Enhanced Boulder Detection in Subway Construction through 3D Cross-Hole Electrical Resistivity Tomography

Abstract

In subway construction, the presence of boulders can significantly impact excavation and tunneling processes. However, despite these challenges, an effective and reliable method for detecting boulders in advance has not yet been established. This paper presents a novel method for detecting and characterizing boulders using 3D cross-hole electrical resistivity tomography (ERT). The proposed technique involves the strategic deployment of multiple borehole electrodes, which work together to create a comprehensive three-dimensional resistivity model of the subsurface. This model allows for the identification and characterization of boulders, providing crucial information about their location and size. We demonstrate the efficacy of this approach in a physical flume experiment and a case study of subway construction, The findings from both the laboratory and field studies indicate that the 3D cross-hole ERT method is not only effective in detecting boulders and providing detailed information about their size and spatial distribution but also optimizes construction planning, reduces unexpected disruptions and additional costs, and enhances overall construction safety. The results highlight the potential of 3D cross-hole ERT as a valuable tool for geological assessments during infrastructure development.

1. Introduction

Boulders, defined as spheroidal weathering bodies of granite, are commonly encountered in coastal areas [1]. These boulders, which can reach diameters of up to 30 cm, are often embedded within soft sediments. Their presence can significantly impact tunnel boring machine (TBM) cutter tools and cutterheads during subway excavation, frequently causing construction delays and increased costs. As a result, boulders represent a substantial risk factor for shield tunneling projects [2,3,4,5]. Effective detection of boulders before the commencement of shield construction is essential for thorough planning and mitigation. Accurate preconstruction detection allows for the development of strategies to address potential challenges, ensuring both the safety and efficiency of the tunneling process. However, despite advancements in detection technologies, boulder detection remains a persistent global challenge [6,7]. The complexity of accurately identifying boulders, particularly in varying geological conditions and depths, continues to hinder efforts to mitigate associated risks and optimize construction operations.

The primary exploration methods currently employed for addressing the challenge of boulder detection in subway construction include geotechnical investigations and geophysical surveys. Geotechnical investigations, such as borehole drilling, provide detailed subsurface data but are time-consuming and expensive when conducted on a large scale [8]. Geophysical surveys, including electrical resistivity tomography (ERT), seismic refraction, and ground-penetrating radar (GPR), are effective for identifying anomalies in subsurface resistivity or seismic wave velocities that may indicate the presence of boulders [9,10,11]. Various studies have been conducted to improve the accuracy and efficiency of boulder detection methods [12,13]. During the construction of the Guangzhou metro in southern China in 2012, Dang conducted comprehensive geophysical tests and specialized research on boulder detection [14]. Over ten geophysical methods were carefully chosen to suit the subway construction environment, demonstrating the variety and adaptability of geophysical techniques in such complex settings. Geophysical methods offer noninvasive and rapid surveys but may have limited penetration depth or resolution in challenging geological conditions. The article suggests that geophysical methods conducted in boreholes may yield better results. Common geophysical methods in wells include borehole seismic tomography and borehole electrical resistivity tomography [15,16]. Compared to borehole seismic tomography, ERT can delineate subsurface anomalies based on variations in electrical resistivity without requiring an electric spark as the source, making it effective for identifying boulder locations [17]. However, the current cross-hole ERT method acquires the electrical resistivity profile between two boreholes, which is essentially a 2D detection method with significant limitations [18,19]. This 2D approach may not fully capture the three-dimensional nature of the subsurface anomalies, thus potentially overlooking critical details about boulder size and distribution [20].

In this paper, we propose a method that enhances the detection of boulders by arranging electrodes in boreholes and utilizing parallel electrical method technology for hole-to-hole electrical penetration. This unique data collection approach allows us to obtain a massive amount of data, significantly improving collection efficiency. By arranging a certain number of electrodes in multiple boreholes, we create a three-dimensional vertical observation system, enabling the acquisition of three-dimensional detection results between the holes. This method provides a more comprehensive and accurate characterization of the subsurface, improving the detection and assessment of boulders in subway construction environments.

