## 3 Results and Discussion
### Effects of Rib Spacing
Across all grout annuli, a reduction in bond performance was seen with increased rib spacing. This was observed by the strain being less effectively attenuated, and the attenuation rate appearing more linear, suggesting weaker bond performance. With increased rib spacing there also appeared to be more variance along the strain profile, which is logical as with increased rib spacing the locations  
Figure 10: Load stroke response of various rib spacing in grout annulus A (7.7 mm). **(A)** Full test range, (**B**) zoomed in of the initial 15 mm of stroke. of mechanical interlock are further apart. An example of this can be found in Figure 11, which highlights results from annuli size A and B from loading at 90 kN. For the given annuli, it can be seen that the specimens with smaller rib spacing generally attenuated strain better. This is also true in annulus B, in which a large dichotomy exists between the altered and the unaltered bars. There are some exceptions to the general trend, where typically certain rib spacing may perform better than others in specific load ranges. For example, the 41 mm rib spacing in grout annulus A (7.7 mm) which attenuated stress the best for loads under 40 kN. Utilizing LFRM, multiple linear regression confirmed this reduction in bond performance where rib spacing was seen as a negative predictor and the average grout strength was a positive predictor; see Equation (8). This relationship was seen as statistically significant where LFRM F (2,17) = 26.37, \(p\) < 0.001, adj. R2 = 0.73). The regression coefficients and standard errors can be found in Table 7. All required assumptions were found to be met; \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Model** & \multicolumn{2}{c}{**Unstandardized Coefficients**} & **Standard Error** & **Standardized Coefficients** & **t** & \(p\) \\ \hline \(\mathrm{H_{1}}\) & (Intercept) & \(-\)465.31 & 101.668 & & \(-\)4.58 & \(<\)0.001 \\  & Average compression & & & & & \\  & strength of grout (MPa) & 14.31 & 2.49 & 0.71 & 5.75 & \(<\)0.001 \\  & Rib spacing (mm) & \(-\)0.74 & 0.29 & \(-\)0.31 & \(-\)2.51 & 0.023 \\ \hline \multicolumn{2}{c}{**Boostrapped Model**} & \multicolumn{2}{c}{**Unstandardized Coefficients**} & **Standard Error** & **Standardized Coefficients** & & **95\% box * CI** \\ \cline{2-6}  & & & & & Lower & Upper \\ \hline \(\mathrm{H_{1}}\) & (Intercept) & \(-\)456.66 & 14.77 & 114.50 & \(-\)705.9 & \(-\)271.9 \\  & Average ICS of & 14.12 & \(-\)0.40 & 3.03 & 9.28 & 20.54 \\  & grout (MPa) & \(-\)0.73 & \(-\)0.00 & 0.30 & \(-\)1.42 & \(-\)0.24 \\ \hline \multicolumn{6}{c}{Note: bootstrapping based on 5000 replicates; coefficient estimates are based on the median of the bootstrap distribution. * Bias corrected accelerated.} \\ \end{tabular}
\end{table} 
Table 6: Coefficients for predicting stiffness and robust analysis results. Figure 11: Rib spacing comparison across grout annulus A (**top**) and B (**bottom**) at 90 kN; red dots show theorical strain at zero. however, there was a degree of non-linearity. This non-linearity is logical as, if we examine either limit of rib spacing, it approaches a smooth bar. Therefore, caution should be used if the range of inputs are outside of the dataset used to form this model. \[Y(\text{{Predicted }LRFM}\left(\text{kN}\right))=-31.56-1.28(\text{{rib spacing }}\left(\text{mm}\right))+4.24(UCS(\text{MPa})) \tag{8}\]  
These strain data can also be explored through shear displacement profiles. When exploring these profiles, although the general patterns were similar, there seemed to be effects of increased rib spacing. Specifically with increased rib spacing, higher values of maximum shear stress developed, shear stress developed slower (higher levels of axial displacement required) and great variance was observed. An example of this can be seen below in Figure 12. This shows the response of specimens D-1, D-3 and D-5, and was selected as it most clearly shows these observed patterns.