Research on Tunnel Boring Machine Tunnel Water Disaster Detection and Radar Echo Signal Processing

Abstract

This study focused on the detection of water inrush in tunnels excavated by full-section hard rock tunnel boring machines (TBMs) and employed ground penetrating radar methods for conducting research on radar signal processing algorithms. The research demonstrates that conventional techniques are inadequate for eliminating the interference of TBM equipment on radar signal propagation. This study employs a radar antenna array method for signal transmission, utilizing a wavelet double-threshold filtering algorithm and wave propagation theory to suppress clutter. These methods exhibit strong signal reception capabilities and are effective in eliminating 13.1% of the direct wave components. The adoption of a novel, efficient radar signal imaging algorithm simplifies the imaging process. Results of verification indicate that the synthetic aperture algorithm, enhanced with cross-correlation calculation, yields the optimal imaging effect. This investigation, which was conducted in conjunction with the construction of a diversion tunnel in a specific region, has confirmed the applicability of the ground penetrating radar method for the detection of water inrush in TBM tunnels by conducting a comparative analysis of the direct wave removal algorithm and the integration of the optimal imaging algorithm. The innovative application of ground penetrating radar within TBM tunnels, along with a targeted technology to mitigate signal interference from metal equipment, has led to the selection of an appropriate algorithm for both signal processing and imaging. This approach offers a novel solution for the detection of water source disasters in TBM tunnels.

1. Introduction

When a full-face hard rock tunnel boring machine (TBM) is constructed in water-rich geology, water and mud inrush disasters are likely to occur at the tunnel face, and water leakage is also frequently observed within the tunnel post-support installation [1,2]. Therefore, it is imperative that both engineers and researchers refine traditional geological prediction methods; concurrently, the introduction of an innovative detection technique is essential to accurately detect the location, scale, and nature of unfavorable geology in the tunnel crossing area [3,4,5,6]. During complex geological construction, non-destructive testing technology, such as the ground penetrating radar (GPR) technique, can provide clear survey results over a broad area for the advanced geological prediction of tunnels and the identification and processing of underground targets. It is also applicable to detecting short-distance karst caves and water-rich broken rock masses without causing structural damage to the rock mass being examined. This technique constitutes a significant aspect of the issue of water inrush encountered in the tunnel [7,8,9].

During the study of ground penetrating radar methods, Li et al. [10] gained preparation time for the construction unit by detecting the water-bearing fault in the Jiaozhou Bay subsea tunnel project. Liu et al. [11] analyzed the relationship between ground penetrating radar signal attributes and the karst adverse geological phenomenon. However, because of the ultra-wideband characteristics of the electromagnetic waves emitted by ground penetrating radar, numerous interference signals are received. Consequently, the analysis and processing of radar signals become difficult, and even effective data can be obscured, leading to the misidentification of unfavorable geological bodies and threatening the safety of tunnel construction and operation [12,13]. Therefore, selecting and developing methods for a radar signal analysis and processing are particularly important.

Scholars internationally have contributed significantly to the application of the ground penetrating radar (GPR) method in the field of water exploration in TBM tunnel excavation. Professor Jürgen Adam’s research in Germany enhances the detection capabilities of the GPR system in complex underground environments, significantly contributing to its application in tunnel engineering. Dr. Umberto Tammaro of Italy has performed extensive research on integrating GPR with other geophysical methods for enhanced groundwater detection in tunnel construction. Dr. Scott J. Hagan’s research significantly enhances the accuracy and reliability of GPR in detecting water in TBM operations. Dr. Ronny S. Galindo-Torres from Australia employed innovative techniques for integrating multiple sets of GPR data to improve water prediction capabilities in TBM tunnel construction. Professor Maurizio Bruno’s work regarding the theoretical aspects of GPR wave propagation through inhomogeneous media provides a solid foundation for the application of GPR in TBM water detection.

In addition to the contributions of explanation made by the aforementioned scholars, several scholars have conducted extensive research regarding the analysis and processing of radar signals and algorithmic pre-processing of radar data. Yakov et al. [14] and Guillaume et al. [15] have significantly enhanced the interpretability of GPR signals to different extents through their in-depth research on clutter suppression. Vinicius Rafae Santos [16] significantly enhanced the detection effect of underground objects by combining radar data with time reversal technology (TRT). Yang et al. [17], Bao [18], Qin et al. [19], and Wang et al. [20], respectively, employed wavelet transform, adaptive filtering, hard threshold function, and shearlet transform data processing methods to remove clutter interference and noise from the signal, thereby enhancing the signal-to-noise ratio of the radar data. Liu and Li et al. [21] introduced complex signal analysis technology into the study of ground penetrating radar for water body detection, extracting multiple parameters for a more comprehensive assessment.

