100

shows the calculation results of each component in the principal component analysis, displaying the eigenvalues, contribution ratios, and cumulative contribution ratios of the principal components. Larger eigenvalues indicate greater importance. As shown in Table 5, the eigenvalues of the first three principal components are greater than 1, with a cumulative contribution ratio of 0.8152 for these three components. The cumulative contribution ratio explains 81.52% of the data variance.

Thus, the first three principal components with their variance contribution ratios were utilized to determine the weights of all factors. First, the factor loadings were derived according to Equation (1), as shown in the upper part of

Table 6. Factor loadings and linear combination coefficients for the first to third principal components.

Factor Loadings
factors	PC1	PC2	PC3
1-RQD	0.939	−0.160	−0.105
DI	0.093	−0.543	0.699
1-GCD	0.185	0.689	−0.228
LPI	−0.109	0.712	0.636
FW	0.804	0.288	0.291
FF	0.928	0.017	−0.048
Linear combination coefficients
factors	PC1	PC2	PC3
1-RQD	0.589	−0.140	−0.103
DI	0.058	−0.474	0.685
1-GCD	0.116	0.602	−0.223
LPI	−0.068	0.622	0.623
FW	0.505	0.251	0.285
FF	0.582	0.015	−0.047

. Then, the eigenvector coefficients for the three principal components were calculated using Equation (2). The resulting linear combination equations for the three principal components are as follows:

$$\mathrm{F}1=0.589\times \left(1-\mathrm{R}\mathrm{Q}\mathrm{D}\right)+0.058\times \mathrm{D}\mathrm{I}+0.116\times \left(1-\mathrm{G}\mathrm{C}\mathrm{D}\right)-0.068\times \mathrm{L}\mathrm{P}\mathrm{I}+0.505\times \mathrm{F}\mathrm{A}+0.582\times \mathrm{F}\mathrm{D}$$

(6)

$$\mathrm{F}2=-0.14\times \left(1-\mathrm{R}\mathrm{Q}\mathrm{D}\right)-0.474\times \mathrm{D}\mathrm{I}+0.602\times \left(1-\mathrm{G}\mathrm{C}\mathrm{D}\right)+0.622\mathrm{L}\mathrm{P}\mathrm{I}+0.251\times \mathrm{F}\mathrm{A}+0.015\times \mathrm{F}\mathrm{D}$$

(7)

$$\mathrm{F}3=-0.103\times \left(1-\mathrm{R}\mathrm{Q}\mathrm{D}\right)+0.685\times \mathrm{D}\mathrm{I}-0.223\times \left(1-\mathrm{G}\mathrm{C}\mathrm{D}\right)+0.623\times \mathrm{L}\mathrm{P}\mathrm{I}+0.285\times \mathrm{F}\mathrm{A}-0.047\times \mathrm{F}\mathrm{D}$$

(8)

Third, the weighted average of the linear combination coefficients of the three principal components was calculated to obtain the coefficient of the composite score model using Equation (3), as shown in

Table 7. Composite scores model coefficients.

Controlling Variables	Coefficients
1-RQD	0.247
DI	0.049
1-GCD	0.174
LPI	0.264
FA	0.390
FD	0.296

. The composite model Equation is given as follows:

$$\mathrm{Y}=0.247\times \left(1-\mathrm{R}\mathrm{Q}\mathrm{D}\right)+0.049\times \mathrm{D}\mathrm{I}+0.174\times \left(1-\mathrm{G}\mathrm{C}\mathrm{D}\right)+0.264\times \mathrm{L}\mathrm{P}\mathrm{I}+0.39\times \mathrm{F}\mathrm{A}+0.296\times \mathrm{F}\mathrm{D}$$

(9)

Finally, based on the requirement that the weights of all factors need to be normalized in the composite score model, the weight values for each factor were obtained, as shown in

Table 8. Weights for each factor.

Controlling Variables	Weights
1-RQD	0.174
DI	0.034
1-GCD	0.123
LPI	0.186
FA	0.275
FD	0.209

.