2. Three-Dimensional Cross-Hole Electrical Resistivity Tomography

The ERT method involves injecting a steady current into the ground through two electrodes (one positive, one negative) placed on the surface or underground. This creates a stable current field. Due to the electrical differences between rock formations and geological anomalies, the observed current field distribution will vary. By recording the relevant parameters with a DC resistivity instrument, the apparent resistivity can be calculated. Changes in resistivity can then be used to infer geological anomalies underground. The cross-hole ERT detection method is a refined borehole detection technique that involves placing detection electrodes in boreholes to collect signals. By utilizing the resistivity differences between adverse geological bodies and the surrounding medium, it achieves the localization and identification of geological anomalies. In cross-hole ERT measurements, there are three observation configurations: dipole–dipole (AB-MN), bipole–bipole (AM-BN), and pole–tripole (A-BMN) [21].

In a dipole–dipole (AB-MN) configuration, the current and potential bipoles are placed in different boreholes (Figure 1a). In a bipole–bipole (AM-BN) configuration, the electrodes of each bipole are placed in different boreholes (Figure 1b). The electrode positions in one borehole are fixed with a constant electrode spacing. After measurements are taken, the electrode is moved to the other borehole for subsequent measurements. This process is repeated by selecting another fixed position with the same electrode spacing until all positions in the borehole are covered. Finally, the positions of the two drilling electrodes are interchanged, and the same process is repeated for the second measurement. The third array is known as the pole–tripole (A-BMN) configuration (Figure 1c), where the first current electrode moves along one borehole, and the second current electrode, along with the potential bipole, moves along the other borehole. In previous simulation studies on boulder detection, it was found that due to differences in the amount of data obtained from observations and the varying spatial distribution of electric fields, the spatial resolution of different device types can vary significantly. The A-M dipole array device can obtain strong observation signals but has relatively low spatial resolution. The spatial resolution of the A-MN tripole array device is greatly influenced by the distance between measurement electrodes (i.e., the MN spacing), making it difficult to determine scientific and reasonable parameters in advance for unknown strata, and it can only be controlled based on experience. The AB-MN quadrupole array device is easily affected by the current channeling effect, especially when there is a large range of low-resistivity layers near the electrodes, which influences the spatial distribution of the current and thus affects the detection results. In 2015, Liu proposed a bipole–bipole electrode configuration that has high boulder-detection resolution and sensitivity [22].

The 3D cross-hole ERT method involves placing electrode arrays in three or more parallel boreholes to obtain potential gradient data through cross-borehole measurements (Figure 2). Through inversion interpretation methods, 3D resistivity imaging of the region between the boreholes is performed to achieve 3D localization and identification of adverse geological bodies hidden within the rock mass. In the engineering practice of boulder detection in metro shield zones, the typical observation model of the 3D cross-hole ERT is shown in Figure 1. It involves a “perspective cross-borehole” observation mode with four parallel boreholes. Well 1, Well 2, Well 3, and Well 4 are four boreholes drilled vertically into the strata. By inserting ERT cables into 4 boreholes, the detection electrodes are dispersed in three-dimensional space. Leveraging the mutual constraints among boreholes and dense sampling points improves the precision and spatial resolution of data collection. The capacity to acquire extensive potential gradient information is a crucial feature of the 3D cross-hole ERT survey. It furnishes a rich data basis for high-resolution and detailed detection, contributing to mitigating inversion’s multi-solution aspects. Its imaging quality and spatial resolution surpass those of typical ground resistivity detection methods, while its spatial accuracy exceeds that of conventional 2D surveys.

