Study on the Optimized Perception of Structural Behavior in Shield Tunneling by Fiber Grating Layouts

Abstract

Shield tunnels’ structural stability is challenged due to the fact that they are often built under rivers, lakes, and oceans. It is crucial to execute the structural deformation perception of the shield tunnel. Fiber Bragg grating (FBG) sensing technology is sensitive to deformation information, making it one of the greatest options for shield tunnels to perceive structural deformation. In this study, a 1:20 scale model test was carried out to investigate the deformation perception of the shield tunnel structure under three different layouts of surface-mounted FBG sensors. The deformation law of the tunnel is discussed, under the condition of two-factor cross fusion and especially under the condition of constant water pressure and soil pressure change. The results indicate that, under the combined action of water and soil pressure, the uniform water pressure of 0.33 MPa has a stabilizing effect on the segment strain under the vertical load of 0.4 MPa. The traditional four-point layout and the 18° uniform layout are more effective in detecting changes in local tunnel curvature and strain, respectively, compared to the 36° uniform layout mode. It is advised that the traditional four-point layout be used to collect information for other sections’ monitoring and that the 18° uniform layout is for harsh terrain conditions.

1. Introduction

Shield tunnel construction is fraught with terrain factors like high water pressure, high ground loads, and fault fracture zones. These factors challenge the shield tunnel’s structural safety. The water–earth pressure is the most frequent factor of tunnel operation, which leads to segment transverse convergence and deformation. As a result, it is essential to study the perception of structural deformation. Specifically, the key is to master the structure perception method and summarize the structural deformation rule.

The choice of monitoring transducer is the foundation of structural deformation perception. There are faults in traditional monitoring transducers [1], such as them having a single data type, low survival rate, poor accuracy, etc. Traditional monitoring methods cannot provide a realistic reflection of the lining structure’s overall deformation [2]. With the rapid development and use of fiber Bragg grating (FBG) sensing technology in recent years, FBG sensing technology offers a wide range of potential applications in monitoring tunnel structure health [3,4,5].

Many researchers have conducted a lot of research on the use of FBG for tunnel monitoring. Sun et al. [6] determined the link between the wavelength change in the fiber Bragg grating (FBG) sensor and the stress of the anchor bolt and showed that the FBG sensor satisfies the monitoring needs of the tunnel structure. Using the FBG sensor for high-precision structure monitoring, Li et al. [7] confirmed that the sensor is appropriate for displacement and stress monitoring in quasi-static structure studies. Structural health monitoring (SHM) applications for tunnel roads have to be researched and developed by means of fiber Bragg grating (FBG) optical temperatures and strain sensors [8]. The findings in this research illustrate that the data gathered from embedded FBG optical sensors provide the essential information on how the pavement structure could sustain the load and information about the traffic intensity on the specific road section; the structural life of the pavement could be evaluated and predicted. Wang et al. [9] employed FBG sensors to continuously track the convergence deformation of tunnels. The FBG sensor could accurately assess the convergence deformation and satisfy tunnel management requirements, according to experiments. To track the three-dimensional stress of the rock surrounding the tunnel in the Liang et al. [10] investigation, FBG sensing technology is employed. The experimental results demonstrate that the relative error of the recorded stress is less than 4%, demonstrating that the FBG sensor has good linearity and repeatability and has a wide range of application prospects in the area of monitoring the safety of underground engineering structures such as coal mines and tunnels. A mechanical analysis model of shear strain transmission that takes into account the viscoelastic impact of optical fiber sensing apparatus was developed by Liang et al. [11]. The effect of shear modulus and cement layer thickness on quasi-static strain transfer was examined by the uniaxial tensile test of a bolt. Sigurdardottir et al. [12] found a substantial correlation between curvature change and structural deformation. According to research by Urszula et al. [13], sensing modal strain and curvature with an FBG sensor could increase monitoring sensitivity by around 30 times and be utilized to be more sensitive to local deformation or even damage. In experiments, Liu et al. [14] concurrently measured temperature and curvature using an integrated fiber optic sensor. The potential of FBG sensing components for structural deformation is demonstrated by the relative errors of temperature and curvature, which are, respectively, 2.22% and 2.58%.