Within the realm of water-rich geology detection in TBM tunnel excavation, advanced prediction technology is frequently utilized, including the seismic wave method (TST) [22] and the complex frequency conductance method (CFC) [23,24], among others. Nevertheless, challenges include demanding data analysis expertise, time-consuming processes, and the necessity for sophisticated data correction methodologies. In this study, the ground penetrating radar (GPR) method is utilized for the advanced lag detection of water inrush disasters in TBM tunnels. The detection creatively employs antenna array technology within multi-antenna systems. In processing radar signals and data, this study initially analyzes the characteristics of underwater electromagnetic signals, then extracts useful data from the noisy signal using the wavelet transform method, leveraging the benefits of the wavelet double-threshold filtering method for denoising. This study forms an algorithmic approach with a better signal processing effect from the advantages of offset-free autocorrelation synthetic aperture imaging technology, replicates its application, and applies it to actual engineering on-site. Ground penetrating radar has been utilized in the detection of underground pipelines and road defects in previous studies [25]. This study combines common signal processing methods with specific techniques for addressing signal clutter, studying the challenges of radar detection and signal processing under TBM conditions. The innovative employment of the high-efficiency advantage of radar detection in advanced water detection for TBM tunnels, along with the adoption of the most suitable signal processing algorithm, thereby offers a novel alternative for ensuring the efficiency and safety of TBM tunneling in water-rich strata.

2. Electromagnetic Signal Characteristics of TBM Water Exploration

The ground penetrating radar prediction method is primarily based on the differences in the dielectric constants of rock strata, with the electrical parameters of the common media listed in

Table 1. Electrical parameters of common dielectrics.

Medium	Conductivity S/m	Relative Dielectric Constant	Velocity/ (m·μs−1)
Air	0	1	300
Dry sand	10−7~0.001	2~6	212~122
Wet sand	0.001~0.01	10~30	95~54
Dry clay	0.1~1	2~6	212~122
Wet clay	0.1~1	5~40	134~47
Adhesive dry soil	0.01~0.1	4~10	150~95
Dry concrete	0.001~0.01	4~40	150~47
Wet concrete	0.01~0.1	10~20	95~67
Fresh water	10−6~0.01	81	33
Dry soil	10−4~10−3	4~10	150~95
Wet soil	0.01~0.1	10~30	95~94
Dry limestone	10−8~10−6	7	113
Wet limestone	0.01~0.1	8	106
Sludge	0.001~0.1	5~30	70
Dry granite	10−8~10−6	5	134
Wet granite	0.001~0.01	7	113

[26].

It can be seen from Table 1 that water content is one of the main factors affecting the dielectric constant of rocks, and the dielectric constant of rock masses is positively correlated with water content. That is, the greater the water content of rock masses, the greater the dielectric constant. Among the commonly used detection methods, electromagnetic methods are more effective in detecting water-related disasters in tunnels.

The ground penetrating radar emits high-frequency electromagnetic waves (1 MHz to 1 GHz) through the transmitting antenna. Upon encountering underground targets with electrical differences, these waves are reflected and transmitted, then received by the receiving antenna to form a time-domain profile. The radar signal processing algorithm is utilized to analyze the data and determine the structure, properties, geometric shape, and spatial distribution characteristics, and subsequently to distinguish the distribution of and changes in water-rich zones within the geological formation. The operational record of the ground penetrating radar is depicted in Figure 1.

When the ground penetrating radar is applied to the TBM tunnel during the tunneling process, electrical disparities within electronic equipment, the depth of the underground target, and the attenuation of electromagnetic waves, among other factors, will affect signal propagation within the geological medium. Therefore, it is essential to understand the principles of wave propagation and subsequently to accurately determine the location of water-rich geology within the complex radar signal data.

(1) Analyzing the amplitude and direction of the reflected electromagnetic wave reveals that the greater the disparity in electromagnetic properties across the dielectric interface, the stronger the wave reflected, and vice versa. When an electromagnetic wave transitions from a high-speed to a low-speed medium, the amplitude of the wave reflected is also reversed, and vice versa.

(2) Analyzing the spectral characteristics of the reflected electromagnetic wave shows that different structural features result in significantly different high- and low-frequency attributes of the reflected waves. Experimental observations indicate that geological features indicating water presence within the surrounding rock during detection exhibit reflection characteristics of low frequency and high amplitude, which are readily identifiable.

(3) Analyzing the morphological characteristics of coaxial reflected electromagnetic waves involves establishing a contour line that connects points of the same phase on the reflected waves from adjacent channels of the ground penetrating radar. When there is a fault or void within the rock mass, it causes a dislocation of the coaxial line. If the fracture extends unevenly across the rock mass, it can result in the local loss of the coaxial line.

2.1. The Reflection Characteristics of Radar Signal to Water Body

In a low-loss medium, energy dissipation is typically less than energy storage, allowing for effective detection using ground penetrating radar. Assuming a low-loss medium that is uniform, linear, and isotropic, the Maxwell equation for electromagnetic waves can be expressed in terms of the electric field as shown in Formula (1):

$$\nabla \times \nabla \times E+\mu \sigma \cdot \frac{\partial E}{\partial t}+\mu \epsilon \cdot \frac{{\partial }^{2}E}{\partial t^2}=0$$

(1)

The electric field expression of the electromagnetic wave in an unbounded uniform lossy medium, as shown in Formula (2):

$$E\left(r\right)=E_0{e}^{-jKr}$$

(2)

$E_0$ is the electric field intensity at the field source; r is the spatial coordinate.

