# Permanent Deformation and Temperature Monitoring of Subgrades Using Fiber Bragg Grating Sensing Technology

Authors: Youkun Cheng; Zhenwu Shi
Journal: Journal of Sensors
 (2021)

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## Abstract

The hidden nature of subgrades makes the effective monitoring of their deformation very difficult. This paper addresses this issue by proposing the use of fiber Bragg grating (FBG) sensing technology. Here, an FBG is encapsulated within a monitoring tube formed from a polyvinyl chloride tube, and one end of the monitoring tube is fixed perpendicular to a concrete column, forming a cantilever beam monitoring system. The deformation is assessed according to the theoretical relationship between the horizontal strain on the FBG embedded in the monitoring tube and the vertical displacement of the cantilever beam. Then, the relationship between the variation in the wavelength of light reflected by the encapsulated FBG and the temperature and horizontal strain is obtained on this basis by calibration experiments. The monitoring tubes are buried at a proscribed depth below the top surface of the subgrade, which facilitates the monitoring of the deformation and temperature of the subgrade at different stages of construction through the collection of FBG wavelength data during different periods, such as after embedding the monitoring tubes, the completion of the test road surface, and during the period of operation. The proposed technology is verified by employing the system to monitor the instantaneous maximum deformation and permanent deformation of a subgrade under dynamic loads. The monitoring results demonstrate that the instantaneous maximum deformation values of the subgrade at 0.25 m and 0.5 m below the surface are 695.40μm and 574.02 μm, respectively, and the corresponding permanent deformation values are 53.00 μm and 41.54 μm, respectively. The FBG sensor system is thereby verified to provide a reliable method for conducting long-term continuous, accurate, and efficient subgrade deformation and temperature monitoring.


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## Body

## 1. Introduction

There are many factors that affect road service life [1]. Excessive settlement of highway subgrades is one of the main causes of roadway degradation, which can lead to serious driving safety risks [2–4]. However, conventional subgrade deformation monitoring methods are typically unable to provide timely and accurate information regarding the occurrence of subgrade deformation [5–7]. Accordingly, the development of effective subgrade deformation monitoring and early warning methods is essential for the prevention and control of highway degradation [8].Fiber Bragg grating (FBG) sensing technology has developed rapidly over the past years [9–11] and represents an excellent alternative to conventional subgrade deformation monitoring methods owing to its many advantages such as corrosion resistance, electromagnetic interference resistance, good waterproof performance, and high measurement precision [12]. Here, an FBG sensor employs a periodic variation in the refractive index along a short length of an optical fiber to obtain an optical filter that reflects specific bandwidths of light in response to the transmission of broad-spectrum light through the optical fiber. The periodic variation in the refractive index of optical fibers can be either uniform or nonuniform [13], and because the refractive index varies along the length of an optical fiber, the specific bandwidth of light reflected by the FBG is sensitive to temperature and strain. This sensing technology has been applied gradually over recent years for conducting engineering health monitoring [14–16] and geotechnical engineering monitoring [17, 18]. The specific applications have also varied widely to include numerous settings such as roadways [19], bridges [20, 21], high-speed railways [22], tunnels [23], aeronautics and astronautics [24, 25], oil recovery [26], and mining [27].The specific designs and applications of FBG sensing technology have been the subject of intense development in recent years. For example, Guo et al. [28] applied a surface-mounted FBG strain sensor to successfully monitor the magnitude of the strain and its variation in an expressway via duct due to vehicle load pressure. Kesavan et al. [29] proposed an FBG sensor application for measuring the interfacial strain of reinforced concrete beams strengthened with carbon fiber-reinforced polymer (CFRP). An experimental application verified that the FBG sensor array effectively identified the beginning and expansion of CFRP separation from the concrete surface. An FBG humidity sensor has also been designed to monitor the corrosion rate of concrete sewer walls [30]. The FBG sensor was verified to provide high durability, good time response, and stability over an extended period in the corrosive hydrogen sulfide gas environment with high humidity. Accordingly, the FBG sensor was shown to have broad application prospects in harsh environments. Both long-gauge FBG and point FBG strain sensors were developed for monitoring the static and dynamic loads of a concrete railway bridge [31]. Experimental results demonstrated that both sensors were able to provide accurate strain measurements. A new type of mechanical sensor employing an FBG was proposed, and the design was demonstrated to improve the accuracy of damage detection and localization for civil engineering structures by amplifying the strain applied to the FBG sensor by a factor of about 36 [32]. Dyshlyuk et al. [33] presented the experimental application of an FBG-based measurement method based on optical time-domain reflectometry (OTDR) for monitoring strain in bent reinforced concrete beams. The proposed method was demonstrated to provide results that were consistent with those of direct spectral measurements. A vibration detection method based on FBG sensing technology was proposed to accurately measure the physical and mechanical properties of soil [34]. The data collected by the FBG sensor were demonstrated theoretically and experimentally to reflect vibration conditions clearly and quantitatively. Bellas and Voulgaridis [35] responded to the impact of geotechnical disasters on community housing by developing an advanced FBG-based method for monitoring the health of housing structures and serving as an early warning system. Nan et al. [36] contributed toward the prevention of subway tunnel collapse by applying ultraweak FBG sensing technology to detect the distributed vibrational response of the FBG positioned on the tunnel wall and the track bed, and the occurrence and characteristics of intrusion events simulated by the discrete and continuous pulses of an excavator were recognized under two loading attitudes. The above studies have demonstrated that FBG sensing technology can be implemented in a wide array of engineering applications under complex and harsh conditions. Accordingly, this technology has been applied for monitoring subgrade deformation [37, 38]. However, a sufficiently exact relationship between the specific bandwidth of light reflected by the FBG and the vertical displacement of the subgrade was not established in these past studies, and the proposed methodology was unable to monitor subgrade temperature.The present work addresses the shortcomings of past efforts seeking to apply FBG sensing technology toward subgrade deformation and temperature monitoring. Here, an FBG with a uniformly distributed variation in the index of refraction is encapsulated within a monitoring tube formed from a polyvinyl chloride (PVC) tube, and one end of the monitoring tube is fixed perpendicular to a concrete column, forming a cantilever beam monitoring system. The deformation is assessed according to the theoretical relationship between the horizontal strain on the FBG embedded in the monitoring tube and the vertical displacement of the cantilever beam. Then, the relationship between the variation in the wavelength of light reflected by the encapsulated FBG and the temperature and horizontal strain is obtained on this basis by calibration experiments. The monitoring tubes are buried at a proscribed depth below the top surface of the subgrade, which facilitates the monitoring of the deformation and temperature of the subgrade at different stages of construction through the collection of FBG wavelength data during different periods, such as after embedding the monitoring tubes, the completion of the test road surface, and during the period of operation. The proposed technology is verified by employing the system to monitor the instantaneous maximum deformation and permanent deformation of a subgrade under dynamic loads. The results verify that the deformation and temperature of the subgrade can be monitored in situ even after the completion of highway pavement construction, and each measurement can be completed in a few minutes.


