## 2 Materials and Methods
### Data Analysis Methodology  
In order to capture the effects of rib spacing and grout annulus, data from the component monitoring provided by the DOS, global data, and post-testing observations were combined. This methodology has been utilized previously [54] by this group. Additional investigation will be described. The embedment length selected for testing was based on previously conducted research [18]. However, with modification to the monitoring technique strain response in the embedment length at loading, post yield was captured. This meant some of the specimens became fully active prior to ultimate loading; so to quantitively capture bond performance, the load required to fully mobilize the embedment length (LRFM) was collected. This process can be seen visually in Figure 5. Additionally, to provide further insights on the effects of the parameters on the bond performance, shear displacement curves were also calculated [10; 23; 55; 56; 57]. This process is depicted visually in Figure 6. These formulas are essentially describing the derivative and integrals for a given distance (x) and an applied load (F). These shear displacement plots were generated by calculating the axial displacement for each position X and plotting it against the average shear stress over a 2.5 cm length (to help with noise). This was done at 10 kN intervals for loading in the elastic range.  
To explore the effects of the three independent variables (rib spacing, grout annulus and compression strength of grout) multiple linear regression was conducted. This analysis does not attempt to provide generalizations, but to present the significance and relationship of the independent variables to the selected dependent variables. The dependent variables selected were LFRM and initial tangent stiffness. The first step of this analysis evaluated general linearity and unusual cases using a series of scatter plots. During this stage, grout annulus showed very little relation to the dependent variables and was not significant (\(p=0.53\) and \(p=0.17\)); therefore, it was removed from the analysis. This analysis was conducted using JASP software (0.14.1) [58] with guidance in reporting and analysis from [PERSON] [59]. It should be noted that the presented results have the following limitations: a lack of variability in grout strength, few repeated specimens and a small sample size.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Part** & **Material** & **Material Model** & **Modulus of Elasticity, E, (GPa)** & **Poisson’ Ratio, v** & **Yield Stress (MPa)** & **Tensile Strength (MPa)** & **Compressive Strength (MPa)** \\ \hline Rebar & Rebar & Linear isotropic elastic & 200 & 0.3 & 420 & 620 & \(\mathrm{N/A}\) \\ \hline Confining pipe & Structural steel & Linear isotropic elastic & 200 & 0.3 & 250/240 & 460/415 & 250/240 \\ \hline Grout & Grout—40\% wc & Linear isotropic elastic & 8.19/7.62 & 0.14/0.18 & NA & 1.8/2.88 & 40/39.5 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Selected material properties for numerical modelling.  
Figure 5: Demonstrating selection of Load Required to Fully Mobilize the Embedment Length (LRFM); the example shown is specimen A-4.