Assessment Rainfall-Induced Landslides Using Arbitrary Dipole–Dipole Direct Resistivity Configuration

Abstract

Landslides are one of the primary geological disasters posing significant threats to life and property. Strengthening the monitoring of rainfall-induced landslides is, therefore, crucial. The Direct Resistivity (DC) method can accurately map the subsurface electrical resistivity distribution, making it an essential tool for predicting the position of the slide face. However, when conducting landslide surface DC surveys, various undulating terrains such as ridges and steep slopes often pose accessibility challenges. In such topographies, conventional regular grid measurements become very difficult. Additionally, when the terrain is highly undulating and complex, interpreting apparent resistivity data can lead to erroneous results. In this study, we propose using the DC method to monitor rainfall-induced landslides. By moving away from traditional device setups and utilizing an arbitrary dipole–dipole observation system, we aim to improve efficiency, enhance data resolution, and reduce costs. The resistivity of the slope was found to change significantly during the incubation, formation, and development of a landslide in physical model experiments. Furthermore, the feasibility of our proposed method for assessment rainfall-induced landslides was illustrated by a real case study in South China.

1. Introduction

Rainfall-induced landslides are major geologic disasters that cause significant losses to people’s lives and properties. The real-time assessment of landslides is crucial for disaster prevention and mitigation. Various techniques have been developed for landslide assessment. Traditional methods rely on geological surveys [1,2,3]. However, observations at discrete sites are restrictive in temporal and spatial scales and cannot accurately monitor rainfall-induced landslides.

In recent decades, remote sensing technology has been extensively applied for landslide assessment. Synthetic Aperture Radar (SAR) with numerous operational systems onboard satellites [4,5,6] and aircraft [7,8] has become an effective and valuable tool for mapping and quantifying geomorphological changes. It achieves high spatial resolution and provides all-weather, all-time observations, making it suitable for assessment rainfall-induced landslides. However, due to high costs, remote sensing technology is not widely used in many mountainous areas [9,10]. More importantly, almost all of these technologies are restricted to surface observations and cannot monitor subsurface movements of landslides, particularly changes in soil moisture during the formation of the slide face.

As a high-efficiency and low-cost nondestructive detection technology, the geophysical direct resistivity (DC) method offers a new approach for assessing rainfall-induced landslides [11,12]. It involves injecting an electrical current into the ground through a pair of electrodes and measuring the resulting potential differences with other pairs of electrodes. The data collected are used to create a subsurface resistivity distribution, which can indicate different geological and hydrological conditions [13,14,15]. Rainfall generally increases the water content of underground soil, leading to changes in soil resistivity. Studying these resistivity changes is useful for tracking the sliding surface and the movement of groundwater [16,17]. This information aids in the risk analysis of natural hazards caused by landslides.

Landslides generally occur in mountainous areas; traditional ground geophysical surveys often require the establishment of a manual survey grid, which is a laborious field task with low efficiency and high cost. In mountainous and forested areas with poor line of sight conditions, few national control points that are far from the work area make it nearly impossible to determine the coordinates of electric observation points using traditional theodolites [18,19,20]. Additionally, when the terrain is highly undulating and complex, interpreting apparent resistivity data can lead to erroneous results. Many scholars have conducted research on how to mitigate the effects of undulating terrain. A common approach is to use numerical simulations to apply topographic corrections to observational data by accounting for the pure topographic response [21,22]. Topographic correction methods have a certain effect on mitigating the impact of terrain. However, they can only completely eliminate the influence of topography when the subsurface electrical properties are homogeneous. To overcome this issue, inversion with topography is essential. The arbitrary dipole–dipole configuration offers significant advantages in terms of flexibility, resolution, efficiency, and cost-effectiveness. Its ability to adapt to complex terrains and specific monitoring needs makes it a valuable tool for a wide range of geophysical applications, particularly in the assessment and prevention of geological hazards like rainfall-induced landslides [23].

In this paper, arbitrarily placed electrodes are combined with unstructured finite element methods to achieve the incomplete Gauss–Newton inversion of arbitrary dipole–dipole apparent resistivity observation data under arbitrary terrain conditions (flat or undulating). This strategy enables the effective handling of measurement challenges posed by complex terrain, thereby enhancing the accuracy of landslide surface detection. Physical model experiments and a field case study were conducted to demonstrate the feasibility of the proposed DC configuration for assessing rainfall-induced landslides.

2. Methodology

To assessment rainfall-induced landslides using the arbitrary dipole–dipole direct resistivity configuration, the feasibility of dipole–dipole observations was determined through numerical simulations. The dynamic response characteristics of slope resistivity during the stable-to-unstable evolution induced by rainfall were studied using physical model experiments.

