Tools › Civil and Geotechnical › Concrete Design › Concrete Mix and Quantities › Example
Trial mix for a retaining wall by absolute volume: required average strength, water-cement ratio, proportions and three-bag batch weights (Concrete Manual Example 1)
| Tool | Concrete Mix and Quantities |
| Source | U.S. Bureau of Reclamation (1975). Concrete Manual: A Manual for the Control of Concrete Construction, 8th ed. U.S. Government Printing Office, Washington, DC. Chapter III, sections 45 to 49, Tables 14 and 16, Example 1, pp. 133 to 141; section 62, pp. 173 to 175. |
| Level | Undergraduate |
Problem
A reinforced retaining wall with a minimum thickness of 11 in is exposed to a severe climate. The design strength is 3,000 lb/in² at 28 days, to be exceeded by 80 percent of the cylinders with a coefficient of variation of 15 percent. The aggregate is 1½ in maximum size; cement specific gravity 3.15, sand 2.63, coarse aggregate 2.68, water 62.3 lb/ft³. Proportion one cubic yard of air-entrained concrete by absolute volume with the values of the manual's Table 14, then give the weights for a three-bag batch (0.575 yd³) with 5 percent free moisture in the sand and 1 percent in the coarse aggregate.
Inputs to Enter
- Specified strength 3,000 lb/in²; required average by the coefficient of variation, V = 15 percent, t = 0.883
- Ratio for strength from Table 16 (air-entrained); durability limit 0.50
- Table 14 row for 1½ in aggregate: water 245 lb/yd³, air 4.5 percent, sand 34 percent of the aggregate by solid volume (fields left blank)
- Specific gravities 3.15 / 2.63 / 2.68; water 62.3 lb/ft³; aggregate proportioned by percent sand
- Batch 0.575 yd³; sand moisture 5 percent, coarse aggregate 1 percent, absorptions 0
Answers
- f′_cr = 3,000 / (1 − 0.883 × 0.15) = 3,458 lb/in² (book 3,460)
- Ratio for strength 0.564 by interpolation in Table 16 (book 0.56); durability controls, w/c = 0.50
- Cement 245 / 0.50 = 490 lb; solid volumes: water 3.93 ft³, cement 2.50 ft³, air 1.215 ft³ (book 1.21), aggregate 19.36 ft³ (book the same)
- Sand 0.34 × 19.36 = 6.58 ft³ = 1,078 lb (book 1,078); coarse aggregate 12.77 ft³ = 2,133 lb (book 12.78 ft³ and 2,134 lb, from volumes rounded to 0.01 ft³)
- Total 3,946 lb/yd³ (book 3,947), 27.00 ft³; unit weight 146.2 lb/ft³; cement factor 5.21 bags per cubic yard
- Three-bag batch, saturated surface-dry: water 140.9 lb, cement 281.8 lb, sand 620.0 lb, coarse aggregate 1,226.4 lb (book 141, 282, 620, 1,227)
- Weights to batch: moist sand 651.0 lb, moist coarse aggregate 1,238.7 lb, free water 31.0 and 12.3 lb, water to add 97.6 lb (book 651, 1,239, 31 and 12 lb)
- Tool only: paste 23.8 percent, mortar 52.7 percent and coarse aggregate 47.3 percent of the volume
Notes
The tool's default inputs are this case; press Submit. The manual computes each weight from a volume rounded to 0.01 ft³, which accounts for the one-pound differences. The admixture line of the default page (0.25 percent of lignin solids at 0.40 g/mL) gives 1,389 mL per cubic yard for 490 lb of cement; the manual's 1,304 mL is for the 460 lb of its water-reduced variant. The Quantities analysis opens on the retaining wall of Army FM 5-428 (63.7 yd³) and the mix of that manual is reproduced by the test script.