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The capillary porosity and Gel/Space ratio of a cement paste (mixture of cement and water) one year after mixing are 0.30 and 0.66. Determine the degree of hydration and w/c ratio initially used to make the cement paste.

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danialamin

Answer:

The degree of hydration is 0.8571 or 85.71% while value of w/c is 0.608

Explanation:

As per given data Capillary porosity=P_c=0.3

Gel/Space ratio of  the cement paste is given as gs= 0.66.

Also

[tex]P_c=w/c-0.36 \alpha[/tex]

Here

  • Pc is the capillary porosity which is given as 0.3
  • w/ is the ratio which is to be calculated
  • α is the degree of hydration which is also to be calculated.

Now

[tex]w/c=0.3+0.36 \alpha[/tex]

Now the  Gel/Space ratio is

[tex]gs=\frac{V_gp}{V_g+V_p}[/tex]

Here

  • V_gp is the volume of gel inclusive of pores which is given as 0.68 α
  • V_g+V_p is the total volume of gel  and the capillary pores which is given as 0.32+w/c

[tex]gs=\frac{V_gp}{V_g+V_p}\\0.66=\frac{0.68 \alpha}{0.32 \alpha +w/c}\\0.66=\frac{0.68 \alpha}{0.32 \alpha +0.3+0.36\alpha}\\0.66=\frac{0.68 \alpha}{0.68 \alpha +0.3}\\\alpha=0.8571\\\alpha=85.71\%[/tex]

So the degree of hydration is 0.8571 or 85.71%.

Putting value of α in equation of w/c as

[tex]w/c=0.3+0.36 \alpha\\w/c=0.3+0.36\times 0.8571\\w/c=0.608[/tex]

the value of w/c ratio is 0.608.