--- title: "Gel/space ratio and strength (550 gm cement)" subject: "Concrete Technology and Masonry Structure" chapter: 4 key: "semester_5/concrete_technology_and_masonry_structure:gel-space-ratio-550g" source: https://www.bctengineer.com/q/semester_5/concrete_technology_and_masonry_structure/gel-space-ratio-550g site: BCT Engineering --- # Gel/space ratio and strength (550 gm cement) Concrete Technology and Masonry Structure · Chapter 4: Properties of hardened concrete - Asked in: 2081 Baisakh, 6 marks; 2079 Baisakh, 4 marks (asked 2 times) - Answer checked by Claude Sonnet 5.5 on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_5/concrete_technology_and_masonry_structure/gel-space-ratio-550g - Whole chapter: https://www.bctengineer.com/md/semester_5/concrete_technology_and_masonry_structure/chapter-4 ## Question Calculate the gel/space ratio and the theoretical strength of a sample concrete made with 550 gm of cement with 0.45 water/cement ratio, on full hydration and at 60 percent hydration. ## Short answer Gel/space ratio x = 0.657α/(0.319α + w/c) with α hydration degree. Full hydration (α=1): x = 0.854, theoretical strength fc = 240x³ = 149.7 MPa. 60% hydration (α=0.6): x = 0.615, fc = 55.7 MPa. ## Answer 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 = 550 g; $w/c$ = 0.45, so water = $0.45\times550 = 247.5$ g. #### Full hydration ($\alpha = 1$) Volume of cement $= 550\times0.319 = 175.5$ cm$^3$. Gel volume $= 550\times0.657 = 361.4$ cm$^3$. Space available $= 175.5 + 247.5 = 423.0$ cm$^3$. $$ \begin{aligned} x &= \frac{0.657\times1}{0.319\times1+0.45} = \frac{0.657}{0.769} = 0.854 \\ f_c &= 240\times(0.854)^3 = 149.7\ \text{MPa} \end{aligned} $$ #### 60% hydration ($\alpha = 0.6$) Gel $= 361.4\times0.6 = 216.8$ cm$^3$; space $= 175.5\times0.6 + 247.5 = 352.8$ cm$^3$. $$ \begin{aligned} x &= \frac{0.657\times0.6}{0.319\times0.6+0.45} = \frac{0.3942}{0.6414} = 0.615 \\ f_c &= 240\times(0.615)^3 = 55.7\ \text{MPa} \end{aligned} $$ **Answer: gel/space ratio 0.854 and strength 149.7 MPa at full hydration; gel/space ratio 0.615 and strength 55.7 MPa at 60% hydration.** (Powers' theoretical strengths are for the paste; actual concrete strength is lower.) ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Powers' gel/space ratio is: A. 0.319 alpha / (0.657 alpha + w/c) B. 0.657 alpha / (0.319 alpha + w/c) C. 0.657 / (w/c) D. alpha / (w/c + 1) Answer: B. Gel volume is 0.657 alpha and space is 0.319 alpha + w/c per gram of cement. (Key point: Gel/space formula) 2. Strength from Powers' model is: A. f_c = 240 x MPa B. f_c = 240 / x^3 MPa C. f_c = 240 x^3 MPa D. f_c = 24 x^2 MPa Answer: C. 240 MPa is the intrinsic gel strength and x is cubed. (Key point: Strength relation) 3. The cement mass of 550 g affects the gel/space ratio: A. not at all; x depends only on alpha and w/c B. directly, in proportion C. inversely D. only at full hydration Answer: A. Mass only gives volumes; it cancels in the ratio. (Key point: Effect of cement mass) 4. At alpha = 1, w/c = 0.45 the gel/space ratio and strength are: A. 0.615 and 55.7 MPa B. 0.657 and 100 MPa C. 0.769 and 240 MPa D. 0.854 and about 149.7 MPa Answer: D. x = 0.657/0.769 = 0.854; 240 x 0.854^3 = 149.7 MPa. (Key point: Result at full hydration) ## Close variants set in other exams - [Gel/space ratio and strength (600 gm cement)](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Agel-space-ratio-600g) — Concrete Technology and Masonry Structure, chapter 4, asked 3× ## Related in Concrete Technology and Masonry Structure - [Theoretical strength of moist cured concrete (1 kg cement)](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Atheoretical-strength-1kg-cement) — Concrete Technology and Masonry Structure, chapter 4 - [Effect of gel/space ratio on strength](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Agel-space-ratio-effect) — Concrete Technology and Masonry Structure, chapter 4 - [Strength of paste: 300 gm cement](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Acement-strength-300g-150g) — Concrete Technology and Masonry Structure, chapter 4 - [Percent strength gain at 14 days](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Astrength-gain-14-days) — Concrete Technology and Masonry Structure, chapter 4 - [Effect of water cement ratio on strength](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Awc-ratio-effect-strength) — Concrete Technology and Masonry Structure, chapter 3, asked 4×