Many researchers have conducted a lot of research on structure health monitoring. Sun et al. [15] proposed a sensor anomaly diagnosis method based on the characteristics that the original output of the fiber grating strain gauge has the same law in the same kind of structure monitoring. Zhou et al.’s team [16] used a three-dimensional point cloud as the data basis and used the fusion of machine vision structural disease detection information to monitor the health and safety status of the tunnel structure. Chen et al. [17] proposed a new comprehensive monitoring method for tunnel section deformation based on the inclination angle of monitoring points and further verified the accuracy of the method in practical applications through experiments. Zhou et al. [18] proposed a tunnel risk mathematical model and tunnel deformation monitoring method based on the three indicators of current change, cumulative change, and change rate of monitoring points. Sui et al. [19] arranged the distributed optical fiber along the circumferential direction on the upper and lower surfaces of the steel cage inside the segment and obtained the strain distribution inside the segment. Zheng [20] collected the curvature data of discrete points on the inner surface of the tunnel through neural network processing. Finally, a more accurate tunnel section curve is obtained. Letsios et al. [21] detects newly built buildings and estimates their height in the study area based on permanent scatterer interferometry (PSI) technology. Its overall goal is to obtain timely spatial information for construction activities. Using Permanent Scatterer Interferometry (PSI) analysis, Roccheggiani et al. [22] revealed regional subsidence in great detail, particularly where the ground is characterized by clay and alluvial deposits and where large buildings exist. Xu et al. [23] proposed a structural health monitoring method combining optical fiber sensing and piezoelectric sensing and constructed a structural load identification method based on optical fiber sensing. Ghaderpour et al. [24] uses the sequential turning point detection (STPD) method to estimate the trend turning point and its direction in the PS-InSAR time series to explore its potential impact on ground deformation.

Although numerous researchers have conducted pertinent research, the study of the shield tunnel deformation law is still in its early stage. Utilizing a three-dimensional soil-shield tunnel similar model test system, Tang et al. [25], and colleagues conducted experimental research on the structural deformation state and mechanical behavior of shield tunnel segment lining of Nanjing Metro station under various assembly modes. In a related model test for the Nanjing Yangtze River Tunnel, He et al.’s team [26] took into account the interactions between formation, water pressure, and tunnel segments and analyzed the impact of segment lining assembly mode on the internal force distribution of the structure. Kang et al. [27] studied the longitudinal deformation and damage of shield tunnels caused by ground stress and surface overload. It is proved that when the surface load is far away from the tunnel, the shallow shield tunnel has a large settlement, and it is concluded that increasing the equivalent shear stiffness will significantly reduce the dislocation between the longitudinal adjacent segment rings. Ding et al. [28] analyzed the effect of soft soil grouting on the deformation of the closed shield tunnel with the measured data. Combining the measured data of vertical, horizontal, and convergence deformation of the adjacent tunnel during the grouting construction in foundation pit engineering, the influence of grouting on the metro tunnel in soft soil area is analyzed. Zhang et al. [29] measured the influence of relevant tunnel coefficients on lining displacement and internal force through parameter analysis, that is, the soil Young’s modulus, soil unit weight, soil lateral pressure coefficient, tunnel radius, tunnel depth, and gap parameters. Wang et al. [30] studied the progressive instability and failure process of the large-diameter underwater shield tunnel segmental lining structure, from the microscopic damage of the material to the overall instability of the structure, by the model test method. The progressive failure process is divided into three stages: initial elastic phase, local damage phase, and overall instability failure phase. And the influences of the assembly method, the position of the capping block, the lateral pressure coefficient of the stratum and the amount of water pressure on the deformation characteristics and the critical instability state of the segmental lining structure are, respectively, analyzed. To direct the construction design and carry out the targeted treatment of structure characteristics at the intersection of cross passages, Tan et al. [31] examined the structural deformation rule of large-diameter shield tunnel segments at the intersection of cross passages. Civera et al. [32] studied the seismic response of an underwater railway tunnel and two nearby highway tunnels in the same near-field seismic event. Arias Intensity (AI) and significant duration (Ds₅₉₅) are proposed as potential explanations for the different seismic susceptibility of these different tunnels.

The existing research results show that sensing information in tunnel health monitoring is single, and the correlation between indicators is not clear. FBG monitoring technology can effectively and accurately monitor the deformation data of curvature and strain. However, the existing research rarely discusses the influence of different FBG layouts on the accurate monitoring of the local strain and curvature of tunnels. Moreover, under the condition of two-factor cross-fusion, especially under constant water pressure and variable earth pressure, the structural deformation law is uncertain. Therefore, it is necessary to carry out relevant research. In this study, the strain and curvature of the segment’s inner surface were sensed and measured using the surface-mounted FBG sensing element. The deformation law of the shield tunnel segment structure under the action of water–earth pressure is explored. The second section of this article mainly describes the basic situation and preparation of the test. The third section is the analysis and discussion of the test results. The main contents of the four sections are conclusions and deficiencies. The following contributions are provided: (1) By optimizing and strengthening the layout of structural monitoring, accurate deformation data can be provided and the requirements of structural health monitoring of shield tunnels can be met. (2) By collecting the deformation information of the shield tunnel segment under the combined action of water and soil pressure, the deformation characteristics of the segment are summarized. This provides a reference for health monitoring, disease prediction, and disaster warning threshold determination for shield tunnel segments.