## 2. Working Principles of FBG Sensors

### 2.1. Transmission Principle

The axial refractive index distribution of a uniform period FBG can be given as follows [39]:
(1)nz=n0+Δnmax·cos2πΛz,where n0 is the refractive index of the optical fiber core, Δnmax is the maximum change in n0, Λ is the period length of the uniform grating, and z is the axial position along the optical fiber. The refractive index distribution is illustrated in Figure 1 [40].Figure 1
Refractive index distribution of fiber Bragg grating (FBG).According to coupled mode theory, the wavelengths of broad-spectrum light transmitted through an optical fiber that meet the Bragg wavelength condition of the FBG will be reflected back to the incident end of the optical fiber, and the light of all other wavelengths will pass through freely [41]. This condition is illustrated in Figure 2.Figure 2
Schematic illustrating the spectral response of an FBG.


### 2.2. Basic Sensing Principle

Through coupling between the core mode of forward light transmission and the core mode of backward light transmission, the energy of the core mode of forward transmission is transferred to the core mode of backward transmission, forming the reflection of the incident wave [42]. The reflected wavelength of an FBG is given as follows:
(2)λB=2neffΛ,where neff is the equivalent refractive index of the optical fiber core. The elastooptic effect of the fiber itself causes the value of neff to change with changes in the strain state of the fiber, which changes the value of λB reflected from the FBG [43]. As such, the value of λB represents a measure of the strain state of the optical fiber.If the influence of changes in the temperature is not taken into account, the change inλB owing to tensile and compressive axial strain ε on the FBG can be expressed as follows:
(3)ΔλB=λB1−Peε,where Pe is the effective photoelastic coefficient. Therefore, the axial strain can be calculated as follows:
(4)ε=11−PeΔλBλB.When accounting for changes in the temperature, the thermooptic effect and thermal expansion effect of FBG materials lead to a shift inλB owing to a change ΔΛ in the value of Λ [43, 44]. From equation (2), the value of ΔλB caused by a temperature change ΔT can be expressed as follows:
(5)ΔλB=2Δneff·Λ+2neff·ΔΛ=2∂neff∂TΔT+Δneffep+∂neff∂rΔrΛ+2neff·∂Λ∂TΔT.Here,∂neff/∂T is the refractive index temperature coefficient of the fiber grating; Δneffep is the elastooptic effect produced by the thermal expansion effect; ∂neff/∂r is the waveguide effect produced by the thermal expansion effect, where r is the diameter of the optical fiber; and ∂Λ/∂T is the linear thermal expansion coefficient of the FBG. The right side of equation (5) can now be divided by the right side of equation (2) to obtain the following:
(6)ΔλBλB=∂neff∂T·1neff+ΔΛΔT·1Λ·ΔT+1neffΔneffep+∂neff∂r·Δr,where ∂neff/∂T·1/neff is the thermooptic coefficient of the FBG, which is expressed by ζ; ΔΛ/ΔT·1/Λ is the thermal expansion coefficient of the optical fiber, which is expressed by α; and 1/neffΔneffep+∂neff/∂r·Δr is the comprehensive action coefficient of the elastooptic and waveguide effects, which can be expressed by KH. Accordingly, equation (6) can be arranged as follows:
(7)ΔλBλB=ζ+α·ΔT+KH,which yields the following expression:
(8)ΔλB=ζ+α·ΔT+KH·λB.However, the influence of the elastooptic and waveguide effects caused by thermal expansion on the temperature sensitivity coefficient is very weak. Therefore,KH can be ignored, and equation (8) can be simplified as
(9)ΔλB=ζ+α·ΔT·λB.We can then combine equations (3) and (9) to obtain the change in λB owing to both strain and temperature as follows:
(10)ΔλB=1−Peε+ζ+αΔT·λB.This can be further simplified using the definitions1−Pe·λB=Kε and ζ+α·λB=KT, as follows:
(11)ΔλB=Kεε+KTΔT.Here,Kε is denoted as the strain sensitivity coefficient, and KT is denoted as the temperature sensitivity coefficient.


## 2.1. Transmission Principle

The axial refractive index distribution of a uniform period FBG can be given as follows [39]:
(1)nz=n0+Δnmax·cos2πΛz,where n0 is the refractive index of the optical fiber core, Δnmax is the maximum change in n0, Λ is the period length of the uniform grating, and z is the axial position along the optical fiber. The refractive index distribution is illustrated in Figure 1 [40].Figure 1
Refractive index distribution of fiber Bragg grating (FBG).According to coupled mode theory, the wavelengths of broad-spectrum light transmitted through an optical fiber that meet the Bragg wavelength condition of the FBG will be reflected back to the incident end of the optical fiber, and the light of all other wavelengths will pass through freely [41]. This condition is illustrated in Figure 2.Figure 2
Schematic illustrating the spectral response of an FBG.


## 2.2. Basic Sensing Principle

Through coupling between the core mode of forward light transmission and the core mode of backward light transmission, the energy of the core mode of forward transmission is transferred to the core mode of backward transmission, forming the reflection of the incident wave [42]. The reflected wavelength of an FBG is given as follows:
(2)λB=2neffΛ,where neff is the equivalent refractive index of the optical fiber core. The elastooptic effect of the fiber itself causes the value of neff to change with changes in the strain state of the fiber, which changes the value of λB reflected from the FBG [43]. As such, the value of λB represents a measure of the strain state of the optical fiber.If the influence of changes in the temperature is not taken into account, the change inλB owing to tensile and compressive axial strain ε on the FBG can be expressed as follows:
(3)ΔλB=λB1−Peε,where Pe is the effective photoelastic coefficient. Therefore, the axial strain can be calculated as follows:
(4)ε=11−PeΔλBλB.When accounting for changes in the temperature, the thermooptic effect and thermal expansion effect of FBG materials lead to a shift inλB owing to a change ΔΛ in the value of Λ [43, 44]. From equation (2), the value of ΔλB caused by a temperature change ΔT can be expressed as follows:
(5)ΔλB=2Δneff·Λ+2neff·ΔΛ=2∂neff∂TΔT+Δneffep+∂neff∂rΔrΛ+2neff·∂Λ∂TΔT.Here,∂neff/∂T is the refractive index temperature coefficient of the fiber grating; Δneffep is the elastooptic effect produced by the thermal expansion effect; ∂neff/∂r is the waveguide effect produced by the thermal expansion effect, where r is the diameter of the optical fiber; and ∂Λ/∂T is the linear thermal expansion coefficient of the FBG. The right side of equation (5) can now be divided by the right side of equation (2) to obtain the following:
(6)ΔλBλB=∂neff∂T·1neff+ΔΛΔT·1Λ·ΔT+1neffΔneffep+∂neff∂r·Δr,where ∂neff/∂T·1/neff is the thermooptic coefficient of the FBG, which is expressed by ζ; ΔΛ/ΔT·1/Λ is the thermal expansion coefficient of the optical fiber, which is expressed by α; and 1/neffΔneffep+∂neff/∂r·Δr is the comprehensive action coefficient of the elastooptic and waveguide effects, which can be expressed by KH. Accordingly, equation (6) can be arranged as follows:
(7)ΔλBλB=ζ+α·ΔT+KH,which yields the following expression:
(8)ΔλB=ζ+α·ΔT+KH·λB.However, the influence of the elastooptic and waveguide effects caused by thermal expansion on the temperature sensitivity coefficient is very weak. Therefore,KH can be ignored, and equation (8) can be simplified as
(9)ΔλB=ζ+α·ΔT·λB.We can then combine equations (3) and (9) to obtain the change in λB owing to both strain and temperature as follows:
(10)ΔλB=1−Peε+ζ+αΔT·λB.This can be further simplified using the definitions1−Pe·λB=Kε and ζ+α·λB=KT, as follows:
(11)ΔλB=Kεε+KTΔT.Here,Kε is denoted as the strain sensitivity coefficient, and KT is denoted as the temperature sensitivity coefficient.