$K=\beta -j\alpha$ (α is the attenuation coefficient and β is the phase constant).

Since the permeability ($\mu$) varies less within the medium, the wave impedance is predominantly determined by the relative permittivity. In the event of vertical incidence from a medium with a relative permittivity of ${\epsilon }_1$ to a medium with a relative permittivity of ${\epsilon }_2$, the power reflection coefficient R can be expressed as shown in Formula (3)

$$R=\frac{\sqrt{{\epsilon }_1}-\sqrt{{\epsilon }_2}}{\sqrt{{\epsilon }_1}+\sqrt{{\epsilon }_2}}$$

(3)

At normal temperature, the relative permittivity of soluble rocks (such as limestone, dolomite, etc.) within the stratum ranges from approximately 4 to 15. In contrast, the relative permittivity of the water medium is about 81. Consequently, the radar reflection signal is particularly strong at the interface between saturated limestone and water. At the aquifer interface, the phase of the reflected radar wave is 180 degrees out of phase with the incident wave.

2.2. Research on the Estimation Principle of Radar Signal to Water Content

The propagation speed of electromagnetic waves within a medium is predominantly determined by the formation’s dielectric constant. During the advance prediction phase of tunneling, the primary frequency of the antenna is generally low, ranging from 20 to 200 MHz. The formulas for calculating the dielectric constant and the wave speed are as shown in Formula (4):

$$\upsilon =\frac{c}{\sqrt{{\epsilon }^{\prime }}}$$

(4)

In the model experiments and field tests conducted by G.C. Topp et al., the empirical relationship between water content and the dielectric constant is established as shown in Formula (5):

$$\theta =-0.053+0.0292\epsilon -5.5\times 10^{-4}{\epsilon }^2+4.3\times 10^{-6}{\epsilon }^3$$

(5)

In most current ground penetrating radar (GPR) signal analysis software [27], the velocity (υ) can be determined by analyzing the test signal, which subsequently allows for the calculation of the relative dielectric constant of the anomalous body, and an estimation of the water content ahead can be made. As the water content within the rock mass increases, the amplitude of the electromagnetic reflection waves increases, resulting in a pronounced radar reflection signal. The predictive range of the GPR method is limited to a depth of approximately 20 to 30 m. Despite this limitation, it is effective for predicting water-rich faults, underground rivers, and other geological features ahead of the TBM face, as well as detecting water inrush post-support installation.

3. Radar Signal Processing Algorithm

3.1. Clutter Suppression of Fractional Wavelet Transform

In ground penetrating radar (GPR) signals, clutter significantly affects detection performance by mingling with the echo of the target object. This impact is particularly pronounced during TBM tunneling, where electronic equipment significantly perturbs the electromagnetic field. Traditional GPR first examines radar signal propagation theory and employs a single dipole antenna, resulting in broad transmitting and receiving beams. This approach leads to low antenna power gain, weak effective excitation and scattering signals detected, weak anti-interference ability, and deteriorating resolution with increased detection depth.

To mitigate these issues, antenna array technology is utilized, enabling the simultaneous operation of multiple antennas. This methodology involves sequential operations that can yield multiple distinct scans, with the capability to overlay these results, and simultaneous operations that facilitate the creation of a composite radar record. The application of this technology can improve the system’s signal-to-noise ratio and enhance the directional characteristics of the antenna. However, the efficacy of denoising and information extraction from the collected signals, which are inevitably affected by clutter, cannot be assured [28].

A wavelet transform [17] is a time-frequency domain method. As the spatial scale coefficient increases, the wavelet becomes more stable. Details can be filtered through the transformation of the window function, with minimal alteration to the original signal, and its order is adjustable, making it adaptable to complex environments. Ground penetrating radar (GPR) data undergo a wavelet transform, followed by the selection of spatial scales with high signal-to-noise ratios for signal reconstruction. Clutter interference can be extracted and processed [29], thereby isolating the echo signal of the target object.

The algorithm delineates the target signal echo within a specific range through time-frequency domain transformation, thereby enabling the removal of GPR clutter. This algorithm is capable of adjusting the fractional order, can accommodate variations within GPR data, and thereby achieves superior processing and analysis outcomes.

3.2. Radar Signal Den-Oising Processing

Noise present in ground penetrating radar (GPR) signals degrades the resolution of the informative content, obscures the identification of the informative signal, and hinders the accurate inference of the detection target’s shape. Therefore, signal denoising methods are utilized in the processing of radar data to enhance the signal-to-noise ratio within the data, thereby enhancing the interpretive accuracy of GPR data to a certain degree. The following sections review commonly utilized signal denoising methods.