The 3D Cartesian coordinate system is established for the drilling site coordinates. The adaptive grid is divided by the finite element numerical analysis method. The initial resistivity value $\rho$ of the grid element is given, and the potential field data is calculated according to Formula (1), and the result is taken as the forward theoretical value.

$${\displaystyle \frac{\partial }{\partial x}}\left({\displaystyle \frac{1}{\rho }}{\displaystyle \frac{\partial U}{\partial x}}\right)+{\displaystyle \frac{\partial }{\partial y}}\left({\displaystyle \frac{1}{\rho }}{\displaystyle \frac{\partial U}{\partial y}}\right)+{\displaystyle \frac{\partial }{\partial z}}\left({\displaystyle \frac{1}{\rho }}{\displaystyle \frac{\partial U}{\partial z}}\right)=-I\delta \left(\mathrm{x}-{\mathrm{x}}_0\right)\delta \left(\mathrm{y}-{\mathrm{y}}_0\right)\delta \left(\mathrm{z}-{\mathrm{z}}_0\right),$$

(1)

In the formula, ρ is the medium resistivity (Ω·m); U is the potential at any point in space (V); I is the excitation current (A); δ is the Dirac function; (x, y, z) is the space coordinate of the observation point; and (x₀, y₀, z₀) is the space coordinate of the excitation source.

To reconstruct the inversion image, the measured potential dobs are fitted with the forward theoretical value g(m), and the objective function is

$$S\left(m\right)=(d_{obs}-g(m\left){)}^T{W}_d\right(d_{obs}-g\left(m\right)),$$

(2)

where m is the resistivity parameter matrix, and Wd is the weight coefficient matrix. The objective function has no model constraints, which may lead to inversion failure.

Due to the large amount of potential field data, which is not conducive to the convergence of inversion data, the model parameter m needs to be modified many times during inversion, and the modification relationship is

$$(J^{{\rm T}}{W}_{d}J+\mathsf{\lambda }I)\Delta m=J^{{\rm T}}{W}_d(d_{obs}-g(m)),$$

(3)

where J is a Jacobi matrix, and λ is the damping factor.

When S(m) meets the given constraints, resistivity inversion is finished. Extract the resistivity value of each grid unit as the real value between the two boreholes to achieve resistivity imaging [23,24].

Compared with the above three types of devices, the AM-BN quadrupole array device has more prominent advantages for 3D cross-hole ERT detection: From the perspective of electrode array distribution, the power supply electrodes A and B of the AM-BN quadrupole array are located in different boreholes. This distribution facilitates current penetration through the strata between the boreholes, thereby reducing the impact of the current channeling effect and better meeting the “perspective cross-borehole” observation requirements of cross-hole. Since the measurement electrodes M and N are closer to the power supply electrodes in the same borehole, stronger observation signals can be obtained. In metro shield zones, the resistivity of boulders is relatively high, making them high-resistivity anomalies compared with the surrounding rock and soil media. The magnitude difference is significant (the resistivity of the surrounding rock is generally less than 500 Ω·m, while the resistivity of boulders is generally above 2000 Ω·m), allowing geophysical instruments to observe changes in the geoelectric field caused by this difference. This provides the physical basis for the resistivity method to detect boulders.

3. Experimental Tank Facility

To validate the detection effectiveness of 3D cross-hole ERT for identifying boulders, a physical model experiment was conducted using a hydraulic tank. The experimental setup was meticulously designed to simulate real-world conditions, ensuring the results would be applicable to practical scenarios. The physical model, as illustrated in Figure 3, was constructed with dimensions of 2 m in length, 1.8 m in width, and 0.8 m in height. The water temperature in the tank is maintained at 20 °C. This sizable model allowed for a comprehensive analysis of the 3D ERT method’s capability to detect boulders. Various materials were used to replicate different geological conditions, and multiple electrodes were strategically placed within the model to accurately capture the potential gradient data necessary for 3D resistivity imaging.

The resistivity and size parameters of each physical body are shown in

Table 1. Model parameters.

Model	Material	Resistivity (Ω·m)	Model Size (cm)
Background	Tap Water	1–16	/
Boulder	Concrete Block	2000–2500	12 cm

. The observation apparatus, depicted in Figure 4, utilizes porous electrode arrays constructed from Ethernet cables and PVC pipes. Each electrode string spans 4 cm with 16 channels. Four electrode arrays are designed and fixed with PVC pipes to maintain the consistent relative positions of the observation system. This setup ensures precise and reliable data collection by keeping the electrodes stable and correctly positioned. The use of Ethernet cables for the electrode arrays allows for robust signal transmission, while the PVC pipes provide a durable and stable structure to support the arrays throughout the experiment. By meticulously controlling the parameters and arrangement of the electrodes, the experiment aims to produce high-quality data that will facilitate a detailed analysis of the 3D ERT method’s effectiveness in detecting boulders.