## 3. Monitoring Tube Design and FBG Calibration

### 3.1. FBG Monitoring Tube Design

An FBG is fragile and vulnerable to damage, so it cannot be directly embedded in the subgrade. Therefore, an FBG must be packaged within a suitable carrier structure, which can then be embedded in the subgrade. The present work employs a circular PVC tube with a diameter of 10 cm as the FBG carrier. As shown in Figure3(a), the PVC tube is first slotted in advance, and slotting is applied symmetrically to the other side of the tube as well. Then, a single FBG is fixed in the upper and lower slots of the PVC tube using 101 glue and then encased with NANDA 703 silicone rubber, as shown in Figure 3(b) for the upper FBG. The technical parameters of FBGs used in the paper are shown in Table 1.Figure 3
FBG packaging: (a) PVC tube slotting; (b) silicon rubber packaging.
(a)(b)Table 1
The technical parameters of FBGs.
ItemTechnical parametersCentral wavelength1510-1590 nmWavelength tolerance±0.3 nm3 dB bandwidth≤0.3 nmReflectivity≥90%Isolation≥15 dBFiber typeSMF-28Grating lengthGratinglength≤10 mmFigure4 presents a cross-sectional schematic of the traffic lanes of a standard roadway. Past studies have demonstrated that the maximum dynamic stress generated by vehicle loading appears directly under the wheels over a specific depth range of the subgrade [45]. Moreover, according to traffic rules and standard driving habits, the slow lane is mainly used by large and heavy vehicles, which travel down the middle of the slow lane under normal circumstances. Therefore, these positions in the slow lane represent the points of maximum subgrade deformation. Accordingly, the present work adopts the cantilever beam monitoring system illustrated in Figure 5. Here, the base end of the cantilever beam is embedded within a concrete column, and two FBGs are packaged symmetrically in the upper and lower slots at the end of the monitoring tubes.Figure 4
Layout of one half of a standard four-lane roadway.Figure 5
FBG cantilevered monitoring tube structure.The positioning of the FBGs is based on a standard heavy truck wheelbase width of 2 m with consideration for the contact area between the tire and the ground. The standard width of tire contact with the ground is approximately 0.3 m based on the heavy vehicle tire most commonly used, an axle load of 100 kN, and tire pressure of 0.7 MPa. Accordingly, the distance between the inner and outer FBGs and the base end of the cantilever beam is 2.85 m and 3.15 m, respectively, and the FBGs are arranged symmetrically at the upper and lower positions of the monitoring tube to realize simultaneous monitoring of subgrade deformation and temperature. As shown in Figure5, the centers of FBG1 and FBG2 are on the same plumb line, and the centers of FBG3 and FBG4 are on the same plumb line. This represents an improved configuration relative to previously published work [46], where each monitoring tube was equipped with 8 FBG monitoring points typically. However, the monitoring points close to the base end of the cantilever provided limited information due to the fixed constraint at the base end. Therefore, the FBGs are placed only directly under the vehicle track in the present work.


### 3.2. Monitoring Scheme Design

As shown in Figure6, past research has demonstrated that the vertical dynamic stress of a subgrade owing to automobile loading decreases linearly with increasing subgrade depth in the range of 0.0–0.6 m, and that the dynamic stress decreases much more slowly at depths greater than 0.6 m [47, 48]. This linearity is employed in the present work by adopting two FBG monitoring tubes buried at 0.25 m and 0.50 m below the top surface of the roadbed, as illustrated in Figure 7, which includes the optical fiber configuration employed in conjunction with an FBG acquisition demodulator and data processing module. FC/APC connector was welded to one end of the optical fiber using a fiber fusion splicer, which would be connected to the interrogator when conducting tests. The monitoring system has 4 arrays of 2 FBG sensors each, as Figure 7 shows with the 4 lines coming out from the monitoring tubes.Figure 6
Vertical dynamic stress of a subgrade with respect to depth owing to vehicle loading [46].Figure 7
Cross-sectional layout plan of monitoring tubes.


### 3.3. FBG Calibration

Accurate monitoring of the subgrade deformation and temperature requires that we first calibrate the strain sensitivity coefficientKε and temperature sensitivity coefficient KT of the FBGs employed in the proposed monitoring system. However, we first obtained the values of λB for 8 representative FBGs installed within monitoring tubes in the absence of strain at a temperature of 21.3°C, and the results are listed in Table 2.Table 2
Center reflection wavelengthλB of representative FBGs in the absence of strain at a temperature of 21.3°C.
FBG numberWavelengthλB (nm)FBG numberWavelengthλB (nm)11528.674351549.987621533.182161554.617631538.289471559.189041544.919781563.0514The monitoring tubes were so long that the FBGs on them were not easy to be calibrated after encapsulation, so 2 FBGs were selected for calibrating the strain sensitivity coefficientKε and the temperature sensitivity KT in the laboratory. According to the previous calibration experiment results, there is little difference between the Pe, ζ, and α values of the same model FBGs from the same manufacturer, so it was assumed that the Pe, ζ, and α values of the 8 FBGs used on the monitoring tubes are equal to those of the 2 FBGs used in the calibration experiment.