3.2.1. Median Filtering

When applying the median filtering method to radar data, the neighborhood surrounding a central data point (referred to as a pixel) is first determined. Subsequently, the gray values of all data points within the selected neighborhood are ordered by magnitude. The median of these gray values is taken as the output value, thereby approximating the radar data value to its true value and, concurrently, isolated noise points are eliminated.

This method effectively suppresses noise points, thereby mitigating the impact of noise, and the implementation of the algorithm is relatively simple.

3.2.2. Wavelet Threshold Filtering

Wavelet threshold filtering [30] involves the concentration of signal energy into a few wavelet coefficients post the wavelet transform. An appropriate threshold must then be chosen to quantify the wavelet coefficients, thereby removing the noise components, retaining and enhancing the signal components, and achieving the desired filtering effect. A common threshold formula is $T_j=\sigma \sqrt{2\log \left(N\right)}/\log (j+1)$, where σ represents the variance of the mixed noise and N represents the length of the signal. This method includes hard and soft thresholding techniques, suitable for processing signals with varying levels of noise. In practice, it is essential to evaluate the denoising performance of both the threshold function and the wavelet basis in light of specific conditions [31].

3.2.3. F-X Predictive Filtering

The F-X domain predictive filtering algorithm [32] posits that coherent signals within the frequency-space domain are predictable, whereas noise is deemed unpredictable. Based on the criterion of similarity, the direction of the radar signal’s phase axis is quantified by its correlation coefficient using an orthogonal polynomial approximation. Subsequently, the radar signal is linearized and its trajectory is predicted in the spatial domain based on this correlation coefficient. Denoising is then finalized through an inverse transformation of these results.

The radar signal generally contains noise. The rationale for transforming radar signals from the time-space (T-X) domain to the frequency-space (F-X) domain is as shown in Formula (6):

$$Y_N=S_N+W_N$$

(6)

In Formula (6), $S_N$ is the effective signal of the F-X domain and the $W_N$ is random noise of the F-X domain.

3.2.4. Wavelet Double-Threshold Filtering

Considering the complexity inherent in TBM radar signals during tunnel excavation, an enhanced wavelet double-threshold filtering approach is employed to maintain the continuity of the signal and eliminate the fixed bias within the signal. In this study, the upper threshold is defined by the enhanced threshold formula $T_j=\sigma \sqrt{2\log \left(N\right)}/\log (j+1)$, and the lower threshold is set to a coefficient of k = 0.5, where j represents the number of decomposition levels [33]. In the application of double-threshold detection, as the signal must consistently surpass the primary threshold within a designated timeframe to validate the target, stringent detection criteria are applied to the system, thus improving the reliability of signal processing outcomes.

3.2.5. Comparison of Den-Noising Effects of Filtering Algorithms

Based on an advanced geological predictive analysis, a preliminary determination can be made regarding the presence of water-rich strata along the TBM tunneling path. However, the precise location of water-rich strata relative to the tunnel face must be ascertained through detection methods. In practice, once the TBM has excavated to the approximate area of the water-rich zone, the cutterhead ceases rotation, the machine retreats, a ground -penetrating radar (GPR) unit is mounted onto the cutterhead, and antenna array technology is utilized to emit signals into the forward geology, allowing for signal reception back at the tunnel face. The reflected signal is then further processed.

In this study, considering the actual field engineering context, simulations are conducted, employing a noise signal of comparable intensity to denoise the radar signal via the filtering algorithm. The resulting signal-to-noise ratios for the radar signals, both pre- and post-denoising with various methods, are detailed in

Table 2. Signal-to-noise ratio of filtering algorithm before and after denoising.

Algorithm Name	Initial Signal-to-Noise Ratio (dB)	Noise Signal SNR (dB)
Median filtering	7.3113	14.9003
The wavelet threshold for denoising	7.0529	17.6065
F-X prediction filtering	7.1948	22.7515
Wavelet double-threshold filtering	7.0529	21.8693

. The tabulated data enable a comparative analysis of the enhanced signal extraction efficacy following the application of the noise removal algorithm via filtering techniques.

The signal-to-noise ratio (SNR) in radar signals, a critical parameter, quantifies the ratio of signal strength to background noise intensity, commonly represented as a logarithmic scale in decibels (dB). The SNR serves as a pivotal indicator of radar system performance, impacting both the fidelity of radar signal processing and the radar’s detection capabilities. The definition of SNR is articulated as the ratio of signal power to noise power, mathematically expressed as shown in Formula (7):

$$SNR\left(dB\right)=P_s/P_n$$

(7)

Let $P_s$ represent the power of the signal, and $P_n$ represent the power of the noise. In practical applications, the signal-to-noise ratio (SNR) is often articulated in terms of a base-10 logarithmic expression, as shown in Formula (8)

$$SNR\left(dB\right)=10{\log }_{10}\left(P_s/P_n\right)$$

(8)

A high signal-to-noise ratio (SNR) indicates a signal that is distinct and readily detectable and interpretable, whereas a low SNR suggests that the signal may be obscured by noise, rendering it challenging to distinguish or recover the signal. Optimizing the SNR is critically important for enhancing radar detection capabilities and the precision of target recognition.

