# Analysis of Vertical Earth Pressure Acting on Box Culverts through Centrifuge Model Test
## 5 Variability Analysis of Vertical Earth Pressure Acting on Box Culvert
### Calibration of Earth Pressure Sensors  
The centrifuge model test was conducted repeatedly in a strictly controlled environment. In the graph shown in Figure 11, the factors that can cause uncertainty include (1) inherent variability of soil such as unit weight and degree of compaction, and (2) measurement error.  
In the case of the measurement error, the vertical earth pressure is generally measured using an earth pressure gauge, where the load is transmitted to the earth pressure sensor through the soil particles. However, if the load is not transmitted consistently to the earth pressure sensor, as shown in Figure 11, the measured earth pressure may not be accurate. In the cases of Sensors A and C, the earth pressure is underestimated, and in the case of Sensor B, the earth pressure is overestimated. In addition, when the gravitational acceleration is set to 50 g during the centrifugal model test, the sensor size is important because the sensor diameter is enlarged by 50 times compared to that in the 1 g condition.  
The best approach to overcome these inconsistencies in earth pressure measurement is to calibrate the sensor size, as shown in Figure 12. [PERSON] et al. [39] proposed a sensor size for reliable earth pressure measurement based on the relationship between the sensor diameter (\(d\)), and the maximum sample particle diameter (\(D_{max}\)). If \"\(d/D_{max}>5\)\", the reliability of the error is 10% (at least two sensors); if \"\(d/D_{max}>8\)\", the reliability of the error is 5% (at least five sensors). However, the sensor diameter (d) was 7.6 mm, \(D_{max}\) was 2 mm in the centrifuge model test conducted in this study, and \(d/D_{max}\) was only 3.8. Therefore, the measured earth pressure contains a significant error, and error correction is required.  
Therefore, for calibrating the sensor size, three data points measured in one test process were integrated. In other words, we assumed that Sensors A, B, and C in Figure 11a represent one integrated sensor as opposed to three different sensors, as shown in Figure 11b. The average of the vertical earth pressure values obtained using the three sensors was calculated, and this value was considered as the value measured using one sensor.  
Here, the diameter of the integrated sensor \(d_{integrated}\), as calculated using Equation (3), is 13.16 mm, and \(d/D_{max}\) is 6.58. Therefore, based on the existing theory [40] the reliability of the error is 5-10%. In addition, in the subsequent analysis, a total of 12 data points obtained under the loading and unloading conditions at a specific gravitational acceleration were integrated, and only four data points at a specific gravitational acceleration are shown. The data in Figure 11 were recalculated after sensor size correction, and the bias factor of vertical earth pressure for this correction is presented in Figure 13. Compared to the data in Figure 11, the spread range of the bias factor is reduced.  
Figure 11: Bias factors of vertical earth pressure at cover depths of (**a**) 4 cm, (**b**) 8 cm, and (**c**) 12 cm.