2. Experimental Preparation

2.1. Project Description

Based on the Yellow River tunnel project, this paper carries out a scale test on the shield tunnel. The landform of the tunnel site is alluvial plain, and the terrain is relatively flat. The shield tunnel’s smallest thickness of covering soil is 11.2 m, and its maximum thickness of covering soil is 42.3 m. The thickness of covering soil of the Yellow River section is 25 to 38 m. In this project, the Yellow River’s flood level is 34.18 m, and the tunnel’s maximum water pressure is roughly 0.65 MPa. The shield tunnel has two layers: a lower subway layer and an upper driving layer with three lanes. The lining ring is 15.2 m in outside diameter, 13.9 m in inner diameter, and 0.65 m thick. The material is reinforced concrete type C60 (cube compressive strength). The segment ring is 2.0 m wide and it is divided into 7 + 2 + 1 pieces. The standard section layout of shield tunnel is shown in Figure 1.

2.2. Soil Materials and Lining Models

The similarity theory in this section mainly refers to the second similarity theorem, also known as the π theorem. According to the similarity criterion corresponding to the similar mechanical phenomena, Equation (1) can be obtained. We select a basis similarity ratio of 1:20 for geometrical similarity and 1:1 for bulk density similarity to regulate the similarity of physical and mechanical characteristics in the elastic range. According to the basis relation, the similarity relation of strain, friction force, and Poisson’s ratio is C_μ = C_ε = C_φ = 1. The similarity relation of strength, stress, cohesion, and elastic modulus is C_R = C_s = C_c = C_E = 20. The heavy similarity ratio in terms of geometry is C_γ = γ_p∕γ_m = 1.

$${\displaystyle \frac{C_{\sigma }}{C_X{C}_l}}=1; C_{\epsilon }=1; {\displaystyle \frac{C_E}{C_X{C}_l}}=1; C_{\mu }=1; {\displaystyle \frac{C_{\overline{X}}}{C_X{C}_l}}=1; {\displaystyle \frac{C_{\delta }}{C_l}}=1$$

(1)

The ratio of soil mass–similar materials is based on the test geometric similarity ratio of 1:20, and the values of soil–similar materials are based on the project’s real physical and mechanical properties. The mechanical parameters are shown in

Table 1. Test soil similarity parameters.

Mechanical Parameters	Severe γ	Elastic Modulus	Cohesive Forces	Internal Friction Angle
	(kN/m3)	(MPa)	(MPa)	φ (°)
Prototype soil	19	45	38	20
Model soil	19	2.25	1.95	20

. According to the soil parameters, combined with the study of the shield similar stratum model [33], a direct shear test and compression test were conducted. Then, the weights of barite powder, fly ash, oil, and river sand were determined. The weight ratio is shown in

Table 2. Test soil material ratio (weight ratio).

Barite	Fly Ash	Engine Oil	Sand
0.25	0.225	0.125	0.4

. The similar parameters of model test segment are shown in

Table 3. Similar parameters of model test segment.

Mechanical Parameters	Gravity	Elastic Modulus	Single Axis Compressive Strength	Poisson’s Ratio
	(kN/m3)	(GPa)	(MPa)
Prototype segment	23	36	38.5	0.2
Mode segment	23	1.8	1.925

.

The segment model was made according to the similarity ratio, and the similar materials were made according to the ratio of fixed water–gypsum = 1:1.4. The shield tunnel segment joint was simulated to understand the special link between the segment and the ring indirect head of the shield tunnel. For the joint form of the longitudinal joint of the segment, the longitudinal joint is simulated by slotting. A certain depth of slot is cut in the model ring corresponding to the part of the tunnel joint to weaken the bending stiffness of the part. The slot depth is determined by the equivalent bending stiffness of the prototype joint [34]. To join the segment ring to the ring and simulate the indirect head of the segment ring, we used a bolt with a diameter of 4 mm and a length of 20 mm at the indirect head of the model ring. The simulation measures at the model joint are shown in Figure 2 and Figure 3.

