Identification and Analysis of Fracture Zones in Tunnels Based on GPR Wave Characteristics

Abstract

With the growing complexity of mountain tunnel construction and the increasing engineering demand for rapid detection, ground-penetrating radar (GPR) has become a core technique for engineering-scale fracture detection. Fracture zones are not only a major obstacle to tunneling through complex geological sections but also a key trigger of tunnel hazards, posing a serious threat to construction safety. Consequently, the effective identification of fracture zones and the investigation of their development characteristics remain central challenges in advance geological prediction for mountain tunnels. Owing to the complex morphology of fracture zones, existing approaches—including simple model simulation, single-parameter identification, and integrated prediction methods—cannot adequately characterize core attributes such as connectivity and development degree. To address this challenge, this study constructed a fracture attribute model and established a multidimensional collaborative identification system covering fracture scale, connectivity, and density, integrating time-domain wave-frequency morphology with the two instantaneous attributes in the spatial domain, namely instantaneous frequency and instantaneous amplitude. A collaborative analysis scheme based on multiple GPR statistical attributes was adopted to perform a qualitative comparison of fracture development characteristics by tracking multidimensional parameter trends. The results reveal that fracture zones in different development states exhibit certain correlation trends between their internal structural features (e.g., connectivity and compactness) and the frequency-related physical attributes of electromagnetic waves (e.g., wave-frequency morphology and instantaneous frequency). Based on the simulation results, the analysis of waveform characteristics, spatial variations of the two instantaneous attributes, and multi-attribute evolution trends clarified the correlation trends between the wave-frequency response patterns and the fracture development degree. These findings provide scientific and theoretical guidance for geological prediction in tunnel engineering in Hunan, China, and lay a foundation for the GPR-based identification of fracture zones in tunnels.

1. Introduction

As transportation infrastructure in China extends further into mountainous regions, the scale of mountain tunnel construction continues to expand and construction difficulty keeps increasing, making it increasingly common for tunnels to pass through complex geological sections such as fracture zones. The rock mass within fracture zones is characterized by densely developed joints and fractures, an overall fragmented structure, and a strong tendency to accumulate groundwater. Fracture zones have been widely recognized as a major source of geological hazards in tunnel construction: when the tunnel face advances into such zones, the broken rock mass readily induces rockfalls, roof collapse, and even landslides [1], while water-filled fracture networks often serve as preferential seepage pathways, triggering water and mud inrush accidents [2]. Similar fracture-related hazards also threaten other engineering structures: voids and cavities formed behind tunnel linings or beneath reinforced concrete foundations cause differential settlement, stress concentration, and cracking in load-bearing structures, seriously endangering structural stability and service safety [3,4]. These adverse geological features readily induce geological hazards such as water and mud inrush at the tunnel face and large deformation of the surrounding rock, seriously threatening the safety of construction personnel and project progress. Therefore, the precise location, identification, and discrimination of fracture zones constitute one of the core difficulties in advanced geological prediction for mountain tunnels [5].

Owing to its advantages of non-destructive detection and high resolution, ground-penetrating radar (GPR) has become the main method for long-distance, engineering-scale fracture detection in the infrastructure field; however, its identification under complex geological conditions still faces numerous bottlenecks [6,7]. Research on fracture zones started earlier abroad: for instance, automatic surface-wave identification and seismic full-waveform inversion have been applied to locate fracture zones in tunnels, yet these techniques cannot precisely reproduce their physical attribute characteristics [8,9]. Although multi-azimuth and multi-polarization radar data enable the identification of fracture strike and filling media, their adaptability under complex geological conditions is limited, making it difficult to achieve refined simultaneous inversion of the fragmentation degree and connectivity of fracture zones [10]. In addition, inversions of characteristic attributes such as fracture zone thickness and dip based on amplitude and phase suffer from ambiguous identification and large errors caused by detection interference, compromising the reliability of quantitative results [11]. For integrated detection approaches, the joint use of seismic waves and GPR can identify and locate fracture anomaly zones but fails to achieve the inversion of key parameters such as fracture density and connectivity [12]. In China, the multiphase discrete random medium model [13] and the optimization of finite-difference time-domain (FDTD) numerical simulation for GPR can improve the accuracy of wavefield simulation, while improved full-waveform dual-parameter inversion and three-dimensional simulation can also enhance the identification accuracy of underground structures [14,15,16]. However, these studies are mostly based on simple fracture models without fully considering fracture attributes in actual engineering (e.g., random distribution, connectivity, and compactness), resulting in considerable deviations between simulated and field-measured signals. Moreover, although the variation patterns of travel-time curves and amplitude characteristics extracted directly from fracture numerical simulation can serve as identification markers [17], the identification accuracy of such a single parameter (e.g., amplitude) is insufficient to meet engineering requirements under complex geological conditions. At present, detection studies of fracture zones in tunnels, both at home and abroad, are mostly confined to single-parameter or single-dimensional analysis. Although GPR can provide theoretical constraints on fracture aperture and filling media through amplitude-versus-angle (AVA) responses, the identification of fracture scale, connectivity characteristics, and filling media by GPR remains insufficient owing to medium heterogeneity and solution non-uniqueness; existing methods can hardly acquire fracture geometric dimensions, filling material properties, and network connectivity information simultaneously [18,19], and the insufficient synergy of multidimensional information cannot support result analysis, while verification means remain weak.

