## 4 System Validation and Case Study  
To apply and validate the developed BIM-based concrete formwork control system, a case study was conducted on a beam with a span of seven meters in a building construction project (the Baran building) in Mashhad, Iran. A geometric 3D model of the Baran building was developed in BIM. The module was simultaneously connected to three sensors. During the construction project execution, the sensors were embedded in the concrete, and the temperature data was collected during the concrete placement. The average of the temperatures measured by these three sensors was used in the calculations. Figure 5 shows the core temperature of the concrete automatically measured by the SHT21, Lm35, and Ds18b20 sensors at 1-minute intervals. Considering the size of the dataset collected, the figure presented only covers 44 min. The compressive strength of concrete can be formulated based on the maturity concept, as defined by [PERSON] [20,52]. The equivalent age was computed using Equation (1):  
\[\mathbf{t_{e}}=\sum_{0}^{t}\mathbf{exp}\bigg{[}\frac{-\mathbf{E_{a}}}{\mathbf{R}}\bigg{(}\frac {\mathbf{1}}{\mathbf{T}}-\frac{\mathbf{1}}{\mathbf{T_{r}}}\bigg{)}\bigg{]}\Delta t \tag{1}\]  
(where, \(\mathbf{t_{e}}\): equivalent age at the temperature; E\({}_{a}\): activation energy; R: universal gas constant; T: average absolute temperature during interval time, \(\Delta\)t)  
The activation energy was considered to be constant for all cement types (in accordance with the recommendation in [PERSON] and ASTM C1074). Many studies have argued that activation energy can depend on time and temperature [10,52,53,54,55]. However, it is customary to assume constant activation energy. The concrete's strength was estimated using parabolic Equation (2). \[\mathbf{S}=\mathbf{S}_{\infty}\frac{\sqrt{\mathbf{K_{T}}(\mathbf{t_{e}}-\mathbf{t_{0}})}}{\mathbf{1}+ \sqrt{\mathbf{K_{T}}(\mathbf{t_{e}}-\mathbf{t_{0}})}} \tag{2}\]  
(where, S: strength; K: constant rate)  
The cement used in the case study was ordinary Portland cement (OPC). As suggested by [PERSON] and [PERSON] [56], the activation energy for OPC was assumed to be 41 kJ. It should be noted that some researchers have recommended slightly different values for this parameter [57,58]. Table 1 shows the performance coefficient and activation energy values used in this case study. By employing Equation (1), the equivalent time \(\mathbf{t_{e24}}\) was calculated for a normal day of the month. The times \(\mathbf{t_{50\%}}\), \(\mathbf{t_{70\%}}\), and \(\mathbf{t_{85\%}}\) were required for the concrete to gain 50%, 70%, and 85% of its designed compressive strength, respectively, at the reference temperature (i.e., 20 \({}^{\circ}\)C); these were calculated using Equation (2). The times \(\mathbf{t_{50\%}}\), \(\mathbf{t_{50\%}}\), and \(\mathbf{t_{85\%}}\) were required for the concrete to gain 50%, 70%, and 85% of its designed compressive strength, respectively, at the site temperature. Figure 5: Temperature data collected from the SHT21, Lm35, and Ds18b20 sensors. The \(\mathrm{t_{e}}\) value obtained from Equation (1) depended on the cement type (i.e., activation energy) and daily temperature variations. In this case study, particularly for a beam with a span of seven meters were used to test the BIM interoperability developed. For the selected beam element (spanning over six meters), 14 days were indicated in the standard building code as the minimum time required before formwork removal (BS8110:1997) and 28 days are required as the maximum time to strike the formwork (PN-B-06251:1963). The results of the \(\mathrm{t_{e}}\) calculations for the selected beam are presented in Table 2. Temperature data have been collected through three sensors during two tests. It is assumed that the concrete should gain at least 85% of its design strength before the formwork can be removed [8]. As a result, the formwork removal time was computed as 9.6 days, ensuring 85% of the designed concrete strength at the second test.