Ground penetrating radar detection of steel fiber reinforced composite linings in shield tunnels: Experimental and field studies

Abstract

Steel fiber reinforced concrete-reinforced concrete (SFRC-RC) composite linings are popular in shield tunnel construction due to exceptional strength and waterproofing properties. Non-destructive testing methods are essential for assessing the quality of these linings and ensuring tunnel construction safety. This study investigates the potential and parameters of ground penetrating radar (GPR) detection for the composite linings, using the Deep Tunnel Sewerage System-Phase 2 project in Singapore as a case study. The gprMax simulations incorporated the random distribution and precise parameters of steel fibers to conduct preliminary frequency selection studies. The structural setup of the model experiments mirrored that of the actual tunnel, allowing for an analysis of GPR penetration capabilities at various frequencies. Field testing provided authentic GPR data, validating conclusions drawn from simulations and model experiments and examining GPR power attenuation patterns. Findings indicate that GPR is effective for the quality detection of composite linings. The optimal frequency for detecting SFRC-RC composite linings is 300 MHz, which resolves the interfaces of different layered media. Based on single-parameter exponential and power function fitting, empirical formulas for power attenuation quantitatively characterize GPR signal attenuation in SFRC-RC composite linings. This paper offers valuable references for GPR detection of SFRC-RC composite linings.

Graphical abstract

Keywords

shield tunnel / steel fiber reinforced concrete / composite lining / ground penetrating radar / model experiment / field test

1 Introduction

With the continuous increase in the world’s population and the limitations of surface space, the development and utilization of urban underground space have become one of the primary objectives in current underground engineering [1–3]. As a typical form of underground engineering, tunnels play a significant role in various fields such as urban transportation [4–6], including subways [7–9], water supply and drainage [10], energy transmission [11–13], and many others. Due to strict control requirements for surface and building safety and high efficiency during tunnel construction, the shield tunneling method is the mainstream approach for urban underground tunnel construction [14,15]. Timely segment assembly and synchronized grouting during shield tunnel construction can effectively control the of ground loss, manage ground disturbance, and improve the structural integrity of the tunnel itself [16–18]. Traditional shield tunnel linings are mainly composed of precast reinforced concrete (RC) [19], but their crack resistance and water-sealing performance often face challenges in high-water-pressure environments. The steel fiber reinforced concrete (SFRC) segment, as a novel form of structural support, benefits from an extensive distribution of fibers within, which significantly enhances its crack resistance and impermeability [20–22]. Its utilization in shield tunnel support is experiencing a growing trend. For tunnels with higher impermeability requirements, such as water conveyance tunnels, the adoption of novel multi-layer composite linings including an SFRC layer, RC layer, waterproof layer and grouting layer can endow the lining with superior waterproofing capabilities.

However, due to the invisibility of composite lining materials, the quality of the lining cannot be evaluated through direct visual observation. Traditional core drilling sample methods and impact-echo methods hurt the mechanical properties, suffering from low precision and low efficiency [23]. As a mature, efficient, and highly accurate non-destructive testing technique, ground penetrating radar (GPR) has been widely applied in tunnel lining quality inspection [24–27]. GPR detection of shield tunnel linings has primarily focused on RC structures over the past few decades. In the case of SFRC segments, the presence of steel fibers results in multiple reflections of GPR waves during propagation through the medium, leading to greater interference. Currently, there is limited research on the detection of SFRC segments [28]. conducted numerical simulations and model experiments to study the penetration capability of GPR waves through SFRC segments [29]. investigated the steel fiber density and weak zones in SFRC elements by GPR. However, there is a scarcity of reports on the engineering application of GPR in SFRC segments or composite linings containing SFRC.

This study investigates the feasibility of GPR detection for the steel fiber reinforced concrete-reinforced concrete (SFRC-RC) composite lining of shield tunnel taking the Deep Tunnel Sewerage System (DTSS) Phase 2 in Singapore as an engineering background. Through numerical simulations, model experiments, and field data collection, the optimal GPR detection frequency is determined. The study also examines the waveform characteristics and imaging effects of GPR waves in the multi-layered medium of SFRC-RC composite lining, guiding the parameters of GPR application. Specifically, Section 2 introduces the research background, including the principle differences of GPR detection between SFRC segments and RC segments, the project overview of the DTSS, and the structure of SFRC-RC segments. In Section 3, numerical simulations are conducted for GPR detection of SFRC-RC composite lining. The study focuses on investigating the detection effectiveness of various medium interfaces and defects under different GPR frequencies. Section 4 involves model experiments and field detection conducted within DTSS Phase 2 in Singapore. The study analyzed imaging characteristics at different frequencies and compared and evaluated the detection effectiveness. Sections 5 and 6 present the discussion and conclusions of the paper, respectively.