#### 3.3.1. Calibration of Strain Sensitivity Coefficient

Two FBGs were selected for calibrating the strain sensitivity coefficientKε at a temperature of 21.3°C according to the experimental setup illustrated in Figure 8. Here, 60 cm sections of PVC monitoring tubes were applied, and FBGs were installed on the lower tube sides in an equivalent manner as described in Subsection 3.1. Center reflection wavelengths λB of 1536.593 nm and 1561.129 nm were first obtained for these two FBGs in the absence of strain. In addition, resistance strain gauges were pasted on the upper tube sides directly above the FBGs. The two ends of the PVC tube were fixed, and a variable weight was applied at the midpoint of the tube. Then, strain and λB data were collected simultaneously from the resistance strain gauge monitor and the grating acquisition demodulator, respectively. The experimental resistance strain gauge setup provided an accuracy of 1 με and a measurement range of −19999 με to +38000 με. The relationships between λB and the measured strain are presented in Figure 9. The calibration results indicate that the values of λB for the FBGs change linearly with respect to strain over the investigated strain range, indicating that the FBGs respond uniformly over that range. The values of Kε were obtained for the two FBGs from the slopes of the lines fitted to the plotted data, which were 1.37 pm/με and 1.39 pm/με. According to the calibration results, the strain sensitivity coefficients Kε of the FBGs on the monitoring tube could be calculated by Kε=1−Pe·λB. The values of Kε obtained similarly for all 8 FBGs listed in Table 2 are listed in Table 3.Figure 8
Layout of strain sensitivity coefficient calibration experiments.Figure 9
Calibration curves of the strain sensitivity coefficientsKε: (a) FBG with an initial λB value of 1536.593 nm; (b) FBG with an initial λB value of 1561.129 nm.
(a)(b)Table 3
Strain sensitivity coefficientsKε of representative FBGs.
FBG numberStrain sensitivity coefficient (pm/με)FBG numberStrain sensitivity coefficient (pm/με)11.3651.3821.3761.3931.3771.3941.3881.39


#### 3.3.2. Temperature Sensitivity Calibration

The two FBGs employed for strain sensitivity coefficient calibration were again employed for temperature sensitivity calibration over an experimental temperature range of −20°C to 30°C. A frequency conversion refrigerator was used to control the temperature between −20°C and 10°C, and the temperature inside the refrigerator was monitored using a K-type thermocouple connected with a tt-k-24-sle thermocouple line to a temperature monitor located outside of the refrigerator. Testing at temperatures in the range of 10°C to 30°C was conducted in a laboratory equipped with a constant frequency air conditioner, and the temperature was again monitored with a K-type thermocouple. The change in the values ofλB for the FBGs with respect to temperature was monitored every 5°C in the absence of strain. The experimental results are shown in Figure 10. The temperature calibration results indicate that the values of λB for the FBGs change linearly with respect to the temperature over the investigated temperature range, indicating that the FBGs respond uniformly over that range. The values of KT were obtained for the two FBGs from the slopes of the lines fitted to the plotted data, which were 43.94 pm/°C and 44.61 pm/°C. According to the calibration results, the temperature sensitivity coefficients KT of the FBGs on the monitoring tube could be calculated by KT=ζ+α·λB. The values of KT obtained similarly for all 8 FBGs listed in Table 2 are listed in Table 4.Figure 10
Calibration curves of temperature sensitivity coefficientsKT: (a) FBG with an initial λB value of 1536.593 nm; (b) FBG with an initial λB value of 1561.129 nm.
(a)(b)Table 4
Temperature sensitivity coefficientsKT of representative FBGs.
FBG numberTemperature sensitivity coefficient (pm/°C)FBG numberTemperature sensitivity coefficient (pm/°C)143.71544.32243.84644.46343.99744.59444.18844.70


## 3.1. FBG Monitoring Tube Design

An FBG is fragile and vulnerable to damage, so it cannot be directly embedded in the subgrade. Therefore, an FBG must be packaged within a suitable carrier structure, which can then be embedded in the subgrade. The present work employs a circular PVC tube with a diameter of 10 cm as the FBG carrier. As shown in Figure3(a), the PVC tube is first slotted in advance, and slotting is applied symmetrically to the other side of the tube as well. Then, a single FBG is fixed in the upper and lower slots of the PVC tube using 101 glue and then encased with NANDA 703 silicone rubber, as shown in Figure 3(b) for the upper FBG. The technical parameters of FBGs used in the paper are shown in Table 1.Figure 3
FBG packaging: (a) PVC tube slotting; (b) silicon rubber packaging.
(a)(b)Table 1
The technical parameters of FBGs.
ItemTechnical parametersCentral wavelength1510-1590 nmWavelength tolerance±0.3 nm3 dB bandwidth≤0.3 nmReflectivity≥90%Isolation≥15 dBFiber typeSMF-28Grating lengthGratinglength≤10 mmFigure4 presents a cross-sectional schematic of the traffic lanes of a standard roadway. Past studies have demonstrated that the maximum dynamic stress generated by vehicle loading appears directly under the wheels over a specific depth range of the subgrade [45]. Moreover, according to traffic rules and standard driving habits, the slow lane is mainly used by large and heavy vehicles, which travel down the middle of the slow lane under normal circumstances. Therefore, these positions in the slow lane represent the points of maximum subgrade deformation. Accordingly, the present work adopts the cantilever beam monitoring system illustrated in Figure 5. Here, the base end of the cantilever beam is embedded within a concrete column, and two FBGs are packaged symmetrically in the upper and lower slots at the end of the monitoring tubes.Figure 4
Layout of one half of a standard four-lane roadway.Figure 5
FBG cantilevered monitoring tube structure.The positioning of the FBGs is based on a standard heavy truck wheelbase width of 2 m with consideration for the contact area between the tire and the ground. The standard width of tire contact with the ground is approximately 0.3 m based on the heavy vehicle tire most commonly used, an axle load of 100 kN, and tire pressure of 0.7 MPa. Accordingly, the distance between the inner and outer FBGs and the base end of the cantilever beam is 2.85 m and 3.15 m, respectively, and the FBGs are arranged symmetrically at the upper and lower positions of the monitoring tube to realize simultaneous monitoring of subgrade deformation and temperature. As shown in Figure5, the centers of FBG1 and FBG2 are on the same plumb line, and the centers of FBG3 and FBG4 are on the same plumb line. This represents an improved configuration relative to previously published work [46], where each monitoring tube was equipped with 8 FBG monitoring points typically. However, the monitoring points close to the base end of the cantilever provided limited information due to the fixed constraint at the base end. Therefore, the FBGs are placed only directly under the vehicle track in the present work.


## 3.2. Monitoring Scheme Design

As shown in Figure6, past research has demonstrated that the vertical dynamic stress of a subgrade owing to automobile loading decreases linearly with increasing subgrade depth in the range of 0.0–0.6 m, and that the dynamic stress decreases much more slowly at depths greater than 0.6 m [47, 48]. This linearity is employed in the present work by adopting two FBG monitoring tubes buried at 0.25 m and 0.50 m below the top surface of the roadbed, as illustrated in Figure 7, which includes the optical fiber configuration employed in conjunction with an FBG acquisition demodulator and data processing module. FC/APC connector was welded to one end of the optical fiber using a fiber fusion splicer, which would be connected to the interrogator when conducting tests. The monitoring system has 4 arrays of 2 FBG sensors each, as Figure 7 shows with the 4 lines coming out from the monitoring tubes.Figure 6
Vertical dynamic stress of a subgrade with respect to depth owing to vehicle loading [46].Figure 7
Cross-sectional layout plan of monitoring tubes.