The segment similarity model is created by vertically superimposing the segment in the form of one full ring and two half rings (1/2 + 1 + 1/2). The model’s overall height is 20 cm (the whole ring is 10 cm high, the half ring is 5 cm), its outer diameter is 0.38 m, and its inner diameter is 0.35 m, as illustrated in Figure 4.

2.3. Test Scheme

For the underwater shield tunnel, set the load mode [35] as shown in Figure 5. In the figure, $R$ is the radius of the tunnel. $P$ is the vertical earth pressure.$q$ is the horizontal earth pressure.$P_w$ is the water pressure and $P_K$ is the ground resistance. The water pressure is simulated by hoop force. The concentrated stress force is used to approximately simulate the earth pressure. The concentrated pull force perpendicular to the vertical earth pressure is used to introduce the formation resistance.

This experiment examines how shield pipe liners deform when subjected to the combined effects of water and ground pressure. Decide the shield tunnel–stratum similar model test system to load the formation pressure. Select the uniform hydraulic pressure loading device to load water pressure. The shield tunnel–stratum similar model test system as shown in Figure 6. Hydraulic pressure loading device as shown in Figure 7.

According to the real project and the notion of model test resemblance, the model’s water pressure was ultimately decided upon as 322 N, and the formation side pressure coefficient as 0.5. The model test will apply formation pressure in three directions, namely the vertical X direction corresponding to the shield tunnel, the lateral Y direction corresponding to the tunnel, and the radial Z direction corresponding to the tunnel, by the shield tunnel–stratum similar model test system. The loading grade is 0.4 MPa per stage, and the vertical formation pressure of the tunnel is loaded incrementally from 0.4 MPa to 6.0 MPa. The loading grade is 0.2 MPa per stage, and the lateral formation pressure of the tunnel is gradually loaded from 0.2 MPa to 3.0 MPa. The radial formation pressure of the tunnel is kept constant at 16.0 MPa to prevent any radial deformation between the pipe segment and the formation. After each stage of the test’s formation pressure loading was finished, a steady pressure condition was maintained for five minutes in order to record the segment’s deformation data. The loading circumstances are presented in

Table 4. Test conditions.

Test Water Pressure	Test Surrounding Rock Pressure (Lateral Pressure Coefficient 0.5)
322 N	Direction I/Vertical (0.4 MPa/level)	Direction II/Lateral (0.2 MPa/level)	Direction III/Radial
	0.4–8.0 MPa	0.2–3.0 MPa	16.0 MPa

.

Because the similar soil around the segment is not entirely dense during the model loading test, a hydraulic loading device must be used to force the similar soil to act on the surface of the segment once it is fully dense. The hydraulic loading device exhibits a value of 3.6 MPa when the segment is subjected to a complete load, according to data from the entire process recorded by the model test. As a result, the hydraulic device’s display of 3.6 MPa in this experiment’s model test corresponds to a real stress on the segment of 0 MPa.

2.4. Measuring Scheme

The core part of the fiber grating (FBG) sensing element is the grating, which determines the sensing performance of the sensing element. The central wavelength, grating length, and effective reflectivity are three of the grating’s primary characteristic factors that could accurately reflect the sensing performance. Figure 8 and

Table 5. Main parameters of fiber grating.

Name	Center Wavelength	Grating Length	Reflection Bandwidth	Array Wavelength Interval	Resolution Ratio	Effective Reflectance
parameter	1510~1560 nm	10 mm	0.2~0.3 nm	5 nm	0.2 pm	95%

display the characteristic parameters and structure diagram of the MMF-G652 fiber grating used in this experiment.