The weight analysis shows that FA and FD have the highest values, indicating their importance in landslide-prone areas. This suggests that the degree of fracture network development plays a major role in evaluating the hydraulic conductivity of fractured rock masses in such regions. Additionally, except for DI, which has a relatively low weight, the other factors are more balanced. The lower influence of DI in the principal component analysis suggests that, given the maximum borehole depth of 80 m, the effect of tectonic stress is less significant within the limited depth range.

4.4. Establishment and Evaluation of the Predictive Model

Based on the results of the weight analysis on six geological factors through PCA in Section 4.3, each factor was multiplied by its respective weight and then linearly added to obtain the integrated permeability indicator HCPI. Next, by applying common mathematical models (including simple linear, logarithmic, exponential, or power law models) for regression analysis, the model was constructed using double-packer hydraulic test data and the HCPI data calculated from core samples. The coefficient of determination (R²) was used to identify the optimal regression mathematical model, thereby deriving the permeability estimation model for landslide-prone rock masses. The regression analysis results, as shown in Figure 4, indicate that the power law formula best fits the relationship between HCPI and K, with an R-squared value of 0.8953, demonstrating good predictive capability.

Furthermore, the optimal regression model underwent an F test to examine the overall significance of the model and whether the error terms satisfy the assumptions of normality (Kolmogorov–Smirnov statistic), independence (Durbin–Watson statistic), and homoscedasticity (Spearman rank correlation coefficient). The results of these statistical evaluations are shown in

Table 9. Evaluation results for the empirical model.

Independence (D-W Statistic)	Normality (K-S Statistic/p-Value)	Constant of Variance (Spearman/p-Value)	F Test Statistic
			F Ratio	p-Value
1.5014	0.0910	0.5824	1419.1	<0.0001

.

The F test statistic measures the contribution of the HCPI value in predicting the hydraulic conductivity. If the F value is large, the HCPI that contributes to the prediction of the hydraulic conductivity variable can be concluded. Besides, if the p value is less than 0.05, the same conclusion can also be made. Table 9 shows the results of the F test statistic. The best estimation model achieves significance, indicating that the model is predictive. As for the three assumptions, if the residuals are correlated, then the Durbin–Watson statistic values are higher than 2.5 or less than 1.5. If the p values calculated by normality and constant variance tests are higher than 0.05, two tests pass. As shown in Table 9, the results of three assumptions are presented. The Durbin–Watson statistic of 1.5014 indicates no autocorrelation in the residuals. The p values for normality (0.0910) and constant variance (0.5824) tests are greater than 0.05. Thus, the residuals are normally distributed, and the constant variance assumption is valid.

These five validation tests confirm the effectiveness of the permeability estimation model for landslide-prone rock masses. Therefore, in future applications, the developed landslide rock mass permeability estimation model can effectively and cost-efficiently obtain detailed and continuous hydraulic conductivity profiles. This work can be achieved at any active landslide site by obtaining six geological indicator parameters from core samples and double-packer hydraulic test data.

4.5. Comparisons of the Previous and Newly Developed Models

In addition to developing a permeability estimation model for landslide-prone rock layers (named the HCPI model), another research objective of this study was to test the differences in hydrogeological characteristics between disturbed and undisturbed fractured rock formations. The disturbed model is the HCPI model, while a brief introduction to the undisturbed model is provided here. Hsu [24] collected hydrogeological investigation data from boreholes in the mid and upper river basin of the Choshui river in Taiwan and developed an integrated permeability estimation model (named HCB2 model) using geological characteristic indicators and hydraulic conductivity data from double-packer test sections. This study successfully proposed a model applicable to the complex and fractured geological environments in the mountainous regions of Taiwan. While Hsu’s model [24] is applicable to sites of different lithologies with a wide application range, the data collected in their study did not specifically consider sites with the potential for stratum sliding. The hydrogeological characteristics of such potentially active landslide sites may differ from typical mountainous sites in Taiwan. As a result, this study aimed to compare the hydrogeological characteristics of the HCB2 and HCPI models. Before conducting this comparison, this study expanded the HCB2 model by incorporating more data points. In addition to the original 104 sample points, 352 data points from undisturbed strata in other major mountain basins of Taiwan were collected. The HCB2 model was then reconstructed to make the estimation of hydraulic conductivity more representative (named NHCB2).

