Research on the deformation and settlement characteristics of tunnel lining structures based on distributed fibre optic sensing technology

Abstract

To study the deformation and settlement characteristics of tunnel lining structures, a tunnel lining structure model was designed based on distributed fibre optic sensing technology. Compared to the cylindrical model used in traditional tunnel lining structural model experiments, in this study, a reinforced concrete structural model was adopted, which can embed fibre optics in the structure, which is closer to actual tunnel engineering conditions. Central and symmetrical concentrated loading experiments were carried out with a simply supported reaction frame. The results of the distributed fibre optic monitoring were compared and analysed with those of traditional monitoring methods to verify the reliability of the distributed fibre optic monitoring results. The numerical simulations of the experiments were conducted by using finite element analysis. By comparing and analysing the simulation and experimental results, the correctness of the simulation calculation results were verified. On this basis, the impact of concrete strength, circumferential reinforcement spacing, and longitudinal reinforcement strength on the deformation and settlement of the tunnel lining structure were analysed. The results show that the hierarchical effect of the strain monitoring results obtained by the embedded fibre optic is more obvious, indicating that the radial monitoring effect of the embedded fibre optic on the tunnel structure is less affected by other external factors than the strain gauge, and the monitoring data are more accurate and effective, with good engineering characteristics. Improving the concrete strength, appropriate circumferential reinforcement spacing, and increasing the longitudinal reinforcement strength can effectively enhance the ability of the structure to resist deformation at the stress location. These factors play a significant role in improving the overall resistance to deformation and safety of the structure. The research results provide a theoretical basis and experimental data for the application of distributed fibre optics in monitoring the deformation and settlement of tunnel lining structures.

Keywords

tunnel engineering lining structure model experiment distributed fibre optic deformation monitoring

Introduction

In the engineering field, the problem of deformation monitoring of tunnel lining structures has always been a focus that cannot be ignored (Domaneschi et al., 2020; Giardina et al., 2019; Soomro et al., 2018; Zhang et al., 2008) and plays a very important role in the whole cycle health monitoring of tunnels. With increasing tunnel operating mileage and service life, the issues that need to be considered for its structural performance and overall safety are becoming increasingly prominent. Achieving real-time, accurate, long-distance, and large-scale access to deformation data and variation patterns of tunnel lining structures is a fundamental scientific issue that is currently a key focus of tunnel engineering monitoring.

To date, considerable research has been devoted to tunnel monitoring. Farahani et al. (2019) proposed compressing and loading a tunnel model by applying the displacement from the exterior wall and monitoring deformation through a three-dimensional digital image correlation (DIC) system adopted for the track structure. However, DIC technology also has drawbacks such as consuming a large amount of computing resources and requiring high image quality requirements. Huang et al. (2017) introduced mobile tunnel inspection (referred to as MTI-100) and designed a charge coupled device (CCD)-based image acquisition system for camera scanning to monitor tunnel surfaces, which also requires high hardware and pixel requirements. Montero et al. (2015) introduced the key issues of tunnel monitoring and proposed using the latest developed tunnel robot monitoring system to monitor tunnels. In the process of existing tunnel monitoring research, various monitoring methods (Yang and Xu, 2021) and monitoring instruments (Attard et al., 2018) have been applied, but none of them can escape the problem of monitoring costs. Therefore, researchers have turned their attention to the method of mutual verification between on-site measured data and numerical calculations (Anastasopoulos et al., 2008; Tan et al., 2020; Yan et al., 2020), for example Han et al. (2018) proposed a risk assessment method aimed at assessing the risk of circumferential cracks in existing shield tunnels, assuming the existing tunnel to be a beam elastic foundation. Zhang et al. (2020) simulated the shield tunnelling process in curved sections using finite element software, taking the shield tunnel of Zhuhai Metro as the engineering background, and conducted parameter analysis on the distribution of overbreak on the inner and outer sides of the tunnel. Sugimoto et al. (2007) proposed a specific shield tunnelling motion model to describe the excavation process of shield tunnelling. These researchers simulated the excavation process of a slurry water balance shield tunnelling machine along a curved tunnel and compared it with measured data for verification. However, the environmental conditions in actual tunnel engineering are very complex, and there may be some differences between numerical simulation and actual situations. In addition to the monitoring methods and means mentioned above, researchers have started monitoring tunnels from various aspects, Gómez et al. (2020) introduced the application of distributed fibre optic sensing technology in structural health monitoring of a subway tunnel in Barcelona. Kontogianni and Stiros (2005) summarized the commonly used types of ground deformation measurements in tunnel excavation, the difficulties in obtaining these measurement values, and the most commonly used methods in evaluation. Yang et al. (2018) studied the cracking and failure of the tunnel lining in the Shanghai subway system through on-site observation and measurement, analysed the proportion and radius ellipticity of the damage ring, and described the degree of damage to the tunnel section lining ring and the lateral deformation of the lining ring. The abovementioned experts and scholars use various methods to monitor tunnels. The above methods not only have the characteristics of high monitoring costs and large data deviations, but also often have low durability and may not be able to meet the requirements of long-distance and large-scale monitoring work.

Distributed fibre optic sensing technology has shown good monitoring performance. For example, Klar et al. (2014) utilized distributed fibre optic sensing technology to monitor surface displacement models by appropriately optimizing and analysing the information obtained from horizontally laying fibre optics above the tunnel in both 2D and 3D directions. Buchmayer et al. (2021) proposed a tunnel monitoring method based on distributed fibre optic sensing (DFOS), which provided hundreds of strain- and temperature-sensitive points within the structure and provided new information regarding the performance of tunnel linings. Distributed fibre optic sensing technology was also widely used in data monitoring of reinforced concrete components, especially in structural tests (Bado et al., 2021; Berrocal et al., 2021). Barrias et al. (2018) used distributed fibre optic sensors to provide continuous (in space) strain data along the fibre with high spatial resolution. In order to better apply distributed sensing technology, many experts invented different types of distributed fibre optic sensors (Parker et al., 2014). The emergence of these different types of distributed fibre optic sensors have solved some practical problems in engineering, such as using alkali resistant glass fibre optic sensors (Bremer et al., 2017) to monitor concrete and using distributed acoustic sensors (Lindsey et al., 2017) to transmit seismic wave information. Regier and Hoult (2014) studied the performance of a distributed fibre optic strain measurement technology with high accuracy and spatial resolution during the loading process on reinforced concrete bridges. Sun et al. (2021) discussed three typical DFOS deployed ground military system projects and explored two research results to guide the on-site application of ground military systems for wide use in future large-scale all optical ground military system monitoring stations. The application of distributed fibre optic sensing technology has been greatly expanded in the oil and gas industry (Baldwin, 2015; Skinner and Maida, 2014), especially in the field of well monitoring (Sasaki et al., 2019).