## 3.3. FBG Calibration

Accurate monitoring of the subgrade deformation and temperature requires that we first calibrate the strain sensitivity coefficientKε and temperature sensitivity coefficient KT of the FBGs employed in the proposed monitoring system. However, we first obtained the values of λB for 8 representative FBGs installed within monitoring tubes in the absence of strain at a temperature of 21.3°C, and the results are listed in Table 2.Table 2
Center reflection wavelengthλB of representative FBGs in the absence of strain at a temperature of 21.3°C.
FBG numberWavelengthλB (nm)FBG numberWavelengthλB (nm)11528.674351549.987621533.182161554.617631538.289471559.189041544.919781563.0514The monitoring tubes were so long that the FBGs on them were not easy to be calibrated after encapsulation, so 2 FBGs were selected for calibrating the strain sensitivity coefficientKε and the temperature sensitivity KT in the laboratory. According to the previous calibration experiment results, there is little difference between the Pe, ζ, and α values of the same model FBGs from the same manufacturer, so it was assumed that the Pe, ζ, and α values of the 8 FBGs used on the monitoring tubes are equal to those of the 2 FBGs used in the calibration experiment.


### 3.3.1. Calibration of Strain Sensitivity Coefficient

Two FBGs were selected for calibrating the strain sensitivity coefficientKε at a temperature of 21.3°C according to the experimental setup illustrated in Figure 8. Here, 60 cm sections of PVC monitoring tubes were applied, and FBGs were installed on the lower tube sides in an equivalent manner as described in Subsection 3.1. Center reflection wavelengths λB of 1536.593 nm and 1561.129 nm were first obtained for these two FBGs in the absence of strain. In addition, resistance strain gauges were pasted on the upper tube sides directly above the FBGs. The two ends of the PVC tube were fixed, and a variable weight was applied at the midpoint of the tube. Then, strain and λB data were collected simultaneously from the resistance strain gauge monitor and the grating acquisition demodulator, respectively. The experimental resistance strain gauge setup provided an accuracy of 1 με and a measurement range of −19999 με to +38000 με. The relationships between λB and the measured strain are presented in Figure 9. The calibration results indicate that the values of λB for the FBGs change linearly with respect to strain over the investigated strain range, indicating that the FBGs respond uniformly over that range. The values of Kε were obtained for the two FBGs from the slopes of the lines fitted to the plotted data, which were 1.37 pm/με and 1.39 pm/με. According to the calibration results, the strain sensitivity coefficients Kε of the FBGs on the monitoring tube could be calculated by Kε=1−Pe·λB. The values of Kε obtained similarly for all 8 FBGs listed in Table 2 are listed in Table 3.Figure 8
Layout of strain sensitivity coefficient calibration experiments.Figure 9
Calibration curves of the strain sensitivity coefficientsKε: (a) FBG with an initial λB value of 1536.593 nm; (b) FBG with an initial λB value of 1561.129 nm.
(a)(b)Table 3
Strain sensitivity coefficientsKε of representative FBGs.
FBG numberStrain sensitivity coefficient (pm/με)FBG numberStrain sensitivity coefficient (pm/με)11.3651.3821.3761.3931.3771.3941.3881.39


### 3.3.2. Temperature Sensitivity Calibration

The two FBGs employed for strain sensitivity coefficient calibration were again employed for temperature sensitivity calibration over an experimental temperature range of −20°C to 30°C. A frequency conversion refrigerator was used to control the temperature between −20°C and 10°C, and the temperature inside the refrigerator was monitored using a K-type thermocouple connected with a tt-k-24-sle thermocouple line to a temperature monitor located outside of the refrigerator. Testing at temperatures in the range of 10°C to 30°C was conducted in a laboratory equipped with a constant frequency air conditioner, and the temperature was again monitored with a K-type thermocouple. The change in the values ofλB for the FBGs with respect to temperature was monitored every 5°C in the absence of strain. The experimental results are shown in Figure 10. The temperature calibration results indicate that the values of λB for the FBGs change linearly with respect to the temperature over the investigated temperature range, indicating that the FBGs respond uniformly over that range. The values of KT were obtained for the two FBGs from the slopes of the lines fitted to the plotted data, which were 43.94 pm/°C and 44.61 pm/°C. According to the calibration results, the temperature sensitivity coefficients KT of the FBGs on the monitoring tube could be calculated by KT=ζ+α·λB. The values of KT obtained similarly for all 8 FBGs listed in Table 2 are listed in Table 4.Figure 10
Calibration curves of temperature sensitivity coefficientsKT: (a) FBG with an initial λB value of 1536.593 nm; (b) FBG with an initial λB value of 1561.129 nm.
(a)(b)Table 4
Temperature sensitivity coefficientsKT of representative FBGs.
FBG numberTemperature sensitivity coefficient (pm/°C)FBG numberTemperature sensitivity coefficient (pm/°C)143.71544.32243.84644.46343.99744.59444.18844.70


## 3.3.1. Calibration of Strain Sensitivity Coefficient

Two FBGs were selected for calibrating the strain sensitivity coefficientKε at a temperature of 21.3°C according to the experimental setup illustrated in Figure 8. Here, 60 cm sections of PVC monitoring tubes were applied, and FBGs were installed on the lower tube sides in an equivalent manner as described in Subsection 3.1. Center reflection wavelengths λB of 1536.593 nm and 1561.129 nm were first obtained for these two FBGs in the absence of strain. In addition, resistance strain gauges were pasted on the upper tube sides directly above the FBGs. The two ends of the PVC tube were fixed, and a variable weight was applied at the midpoint of the tube. Then, strain and λB data were collected simultaneously from the resistance strain gauge monitor and the grating acquisition demodulator, respectively. The experimental resistance strain gauge setup provided an accuracy of 1 με and a measurement range of −19999 με to +38000 με. The relationships between λB and the measured strain are presented in Figure 9. The calibration results indicate that the values of λB for the FBGs change linearly with respect to strain over the investigated strain range, indicating that the FBGs respond uniformly over that range. The values of Kε were obtained for the two FBGs from the slopes of the lines fitted to the plotted data, which were 1.37 pm/με and 1.39 pm/με. According to the calibration results, the strain sensitivity coefficients Kε of the FBGs on the monitoring tube could be calculated by Kε=1−Pe·λB. The values of Kε obtained similarly for all 8 FBGs listed in Table 2 are listed in Table 3.Figure 8
Layout of strain sensitivity coefficient calibration experiments.Figure 9
Calibration curves of the strain sensitivity coefficientsKε: (a) FBG with an initial λB value of 1536.593 nm; (b) FBG with an initial λB value of 1561.129 nm.
(a)(b)Table 3
Strain sensitivity coefficientsKε of representative FBGs.
FBG numberStrain sensitivity coefficient (pm/με)FBG numberStrain sensitivity coefficient (pm/με)11.3651.3821.3761.3931.3771.3941.3881.39


