# Aggregate Type and Concrete Age Effects on Anchor Breakout Performance: Large Database and Insights
## 4 Discussion
### Anchor Results under Tensile Loading  
#### 4.1.1 Empirical Equation for Concrete Cone Breakout Capacity  
Current anchor design according to ACI 318 [28] or EN1992-4 [33] is based on an empirical prediction model as given by Equation (1) to calculate the concrete cone capacity. This approach is known as concrete capacity design (CCD) in the US and was first introduced as concrete capacity method (CC) method by [PERSON] et al. [19].  
\[N_{CCD}=k\cdot h_{cf}^{1.5}\cdot\sqrt{f_{c}} \tag{1}\]  
According to Equation (1), the concrete cone capacity \(N_{CCD}\) [N] depends on a product-dependent calibration factor \(k\) with dimensional units [N\({}^{0.5}\)/mm\({}^{0.5}\)], the anchor embedment depth \(h_{cf}\) [mm], and the concrete compressive strength \(f_{c}\) [MPa]. Calibration factor \(k\) depends on the anchor type (e.g., cast-in or post-installed anchors) and differences in codes exist owing to the choice of unit system (SI or USCS). In the case of cast-in headed studs, \(k\) = 15.5 (SI units) is recommended in combination with a concrete strength [MPa] measured on cubes with a size of 200 mm (7.78 in.). If USCS units are used with concrete compressive strength [psi] measured on 6 \(\times\) 12 in. cylinders, \(k\) = 40 (lb\({}^{0.5}\)/in\({}^{0.5}\)).  
It has to be noted that compressive strength is used in the CCD method out of convenience only since it is the material property available in design. The actual failure mechanism is determined by fracture mechanics and depends on tensile strength, Young's modulus, and fracture energy. This is also the reason for the dependence on _left_[1; 5], the  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Class** & **Batch/Agg. Type** & \
\begin{tabular}{c} _Vexp_ **at 1 st Age** \\ **kN (kip)** \\ \end{tabular} &
\begin{tabular}{c} _Vexp_ **at 2 nd Age** \\ **kN (kip)** \\ \end{tabular} \\ \hline \multirow{6}{*}{low strength} & CSTB 1a/Agg. 4 & 32.5 (7.3) \(\pm\) 6.8\% & 32.5 (7.3) \(\pm\) 6.1\% \\ \cline{2-4}  & CDL 1/Agg. 1 & 33.2 (7.5) \(\pm\) 1.5\% & - \\ \cline{2-4}  & CSTB 2a/Agg. 5 & 30.8 (6.9) \(\pm\) 6.5\% & - \\ \cline{2-4}  & CDL 2/Agg. 2 & 37.4 (8.4) \(\pm\) 9.0\% & 42.9 (9.6) \(\pm\) 4.6\% \\ \cline{2-4}  & CSTB 3a/Agg. 6 & 29.1 (6.7) \(\pm\) 9.9\% & 34.5 (7.8) \(\pm\) 11.9\% \\ \cline{2-4}  & CDL 3/Agg. 3 & 36.1 (8.1) \(\pm\) 4.7\% & 44.3 (10.0) \(\pm\) 2.3\% \\ \cline{2-4}  & CSTB 4a/Agg. 7 & 29.9 (4.0) \(\pm\) 14.5\% & - \\ \hline \multirow{6}{*}{High strength} & CSTB 1b/Agg. 4 & 52.9 (11.9) \(\pm\) 17.8\% & 53.7 (12.1) \(\pm\) 3.9\% \\ \cline{2-4}  & CSTB 2b/Agg. 5 & 46.3 (10.4) \(\pm\) 10.5\% & 56.5 (12.7) \(\pm\) 14.7\% \\ \cline{1-1} \cline{2-4}  & CSTB 3b/Agg. 6 & 43.4 (9.8) \(\pm\) 9.2\% & 44.1 (9.9) \(\pm\) 15.3\% \\ \cline{1-1} \cline{2-4}  & CSTB 4b/Agg. 7 & 61.5 (13.8) \(\pm\) 10.4\% & - \\ \hline \hline \end{tabular}
\end{table}
Table 7: Experimentally obtained concrete edge breakout capacities.  
strongest possible size effect according to linear elastic fracture mechanics (LEFM). The square root of compressive strength is only an empirical approximation for the actually relevant material parameters and was calibrated on tests typically performed at 28 days. The actual behavior may, thus, deviate from this approximation for other ages or specific concrete mixes, e.g., as a function of coarse aggregate type. Further deviations can be expected, e.g., dependent on the head size [34] or specific anchor geometry.