In this study, GPR signals of rock masses with different degrees of fracture development were systematically simulated, and the characteristics of various parameters were extracted and quantitatively analyzed to establish a correlation model between parameters and fracture development grades. Breaking through the traditional single-parameter identification approach, a multidimensional collaborative identification system was constructed that combines time-domain wave-frequency morphology with the two instantaneous attributes in the spatial domain (instantaneous frequency and instantaneous amplitude), corresponding to fracture attributes such as scale, connectivity, and density. Ground boreholes were also integrated as a means of anomaly verification. Abandoning the single absolute-parameter matching approach, a collaborative analysis scheme based on multiple GPR statistical attributes was adopted to perform a qualitative comparison of fracture development characteristics by tracking multidimensional parameter trends. Through the analysis of waveform characteristics, spatial variations of the two instantaneous attributes, and multi-attribute evolution trends, a correlation trend between the wave-frequency response patterns and the fracture development degree was identified.

This study not only enriches the theory of GPR identification but also provides practical technical support for advanced geological prediction in tunnel engineering, holding important theoretical value and broad engineering application prospects for reducing geological hazards and ensuring engineering safety.

2. Study Area and Methods

2.1. GPR Detection Technique

The transmitting antenna emits high-frequency short-pulse electromagnetic (EM) waves into the ground. During underground propagation, reflection and transmission occur when the waves encounter interfaces between media with different dielectric properties. The receiver acquires the EM wave data for analysis, thereby enabling the detection of the distribution and structural composition of subsurface media. The working principle is illustrated in Figure 1.

Figure 1. Working principle of GPR.

2.2. Numerical Forward Modeling of GPR

The finite-difference time-domain (FDTD) method discretizes Maxwell’s equations in both the time and spatial domains to establish an iterative solution framework, through which the spatial distribution characteristics and temporal evolution of the electromagnetic field are obtained, ultimately realizing the numerical simulation of EM wave propagation [20].

2.2.1. Maxwell’s Curl Equations (TM Mode)

The time-domain Maxwell’s curl governing equations are as follows:

$$\begin{array}{c}\nabla \times H = \epsilon {\displaystyle \frac{\partial E}{\partial t}} + \sigma E\end{array}$$

(1)

$$\begin{array}{c}\nabla \times E=-\mu {\displaystyle \frac{\partial H}{\partial t}}\end{array}$$

(2)

where $\mathrm{E}$ denotes the electric field intensity (V/m); $\mathrm{H}$ denotes the magnetic field intensity (A/m); $\mathsf{\epsilon } = {\mathsf{\epsilon }}_{\mathrm{r}}{\mathsf{\epsilon }}_0$ is the absolute permittivity of the medium (F/m); $\mathsf{\mu } = {\mathsf{\mu }}_{\mathrm{r}}{\mathsf{\mu }}_0$ represents the magnetic permeability of the medium (H/m); $\mathsf{\sigma }$ stands for the electrical conductivity of the medium (S/m).

By expanding the vector curl equations under the two-dimensional transverse magnetic (TM) mode:

$$\begin{array}{c}{\displaystyle \frac{\partial E_z}{\partial t}} = {\displaystyle \frac{1}{\epsilon }}\left({\displaystyle \frac{\partial H_y}{\partial x}} - \sigma E_z\right)\end{array}$$

(3)

$$\begin{array}{c}{\displaystyle \frac{\partial E_x}{\partial t}}=-{\displaystyle \frac{1}{\epsilon }}\left({\displaystyle \frac{\partial H_y}{\partial z}}+\sigma E_x\right)\end{array}$$

(4)

$$\begin{array}{c}{\displaystyle \frac{\partial H_y}{\partial t}}={\displaystyle \frac{1}{\mu }}\left({\displaystyle \frac{\partial E_z}{\partial x}} - {\displaystyle \frac{\partial E_x}{\partial z}}\right)\end{array}$$

(5)

where ${\mathrm{E}}_{\mathrm{x}}$ and ${\mathrm{E}}_{\mathrm{z}}$ represent the electric field intensities in the X and Z directions, and ${\mathrm{H}}_{\mathrm{y}}$ denotes the magnetic field intensity in the Y direction.

