# Aggregate Type and Concrete Age Effects on Anchor Breakout Performance: Large Database and Insights
## 4 Discussion
### Anchor Results under Tensile Loading
#### 4.1.2 Aggregate Effect at Given Age  
A simple approach to detect systematic errors in an empirical model, such as an aggregate effect, is the comparison with an experimental data set that covers a large range of different realizations of the parameter in question (here, coarse aggregate type, L.A. coefficient). The ratio between measurement \(N_{exp}\) and predicted concrete cone capacity \(N_{CCD}\) is a straightforward quantitative measure of prediction quality and is often calculated as relative prediction error.  
The inverse of the relative prediction error can be interpreted as normalized measurement values in which the known functional dependence on important input parameters is removed. In this case, the relative concrete cone capacity in tension is defined by Equation (2):  
\[\
u_{t}(t)=\frac{N_{exp}(t)}{N_{CCD}(t)}=\frac{N_{exp}(t)}{k\cdot h_{ef}^{1.5} \cdot\sqrt{f_{c}(t)}} \tag{2}\]  
and can be calculated for all mixes and ages. Ideally, \(\
u_{t}\) is equal or close to 1.0 for all tested concrete mixes and ages. A systematic deviation from 1.0 would indicate that the empirical model is (i) not properly calibrated for the specific anchor type (\(k\) factor) or (ii) does not account for an essential influence factor. The latter case can be detected by a large variability in relative concrete cone capacities. Naturally, the results have to be interpreted with respect to the typical experimental scatter caused by imperfections in the setup and material uncertainties, among others. Therefore, only a large variability that by far exceeds typical experimental scatter (for these types of tests that is 5-15%) clearly indicates the presence of additional effects (e.g., aggregate or age effect).  
Figure 6 shows all relative cone capacities (\(\
u_{t}\) (\(t\))) plotted against the corresponding L.A. coefficients, following the previously introduced marker and color code.  
First, it can be clearly seen that the results show an offset from the target value of 1.0, indicating that the default product-specific factor (\(k\)) is rather conservative for this anchor type and geometry. The mean relative cone capacity at 28 days is \(\
u_{t}\) (28 d) = 1.33 \(\pm\) 7.27%, i.e., the prediction underestimates the real capacity by about 25%. Second, no significant  
Figure 6: Relative concrete cone capacities for all different concretes and aggregates.  
trend in terms of L.A. coefficient is present. Third, considering the 28-day test results (empty circles and diamond markers) only, the difference between concretes expressed as a COV is only 7.3% and lies in the expected range of experimental scatter. The difference between concretes at the second age is 5.6% if only CDL concretes tested at 70 days are considered and 12.7% in the case of only CSTB tests at 184 days. If the data for all ages are combined, the COV increases to 15%, while the increase is limited to 10% in the case that the 70-day CDL data are not included (\(\
u_{t}\) = 1.33 \(\pm\) 9.57%). A detailed discussion of age and curing effects follows in the next chapter.  
Overall, differences in concrete cone capacity exist between different concretes. However, they can be largely explained by corresponding variations in compressive strength. The overall variability in relative concrete cone capacities lies within the range of typical experimental scatter. This conclusion is in agreement with previous studies on other anchor types [35; 36; 37] and is now confirmed on a larger data set obtained independently from two research groups for a total of 11 different concretes with 7 different coarse aggregate types and compressive strengths between 27 and 80 MPa.