In this experiment, the information acquisition form of a surface-mounted FBG sensing element combined with a wavelength demodulator was adopted. The distributed sensor network was formed in the form of circumferential distribution along the inner surface of the segment, and the overall deformation information of the segment structure was accurately and automatically perceived in real time. To fully monitor the tunnel segment for more information, considering the relationship between the length of the optical fiber substrate and the size of the segment, we consider the 18° uniform layout of FBG sensing elements. According to the needs of general engineering monitoring and previous research [34], under the requirements of accuracy and cost, the traditional four-point supplementary layout method is selected. According to the difference between the above two layouts, the third layout is selected as a 36° uniform layout. Therefore, this experiment will use three kinds of distribution methods, and investigate the influence of different distribution methods for surface-mounted FBG sensing elements in the local monitoring of tunnels. The first is an 18° uniform layout mode, in which the FBG sensing element is uniformly arranged in a ring direction on the inner surface of the tube segment, the element’s length is chosen to be 8 cm, the ring direction is arranged in a total of 20 elements, and the angle spacing of the element is 18°. The second is a 36° uniform layout mode, in which the component lengths are placed ten times in a ring pattern with a 36° angle between them. The third option is the traditional four-point supplementary layout, in which one measuring point is placed in the vault, one in the bottom of the arch, one in each of the left and right arches, and two more are placed between the four points at angles of 18 degrees and 36 degrees, respectively. In order to eliminate the influence of temperature effect on fiber grating, a temperature compensation fiber is placed near the remaining idle segments. The layout of FBG sensing elements is shown in Figure 9.

3. Tunnel Performance Analysis from Monitoring Results

3.1. Analysis of Segment Strain

Before the loading of surrounding rock pressure, the strain data of the model under no load conditions were measured by the FBG sensing element. Then, the strain data of the model after loading water pressure were measured. Finally, the segment model was loaded according to the test scheme, and the strain information at each position on the inner surface of the model was measured.

The segment’s strain information was gathered under varied load and layout situations by the test plan. Figure 10 and Figure 11 illustrate the segment strain following water pressure loading and segment strain during ground loading for Layout 1 (18° uniform layout).

As seen in Figure 10, when subjected to a 322 N circumferential uniform load, the segment’s inner surface experienced a maximum tensile strain of 43.56 με and a maximum compressive strain of 47.68 με. As seen in Figure 11a,b, under the condition of circumferential, uniform water pressure load, the tensile and compressive strains of the segment structure gradually increased again as the formation pressure increased from 0.4 MPa to 3.6 MPa. In general, the strain variation of the segment model is small in the early stage of stratum load loading. Under uniform water pressure, compressive strain occurs on the inner surface of the segment model. The circumferential compressive strain inside the model structure increases. On the whole, the segment has a tendency to shrink inward. The presence of water pressure lessens the strain on the segment lining structure, and its distribution is advantageous to the structure within its permissible range. The strain distribution of the segment exhibits a significant increase when the test loading device is loaded with a 3.6 MPa formation load. The strain on both sides of the segment arch is shifted inward, and the offset gradually increases.

According to the segment diagram of strain distribution, the strain of the segment structure increases continuously during the formation pressure loading process, with compressive strain occurring in the section between the left and right arches and tensile strain occurring between the arch and the arch bottom. The left and right arches protrude outward, while the arch and arch bottom tend to converge inward, in the genuine structural deformation of the segment. The shield tunnel segment’s convergence and distortion are elliptical.

In the instance of Layout 2 (36° uniform layout), Figure 12 and Figure 13 illustrate segment strain following water pressure loading and segment strain during ground loading.

According to Figure 12, when subjected to a 322 N circumferential uniform load, the segment’s inner surface experienced a maximum tensile strain of 19.36 με and a maximum compressive strain of 35.11 με. The tensile and compressive strain are not axisymmetric, contrary to Layout 1’s finding. The tunnel’s general deformation law is the same as Layout 1. It is worth noting that the maximum tensile stress monitored by Layout 1 and Layout 2 is different. In particular, with underwater pressure load and no formation load, the maximum tensile stress of Layouts 1 and 2 is 47.68 MPa and 17.10 MPa, respectively. Layout 1 and Layout 2 have essentially the same maximum compressive stress. In general, the segment lining deforms symmetrically. The top and bottom of the arches contract inward, while the arches on both sides expand outward. Eventually, elliptical distortion can be seen in the segment lining.

When the formation load is 3.6 MPa and 4.8 MPa, the comparison between Layout 1 and Layout 2 reveals that the maximum tensile and compressive stress point of Layout 2 is different from that of Layout 1. The peak value of tensile and compressive stress is not accurately detected, indicating that Layout 1 could more accurately detect changes in tunnel strain.

In the instance of Layout 3 (the traditional four-point supplemental layout), segment strain following water pressure loading and segment strain during ground loading are depicted in Figure 14 and Figure 15.