Upon the examination of the signal-to-noise ratios detailed in Table 2, it is evident that the effectiveness of typical signals has been enhanced by over 100% subsequent to denoising using the filtering algorithm. Among the filtering algorithms, the traditional median filtering method exhibits the least effective denoising, with a signal-to-noise ratio that is 103.80% greater than the initial value. Post-processing following F-X domain predictive filtering is characterized by a ‘clean’ signal, resulting in more comprehensive noise removal. However, this method also results in a signal-to-noise ratio that is 216.22% elevated compared to the pre-denoising value, and may lead to the removal of some deep, weak signals. Wavelet threshold filtering, while less effective in denoising, achieves a signal-to-noise ratio that is 149.63% above the pre-denoising value, yet it can remove most of the noise from radar data while retaining some deep, weak signals. Upon a thorough analysis, the wavelet threshold filtering method effectively addresses noise suppression within both the wavelet and time–frequency domains, thus providing superior results. Nevertheless, in the context of TBM detection within water-rich tunnel strata, theoretical and simulation analyses indicate that the initial signal remains consistent. With respect to the signal-to-noise ratio, the enhanced wavelet double-threshold method outperforms the traditional wavelet threshold filtering approach, resulting in a signal-to-noise ratio that is 210.08% elevated compared to the pre-denoising value.

3.3. Radar Data Imaging

3.3.1. F-K Migration Imaging

F-K migration imaging technology is capable of eliminating distorted images and radar diffraction waveforms present within radar echo signals. It restores radar reflection points to their true spatial coordinates and accurately reconstructs the image of the target object along with its actual spatial orientation, thereby mitigating the impact of diffractive phenomena on radar data processing. This advancement is crucial for enhancing the accuracy and reliability of radar data preprocessing in various applications, including geological surveys and non-destructive testing. Suppose the raw data are x (u, z = 0, t), z is the vertical axis, u is the horizontal axis, and t is the time, and assume x (u, z = 0, t) is the profile after the offset, after DFT transformation, as shown in Formula (9):

$$C(k_{\infty },z,w)=\iint x(u,z=0,t)x^{-j(k_{\infty }\infty +w_t)}dudt$$

(9)

When ground-penetrating radar (GPR) transmits and receives signals through a colocated antenna setup, resulting in identical transmission and reception paths, this results in a wave speed that is half the stratum’s propagation speed. This establishes the following relationship among the wavenumber components $k_{\infty }$ and $k_y$, and the angular frequency w, as shown in Formula (10):

$$\frac{w^2}{(v/2{)}^2}=k^2={k_{\infty }}^2+{k_y}^2$$

(10)

Subsequently, the original data are subjected to an offset operation, yielding the offset data. The F-K migration technique is then employed for a comparative analysis of the imaging data from a tunnel boring machine (TBM) engineering example, as depicted in Figure 2.

In comparison to the imaging display effect of the original data in Figure 2a, the F-K migration imaging display effect in Figure 2b is more pronounced, and the diffraction wave is significantly reduced. This enhancement in imaging clarity and the reduction of diffraction artifacts demonstrate the effectiveness of the F-K migration method in improving subsurface imaging quality. As illustrated in the figure, diffraction waves at sampling points 40 and 80 are effectively eliminated, with rapid computational performance. However, the method’s effectiveness in mitigating diffraction waves is less pronounced with respect to transverse and longitudinal variations, making it more suitable for media with a uniform distribution.

3.3.2. Rear-Direction Projection Imaging Algorithm

Let us designate the x-axis as representing the ground surface, with the relative permittivity (dielectric constant) of the subsurface material denoted as ${\epsilon }_s$. The transmitting and receiving antenna are aligned along the x-axis and transmit n-channel data. The coordinates of a point on the ground surface are given as (x, 0), and the coordinates of the subsurface point B are given as $(x_B,z_B)$. The reflection delay from point B to the k antenna is denoted as $t_{A,K}$, with the speed of electromagnetic waves in vacuum denoted as c. The relationship between these quantities can be mathematically expressed as shown in Formula (11)

$$t_{B,k}=\frac{2\sqrt{(x_B-x_k{)}^2+{z_B}^2}}{c/\sqrt{{\epsilon }_s}}$$

(11)

The radar echo data for point B corresponding to the k signal are given by $v_{B,k}=s_k(t=t_{B,k})$. The set of radar response values for point B across signals 1 through n is $\{v_{B,1},v_{B,2},...,v_{B,k},...,v_{B,n}\}$. Subsequently, by summing these values, we can achieve the imaging of point B, as shown in Formula (12):

$$P_B=\sum _{k=1}^n{V}_{A,k}$$

(12)

Subsequently, the imaging of the radar signal is accomplished through a traversal of every point within the GPR signal’s domain [34]. During this traversal, the two-way delay time t is computed for each point within the survey area relative to the radar antenna, thereby deriving the radar response value for each imaging point through the coherent accumulation of the respective echo signals. Subsequently, attenuation compensation and normalization are applied to reconstruct the image of the survey area. The flow of the back projection algorithm is illustrated in Figure 3.