2.2.2. Yee Grid Discretization

Yee derived the finite-difference form of Maxwell’s equations in his study. Accordingly, the FDTD method is discretized here using the central difference approximation. The two-dimensional space is discretized into grid points (i, j) with grid spacings (Δx, Δz) by central differences, with Δt adopted as the uniform time step in the time domain and the nth time instant denoted as t = nΔt. All spatiotemporal partial derivatives are uniformly discretized using second-order central differences [21,22]:

Temporal discretization scheme:

$$\begin{array}{c}{\displaystyle \frac{\partial f}{\partial t}}{|}^n \approx {\displaystyle \frac{f^{n + 1/2} - f^{n - 1/2}}{\Delta t}}\end{array}$$

(6)

Spatial discretization scheme:

$$\begin{array}{c}{\displaystyle \frac{\partial f}{\partial x}}{|}_{i,j} \approx {\displaystyle \frac{f_{i + 1/2,j} - f_{i-1/2,j}}{\Delta x}}, {\displaystyle \frac{\partial f}{\partial z}}{|}_{i,j} \approx {\displaystyle \frac{f_{i,j +1/2} - f_{i,j - 1/2}}{\Delta z}}\end{array}$$

(7)

Substituting the discretization schemes into the scalar governing equations of the TM polarization and introducing a lossy-medium correction coefficient “1/(1 + σΔt/(2ε))” into the electric field iteration equation, the electromagnetic field update equations are obtained:

Electric field update formula (t = (n + 1) Δt):

$$\begin{array}{c}{E}_x^{n + 1}(i,j + {\displaystyle \frac{1}{2}}) = {\displaystyle \frac{1}{1 + \sigma \Delta t/(2\epsilon )}} [E_x^n(i,j + {\displaystyle \frac{1}{2}}) + {\displaystyle \frac{\Delta t}{\epsilon }}·{\displaystyle \frac{H_y^{ n+ 1/2}(i,j + 1) - H_y^{n + 1/2}(i,j)}{\Delta z}}]\end{array}$$

(8)

$$\begin{array}{c}{E}_z^{n +1}(i+{\displaystyle \frac{1}{2}},j)={\displaystyle \frac{1}{1+\sigma \Delta t/(2\epsilon )}} [E_z^n(i+{\displaystyle \frac{1}{2}},j) - {\displaystyle \frac{\Delta t}{\epsilon }}·{\displaystyle \frac{H_y^{n +1/2}(i +1,j) - H_y^{n +1/2}(i,j)}{\Delta x}}]\end{array}$$

(9)

Magnetic field update (t = (n + 1) Δt):

$$\begin{array}{c}{H}_y^{n + 1/2}(i,j) = H_y^{n - 1/2}(i,j) + {\displaystyle \frac{\Delta t}{\mu }} [{\displaystyle \frac{E_z^n(i,j + 1/2) - E_z^n(i,j - 1/2)}{\Delta x}} - {\displaystyle \frac{E_x^n(i + 1/2,j) - E_x^n(i - 1/2,j)}{\Delta z}}]\end{array}$$

(10)

2.2.3. CFL Stability Condition

The core constraint, imposed to prevent divergence of the numerical solution and the occurrence of non-physical oscillations, is expressed as follows:

$$\begin{array}{c}c·\Delta t \le {\displaystyle \frac{1}{\sqrt{\frac{1}{\Delta x^2} + \frac{1}{\Delta z^2}}}}\end{array}$$

(11)

where $\Delta x$ and $\Delta z$ denote the spatial steps, c represents the speed of light in vacuum, and $\Delta t$ is the time step.

2.2.4. Absorbing Boundary Conditions

The implementation of FDTD discretization relies on the reasonable specification of initial and boundary conditions. The initial conditions define the specific values of the field quantities at all grid points at the initial time, whereas the boundary conditions describe the variation patterns of the field quantities at the spatial boundaries of the computational domain, serving to simulate phenomena such as wave reflection and transmission at the boundaries [23].

Absorbing layers are introduced at the boundaries, and the modified governing equations for the TM mode are expressed as follows:

$$\begin{array}{c}{\displaystyle \frac{\partial H_{\mathit{yx}}}{\partial t}} + {\displaystyle \frac{{\sigma }_x}{\mu }}{H}_{\mathit{yx}} = {\displaystyle \frac{1}{\mu }}{\displaystyle \frac{\partial E_z}{\partial x}}\end{array}$$

(12)

$$\begin{array}{c}{\displaystyle \frac{\partial H_{\mathit{yz}}}{\partial t}}+{\displaystyle \frac{{\sigma }_z}{\mu }}{H}_{\mathit{yz}}=-{\displaystyle \frac{1}{\mu }}{\displaystyle \frac{\partial E_x}{\partial z}}\end{array}$$

(13)

$$\begin{array}{c}{\displaystyle \frac{\partial E_x}{\partial t}}+{\displaystyle \frac{{\sigma }_z}{\epsilon }}{E}_{x }=-{\displaystyle \frac{1}{\epsilon }}{\displaystyle \frac{\partial H_y}{\partial z}}\end{array}$$

