Assignment Sample: Concrete Mix Design to BS 8500

Model Answer

Introduction

Reinforced concrete elements exposed to UK weather, groundwater and de-icing salts must be specified not only for structural strength but also for long-term durability, and BS 8500 provides the current UK complementary standard for translating a given exposure environment into constituent and cover limits (BSI, 2015). This assignment develops a full trial mix design, from exposure classification through to moisture-corrected batch quantities, for a reinforced concrete retaining wall forming part of a highway drainage structure. The wall is a buried, ground-facing element subject to intermittent wetting from surface water and, because it stands adjacent to a gritted carriageway, to occasional exposure to chloride-bearing spray and to freeze–thaw cycling during winter months.

The Department of Environment (DoE) method, now maintained by the Building Research Establishment, remains the standard UK approach taught for proportioning normal-strength concrete and is compatible with the limiting values set out in BS 8500-1 (Teychenné, Franklin and Erntroy, 1997). The aim of this assignment is threefold: first, to classify the governing exposure conditions and derive the corresponding limiting mix parameters from BS 8500-1; second, to carry out a full DoE trial mix design that meets or exceeds those limits and the specified strength class; and third, to correct the resulting design (saturated-surface-dry, SSD) batch quantities for the as-delivered moisture content of the fine and coarse aggregate stockpiles, since concrete is always batched by mass in its natural moist state rather than in the SSD condition used in design tables.

Durability design of this kind sits alongside, rather than in place of, structural design to Eurocode 2: the exposure classification and DoE mix design developed here establish the concrete’s resistance to environmental deterioration mechanisms such as carbonation-induced and chloride-induced reinforcement corrosion and freeze–thaw damage, while separate structural calculations (not reproduced in this assignment) would establish the wall’s section thickness, reinforcement area and stability against overturning and sliding (Mosley, Bungey and Hulse, 2012). Buildability is also a relevant constraint on the mix: because the wall stem will be cast in a single lift against permanent formwork with congested reinforcement at the toe, the target workability must be sufficient to achieve full compaction around the bars without excessive vibration, which is reflected in the medium-workability slump class selected in Step 3 below.

Design Specification and Exposure Classification

The retaining wall is a buried reinforced element, so carbonation-induced corrosion is classified under Exposure Class XC3 (moderate humidity, cyclic wet and dry) rather than the more severe XC4 used for elements directly exposed to driving rain, because the wall face is largely shielded by backfill except at its exposed stem (BSI, 2015). Because the structure sits within the highway splash zone and can receive de-icing salt spray during winter gritting, Exposure Class XD1 (chloride-induced corrosion, moderate humidity) is also applied rather than the more severe XD3 reserved for elements in direct, repeated contact with spray, and Freeze–Thaw Class XF1 (moderate water saturation, no de-icing agent in direct contact) is adopted for the below-ground stem, since the wall itself is not repeatedly ponded and is not treated directly with de-icing salt. A design working life of 50 years and a nominal cover of 45 mm to the outer reinforcement (a minimum cover of 35 mm plus a 10 mm fixing allowance) are adopted, consistent with BS 8500-1 guidance for this exposure combination and structural class S4.

Table 1 summarises the limiting values BS 8500-1 places on each governing exposure class and the combined, most onerous requirement that controls the design, since more than one class applies to this element and the standard’s own combined-exposure tables are followed rather than treating each class in isolation (BSI, 2015).

Table 1. Individual and combined limiting values for the governing exposure classes (BSI, 2015).

A chemical (ACEC) exposure assessment to BRE Special Digest 1 was also considered, since the wall retains natural ground that could contain sulfates or acidic groundwater; however, preliminary ground investigation data for the site records negligible water-soluble sulfate and a near-neutral pH, placing the ground in Design Sulfate Class DS-1 and ACEC Class AC-1, the least aggressive classes in the BRE framework, so no additional sulfate-resisting cement content or enhanced cover is required beyond the XC3/XD1/XF1 provisions already established (BRE, 2005). Had the ground investigation instead indicated a more aggressive DS class, the governing cement content and cover would need to be re-derived from the BRE Special Digest 1 tables rather than from BS 8500-1 alone.