In recent years, many experts and scholars have used distributed fibre optic sensing technology for monitoring in different fields, and these experts have made significant progress in fibre optic sensing in various fields (Amer et al., 2021; Bassil et al., 2019; Han et al., 2023a, 2023b; Narisetty et al., 2021; Xu et al., 2018; Zhang et al., 2018; Zheng et al., 2021). However, there is currently relatively little research on the deformation characteristics of tunnel lining structures using this technology, especially for actual concrete tunnel lining structures.

In this study, distributed fibre optic sensing technology is employed to design a tunnel lining structure model and conduct experiments. Compared to the cylindrical model used in traditional tunnel lining structure model experiments, here, a reinforced concrete structure model is used, which can deploy distributed fibre optics inside and outside the tunnel lining structure, which is closer to the actual tunnel engineering conditions. By applying different types of loads and monitoring distributed fibre optic data and strain gauge data at different loading stages, the deformation and settlement characteristics of tunnel lining structures are studied. Finally, numerical simulations of the experiments are conducted to analyse the deformation and settlement characteristics of the tunnel lining structure. The impacts of the concrete strength, circumferential reinforcement spacing, and longitudinal reinforcement strength on the deformation and settlement of the tunnel lining structure are analysed. The research results can provide a theoretical basis for applying distributed fibre optic sensing technology to tunnel deformation monitoring.

PPP-BOTDA sensing technology

Pulse prepump Brillouin optical time domain analysis (PPP-BOTDA) sensing technology based on the principle of Brillouin scattering light analysis as the main method of fibre strain monitoring was adopted in this investigation. BOTDA is a new sensing technology with the rapid development of fibre optic and fibre optic communication technology. This technique uses light as the information carrier and fibre optics as the medium and detects changes in the Brillouin scattering frequency shift in the fibre optics. Then, it uses the linear relationship between its frequency shift change and time to perceive changes in the physical properties of the tested object. Brillouin scattering can be further divided into self-issued Brillouin scattering and stimulated Brillouin scattering, where the signal intensity of stimulated Brillouin scattering is higher than that of self-issued Brillouin scattering and it is easier to capture by optical instruments. The BOTDA system architecture is shown in Figure 1.

Figure 1.

BOTDA system architecture diagram.

Figure 1 depicts a common BOTDA system architecture diagram. The continuous light of a certain wavelength generated by the optical transmitter enters the detection branch of the detection light and pump light through an optical wave machine. The pump light is amplified by a reference light amplifier and demodulated into pulse light. The detection light is controlled by a microwave generator and voltage generator and is protected by a scrambler. When the detection light meets the pulse light in the sensing fibre, Brillouin scattering occurs. The corresponding data are extracted and demodulated by an optical circulator and recognized and displayed using a photodiode connected to an oscilloscope.

Assuming that the sound waves of fibre optic decay exponentially, the Brillouin scattering gain spectrum is commonly represented by the Lorentzian curve shape (Horiguchi et al., 1989; Nikles et al., 1997):

g_{B} (v) = \frac{{(Δ v_{B})}^{2}}{{(v - v_{B})}^{2} + {(Δ v_{B} / 2)}^{2}} g_{0}

(1)

where

g_{0}

is the peak of the stimulated Brillouin gain spectrum,

Δ v_{B}

is the maximum half width of the gain spectrum, and

v_{B}

is the Brillouin centre frequency.

For incident light with a wavelength of 1550 nm propagating in a quartz fibre, its corresponding Brillouin gain coefficient $g_{0} = 5 \times 10^{- 11} m / W$ . Brillouin scattering only occurs in backscattering, and the frequency shift of backscattered light is (Nikles et al., 1997):

v_{B} = 2 n v_{A} / λ_{p}

(2)

where n is the refractive index of the fibre optic,

λ_{p}

is the wavelength of the pump light, and

v_{A}

is the velocity of sound waves. The Brillouin frequency shift

v_{B}

refers to the frequency corresponding to the peak in the stimulated Brillouin gain spectrum. The velocity of sound waves can be given by the following equation (Horiguchi et al., 1989):

v_{A} = \sqrt{\frac{(1 - μ) E}{(1 + μ) (1 - 2 μ) ρ}}

(3)

where

E

is the elastic modulus of the medium,

μ

is the medium ratio, and

ρ

is the density, which is a modulation tool for the influence of temperature and strain on the speed of sound, which can be expressed as a function of temperature

T

and strain

ε

. Meanwhile, temperature and strain cause changes in the refractive index through thermal and elastic optical effects. According to the above formula, it can be concluded (Horiguchi et al., 1989; Nikles et al., 1997):

v_{B} (T, ε) = 2 n (T, ε) \frac{\sqrt{\frac{[1 - μ (T, ε)] E (T, ε)}{[1 + μ (T, ε)] [1 - 2 μ (T, ε)] ρ (T, ε)}}}{λ_{P}}

(4)

When the fibre is affected by temperature or strain, the Brillouin gain spectrum shifts, and the Brillouin frequency corresponding to the peak of the gain spectrum also changes.

Description of the experiment

Design and production of model specimens

The tunnel lining structure model we designed is based on actual tunnel engineering, considering the common thickness of the initial and secondary lining, and is designed as a reinforced concrete model. Compared with the cylindrical model, it is closer to the actual tunnel engineering. At the same time, monitoring points can be placed not only on the surface of the model, but also inside the model to achieve research on the monitoring effect of embedded optical fibres.

The total length of the specimen model structure used in the experiment was 300 cm, and the calculated bending length was 260 cm, as shown in Figure 2(a). According to the actual design dimensions of the composite lining structure in tunnel engineering, the lining thickness of the tunnel lining structure model was 148 mm. The internal reinforcement cage of the specimen was composed of longitudinal and circumferential reinforcements, with specific locations shown in Figure 2(b). Among them, 26 external longitudinal reinforcements were set, 20 internal longitudinal reinforcements were set, and a total of 15 sets of circumferential reinforcements were set. The thickness of the concrete protective layer of the specimen was 30 mm. The specimen material was made of concrete with a strength grade of C40, the longitudinal reinforcement was made of HRB400 grade C10 ribbed steel, and the circumferential reinforcement was made of HRB335 grade ribbed steel.

Figure 2.

Schematic diagram of the specimen model structure.

During the production process of the model specimen, the internal formwork of the specimen was first subjected to waterproofing treatment and then placed inside the reinforcement cage that had already been arranged for monitoring. The internal formwork was separated from the reinforcement cage by adding a concrete grid block with a strength of C40. The specific production process is shown in Figure 3.