(14)

$$\begin{array}{c}{\displaystyle \frac{\partial E_z}{\partial t}}+{\displaystyle \frac{{\sigma }_x}{\epsilon }}{E}_z={\displaystyle \frac{1}{\epsilon }}{\displaystyle \frac{\partial H_y}{\partial x}}\end{array}$$

(15)

where ${\mathrm{E}}_{\mathrm{x}}$ and ${\mathrm{E}}_{\mathrm{z}}$ are the electric field components within the profile plane, and ${\mathrm{H}}_{\mathrm{y}}$ is the magnetic field component perpendicular to the profile plane, with ${\mathrm{H}}_{\mathrm{y}}$ = ${\mathrm{H}}_{\mathrm{yx}}$ + ${\mathrm{H}}_{\mathrm{yz}}$; ${\sigma }_x$ and ${\sigma }_z$ are the attenuation coefficients in the X and Z directions, respectively, which are nonzero only within the PML region and increase polynomially along the normal direction of the boundaries to suppress boundary reflections.

3. Numerical Simulation and Data Acquisition

3.1. FDTD Numerical Simulation of Tunnel Fractured Zones

3.1.1. Model Design

To accurately define the geometric parameters (fracture density and connectivity) and petrophysical parameters (dielectric permittivity and electrical conductivity) of fractures, and to quantitatively reproduce the propagation behavior of electromagnetic waves within fractured zones, a numerical modeling approach was adopted. This compensates for the limitations of field surveys in characterizing complex geological conditions and provides a theoretical basis for the interpretation of measured GPR profiles. Based on ground-penetrating radar (GPR) electromagnetic imaging, this study investigates the frequency-domain identification characteristics and patterns of fractured zones in tunnels. To closely replicate actual field conditions, a numerical model measuring 4 m in width and 30 m in depth was established; the 30 m depth corresponds to the optimal detection depth for segmented tunnel surveys in the study area. The entire model is composed of argillaceous sandstone, with a fractured zone occupying the interval from 13 m to 26 m in depth. Within this zone, the 13–18 m interval is designated as a low joint-fracture development zone, the 18–22 m interval as a medium joint-fracture development zone, and the 22–26 m interval as a high joint-fracture development zone. All fractures are air-filled. A schematic illustration of the numerical fractured-zone model is shown in Figure 2. Key geometric parameters of the fractured-zone model, including fracture length, aperture, dip angle, spacing, and trace length, are listed in Table 1 (Table S1).

Figure 2. Schematic illustration of the detailed structure of the numerical fractured-zone model.

Table 1. Fracture structure parameters of the model.

Development Level	Total Number of Fractures	Aperture/m: Mean ± Std [Min, Max]	Trace Length/m: Mean ± Std [Min, Max]	Dip Angle/(°): Mean ± Std [Min, Max]	Minimum Center-to-Center Spacing/m
Low fracture density (13–18 m)	1	0.113 [0.113, 0.113]	0.723 [0.723, 0.723]	86.6 [86.6, 86.6]	4.761
Medium fracture density (18–22 m)	4	0.155 ± 0.039 [0.122, 0.197]	1.149 ± 0.203 [0.934, 1.396]	66.4 ± 15.6 [53.0, 83.6]	0.636
High fracture density (22–26 m)	9	0.245 ± 0.089 [0.152, 0.380]	1.287 ± 0.415 [0.824, 1.989]	61.1 ± 20.0 [34.0, 88.1]	0.269

Based on Figure 2, the model attributes of the specific regions are as follows: For the low-development fracture zone, the number of fractures is small, with a minimum center-to-center spacing of 4.761 m and relatively small aperture and trace length; the fractures are isolated with no intersections, resulting in poor geometric connectivity and no through-going fractures. For the medium-development fracture zone, the number of fractures is moderate, with a minimum center-to-center spacing of 0.636 m and intermediate aperture and trace length; the fractures remain independent and non-intersecting, with weak connectivity. For the high-development fracture zone, the number of fractures is large, with a minimum center-to-center spacing of 0.269 m and larger aperture and trace length; the fractures are densely arranged, with five pairs of intersecting fractures and five fractures forming a connected domain, and the overall connectivity is relatively good.

3.1.2. Simulation and Analysis of Electromagnetic Wave Propagation

In the numerical simulation, a first-order Debye relaxation model is adopted to describe the dielectric dispersion behavior of the medium, in which the complex relative permittivity is defined as ${\mathsf{\epsilon }}_{\mathrm{r}}\left(\mathrm{f}\right)={\mathsf{\epsilon }}_{\mathrm{r}}^{\prime }\left(\mathrm{f}\right)-\mathrm{j}{{\mathsf{\epsilon }}_{\mathrm{r}}}^{″}\left(\mathrm{f}\right)$. The electromagnetic characteristic parameters of the media adopted in the numerical simulations are listed in Table 2.