In this physical model test, a 12 cm cubic cement block is secured with thin wires and suspended at the center of the observation system. Positioned 45 cm above the lowest electrode, its center aligns with the midpoint of a square formed by four “boreholes”. Using the first electrode of Hole 1 as the reference point, the coordinates of the cement block’s center are (0.3, 0.3, 0.3). The system operates on a 48V power supply for 0.2 s with a sampling interval of 50 ms, employing the AM-BN electrode configuration. This setup ensures that the electric current penetrates the test area effectively, enabling accurate detection of the cement block’s resistivity characteristics.

The experimental results, shown in Figure 5, reveal that the inversion results exhibit a background resistivity value of 2 Ω∙m in the model. Although the anomaly center is mostly positioned as specified in the model, it displays slight lateral expansion. At the center of the high resistivity anomaly, the resistivity value measures 113 Ω∙m, demonstrating the effectiveness of the 3D cross-hole resistivity imaging method in detecting high resistivity anomalies, such as isolated boulders. The experiment demonstrates the system’s ability to accurately capture and image the cement block’s presence within the observation area. These findings validate the effectiveness of the 3D cross-hole ERT method for detecting and characterizing subsurface anomalies, such as boulders, in practical applications.

4. Case Study

The study site is situated in Xiamen City along China’s eastern coast (Figure 6). Xiamen Island occupies a strategic position within the “Yanshan Fault Depression Zone in Eastern Fujian”, where it interfaces with the metamorphic belt along the coastal region of Eastern Fujian. This geological setting has led to a widespread distribution of granite across the area. Granite formations in Xiamen have been significantly influenced by multiple joint sets, resulting in their fragmentation into angular blocks. Over time, prolonged exposure to physical and chemical weathering processes has transformed these angular blocks into spherical rock masses known as granite spheroidal weathering bodies. These weathering bodies, colloquially referred to as “boulders”, are a distinctive and prominent geological feature within granite-rich regions. Their presence not only underscores the complex geological history of the area but also poses significant challenges in engineering and construction due to their variable sizes and resistivity characteristics. Understanding and accurately detecting these granite spheroidal weathering bodies are crucial for effective urban planning, infrastructure development, and environmental management in Xiamen City and similar geological contexts along China’s eastern coastline.

Specifically, the metro exploration test area, strategically positioned within a precisely delineated rectangular zone proximate to drill hole MIZ3-TGJ-18 along Haidi Road, spans the vital link between Gaoqi Station and Jimei Xuecun Station of Xiamen Metro Line 1. As depicted in Figure 7, this comprehensive testing zone encompasses four strategic drill holes—ZK1, ZK2, ZK3, and ZK4—each bored with a uniform diameter of 90 mm to ensure consistency in data acquisition. ZK1 delves 15 m deep, while ZK2 reaches 14 m, showcasing slight variations in penetration depths tailored to geological nuances. ZK3 and ZK4 extend even further, with ZK3 piercing to 16.75 m and ZK4 achieving a depth of 16.8 m, demonstrating the detailed attention paid to capturing the full extent of subsurface variations. The spacing between these holes is meticulously planned, with ZK1 and ZK2 separated by 16 m, ZK2 and ZK4 by 15 m, ZK3 and ZK4 by a closer 4.6 m, and a triangular arrangement among ZK1, ZK3, and ZK4 maintaining a consistent 12.4 m distance, providing a dense and comprehensive network for geological analysis. Notably, during drilling operations, ZK2 uniquely encountered a layer of boulders between depths of 11 m and 14 m, necessitating adjustments and highlighting the unpredictable challenges encountered in subway construction geology. In contrast, the remaining three boreholes progressed smoothly, further emphasizing the intricate geological makeup of the area and the importance of rigorous exploration prior to construction.

