The water/cement (w/c) ratio is one of the most crucial factors affecting the strength, durability, and overall quality of concrete. It represents the ratio of the weight of water to the weight of cement used in a concrete mix. Controlling this ratio is essential to achieving desired concrete properties for construction applications.

In engineering practice, the strength of concrete at a specified age, when cured under controlled temperature conditions, is generally considered to be primarily influenced by two key factors: the water/cement ratio and the degree of compaction. When concrete is fully compacted, its strength is assumed to be inversely proportional to the water/cement ratio. This relationship was first articulated by Duff Abrams in 1919, initially described as a law but more accurately regarded as an empirical rule. He formulated strength as:

Here, w/c denotes the water/cement ratio of the mix, originally measured by volume, while K₁ and K₂ are empirical constants. The typical relationship between strength and the water/cement ratio is illustrated in Figure 1.

Fig. 1 The relation between strength and water/cement ratio of concrete (Neville)

Abrams' rule, though developed independently, closely resembles a general principle proposed by René Féret in 1896, as both establish a relationship between concrete strength and the volumes of water and cement. Féret's rule was expressed as:

where fc is the strength of concrete, c, w, and a are the absolute volumetric proportions of cement, water, and air, respectively, k is a constant.

Figure 1 illustrates that the validity of the water/cement ratio rule is limited. At very low water/cement ratios, the curve deviates from the expected trend when full compaction becomes unachievable, with the precise point of deviation depending on the compaction method used. Additionally, mixes with an extremely low water/cement ratio and a very high cement content—likely exceeding 530 kg/m³ (900 lb/yd³)—may experience strength retrogression when large aggregates are used. At later stages, in such mixes, reducing the water/cement ratio further may not necessarily result in higher strength. This phenomenon is likely attributed to shrinkage-induced stresses, where the restraint imposed by aggregate particles leads to cracking of the cement paste or a weakening of the cement-aggregate bond.

The water/cement ratio rule has occasionally been criticized for lacking fundamental rigor. However, in practical applications, it remains the most significant factor influencing the strength of fully compacted concrete. According to Gilkey, For a given cement and acceptable aggregates, the strength achievable in a workable, properly placed concrete mixture, under consistent mixing, curing, and testing conditions, is determined by:

1. The ratio of cement to mixing water
2. The ratio of cement to aggregate
3. The grading, surface texture, shape, strength, and stiffness of aggregate particles
4. The maximum size of the aggregate.

Gilkey mentioned that factors (b) to (d) are of lesser importance than factor (a) when usual aggregates up to 40 mm (1.5 in.) maximum size are employed. Further, Walker and Bloem points out that the strength of concrete results from: (1) the strength of the mortar; (2) the bond between the mortar and the coarse aggregate; and (3) the strength of the coarse aggregate particle, i.e. its ability to resist the stresses applied to it.

Figure 2 illustrates that the relationship between strength and the water/cement ratio follows an approximately hyperbolic trend. The relationship between strength and the cement/water ratio is approximately linear within the range of cement/water ratios from about 1.2 to 2.5. This linear correlation has been validated by Alexander and Ivanusec, as well as Kakizaki et al. Compared to the traditional water/cement ratio curve, the linear representation offers greater convenience, particularly for interpolation purposes.

Fig. 2 Relation between 7-day strength and water/cement ratio for concrete made with a rapid-hardening Portland Cement (Neville)

Figure 3 presents the data from Figure 2, plotted with the cement/water ratio on the x-axis. The values shown are specific to the given type of cement, and in practical applications, the exact relationship between strength and the cement/water ratio must be determined based on the specific materials used.

Fig. 3. A plot of strength against cement/water ratio for the data of Fig. 2 (Neville)

Fig. 4 Relation between calculated strength of neat cement paste and cement/water ratio. Maximum possible hydration is assumed to have taken place (Neville)

The linear relationship between strength and the cement/water ratio is valid only up to a cement/water ratio of 2.6, which corresponds to a water/cement ratio of 0.38. Beyond this point, for cement/water ratios greater than 2.6, a different linear relationship with strength emerges, as illustrated in Figure 4.

For water/cement ratios below 0.38, complete hydration is not achieved, resulting in a change in the slope of the strength curve compared to mixes with higher water/cement ratios. This distinction is important, as modern concrete mixes frequently incorporate water/cement ratios both slightly above and below 0.38.

In contrast, high-alumina cement concrete exhibits a different strength development pattern than Portland cement concrete. In this case, strength continues to increase with the cement/water ratio but at a progressively diminishing rate.

According to Neville, these relationships may not be exact, and alternative approximations can be considered. For example, it has been proposed that the relationship between the logarithm of strength and the actual water/cement ratio can be approximated as linear, similar to Abrams' formulation. To illustrate this concept, Figure 5 presents the relative strength of concrete mixes with varying water/cement ratios, using the strength at a water/cement ratio of 0.4 as the reference value (unity).

Fig. 5 Relation between logarithm of strength and water/cement ratios (Neville)

CONCLUSION

The water/cement ratio is a fundamental factor in determining the strength of concrete. Although the relations may not be exact. Maintaining an optimal w/c ratio ensures that concrete achieves the desired balance of workability, strength, and longevity. Proper mix design, along with the use of admixtures, can help achieve the best performance for specific construction needs.

REFERENCES

1. Neville, A.M. (2011) Properties of Concrete.
2. Walker, S. and Bloem D.L. (1956). Studies of Flexural Strength of Concrete, Part 1 Effects of Different Gravels and Cements. Nat. Ready Mixed Concrete Associations Joint Research Laboratory Publ. No. 3.
3. Alexander, K.M. and Ivanusec, I. (1982) Long term Effects of Cement SO3 Content on the Properties of Normal and Hight Strength Concrete. Cement and Concrete Research.

ABOUT AUTHORS

ALI ARYO BAWONO, Dr.-Ing. is an esteemed civil engineering and urban transport infrastructure specialist with a doctoral degree and more than 14 years of experience. With practical expertise in project and program management, technical and policy analysis, business models, and capacity building, Bawono possesses a well-rounded skill set. He holds a Ph.D. in Material Science from Nanyang Technological University (NTU) in Singapore, an M.Sc. in Transportation System from Technische Universität München (TUM) in Germany and bachelor’s degree in Civil Engineering from the Bandung Institute of Technology.

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