Table 2. Electromagnetic parameters of model media.

Medium	High-Frequency Relative Permittivity ${\mathsf{\epsilon }}_{\infty }$	Static Relative Permittivity ${\mathit{\epsilon }}_{\mathit{S}}$	Relaxation Time $\mathit{\tau }\left(\mathit{ps}\right)$	Frequency-Dependent Conductivity at $\mathit{\sigma }\left({\mathit{f}}_0\right)$ (S/m)	Relative Permeability ${\mathit{\mu }}_{\mathit{r}}$	Magnetic Loss Tangent $\mathbf{tan}{\mathit{\delta }}_{\mathit{\mu }}$
Air	1.00	1.00	—	0	1.0	0
Argillaceous sandstone	8.00	12.00	1.2	0.025	1.0	0
Cataclastic rock	7.5	16.0	0.8	0.060	1.0	0
Fractured zone	15.0	28.0	0.45	0.180	1.0	0

The model is 4 m wide and 30 m deep, with a grid step of 0.01 m, corresponding to grid dimensions of 400 × 3000. The source frequency is 400 MHz, the number of time steps is 12,000, and the total propagation time is 282.8 ns.

To investigate the specific wave-frequency variation patterns of radar waves encountering fractured rock sections within fracture zones, the anomalous electromagnetic wave frequencies of rock sections with different degrees of joint and fracture development were examined. Accordingly, wavefield snapshots of electromagnetic wave propagation in the x–z plane of the fracture zone model at t = 282.8 ns were extracted for refined analysis, as shown in Figure 3.

Figure 3. Electromagnetic wave propagation in the fractured-zone model: x–z plane wavefield snapshot (t = 282.8 ns).

As shown in Figure 3, at the interface of the fracture zone at 13 m, strong scattering attenuation occurs, causing the dominant frequency of the signal to shift toward lower frequencies, accompanied by the loss of high-frequency components and an increase in vibration amplitude. Within the fractured rock section filled with fracture zones (13–26 m), more intense reflection and scattering attenuation are observed, and the reflection events exhibit poor continuity, appearing as discontinuous zones or interbedded patterns. In the 18–22 m region, where fracture zones are relatively well developed, the reflection events show interruptions and poor continuity, with blurred signal waveforms and small-amplitude variations. In the 22–26 m region, where fracture zones are densely developed, the reflection events exhibit good continuity and a bedded distribution, with sharp signal peaks and overall enhanced reflection energy, whereas the waveform in the extension area of the main fracture zone band shows a depression.

3.1.3. Analysis of Directional Component Variations of Electromagnetic Waves

To quantitatively analyze the density of fracture and fracture-zone development in each rock section, the stacked analysis of energy variations in the electromagnetic field directions was refined, extracting the spatial–frequency domain amplitude variations in different components (Ez, Ex) as well as the multi-trace time-domain waveform variations, so as to investigate the energy variations of each component and its profiles in three dimensions. The spatial–frequency domain amplitude distributions of the main components and the common-offset profile waveforms of the different components are shown in Figure 4 and Figure 5, respectively.

Figure 4. Spatial-frequency domain amplitude distribution of the Ez component: (a) The 3D spatial–frequency domain amplitude distribution of the Ez component. (b) Stacked plot of the amplitude distribution of the Ez component.

Figure 5. Common-offset detection profile waveforms of different components (Ez and Ex): (a) Multi-channel time-domain waveforms of the Ez component. (b) Multi-channel time-domain waveforms of the Ex component.

As shown in Figure 4a, before grid 1300, high-frequency components still dominate the signal, with a smooth amplitude distribution. In the grid range 1300–3000, corresponding to the rock section of 13–30 m, numerous amplitude spikes appear with significant frequency-domain distortion; the high-frequency signals are markedly attenuated, and the dominant frequency shifts toward lower frequencies (from 400 MHz to 200–300 MHz). According to Figure 4b, for the fracture-developed rock sections as a whole, the Ez component exhibits sidelobe enhancement and main-peak splitting in all cases. In the Z direction, clear and sharp energy peaks appear in three grid ranges—approximately 1200–1300, 1800–2200, and 2200–2600—corresponding to the rock sections of 12–13 m, 18–22 m, and 22–26 m, respectively. Among them, the 12–13 m rock section (at the interface between different rock sections) exhibits pronounced peak splitting; the 18–22 m rock section shows small-amplitude abrupt variations with fewer secondary peaks; and the 22–26 m rock section exhibits large peaks with no obvious main peak, splitting into multiple secondary peaks of similar intensity and possessing the largest bandwidth.