As shown in Figure 14 and Figure 15, under the action of 322 N circumferential uniform load, the maximum tensile strain on the inner surface of the segment model is 19.36 με, and the maximum compressive strain on the surface is 35.11 με. Different from the results of Layout 1, the tensile and compressive strains are not axially symmetrical. As shown in Figure 15 a, d, the maximum compressive strain is 32.44 με, which lowers by 2.67 με when the hydraulic device value increases from 0 to 0.4 MPa. The maximal tensile strain is 15.89 με, which decreases by 3.47 με. The maximum tensile and compressive stress in Layout 3 is the same as that in Layout 1 when the ground load is between 3.6 and 4.8 MPa. The arch top and arch bottom contract inward and the arch waist expands outward on both sides during the deformation of segment lining, which often takes the form of a symmetrical elliptical deformation. Due to the different monitoring arrangements, the measured deformation positions of the tunnel are different, and the deformation of each point of the tunnel is also different. This also leads to differences in measurement data under different monitoring arrangements for the same loading mode. However, the tunnel deformation law of the overall monitoring is the same.

The conclusion of Layout 3 is the same as that of Layout 1 under the reduction in FBG sensing points, and the peak value of tensile and compressive stress is the same under various loads. The comparison of the two layouts demonstrates that Layout 3 could also satisfy the requirements for stress monitoring under the reduction in the number of monitoring points. Thus, Layout 3 is preferred for monitoring tunnel stress parameters.

The maximum tension and compression strains under each load in Layout 1 were utilized as the primary reference indices to construct the segment load–strain curve, appropriately showcasing the structure’s deformation state. As demonstrated in Figure 16, the maximum compressive strain of the segment lining structure steadily rises, from −41.63 με to −74.63 με, a 73% increase, when the ground load is in the range of 0–3.6 MPa. The maximum tensile strain initially rises and then gradually falls to around 50 με. The segment structure’s maximum compressive and tensile strains rose sharply between 3.6 MPa and 4.8 MPa, with the compressive strain rising by 481% from 74.63 με to 433.43 με. Following the formation load of 4.0 MPa, the segment structure deforms rapidly. The portion has fissures, which eventually progress gradually. Finally, the structure sustains extensive damage from numerous secondary cracks that grow and penetrate.

Figure 16 shows a comparison between the numerical simulation results and the experimental data of the same full-scale tunnel [36]. The scale test of 0–3.6 MPa is in the stage of soil relaxation. Therefore, compared with the situation after 3.6 MPa, the results of the scaled segment are similar to those of the numerical model between the crack initiation and expansion at 5.2 MPa. After 5.2 MPa, because the numerical model adopts the Moore algorithm, the strain results after the crack attempt cannot be considered. Therefore, the difference between the data is relatively large. This also proves the feasibility of the test results.

Combined with the deformation information of the segment structure provided above, the following conclusions could be derived:

(1)

The segment structure benefits from circumferential uniform water pressure and a water pressure of 322 N could effectively limit the structural deformation of the segment under a vertical formation load of 0.4 MPa;

(2)

When the segment structure is subjected to formation pressure, the tensile strain of the arch and arch bottom gradually increases, causing the arch and arch bottom of the structure to shrink inward and deform; the compressive strain of the arch gradually increases, causing both sides of the arches to bulge out and deform;

(3)

For all three layouts, the segments’ derived strain laws are essentially the same. Layout 3 (traditional four-point supplementary layout) performs better when the strain of the segments is monitored by the FBG sensing element. Layout 3 could effectively gather data on structural strain when the number of layout points is minimized.

3.2. Analysis of Segment Curvature

The initial curvature, as determined by the test methodology, was 0.0253 m⁻¹ before the start of the formation pressure loading. This curvature was determined by using the relationship between the radius and curvature. The segment was then loaded by the test plan, and the wavelength drift following the loading of the earth pressure was determined by the surface-mounted FBG sensing element. The relationship between the wavelength drift and the curvature was used to calculate the curvature information for each place on the inner surface of the model.

Figure 17 depicts the variance in segment curvature during formation loading for Layout 1 (18% uniform layout).

As seen in Figure 17a,b, at this point, formation pressure gradually affected the segment. The inner surface of the segment exhibited primarily negative curvature growth changes, indicating that more pressure strain occurred inside the model’s structure, and the segment as a whole displayed a trend of inward contraction and deformation. In the early stages of formation loading, the segment curvature does not vary much. The curvature of the segment dramatically alters when the test loading device is loaded with a 3.6 MPa formation load, as shown in Figure 17c–f. The segment’s highest curvature, with 4.8 MPa ground load, is 0.3973 m⁻¹, while its smallest curvature is −1.613 m⁻¹. This is because as ground load increases, the segment’s curvature on both sides of the arch waist grows negatively, indicating an outward displacement, while the segment’s curvature in the vault and arch bottom area grows positively, indicating an inward displacement.

