# Research on the Self-Drilling Anchor Pull-Out Test Model and the Stability of an Anchored Slope
## 2 Experimental Analysis of the Key Performance of Hollow Self-Drilling Anchor Bolts
### Analysis of the Experimental Results
After calculation, the average bond strengths for the four groups of anchor bolts are found to be 0.163 MPa, 0.142 MPa, 0.154 MPa, and 0.129 MPa, respectively. This bond strength value is derived from the average ultimate uplift capacity of each group of anchor bolts and directly reflects the relationship between the average ultimate uplift capacity and the average anchorage length for each group of anchor bolts. Although the standard does not provide explicit information about the average average and the average average and the average average and the average average and the average average and the average average average and the average average average are the average and the average average average and the average average average. Figure 5: Experimental analysis curves for each set of anchor bolts. guidance on how to determine the bond strength for each group of anchor bolts, the results can be considered reliable. To ensure the rigor of the data, the coefficient of variation can also be introduced for verification. Generally, the coefficient of variation is used to compare the dispersion of different data sets. A smaller coefficient indicates lower dispersion and better data stability, while a larger coefficient suggests higher dispersion and poorer data stability. For continuous data, the normal range for the coefficient of variation is typically between 0% and 30%, while for discrete data, it generally ranges from 0% to 100%. Since the bond strength values for all anchor bolts are calculated using Equation (1), we consider the data to be relatively continuous. Consequently, the range for the coefficient of variation is also stricter in this case. The calculation of the coefficient of variation is illustrated using the data from the RS4 group as an example. The average value (\(\mu\)) for this set is calculated as follows:  
\[\mu=\frac{0.155+0.172+0.161+0.188+0.169+0.141}{6}=0.163 \tag{2}\]  
The standard deviation (\(\sigma\)) is calculated as follows:  
\[\sigma=\sqrt{\frac{(0.155-0.163)^{2}+(0.172-0.163)^{2}+(0.161-0.163)^{2}+}{(0.1 88-0.163)^{2}+(0.169-0.163)^{2}+(0.141-0.163)^{2}}{5}}\approx 0.016 \tag{3}\]  
From this, the coefficient of variation (\(C_{\mathrm{v}}\)) can be obtained. \[Cv=\frac{0.016}{0.163}\times 100\%\approx 9.8\% \tag{4}\]  
By following the same method, we can sequentially calculate the coefficient of variation for the experimental data of the four groups of anchor bolts. The coefficients of variation for RS4 to RS10 are 9.8%, 7.2%, 6.3%, and 4.7%, respectively. The coefficient of variation curve is shown in Figure 5b (blue curve). It can be seen that all the coefficient values are below 30%, which sufficiently demonstrates that the average bond strength values for each group of anchor bolts are reliable. Therefore, we can plot the red curve in Figure 5b using the average bond strength values of 0.163 MPa, 0.142 MPa, 0.154 MPa, and 0.129 MPa for the four groups of anchor bolts. Taking the red curve in Figure 5a as the focus of the study, we can analyze the relationship between the ultimate uplift capacity of self-drilling anchor bolts and the anchorage length. Starting with the average anchorage length and ultimate uplift capacity of the first group of anchor bolts, we observe that as the average anchorage length increases from 3.64 m to 9.65 m, the ultimate uplift capacity increases from 187 kN to 391 kN. The ultimate uplift capacity of self-drilling anchor bolts increases nonlinearly with anchorage length. The curve shows that as the anchorage length increases, the growth rate of ultimate uplift capacity increases from 56% to 165%, while the growth rate of ultimate uplift capacity increases from 47% to 109%. This phenomenon can be explained by the mechanical mechanism at the anchorage interface: in loose and fractured strata, the shear resistance between the grouting material and the rock-soil mass is evenly distributed along the anchorage section, and the total uplift capacity is approximately the product of the anchorage length and the bond strength per unit length.