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DOE method of mix design steps

Short answer

DOE method: target mean strength f_m = f_ck + 1.64s; w/c from chart; free water from table (slump, size, aggregate type); wet density from chart; total aggregate = density - cement - water; fine aggregate % from chart (600 µm passing). Example: target 38.2 MPa gives w/c 0.48, water 205 kg/m³, cement 427 kg/m³, total aggregate 1768 kg/m³.

Describe the stepwise procedure of concrete mix design by the DOE method (key concepts, with schematic diagram and table where possible).

The DoE (British) method (UK Department of the Environment; BRE 1988 "Design of normal concrete mixes", which replaced the older Road Note No. 4 method) selects the mix from charts and tables. It is based on the w/c ratio, the free-water content and the proportion of fine aggregate.

Key concepts

  • Target mean strength = characteristic strength + margin, where margin = k×sk \times s.
  • The w/c ratio is read from the strength vs w/c chart for the type of cement and aggregate, and compared with the durability limit.
  • The free-water content depends on the slump/Vebe time, the maximum size and the aggregate type (crushed/uncrushed).
  • The wet density of fresh concrete comes from a chart (it depends on the free water and the aggregate density).
  • The fine aggregate proportion comes from a chart (maximum size, slump, w/c, grading zone).
 f_ck -> target f_m -> w/c (chart) -+
 slump,size,type -> water (table) --+-> cement
 free water + SG -> density (chart) -> total aggregate
 w/c,slump,zone -> %fines (chart)  -> FA, CA

Steps

  1. Target mean strength: fm=fck+1.64sf_m = f_{ck} + 1.64 s (margin =ks= k s, k=1.64k = 1.64 for 5% defectives; IS uses 1.65s1.65 s). The standard deviation ss comes from site data or a table (e.g. 4-5 MPa).
  2. w/c ratio: Table 2 gives the 28-day strength at w/c 0.5 for the cement/aggregate type; draw the curve through this point on Fig 1 and read the w/c for the target strength. Check the maximum w/c limit for the exposure.
  3. Free-water content from Table 3 (kg/m3^3) for the slump (0-10, 10-30, 30-60, 60-180 mm), the size (10, 20, 40 mm) and crushed/uncrushed aggregate.
  4. Cement content = water/(w/c); check the minimum and maximum limits (e.g. 300 and 550 kg/m3^3).
  5. Wet density of concrete from Fig 3 (free water, aggregate SG).
  6. Total aggregate content = wet density - cement - water.
  7. Proportion of fine aggregate from Fig 4 (using the % passing the 600 micron sieve).
  8. Fine and coarse aggregate = proportion ×\times total aggregate; the coarse aggregate is split into sizes (e.g. 10/20/40 mm in the ratio 1:1.5:3).
  9. Trial mix: check the workability and strength, and adjust.

Sample table (illustration)

ItemValue
f_ck / target30 / 38.2 MPa
w/c0.48
Water205 kg/m3^3
Cement427 kg/m3^3
Wet density2400 kg/m3^3
Total aggregate1768 kg/m3^3

✓ Answer checked by Claude Opus 5.5 (high effort)

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