The combined requirement is therefore a maximum free water/cement (w/c) ratio of 0.50, a minimum cement content of 320 kg/m³, and a minimum characteristic strength class of C32/40, and it is these three figures that the trial mix design below must meet or exceed.

Mix Design Method

The DoE method, though still widely taught and used for preliminary proportioning in the UK, predates the current BS EN 206 conformity framework; in commercial practice, a specifier increasingly relies on a concrete producer’s own quality-controlled standard mixes or on performance-based specification, with the DoE trial calculation retained primarily as an independent design check and as the basis for understanding how the constituent proportions relate to strength and durability. The method itself proceeds through five linked stages, each of which is either taken directly from standard design charts and tables (as published in Teychenné, Franklin and Erntroy, 1997, and reproduced in current UK concrete technology texts) or calculated from the results of the previous stage. First, the target mean strength is calculated by adding a statistical margin to the specified characteristic strength, so that the mix is proportioned to a strength comfortably above the minimum acceptance criterion rather than to the minimum itself. Second, the free w/c ratio is read from the standard strength-versus-w/c-ratio chart for the chosen cement type and coarse aggregate type at the required age, and this value is then compared with the durability-driven maximum from Table 1, with the lower (more onerous) of the two values carried forward. Third, the free water content is read from a standard table according to the required workability (slump class), the maximum aggregate size and the aggregate shape (crushed or rounded). Fourth, the cement content is obtained by dividing the free water content by the free w/c ratio, and this is again checked against the Table 1 minimum. Fifth, the total aggregate content is estimated from a wet-density chart using the relative density of the aggregate, and this total is split into fine and coarse fractions using a grading-based proportioning chart appropriate to the maximum aggregate size and workability. Once the SSD design quantities are established, they are converted into practical batch quantities by correcting for the moisture actually present in the aggregate stockpiles on the day of mixing.

Worked Mix Design Calculation

Step 1 – Target mean strength. With no prior production data available for this concrete supplier and mix combination, a standard deviation of s = 8 N/mm² is assumed and a margin is calculated using the statistical factor k = 1.64 (corresponding to a 5% probability of a result falling below the characteristic value):

Margin = k × s = 1.64 × 8 = 13.1 ≈ 13 N/mm²

The characteristic cube strength for class C32/40 is 40 N/mm², so the target mean strength is:

f_m = f_c + margin = 40 + 13 = 53 N/mm²

Step 2 – Free water/cement ratio. Reading the standard 28-day strength-versus-free-w/c-ratio chart for CEM I 42.5N with crushed granite coarse aggregate at a target mean strength of 53 N/mm² gives a free w/c ratio of approximately 0.44. Comparing this with the durability-driven maximum of 0.50 from Table 1, the strength-derived value is lower and therefore governs, so a free w/c ratio of 0.44 is adopted.

Step 3 – Free water content. For a medium workability mix (slump class S2, target slump 50–100 mm, suitable for a reinforced wall placed by pump with moderate reinforcement congestion), 20 mm maximum aggregate size and angular (crushed) coarse aggregate, the DoE free-water table gives a free water content of 195 kg/m³.

Step 4 – Cement content. Dividing the free water content by the free w/c ratio:

Cement content = 195 ÷ 0.44 = 443.2 ≈ 443 kg/m³

This exceeds the Table 1 minimum of 320 kg/m³, so no adjustment is required on durability grounds; however, at 443 kg/m³ the mix is approaching the practical ceiling of around 450 kg/m³ typically applied to limit heat of hydration and early-age thermal cracking in restrained sections, a point returned to in the discussion below.

Step 5 – Aggregate content. Using the wet-density chart for an aggregate of relative density (SSD) 2.60 and a free water content of 195 kg/m³, the wet concrete density is read as approximately 2,410 kg/m³. The total aggregate content is then found by difference:

Total aggregate = wet density − cement content − free water = 2,410 − 443 − 195 = 1,772 kg/m³

Reading the grading-proportion chart for 20 mm maximum aggregate size, medium workability and a fine aggregate conforming to a medium (Zone 2) grading gives a recommended fine aggregate proportion of 35% of total aggregate by mass:

Fine aggregate = 0.35 × 1,772 = 620 kg/m³   |   Coarse aggregate = 0.65 × 1,772 = 1,152 kg/m³