2 Background

2.1 Differences in ground penetrating radar detection principles for reinforced concrete and steel fiber reinforced concrete layers

The principle of GPR is to use electromagnetic waves to reflect at different material interfaces due to variations in the materials’ dielectric constants, which enables the analysis of waveform reflections to obtain information about the detected targets’ size, location, and other characteristics. The reflection intensity of electromagnetic waves at material interfaces is determined by the reflection coefficient shown in Eq. (1) [30]. The greater the difference in {\epsilon }_1 between {\epsilon }_2, the stronger the reflection intensity of the GPR waves at that interface, leading to a more pronounced corresponding reflection waveform.

(1)C_{\mathrm{r}}=\left|\frac{\sqrt{{\epsilon }_1}-\sqrt{{\epsilon }_2}}{\sqrt{{\epsilon }_1}+\sqrt{{\epsilon }_2}}\right|,

where {\epsilon }_1 and {\epsilon }_2 represent the relative dielectric constants of the two materials.

As shown in Fig.1, there are certain differences in the detection of GPR in RC and SFRC segments. For RC segments, the incident electromagnetic waves generated by the GPR transmitting antenna T_x will undergo reflections at the interfaces of the segment’s edges and rebars. As rebars are strong reflectors, multiple reflections occur around them, resulting in strong multiple waves. These interfaces and multiple waves will be detected by the receiving antenna R_x. Unlike RC segments, SFRC segments incorporate a significant concentration of internal steel fibers, resulting in a more intricate reflection path for electromagnetic waves within the SFRC segments, as illustrated in Fig.1(b). As a result, the reflected waveforms captured by the receiving antenna contain more interference.

2.2 Structure of the steel fiber reinforced concrete-reinforced concrete composite lining

As shown in Fig.2(a), the novel multi-layer composite lining mainly consists of three parts from the outside: primary lining predominantly made of RC, secondary lining made of SFRC and high-density Polyethylene (HDPE) [31] waterproof layer. The thickness of these three layers is 200, 225, and 2.5 mm, respectively. Simultaneously, to compensate for the shield tai gap caused by cutter over-excavation, it is necessary to carry out synchronous grouting during the construction process to improve the lining’s stress distribution and compensate for ground losses.

As shown in Fig.2(b), different interfaces of the composite lining are labeled with different numbers for ease of distinction. Here, I represents the interface between free space and the HDPE layer, II represents the interface between the SFRC layer and the RC layer, III represents the interface between the RC layer and the grouting layers, IV represents the interface between the grouting layer and the geological stratum. Due to the relatively small thickness of the HDPE layer and its minimal interference with electromagnetic waves, it is not considered a detection target in the GPR research and it is not numbered among the interfaces with the SFRC layer.

The parameters and content of steel fibers in the composite lining have a significant impact on GPR detection performance, but their specific values are determined by the strength requirements of the lining in the particular project, which may vary between different projects [32]. The parameters of the steel fibers in SFRC layers of Phase 2 of DTSS are displayed in Tab.1. The dosage of the steel fibers in the SFRC layer is 40 kg/m³, which can be converted to a content of \omega = 0.513%. The density of a single steel fiber is 7.8 g/cm³, donated as {\rho }_0. The diameter D and length L are 0.75 and 60 mm, respectively.

2.3 Research approach

The research approach of this paper is illustrated in Fig.3. Three main research methods, namely numerical simulation, model testing, and field testing, are employed to investigate the feasibility and application of GPR on the SFRC-RC composite lining of shield tunnels. The proles of the three research methods are as follows.

1) Numerical simulation provides initial comparative options and guidance for the frequency selection of GPR in detecting SFRC-RC composite lining.

2) After the preliminary frequency range is determined, model testing is employed to assess the penetration performance of GPR waves in SFRC-RC composite lining within the selected frequency range.

3) Field GPR testing is conducted within a localized section of DTSS Phase 2. The optimal GPR detection frequency for the SFRC-RC composite lining is determined based on the analysis of collected GPR data’s waveform characteristics (A-scan), imaging features (B-scan), and power attenuation characteristics. Simultaneously, this process validates the results obtained from numerical simulation and model experimentation.

