# Comparison of Prediction Methods for Axial Strength of Ground Connections with Shear Keys
## 2 Methodology for Predicting Axial Strength
### Method of Calculation  
DNV-GL follows the ISO and NORSOK shear strength calculation formulas for grouted connections. Therefore, the prediction methods of ISO and NORSOK will not be contrasted here. The HSE's calculation of shear strength \(f_{\text{bk}}\) of grouted connections considers the effects of radial stiffness, \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Parameter** & \begin{tabular}{c} **DNV GL-ST-0126 (2016)** \\ **Jackets** \\ \end{tabular} & \begin{tabular}{c} **DNV (2013)** \\ **Single Pile** \\ \end{tabular} & \begin{tabular}{c} **NORSOK (2013)** \\ **Jackets/Single Pile** \\ \end{tabular} & \begin{tabular}{c} **API (2007)** \\ **Jackets** \\ \end{tabular} & \
\begin{tabular}{c} **ISO (2007)** \\ **Jackets** \\ \end{tabular} &
\begin{tabular}{c} **HSE (2007)** \\ **Jackets** \\ \end{tabular} \\ \hline \(D_{\text{y}}\)/\(p_{\text{g}}\) & 20–60 & 20–60 & 10–60 & 20–40 & \(\leq\)40 & 20–40 & 24–40 \\ \(D_{\text{y}}\)/\(t_{\text{s}}\) & 30–140 & 18–140 & 18–140 & 30–140 & \(\leq\)80 & 30–140 & 50–140 \\ \(D_{\text{g}}\)/\(t_{\text{g}}\) & 10–45 & / & / & 10–45 & 7–45 & 10–45 & 10–45 \\ \(t_{\text{g}}\) & / & / & / & / & 238 mm & \(\geq\)40 mm & / \\ \(f_{\text{cu}}\) (MPa) & / & / & / & 20–80 & 17.725–110 & 20–80 & / \\ \(L_{\text{g}}\)/\(D_{\text{p}}\) & 1.0–10.0 & 1.5–2.5 & / & 1.0–10.0 & / & 1.0–10.0 & \(\geq\)2.0 \\ \(h\) & \(\geq\)5 mm & \(\geq\)5 mm & / & 0–0.0122\(\,\)D\({}_{\text{p}}\) & / & 0–0.0122\(\,\)D\({}_{\text{p}}\) & 0–0.006\(\,\)D\({}_{\text{p}}\) \\ \(s\) & \(\geq\)0.8 & \(\sqrt{R_{\text{g}}/t_{\text{g}}}\) & \(\geq\sqrt{R_{\text{g}}/t_{\text{g}}}\) & \(\geq\sqrt{R_{\text{g}}/t_{\text{g}}}\) & \(\geq\)D\({}_{\text{p}}\)/\(t_{\text{g}}\) & \(\geq\)D\({}_{\text{p}}\)/\(t_{\text{g}}\) & \(\geq\)D\({}_{\text{p}}\)/\(t_{\text{g}}\) \\ \(h\)/\(s\) & 5.0–1 & 5.0–1 & 5.0–1 & 0–0.1 & 0–0.1 & 0–0.1 & \(\leq\)0.04 \\ \(w\)/\(h\) & 1.5–3.0 & 1.5–3.0 & / & / & 1.5–3.0 & 1.5–3.0 & 1.5–3.0 \\ \hline \hline \end{tabular} \(L_{\text{g}}\), length of grouted;\(f_{\text{cu}}\), cubic compressive strength of grouted body.  
\end{table} 
Table 1: Geometric and material parameters in different codes. DNV-GL, Det Norske Veritas–Germanischer Lloyd; API, American Petroleum Institute; ISO, International Organization for Standardization; HSE, Health and Safety Executive. Figure 1: Geometric parameters of grouted connection. \(D_{\text{p}}\), diameter of steel pile; \(D_{\text{g}}\), diameter of grouted; \(D_{\text{s}}\) diameter of sleeve; \(R_{\text{p}}\), radius of steel pile; \(R_{\text{g}}\), radius of group; \(R_{\text{s}}\), radius of sleeve; \(t_{\text{p}}\), thickness of steel pile; \(t_{\text{g}}\), thickness of grouted; \(t_{\text{s}}\), thickness of sleeve; \(w\), width of shear key; \(h\), height of shear key; \(s\), spacing of shear key. the length of the grouted seam, surface roughness, the dimensions of the shear key, and the cubic compressive strength of the grouted body; related formulas are shown as Equations (1) and (2)  
\[f_{\rm{bk}}=C_{\rm{L}}\left(9C_{\rm{S}}+1100\frac{h}{s}\right)\!\!kf_{\rm{cu}}^ {0.5} \tag{1}\]  
\[k=\left(\frac{D_{\rm{P}}}{t_{\rm{P}}}+\frac{D_{\rm{s}}}{t_{\rm{s}}}\right)^{-1 }+\frac{1}{\rm{m}}\!\left(\frac{D_{\rm{g}}}{t_{\rm{g}}}\right)^{-1} \tag{2}\]  
where k is the radial stiffness coefficient; \(f_{\rm{cu}}\) is the cubic compressive strength of the grouted body; \(C_{\rm{S}}\) is the surface state coefficient, and \(C_{\rm{S}}\) = 1.0 when \(h/s\geq 0.005\); \(m\) is the ratio of [PERSON]'s modulus for steel and for grout material, and \(m\) = 18 can be used if the Young's modulus for grout material is not known. In the absence of geometric data of the steel tube and shear key, see Table 2 for \(C_{\rm{L}}\) parameter values, where \(L\) is the nominal length of the grouted connecting section. The parameter value between two data points in the table is calculated using the linear difference method.