Step 6 – Moisture correction for batching. The four quantities above (cement 443, water 195, fine aggregate 620, coarse aggregate 1,152 kg/m³) are the SSD design mix; concrete is batched by mass in the moist, as-delivered condition, so the free water content actually added at the mixer must be reduced by the free (surface) moisture already carried by the aggregate, and the aggregate masses batched must be increased to reflect that moisture. Taking a fine aggregate stockpile with a total moisture content of 5% and an absorption of 1% (free moisture 4%), and a coarse aggregate stockpile with a total moisture content of 2% and an absorption of 0.5% (free moisture 1.5%), relative to the SSD masses above:

Free moisture from fine aggregate = 0.04 × 620 = 24.8 kg   |   Free moisture from coarse aggregate = 0.015 × 1,152 = 17.3 kg

Water to be added at the mixer = 195 − (24.8 + 17.3) = 195 − 42.1 = 152.9 ≈ 153 kg/m³

Batched fine aggregate = 620 × 1.05 = 651 kg/m³   |   Batched coarse aggregate = 1,152 × 1.02 = 1,175 kg/m³

Table 2 summarises the SSD design quantities and the corresponding as-batched (moisture-corrected) quantities that would actually be weighed out at the mixer on the day of production.

Table 2. SSD trial mix design and moisture-corrected batch quantities per m³.

The as-batched total (2,422 kg/m³) is marginally higher than the theoretical SSD wet density of 2,410 kg/m³ because the moisture-content figures are expressed relative to the SSD aggregate mass for simplicity. A second-order discrepancy of this size, under 0.5% of the total batch mass, is normal in hand calculations of this kind and is well within the ±3% batching tolerance permitted for individual constituents in practice (BSI, 2015).

One further durability consideration specific to the freeze–thaw exposure class is air entrainment. BS 8500-1 requires a minimum entrained air content only for the more severe Freeze–Thaw Classes XF3 and XF4, where the concrete is repeatedly saturated and in direct contact with de-icing salt; for the moderate XF1 class applicable to this buried wall stem, no minimum air content is specified, and the mix above has therefore been designed without a deliberate air-entraining admixture. If the exposure classification were revised during detailed design – for example, if the top of the wall were found to pond surface water in a manner not anticipated at this stage – the design team should reconsider whether XF3 applies, in which case a target entrained air content of around 4–6% would need to be introduced, and the fine and coarse aggregate proportions in Table 2 recalculated to allow for the volume occupied by the entrained air.

Compliance Check and Discussion

Checked against the governing limits in Table 1, the trial mix design achieves a free w/c ratio of 0.44 against a maximum permitted value of 0.50, a cement content of 443 kg/m³ against a minimum of 320 kg/m³, and a target mean strength of 53 N/mm² against a characteristic requirement of 40 N/mm² (class C32/40), so the design satisfies all three governing criteria with a reasonable margin.

Although the cement content comfortably exceeds the durability minimum, at 443 kg/m³ it sits close to the practical ceiling of around 450 kg/m³ commonly applied to limit heat of hydration and the associated risk of early-age thermal cracking in a restrained section such as a retaining wall stem cast against a rigid base. A cement combination using CEM I with 50% ground granulated blastfurnace slag (GGBS) would be a sensible refinement to investigate: GGBS combinations reduce the rate and peak of heat evolution, lower the effective chloride diffusion coefficient (a direct benefit for the XD1 exposure identified above), and reduce the embodied carbon of the mix, and Concrete Centre guidance confirms that GGBS/CEM I combinations of this type are recognised within BS 8500 as an equivalent means of meeting the same durability class (Gibbs and Harrison, 2010). The principal trade-off is slower early strength gain, which would need to be reflected in the striking time for wall formwork and in cold-weather working procedures.

The design is also sensitive to on-site control of aggregate moisture. If the stockpile moisture content on the day of production differs from the 5% (fine) and 2% (coarse) values assumed here – for example after heavy rainfall – and the batching water is not re-corrected accordingly, the effective free w/c ratio of the concrete actually placed will differ from the 0.44 design value, with a wetter-than-assumed aggregate producing a higher effective w/c ratio and a corresponding loss of both strength and durability performance. Site quality procedures should therefore include a daily moisture check on both aggregate stockpiles, with the added water and batched aggregate masses recalculated using the method demonstrated in Step 6 whenever the moisture content changes materially.