Combining the time-domain waveform variations of the Ez and Ex components in Figure 5, the amplitudes of the electromagnetic wavebands in the three grid ranges of 1200–1300, 1800–2200, and 2200–2600—i.e., the three rock sections of 12–13 m, 18–22 m, and 22–26 m—undergo abrupt changes with intense fluctuations. Specifically, in the 12–13 m rock section, the waveform signals are distorted, yet the fluctuations are not continuous; in the 18–22 m rock section, the amplitude exhibits stepwise variations with strong fluctuations, and the pulse fluctuation band shows poor continuity; in the 22–26 m rock section, the amplitude increases significantly with intense and disorderly fluctuations, and the pulses merge into a “continuous strong fluctuation band”.

Integrating the numerical simulation data of the radar wave propagation process and the variation patterns of each component, the quantitative analysis of fracture zones can be conducted based on wave-frequency morphology (e.g., reflection events), amplitude variations, component strength, and frequency shift, with the specific patterns summarized in Table 3.

Table 3. Fitted wave-frequency response patterns for fracture zones.

Fracture Development	Wave Event	Amplitude Variation	Variation of Ez Component	Frequency Shift
Low	Basically continuous	Low amplitude	No obvious pulsed fluctuations; strong overall continuity	Small shift; dominated by high–medium frequency signals
Medium	Discontinuous with interval gaps	Relatively high amplitude with small variations	Relatively intense fluctuations; poor continuity; fewer split secondary peaks	High-frequency loss; large dominant-frequency shift
High	Relatively continuous, bedded or interbedded	High amplitude with large variations	Intense and disorderly fluctuations, forming continuous strong fluctuation bands and multiple split secondary peaks	Significant shift of the dominant frequency toward low frequencies; severe high-frequency loss

3.2. Analysis of Field-Measured Ground-Penetrating Radar (GPR) Survey Data

3.2.1. Engineering Background and Data Acquisition

The test section is located at chainage K38+047–K38+077 of the right tube of the Zijinshan No. 3 Tunnel. According to the engineering geological investigation, the rock formations in the tunnel area are dominated by argillaceous sandstone, with sandy mudstone, sandstone, and quartz sandstone occurring as intercalations or interbeds. Three sets of joints and fractures are mainly developed in the tunnel body, mostly steeply dipping with spacings of approximately 0.2–0.5 m and exhibiting a regular “X”-shaped pattern on the plane. The fractures are mostly of the open, slightly open, to basically closed types, and the rock mass is cut into blocky to large-blocky fragments, presenting fragmental, fractured blocky, to blocky structures. Rock sections with relatively thick weathering zones exist, and weathering exerts a considerable influence on the surrounding rock.

3.2.2. Surface Borehole Data Acquisition and Analysis

To obtain the actual geological conditions of the tunnel chainage section in the study area, a vertical borehole was drilled at the stake point located 8.00 m to the right of chainage K38+068 of the Zijinshan No. 3 Tunnel. The borehole is designated SDZK38-2, with location coordinates of Y = 2,853,653.550 and X = 562,634.370, a collar elevation of 570.90 m, and a drilling depth of 74.4 m. The drilling results are listed in Table 4.

Table 4. Borehole data of SDZK38-2 for the right tunnel of the Zijinshan Tunnel.

Stratum Elevation (m)	Layer Thickness (m)	Depth to Layer Bottom (m)	Lithological Description
564.90	6.00	6.00	Grayish-brown to grayish-green, loose and moist; composed mainly of sandstone parent rocks with rounded to sub-rounded shapes; gravel content 50–60%, particle size 2–7 cm; minor boulders and cohesive soil locally interbedded; moderately graded.
496.50	68.40	74.40	Moderately weathered purplish-red and blue-gray argillaceous sandstone interbedded with sandstone, with a sandy-argillaceous texture and medium-thick bedded structure. Influenced by the syncline and faults, the rock mass has densely developed joints and fractures and is highly fractured. Rock cores are mostly blocky and fragmented, with columnar and short columnar cores locally. Purplish-red and blue-gray rocks with a sandy texture and medium-thick bedded structure. Joints and fractures are moderately developed. The rock is relatively soft and intact, and the cores are mainly columnar, with blocky and short columnar cores locally and core lengths of 10–48 cm. Iron–manganese staining is observed at depths of 50–54 m, where well-developed joints and fractures have resulted in highly fragmented cores, which are mostly blocky.

According to the table, at chainage K38+068 of the tunnel section in this study (with ground elevations ranging from approximately 524 to 510 m), the drill cores are blocky to fragmental. Owing to the effects of syncline and faulting, joints and fractures are particularly well developed, and the rock mass is broken. It follows that the excavated rock sections around K38+068 are all sections with relatively well-developed joints and fractures, exhibiting loose and fragmental structures and consisting of crushed rock; they are comprehensively classified as moderately broken rock sections with medium connectivity and relatively dense development.