It is evident that, as the process necessitates the consideration of every data point within the radar dataset, coherent superposition can introduce additional interference, resulting in a further distortion of the image. This phenomenon underscores the complexity of radar signal processing and the need for sophisticated algorithms to filter out unwanted signals and enhance the clarity of the final image.

3.3.3. Unbiased Autocorrelation of Synthetic Aperture Imaging

A model for ground penetrating radar (GPR) imaging is established and depicted in Figure 4, where x represents the horizontal direction, and z indicates the vertical direction. With air conductivity denoted by ${\epsilon }_1$ and the relative dielectric constant as $u_1$, the subsurface medium conductivity is ${\epsilon }_2$, and its relative dielectric constant is $u_2$. The distance from the GPR transmitter antenna to the ground surface is denoted as H, and the signal $s_i(x_i,t$ is acquired through sampling along the x-axis.

When the point of interest is located within the stratum, let it be denoted as $A(x_A,z_A)$. The imaging process involves a synthetic aperture length of $L_B$ and a corresponding number of samples $N_B$. If the sampling point $j(x_j,-H)$ lies within the aperture, the reflected data from point A are received at point j via the refraction point $G(x_G,0)$, resulting in the following relationship, as shown in Formula (13):

$$\frac{{z_A}^2+(x_A-x_G{)}^2}{(x_A-x_G{)}^2}\times \frac{(x_G-x_j{)}^2}{H^2+(x_G-x_j{)}^2}=\frac{\sqrt{{\epsilon }_2}}{\sqrt{{\epsilon }_1}}$$

(13)

The delay matrix, denoted as $T_B$, can be derived, thereby enabling the extraction of the reflection delay and amplitude for each data point within the aperture. This allows for the reconstruction of MM data points within the aperture for imaging purposes. The principle underlying synthetic aperture radar (SAR) is the delay-and-sum concept, which inherently incorporates contributions from other data points and is thus susceptible to inadequate clutter suppression, significantly influencing the imaging outcome.

By correlating the focal point within each signal of the geological radar, the autocorrelation for each signal, corresponding to a specific delay, is computed. This algorithmic approach enhances imaging quality by strengthening the signal of pertinent data points, while concurrently attenuating the signal from extraneous data points. Considering the need to balance signal integrity with subsequent signal processing requirements, the autocorrelation algorithm may incorporate an unbiased distance metric to ensure compliance with the uniform standards required for subsequent radar signal preprocessing stages, as shown in Formula (14):

$$I_c=\frac{{\sum }_{n=0}^M{D″}_n}{M}$$

(14)

The post-test analysis, as illustrated in Figure 5, demonstrates that owing to the inherent clutter interference associated with the backward projection algorithm, the imaging quality was markedly enhanced as a result of incorporating an autocorrelation calculation. Clutter is notably absent in the vicinity of the water-filled crack, and the diffraction waves at sampling points 40 and 80 have been entirely mitigated.

3.3.4. Comparative Analysis of the Imaging Effects

For GPR signals within the water-rich areas of TBM tunnels, following the filtration and denoising processes to mitigate electronic equipment interference, the resultant radar signals, devoid of noise, are then imaged. Employing established methodologies and technologies aims to facilitate a rapid and straightforward analysis of the imaging data, and to promptly and accurately identify the presence of water-rich strata ahead of the tunnel face, as well as to assess if the scale and position of these strata are influenced by the tunneling process. Upon the examination of the imaging outcomes utilizing diverse methods for the aforementioned signals, it is observed that F-K migration imaging utilizes the fast Fourier transform (FFT) method, which is characterized by a rapid calculation speed. Nevertheless, this algorithm exhibits certain limitations. This algorithm is particularly sensitive to variations in both lateral and longitudinal velocities, making it more appropriate for scenarios with uniformly distributed media. The back projection algorithm operates in the time domain, based on a relatively straightforward principle, offering accuracy and ease of implementation. However, it does not account for the inter-signal correlation inherent in radar data, which can lead to clutter interference and a subsequent degradation in imaging quality. Building upon the delay-and-sum principle of the back projection algorithm, the unbiased range autocorrelation synthetic aperture radar (SAR) imaging algorithm incorporates autocorrelation calculations between signals of each channel, thereby mitigating clutter and enhancing the quality of the resultant images. Upon comprehensive evaluation, the unbiased range autocorrelation SAR imaging algorithm is deemed most suitable for application in subsequent studies.