Finally, workability should not be adjusted by simply adding water at the mixer if the trial batch slump falls short of the S2 target, since this would raise the w/c ratio above the durability limit; a small proportional increase in paste content at fixed w/c ratio, or the use of a plasticising admixture, are the appropriate remedies. Conformity of the accepted mix should ultimately be confirmed by 28-day cube testing to BS EN 12390, assessed against the statistical acceptance criteria in BS 8500-1 rather than against a single result. Curing also deserves explicit attention in the concrete quality plan: BS 8500-1 links the exposure class to a minimum curing period, and for XC3/XD1 exposure with CEM I cement, a minimum curing period of the order of 4 days at an average surface temperature of 15°C (or a longer period at lower temperatures) would typically be specified to allow the near-surface concrete to gain sufficient maturity to resist the intended exposure, with the GGBS combination discussed above requiring an even longer curing period on account of its slower early strength development. Cover tolerance is a related practical control: BS 8500-1 requires a minimum fixing tolerance to be added to the minimum cover so that reinforcement is not brought closer to the surface than intended by ordinary construction variability, which is why the 45 mm nominal cover adopted here already includes a 10 mm allowance over the 35 mm minimum.

Conclusion

The combined exposure classification of XC3, XD1 and XF1 for this highway retaining wall governs the mix design, requiring a maximum free w/c ratio of 0.50, a minimum cement content of 320 kg/m³, and a minimum strength class of C32/40. The DoE trial mix developed here achieves a free w/c ratio of 0.44 and a cement content of 443 kg/m³, meeting both the strength and durability requirements with a reasonable margin, and yields moisture-corrected batch quantities of 443 kg cement, 153 kg added water, 651 kg fine aggregate and 1,175 kg coarse aggregate per cubic metre. Before this mix is approved for full-scale production, it is recommended that the client investigate a 50% GGBS cement combination to manage heat of hydration and enhance chloride resistance, and that site procedures for daily aggregate moisture testing and slump verification be formally specified in the concrete quality plan. The chemical exposure review confirmed that the site’s benign ground chemistry (Design Sulfate Class DS-1) does not impose additional requirements beyond those already derived from the XC3/XD1/XF1 classification, and curing and cover tolerance provisions have been identified as further quality-plan items to be formally specified alongside the moisture-testing procedure recommended above.

References

• British Standards Institution (2015) BS 8500-1:2015+A2:2019 Concrete – Complementary British Standard to BS EN 206 – Part 1: Method of Specifying and Guidance for the Specifier. London: BSI.
• British Standards Institution (2013) BS EN 206:2013+A2:2021 Concrete – Specification, Performance, Production and Conformity. London: BSI.
• Teychenné, D.C., Franklin, R.E. and Erntroy, H.C. (1997) Design of Normal Concrete Mixes. 2nd edn. Watford: Building Research Establishment.
• Neville, A.M. (2011) Properties of Concrete. 5th edn. Harlow: Pearson.
• Domone, P. and Illston, J. (2010) Construction Materials: Their Nature and Behaviour. 4th edn. Abingdon: Spon Press.
• The Concrete Centre (2020) Guide to the Specification and Use of Concrete. Camberley: MPA The Concrete Centre.
• Bamforth, P. (2007) Enhancing Reinforced Concrete Durability: Guidance on Selecting Measures for Minimising the Risk of Corrosion of Reinforcement in Concrete. Camberley: The Concrete Society.
• Gibbs, J. and Harrison, T. (2010) The Use of Cement Combinations to Comply with BS 8500. Camberley: The Concrete Centre.
• Mosley, B., Bungey, J. and Hulse, R. (2012) Reinforced Concrete Design to Eurocode 2. 7th edn. Basingstoke: Palgrave Macmillan.
• Building Research Establishment (2005) Concrete in Aggressive Ground: BRE Special Digest 1. Watford: BRE.
• Bungey, J.H., Millard, S.G. and Grantham, M.G. (2006) Testing of Concrete in Structures. 4th edn. Abingdon: Taylor and Francis.