4.1. Line Layout

The electrodes are arranged in four boreholes with a polar distance of 0.4 m, forming a three-dimensional observation system. Three boreholes contain electrode strings, while B poles are placed in the fourth borehole. Each survey line consists of 32 electrodes, totaling 96 electrodes across the system. The length of each survey line is 6 m, and data are collected using AM-BN configuration. After collecting data from each set of four boreholes, the entire observation system is raised by 5 m to ensure a 1 m data overlap until the target horizon is detected.

4.2. Result Analysis

In this region, the geological strata exhibit complexity with layers of varying thickness. Based on columnar data from borehole M1Z3-TGJ-18 near the testing site, the depth of the boulder ranges from approximately 12.9 m to 14.5 m. The stratification from top to bottom includes approximately 1.8 m of clay, followed by 11.5 m of residual sandy clay, and finally, weathered granite at the bottom. The groundwater depth varies from 0 to 1.5 m, with corresponding resistivity values ranging from 0 to 1 Ω·m for Quaternary overburden and strongly weathered granite layers, and from 60 to 120 Ω·m for slightly weathered granite.

The resistivity of the boulder is expected to match that of slightly weathered granite due to its location in loose residual soil and strongly weathered layers. This results in higher inversion resistivity values influenced by electrode proximity and varying groundwater conditions. Following inversion, 3D electrical resistivity results between boreholes are obtained, enabling the creation of horizontal resistivity slice maps at different depths. For instance, the depth slice map from 8 m to 15.2 m, depicted in Figure 8, shows inversion resistivity values ranging from 20 Ω·m to 190 Ω·m across the survey area. A significant high-resistance anomaly is observed between ZK4 and ZK2 boreholes at depths ranging from −11 m to −15.7 m. This anomaly exhibits resistivity values exceeding 80 Ω·m, centered approximately 7.5 m in the ZK4-ZK2 direction, interpreted as a solitary rock consistent with observations in the ZK2 borehole. Furthermore, the ZK3 borehole displays a high-resistance anomaly at depths of 14 m to 15.7 nm, albeit with a smaller anomaly range, potentially due to boundary effects at the borehole’s bottom.

The detection results partially illustrate the spatial distribution of underground boulders. Variations in resistivity between boulders and surrounding rock and soil layers stem from several factors, including residual soil heterogeneity, the composition of completely or strongly weathered rocks, differences in structural planes, variations in groundwater development, and the presence of high-resistivity PVC casing in boreholes. Furthermore, the complex underground electric field in urban areas significantly influences detection outcomes and the accuracy of inversion results. Utilizing 3D electrical resistivity tomography (ERT) facilitates comprehensive data acquisition and allows sensors to be positioned closer to target bodies. This approach enhances the resolution of electrical detection, enabling clearer delineation and characterization of subsurface anomalies such as boulders.

To further validate the results of the 3D cross-hole ERT, a measurement line was arranged in the area around borehole ZK2, which is known to contain isolated boulders. The boulder extends approximately 5 to 8 m to the north side of the measurement line. The line is 31 m long with a 1 m electrode spacing, using a total of 32 electrodes arranged in a single deployment. Due to the cement pavement on site, conventional copper electrodes, which are typically used, would be damaging and thus not suitable for use. Instead, bag electrodes filled with yellow clay were employed on site for coupling with the ground. Figure 9 shows the high-density DC resistivity profiling section. Within the shallow 3-m range, the resistivity values are greater than 3000 Ω·m, indicating high-resistivity zones corresponding to the cement pavement and its underlying layers. The resistivity distribution in the lower Quaternary loose layers is relatively uniform, with resistivity values around 800 Ω·m. At depths of −10 m to −12 m, there a high-resistivity anomaly (circled by red circle in the Figure 9) with resistivity values exceeding 3000 Ω·m. These anomalies are isolated and enclosed, with one having a relatively larger area, approximately 2 m in diameter, and the other with an anomaly about 0.5 m in size. Drilling verification confirmed that these two anomalies are indeed isolated boulders.

