## 4 Prediction of Beam's Load Capacity  
The prediction capability of the proposed analytical model for the ultimate moment capacity of the UHPC beams (0) is summarized in Table 7. This table establishes the validity of the proposed analytical approach for predicting the ultimate moment capacity of UHPC beams. For all beams, the proportion of the calculated moment capacity to the experimentally observed one was very close to unity. This mean ratio was above one by 0.6% with a fairly insignificant standard deviation of 0.52%. According to Table 7, the moment capacities for B1 through B5 were fairly accurate, suggesting that reasonable safety levels were attained. Nevertheless, the ACI 544 [41] approach (Section 2.2.4) overestimated B6's moment capacity by a relatively higher margin (+12%). As a result, this approach might be appropriate for UHPC beams with longitudinal reinforcement ratios approaching the balanced ratio (see Section 2.2.2). It is noteworthy that the common analytical data for all beams were \(L_{f}=\)15.123 mm, \(V_{f_{1}}=\)1.934%, \(V_{f_{2}}=\)0.548%, \(V_{f_{3}}=\)0.097%, \(V_{f}=\)2.578%, \(L_{f}=\) 15.126 mm, \(d_{f}=\)0.2 mm, and \(\varepsilon_{f}=\)0.0015. The capacity of the proposed analytical model to reproduce the ultimate moment of UHPC beams is also displayed in Figure 15. It can be seen from this figure that all predicted-observed data points are fairly close to the line of equality. Moreover, all the predicted-observed results were in between (or close to B3) the \(\pm\)90% accuracy zone. UHC is a zero-permeable composite whose preparation relies on the interstitial transition zone with maximal packing density and surface hydration products, rather than full chemical hydration. The main concept of UHPC production is, therefore, to lower water content below 0.2 as it is the primary cause of porosity, which should be avoided in order to achieve zero permeability with high packing density. The effective development of \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Beam**} & \multirow{2}{*}{\(A_{s}\) (mm\({}^{2}\))} & \multirow{2}{*}{\(e\) (mm)} & \multirow{2}{*}{\(c\) (mm)} & \multirow{2}{*}{\(F_{e}\) (kN)} & \multirow{2}{*}{\(F_{f}\) (kN)} & \multicolumn{3}{c}{**Moment Capacity (kNm)**} & \multirow{2}{*}{\(M_{p}/M_{o}\)} \\ \cline{5-5} \cline{7-10}  & & & & & & & & **Tested (\(M_{o}\))** & **Predicted (\(M_{p}\))** \\ \hline B1 & - & 7.266 & 5.284 & 108.9 & 108.9 & - & 16.700 & 16.232 & 0.972 \\ B2 & 100.5 & 12.450 & 7.697 & 158.7 & 106.4 & 52.3 & 23.100 & 22.236 & 0.963 \\ B3 & 157.1 & 12.450 & 9.055 & 186.7 & 105.0 & 81.7 & 25.100 & 25.778 & 1.027 \\ B4 & 226.2 & 14.731 & 10.714 & 220.9 & 103.2 & 117.6 & 30.300 & 29.980 & 0.989 \\ B5 & 402.1 & 20.538 & 14.937 & 307.9 & 98.8 & 209.1 & 42.400 & 40.926 & 0.965 \\ B6 & 628.3 & 28.003 & 20.366 & 419.8 & 93.1 & 326.7 & 48.600 & 54.451 & 1.120 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Prediction data of the UHPC beams. Figure 15: Predicted vs. observed \(M_{u}\). a self-flowable UHPC mix with a very low w/c ratio, even below 0.18, has been enabled by the utilization of optimized content of silica fume, fly ash, and fine powders, and a higher dosage of superplasticizer with cement. As a result, compressive strength of 280 MPa has been achieved using a compacted granular cementitious matrix reinforced with steel fibers. The mix composition specifies the proportion of each individual constituent that provides the most optimal packing density. The optimal superplasticizer dosage for improved workability was also determined. The functionality of the individual and hybridized microfibers was taken into consideration when they were inserted into the final mix, shown in Table 4. The optimization phase that precedes the hybridization process identified and accounted for the influence of each type of fiber on the load-deflection curves.