# An Application of BOTDR to the Measurement of the Curing of a Bored Pile
## 4 Analysis of Monitoring Data
### Compare of Strain Distribution of the Pile  
The deformation of concrete during curing can be divided into self-shrinkage, temperature deformation, drying shrinkage, etc. [27; 28; 29]. In this paper, the deformation caused by hydration of the bored concrete pile is mainly self-shrinkage and temperature deformation.  
Under the condition of no constraint, the free deformation of concrete is:  
\[\varepsilon=\varepsilon_{T}+\varepsilon_{C} \tag{2}\]  
Among them:  
\(\varepsilon\)--free deformation of concrete;  
\(\varepsilon_{T}\)--deformation of concrete produced by temperature;  
\(\varepsilon_{C}\)--the self-shrinkage of concrete.  
According to the results of [PERSON] et al. [2], the temperature deformation and self-shrinkage of concrete under unconstrained conditions can be calculated by the following formula:  
\[\varepsilon_{T}=\alpha_{r}(t)\Delta T \tag{3}\]  
Among them:  
\(\Delta T\)--the temperature change, \({}^{\circ}\)C;  
\(\alpha_{r}(t)\)--expansion coefficient of early concrete.  
Further:  
\[\alpha_{r}(t)=\alpha_{k}(1+41t^{-m}) \tag{4}\]  
\(\alpha_{k}\)--thermal expansion coefficient of concrete at 28 d; in this paper, the value is \(10^{-5}/^{\circ}\)C;  
\(m\)--age correlation coefficient, m = 2.0;  
\(t\)--age of concrete, d;  
In the monitoring of pile foundation in civil engineering, it is generally assumed that the optical fiber and concrete are deformed harmonically. In this study, according to the experience of predecessors, the deformation of optical fiber itself caused by temperature change in this process is smaller than that of concrete, and such deformation can be ignored [2; 11]. Therefore, it can be considered that the optical fiber monitoring result is the deformation of concrete caused by temperature.  
In the end, the proposed formula for the shrinkage deformation of concrete itself is:  
\[\varepsilon^{\prime}_{c}=5936 exp\{-9.54(w/b)\} \tag{5}\]  
\(\varepsilon c\)--final self-shrinkage deformation, \(\mu\varepsilon\);  
\(w/b\)--water cement ratio of concrete. In this paper, the value is 0.5.  
The last test result is selected; the result on day 3 is used to calculate the free strain. The free strain is calculated every 2 m along the length of the pile, and the calculated free strain is connected with a smooth curve. The comparison between the free strain and the measured strain is shown in Figure 9. It can be seen from Figure 9 that the free strain is obviously greater than the measured strain value; it can exceed the measured strain value by up to 15%. This is mainly because the concrete itself deforms during hydration and solidification its release of heat of hydration is affected by the geothermal field, the deformation is constrained by the ground, and the measured strain and free strain are obviously different. This difference reflected in the actual project can cause the pile body to produce non-negligible stress under the restraint of the ground, thereby affecting the quality of the pile and the bearing capacity of the pile foundation. It should be pointed out that it is assumed that in the optical fiber and the concrete coordinated deformation, the strain is measured by the optical fiber, and the concrete deformation is caused by the temperature, which ignores the influence of the external temperature of the pile top to some extent. The influence of external temperature and the degree of soil restraint on pile deformation needs further studies in the future.