3.2.3. GPR Data Acquisition and Analysis

Based on the above drilling data, it can be confirmed that the tunnel rock sections around chainage K38+068 are fragmental rock sections with relatively well-developed joints and fractures and broken structures. To verify the feasibility and accuracy of the wave-frequency patterns derived from the fracture numerical simulation, GPR profile images were acquired for comparative analysis. According to the nature and structural characteristics of the detection target, the surrounding rock at the tunnel face of the K38+047–K38+077 section of the right tube was surveyed, with a total survey length of 30 m. The LTD-2100 GPR (China Research Institute of Radiowave Propagation) system with a 100 MHz antenna was adopted, and two groups of survey lines, four lines in total, were arranged.

After linear reciprocal-point scanning of the rock surface, the radar data of the K38+047–K38+077 chainage section were extracted. Following a series of preprocessing steps, including time-zero correction, background removal, horizontal interference suppression, band-pass filtering, moving-average smoothing, and gain calibration, the survey profiles corresponding to the GPR lines in the tunnel rock section around K38+068 were finally extracted and analyzed in segments using the Hilbert transform. The comparison with the drilling data is shown in Figure 6.

Figure 6. Comparison of the drilling and GPR data.

In addition, ten GPR traces in total were extracted, with traces 1–5 from the fracture zone and traces 6–10 from the intact surrounding rock zone, and five attribute statistics were calculated: relative reflection energy, amplitude variance, C3 coherence coefficient, coefficient of variation, and waveform entropy. Each trace consisted of 128 sampling points, yielding a total of 1280 sampling points. The multi-attribute comparison plot is shown in Figure 7.

Figure 7. Multi-attribute statistical analysis of GPR data.

4. Results

4.1. Comparative Analysis of Borehole and GPR Data

Based on the analysis results of the borehole data in Table 4 and combined with Figure 6, for the tunnel rock section around K38+068 with relatively well-developed joints and fractures, medium connectivity, and a relatively broken rock mass, the corresponding radar profile (rock section at approximately 19 m) reveals, in terms of amplitude variations and reflection events, that the radar reflection waves appear as sparse banded stripes with high amplitude and discontinuous, missing reflection events. The waveform signals exhibit relatively small fluctuations and significant high-frequency loss, accompanied by small patchy anomalous energy regions.

Through segmented refined analysis of the instantaneous frequency and instantaneous amplitude using the Hilbert transform, it can be clearly observed that, in the GPR signals of fractured rock sections with a relatively high development degree and poor connectivity, the instantaneous frequency exhibits significant high-frequency loss and an obvious shift toward low frequencies, while the instantaneous amplitude undergoes abrupt changes with a small-amplitude increase.

4.2. Comparative Analysis of GPR and Numerical Simulation Data

4.2.1. Analysis of Simulated Wave-Frequency Patterns and Radar Profile Data

To verify the feasibility of the wave-frequency patterns obtained from the fracture zone numerical simulation, a refined analysis was conducted on the radar profile data in terms of wave-frequency morphology (continuity, energy cluster distribution, etc.), frequency, and amplitude. The comparison between the numerical simulation data and the actual radar wave frequency is shown in Figure 8.

Figure 8. Comparison of numerical simulation and field GPR signals.

Based on the numerical fitting results of the fracture zone model described above, the refined analysis yields the following findings: the reflection events of both datasets appear as banded stripes with relatively sparse distribution density. In terms of wave-frequency morphology, the fitted fracture wave frequencies exhibit high-frequency loss, and the reflection events show interruptions and discontinuities, with energy clusters regularly concentrated, which is consistent with the actual radar wave-frequency characteristics. In terms of energy amplitude variations, both datasets exhibit relatively high amplitudes with small-amplitude stepwise variations in the broken rock sections with poor fracture connectivity. In terms of frequency variations, the high-frequency shift is significant, with a pronounced transition toward low frequencies. It can therefore be concluded that the connectivity and development density of fracture zones in tunnels can be comprehensively judged from the radar wave-frequency morphology, frequency shift, and energy amplitude variations, allowing the distribution, development state, density, and discontinuity of fracture zones to be identified to a considerable extent.

4.2.2. Comparative Analysis of Simulated Wave-Frequency Patterns and Multi-Attribute Trend Response Characteristics

To further verify the reliability and validity of the fracture zone identification results, a mechanism-based cross-validation was conducted between the field multi-attribute trend response characteristics and the simulated wave-frequency patterns, comparing the multidimensional statistical attribute trends extracted from the field GPR data with the simulated wave-frequency response patterns.

