# Application of Fiber Bragg Grating Sensing Technology for Bol Force Status Monitoring in Roadways
## 2 Structure and Principle of FBG Bolt Force Sensor
### Measuring Principle  
The FBG is an optical fiber device whose grating is directly written by ultraviolet light into a single mode fiber so that the refractive index is axially changed along the optical fiber. When light transmitted along the fiber core scatters on each FBG, if the Bragg condition is satisfied, a reflection peak is formed in the reverse direction. The wavelength corresponding to the apex of this reflection peak is the reflection center wavelength. The basic sensing principle of the FBG is to convert a change in external physical quantities to its center wavelength shift by utilizing the sensitivity of its own grating period and effective refractive index to external physical quantities and then detect the change in the FBG reflected center wavelength to achieve measurement of external parameters. The effect of the strain and temperature changes on the wavelength shift can be expressed as [22; 23]  
\[\frac{\Delta\lambda_{B}}{\lambda_{B}}=(1-P_{e})\epsilon+(\alpha+\zeta)\Delta T \tag{1}\]  
where \(\lambda_{B}\) is the initial center wavelength; \(\epsilon\) is the strain change; \(\Delta T\) is the temperature change; \(P_{e}\) is the effective elasto-optical coefficient; \(\alpha\) is the thermal expansion coefficient; \(\zeta\) is the thermo-optical coefficient of the optical fiber. According to Equation (1), the effect of temperature on wavelength shift shall be eliminated to obtain a separate strain change. When the bolt force \(Q\) is applied to the sensor cylinder and causes the piston to move and compress hydraulic oil in the cylinder to generate a uniform oil pressure \(P\). The expression is as follows:  
\[Q=P\pi\Big{(}R^{2}-r^{2}\Big{)} \tag{2}\]  
where \(R\) is the outer radius of the cylinder, and \(r\) is the inner radius of the cylinder. Oil pressure is transferred to the pressure gauge and the FBG pressure sensor through the tubing and the tee joint. When a uniform pressure is applied to the planar circular diaphragm in the sensor,  
Figure 1: Schematic diagram of an FBG bolt force sensor; (**a**) the overall structure of sensor; (**b**) a schematic diagram of the cylinder; (**c**) a schematic diagram of the FBG pressure sensor. a concentrated force is generated on the equi-intensity cantilever through the dowel bar, as shown in Figure 1c. The center deflection of the diaphragm under the uniform pressure and cantilever reactive force \(F\) is as follows [24;25]:  
\[y=y(P)-y(F) \tag{3}\]  
\[y(P)=\frac{3(1-\mu^{2})PR_{0}^{4}}{16E_{1}t^{3}}\bigg{(}R_{0}^{4}-r_{0}^{4}+4R_{ 0}^{2}r_{0}^{2}\ln(\frac{r_{0}}{R_{0}})\bigg{)} \tag{4}\]  
\[y(F)=\frac{3(1-\mu^{2})FR_{0}^{2}}{4\pi E_{1}t^{3}}\left(1-(\frac{r_{0}}{R_{0}} )^{2}\frac{1-(\frac{r_{0}}{R_{0}})^{2}+4\ln^{2}(\frac{r_{0}}{R_{0}})}{1-(\frac {r_{0}}{R_{0}})^{2}}\right) \tag{5}\]  
where \(E_{1}\) is the [PERSON]'s modulus of the diaphragm; \(\mu\) is [PERSON]'s ratio; \(r_{0}\) is the dowel bar radium; \(R_{0}\) and \(t\) are the radius and thickness of the diaphragm, respectively. The deflection generated at the center of the diaphragm is the same as that of the cantilever under the concentrated force \(F\) according to the deformation compatibility principle and is determined by [26;27]  
\[y=\frac{6 Fl^{3}}{E_{2}bh^{3}} \tag{6}\]  
where \(E_{2}\) is the Young's modulus of the cantilever; \(b\) is the width of the free end of the cantilever; \(l\) and \(h\) are the length and thickness of the cantilever, respectively.