According to the curvature distribution diagram of the segment under Layout 1, in the process of formation pressure loading, positive curvature changes occur in the section of the arch and arch bottom and negative curvature grows in the section of the left and right arch waist. The left and right arch waist protrude outward and the arch and arch bottom converge inward as part of the segment’s actual structural deformation.

Figure 18 depicts the variance in segment curvature during formation loading for Layout 2 (18% uniform layout).

In Figure 18a–f, during the formation pressure loading process, positive curvature changes happen in the section of the arch top and arch bottom while negative curvature increases in the section of the left and right arch waistline. Additionally, the deformation state of the shield tunnel segments exhibits convergence and deformation. Layout 2 shares the same variation in tunnel curvature distribution as Layout 1. By comparing the distribution of the tunnel’s maximum and minimum curvature under Layout 1 and Layout 2, it could be seen that the distribution of the maximum and minimum curvature is the same under the formation loading of 4 MPa, while the other loads are different. The maximum curvature of Layout 2 at 5.6 MPa is 0.3902 m⁻¹, while the maximum curvature of Layout 1 is 2.4267 m⁻¹, demonstrating that Layout 2’s monitoring of local curvature changes is less precise than that of Layout 1. The findings indicate that Layout 1 is superior at monitoring segment curvature because it is not accurate to examine tunnel deformation using the curvature change data gathered in Layout 2 compared to Layout 1.

Figure 19 depicts the variance in segment curvature during formation loading for Layout 3 (the traditional four-point supplemental layout).

Figure 19 illustrates how formation pressure loading causes positive curvature changes in the arch top and arch bottom sections while increasing negative curvature in the left and right arch waist sections. The tunnel curvature distribution alteration rule is the same as Layout 1. According to Figure 19 a, d, the tunnel’s maximum curvature and lowest curvature distribution are compared for Layouts 1 and 3. The distribution of maximum curvature and lowest curvature measurement locations under the two types of layouts is different in the early stages of formation loading, as can be observed, but the difference in peak values is negligible, thus the influence on local curvature monitoring may be disregarded. Figure 19e–f shows that, for ground loads of 5.2 MPa and 5.6 MPa, the maximum curvature distribution is the same as the maximum curvature distribution in Layout 1; however, the extreme curvature position varies for the other ground load.

The deformation state of shield tunnel segments exhibits a convergence deformation under the curvature change in Layout 1 and Layout 3; this can be discovered by contrasting the two layout circumstances of Layout 1 and Layout 3. However, in the case of Layout 3, the position distribution of extreme curvature at the late loading stage is different from that of Layout 1, indicating that Layout 3 is unable to accurately collect the local curvature of tunnel curvature, while Layout 1 is better at monitoring the curvature of segments.

The minimum curvature data varied significantly overall, as shown by the tunnel curvature distribution maps of the three layout modes mentioned above. The maximum curvature under Layout 1 was used as the primary reference index to describe the structure’s state of deformation, and the maximum curvature of the segment was shown as a load–curvature change curve, as shown in Figure 20.

Figure 20 illustrates how ground load causes the segment curvature to progressively increase in the shape of a ‘ladder’.

The curvature change exhibits a clear gradient increase trend when combined with the deformation process information of the segment previously discussed and shows that the total change trend of the maximum curvature of the segment can be separated into five stages. The segment structure primarily deforms into an elastic form in the first stage (0–3.6 MPa), where the curvature is essentially maintained near 0.1 m⁻¹. The maximum curvature gradually increases from 0.1209 m⁻¹ to 2.429 m⁻¹ with a slope of 1.2 m⁻¹/MPa in the second stage (3.6–5.6 MPa). It should be noted that, after 4.8 MPa, the curvature began to rise rapidly. This is because the crack propagation occurs in the segment, which corresponds to the stress release stage of the strain curve. The greatest curvature increases significantly from 2.429 m⁻¹ to 11.2037 m⁻¹ with a slope of 10.97 m⁻¹/MPa in the third stage (5.6–6.4 MPa). Subtle fractures begin to show up inside the structure as the second and third stages of the segment’s strengthening progress, and the fissures steadily deepen as the load increases. The fourth stage (6.4–7.2 MPa) sees the development of internal fissures and the release of tension. After 7.2 MPa, the segment structure enters the fifth stage, when cracks continue to grow, widen, and penetrate until the segment is no longer able to support the weight.

