# Prediction Models for Mechanical Properties of Cement-Bound Aggregate with Waste Rubber
## 2 Materials and Methods  
Within this research, 15 cement-stabilized mixtures were tested. The materials used were natural river sand and gravel, waste granulated rubber, Portland cement of grade 32.5R (CEM II B/M (P-S) 32.5R) as a binder and the optimal amount of water determined according to standard [28]. The density of used materials is presented in Table 1, while the physical and mechanical properties of used binder are presented in Table 2.  
The granulometric composition of the aggregates was determined using the European standard EN 933-1 [29] and is presented in Figure 1. The composition of the mixture shown in Figure 1 is tailored to the inclusion of rubber as per the flexibility allowed in the fifth category of the EN 14227-1 [30]. Cement was used as a binder in proportions of 3%, 5% and 7% of the aggregate mass. Due to their similar granulometric curves, fine-granulated rubber (0-0.5 mm) derived from end-of-life (ELT) car and truck tires was used as a volume replacement for sand in amounts of 10%, 20%, 30% and 40%. The detailed composition of the tested CBA mixtures is presented in Table 3. The rubber content is defined according to previous results, indicating 60% replacement, causing extremely high strength loss [31; 32]. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Aggregate** & **Sand** & & **Gravel** & & **Rubber** & **Cement** \\ \hline Size & 0–2 mm & 0–4 mm & 4–8 mm & 8–16 mm & 0–0.5 mm & \\ Density (g/cm\({}^{3}\)) & 2.86 & 2.96 & 2.63 & 2.70 & 1.12 & 2.92 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Densities of used material. Figure 1: Granulometric composition. Rubber replacing the fine fraction complies with several other research papers [33; 34; 35; 36; 37; 38]. Each rubber proportion was added to each cement amount, resulting in 12 rubberized mixtures. Three standard cylindrical specimens measuring \(\mathcal{O}\)100 mm and with heights of 120 mm of each mixture were compacted by a vibrating hammer according to the procedure prescribed in EN 13286-51 [39]. The specimens were produced in order to test their compressive strength and determine their static (E\({}_{\text{st}}\)) and dynamic (E\({}_{\text{dyn}}\)) moduli of elasticity. The modulus of elasticity is the slope of a material's stress--strain curve with its elastic region. Before destructive testing, the non-destructive method for determining E\({}_{\text{dyn}}\) was employed according to standard EN 12504-4 [40]. This method is carried out on specimens of known dimensions and density, with two transducers applied to opposite bases of cylindrical specimens, emitting ultrasonic waves and measuring the duration of their passage, which is used to calculate the E\({}_{\text{dyn}}\). Poisson's coefficient is needed for the calculation, for which the value 0.25 was adopted in this research as a typical value for CBA. Poisson's ratio usually ranges from 0.15 to 0.30 for cement-stabilized materials; the value of 0.25 was adopted in previous papers [41; 42]. In addition, to neutralize the imperfect contact between the transducer and the rough specimen surface, a gel was applied. The procedure for determining the dimensions and mass of the specimen and the apparatus required for the UPV test are shown in Figure 2.  
The measurement of E\({}_{\text{st}}\) was carried out during the compressive strength test. The test was carried out according to EN 13286-43 [43] from the stress-and-strain relationship. Due to the inaccuracies in using LVDT for strain measurement, caused by the setting of the sample and the breakage of aggregates during the test, such results may be unreliable [6]. Therefore, in this research, a 3D DIC method was used to monitor the displacement of the characteristic points of the specimens. This is an optical non-contact method for monitoring the changes on the observed surface, in this case, vertical displacements. More details on the 3D DIC method used in this research and its applicability are presented in [44].