# Enhancing Cement Paste Properties with Biochar: Mechanical and Rheological Insights
## 2 Materials and Methods
### Methods
After this initial curing, the samples were demolded, and put into a water tank at 20 \({}^{\circ}\)C for curing up to the mechanical tests carried out at 7 and 28 days. Before the test, the specimens were notched employing a cutting machine BRILLANT 220 with a 2 mm-thick diamond cut-off wheel, making a 6 mm deep U-notch, following the Japan Concrete Institute Standard JCI-S-001 [40]. The methodology use for rheology testing is reported in the supporting information. Notched hardened specimens were subjected to a three-point bending test (TPB test) with a single-column Zwick Line-Z050 testing machine with a 1 kN load cell device and the clip-on strain gauge to measure the crack mouth opening displacement (CMOD). The span (distance between the supports) adopted was 65 mm, and a test speed of 0.005 mm/min was set. The evaluation of the flexural strength was done according to Equation (1):  
\[\sigma_{f\ max}=F_{max}.\frac{3L}{2 bh^{2}}\ \ \ \left[\text{MPa}\right] \tag{1}\]  
where \(L\) is the span equal to 65 mm, \(b\) is the specimen depth, and \(h\) is the net ligament height equal to 20 mm and 14 mm, respectively. The evaluation of fracture energy (\(G_{F}\)) was performed according to the Japan Concrete Institute Standard JCI-S-001 [40] (Equation (2)). \[G_{F}=\frac{0.75W_{0}+W_{1}}{A_{lig}}=G_{F0}+G_{Fcorr}\ \ \ \left[\text{N}/\text{mm}^{2}\right] \tag{2}\]  
where \(A_{lig}\) is the area of the nominal ligament equal to 280 mm\({}^{2}\), \(W_{0}\) [N\(\cdot\)mm] is the area below the CMOD curve up to the rupture of specimen and \(W_{1}\) [N\(\cdot\)mm] is the work done by the deadweight of the specimen and loading, calculated according to Equation (3):  
\[W_{1}=0.75\left(\frac{l}{L}m_{1}+2m_{2}\right)g\cdot CMOD_{c}\ \ \left[\text{N} \cdot\text{mm}\right] \tag{3}\]  
where \(l\) is the loading span (distance among the supports), equal to 65 mm, \(L\) is the total length of specimen, equal to 80 mm, \(m_{1}\) (kg) is the mass of the notched specimen, \(m_{2}\)(kg) is the mass of the loading arrangement not attached to the testing machine but placed on the beam until rupture, \(g\) is the gravity acceleration and \(CMOD_{c}\) is the crack mouth opening displacement at the rupture. The compression test was performed employing the same testing machine, changing the load cell capacity to 50 kN and setting a displacement rate \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Mechanical Test Activity**} & \multicolumn{3}{c}{**Rheological Test Activity**} \\ \hline
**LD.** & **Cement (g)** & **Water (g)** & **B (g)** & **SP (g)** & **Cement (g)** & **Water (g)** & **B (g)** & **SP (g)** \\ \hline Reference OPC & 460 & 161 & - & 4.6 & 50 & 17.5 & - & 0.5 \\ \hline B 1\% & 460 & 161 & 4.6 & 4.6 & 50 & 17.5 & 0.5 & 0.5 \\ \hline B 2\% & 460 & 161 & 9.2 & 4.6 & 50 & 17.5 & 1.0 & 0.5 \\ \hline B 3\% & 460 & 161 & 13.8 & 4.6 & 50 & 17.5 & 1.5 & 0.5 \\ \hline B 5\% & 460 & 161 & 23.0 & 4.6 & 50 & 17.5 & 2.5 & 0.5 \\ \hline B 7\% & - & - & - & - & 50 & 17.5 & 3.5 & 0.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Material compositions of pastes tested for mechanical and rheological properties. equal to 0.5 mm/min, utilizing the two broken prisms from the TPB test. The compressive strength is computed as follows:  
\[\sigma_{c\ max}=\frac{F_{max}}{bh}\ \ \ [\mathrm{MPa}] \tag{4}\]  
where \(F_{max}\) is the maximum force supported by the specimen before rupture, and \(b\) and \(h\) are the specimen thicknesses (20 mm on either side).