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Research Article: Tawashi & AlAmoudi 67

continuous sharp decline in the strength proportion of plasticizer used in the mixture.
between the defined points, and an infinitely Data were processed and converted into non-
increasing of strength. This contradicts the dimensional relative values allowing the
relation between the concrete strength and the conversion of the data from the specific case
cement grade. into the general state of the tested concrete.

The Equation of Rational Function is given as:
+
= (8)
1+ + 2 ϭ
: Compression Strength of SCC (MPa). 1.0

3
: Cement Grade (kg/m ).
0.8
a,b,c,: Equation constants, substituting the
values of the constants into Equation (1). 0.6
Founded that the equation takes the following
form (9): 0.4
−45572.93+48.36
= (9)
1−7.74 +0.0124 2 SCC-HRW-3500-550
SCC-HRW-3500-500
Proposed Model of the Stress-Strain Formula 0.2 HOGNESTAD
POPOVICS
for the Self-Compacting Concrete CARREIRA
ξ=∆L/L
The chemical materials in the self-compacting 0.0
0 0.2 0.4 0.6 0.8 1 1.2 1.4
concrete led to a change in the molecular
Fig. 7. SCC and Reference Stress-Strain Curves
composition of the material. Thus, a change in
its mechanical properties affects the behaviour
It was started from the same premise of
of the concrete in the fresh and hardened cases. previous studies and models in mathematical
Through the application and analysis of
treatment by converting stress into relative
previous models of the relation between stress-
stress by dividing it by ′ , and the measured
strain on SCC prepared in the lab, it was found

that models can express the behaviour of strain into relative strain by dividing it by .
concrete SCC in varying proportions. As for, the So, the values of the mathematical treatment
convergence was clear with the lab model, in for stress and strain, are according to the
the ascending part of the curve until reaching following:
the ultimate stress Figure 7. But the difference : nominal relative stress, where: ′ : the

was in the descending part of the curve. ′
Therefore, it was interesting to search for a maximum cylindrical strength of the concrete.

mathematical model that describing and : nominal relative strain, where: : strain
expressing the closest behaviour for SCC in corresponding to the maximum stress of the
ascending and descending parts of the curve. concrete.
To understand the behaviour of hardened To find a mathematical model that expresses the
concrete, and through accurate processing of behavior of this type of concrete, the results of
the numerical results of the fracture tests on lab experiments of samples produced of SCC
the uni-axial compression of cylindrical were entered at several cement quantities, and by
samples. Models were achieved to describe the
,
stress-strain occurred under the influence of defining it as nominal relative values ′ to
the uni-axial compressive force. To obtain a obtain the optimal mathematical curve for this
general unconditional formula, unrestricted in case, which gives the best correlation coefficient
terms of the quantity of cement and the R and the smallest standard error. The treatment

SJSI – 2023: VOLUME 1-1