Figure 5 shows the comparison of hydrogeological properties between the NHCB2 and HCPI models. As shown in this figure, both models cover common metamorphic and sedimentary lithologies, indicating a wide range of lithologies. However, the HCPI model does not include samples of igneous rocks, suggesting the potential for future enhancement by collecting similar lithologies to expand the model’s applicability. In addition, both models have determination coefficients (R²) above 0.7, indicating a certain degree of explanatory power. The HCPI model performs better than the NHCB2 model, possibly due to the smaller sample size. The analysis samples for the two models differ by approximately three times, and the determination coefficient decreases with fewer samples. However, a larger sample size signifies a more statistically significant model. Future efforts can continue to collect landslide samples in order to build a more representative model while noting changes in the determination coefficient values with increasing sample size.

Finally, Figure 5 reveals differences in the estimated curve trends between the two integrated indices (HCPI and NHCB2) and K, with more pronounced differences when K is smaller. The NHCB2 model estimates higher values of permeability coefficient K, suggesting higher overall hydraulic conductivity in the major mountainous watersheds of Taiwan. In contrast, the hydraulic conductivity values estimated by the HCPI model are generally lower, implying a geological environment in landslide areas characterized by significant disturbance and more clay shear in geological strata, resulting in lower trends of hydraulic conductivity. Thus, based on the comparison results, both models can estimate the hydraulic conductivity of fractured rock masses using geological characteristic factors. However, selecting the appropriate model depends on whether the strata have been disturbed to capture the site’s hydraulic characteristics accurately.

4.6. The Relationship Between Hydraulic Conductivity Distribution Patterns and the Locations of Sliding Surfaces

This study utilized the HCPI model to generate continuous depth-by-depth hydraulic conductivity distribution charts for each borehole equipped with an inclinometer across the 24 landslide sites. The findings revealed that in most landslide sites, there were specific intervals where hydraulic conductivity either markedly increased or decreased with depth. Figure 6 illustrates the hydraulic conductivity profile of the Wanda landslide site. The hydraulic conductivity values are presented on a per-meter scale, from beneath the regolith layer (15 m below the surface) to the bottom of the borehole (80 m). The area above a depth of 34 m exhibited higher permeability than the area below. Overall, the average hydraulic conductivity value differed by two to three orders of magnitude. Meanwhile, significant variations in hydraulic conductivity values at depths above and below 34 m (as highlighted in red boxes) were observed.

According to previous studies on deep-seated landslides [10,22,23], the upper and lower layers above the sliding surface often exhibit a trend where the upper layer is more permeable (K > 10⁻⁶ m/s, [49]) than the lower layer. The difference in hydraulic conductivity between the upper and lower layers typically falls within one to three orders of magnitude [10,22,23]. Thus, the depth of 34 m at the Wanda landslide site may have the potential to develop a slip surface.

To determine if the landslides in this study follow patterns similar to those identified in previous research, comparisons can be made by cross-referencing existing inclinometer data that displays distinct deformation and hydraulic conductivity profiles. Upon reviewing the inclinometer monitoring data from the 24 landslide sites, it was observed that 14 of them have clear records of sliding. These sites include the Caoling, Wanda, Yixing, Songmao, Xinjiayang, Longhua, Hongcaiping, Wushe, Huayuan, Baolong, Lantai, Kanjiao, Taipingshan, and Dayuling landslide sites. Therefore, the inclinometer data from the 14 sites were overlaid with the hydraulic conductivity distribution charts estimated by the HCPI model. Upon comparison, it was observed that for 12 inclinometer boreholes, there were clear interfaces of significant changes in hydraulic conductivity values corresponding to sliding depths. Figure 7 exemplifies the comparison results for the Longhua landslide site. The interrupted red line of Figure 7, showing significant differences in hydraulic conductivity values above and below the depth of 44 m, coincides precisely with the sliding depth recorded by the inclinometer. The segment above a depth of 44 m also exhibited higher permeability than the segment below. Overall, the average hydraulic conductivity value differed by two orders of magnitude. The average hydraulic conductivity values in the upper segments were greater than 10⁻⁶ m/s, indicating potential groundwater accumulation at the interface, leading to increased pore water pressure and decreased slope stability.