Figure 3.

Schematic diagram of the formwork layout in the specimen of the tunnel lining model.

In the central concentrated loading specimen, a total of three optical fibres were laid, with the first fibre laid on the outer reinforcement cage of the arch and the left side of the structure, tied together with the reinforcement cage to form a whole. The second fibre optic is a surface-mounted fibre optic, which is placed on the surface of the concrete on the left and right sides of the structure. It is bonded to the surface of the structure using fibre optic adhesive and used to monitor the strain of the concrete on both sides of the tunnel. The third optical fibre is protected by a sheath and placed at the arch bottom, tied together with the reinforcement cage at the arch bottom, to monitor the strain of the arch bottom.

In the symmetrical concentrated loading specimen, a total of three optical fibres were laid, with the first fibre laid out in the same way as the central concentrated loading specimen. The second optical fibre is laid in the circumferential direction of the reinforcement cage on the outside of the tunnel, with specific locations at the midpoint and third point. A total of three circumferential optical fibres are laid and tied together with the outer reinforcement cage to monitor the circumferential strain of the tunnel structure. The third optical fibre is also laid at the arch bottom and is protected by a sheath to monitor the strain of the arch bottom.

As shown in Figure 3, after the internal formwork was firmly connected to the reinforcement cage, the composite body was placed in a vertically placed external formwork formed by splicing six steel plates for pouring work. To evenly distribute the internal materials of the model specimens and completely fill them inside the formwork, the model specimens involved were all poured vertically. The poured model specimens were cured according to relevant standards. After reaching the designed usage condition, the internal and external formworks were removed, and the production of the model specimens was completed.

Experimental monitoring point design and data collection

Experimental monitoring point design

There were three longitudinal fibre optics sensors arranged inside the central concentrated loading specimen that were closely attached to the external longitudinal reinforcement. The positions were at the top, left, and bottom of the specimen. Two longitudinal glass fibre cloth sensing fibre optic sensors were respectively arranged on the specimen surface, located at the waist positions of the specimen and closely attached to the concrete surface. The specific deployment method is shown in Figure 4(a). ① is the placement position of the embedded reinforcement base cable fibre optic located on the vault and the left side of the waist of the specimen. ② is the placement position of the glass fibre cloth sensing fibre optic on the two waist sides of the specimen surface. ③ is the placement position of the embedded sheath fibre optic at the arch bottom of the specimen.

Figure 4.

Schematic diagram of the distributed fibre optic layout for the experimental specimens.

Six parts of the fibre optics were arranged inside the symmetrical concentrated loading specimen. Three longitudinal fibre optic sensors were arranged at the same position as the internal fibre optics of the central concentrated loading specimen, and three circles of the embedded reinforcement base cable fibre optic were arranged at the midpoint and the three points of the specimen. The specific deployment method is shown in Figure 4(b). ① is the placement position of the embedded reinforcement base cable fibre optic located on the vault and the left side of the waist of the specimen. ② is the placement position of the embedded reinforcement base cable fibre optic located in the circumferential direction inside the specimen. ③ is the placement position of the embedded sheath fibre optic at the arch bottom of the specimen.

The layout of the strain gauge inside the experimental specimen is shown in Figure 5. The blue square point is the layout position of the reinforcement strain gauge, and the red triangle point is the layout position of the concrete surface strain gauge; they are arranged at the midpoint and three-point point of the specimen, respectively. To accurately measure the settlement state of the specimen and control the overall specimen during the loading process, dial indicators were installed at the middle position at the bottom of the specimen, the three-point position at the bottom of the specimen, and the position of the openings at both ends of the specimen. The specific layout position is shown in Figure 5. Corresponding position displacement data were recorded in real time by connecting computers. The crack and vertical displacement changes at key locations were observed in real time and adjusted in a timely manner, which could provide guarantees and support for experimental safety and subsequent data analysis.

Figure 5.

Schematic diagram of the strain gauge layout for the experimental specimens.

Data collection

The collection, demodulation, and organization of fibre optic data in the experiment were carried out using an NBX-6050A optical nanometre. It is a Brillouin optical time-domain analysis and demodulation instrument with centimetre level accuracy developed by Neubrex Co., Ltd., Japan. The longest wavelength that can be monitored via PPP-BOTDA is within a range of 27 km. The frequency range measured by this sensor is 9–13 GHz (−3%∼4% microstrain), and the measured strain range is −30000∼+30000 $μ ε$ . The measurable length ranges include 20 m, 50 m, 100 m, 250 m, 1 km, 2.5 km, 5 km, 10 km, and 25 km. The strain measurement accuracy of this sensor is ± 7.5 $μ ε$ . It is a TDS-530 static strain analyser that was used to collect and sort strain gauge data. This device can test the performance of the strain gauge data 80 points at a time.

Loading scheme

The experiment used a 2000 kN lifting jack-reaction frame system to perform loading on the specimens. It was divided into two methods: central concentrated loading and symmetrical concentrated loading. In practical engineering, the loading on tunnel lining structures may be complex and diverse. The two loading methods used in this paper are representative in terms of loading forms. Moreover, central concentrated load and symmetric concentrated load are also common loading methods for specimens in laboratory experiments. Therefore, the two common and laboratory achievable loading scheme were used in the research. The experimental specimens were placed on the lower side of the lifting jack through a steel support bracket. For the central concentrated loading, a rubber buffer block was placed between the specimen and the lifting jack to ensure uniform force application in the middle of the specimen while protecting the lifting jack. For the symmetrical concentrated loading, rubber buffer blocks were placed at two symmetrical concentrated positions on the upper platform of the experimental specimen, and a distribution beam was added on the rubber buffer blocks to transmit the load applied by the lifting jack-reaction frame system. The experimental layout is shown in Figure 6.

Figure 6.

Layout of the specimen loading.

In the preloading stage, the specimen was first preloaded with 10 kN and subjected to a continuous load of 5 min. After the overall structure was stable, the dial gauge and strain gauge data at three positions were cleared, and the initial fibre optic data were recorded and saved. After the preloading was completed, further adjustments were made to the equipment that needed to be adjusted, and the pressure applied to the specimen by the loading equipment and the dial gauge reading were reset to zero. After the preparation work was completed, formal loading could be carried out.

During the formal loading stage, the loading was carried out according to a gradient of 20 kN per level after the initial data testing was completed. The load continued for 5–8 min after each level of loading was completed. The dial gauge readings, strain gauge and fibre optic data, and the crack development state were measured and saved after stabilization. When the crack or displacement reached a state of rapid increase and the specimen could not withstand force, loading stopped, and the experiment terminated.

