Theoretical strength of moist cured concrete (1 kg cement)

Powers' model gives the strength of concrete in terms of the gel/space ratio $x$:

$$x = \frac{\text{volume of gel}}{\text{volume of gel} + \text{capillary pores}} = \frac{0.657\,\alpha}{0.319\,\alpha + w/c}$$

where $\alpha$ is the degree of hydration and $w/c$ the water-cement ratio by mass. The numbers come from cement of specific gravity about 3.14: 1 g of cement has 0.319 cm$^3$ volume and produces gel of $2.06\times0.319 = 0.657$ cm$^3$ (including gel pores). Compressive strength:

$$f_c = 240\,x^3\ \text{MPa}$$

(240 MPa is the intrinsic strength of the gel; it varies from about 234 to 255 MPa for different cements.) The ratio $x$ does not depend on the mass of cement; the mass is only needed to give volumes.

Given

Cement = 1 kg; $w/c = 0.5$ (water = 0.5 kg); hydration at 28 days $\alpha = 0.9$.

$$\begin{aligned} x &= \frac{0.657\times0.9}{0.319\times0.9+0.5} = \frac{0.5913}{0.7871} = 0.751 \\ f_c &= 240\times0.751^3 = 101.7\ \text{MPa} \end{aligned}$$

(Volumes for 1 kg: gel $= 1000\times0.657\times0.9 = 591.3$ cm$^3$; space $= 1000\times0.319\times0.9 + 500 = 787.1$ cm$^3$; ratio 0.751.)

Answer: gel/space ratio = 0.751 and theoretical strength at 28 days = 101.7 MPa.