The curvature of the arch measuring point, which is the important position of the segment, is used as an example to evaluate the deformation rule of the shield tunnel segment structure because the arch is a frequent deformation notable place in engineering. Figure 21 depicts the load–curvature change curve of the segment measuring point for the arch roof.

In the load range of 0–3.6 MPa, Figure 21 shows that the segment measuring point arch’s curvature steadily reduces. The fracture was broken through and the structure tension was released when the vertical formation load was 4.4 MPa; the curvature of the arch abruptly decreased (slope 0.3), indicating that the fracture had finally occurred.

The following conclusions could be drawn from the study presented above. Under the combined action of ground load and water pressure, the curvature of the segment lining changes in a ‘ladder’ shape, which increases with the increase in ground load. The strengthening effect of constant dispersed water pressure on the segment structure’s deformation resistance is more noticeable the smaller the ground load and the effect of uniform water pressure is negated when the ground load surpasses 4.0 MPa. An incompletely symmetrical outward spreading deformation occurs in the left spandrel area of the segment lining when uniform water pressure is applied to the formation load below 4.0 MPa. The derived segment curvature change law is the same for all three layout situations. Layout 1 (18° uniform layout mode) performs better under the monitoring segment curvature condition. It is advised to use a 18° uniform layout of FBG sensing elements for information collection when monitoring tunnel sections in challenging terrains.

4. Conclusions

This study thoroughly examines the impact of various layout schemes on the accurate monitoring of local tunnel deformation and the overall deformation law of shield segments under the action of water pressure and formation load; three surfacing FBG sensing element layout schemes were adopted. A 1:20-scale model test was carried out using a rotary hydraulic loading device and the shield tunnel formation complicated the simulation test system. In this study, the deformation characteristics of tunnel segments were studied by combining two kinds of change information on strain and curvature. This experiment only studied the influence of strain and curvature under different FBG layouts for fixed water pressure and variable soil pressure. The following conclusions were obtained.

(1)

In the 1:20-scale model test, uniform water pressure causes the entire segment to contract inward into a ‘circular’ shape, while strata load gradually deforms the segment into an elliptical shape. The structural deformation of the segment lining is asymmetrical for ground loads between 0.4 and 3.6 MPa. The segment lining’s left spandrel has a propensity to enlarge outward, whilst the right spandrel has a propensity to contract inward. The deformation of the segment lining restores symmetry after the ground load period of 3.6 MPa.

(2)

In the experiment, the curvature change shows a ‘ladder’ transformation as a whole, which can be divided into three major stages. In the 0–3.6 MPa stage, the segment is in the elastic stage, and the curvature is basically guaranteed to be 0.1 m⁻¹/MPa. In the 3.6–6.4 MPa stage, the segment is in the strengthening stage and the curvature is greatly improved, up to 10.97 m⁻¹/MPa. After 6 MPa, the stress is released and the curvature is further improved after stabilization.

(3)

The appearance of cracks after 4.4 MPa has an important influence on the curvature change. The percentage of curvature change in the 0–4.4 MPa stage is 188%, but the percentage of curvature change in the 4.4–8.0 MPa stage is as high as 2900%.

(4)

Before cracks appear in the scale model, the strain and curvature of the tunnel segment increase steadily in a small range. When cracks appear, the values of strain and curvature fluctuate obviously. The combination of the strain and curvature of the shield tunnel segment structure can well reflect the deformation information of the structure.

(5)

According to research on the effects of three surface-mount FBG sensing elements, the traditional four-point supplementary layout could more accurately perceive tunnel strain changes, and the 18° uniform layout could more accurately perceive local tunnel curvature changes. It is recommended that the FBG sensing elements with a uniform layout of 18° be used to collect data for monitoring tunnel sections in harsh terrain and the FBG sensing elements with a four-point additional configuration be used to collect data for monitoring other sections.

In this study, a 1:20 scale model test was carried out to investigate the deformation perception of the shield tunnel structure under three different layouts of surface-mounted FBG sensors. Due to the influence of scale effect, the layout method will have errors in practical engineering, which need to be verified in the next step. The above research focuses on the section form of the shield tunnel, and the horseshoe tunnel needs to be further studied. The wall thickness of the tunnel designed in this experiment is a fixed value, and it is not used as a parameter to study the critical pressure. The tunnel wall thickness should be further studied as a variable parameter. The focus of the test is to study the influence of hydrostatic pressure and changing earth pressure on tunnel deformation. The influence of live load on tunnel deformation needs to be further studied.