Experimental results and analysis

Central concentrated loading experimental results and analysis

Analysis of the final state and crack development of the specimen

Through observation and recording, in this experiment, the loading of the specimen was terminated at 440 kN. The state on the right side of the specimen after terminating loading is shown in Figure 7. The specimen surface is mainly composed of vertical cracks and oblique cracks. As shown in Figure 8, the specimen will experience a certain degree of settlement displacement after being subjected to external forces. The closer it is to the middle, the greater the settlement displacement.

Figure 7.

Site diagram of the final state on the right side of the central concentrated loading specimen.

Figure 8.

Settlement results of the middle part of the bottom of the central concentrated loading specimen.

As the loading force increases, the settlement displacement gradually increases significantly. Using the total length of the specimen of 300 cm as the analysis object, the settlement data of the specimen bottom under 7 different loading force states at intervals of 60 kN were plotted (see Figure 9).

Figure 9.

Settlement of the bottom of the central concentrated loading specimen.

As shown in Figure 9, with the continuous application of an external loading force, the settlement increase in the middle part of the specimen is particularly significant compared to other parts. This indicates that the specimen is in good condition during this loading process, and all values have basically reached the preset state. Figure 10 is a schematic diagram of the development of the cracks in the central concentrated loading specimen.

Figure 10.

Schematic diagram of crack development in the central concentrated loading specimen.

As shown in Figure 10, the time when cracks began to appear on the right side of the specimen is generally consistent. However, as the load continues to increase, the number, length, and width of the cracks also continue to expand, with the development of the cracks on the right side being particularly significant. Combined with the settlement of the central concentrated loading specimen, it can be found that the settlement state at the corresponding position is significantly positively correlated with the number and length of the cracks. The closer the distance to the force point is, the greater the settlement displacement is with increasing concentrated force, and the increase in the number and length of the cracks is also more significant.

Comparison and analysis of the results of the fibre optic and strain gauge

Strain gauge data collected by the TDS-530 static strain analyser and fibre optic strain data collected by the NBX-6050A optical nanometre were collated and compared with the corresponding representative key monitoring position data.

First, the data of the concrete strain gauge, reinforcement strain gauge, embedded fibre optic and surface-mounted fibre optic at the left waist side of position ① in Figure 5 were sorted out, and the specific strain is shown in Figure 11.

Figure 11.

Strain comparison at the left waist side of position ① of the central concentrated loading specimen.

Through the analysis of the strain monitoring life length, it can be found that the effective length of the monitoring data of the three monitoring materials presents the following trend: concrete strain gauge < reinforcement strain gauge < fibre optic with increasing loading time and load force. A comparison of the integrity of the strain monitoring data shows that concrete strain gauge < reinforcement strain gauge and fibre optic. According to the comprehensive analysis, the main reason for this phenomenon is that the three monitoring material layouts are different from the environment. When the concrete strain gauges adhere to the specimen surface through cementitious materials such as epoxy resin, some concrete strain gauges will not stick well. At the same time, the surface tension of the specimen will cause the earliest tensile crack of concrete in the area monitored by the concrete strain gauges to exit service. This results in the condition that the time of the effective monitoring data is too short. For the reinforcement strain gauge, because the reinforced concrete structure is in the stress state, the concrete first serves, and the reinforcement begins to serve after reaching a certain strength. There is no obvious strain change in the early stage of structure stress, and there will be obvious mutation points after the reinforcement serves at a certain stage. For the fibre optic, whether it is surface mounted or embedded, the longitudinal direction data are basically consistent with the data shown by the reinforcement strain gauge, and the later development data are complete. Therefore, it can be considered that its overall coordinated deformation with the specimen is good, which can reflect the strain situation at the corresponding position of the specimen more accurately. For the three-point position, position ③ in Figure 5 was selected as the representative to analyse the strain monitoring data, as shown in Figure 12.

Figure 12.

Strain comparison at both waist sides of position ③ of the central concentrated loading specimen.

As shown in Figure 12, the strain variations at the left and right waist positions are basically the same, and the fluctuations at the end are probably caused by factors such as the failure of the reinforced concrete member to achieve a fully uniform distribution of the internal material during fabrication. The reasons for the differences between the data monitored by the left concrete strain gauge and other strain data may be due to the insufficient adhesion of the left concrete strain gauge to the structure during the experiment, resulting in significant differences between the monitored data and other monitoring data. This also indirectly indicates that the fibre optic monitoring method has the characteristic of being less affected by environmental conditions. The strain gauge at the right side of the concrete exits service after the cracks occur, and the data obtained begin to fluctuate in the corresponding state, while the fibre optic data show a growth trend consistent with that shown in Figure 11. Overall, the analysis shows that fibre optic monitoring can more completely and effectively reflect the actual structural strain variation law than the concrete strain gauge.

In conclusion, the distributed fibre optic monitoring results are more effective and accurate than the strain gauge monitoring results in terms of monitoring time, data integrity, etc.

Comparative analysis of the radial fibre optic strain results

The radial fibre optic monitoring results of the five positions in the specimen were extracted and sorted out. The analysis work was carried out one by one, mainly aiming at the calculated bending length of the specimen. First, the strain data of the longitudinal embedded reinforcement base cable fibre optic at the top of the specimen were processed, and 7 loading levels of data were selected to draw the strain diagram of the fibre optic (see Figure 13).

Figure 13.

Radial embedded fibre optic strain at the top of the central concentrated loading specimen.

As shown in Figure 13, through the analysis of the strain diagram of the radially embedded fibre optic, it can be found that with the step-by-step increase in the external loading force, the radial deformation of the specimen becomes increasingly clear. The closer the fibre optic is to the central position, the faster the strain growth rate; the growth state shows an overall parabolic shape. Although the overall strain of the specimen varies parabolically as a function of position, compared to other positions, the strain growth rate is significantly lower at the position where the circumferential reinforcement is placed during the early loading stage. This shows that the arrangement of the circumferential reinforcement can effectively improve the service life of the specimen to a certain extent.Figure 14 shows the strain diagram of the three radial fibre optics at the two waist sides of the specimen.

Figure 14.

Strain of the three radial fibre optics at the two waist sides of the specimen.

As shown in Figure 14, for either the embedded fibre optics inside the specimen or the surface-mounted fibre optics outside the specimen, the data show that the increase in strain is more pronounced in the region closer to the middle as the loading force continues to increase. When the loading force is in the range of 0–180 kN, the whole specimen exhibits a stable state. The strain increases slightly, and the corresponding monitoring area shows a compressive state. When the loading force is 180 kN, the specimen exhibits a stable state near the force point and is in tension-compression equilibrium. When the loading force is in the range of 180–360 kN, the strain at the position within ± 0.5 m in the middle of the specimen begins to increase significantly, showing a trend similar to a parabolic state overall. From the loading force of 360 kN until the end of the experiment, the strain growth rate at the centre of the specimen further accelerates, and the surface-mounted fibre optic data curve begins to show extremely obvious fluctuations.