4. Analysis of Engineering Examples

In this study, ground penetrating radar (GPR) is integrated with the TBM tunneling method. Accounting for the intricate and variable subsurface conditions, as well as the complex electromagnetic environment induced by the electronic equipment on the TBM, two or more antenna arrays, operating at distinct frequencies or a unified frequency, are utilized for detection purposes. The antenna array technology is strategically positioned on the TBM cutterhead, enhancing the dual-threshold algorithm to address the issues of false alarms and erroneous detections that arise during the detection process, as depicted in Figure 6. Concurrently, a thorough investigation of wave propagation theory is essential. During a radar signal analysis, by considering both the amplitude and directional attributes of the reflected waves, and by focusing on their spectral and co-axial state characteristics, the impact of tunneling operations on the reflected waves can be minimized. This approach facilitates the identification of adverse geological conditions, such as water-rich layers, based on the reflective signatures.

Consider the diversion tunnel project of a hydropower station as a case study, where a hybrid construction approach utilizing both double-shield TBM and drilling and blasting techniques is employed. The tunnel’s maximum depth below the surface is approximately 700 m, with an average depth of about 500 m. The tunnel excavation traverses strata composed of andesite, basalt, rhyolite, and other rock types. Small-scale faults are present along the tunnel’s length, with the majority being less than 10 m in width. All tunnels are situated below the water table. Tunnel excavation occurs during a period of heavy rainfall, characterized by abundant sources of groundwater replenishment. There is a preliminary assessment suggesting the potential for water and mud inrushes within fault fracture zones and densely jointed areas. Based on an initial analysis, it is hypothesized that the primary geological challenges for the hydropower station’s diversion tunnel include instability and collapse within fault fracture zones and densely jointed areas, as well as the risk of tunnel water inrush. These factors are anticipated to significantly influence the TBM tunneling process, both prior to and following construction. The classification of the surrounding rock at the construction site is depicted in Figure 7. The cyan section represents Grade II surrounding rock, the green section represents Grade III surrounding rock, the blue section represents Grade IV surrounding rock, and the red section represents Grade V surrounding rock, which corresponds to the fault. This zone is susceptible to water inrush incidents.

The predominant type of groundwater present is bedrock fissure water, which is predominantly replenished through the infiltration of rainwater, with minimal surface runoff. The water-rich zones have not been fully mitigated, potentially leading to water leakage within the tunnel post-excavation. GPR detection was conducted utilizing an antenna with a central frequency of 40 MHz at the TBM cutterhead and the segment support immediately posterior to the operating platform. Accounting for the complexities imposed by the geological formation and the presence of construction machinery, a filtering processing technique that preserves certain deep, weak signals is employed to mitigate the clutter within the detection signal. Signal samples with comparable initial energy levels, as gathered from the site, are selected for the analysis, subsequently applying various conventional methods for direct wave processing. The outcomes of these analyses are detailed in

Table 3. Energy comparison of wavelet transform filtering algorithm before and after removing direct wave.

Algorithm Name	Initial Signal Energy (dB)	To Direct Wave Signal Energy (dB)
Wavelet double-threshold filtering	185.3490	161.0909
Median filtering	187.6325	170.2364
F-X prediction filtering	183.6943	162.1589

.

Upon the comparison of the aforementioned data, it is observed that the median filter eliminates 9.2% of the direct wave in the original signal; the F-X domain predictive filter eliminates 11.7% of the direct wave. The wavelet double-threshold filter reduces 13.1% of the direct wave. Upon the comparative analysis, it is evident that the wavelet double-threshold filtering provides the most effective removal of direct waves. These outcomes, derived from a comprehensive analysis and inference, are substantiated by experimental and engineering evidence. An antenna array technique is utilized for the transmission and reception of radar signals. A thorough examination of wave propagation theory informs the application of the wavelet double-threshold filtering algorithm for signal processing, which ensures that the target signal’s information remains intact through time-frequency domain transformation. The radar signal processing has successfully met the anticipated objectives, accurately delineating the fracture zones and estimating water content, as confirmed through excavation.

Upon analyzing the data resulting from the application of the three algorithms presented in Table 3, it is determined that the wavelet double-threshold change processing algorithm provides the most effective removal of direct waves. Consequently, this algorithm is deemed to be the most suitable and is thus selected for separate consideration. The unbiased range autocorrelation synthetic aperture algorithm, demonstrated to yield the optimal imaging results through the analysis, is subsequently employed to process the radar data. The outcomes of this processing are depicted in Figure 8.

The analysis indicates that Figure 8a is the actual photograph of the water inrush disaster at the tunnel site. Figure 8b illustrates the detection of the rock mass in front of the tunnel face using ground penetrating radar. The red box in the figure indicates the abnormal section detected between depths of 5 m to 15 m, which is the water-rich area ahead of the tunnel face. Figure 8c demonstrates that the clutter removal effect of ground penetrating radar data post wavelet transform processing is significantly pronounced, indicating that the wavelet transform processing method is more suitable for radar signal denoising. Figure 8d presents the waveform effect diagram of the radar signal in the abnormal section of the red box post wavelet transform, with the trend of the processed waveform being more distinct.