The three methods possess a characteristic progression from simplicity to complexity, from ideality to reality in terms of working conditions. They investigate the detection effectiveness of the SFRC-RC composite lining in shield tunnels from different perspectives, which enhances the persuasiveness and credibility of the research outcomes.

3 Numerical simulations for the composite lining detection

3.1 Finite Difference Time Domain (FDTD) method and gprMax

The propagation of electromagnetic waves in a medium is governed by Maxwell’s equations as shown in Eq. (2) [33]. The key challenge in numerical simulations for GPR is to solve the equations in complex media.

(2)\{\begin{array}{l}\mathrm{\nabla }\times H=\sigma E+\epsilon {\displaystyle \frac{\mathrm{\partial }E}{\mathrm{\partial }t}},\\ \mathrm{\nabla }\times E=-\mu {\displaystyle \frac{\mathrm{\partial }H}{\mathrm{\partial }t}},\\ \mathrm{\nabla }\cdot E=0,\\ \mathrm{\nabla }\cdot H=0,\end{array}

where E and H are the electric field intensity and the magnetic field intensity, respectively. \epsilon and \mu represent the relative dielectric constant and relative magnetic permeability of the medium, respectively.

gprMax 3.0 is an open-access numerical software widely utilized for GPR simulations [34–37]. Its principle is to solve Maxwell’s equations in three-dimensional (3D) using FDTD [38]. The Yee’s algorithms are utilized to discretize the spatial 3D medium into Yee cells, as illustrated in Fig.4. As can be seen from the figure, the magnetic field H and electric field E are spatially interleaved in the Yee cells, and each spatial component is well-suited for solving Maxwell’s equations using the finite difference method.

The main drawback of FDTD is its low computational efficiency. To improve computational efficiency in this paper, a 2D numerical model is employed, which involves the construction of a multi-layered composite lining.

3.2 Setup of the numerical model

3.2.1 Modeling method for steel fiber reinforced concrete layer

The numerical model of the SFRC layer needs to consider the random distribution and actual dimensions of the steel fibers. The generation process and principle of steel fibers are presented in Fig.5(a) and Fig.5(b), respectively. The quantity of steel fibers is calculated using Eq. (3), where both the area ratio and content are taken into consideration. After determining the number of steel fibers, random starting coordinates (x_0,y_0) for the steel fibers are generated within the SFRC layer. Subsequently, the endpoint coordinates (x_n,y_n) are calculated using Eq. (4), where the fixed distance L is maintained, but the distribution angle \alpha is randomized. Steel fibers continue to be generated until reaching a total of n, and the portion beyond the SFRC range is removed, resulting in the SFRC layer.

In gprMax, the steel fiber model is established using the built-in “cylinder” component. This involves generating random cylinders within the model, with (x_0,y_0) as the starting point and (x_n,y_n) as the endpoint, and having a diameter of D.

(3)n=\frac{\omega V}{V_0}=\frac{\omega S}{S_0},

where n is the number of steel fibers in the numerical model; V is the volume of the SFRC layer; V₀ is the volume of a single steel fiber; when the numerical model was in two-dimensional, the V and V₀ are replaced by corresponding area values S and S₀, respectively.

(4)\left(x_n,y_n\right)=\left(x_0+L\cos \alpha ,y_0+L\sin \alpha \right),

where (x_0,y_0) represents the starting point of the steel fibers numerical model; (x_n,y_n) represents the ending point of the steel fibers; \alpha is the inclination angle of the steel fibers.

3.2.2 Characteristics of the numerical model

3.2.2.1 Model dimensions and boundary conditions

The gprMax numerical model, as shown in Fig.6, has a length of 1 m, and a height is 0.65 m. To achieve detailed modeling of a large number of randomly distributed steel fibers, the minimum mesh size is set to 0.0005 m. The thickness of the HDPE layer, SFRC layer, and RC layer in the model is 2.5 mm, 0.225 m, and 0.2 m, respectively. The Perfectly Matched Layer [39] was used as the boundary absorbing condition in numerical simulations to avoid the reflection of GPR waves at the model boundary, with a thickness of 10 times the minimum grid size of the model.

