## 5 Results
### Analysis of Accuracy and Reproducibility  
The results of the flat-jack tests were evaluated in terms of both accuracy and reproducibility. Accuracy refers to how the mean of a set of measurements is closed to the \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**Flat Jack 25 cm**} \\ \hline \(\sigma_{\text{c}}\) **[MPa]** & \multicolumn{2}{c}{**14 cm Gage Length**} & \multicolumn{2}{c}{**20 cm Gage Length**} \\  & \(E\) & \(CoV\) & \(E\) & \(CoV\) \\ \hline
2 & \(1\%\) & \(36\%\) & \(20\%\) & \(40\%\) \\
3 & \(1\%\) & \(40\%\) & \(23\%\) & \(10\%\) \\
4 & \(8\%\) & \(17\%\) & \(17\%\) & \(24\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Average error \(E\) and coefficient of variation \(CoV\) of tests conducted with the 33 cm flat jack. Figure 12: Calculated and applied stress on sample 4 using the (**a**) 25 mm flat jack and (**b**) 33 mm flat jack. Figure 13: Average concrete stress estimated in flat-jack tests. Labels: M25_14, 25 cm flat jack, 14 cm gage length; M25_20, 25 cm flat jack, 20 cm gage length; M33_14, 33 cm flat jack, 14 cm gage length; and M33_20, 33 cm flat jack, 20 cm gage length. \"true\" stress, while reproducibility indicates how consistent the measurements are when performed under varying boundary conditions (e.g., on different samples). A notable observation was the large scatter in error (\(E\)) and coefficient of variation (\(CoV\)), indicating variability in both accuracy and reproducibility depending on the specific test conditions, namely, the instrument used and the chosen gage length. To understand this variability, an attempt was made to distinguish between systematic and random errors. Systematic errors are those inherent to the measurement setup or procedure, consistently biasing results, whereas random errors are unpredictable variations. Systematic errors related to instrumentation were deemed to be largely controlled. Both flat jacks and extensometers underwent thorough calibration, ensuring an accuracy better than 1%. Also the correct alignment of the concrete slab with respect to the axis of load application was accurately assessed by checking the uniformity of the deformation patterns on the test area of the sample before the cut, as shown, e.g., in Figure 11b. This suggested that any consistent bias due to the primary measuring devices was minimized. However, other sources of error, which can manifest as either systematic or random depending on their nature, significantly influenced the results. Random errors primarily included the heterogeneity of concrete among different samples. While in each slab, the cut slots for both the 25 cm and 33 cm flat jacks were made at the same location to mitigate within-sample variability, differences in concrete properties between distinct samples would contribute to random error in reproducibility, which could not be estimated due to the limited number of samples. Conversely, potential random errors arising from variations in the dimensions of the cut slots, due to imperfections in their execution, were minimized through the use of the calibration factor \(K_{m}\) and the correction factor \(K_{a}\) adjusted to the actual measured dimensions of each slot. Additional random errors may be associated with variations in the applied stress; however, since the hydraulic jack was servo-controlled in force mode, such variations were considered negligible compared with the average stress value. Another crucial factor influencing accuracy and reproducibility, considered a systematic error related to the test setup and concrete interaction, was the distribution of stress in the concrete around the cut slot and its interaction with the gage length. The act of creating the slot for the flat jack fundamentally altered the stress field around the measurement area. The effectiveness and consistency of this stress relief and subsequent redistribution (when the jack is pressurized) were critical.