Arbitrary Dipole–Dipole DC Measurements

With the rapid development of GPS/GNSS (Global Navigation Satellite System) navigation and positioning technology [24] and the increasing maturity of China’s BeiDou Satellite Navigation System [25], the positioning accuracy of handheld devices is continuously improving [26,27]. This provides a new approach for setting up electrode grids in electrical exploration [28,29]. When conducting regional geophysical surveys, a flexible three-dimensional electrode arrangement can be adapted to the terrain and environmental conditions of the work area without the need to strictly follow a predetermined grid order.

In a dipole–dipole configuration, A and B are the current electrodes and M and N are the potential electrodes (Figure 1). The control equation for the direct current resistivity method with dual-electrode power supply can be expressed as:

$$\nabla ·\left(\sigma \nabla \phi \right)=-\mathrm{I}\left[\mathsf{\delta }\left(\mathrm{r}-{\mathrm{r}}_{\mathrm{s}}^{+}\right)-\mathsf{\delta }\left(\mathrm{r}-{\mathrm{r}}_{\mathrm{s}}^{-}\right)\right]$$

(1)

where φ represents the electrical potential, the supply current is I, the positive electrode position is ${\mathrm{r}}_{\mathrm{s}}^{+}$, the negative electrode position is ${\mathrm{r}}_{\mathrm{s}}^{-}$, and $\sigma$ represents conductivity. The forward problem is to solve the distribution of electric potential in a known region, given the conductivity and source distribution. Using finite element discretization to solve the region, this equation can be written in matrix form:

$$F\left(\sigma \right)\mathit{u}=\mathit{q}$$

(2)

u is a vector representing the potential distribution at the mesh nodes, F represents the forward Laplace operator, which is actually a symmetric and sparse matrix related to the mesh discretization and conductivity distribution, and q is a vector describing the source distribution.

We used the incomplete Gauss–Newton method [30] to realize inversion resistivity of the arbitrary dipole–dipole configuration. In any dipole–dipole configuration, selecting multiple sets of appropriate power supply current electrodes and corresponding receiving potential electrodes can greatly improve field observation efficiency, reduce observation costs, and enhance the resolution of the observation data.

In the DC incomplete Gauss–Newton inversion, the observed data d is generally a subset of the potential u at the mesh nodes; observations are made only at a limited number of positions. This can be expressed as:

$$\mathit{d}=Q{F}^{-1}\left(\mathit{u}\right)$$

(3)

In this context, Q is the mapping matrix from u to d. The goal of the inversion is to obtain the subsurface conductivity σ (or resistivity) distribution from the potentials d observed at these limited positions.

In order to verify the advantages of using arbitrary dipole–dipole configuration in landslide detection, we conducted numerical model tests. The model for the numerical study has dimensions of 107 m (length) by 40 m (depth). The profile is divided into two layers. The first layer is an irregular strip-shaped soil layer 107 m long and 11 m thick, and its resistivity varies with relatively low resistivity values. The second layer is a trapezoidal bedrock layer 98 m long and 29 m thick, with a resistivity of 1000 Ω·m. A total of 24 electrodes are arranged along the length of the profile (Figure 2).

We used arbitrary dipole–dipole, Wenner, and Schlumberger arrays to model the sensitivity of the landslide body at different rainfall moments. The resistivity values for the overlying soil layers are set to 100 Ω m, 50 Ω·m, and 10 Ω·m, respectively. The apparent resistivity profiles collected by the three arrays were subjected to inversion processing. The inversion results of the three arrays were then compared and analyzed (Figure 3). The root mean square (RMS = 1.2). From the simulated results, three arrays can all depict the electrical interfaces of the landslide body quite effectively. However, when the resistivity of the overlying soil decreases, the Wenner and Schlumberger arrays show lower sensitivity to changes in resistivity. In contrast, the arbitrary dipole–dipole array can better capture changes in resistivity, especially at the bottom of the slope. This indicates that under different soil resistivity values, the arbitrary dipole–dipole array provides a better characterization of the electrical interfaces of the landslide body (indicated by the red ovals in Figure 3).

3. Physical Model Experiment

We established the soil–rock interface slope model in the laboratory to simulate the rainfall-induced landslide process (Figure 4). In total, 24 electrodes were randomly distributed on the slope. The flow rate was maintained at approximately 15 mL/s. Rainfall was applied for 5 min intervals, after which it was suspended to allow for measurements until the slope was completely damaged. The original data were inverted to obtain a series of resistivity profiles. We used the DC method to repeatedly detect the resistivity of the underground medium in the landslide body, thereby obtaining the changes in resistivity values at different locations and times. A comprehensive analysis was then performed on the resistivity value changes and their time-lag characteristics in the landslide body.

