M30 mix proportioning where durability governs, and a water addition on site
A ready-mix plant is proportioning M30 concrete for a water-retaining structure. Specification: characteristic cube strength 30 MPa at 28 days, maximum free water/cement ratio 0.45, minimum cement content 340 kg/m3, slump at discharge 75 +/- 25 mm. The plant has no past record for this mix, so the standard deviation is assumed as 5.0 MPa.
Two plant trials with 20 mm graded coarse aggregate gave 28-day mean cube strengths of 41.5 MPa at w/c 0.42 and 36.2 MPa at w/c 0.48, all else equal. Water demand for the required workability is 168 kg/m3, and a superplasticiser is available at 0.5 to 1.2% by mass of cement.
On the first site pour the slump measured 45 mm at the chute. The site team added 14 kg of water per m3 and finished the pour. The batch sheet showed the concrete left the plant at w/c 0.45. The next morning the site engineer must decide whether to accept the pour and what to change for the remaining 400 m3.
1. Determine the target mean strength and the w/c needed to reach it, then state which limit actually governs the mix and what cement content results.
Read the worked answer
Target mean strength = fck + 1.65 sigma = 30 + 1.65(5.0) = 38.25 MPa.
Interpolate the trials for the w/c giving 38.25 MPa: w/c = 0.42 + 0.06 x (41.5 - 38.25)/(41.5 - 36.2) = 0.42 + 0.06 x (3.25/5.3) = 0.457.
Strength alone would permit 0.457. The durability limit of 0.45 is lower, so 0.45 governs. Cement content = 168/0.45 = 373 kg/m3, which also satisfies the 340 kg/m3 minimum.
Check that the durability-driven mix is not strength-deficient: at w/c 0.45 the interpolated strength is 41.5 - (0.03/0.06)(5.3) = 38.85 MPa, above the 38.25 MPa target.
Adopt w/c 0.45, cement 373 kg/m3 (round to 375), water 168 kg/m3. The reasoning matters more than the digits: if the plant had simply taken the strength-derived 0.457 it would have produced a mix that passes cubes but fails the specification for a water-retaining element.
2. Evaluate the site's 14 kg/m3 water addition: quantify the effect and state whether the pour should be accepted.
Read the worked answer
Total water becomes 168 + 14 = 182 kg/m3. New w/c = 182/373 = 0.488, which exceeds the specified maximum of 0.45. That alone makes the concrete non-compliant on durability grounds, whatever the cubes say.
Strength impact, using the same trial trend: 36.2 - (0.008/0.06)(5.3) = 35.5 MPa mean. With sigma = 5.0, the implied characteristic value is about 35.5 - 1.65(5.0) = 27.3 MPa, below the specified 30 MPa. This extrapolates slightly beyond the trial range, so it is an estimate, but the direction and size of the effect are unambiguous.
For scale, 14 kg/m3 of extra water typically gains only 15 to 20 mm of slump, so a large durability price was paid for a partial fix.
Judgement: do not accept the pour on the strength of the batch sheet. Require 28-day cubes; if they are marginal or fail, order cores (three per 50 m3 or part) and decide on acceptance with the designer, recording the non-conformance either way. Parallel action: check the delivery records for the cause of the 45 mm slump before the next pour.
3. Recommend how the workability problem should be solved on the remaining 400 m3, with the reasoning behind each step.
Read the worked answer
Fix workability at source; never with water, because water changes w/c permanently while admixture changes only rheology.
- Dose the superplasticiser at 0.6 to 0.8% by mass of cement, added with the mixing water at the plant, to gain 50 to 75 mm of slump at constant w/c. Verify no segregation or bleeding results.
- Find the real cause of the 45 mm slump: uncorrected aggregate moisture after rain, batching error, or over-long transport. Compare the batch sheet against the moisture probe log for that load.
- Write a retempering rule into the delivery note: admixture only, on the engineer's instruction, with a remix of at least 30 revolutions; reject loads older than 90 minutes or 300 drum revolutions.
- Increase slump testing to one per 25 m3 for the next 100 m3 until the mix is stable, then revert to normal frequency.
- Confirm the slump is measured at the point of discharge, as the specification states; a 45 mm reading at the chute may partly reflect a site measurement made after a long wait rather than a genuinely dry mix.
The principle to state to the site team: admixture is a rheology tool, water is a strength and durability variable.