# Experimental Study on Deformation Monitoring of Bored Pile Based on BOTDR
## 2 Principle of BOTDR  
BOTDR is the distributed optical fiber sensing technology which based on Brillouin optical time domain reflectometry [6; 7]. The technology uses back Brillouin scattering frequency to react quickly to the temperature and strain received by the optical fiber; there is a linear relationship between the two to perform real-time distributed monitoring of the object. Its working principle is: the pulsed light of a certain frequency is injected into the optical fiber medium, and the pulse light entering the inside of the optical fiber interacts with the elastic acoustic wave therein to generate back Brillouin scattering, which causes Brillouin scattering due to the temperature and the stress received. Brillouin scattering occurs in the optical fiber, and the brillouin backlight generates a frequency shift. By measuring the frequency shift, the relationship of the frequency shift with the temperature and strain of the optical fiber can be used to obtain the external information of the optical fiber [8]. When one end of the optical fiber receives the pulsed light of the specified frequency, the pulsed light interacts with the elastic acoustic wave in the optical fiber to form Brillouin scattering, then the back Brillouin scattered light returns through the original path of the optical fiber and enters the BOTDR light receiving part and the signal processing unit. The conversion of the optical signal and electrical signal is completed in the receiving part, the electrical signal is transmitted to the receiver through the broadband amplifier. The digital signal processor is used to perform the average processing, the specific distribution of Brillouin scattering light power in each sampling point of the fiber is obtained.  
By using the frequency shift of Brillouin scattered light in a linear relationship with the temperature and strain received, the temperature and strain of the object can be monitored by BOTDR technology. Equation (1) is the relationship of Brillouin frequency shift with temperature and strain [9; 10; 11; 12; 13]:  
\[\Delta\upsilon_{B}(\Delta\mathrm{T},\Delta\varepsilon)=\upsilon_{B}( \varepsilon,\mathrm{T})-\upsilon_{B}(0,\mathrm{T}_{0})=C_{T}\cdot(\mathrm{T}- \mathrm{T}_{0})+C_{\varepsilon}\cdot(\varepsilon-\varepsilon_{0}) \tag{1}\]  
Among them:  
1. \(\Delta\upsilon_{B}(\Delta\mathrm{T},\Delta\varepsilon)\)--the amount of change in Brillouin frequency shift.
2. \(\upsilon_{B}(\mathrm{T},\varepsilon)\)--the Brillouin frequency shift corresponding to the ambient temperature \(\mathrm{T}\) and the strain \(\varepsilon\).
3. \(\upsilon_{B}(0,T_{0})\)--the Brillouin frequency shift corresponding to the initial temperature \(\mathrm{T}_{0}\) and the strain is 0.
4. \(\mathrm{C_{T}}\)--the temperature coefficient, \(C_{T}=\frac{\partial\upsilon_{B}(\mathrm{T})}{\partial T}\).
5. \(C_{\varepsilon}\)--the strain coefficient, \(C_{\varepsilon}=\frac{\partial\upsilon_{B}(\varepsilon)}{\partial\varepsilon}\).
6. \(\mathrm{T_{0}}\)--the initial temperature.  
\(\varepsilon\)--the actual amount strain of the optical fiber.  
8. \(\varepsilon_{0}\)--the initial strain of the optical fiber.  
It is seen from the formula (1) that there is a linear relationship of the frequency shift with the temperature and strain [14; 15; 16]. When the temperature change is less than 5 \({}^{\circ}\)C, the influence of temperature on the Brillouin frequency drift can be neglected, then the formula (1) can be changed to [17; 18]:  
\[v_{B}(\varepsilon)=v_{B}(0)+C_{\varepsilon}\cdot\Delta\varepsilon \tag{2}\]  
where:  
1. \(v_{B}(\varepsilon)\)--frequency shift of fiber when the strain is \(\varepsilon\);
2. \(v_{B}(0)\)--the ambient temperature around the optical fiber under the same condition, the corresponding Brillouin frequency shift amount when the optical fiber strain is 0.  
It can be seen that the temperature and strain change of measured object can be obtained by the distributed real-time monitoring method based on BOTDR [19; 20; 21].