# Dimensional Stability of SBR-Modified Cementitious Mixtures for Use in 3D Additive Construction
## 5 Results and Discussion
### Thermal Expansion  
Thermal expansion occurs when the internal and external temperatures of a cementitious mixture rise. There are two factors that cause temperature changes: cement hydration and temperature change. Figure 9: Drying shrinkage strains for different SBR/cement ratios. These factors cause the volume to change. Cracks occur when the stress generated by the strain of such a volume change exceeds the allowable tensile stress of the cementitious mixture. Thermal shrinkage is very important for massive concrete elements. When the internal temperature rises due to hydration heat, a significant temperature difference is generated between the concrete surface and the part deep within. Here, tensile stress is generated by shrinkage at the lower-temperature concrete's surface, resulting in cracks. Its magnitude can be controlled by controlling the coefficient of thermal expansion of the aggregate cement content and type, as well as the temperatures of the materials used to make the concrete [19]. Thermal expansion can be divided into linear thermal expansion and volumetric thermal expansion. The magnitude of the thermal expansion varies based on the crystalline structure and atomic arrangement of the material. This study investigated linear thermal expansion. Figure 10 shows the thermal strain measurement results according to the SBR/cement ratio. The thermal strains were \(437\times 10^{-6}\), \(513\times 10^{-6}\), \(570\times 10^{-6}\), \(774\times 10^{-6}\), and \(914\times 10^{-6}\) for the SBR/cement ratios of 0, 0.05, 0.10, 0.15, and 0.20, respectively. The results reveal an increasing trend in thermal strain as the SBR/cement ratio increased. Figure 11 shows the test results of the linear thermal expansion coefficients, which were \(5.8\times 10^{-6}\)/\({}^{\circ}\)C, \(6.8\times 10^{-6}\)/\({}^{\circ}\)C, \(7.5\times 10^{-6}\)/\({}^{\circ}\)C, \(10.1\times 10^{-6}\)/\({}^{\circ}\)C, and \(12.2\times 10^{-6}\)/\({}^{\circ}\)C for the SBR/cement ratios of 0, 0.05, 0.10, 0.15, and 0.20, respectively. Figure 10: Thermal strains for different SBR/cement ratios. In previous studies, [PERSON] et al. [10] reported the thermal expansion coefficient of polymer-modified cementitious mortar to be \(9\times 10^{-6}\
icefrac{{}}{{}^{\circ}}\)C to \(10\times 10^{-6}\
icefrac{{}}{{}^{\circ}}\)C, stating that the thermal expansion coefficient is directly influenced by that of the aggregate used, such as ordinary cement mortar. [PERSON] [30] showed that the linear thermal expansion coefficient of SBR-modified cementitious mortar was in the range of \(7.7\times 10^{-6}\
icefrac{{}}{{}^{\circ}}\)C to \(8.6\times 10^{-6}\
icefrac{{}}{{}^{\circ}}\)C for the polymer/cement ratio range of 0.10 to 0.20, and the linear thermal expansion coefficient of unmodified mortar was similar at \(7.9\times 10^{-6}\
icefrac{{}}{{}^{\circ}}\)C. Conversely, the linear coefficient of the thermal expansion of hydrated cement paste varied between about \(11\times 10^{-6}\) and \(20\times 10^{-6}\
icefrac{{}}{{}^{\circ}}\)C [31], while those of concrete mixtures with different aggregate types were approximately \(6\times 10^{-6}\
icefrac{{}}{{}^{\circ}}\)C to \(12\times 10^{-6}\
icefrac{{}}{{}^{\circ}}\)C [19]. Compared to these thermal expansion coefficient values, the results obtained in the present work were smaller than those of paste but similar to those of concrete mixtures. As explained above, previous studies found that the thermal expansion coefficient of SBR-modified and ordinary cementitious mixtures tends to be greatly affected by the materials used, including aggregates. However, in this study, the cement, silica sand, fly ash, and silica fume content were kept constant; only the SBR/cement ratio was used as a variable. The results of this study demonstrate that the thermal expansion coefficient increase was affected by the addition of SBR latex.