By comparing Figure 14(a) and (b), it can be found that the data of the embedded fibre optics are smoother than those of the surface-mounted fibre optics. It is considered that the surface-mounted fibre optics are bonded to the specimen surface through adhesives such as epoxy resin, which can easily cause misalignment of the bonding positions, weak bonding, or voids. This results in significant fluctuations in the data curve, which can affect the accuracy of the monitoring data. These data may also indicate that the radial monitoring effect of the embedded fibre optics on tunnel structures is less affected by external factors compared to surface-mounted fibre optics, and the monitoring data are more accurate and effective in engineering features. Figure 15 shows the strain cloud image of the three fibre optics at the two waist sides of the specimen.

Figure 15.

Strain cloud diagram of the three radial fibre optics at the two waist sides of the specimen.

As shown in Figure 15, similar to the strain curve, all three distributed fibre optics well reflect the actual strain trend of the specimen. Through a comparison, it can be found that the strain monitoring results obtained by the embedded fibre optic are smoother and reflect a certain degree of fluctuation in the location of the circumferential reinforcement. The analysis shows that for the radial monitoring effect of tunnel lining structures, embedded fibre optics are less affected by external factors and are more accurate and effective than surface-mounted fibre optics.

Symmetrical concentrated loading experimental results and analysis

Analysis of the final state and crack development of the specimen

Through observation and recording, the loading of the specimen was terminated at 560 kN in this experiment. The state on the right side of the specimen after terminating loading is shown in Figure 16. The distribution of inclined cracks is most obvious on the right side. The remaining surfaces of the specimen are mainly vertical and oblique cracks. As shown in Figure 17, the closer it is to the middle, the greater the settlement displacement during the loading process. Near 360 kN, there is a significant increase in the displacement curve fluctuation in the middle position of the specimen.

Figure 16.

Site diagram of the final state on the right side of the symmetrical concentrated loading specimen.

Figure 17.

Settlement results of the middle part of the bottom of the symmetrical concentrated loading specimen.

The settlement data of the specimen bottom under 9 different loading force states at intervals of 60 kN were plotted (see Figure 18).

Figure 18.

Settlement of the bottom of the symmetrical concentrated loading specimen.

As shown in Figure 18, with the continuous application of external loading forces, the settlement increase at position ② is greater than that at position ③, which is consistent with the experimental situation where the specimen at position ① is first damaged. Analysis of the full length of the specimen reveals that the settlement increase in the central position is particularly significant compared to other parts, indicating that the specimen is in good condition during this loading process and that all values have basically reached the preset state. Figure 19 depicts a schematic diagram of the development of the cracks in the symmetrical concentrated loading specimen.

Figure 19.

Schematic diagram of the crack development in the symmetrical concentrated loading specimen.

As shown in Figure 19, during the initial loading stage, the time when cracks begin to appear on both sides of the specimen is generally consistent. As the external load continues to increase, the number and length of the cracks also exhibit varying degrees of expansion. When the external load is loaded to 360 kN, the specimen begins to show long cracks. The displacement begins to retract near 400 kN. At this point, the specimen stress tends to stabilize, and the oblique crack on the right side has grown rapidly. In the final stage of loading, the specimen retraction intensifies and is subsequently destroyed.

Comparison and analysis of the results of the fibre optic and strain gauge

According to the strain gauge data collected by the TDS-530 static strain analyser and the fibre optic strain data collected by the NBX-6050A optical nanometre, a comparative analysis was carried out.

First, the data of the concrete strain gauge, reinforcement strain gauge and embedded fibre optic at the top side of position ① in Figure 5 were sorted out, and the specific strain is shown in Figure 20.

Figure 20.

Strain comparison at the top side of position ① of the symmetrical concentrated loading specimen.

As shown in Figure 20, under the stress state, for the strain monitoring changes, the reinforcement strain gauge data < the concrete strain gauge data and the fibre optic data. Analysis suggests that due to the external loads, the internal concrete of reinforced concrete structures first serves and only gradually enters the service state after reaching a certain strength. Therefore, the strain change in the concrete strain gauge and fibre optic is more obvious than that of the reinforcement strain gauge, and the change rule of the fibre optic is more consistent with the deterioration state of the actual structure. For the three-point position, position ③ in Figure 5 was selected as the representative. The results of the reinforcement strain gauge at the top, left and bottom of position ③ were compared with those of the fibre optic, as shown in Figure 21.

Figure 21.

Strain comparison at the top, left and bottom of position ③ of the symmetrical concentrated loading specimen.

Figure 21 shows that the strain growth trend of the reinforcement strain gauge and fibre optic is basically the same. However, compared with the large fluctuation state of the reinforcement strain gauge monitoring data, the fibre optic data are relatively smooth. It can be concluded that both fibre optic and reinforcement strain gauges can reflect the structural growth at this location, and their data fluctuations are very similar. However, compared with the reinforcement strain gauge, the growth of the embedded fibre optic is closer to the actual change in the tunnel circumferential direction.

Comparative analysis of the radial fibre optic strain results

Using the results extracted from the Neubrex system, the fibre optic strain was processed using data processing software, mainly for analysing the calculated bending length of the specimen. After data processing on the longitudinal embedded reinforcement base cable fibre optic at the top of the specimen that is closest to the force application point, a strain diagram of the fibre optic is drawn based on 9 levels of data, as shown in Figure 22.

Figure 22.

Radial embedded fibre optic strain at the top of the symmetrical concentrated loading specimen.

As shown in Figure 22(b), through the fibre optic strain diagram, it can be observed that as the loading force continues to increase, the specimen deformation gradually becomes clearer, the strain growth rate in the central ±0.5 m area gradually accelerates, and the strain change in the area far from the central position decreases. As shown in Figure 22(a), when the loading force is in the 120–180 kN range, the trapezoidal curve gradually shows a depression in the middle position due to no force as the strain gradually increases. When the loading force is in the range of 180–240 kN, the settlement of the specimen increases, the strain in the middle position accelerates, and the overall regression to the inverted trapezoidal strain state. When the loading force is in the range of 240–360 kN, the specimen continues to be subjected to force, and the strain changes in the internal region of the three-point steadily and rapidly increase. When the loading force is in the range of 360–420 kN, the specimen is in a stable state, and the strain growth rate decreases. After loading a force of 420 kN, the strain growth rate at this location showed a secondary acceleration trend, with significant changes occurring near the force point. Compared to other positions, the strain growth rate is significantly lower at the position where the circumferential reinforcements are placed in the early stage of loading, indicating that the arrangement of the circumferential reinforcement can effectively improve the service life of the structure to a certain extent.Figure 23 shows the strain of the radial embedded fibre optic at the left waist side of the specimen.