For the distribution of reinforcing mesh in tunnel linings, different simplification methods are usually adopted when simulating with gprMax. For example, some researchers simplify the mesh by modeling a few rebar elements [40,41], while others use isotropic media with equivalent dielectric constants [42]. This study adopts the latter simplification method for the following three reasons. 1) This study does not focus on the propagation laws and characteristics of electromagnetic waves within RC layers, but instead aims to simulate the overall behavior of electromagnetic wave penetration through the medium. Therefore, from the results perspective, this simplification is acceptable. 2) The distribution of the rebar mesh in the RC layer is complex, making it difficult for the gprMax software to create a model that perfectly replicates the actual engineering scenario. Even if a simplified rebar model is established, the imaging results would differ significantly from the actual outcomes. 3) The distribution of the rebar mesh in the RC layer is relatively uniform; therefore, the composite structure formed by the rebar mesh and concrete can be simplified to a homogeneous medium with an equivalent relative permittivity.

3.2.2.2 Grout thickness distribution

In addition, the model considered the uneven grouting body to simulate the randomness of grout distribution in actual projects. The statistical results of the distribution of grout thickness are shown in Fig.7, which is distributed between 0.05 and 0.16 m, with mean and median values of 0.116 m and 0.107, respectively. The range of grout thickness distribution in the model is representative of different thicknesses in real projects. At the back of the grouting body, there is a rock/soil layer.

3.2.2.3 Material parameters

In the SFRC-RC composite lining, electrical parameters, including relative dielectric constant, conductivity, and relative magnetic permeability, have a significant impact on the propagation of GPR waves. The medium parameters of the numerical model are shown in Tab.2. Specifically, since all materials used in the study are non-magnetic or irrelevant to magnetism, the relative magnetic permeability of all materials was set to 1. The “free_space” material in gprMax was used to simulate voids [43], and the “pec” material was used to simulate steel fibers [44,45].

3.2.3 Parameters for ground penetrating radar detection

As displayed in Fig.6, we selected the Hertzian dipole model in gprMax to simulate the GPR antenna, with a fixed antenna spacing of 0.005 m in the detection process. The starting point of the monitoring line is located at the lower-left corner of the numerical model, and the GPR antenna moves with a step size of 0.005 m. Regarding the GPR data acquisition parameters, each survey line collects data from 147 monitoring points, and the sampling time window is set to 40 ns.

Existing research outcomes [28] demonstrated that in comparison to frequencies of 200 and 1000 MHz, GPR at 500 MHz exhibits superior penetration capability for SFRC segments. While the focus of this study is on SFRC-RC composite lining rather than pure SFRC segments, their outcomes still offered valuable insights that can inform the frequency selection in our study. Hence, frequencies of 300, 400, 600, and 700 MHz, chosen for their proximity to the 500 MHz frequency, were individually employed in numerical simulations of the identical model. This was undertaken to explore the efficacy of detecting SFRC-RC composite lining at varying frequencies, as well as to probe the response characteristics of diverse GPR frequencies to dissimilar material interfaces.

3.3 Numerical analysis at various ground penetrating radar frequencies

The B-scans at four different GPR frequencies are shown in Fig.8, and it can be observed from the figure that GPR exhibits significant variations in its detection capabilities for the interface of the SFRC-RC composite lining at different probing frequencies. The specific characteristics are as follows.

1) The results at 300 and 400 MHz are similar, as depicted in Fig.8(a) and Fig.8(b). Both frequencies exhibit more pronounced detection effects on interfaces I, III, and IV, while the detection effect on interface II is not significant.

2) As shown in Fig.8(c) and Fig.8(d), the numerical results at 600 and 700 MHz are quite similar as well. They exhibit relatively clear resolution for interfaces I and II, but their ability to reflect deeper interfaces III and IV is limited, with visibility only in localized regions.

3) Steel fibers exhibit a more complex wave reflection in the B-scans. Regarding the characterization of steel fiber reflection in GPR imaging, it can be analyzed that the sensitivity of 300 and 400 MHz to steel fiber reflections is lower compared to 600 and 700 MHz.

Due to the identical material parameters of concrete in the numerical model for both the SFRC layer and the RC layer, and considering the random distribution of steel fibers within the SFRC layer, the interfaces between the SFRC layer and the RC layer are not perfectly straight and regular. This non-uniformity in the interface geometry leads to a nonlinear distribution of the reflective surface in the B-scans. In Fig.8(c) and Fig.8(d), the criterion for identifying interface II is based on the presence of significant steel fiber reflections within the SFRC layer, while there are no such reflections within the RC layer.

In summary, compared to 600 and 700 MHz, 300 and 400 MHz exhibit stronger detection capabilities for deeper interfaces such as III and IV, whereas the 600 and 700 MHz provide a better response to the characteristics of the SFRC layer. In practical engineering applications, the SFRC layer and RC are artificially prefabricated with more controllable quality, while there is greater uncertainty in the quality of the grouting layer. Therefore, when conducting quality assessments of the grouting layer, it is advisable to choose lower-frequency GPR.

