Mathematical Modeling of the Self-Compacting Concrete Samples Behavior Produced from the Syrian Raw Materials

The main purpose of the research is to find a mathematical model describing the behaviour of self-compacting concrete SCC produced from local raw materials only by using mathematical analysis and experimental test results. Three mixtures of SCC were produced: the mixtures with a cement quantity of (550 kg/m3) had been shown satisfying results in the fresh and hardened states and an increase in compression strength up to (12%) and a decrease in the W/C ratio to (13%) compared to the reference samples. The stress-strain (σ,ε) curve was measured for them and compared with the reference curves. The results showed incomplete similarity and the convergence of the curves reaching up to (80%). The closest curve that describes the case is the "POPOVICS" curve with its ascending part and the European Code "EURO-CEB" curve with its descending part. To avoid the presence of two completely different mathematical equations describing the (σ,ε) curves for the SCC made of local materials, a mathematical equation was derived that has one general form, for the two parts of the ascending-descending curve. A direct mathematical calculation and find (σ,ε) curve has been done which accurately describes the behavior of the SCC whatever the quantity of cement.