## 3.3.2. Temperature Sensitivity Calibration

The two FBGs employed for strain sensitivity coefficient calibration were again employed for temperature sensitivity calibration over an experimental temperature range of −20°C to 30°C. A frequency conversion refrigerator was used to control the temperature between −20°C and 10°C, and the temperature inside the refrigerator was monitored using a K-type thermocouple connected with a tt-k-24-sle thermocouple line to a temperature monitor located outside of the refrigerator. Testing at temperatures in the range of 10°C to 30°C was conducted in a laboratory equipped with a constant frequency air conditioner, and the temperature was again monitored with a K-type thermocouple. The change in the values ofλB for the FBGs with respect to temperature was monitored every 5°C in the absence of strain. The experimental results are shown in Figure 10. The temperature calibration results indicate that the values of λB for the FBGs change linearly with respect to the temperature over the investigated temperature range, indicating that the FBGs respond uniformly over that range. The values of KT were obtained for the two FBGs from the slopes of the lines fitted to the plotted data, which were 43.94 pm/°C and 44.61 pm/°C. According to the calibration results, the temperature sensitivity coefficients KT of the FBGs on the monitoring tube could be calculated by KT=ζ+α·λB. The values of KT obtained similarly for all 8 FBGs listed in Table 2 are listed in Table 4.Figure 10
Calibration curves of temperature sensitivity coefficientsKT: (a) FBG with an initial λB value of 1536.593 nm; (b) FBG with an initial λB value of 1561.129 nm.
(a)(b)Table 4
Temperature sensitivity coefficientsKT of representative FBGs.
FBG numberTemperature sensitivity coefficient (pm/°C)FBG numberTemperature sensitivity coefficient (pm/°C)143.71544.32243.84644.46343.99744.59444.18844.70


## 4. Principle of Deformation Calculation

As discussed above, the horizontal strain on a monitoring tube can be determined according to the changeΔλB in the wavelength of the light reflected by the FBG. However, monitoring the deformation of the subgrade based on the cantilevered monitoring tubes illustrated in Figures 5 and 7 requires that the relationship between the horizontal strain and the vertical deflection of a monitoring tube be determined. This is evaluated according to the stress conditions acting on the axis of the cantilever beam, as illustrated in Figure 11. Here, the beam length between points A and B is l, x is the horizontal distance from the fixed end to any position along the cantilever beam, and q1 and q2 are uniformly distributed loads, respectively, on the upper and lower surfaces of the beam owing to a force F applied at point B.Figure 11
Stress analysis of the cantilevered monitoring tube structure.The conditions illustrated in Figure11 are further analyzed by considering the bending moments under load F and distributed loads q1 and q2. First, the moment equation of the cantilever beam under load F is given as
(12)Mx=−Fl−x,according to the moment diagram shown in Figure 12, where c1 is the centroid of the bending moment diagram. The bending moments of the cantilever beam under q1 and q2 are, respectively, analyzed accordingly to the moment diagrams shown in Figures 13 and 14, where c2 and c3 are the respective centroids of the two bending moment diagrams, and the bending moment equations are given as follows:
(13)M1x=−q1l−x22,M2x=q2l−x22.Figure 12
Schematic illustrating the bending moment of the cantilever beam under loadF.Figure 13
Schematic illustrating the bending moment of the cantilever beam under distributed loadq1.Figure 14
Schematic illustrating the bending moment of the cantilever beam under distributed loadq2.Accordingly, these bending moment diagrams represent quadratic parabolas.Extending the above analysis, a unit forcef is applied to the end of the cantilever beam, as shown in Figure 15(a), and the bending moment diagram is shown in Figure 15(b). Accordingly, the bending moment equation is given as follows:
(14)Mx¯=−l−x.Figure 15
Load diagram (a) and bending moment diagram (b) under a unit forcef.
(a)(b)The ordinate values of the unit load bending moment diagram corresponding to the center of gravity of the bending moment of the cantilever under applied loadsF, q1, and q2 are, respectively,
(15)MC1⃑=2l3,MC2⃑=3l4,MC3⃑=3l4.The vertical deformation of pointB can be obtained using graph multiplication as follows:
(16)ΔB=1EIFl·l·2l3+12q1l2·l·l4−12q2l2·l·l4,where EI is the bending stiffness. This can be rewritten as follows:
(17)ΔB=∫0lMxMx¯EIdx+∫0lM1xMx¯EIdx+∫0iM2xMx¯EIdx,where the terms Mx, M1x, and M2x are the bending moments of the cantilever beam under an external load (F,q1,q2), which are defined as follows:
(18)Mx=εxEIy.Here, the horizontal strainε is now a function of x, and y is the distance from a point on the monitoring tube along the radial direction to the beam centerline axis.The analysis at pointB is now extended to some arbitrary point C along the horizontal direction of the cantilever beam of radius R, as shown in Figure 16. Here, the bending moment equation under f is given as
(19)M¯x=−x.Figure 16
Load per unit forcef at any point along the cantilever beam.The relationship between the vertical displacement and the horizontal strain at pointC is given as follows:
(20)ΔC=∫0xMxM¯xEIdx=∫0xεxy·−xdx.The horizontal strain can be analyzed more clearly by considering a short segment of the cantilever beam of lengthdx at C in Figure 16 and expanding it as illustrated in Figure 17(a), where y is the distance between any longitudinal line segment MM′ and the centerline axis OO′. This is applied to a case of pure beam bending through an arc of dθ, as illustrated in Figure 17(b), where the strain is given as
(21)εx=ρ+ydθ−ρdθρdθ=yρ,and ρ is the radius of curvature of the centerline axis after bending. According to formulas (20) and (21), the deflection of point C under stress can be obtained as follows:
(22)ΔC=−x22ρ,which represents the collaborative deformation of the monitoring tube and soil under an applied force. Here, the minus sign (−) indicates that the deflection is downward, and the value of ρ can be determined from experimental measurement data.Figure 17
Bending strain diagrams: (a) unstressed diagram; (b) poststressed diagram.
(a)(b)


## 5. On-Site Monitoring of Subgrade Deformation

### 5.1. Monitoring Tube Installation under Test Roadway

The monitoring tubes were packaged according to the design in Figure5 and installed in the subgrade soil underneath a test roadway section according to the layout scheme illustrated in Figure 7. The embedding process is shown in Figure 18.Figure 18
Monitoring tube embedding process underneath a section of a test roadway: (a) trenching; (b) concrete column pouring for anchoring cantilevers; (c) laying of a monitoring tube.
(a)(b)(c)