4 Model experiments and field testing

4.1 Engineering background

The DTSS is a superhighway for Singapore’s used water management, which conveys used water entirely by gravity to three centralized treatment plants strategically located in coastal areas [46]. The project is divided into Phase 1 and Phase 2, and this paper mainly focuses on Phase 2. Phase 2 covers the western part of the country with an additional 100 km of sewers that would end at the Tuas Water Reclamation Plant. The Phase 2 consists of 40 km of deep tunnels with internal diameters of 3–6 m and 10 km of the larger diameter Link Sewers, which are both constructed using a shield tunnelling method.

Taking the Southern Region Link Sewer Tunnel as an example, the geology where the tunnel passes is predominantly as follows. 1) Sedimentary rocks and soils of the Jurong Formation; 2) completely and highly weathered rocks which are highly undulating and variable due to faulting and folding. The main geotechnical risks of tunnel boring are tunneling in the mixed face, water ingress, ground settlement, and tunneling below the sea, which imposes high requirements on the lining support of the tunnel. To ensure the tunnel lining possesses excellent mechanical and impermeable properties, this project adopts a composite lining structure composed of a waterproof layer, an SFRC layer, and an RC layer.

4.2 Ground penetrating radar equipment

4.2.1 Ground penetrating radar hardware and parameter settings

The GPR used for this study is a dual-channel antenna, meaning each antenna has two different frequencies. The frequency combinations of the two antennas are 300/700 MHz and 400/600 MHz, respectively. The main parameters of the two GPR antennas are displayed in Tab.3. The composition of the dual-channel antenna allows for a more compact hardware structure, making the detection more efficient. The GPR does not have a main unit but instead transfers data directly to a computer through an Ethernet cable. During the detection process, it can be triggered through a measuring wheel to assist in accurately recording the detection distance.

4.2.2 Time–frequency characteristics of source wave

The time–frequency characteristics of GPR have a significant impact on its performance. The time–frequency spectra of two types of GPR antennas with frequencies used in this study are shown in Fig.9. As can be seen from the figures, The four frequencies, 300 and 400 MHz are not specific values but rather distributed within certain frequency bands. The frequency band of the GPR raw waveforms increases with the increase in frequency. The frequency band around 300 MHz is more concentrated, while the frequency range around 700 MHz is the widest. However, the position of the maximum intensity of the frequency of these frequencies, matches well with the nominal frequencies and demonstrates the good time–frequency characteristics of the GPR device itself.

4.3 Testing scheme

The testing is mainly divided into two parts: a full-scale model experiment and the field test, as shown in Fig.10. The full-scale model was artificially prefabricated in advance, its structure and quality are known, which can help me better eliminate factors other than the experimental variables. Meanwhile, the field test of the tunnel ensures a more realistic detection scenario, guaranteeing that the detection results are more representative and convincing. The specific details of these two schemes are as follows.

4.3.1 Full-scale model experiment

As shown in Fig.10(a), the lining structure of the model experiment is the same as the tunnel design, but it lacks the grouting layer on the outside. The GPR detection line was located on the inner side of the model, with a length of 1.2 m. The steel plate brackets on the outside of the lining can act as strong reflectors, helping us assess the penetration performance of the GPR. When strong reflectors exhibit distinct characteristics in GPR waveforms, it demonstrates that the GPR waves at the corresponding frequency possess favorable penetration capabilities through the SFRC-RC composite lining.

To study the penetrability of the selected frequencies through the SFRC-RC composite lining, we opted for the lowest and highest frequencies among the four, namely 300 and 700 MHz, to conduct line scans and assess their imaging effects.

4.3.2 Field testing for deep tunnel sewerage system phase 2

The monitoring line for the field test inside the tunnel, as shown in Fig.10(b), has a length of 5.6 m, and two antennas with four frequencies were employed to detect the same line. The monitoring line was located in the lower right corner of the tunnel, distributed along the tunnel’s direction to ensure that the detection range covers more rings, thus reducing the random errors introduced by single-ring construction.

The GPR acquisition parameters were the same for both the model experiment and the field test. The time window was set to 40 ns; the sampling interval was 0.5 cm per trace, meaning that each monitoring line collected 1119 A-scans; and the number of waveform stacking was set to 16. Moreover, due to the different propagation speeds of electromagnetic waves at different frequencies in the medium, there are significant differences in the temporal characteristics of their waveforms. To better reflect the detection characteristics at different frequencies, necessary data trimming and processing are essential.