As shown in Figure 7, the relative reflection energy, amplitude variance, and C3 coherence coefficient exhibit excellent discrimination capability: within the fracture zone, the reflection energy and amplitude variance remain at high levels overall, while the C3 coherence coefficient is at a low level; after entering the intact surrounding rock section, the reflection energy and variance decrease markedly and the coherence coefficient increases significantly, reflecting that broken fractures enhance electromagnetic wave reflection and intensify waveform oscillation while destroying the continuity of the radar reflection events. The coefficient of variation can reflect the amplitude fluctuation characteristics of the fracture zone to a certain extent. The waveform entropy shows considerable numerical overlap between the two groups of samples, indicating limited sensitivity for identifying fracture zones in this work area.

Combined with Figure 7 and Table 3, the field radar multi-attribute trend responses—reflecting that relatively broken fractures enhance electromagnetic wave reflection and intensify waveform oscillation while destroying the continuity of the radar reflection events—are consistent with the preliminary wave-frequency evolution patterns of the developed regions in the numerical simulation, namely discontinuous reflection events with interval gaps, relatively intense fluctuations, and large amplitude variations. It can thus be seen that the increasing/decreasing trends, response characteristics, and spectral evolution patterns of the field radar multi-attributes with increasing fragmentation degree are in good agreement with the simulated physical patterns, demonstrating the good feasibility of the identification results.

4.3. Verification by Actual Excavation

Based on the numerical simulation patterns and the measured data described above, the surrounding rock of the K38+047–K38+077 section was excavated. The fracture pattern of the field-excavated tunnel face in the rock section around K38+068 is shown in Figure 9.

Figure 9. On-site excavation at the ground platform of K38+068.

Based on the field excavation images in Figure 9, the comprehensive excavation results validate the feasibility of the wave-frequency patterns derived from the fracture zone numerical simulation. The simulated fracture prediction patterns are applicable to the preliminary quantitative analysis of fracture zones and advance geological prediction in actual tunnel engineering, allowing the development of fracture zones ahead of the tunnel face to be predicted relatively effectively, thereby providing scientific predictive support and safety measure schemes for tunnel excavation.

5. Discussion

The comparative analysis between the numerical simulation and the field GPR data shows that the waveform-frequency characteristics of fracture zones obtained from the forward simulation based on the finite-difference time-domain (FDTD) method are in good agreement with the field observations, particularly in terms of the sparse banded distribution of reflection wave groups, high-frequency attenuation, and the shift toward low frequencies. This consistency demonstrates the feasibility of applying numerical simulation to the qualitative identification of fracture zones in tunnel engineering. Nevertheless, this study still has several limitations. First, the frequency difference between the numerical simulation (400 MHz) and the field GPR (100 MHz) precludes a direct comparison of absolute amplitudes, so the validation can only be limited to qualitative trend analysis. Second, the model only considers fractures filled with dry air, whereas water, clay, or other fillings in actual tunnel fractures can significantly alter the electromagnetic response characteristics. Third, the field validation relies on only a single borehole (SDZK38-2) and a 30 m survey section, making it difficult to fully reflect the various variation characteristics of fracture zones under different geological conditions. Finally, the method is still at the qualitative comparative research stage, and calibration thresholds linking fracture connectivity and development density to GPR characteristic parameters have not yet been established. Future research should further refine the numerical model to incorporate water-filled and clay-filled fracture conditions, construct a more complete waveform-frequency characteristic library, and increase borehole verification points in different tunnel projects to complete the calibration of quantitative identification thresholds.

6. Conclusions

Taking the advanced geological prediction project of the right tube of the Zijinshan No. 3 Tunnel as an example and focusing on the working condition of fractures filled with dry air, the feasibility of the numerical simulation prediction patterns for the identification of the fractured rock mass ahead of the tunnel face was verified by observing the internal and external conditions of the tunnel, combined with surface borehole data, actual radar profile image analysis, and the actual excavation conditions. The following conclusions were drawn:

(1) By establishing a fracture attribute model and constructing a multidimensional collaborative identification system that combines the time-domain wave-frequency morphology with the two instantaneous attributes in the spatial domain (instantaneous frequency and instantaneous amplitude), corresponding to the fracture attributes, the overall density and connectivity of the fracture zone ahead of the tunnel face of the right tube of the Zijinshan No. 3 Tunnel were identified and analyzed.

(2) Based on the GPR forward numerical simulation using the FDTD algorithm, the trend correlations between the key identification indicators of fracture zones (connectivity and development density) and the wave-frequency morphology, spatial-domain instantaneous frequency, and instantaneous amplitude of the radar responses were revealed; the extracted simulation patterns are applicable to the identification and analysis of fracture zones.

(3) Taking the construction of the right tube of the Zijinshan No. 3 Tunnel as the engineering background and conducting detection research on its complex geological conditions ahead, it was confirmed that, in surrounding rock sections with medium fracture connectivity and relatively well-developed joints and fractures, the GPR wave frequencies exhibit typical response characteristics, including sparse banded distribution, discontinuous and missing reflection events, high-frequency shift, and small-amplitude stepwise amplitude variations.