The three main elements of a landslide are the landslide bed, the sliding surface, and the landslide body. Generally, the landslide bed does not slide and can maintain its original structure without deformation, resulting in relatively high resistivity values. The sliding surface is formed by the crumpling and grinding of nearby soil and rock, with a thickness ranging from a few centimeters to several meters. The resistivity value of the sliding surface is generally much lower than that of the landslide bed. The resistivity value of the landslide body is determined by its condition. If the landslide body is relatively fragmented, contains more soil, and has high water content, it will exhibit relatively low resistivity values; if it consists of large broken blocks with less clay content and poor water content, it will exhibit high resistivity values.

The results are shown in Figure 5. The initial resistivity is depicted in Figure 5a, indicating higher overall resistivity values in the absence of rain. After 40 min, an arc-shaped feature suspected to be the sliding face is evident (Figure 5b). Experimental findings demonstrate that the resistivity interface closely aligns with the actual position of the sliding face. Figure 5c shows a low-resistivity band with the left and right sides divided into two separate electrical bodies. At this point, a 2 mm-wide crack emerges between the 10th and 11th electrodes, signaling the onset of landslides. Then, the sliding mass has experienced significant displacement and deformation, with the widest part of the crack expanding to 2.5 cm, as shown in Figure 5d. The landslide event concluded after 128 min.

This experiment displays the area damaged by the landslide aligning with the discontinuous section of the resistivity profile during slope stability, which becomes increasingly pronounced under rainfall. These areas may represent weak points in the slope vulnerable to damage. The suspected sliding surface indicated on the resistivity profile before slope failure matches the actual slide face during failure, showcasing the remarkable accuracy of the DC method in predicting slide faces. During the formation of tensile cracks at the rear edge of the landslide, they manifest as low-resistance strips vertically. Over time with rainfall, this area expands horizontally from the soil–rock interface to the surface. Once the low-resistivity band reaches the surface and separates the left and right sides into independent electrical bodies, early warning signals should be raised.

4. Case Study

The study site is situated on Yuyao City, Zhejiang Province (Figure 6). Zhejiang Province is located on the southeast coast of China; due to its unique geographical location, complex geology, topography, and climate background, Zhejiang has become one of the most frequent regions for rainfall-induced landslides in China. According to statistics, over 82% of the landslides in the Zhejiang region are rainfall-induced landslides (soil landslides and debris flows) [29].

In the Zhejiang region, the main natural environmental factors controlling the occurrence of rainfall-induced landslides include stratigraphic lithology, Quaternary loose deposits (residual, colluvial, and alluvial layers), soil, land use, and topography (elevation, slope, aspect, and slope shape). Currently, there is still a lack of systematic or relatively complete regional data. This paper mainly analyzes the relationships between landslide distribution and stratigraphic lithology, soil texture, land use, and topography. Regarding stratigraphic lithology, areas with Tertiary basalt distribution have the highest landslide frequency per unit area, followed by Sinian volcanic rocks, granite, sandstone, sandy mudstone, Precambrian metamorphic rocks, Cambrian mudstone, muddy limestone, and Carboniferous sandstone and shale. Among various soil types, submerged paddy soil, coarse bone soil, and infiltrated paddy soil are the most prone to landslides. The distribution of landslides also varies among different land use types, with the highest landslide distribution per unit area occurring in terrace fields, drylands, tea gardens, wastelands, and forested areas. According to statistics based on 1 km×1 km grid units, the probability of landslides is highest at an elevation of 200–400 m, with over 95% of landslides occurring on slopes with a gradient of 5–15 degrees. The influence of slope shape on landslide distribution is also significant, with over 50% occurring on convex slopes and about 45% associated with concave slopes.

The survey line layout consists of three survey lines: Survey lines 1 and 2 run parallel to the direction of the landslide trend, while Survey line 3 is perpendicular to the landslide trend (Figure 7). In the results of the three survey lines, the following color-coded areas are observed: The blue area represents the Quaternary soil layer, with resistivity values less than 600 Ω·m. The yellow area above denotes the moderately weathered interface, with resistivity values ranging from 600 Ω·m to 1270 Ω·m. The red area indicates the complete bedrock, characterized by resistivity values exceeding 1800 Ω·m (Figure 8a).