4.4 Model experiment data analysis

The B-scans of the model experiment under 300 and 700 MHz are presented in Fig.11(a) and Fig.11(b), respectively. In the B-scan of 300 MHz, significant co-phased axes were observed at 4, 5, 10, and 16 ns, indicating the presence of interfaces in these locations. These interfaces are tentatively identified as the boundaries of mediums I, II, III, and IV, respectively. Within the range of 0.8 to 1 m, the signal intensity of GPR shows a significant enhancement, and multiple strong reflections are present in the time domain beyond 16. This indicates that the signal enhancement is caused by strong reflections from the steel plate behind the model. Along the monitoring line, except for the range of 0.8 to 1 m, the co-phased axes in other parts are consistently straight and uniform. This indicates that the thickness of each layer is stable, suggesting the absence of voids or debonding within the lining. This confirms the good quality of the prefabricated model.

As shown in Fig.11(b), the B-scan of 700 MHz shows significant differences compared to the 300 MHz. It cannot display the complete interfaces of the composite lining like the 300 MHz B-scan, and can only exhibit the interfaces of shallow layers. It can still capture the strong reflection characteristics of the steel plate and is aligned with the survey positions under 300 MHz. However, the reflection features of the steel plate with the 700 MHz GPR wave are not as pronounced as those observed with the 300 MHz wave.

The model experiment results indicate that the 300 MHz frequency demonstrates more significant penetration capability and detection effectiveness of the interfaces in the SFRC-RC composite lining, compared to 700 MHz. This is because the 700 MHz GPR waves experience more significant attenuation within the composite lining, making it unable to image the interfaces at deeper layers.

4.5 Analysis of field test data

4.5.1 Analysis of A-scan characteristics

The representative A-scans of the field GPR data in the DTSS Phase 2 tunnel can display different waveform characteristics at specific monitoring points. As illustrated in Fig.12, the A-scan at the 500th monitoring point was randomly selected for analysis at four different frequencies. The 300 MHz A-scan exhibits significant amplitude fluctuations around 5, 10, 15, and 20 ns, representing the interfaces of I–IV. Within the range of 5 to 10 ns, the waveform transition is relatively smooth, and there are no strong reflections or multiple reflection characteristics from the steel fibers in the waveform. As shown in Fig.12(b)–Fig.12(d), the A-scans at 400, 600, and 700 MHz can partially display some interfaces to varying degrees, but none of them can present the waveform characteristics of all material interfaces like 300 MHz. The waveforms of displayed interfaces gradually decrease, but higher frequencies make the waveform characteristics of shallow steel fibers more pronounced as the frequency increases.

4.5.2 Power characteristics of ground penetrating radar waves in steel fiber reinforced concrete-reinforced concrete composite lining

4.5.2.1 Analysis of the characteristics of instantaneous power attenuation

The propagation of GPR signals within a medium is accompanied by attenuation, and the varying degrees of attenuation significantly influence the detectability of targets and the quality of imaging. The mean and median of instantaneous power attenuation of GPR signals at four frequencies are shown in Fig.13. These are depicted by the green dotted line and the bold black solid line, respectively. The characteristics of power attenuation were analyzed as follows.

1) When analyzing the instantaneous GPR power attenuation, the median and mean can offer distinct information about data distribution and trends. The median is better suited for situations where there are outliers or anomalies within the data, while the mean is more effective at illustrating the overall average level. The mean and median values at the four GPR frequencies exhibit a notable level of overlap, indicating a relatively consistent pattern of energy attenuation and a limited presence of extreme values.

2) In terms of the general trends, the GPR energy within the SFRC-RC composite lining primarily follows an attenuation pattern. The attenuation of GPR signals at 300 MHz demonstrates consistent stability, with a relatively modest degree of signal loss. GPR waveforms at higher frequencies experience greater interference within the SFRC-RC composite lining.

3) The GPR signals at the three frequencies other than 300 MHz experience a sharp attenuation within the 5–20 ns range. This time range corresponds to the composite lining layer as shown in Fig.14(a). However, within the range of 20 to 30 ns, the GPR signal at 300 MHz continues to exhibit a gradual attenuation at a relatively low rate. On the other hand, the signal at 400 MHz approaches nearly no attenuation (the curve levels off). Meanwhile, at 600 and 700 MHz, there is an observed phenomenon of gradual power increase.