Furthermore, at the Yixing and Huayuan landslide sites, the connection between the predicted sliding depth and the changes in hydraulic conductivity estimated by the HCPI model was less distinct for two of the inclinometer boreholes. Further examination of the inclinometer data at these two sites revealed S-shaped displacement curves, as shown in Figure 8, which differed from the typical significant displacement at a certain depth. This implies that the inclinometer may have experienced compression caused by thick backfilled soil layers, thin fractured rock layers, shear zones, or heavily weathered rock formations. These conditions likely led to subsidence and negative frictional forces on the inclinometer, producing irregular S-shaped buckling patterns. Additionally, irregularities in the S-shaped curve patterns may also arise from inadequate backfilling during inclinometer installation, as indicated by inconsistencies in multiple measurements of S-shaped curve patterns.

In summary, the comparison of continuous hydraulic conductivity distribution diagrams per meter with borehole depth data from 14 landslide sites, along with inclinometer displacement data, reveals a significant correlation. Specifically, the observed deformation at 12 of these landslide sites closely aligns with the model’s estimated sliding results. However, for two landslide sites, direct comparison was not feasible. Overall, the comparative results are generally consistent, verifying that the developed permeability estimation model can effectively predict potential sliding surfaces.

4.7. Establishment of Identification Rules for Sliding Surface Locations

To more accurately estimate the potential sliding surface locations in landslide areas, this study integrates hydraulic conductivity profile information with literature-recommended weak sections of core samples related to the formation of sliding surfaces [10,33,50,51] and groundwater level data [32,33]. This newly proposed approach led to the establishment of an evaluation rule for identifying potential sliding surfaces. The evaluation method and steps are shown in Figure 9. First, it is necessary to determine whether the hydraulic conductivity profile indicates the presence of a rock layer with an average hydraulic conductivity value greater than 10⁻⁶ m/s and a thickness of more than 2 m. If this condition is met, the process can proceed to the following evaluation step. The evaluation items can be divided into three categories, with each item’s evaluation criteria described as follows:

• The magnitude of hydraulic conductivity variation:

If the upper section of a rock mass interval exhibits greater permeability than the lower section, groundwater could gather in the more permeable upper portion of the rock formation. The greater the difference in permeability between the upper and lower sections, the higher the likelihood that water will concentrate in the more permeable upper section, thereby adding more groundwater weight to the upper rock layer. This can reduce the shear strength of the rock layer and lead to rock mass sliding. Therefore, this concept can be used as a basis for weighting the likelihood of sliding in the strata. If the permeability difference between the upper and lower rock layers falls within one to two orders of magnitude, the capacity for water accumulation is low, leading to a weighted score of one. If the difference increases to between two and three orders of magnitude, the water accumulation capacity is higher, resulting in a weighted score of two. When the difference exceeds three orders of magnitude, the water accumulation capacity is at its highest, and a weighted score of three is assigned.

2.

Presence of weak rock mass materials:

The occurrence of deep-seated sliding is often related to the degree of weakness in the properties of the rock material [10,33,50,51]. This study summarized the material properties of sliding surfaces from the 24 landslide sites and found that the materials at the sliding surface typically included shear zones with gouge, highly weathered slate or schist, and water-sensitive shale layers. Therefore, if the core sample contains ‘shear zones with gouge’, ‘highly weathered slate or schist’, or ‘shale layers’, each is given a weighted score of one point.

3.

Position of the groundwater table:

Groundwater can induce weak layers in the strata to become sliding surfaces [32,33]. Therefore, if the potential sliding surface is located below the normal groundwater table, it is assigned a weighted score of one point.