Figure 8b reveals a low-resistance anomaly spanning 25–45 m horizontally along survey line 2. This anomaly may lead to a separation between the left and right sides, potentially triggering a landslide. Therefore, reinforcement measures should be implemented promptly. Outside the landslide body, the resistivity images of the soil only show higher resistivity at the surface. As the depth increases, the resistivity generally shows a monotonic decrease. The resistivity values of the soil inside the landslide body differ significantly from those outside the landslide body. At the position of the sliding surface of the landslide body, the resistivity values show stratification, with noticeable differences in resistivity values above and below the sliding surface. In the profile perpendicular to the sliding direction of the landslide body, the shape of the sliding surface is approximately arc-shaped or an inverted trapezoid. The sliding surface is deepest near the central position of the landslide body, and shallowest near the sliding walls on both sides of the landslide body. Before the landslide body is formed, there is no significant difference or change in the resistivity values of the soil layers above and below the sliding surface position, and there is no typical resistivity stratification at the sliding surface position of the landslide body. After the landslide body is formed, the resistivity values at the sliding surface position show noticeable changes at different periods. Above the landslide body, within the depth range from the surface to the sliding surface, the resistivity values of the soil layers exhibit significant differences, while the resistivity values of the soil layers below the sliding surface show smaller differences. Outside the landslide body, only the resistivity values of the surface soil layers show significant changes, whereas the resistivity values of the soil layers at depths of meters and meters do not exhibit significant differences.

To verify the results of DC method exploration, several boreholes were arranged at the locations of the aforementioned survey lines (

Table 1. Layer contrast of bored and DC method.

Borehole	Drilling Depth(m)	DC Depth(m)
Z1	4.5	-	Line 1
Z2	5	4.5
Z3	2.4	4.3
Z4	2.2	2.2	Line 2
Z5	2.7	2.1
Z6	5.1	6.2
Z7	1.4	-
Z8	3.5	2.7	Line 3
Z9	2.8	2.4
Z10	5.1	5.3
Z11	4.9	5
Z12	3.7	4.1
Z13	1.2	-

). The drilling results showed that the fully weathered bedrock surface is buried at a depth of 0–6 m, with significant undulations and a slope of 25–30°, which is generally consistent with the findings of the high-density resistivity method. This indicates that the high-density resistivity method is effective in the exploration of this landslide.

5. Discussion

The arbitrary dipole–dipole DC configuration is highly advantageous in subsurface investigations for its flexibility in electrode placement, which allows for tailored surveys to fit specific site conditions and objectives. It excels in providing high-resolution images and sensitivity to subtle subsurface variations, essential for detecting small-scale features and delineating geological structures. Its capability to adjust depth of investigation by varying electrode distances enhances its utility in probing deep targets. However, challenges include the complexity of data interpretation due to sensitivity to noise and lateral variations in resistivity, as well as the labor-intensive setup requiring precise electrode placement and connection. Additionally, signal attenuation with increasing electrode distance and sensitivity to electrode contact resistance are factors to consider, influencing data quality particularly in challenging terrains. Despite these challenges, its ability to deliver detailed subsurface images in complex environments, such as urban areas or landslide-prone regions, underscores its value when coupled with rigorous survey design and advanced data processing techniques.

Various parameters such as electrode spacing, soil moisture content, and rainfall intensity critically influence DC survey results in landslide assessment. Electrode spacing determines the depth resolution versus penetration depth, with smaller spacings offering higher resolutions at shallow depths. Soil moisture content directly impacts resistivity, with wetter soils exhibiting lower resistivity due to increased conductivity from water. Rainfall intensity affects how quickly soil moisture levels change, influencing resistivity readings and providing insights into potential landslide triggers. Understanding these parameters is essential for the accurate interpretation of DC data, enabling the effective assessment of subsurface conditions and early detection of landslide risks.

The DC method synergizes effectively with traditional landslide assessment techniques such as inclinometers, piezometers, and surface displacement measurements, augmenting their capabilities by providing deeper insights into subsurface dynamics. While conventional methods predominantly focus on surface and near-surface parameters like movement and pore-water pressure, the DC method introduces a crucial dimension through its ability to map subsurface resistivity variations. These variations offer nuanced indications of moisture distribution, material characteristics such as lithology and compaction, and the potential presence of critical slip planes within the geological strata. Integrating DC surveys with traditional assessments enhances the comprehensiveness of slope stability assessments, strengthens early warning systems by detecting precursory changes in subsurface conditions and ultimately supporting more informed decision-making in landslide hazard management. This integrated approach not only broadens the scope of landslide risk assessment, but also underscores the importance of leveraging diverse assessment techniques to mitigate geological hazards effectively.

6. Conclusions

The arbitrary dipole–dipole configuration in DC surveys demonstrates significant advantages in rainfall-induced landslide assessments. The laboratory and numerical model allowed for controlled experimentation and precise measurements, enabling us to systematically assess the performance of the arbitrary dipole–dipole configuration. The real case study further corroborated the advantages observed in the laboratory model, showcasing the practical applications and implications of our findings in a real-world setting. The findings from both the physical laboratory model and the real case study underscore the significant potential of the arbitrary dipole–dipole configuration in geophysical exploration. Its flexibility, high resolution, efficiency, and cost-effectiveness make it a versatile and powerful tool for a wide range of applications. In particular, its ability to adapt to complex terrains and provide detailed subsurface images enhances our capacity to monitor and mitigate landslide hazards.