4) The manual operation of the GPR device during detection can introduce instability in data collection, potentially leading to variations in the power attenuation patterns of electromagnetic waves across the four GPR frequencies. For example, a sudden drop in power attenuation may occur at 5 ns in the 400 MHz frequency (as shown in Fig.13(b)). Moreover, this instability can potentially be mitigated through the adoption of more stable data collection methods.

Based on the aforementioned analysis, it can be concluded that, in the case of field-tested GPR data, the attenuation is relatively stable but lacks a clear pattern. As a result, the analysis of such data often allows only for qualitative assessments.

4.5.2.2 Empirical function of instantaneous power attenuation

To achieve a more profound understanding and quantitative assessment of the attenuation patterns, we conducted separate exponential and power function fittings combining the attenuation patterns shown in these figures. The instantaneous power, denoted as \eta, corresponds to a specific time value t on the GPR A-scan. The equations for the two types of fitting are presented in Eq. (5):

(5)\{\begin{array}{c}{\eta }_{\mathrm{e}}\left(t\right)={\mathrm{e}}^{-k_{1}t},\\ {\eta }_{\mathrm{p}}\left(t\right)=t^{-k_2},\end{array}

where {\eta }_{\mathrm{e}}\left(t\right) and {\eta }_{\mathrm{p}}\left(t\right) represent the fitting function of the exponential fitting and power fittings; e is a commonly used irrational number, with a value of 2.71828; k_1 and k_2 are the fitting coefficients of two fitting methods.

For a clearer representation of coefficients and patterns in the figure, we conducted natural logarithm and logarithmic transformations on {\eta }_{\mathrm{e}}\left(t\right) and {\eta }_{\mathrm{p}}\left(t\right), respectively. As a result, Eq. (5) becomes Eq. (6):

(6)\{\begin{array}{l}{\eta }_{\mathrm{e}}^{\prime }\left(t\right)=-k_{1}t,\\ {\eta }_{\mathrm{p}}^{\prime }\left(t\right)=-k_2\mathit{l}\mathit{g}(t),\end{array}

where {\eta }_{\mathrm{e}}^{\prime }\left(t\right) and {\eta }_{\mathrm{p}}^{\prime }\left(t\right) represent the transformed fitting functions of {\eta }_{\mathrm{e}}\left(t\right) and {\eta }_{\mathrm{p}}\left(t\right).

The best fitting curve of {\eta }_{\mathrm{e}}^{\prime }\left(t\right) and {\eta }_{\mathrm{p}}^{\prime }\left(t\right) at four frequencies of 300, 400, 600, and 700 MHz within the SFRC-RC composite lining are depicted by the blue dashed line and the red solid line in Fig.13. It is evident that both {\eta }_{\mathrm{e}}^{\prime }\left(t\right) and {\eta }_{\mathrm{p}}^{\prime }\left(t\right) are decreasing functions of their independent variable t. By comparing the magnitudes of the k_1 and k_2 in the fitting functions at different frequencies, the extent of attenuation in GPR signals can be directly determined to some extent. The values of k_1 and k_2 at four different frequencies, along with their corresponding empirical equations, are shown in Tab.4. As shown in the table, apart from the 700 MHz data in {\eta }_{\mathrm{p}}\left(t\right), it is evident that the power attenuation of GPR within the SFRC-RC lining generally follows an increasing trend with higher frequencies. The gradual increase in energy attenuation between 20 to 30 ns has led to a reduction in the value of k_1 in the {\eta }_{\mathrm{e}}\left(t\right) at 700 MHz. Under the same conditions, the {\eta }_{\mathrm{p}}\left(t\right) cannot represent this relationship. These results indicate that the {\eta }_{\mathrm{e}}\left(t\right) function provides a more precise characterization of energy attenuation.

4.5.3 B-scans at different ground penetrating radar frequencies

The B-scans of the field test under GPR frequencies are shown in Fig.14. As shown in Fig.14(a), the results at 300 MHz exhibit a good representation of the interfaces between each layer of the medium. The positions of the interfaces I, II, III, and IV are approximately 5, 11, 16, and 20 ns, respectively. The co-phase axis of each layer is significant and continuous. However, B-scans at the other three frequencies are unable to comprehensively represent all interfaces within the SFRC-RC composite lining. Moreover, as the frequency increases, the display depth of material interfaces becomes more restricted. Fig.14(b) can only display interfaces I and II, while Fig.14(c) and Fig.14(d) can only display interface I. The frequencies of 400 and 600 MHz demonstrate good capabilities in capturing multiple reflections caused by the steel fibers, with 600 MHz exhibiting even stronger capabilities in visualizing the steel fibers than 400 MHz. The GPR signal at 700 MHz only exhibits higher intensity in the surface layer of the SFRC-RC composite lining. However, its ability to detect steel fiber features and deeper interfaces is relatively weak.