Figure 23.

Radial embedded fibre optic strain at the left waist side of the symmetrical concentrated loading specimen.

As shown in Figure 23, through comprehensive analysis of the strain diagrams, under the condition of applying two loading forces at the three points, the strain growth rate at the loading force position on the left waist is greater than that at other positions. When the loading force is less than 240 kN, the strain growth area at the left waist of the specimen is mainly concentrated in two three-point intervals. When the loading force is in the range of 240–480 kN, the strain in the two force point areas of the specimen increases sharply, showing a trend similar to a parabolic state overall. After the loading force exceeds 480 kN, the impact on the second half of the specimen is greater than that on the first half, indicating that the specimen will first fail in the second half and exit work.

Comparative analysis of the circumferential fibre optic strain results

In the experiment, three circumferential positions were arranged using a single fibre optic. Therefore, after obtaining the experimental data, it is necessary to perform data segmentation and circumferential fitting. Figure 24 shows the strain of the circumferential fibre optic at position ① in Figure 5.

Figure 24.

Circumferential fibre optic strain at position ① of the symmetrical concentrated loading specimen.

As shown in Figure 24, when the loading force is in the range of 0–180 kN, the overall force distribution is uniform. When the loading force is in the range of 180–420 kN, the strain data at the right position show an increasing trend. After the loading force exceeds 420 kN, a reverse pressure growth state begins to appear at the waist part, and the oblique cracks on the right side gradually increase and widen. Figure 25 shows the strain of the circumferential fibre optic at position ③ in Figure 5.

Figure 25.

Circumferential fibre optic strain at position ③ of the symmetrical concentrated loading specimen.

As shown in Figure 25, when the loading force is in the range of 0–240 kN, the circumferential force is evenly distributed. When the loading force is in the range of 240–320 kN, there is a significant increase in stress on both waist sides, with one side experiencing a faster speed and strain peaks beginning to appear on both waist sides. When the loading force is in the range of 320–480 kN, sharp points at the waist gradually develop. After the loading force reaches 480 kN, the strain growth rate on the right waist side significantly accelerates and begins to show an uneven state of stress.

Finite element numerical simulation analysis

Finite element model establishment

Geometry model

To further analyse the deformation of the model specimen, finite element analysis was used. The geometry model was established according to the size of the model specimen described in the experiment, as shown in Figure 26. The geometry model consists of two parts: concrete and reinforcement.

Figure 26.

Geometry model of the experimental specimen.

Material parameter selection

According to relevant regulatory documents, to reduce the error between simulation and actual experiments, a plastic damage model was used in the simulation, with a Poisson’s ratio of 0.2. A concrete cube with a compressive strength of 40 MPa was used, and the internal and external reinforcement frameworks were made of HRB335 reinforcement. The thickness of the concrete protective layer was taken as 25 mm. In the numerical model, the plastic parameters of concrete damage were selected in accordance with the relevant requirements, and the variation pattern of the parameters is shown in Figure 27.

Figure 27.

Plastic parameters of concrete damage.

Boundary condition settings

In the displacement boundary conditions, considering that there may be a certain degree of displacement on both sides of the model in the vertical and horizontal directions, the corresponding boundary conditions of the model are shown in Figure 28. To make the model loading closer to the actual situation, a stress shim was added to the stress position to transfer stress.

Figure 28.

Boundary condition settings for numerical models.

Model unit grid division

Based on the comprehensive consideration of the characteristics of the finite element analysis software and the tunnel lining structure model, the status of each component after the model was meshed is shown in Figure 29.

Figure 29.

Schematic of the unit grid division of the numerical model.

As shown in Figure 29, due to the rectangular pressure area in the experiment, a portion of the flat cut area is set up in the upper part of the model, which will have a certain impact on the later grid division, possibly forming irregular grids, leading to nonconvergence of the calculation. Therefore, it is necessary to preliminarily divide the cross section of the concrete to minimize the irregular grids generated in the later stage and increase the accuracy of the calculation.

Comparison and analysis between the simulation results and experimental results

The final vertical displacement cloud diagrams of the numerical model under two loading methods were obtained by loading the numerical model according to the loading method in the experiment, as shown in Figure 30.

Figure 30.

Final vertical displacement cloud diagrams of the numerical model under two loading methods.

Under central concentrated loading, the structure generates a vertical displacement along the stress point in a radial state. In the final state, the support points at both ends of the model undergo slight warping, while other positions show varying degrees of vertical displacement, with significant displacement in the stress area. Under symmetrical concentrated loading, the structure exhibits a vertical movement state of large in the middle and small on both sides along the stress point. The displacement of the middle part of the model is more obvious than that of the stressed area. To verify the correctness and effectiveness of the numerical simulation results, the displacement calculation results were compared and analysed with the experimental results, as shown in Figure 31.

Figure 31.

Comparisons between simulation results and experimental results for the bottom middle settlement.

A comparison of the results of the simulation and the experiment of the settlement of the bottom middle part of the specimen under the two loading methods shows that the simulation results are relatively close to the experimental results, indicating that the simulation results are correct and effective. The settlement results of the symmetrical concentrated loading specimens show slight differences, but the vertical displacement growth trend is consistent, which can be used for subsequent related research.

For the analysis of the strain in the loading process of the specimen, for the central concentrated loading specimen, the key points on the specimen were selected to carry out a comparative analysis of the simulation results and experimental results. A schematic diagram of the key point locations is shown in Figure 32. Among them, key points ① and ② are located around the left waist centre point, key point ③ is located behind the top centre point corresponding to key point ②, and key point ④ is located at the bottom centre point. The comparisons between the simulation and experimental results of the strain changes at the key points are shown in Figure 33.

Figure 32.

Schematic diagram of the key point locations for the central concentrated loading specimen.

Figure 33.

Comparisons between the simulation and experimental results of the strain changes at key points of the central concentrated loading specimen.