This study demonstrates that the unbiased range autocorrelation synthetic aperture imaging algorithm, which boasts superior image quality, is utilized for the precise localization of fluctuation sections within radar data subjected to wavelet transform double-threshold processing, thus enabling the detection of water-rich areas and water inrush sections with greater accuracy. These approaches are capable of mitigating the impact of electronic equipment from TBMs on radar signals, making this methodology well -suited for TBM tunneling applications. Furthermore, the wavelet double-threshold filtering algorithm’s processing methodology is more stringent, resulting in a more precise processed signal. Additionally, antenna array technology has been instrumental in the construction of ordinary tunnels. The principles of signal propagation are universally applicable across all tunneling contexts. Consequently, this research encompasses not just the development of TBM tunnel water detection technology and data processing algorithms, but also introduces a novel water detection approach for the broader spectrum of tunneling endeavors.

5. Discussion

Compared to other methods for detecting water inrush in TBM tunnels, the application of ground-penetrating radar (GPR) in this study offers greater flexibility. Firstly, temporal and spatial influences are negligible when affixed to the TBM‘s hull. Timely installation can ensure the instrument’s service life, and variability in installation positions affects detection accuracy. Secondly, GPR is more efficient in signal transmission and reception, and its operation is more facile. The returned signals are processed using various methods, and the detection efficacy meets the requisite accuracy standards.

Nonetheless, to achieve the requisite precision in detecting water inrush events, numerous factors in signal processing must be taken into account. For instance, the interference from TBM electronic equipment with signals necessitates the use of specialized multi-frequency antennas and multi-threshold filtering techniques. In comparison to sophisticated prediction methods like the seismic wave and CFC methods, the chosen antenna array and wavelet dual-threshold filtering algorithm require a more extended signal processing time. Thus, this study presents an economically viable alternative for the TBM detection of water inrush and other disasters.

6. Conclusions

This paper designates a tunnel constructed via the TBM method as the subject of study, employing ground penetrating radar (GPR) as the investigative methodology, with the primary objectives being the advanced detection of water-rich geology and the timely identification of water inrush incidents. A filtering technique is applied to denoise the radar signals, while an imaging algorithm is utilized to render the radar data. The efficacy of the radar signal processing methodology is then validated against actual field conditions. This article primarily focuses on the processing techniques for ground penetrating radar signals. This paper conducts a comparative analysis of four prevalent radar signal denoising methods and three extensively utilized data imaging algorithms, aiming to identify the optimal algorithm suited to actual project requirements and aligned with on-site construction scenarios. The innovative contribution of this article lies in its integration of tunnel advance detection and safety detection concerns pertaining to both the ground penetrating radar method and TBM construction techniques, advancing three strategies to mitigate TBM-induced electromagnetic field interference: the antenna array detection, in-depth study of signal propagation theory, and application of the wavelet double-threshold algorithm. The research presented in this paper on the signal processing algorithms for ground penetrating radar has led to the following conclusions:

(1) Addressing the issue of noise removal in ground penetrating radar (GPR), the following methods were analyzed: median filtering, wavelet threshold filtering, F-X predictive filtering, and wavelet double-threshold filtering. The analysis reveals that the wavelet double-threshold processing method can effectively suppress radar signal noise, while also preserving certain deep, weak signals. This method is well -suited for scenarios where signals are subject to electromagnetic interference during TBM construction, thus addressing the challenge of misinterpreting chaotic signals during the geological detection of water inrush events within tunnels.

(2) An established, efficient, and straightforward method has been adopted for GPR imaging. A comparative analysis of the imaging effects was conducted for F-K migration, back projection, and synthetic aperture imaging techniques. The findings indicate that the synthetic aperture algorithm not only significantly diminishes clutter generation but also yields the superior imaging quality.

(3) During the field engineering validation within TBM tunnel operations, the wavelet double-threshold method demonstrates optimal performance in the removal of direct wave interference. Furthermore, the unbiased autocorrelation synthetic aperture radar (SAR) imaging algorithm is characterized by its simplicity, efficiency, and superior imaging quality, enabling the radar signal to more accurately represent the underlying geological conditions.

(4) Utilizing the radar antenna array detection method, in conjunction with an analysis of the amplitude, direction, spectral properties, and co-axial state characteristics of the reflected waves, as well as additional wave propagation theory research, this approach can significantly mitigate the impact of electronic equipment and metallic elements on the integrity of the reflected wave signals.

As the complexity of geological construction projects increases, there is a heightened demand for accurate geological condition detection, making the development of preprocessing algorithms for ground penetrating radar (GPR) increasingly significant within engineering applications. Within the scope of this study, the fractional wavelet transform and the synthetic aperture radar (SAR) algorithm have demonstrated promising outcomes. However, the fractional wavelet transform method may occasionally fall short of optimal performance in TBM tunnel environments, thus necessitating the development of an enhanced approach. Research into GPR preprocessing algorithms remains a focal point for future studies. Integrating GPR with TBM tunneling operations, beyond the aforementioned techniques, there is a growing interest in incorporating machine learning and deep learning methodologies to enhance the recognition capabilities regarding adverse geological conditions, particularly those characterized by water and mud inrushes.