The results of the model experiment all indicate that the 300 MHz GPR has a better detection capability for the medium interfaces of the SFRC-RC composite lining. It also serves as validation for the numerical simulation results.

5 Discussion

Compared with traditional RC segmental linings, SFRC-RC composite linings exhibit favorable mechanical strength and impermeability in engineering projects such as shield tunnels. In this paper, our primary focus is on the GPR detection of SFRC-RC composite tunnel lining. We investigated the potential application of GPR in quality assessment within this field and researched suitable detection frequencies and signal attenuation patterns.

There is limited research on GPR detection of SFRC-RC composite segments. Hence, when it came to selecting GPR frequencies, we looked to studies involving the penetration capabilities of pure SFRC segments. Consequently, we opted for frequencies of 300, 400, 600, and 700 MHz, which are near the 500 MHz range. The research results indicate that lower GPR frequencies, such as 300 MHz, offer better delineation imaging of the interfaces within SFRC-RC composite lining. In addition, this study primarily focuses on the penetration performance of GPR on the novel composite lining and does not aim to study the precise determination of interface positions. As a result, the numerical simulations and field testing conditions were relatively simple, leading to correspondingly straightforward waveform characteristics in the detection results. Therefore, the experimental and field data in this study underwent only basic filtering and gain adjustments, without further exploration of advanced data analysis methods. In future research, we anticipate developing data processing methods specifically tailored for composite linings and their associated GPR detection frequencies. This advancement is expected to significantly enhance the detection efficacy of GPR in these tunnel structures.

The HDPE layer is non-metallic and non-magnetic, and its thickness is relatively thin. We speculate that the propagation of GPR in it is essentially unaffected. Therefore, it was not analyzed as a separate layer. While this layer was included in the numerical model, it was not considered a primary focus of our study.

In terms of GPR power attenuation analysis, we can achieve a relatively sound qualitative understanding of energy decay through the patterns of mean and median distribution. However, this understanding cannot be subjected to quantitative analysis and comparison. The exponential and power function fittings we opted for are based on the intrinsic characteristics of the attenuation law itself. By considering the behavior of the functions and the fitting coefficients, we can effectively characterize the degree of attenuation at various frequencies. This approach offers a robust quantitative representation method. We opted for relatively simple function models, such as {\eta }_{\mathrm{e}}\left(t\right) and {\eta }_{\mathrm{p}}\left(t\right), to maintain single coefficients in the empirical equations for fitting. This approach aims to minimize interference in characterizing the attenuation characteristics of GPR signals.

6 Conclusions

This paper takes the DTSS Phase 2 in Singapore as an engineering background to investigate the potential of GPR for quality detection in SFRC-RC composite lining of shield tunnels. Numerical simulations, model experiments, and field engineering tests were carried out to study the GPR waveforms, imaging characteristics, and power attenuation patterns in SFRC-RC lining. Through these studies, this paper proposed the optimal detection frequency for SFRC-RC composite lining and also presented an empirical formula for power attenuation of GPR signals in SFRC-RC composite lining. The specific research conclusions are as follows.

1) A gprMax numerical model, incorporating actual steel fiber parameters, was established for the SFRC-RC composite lining. Numerical simulations indicate that 300 and 400 MHz exhibit superior detection capabilities for deeper interfaces such as III and IV.

2) Based on the analysis of GPR signal attenuation patterns in SFRC-RC composite lining at frequencies of 300, 400, 600, and 700 MHz, the attenuation empirical equations were fitting. This enables a quantitative characterization of different attenuation situations through the fitting coefficients of empirical equations. The exponential function model {\eta }_{\mathrm{e}}\left(t\right) effectively reflects the attenuation characteristics of the four frequencies within the SFRC-RC composite lining. The attenuation coefficients corresponding to 300, 400, 600, and 700 MHz are 0.133, 0.203, 0.349, and 0.261, respectively.

3) GPR was validated as an effective means of non-destructive testing of SFRC-RC composite linings. After selecting and comparing four different frequencies (300, 400, 600, and 700 MHz), it was determined that 300 MHz is the optimal frequency for detecting the interfaces of SFRC-RC composite lining.

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