As shown in Figure 33(a) and (b), the distributed fibre optic obtained strain distribution curves are similar to those of the simulation and strain gauge for the positions at both waist sides of the centre point. As shown in Figure 33(c) and (d), the comparison of the actual strain data obtained through the fibre optic and strain gauge with the strain results obtained through the simulation demonstrates that the strain growth states obtained by the fibre optic recording and simulation are similar.This indicates that the distributed fibre optic monitoring used for the health state of the tunnel lining structure has a stable and good effect. In the results of key points ③ and ④, it can be seen that the strain gauge results are relatively close to the numerical simulation results, while there are some differences in the fibre optic monitoring results before 220 kN. But as the experiment progresses, changes in the structure may also cause damage to the strain gauges, resulting in data distortion and affecting the accuracy of monitoring results. However, distributed optical fibres did not experience any damage during the entire loading process of the specimen, and can continuously monitor the strain situation throughout the entire loading cycle of the specimen, and the results are not significantly different from the simulation results. So, distributed fibre optic monitoring has certain effectiveness and stability.

In the simulation, it is assumed that the concrete material is homogeneous. However, due to the influence of the pouring process, actual specimens may not be able to achieve homogeneous materials, which may be one of the reasons for the differences between simulation results and experimental monitoring results. On the other hand, the boundary conditions set in the simulation may not be completely consistent with those set in the experiment, which may also lead to differences between the simulation results and the experimental monitoring results. But the growth trend of the two results is the same, indicating the effectiveness of the numerical simulation results. Figure 34 shows the plastic strain cloud diagram of the concrete under various levels of load.

Figure 34.

Plastic strain cloud diagram of the concrete under various levels of load of the central concentrated loading specimen.

As shown in Figure 34, the plastic strain first occurs in the middle bottom of the concrete during the continuous loading process until 440 kN. As the external load continues to increase, the model material gradually shows a development trend towards both sides and upwards, and the plastic strain is most obvious near the loading position and at the support, with the maximum plastic strain on the two waist sides in the middle. This also more intuitively explains the reason for the large number of oblique cracks appearing on the surface of the model in the experiments. From the plastic strain cloud diagram at each stage of the bottom position, it can be seen that the plastic strain at the circumferential reinforcement position is more obvious than that in the middle, with the plastic strain becoming less obvious as the distance from the middle position increases. Figure 35 shows the displacement cloud diagram of the numerical model under different load levels.

Figure 35.

Displacement cloud diagram of the numerical model under different load levels of the central concentrated loading specimen.

As shown in Figure 35, with the continuous increase in the external load, the displacement of the model shows a trend where the middle displacement is greater than the side displacement, and the displacement of the top and two waist sides is greater than the bottom displacement. Based on the comprehensive comparison and analysis of the results, the most unfavourable position is mainly distributed on the two waist sides of the stress position and corresponding cross section.

For the symmetrical concentrated loading specimen, the key points on the specimen were selected to carry out a comparative analysis of the simulation results and experimental results. A schematic diagram of the key point locations is shown in Figure 36. Among them, key point ① is located at the left waist position, and key point ② is located at the top of the middle section of the model. The comparisons between the simulation and experimental results of the strain changes at key points are shown in Figure 37.

Figure 36.

Schematic diagram of the key point locations for the symmetrical concentrated loading specimen.

Figure 37.

Comparisons between the simulation and experimental results of the strain changes at key points of the symmetrical concentrated loading specimen.

As shown in Figure 37(a), for the waist position of the force point, the strain mutation points obtained by the three methods are all concentrated at approximately 300 kN. As shown in Figure 37(b), the strain at the top of the middle section obtained through the simulation is extremely consistent with the two strain results obtained from the experiments during the whole loading process. By comparing and analysing the two positions, it can be found that the distribution of the strain development follows a pattern of bottom>waist>top. The strain results recorded through the fibre optic are extremely similar to the strain growth state calculated through the simulation. It is proven again that the distributed fibre optic has a stable and good effect on the strain monitoring of tunnel lining structures. Figure 38 shows the plastic strain cloud diagram of the concrete under various load levels.

Figure 38.

Plastic strain cloud diagram of the concrete under various levels of load of the symmetrical concentrated loading specimen.

As shown in Figure 38, when the symmetrical load force is loaded to 560 kN, the plastic strain is most obvious near the loading position and at the support, and the plastic strain is the highest on the two waist sides in the middle. This also more intuitively explains the reason for the large number of oblique cracks on the surface of the model in the experiments. Figure 39 shows the displacement cloud diagram of the numerical model under different load levels.

Figure 39.

Displacement cloud diagram of the numerical model under different load levels of the symmetrical concentrated loading specimen.

As shown in Figure 39, with the continuous increase in the external load, the overall displacement of the model structure shows a trend where the middle displacement is greater than the side displacement, and the displacement of the top and two waist sides is greater than the bottom displacement. Based on the comprehensive comparison and analysis of the results, the most unfavourable position of the model is basically concentrated between the influence range of the force points.

Influence of the concrete strength on the deformation of the tunnel lining structure

To study the influence of the concrete strength on the deformation of the tunnel lining structure, the concrete strength of the structure was set to C30, C50, and C60 before calculation, and the displacement cloud diagrams of the structure with different concrete strengths were obtained, as shown in Figure 40.

Figure 40.

Displacement cloud diagrams of the structure with different concrete strengths.

As shown in Figure 40, the displacement change at the most unfavourable position of the model gradually decreases as the concrete strength in the structure continues to increase under the influence of the external concentrated loads. The comparison diagram of the displacement changes obtained by summarizing the displacement changes in the corresponding bottom midpoint of the structure is shown in Figure 41.

Figure 41.

Comparison of the bottom midpoint displacement of the structure with different strength concrete.

As shown in Figure 41, with the continuous increase in the concrete strength, the corresponding position displacement at the bottom side of the middle part also shows a significant decreasing trend. As shown in Figure 41(a), compared to the displacement of the structure with concrete strength C40 under central concentrated loading, the corresponding position displacements of the structure with concrete strengths of C30, C50, and C60 are 117.69%, 73.93%, and 42.48%, respectively. As shown in Figure 41(b), compared to that of the structure with concrete strength C40 under symmetrical concentrated loading, the corresponding position displacements of the structure with concrete strengths of C30, C50, and C60 are 119.10%, 85.09%, and 74.91%, respectively. It can be seen that improving the concrete strength used in the structure can effectively enhance the ability of the structure to resist settlement.

Influence of the circumferential reinforcement spacing on the deformation of the tunnel lining structure

By adjusting the circumferential reinforcement spacing in the structure to 140 mm, 175 mm and 280 mm, the displacement cloud diagrams of the structure with different circumferential reinforcement spacings were obtained, as shown in Figure 42.

Figure 42.

Displacement cloud diagrams of the structure with different circumferential reinforcement spacing.

As shown in Figure 42, the displacement change at the most unfavourable position of the model gradually increases as the circumferential reinforcement spacing in the structure continues to increase under the external concentrated loads. As shown in Figure 42(e)–(h), as the circumferential reinforcement spacing increases, the overall structure begins to exhibit a more obvious oblique deformation state. The comparison diagram of the displacement changes obtained by summarizing the displacement changes of the corresponding bottom midpoint of the structure is shown in Figure 43.