Following the scoring criteria outlined earlier, this study calculated the sliding potential score for each identified sliding position across 12 landslide sites with documented sliding activity. This process yielded data on the locations of sliding surfaces, hydraulic conductivity values for both the upper and lower sections of the rock mass, and scoring outcomes for the 12 borehole drilling records. As shown in

Table 10. Sliding potential scores for each sliding position of 12 landslide sites.

Name of Landslide Site (Borehole No.)	Sliding Surface Depth (m)	K in the Upper Rock Formation (m/s)	Difference in K Between Upper and Lower Rock Formation (m/s)	Score for Permeability Difference	Score for Shear Zone with Gouge	Score for Highly Weathered Slate or Schist	Score for Shale Layer	Score for Position of Groundwater Table	Overall Score
Caoling (CH-04)	7	1.6 × 10−5	1.19 × 102	2	-	-	1	-	3
Wanda (CH-09)	33	1.45 × 10−5	1.11 × 102	2	1	1	-	-	4
Songmao (BH-03)	21	6.75 × 10−6	5.63 × 101	1	1	1	-	-	3
Xinjiayang (BH-09)	25	2.35 × 10−6	2.61 × 101	1	1	1	-	-	3
Longhua (CH-03)	41	1.50 × 10−6	1.71 × 102	2	1	-	1	-	4
Hongcaiping (EH-05)	20	7.38 × 10−6	9.79 × 101	1	1	-	1	-	3
Wushe (EH-06)	31	2.87 × 10−6	1.36 × 101	1	1	1	-	-	3
Baolong (FH-05)	17	2.18 × 10−6	4.42 × 102	2	1	-	-	-	3
Lantai (IH-13)	21	1.67 × 10−6	7.63 × 100	-	1	-	1	1	3
Kanjiao (HH-03)	14	2.25 × 10−5	2.73 × 102	2	1	-	-	-	3
Taipingshan (IH-23)	27	1.33 × 10−5	5.19 × 101	1	1	1	-	-	3
Dayuling (MH-01)	46	1.03 × 10−5	1.07 × 102	2	1	-	-	1	4

, the sliding potential scores of the 12 existing sliding sections all exceed three points, and all containedweak layers in the core samples. Therefore, this study concludes that if the sliding potential score of a rock layer section exceeds 3 points, it should be considered a potential sliding surface section. According to this conclusion, if future sites without installed inclinometers or sites where inclinometers have not yet detected signs of sliding are encountered, the evaluation rules proposed in this study can be applied. If a specific rock layer section receives a total score greater than 3 points following the assessment, it indicates a higher likelihood of that section generating a sliding surface in the future. This allows for the advance prediction of the potential sliding surface location.

4.8. Application of the Evaluation Approach—Prediction of Potential Sliding Surfaces

This study has developed an evaluation method for rapidly identifying potential sliding surface locations. This method can also be applied to estimate the potential depths of sliding surfaces in the remaining ten landslides, where no sliding has been detected yet due to the short monitoring period. Through the calculation process shown in Figure 9, a total of 12 potential sliding sections were identified in 9 landslide sites. The depths of each potential sliding surface, hydraulic conductivity values for the upper and lower sections, and scoring conditions of each potential sliding surface in each landslide site are summarized in

Table 11. Sliding potential scores for each sliding position of 10 landslides with no sliding records detected.