The influence of different geological environments and rock composition on ERT (resistivity tomography) results is complex and significant. In terms of geological environment, the distribution and content of groundwater, the porosity of soil and rock, and the complexity of geological structure all have an important impact on ERT detection results. The existence of groundwater can significantly reduce the resistivity of the medium and form a low resistivity anomaly area, especially in the aquifer or groundwater flow channel. At the same time, the larger the porosity of soil and rock, the easier it is to be filled by water or other conductive media and then change the resistivity distribution. Geological structures such as faults and folds may lead to the nonuniformity of resistivity distribution, providing important geological information for ERT detection. The difference in rock composition is also a key factor affecting ERT results. Rocks with different mineral compositions have different resistivity characteristics. For example, rocks with a high content of conductive minerals have lower resistivity, while rocks with a high content of insulating minerals have higher resistivity. In addition, the chemical composition of rocks, such as salt content, will also affect their resistivity. Rocks rich in salt usually show low resistivity. As the channels of groundwater and other conductive media, the cracks and pores in the rock will also reduce the resistivity of the rock and form an obvious low-resistivity anomaly area on the ERT image. To sum up, different geological environments and rock compositions have a significant impact on the ERT detection results by affecting the resistivity distribution of underground media. In the process of ERT detection, these factors should be fully considered, and comprehensive analysis and judgment should be carried out in combination with the knowledge of geological exploration, petrology, geochemistry, and other disciplines so as to improve the accuracy and reliability of the detection results.

5. Discussions and Conclusions

Accurate detection of boulder quantities and sizes before shield construction is crucial for effective planning and risk mitigation. Early identification of potential boulders enables construction teams to make informed decisions regarding equipment use and excavation methods, thereby reducing the likelihood of unexpected obstacles and minimizing associated delays. Urban environments present unique challenges for traditional geophysical methods due to dense infrastructure, high-rise buildings, and complex subsurface geology. Interference factors, such as electromagnetic noise from power lines, vibrations from traffic, and the heterogeneous nature of the subsurface, can obscure valuable geophysical signals. Therefore, there is a pressing need for geophysical techniques specifically tailored to urban settings.

Geophysical methods, such as ground-penetrating radar (GPR) and seismic refraction, have limitations in urban environments. GPR, while effective for detecting nonconductive materials and providing high-resolution images, suffers from signal attenuation in conductive soils. Seismic refraction provides valuable data on subsurface layering and material properties but often struggles with detecting smaller or deeply buried boulders. In contrast, electrical resistivity tomography (ERT) offers several advantages, including the ability to detect deeper underground structures and effectively identify both conductive and nonconductive boulders. ERT’s strength lies in its ability to infer subsurface structures through resistivity measurements, which are relatively insensitive to variations in depth compared with other methods.

The 3D cross-hole ERT configuration has shown promising results in urban environments. By drilling holes near the target bodies and placing sensors within, this method significantly reduces external interference, leading to more accurate and reliable measurements. Physical model tests and field detections confirm the effectiveness of 3D cross-hole ERT in detecting boulders and suggest its potential for mapping other subsurface features, such as utility lines, voids, and groundwater distribution.

However, despite its advantages, the research on 3D cross-hole ERT in urban environments is still in its infancy, and several research gaps remain. Firstly, the resolution and accuracy of the method can be further improved, especially in complex geological settings with high levels of heterogeneity and interference. Secondly, the cost and time associated with drilling boreholes for 3D cross-hole ERT can be prohibitive for some urban projects, necessitating the development of more cost-effective and efficient survey designs. Furthermore, the integration of ERT with other geophysical methods, such as seismic imaging and ground-penetrating radar, could provide a more comprehensive understanding of the subsurface, but this multimethod approach is still underexplored.

Future research should focus on addressing these gaps by developing advanced inversion algorithms capable of handling heterogeneous and noisy data, optimizing borehole drilling strategies to reduce costs and time, and exploring the synergies between ERT and other geophysical techniques. Additionally, more extensive field validation studies are necessary to demonstrate the reliability and applicability of 3D cross-hole ERT in various urban environments. With these advancements, 3D cross-hole ERT has the potential to become a standard tool in urban geophysical surveys, offering critical information for infrastructure planning, construction, and maintenance. Continued development and refinement of this technique will contribute significantly to improving the safety and efficiency of urban excavation and construction projects.