Figure 43.

Comparison of the bottom midpoint displacement of the structure with different circumferential reinforcement spacing.

As shown in Figure 43, the vertical displacement at the bottom of the middle part of the structure also shows a continuous increasing trend as the circumferential reinforcement spacing continues to increase. As shown in Figure 43(a), the central concentrated loading has a relatively small impact on the displacement change of the structure within the range of 175–200 mm circumferential reinforcement spacing. At the same time, it can be found that by adjusting the circumferential reinforcement spacing, the corresponding position displacement of the adjusted structure decreases to 120.33%, 96.14%, and 73.49% under central concentrated loading. As shown in Figure 43(b), the symmetrical concentrated loading has a relatively small impact on the displacement change in the structure within the range of a 200–280 mm circumferential reinforcement spacing. The corresponding position displacement of the adjusted structure decreases to 112.88%, 87.84% and 81.96% under symmetrical concentrated loading by adjusting the circumferential reinforcement spacing. Therefore, the structural safety under certain circumstances may be improved by adopting appropriate circumferential reinforcement spacing for tunnel lining structures with different geological conditions.

Influence of the longitudinal reinforcement strength on the deformation of the tunnel lining structure

By adjusting the longitudinal reinforcement strength in the structure to HPB300, HRB400 and HRB500, the displacement cloud diagrams of the structure with different longitudinal reinforcement strengths were obtained, as shown in Figure 44.

Figure 44.

Displacement cloud diagrams of the structure with different longitudinal reinforcement strengths.

As shown in Figure 44, the ability of the structure to resist settlement displacement at the most unfavourable position gradually increases, and the affected range also gradually increases as the longitudinal reinforcement strength continues to increase under concentrated loading. The comparison diagram of the displacement changes obtained by summarizing the displacement changes in the corresponding bottom midpoint of the structure is shown in Figure 45.

Figure 45.

Comparison of the bottom midpoint displacement of the structure with different longitudinal reinforcement strengths.

As shown in Figure 45, the bottom midpoint displacement of the structure shows a decreasing trend with the continuous increase in the longitudinal reinforcement strength. As shown in Figure 45(a), the structure is less affected by the longitudinal reinforcement strength, and then the slope of the curve begins to change rapidly before the central concentrated loading is loaded to 300 kN. For the corresponding positions of the adjusted structure, the final settlement displacement decreased to 117.53%, 86.71%, and 82.51% of the original model, respectively. As shown in Figure 45(b), the influence of the longitudinal reinforcement strength on the structure is not obvious, and then the settlement displacement starts to change slightly when the symmetrical concentrated loading is not loaded to 500 kN. The settlement displacement of the corresponding position of the adjusted structure decreases to 100.74%, 99.75%, and 99.32% of the original model, respectively. The comparison diagram of the strain changes obtained by summarizing the strain changes in the corresponding bottom midpoint of the structure is shown in Figure 46.

Figure 46.

Comparison of the bottom midpoint strain of the structure with different longitudinal reinforcement strengths.

As shown in Figure 46(a), the strain at the corresponding position of the structure changes significantly with increasing longitudinal reinforcement strength. For the position just below the force point, the strain decreases significantly with increasing longitudinal reinforcement strength. As shown in Figure 46(b), the change in the longitudinal reinforcement strength has a relatively weak effect on the strain directly below the centre of the symmetrical force point connection, but its strain also shows an increasing trend with increasing longitudinal reinforcement strength. It can be concluded that by increasing the longitudinal reinforcement strength in the structure, the ability of the structure to resist deformation at the stress location can be effectively enhanced. This is significant for improving the overall resistance to deformation and safety of the structure.

Conclusions

In this study, the deformation and settlement characteristics of the tunnel lining structure were investigated by combining experiments and numerical simulations based on distributed fibre optic sensing technology. In the experiment, cracks began to appear as the experiment progressed, and the development trend of cracks was mainly vertical cracks and oblique cracks. With increasing loading level, the cracks at the force point became more obvious. The settlement state at the corresponding position was significantly positively correlated with the number and length of cracks. The closer the distance is to the force point, the greater the settlement displacement with increasing concentrated force and the more significant the increase in the number and length of cracks.

The analysis of the monitoring strain indicates that the monitoring results of the distributed fibre optic are more real and effective in monitoring time, data integrity and other aspects than the monitoring results of the strain gauge. Among them, embedded fibre optic technology is less affected by external factors than surface-mounted fibre optics, and the monitoring data are more accurate and effective. The monitoring range is wide and has good engineering characteristics.

The analysis of the circumferential embedded fibre optic strain monitoring data demonstrates that the overall strain at the force position of the specimen presents a similar elliptical shape change trend in the loading stage. From this, it can be concluded that by arranging the circumferentially distributed fibre optic for the tunnel lining structure to conduct deformation monitoring on the structure, the actual change state of each position under the stress state can be well displayed.

From the analysis of the settlement and strain obtained from the experiment and simulation, it can be seen that compared with the strain gauge monitoring, the strain results recorded by the distributed fibre optic are closer to the strain growth state obtained from the simulation. This further verifies the accuracy of the distributed fibre optic monitoring.

Improving the concrete strength, appropriate circumferential reinforcement spacing, and increasing the longitudinal reinforcement strength can effectively enhance the ability of the structure to resist deformation at the stress location. These factors play a significant role in improving the overall resistance to deformation and safety of the structure. When the concrete strength is adjusted to C60, the settlement displacement of the corresponding position of the central concentrated loading and the symmetrical concentrated loading model decreases to 42.48% and 74.91%, respectively. When the circumferential reinforcement spacing is adjusted to 140 mm, the settlement displacement of the corresponding position of the central concentrated loading and the symmetrical concentrated loading model decreases to 73.49% and 81.96%, respectively. When the longitudinal reinforcement strength is adjusted to HRB500, the settlement displacement of the corresponding position of the central concentrated loading and the symmetrical concentrated loading model decreases to 82.51% and 99.32%, respectively.

Through this research study, a useful reference is provided for the application of distributed fibre optics in the longitudinal and circumferential strain monitoring of actual reinforced concrete tunnel lining structures.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The research reported in this manuscript is funded by the National Natural Science Foundation of China (Grant No. 42202319), Liaoning Provincial Department of Education Basic Scientific Research Project (Grant No. LJKMZ20220944), Project funded by China Postdoctoral Science Foundation (Grant No. 2019M651211).

ORCID iD

Wei Sheng

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