Name of Landslide Site (Borehole No.)	Sliding Surface Depth (m)	K in the Upper Rock Formation (m/s)	Difference in K Between Upper and Lower Rock Formation (m/s)	Score for Permeability Difference	Score for Shear Zone with Gouge	Score for Highly Weathered Slate or Schist	Score for Shale Layer	Score for Position of Groundwater Table	Overall Score
Tengzhi (FH-13)	16	1.48 × 10−5	2.29 × 101	1	1	1	-	-	3
Tengzhi (FH-13)	49	2.78 × 10−6	3.87 × 101	1	1	1	-	-	3
Tengzhi (FH-13)	69	4.86 × 10−6	5.04 × 101	1	1	1	-	1	4
Jilou (FH-21)	45	3.59 × 10−6	4.83 × 101	1	1	-	-	1	3
Chaozhouhu (KH-01)	24	3.47 × 10−5	6.39 × 102	2	1	-	-	1	4
Daguan (JH-27)	46	4.54 × 10−6	1.42 × 102	2	1	-	-	1	4
Nanshikeng (KH-11)	10	7.11 × 10−6	2.14 × 102	2	1	-	-	-	3
Yanliao (NH-21)	7	3.83 × 10−6	2.07 × 102	2	1	-	-	1	4
Fengshan (NH-15)	50	3.55 × 10−6	6.18 × 100	-	1	1	-	1	3
Gaoshi (QH-22)	21	6.23 × 10−6	1.93 × 102	2	1	-	1	1	5
Antong (OH-01)	-	-	-	-	-	-	-	-	-
Dawu (QH-13)	14	6.09 × 10−6	1.96 × 101	1	1	-	1	-	3
Dawu (QH-13)	48	6.04 × 10−6	2.15 × 102	2	1	-	1	-	4

. The results show that the sliding surface estimation method designed in this study can identify relatively less stable sliding surfaces in nine of the ten landslide sites, and these sliding depths are more likely to develop into sliding surfaces in the future.

Based on the proposed identification rules, Antong is the only landslide site where no potential sliding sections were identified. According to the rock core photos and core records of the landslide site, it was found that Antong lacks easily sliding-prone strata materials, such as shear mud zones and highly weathered strata. As a result, the identification method did not yield scores for the strata materials, leading to sliding potential scores for the sliding sections that were below 3 points. This results in the conclusion, based on the gathered data, that there is no risk of sliding. Consequently, the geological conditions at this landslide site are relatively more stable compared to the other nine sites.

5. Conclusions

This study proposes a preliminary and efficient assessment method to predict the potential slip surface depth in landslide areas using geological characteristic data and the developed rock mass permeability estimation models, thereby reducing investigation time and economic costs. It also seeks to facilitate early preparation and the formulation of remediation strategies in disaster prevention efforts, ultimately reducing the occurrence probability of slope disasters. The principal findings can be concluded as follows:

• A novel permeability estimation model (HCPI model) applicable to the highly disturbed geological formations of landslide sites has been established using six geological characteristic factors (RQD, DI, GCD, LPI, FA, and FD). This HCPI model, with a high R² value (0.895) and passing statistical tests, can be used to generate hydraulic conductivity profiles.
• By comparing the disturbed rock mass permeability estimation model “HCPI” and the non-disturbed rock mass permeability estimation model “NHCB2”, it is implied that choosing a geologically compatible estimation model is crucial while estimating hydraulic conductivity in the geological environment of mountainous areas.
• The concept of using abrupt changes in hydraulic conductivity data to estimate the depth of potential slip surfaces in landslide areas is feasible and has been confirmed by 12 landslide cases. According to the investigated landslide sites, the sliding surface occurred within a specific depth range of the strata, where the hydraulic conductivity of the upper layer was greater than that of the lower layer by one to three orders of magnitude. Additionally, the hydraulic conductivity of the upper layer is typically greater than 10⁻⁶ m/s.
• An identification rule predicting sliding surface locations has been established through three criteria: the magnitude of hydraulic conductivity variation, the presence of weak rock mass materials, and the position of the groundwater table. This identification rule has been applied to ten landslide sites to seek zones with a high potential for sliding, which can be used as valuable information for slope disaster prevention management.
• Since many factors may control the hydraulic conductivity of fractured rocks, the HCPI model is limited in predicting hydraulic conductivity from the observed range of the composite index HCPI and the collected lithologies. Due to the limitations, reliable hydraulic conductivity may be confined to 10⁻¹⁰ m/s to 10⁻⁴ m/s and applicable to specific lithologies (as shown in Table 1). It should also be noted that hydraulic conductivity prediction for non-deep seated landslide sites should be carefully inspected for reasonability.
• Finally, the HCPI model was constructed based on sedimentary and metamorphic rock data samples, but no samples were examined from igneous rocks. Future work can include igneous rock data and continue collecting more landslide data for analysis and validation, enhancing the model’s reliability and practical application value.