### 5.2. Initial Data Acquisition

The initial center wavelength of the reflected light from the 8 FBGs and the temperature of the subgrade was collected immediately after laying the two monitoring tubes. The test data were collected using a sm130 FBG demodulator (American Micron Optics, Inc.). The sm130 demodulator includes a built-in large-bandwidth scanning laser light source. It also includes 4 channels with a wavelength range of 1510–1590 nm and an accuracy higher than 1 pm. Bluetooth wireless temperature measurement devices with low power consumption were embedded in the subgrade at depths corresponding to the monitoring tubes [49]. The collected data are listed in Table 5. The FBG monitoring system requires only the initial temperature from the wireless temperature sensors, and subsequent subgrade temperatures can be obtained by monitoring the change in the λB values of the respective FBGs.Table 5
Initial center wavelengths of the reflected light from the FBGs and corresponding subgrade temperatures obtained immediately after laying the monitoring tubes.
FBG numberWavelengthλB (nm)FBG numberWavelengthλB (nm)11529.085551550.38321532.934861554.361931538.686471559.572741544.687981562.8105Temperature of subgrade 25 cm below the subgrade surface (°C)23.2Temperature of subgrade 50 cm below the subgrade surface (°C)22.9According to formula (11), the wavelength changes of FBG1 and FBG2 monitoring tube 1 in Figure 7 are as follows:
(23)ΔλB1=Kεε1+KTΔT1,ΔλB2=Kεε2+KTΔT2,whereΔT1 and ΔT2 are the subgrade temperature difference between the monitoring time and the initial time. ΔλB1 and ΔλB2 can be obtained by monitoring. It can be seen from Figure 17 that ε1=−ε2. Since the subgrade temperature change is small within 10 cm, ΔT1=ΔT2 can be set. The strain and temperature changes of FBG1 and FBG2 are calculated as follows:
(24)ε1=−ε2=ΔλB1−ΔλB22Kε,ΔT1=ΔT2=ΔλB1+ΔλB22KT.Therefore, as long as the initial temperature of the monitoring point is known, the subgrade temperature at point ① in Figure7 can be calculated when monitoring. According to the method, the temperature of points ②, ③, and ④ in Figure 7 can also be calculated.Similarly, the center values ofλB obtained from the 8 FBGs were collected immediately after the pavement of the test roadway was completed. The collected data are listed in Table 6. Finally, the deformation of the subgrade at the monitoring points during the construction period was calculated based on the data collected before and after construction, and the subgrade temperature at the completion of roadway paving was also obtained. These results are listed in Table 7 along with vertical deformation and temperatures of the subgrade obtained after construction.Table 6
Center wavelengths of the reflected light from the FBGs obtained immediately after completion of the test roadway pavement layer.
FBG numberWavelengthλB (nm)FBG numberWavelengthλB (nm)11528.794551550.115421532.208761553.68731538.397571559.302941543.970181562.1249Table 7
Subgrade deformation and temperature during construction.
Test pointPosition ①Position ②Position ③Position ④Vertical deformation of subgrade (mm)12.915.411.914.8Subgrade temperature (°C)11.611.811.311.2


### 5.3. Subgrade Deformation Monitoring under Vehicle Loading

Subgrade deformation monitoring of the test roadway under vehicle loading was conducted during the summer of the second year after the roadway was opened to traffic. First, the center wavelengths of the reflected light from the FBGs were collected, and the collection results are listed in Table8. The permanent deformation of the subgrade at the monitoring points since the completion of the roadway surface was then calculated based on the data collected in Tables 6 and 8, and the results are listed in Table 9 along with the calculated subgrade temperature at the time of monitoring.Table 8
Center wavelengths of the reflected light from the FBGs before conducting vehicle load testing.
FBG numberWavelengthλB (nm)FBG numberWavelengthλB (nm)11529.170851550.424521532.286561553.740931538.756771559.617741544.041981562.1852Table 9
Total deformation and temperature of the subgrade during summer.
Test pointPosition ①Position ②Position ③Position ④Vertical deformation of subgrade (mm)8.910.47.59.1Subgrade temperature (°C)16.816.716.416.4We conducted dynamic subgrade deformation monitoring under vehicle loading using a heavy 4-axle truck traveling over the subgrade monitoring area at a speed of 10 km/h. The dynamic load monitoring test process is shown in Figure19. The time histories of the values of λB obtained for the 8 FBGs under vehicle loading are presented in Figure 20. The maximum deformation, elastic deformation, and permanent deformation of each monitoring point under vehicle loading were determined from the collected data, and the results are listed in Table 10.Figure 19
Vehicle load strain monitoring site of the test roadway: (a) FBGs connected with the acquisition equipment; (b) vehicle passing the monitoring section; (c) data acquisition.
(a)(b)(c)Figure 20
Time histories of the values ofλB obtained for the 8 FBGs under vehicle loadingTable 10
Subgrade deformation determined under vehicle loading.
DeformationPosition ①Position ②Position ③Position ④Maximum deformation under dynamic loading (μm)556.32695.40485.58574.02Elastic deformation (μm)515.37642.39451.37532.48Permanent deformation (μm)40.9653.0034.2241.54It can be seen from Figure20 that the FBG monitoring system accurately monitors the process by which the values of λB change with respect to time under dynamic vehicle loading conditions, and the monitoring system can effectively detect the maximum deformation, elastic deformation, and permanent deformation of the subgrade from the time histories. It can be seen from Table 10 that the deformation values obtained by the FBGs increase as the distance between the FBGs on the cantilever beam and the anchor point in the concrete column increases. We then selected the larger value as the monitoring result. We also note that the maximum deformation, elastic deformation, and permanent deformation values of the subgrade decrease substantially with increasing distance from the subgrade surface.The subgrade deformation was obtained by analyzing the data collected by the monitoring tube 1 and tube 2 under the load of vehicles such as a light vehicle, water truck, medium truck, transit mixer truck, and heavy truck during the fall of the second year after the roadway was opened to traffic. These results are shown in Figure21. The subgrade deformation value was randomly monitored during the normal driving process of the vehicles; also, it was affected by many factors such as vehicle speed and cargo load.Figure 21
Subgrade deformation under different loadsIt can be seen from Figure21 that the deformation law of subgrade obtained by the two monitoring pipes under different loads is the same. The permanent deformation values of deep subgrade are smaller than those of shallow subgrade. It indicates that the permanent deformation of the subgrade decreases with the increase of the subgrade depth under the action of load. The permanent deformation of the subgrade is very little under the action of a light truck, but it increases obviously when the load increases. The order of magnitude and variation law of the subgrade deformation obtained by the monitoring method are similar to those obtained in the literatures [46, 50].


## 5.1. Monitoring Tube Installation under Test Roadway

The monitoring tubes were packaged according to the design in Figure5 and installed in the subgrade soil underneath a test roadway section according to the layout scheme illustrated in Figure 7. The embedding process is shown in Figure 18.Figure 18
Monitoring tube embedding process underneath a section of a test roadway: (a) trenching; (b) concrete column pouring for anchoring cantilevers; (c) laying of a monitoring tube.
(a)(b)(c)


## 5.2. Initial Data Acquisition

The initial center wavelength of the reflected light from the 8 FBGs and the temperature of the subgrade was collected immediately after laying the two monitoring tubes. The test data were collected using a sm130 FBG demodulator (American Micron Optics, Inc.). The sm130 demodulator includes a built-in large-bandwidth scanning laser light source. It also includes 4 channels with a wavelength range of 1510–1590 nm and an accuracy higher than 1 pm. Bluetooth wireless temperature measurement devices with low power consumption were embedded in the subgrade at depths corresponding to the monitoring tubes [49]. The collected data are listed in Table 5. The FBG monitoring system requires only the initial temperature from the wireless temperature sensors, and subsequent subgrade temperatures can be obtained by monitoring the change in the λB values of the respective FBGs.Table 5
Initial center wavelengths of the reflected light from the FBGs and corresponding subgrade temperatures obtained immediately after laying the monitoring tubes.
FBG numberWavelengthλB (nm)FBG numberWavelengthλB (nm)11529.085551550.38321532.934861554.361931538.686471559.572741544.687981562.8105Temperature of subgrade 25 cm below the subgrade surface (°C)23.2Temperature of subgrade 50 cm below the subgrade surface (°C)22.9According to formula (11), the wavelength changes of FBG1 and FBG2 monitoring tube 1 in Figure 7 are as follows:
(23)ΔλB1=Kεε1+KTΔT1,ΔλB2=Kεε2+KTΔT2,whereΔT1 and ΔT2 are the subgrade temperature difference between the monitoring time and the initial time. ΔλB1 and ΔλB2 can be obtained by monitoring. It can be seen from Figure 17 that ε1=−ε2. Since the subgrade temperature change is small within 10 cm, ΔT1=ΔT2 can be set. The strain and temperature changes of FBG1 and FBG2 are calculated as follows:
(24)ε1=−ε2=ΔλB1−ΔλB22Kε,ΔT1=ΔT2=ΔλB1+ΔλB22KT.Therefore, as long as the initial temperature of the monitoring point is known, the subgrade temperature at point ① in Figure7 can be calculated when monitoring. According to the method, the temperature of points ②, ③, and ④ in Figure 7 can also be calculated.Similarly, the center values ofλB obtained from the 8 FBGs were collected immediately after the pavement of the test roadway was completed. The collected data are listed in Table 6. Finally, the deformation of the subgrade at the monitoring points during the construction period was calculated based on the data collected before and after construction, and the subgrade temperature at the completion of roadway paving was also obtained. These results are listed in Table 7 along with vertical deformation and temperatures of the subgrade obtained after construction.Table 6
Center wavelengths of the reflected light from the FBGs obtained immediately after completion of the test roadway pavement layer.
FBG numberWavelengthλB (nm)FBG numberWavelengthλB (nm)11528.794551550.115421532.208761553.68731538.397571559.302941543.970181562.1249Table 7
Subgrade deformation and temperature during construction.
Test pointPosition ①Position ②Position ③Position ④Vertical deformation of subgrade (mm)12.915.411.914.8Subgrade temperature (°C)11.611.811.311.2


## 5.3. Subgrade Deformation Monitoring under Vehicle Loading

Subgrade deformation monitoring of the test roadway under vehicle loading was conducted during the summer of the second year after the roadway was opened to traffic. First, the center wavelengths of the reflected light from the FBGs were collected, and the collection results are listed in Table8. The permanent deformation of the subgrade at the monitoring points since the completion of the roadway surface was then calculated based on the data collected in Tables 6 and 8, and the results are listed in Table 9 along with the calculated subgrade temperature at the time of monitoring.Table 8
Center wavelengths of the reflected light from the FBGs before conducting vehicle load testing.
FBG numberWavelengthλB (nm)FBG numberWavelengthλB (nm)11529.170851550.424521532.286561553.740931538.756771559.617741544.041981562.1852Table 9
Total deformation and temperature of the subgrade during summer.
Test pointPosition ①Position ②Position ③Position ④Vertical deformation of subgrade (mm)8.910.47.59.1Subgrade temperature (°C)16.816.716.416.4We conducted dynamic subgrade deformation monitoring under vehicle loading using a heavy 4-axle truck traveling over the subgrade monitoring area at a speed of 10 km/h. The dynamic load monitoring test process is shown in Figure19. The time histories of the values of λB obtained for the 8 FBGs under vehicle loading are presented in Figure 20. The maximum deformation, elastic deformation, and permanent deformation of each monitoring point under vehicle loading were determined from the collected data, and the results are listed in Table 10.Figure 19
Vehicle load strain monitoring site of the test roadway: (a) FBGs connected with the acquisition equipment; (b) vehicle passing the monitoring section; (c) data acquisition.
(a)(b)(c)Figure 20
Time histories of the values ofλB obtained for the 8 FBGs under vehicle loadingTable 10
Subgrade deformation determined under vehicle loading.
DeformationPosition ①Position ②Position ③Position ④Maximum deformation under dynamic loading (μm)556.32695.40485.58574.02Elastic deformation (μm)515.37642.39451.37532.48Permanent deformation (μm)40.9653.0034.2241.54It can be seen from Figure20 that the FBG monitoring system accurately monitors the process by which the values of λB change with respect to time under dynamic vehicle loading conditions, and the monitoring system can effectively detect the maximum deformation, elastic deformation, and permanent deformation of the subgrade from the time histories. It can be seen from Table 10 that the deformation values obtained by the FBGs increase as the distance between the FBGs on the cantilever beam and the anchor point in the concrete column increases. We then selected the larger value as the monitoring result. We also note that the maximum deformation, elastic deformation, and permanent deformation values of the subgrade decrease substantially with increasing distance from the subgrade surface.The subgrade deformation was obtained by analyzing the data collected by the monitoring tube 1 and tube 2 under the load of vehicles such as a light vehicle, water truck, medium truck, transit mixer truck, and heavy truck during the fall of the second year after the roadway was opened to traffic. These results are shown in Figure21. The subgrade deformation value was randomly monitored during the normal driving process of the vehicles; also, it was affected by many factors such as vehicle speed and cargo load.Figure 21
Subgrade deformation under different loadsIt can be seen from Figure21 that the deformation law of subgrade obtained by the two monitoring pipes under different loads is the same. The permanent deformation values of deep subgrade are smaller than those of shallow subgrade. It indicates that the permanent deformation of the subgrade decreases with the increase of the subgrade depth under the action of load. The permanent deformation of the subgrade is very little under the action of a light truck, but it increases obviously when the load increases. The order of magnitude and variation law of the subgrade deformation obtained by the monitoring method are similar to those obtained in the literatures [46, 50].


## 6. Conclusions

The present work addressed the difficulty of monitoring the deformation of highway subgrades in situ using FBG sensing technology. An FBG was encapsulated within a monitoring tube formed from a PVC tube, and one end of the monitoring tube was fixed perpendicular to a concrete column, forming a cantilever beam monitoring system. The deformation was assessed according to the theoretical relationship between the horizontal strain on the FBG embedded in the monitoring tube and the vertical displacement of the cantilever beam. Then, the relationship between the variation in the wavelength of light reflected by the encapsulated FBG and the temperature and horizontal strain was obtained on this basis by calibration experiments. Two monitoring tubes were buried at depths of 25 cm and 50 cm below the subgrade surface of a test roadway, and the system was demonstrated to facilitate the monitoring of the deformation and temperature of the subgrade at different stages of construction through the collection of FBG wavelength data during different periods, which included after embedding the monitoring tubes, after the completion of the test roadway surface, and during a period of operation under dynamic vehicle loading. The proposed monitoring system was verified to effectively detect the maximum deformation, elastic deformation, and permanent deformation of the subgrade from the time histories of the center wavelengths of the light reflected by the FBGs under conditions of dynamic loading. Accordingly, we can conclude that the FBG monitoring system can realize long-term, accurate, and efficient monitoring of subgrade deformation as well as subgrade temperature in the range of −20°C to 30°C.



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*Source: 8824058-2021-01-31.xml*