“Mix Design” is an interesting, challenging, and fundamental task. The objective is to predict the relative quantities of ingredients that will reliably and economically meet the specifications and satisfy the needs of the concrete producer and contractor, preferably using local materials.
A wide variety of mix-design methods are used, varying from simple volumetric batching (by hand) of a 1:2:3 mix (cement:sand:coarse aggregate), to sophisticated, computer-based techniques, all of which are intended to produce a good-first-guess called a “trial mix.” Then the trial mix has to be evaluated at lab- and field-scale, with the expectation of making adjustments based on continued monitoring of performance.
In this test-and-adjust process, actual concrete performance matters more than the mix-design method because there are no guarantees in mix design and each mixture must account for the characteristics and variability of local materials. Even though most concrete is batched by weight, this article also explores the relative volumes of paste, air, and aggregate.
But regardless of the mix-design method, there are three characteristics of concrete that we are trying balance:
1. Water content as adjusted by admixtures defines workability.
2. Water-cementitious materials ratio dictates strength and durability.
3. Total cementitious materials is not only a primary cost factor but also influences heat, chemical reactivity, and shrinkage tendency.
These three factors cannot be independently selected. At best, the mix designer can select any two and accept the dependency of the third, or else turn to admixtures and specialized aggregate grading.
How a Mix Works
A good starting point is to recognize that the paste, consisting of water and cementitious materials, is the adhesive that glues the aggregates together into a strong and durable hardened mass. Except in very high-strength mixes, the aggregates are the strong links in the concrete chain, while the paste is softer, more absorbent, more vulnerable to freeze-thaw damage and deleterious chemical reactions—and it is what shrinks.
Most high-quality natural aggregates have a stiffness (what designers call a modulus of elasticity) four to five times greater than the stiffness of the hardened paste. At low stresses, before concrete begins to crack, the paste and aggregate are locked together and deform equally, with a resulting level of stress in the aggregate particles that can be four to five times greater than the level of stress in the softer paste.
For example, when we say that the compression stress in a concrete cylinder is 4,000 psi, that value is an average of what may be a stress in the aggregates of over 10,000 psi and a stress in the paste around 1,500 psi. Add in the heat generated by the reaction of the cementitious materials and water, and the tendency for paste to shrink far more than aggregates, and we realize that designing an optimal mix means finding a way to minimize the paste and maximize the aggregates. You’re on the right track towards this optimal blend when you choose coarser over finer aggregates and pay attention to blending aggregate sizes so as to not jeopardize workability.
The Paste is a Lubricant
In fresh concrete, the cementitious paste lubricates the aggregate particles, making it easier for them to slip past each other. For example, compare the steepness of the sides of a stockpile of crushed stone with the much shallower “angle of repose” observed with even low-slump concrete.
As with any lubricated surface or greased bearing, the effectiveness of the cementitious paste in reducing the friction between the aggregate particles will depend on the viscosity of the paste and the thickness of the paste layer. While pastes with lower water-cementitious materials ratios are generally stickier and more viscous, this effect can be overcome by increasing the total paste content to build thicker paste layers between the aggregates (this is the strategy adopted in ACI 211.1).
The total amount of paste required in the mix is therefore going to be largely influenced by the total surface area of all the coarse, intermediate, and fine aggregates that must be coated by this paste-lubricant. Figure 1 shows approximate total surface area per ton of coarse aggregate, ranging from about 1,500 square feet per ton for a #467 (11/2-inch) stone, to more than 5,000 square feet per ton for #8 (3/8-inch) stone. Maintaining a thick-enough paste layer for workability with #8 aggregate will require far more paste than for a mix with #67 (3/4-inch) stone that has only half as much aggregate surface area per ton. And since there is only 27 cubic feet in a cubic yard, and all ingredients are claiming their share of that volume, any time that paste content has to increase, aggregate content consequently has to decrease.
This can get dicey when shrinkage is critical since the paste leads to shrinkage while aggregates resist shrinkage. This really comes home to roost where thin slabs and overlays must be cast with small aggregates to meet the building code mandate that the nominal maximum aggregate size of the coarse aggregate not exceed one-third of the slab thickness. Such small aggregates, often 1/2 or 3/8 inch, will require high water content and a high paste content, which increases the likelihood of higher shrinkage. Couple this with the fact that thin slabs and overlays can dry very rapidly because of their high surface-to-volume ratio, and the stage is set for the all-too-common shrinkage cracking in thin unbonded overlays.
The Paste is Also an Adhesive
But the paste, regardless of the blend of cementitious materials, is not only a lubricant for the fresh concrete but also an adhesive for the hardened concrete. In essence, the blended dry cementitious powders constitute a cost-effective, industrial-strength instant glue, activated by the mere addition of water. This reaction, which promotes strength-gain and porosity-reduction, continues only as long as drying is prevented and water is available.
As with any dry instant adhesive, increasing the amount of water added to a fixed amount of powder leads to two fundamental consequences:1. Extra water always leads to increased fluidity and lower viscosity of the liquid lubricant/adhesive.
2. Adding water to a fixed amount of powder will always dilute the adhesive capability of the paste. This is because water-addition pushes the powder particles farther apart, making it more difficult to establish the critical bonds from one particle to the next that give concrete its strength. Water addition also creates larger gaps between the particles that allow the passage of gases, liquids, and contaminants through the hardened concrete.
These simple observations bring us to the fundamental quality-control challenge in the concrete industry: water-addition increases fluidity and workability, and at the same time decreases strength and durability of the hardened product, without exception. The fundamental trade-off in our industry has always been balancing the owner’s needs for strength and durability with the producer’s and contractor’s needs for concrete that can be placed, consolidated, and finished. While admixtures and improved aggregate grading can go a long way toward making this balancing act possible, nobody has yet come up with a fluidity-enhancer that is more effective, cheaper, or more readily available than water, but that does not have the strength-reducing power of water.
Water content is critical for workability because it influences both the lubricating ability of the paste and the thickness of the paste-layer coating the aggregate particles. This relationship can be seen in Figure 2 showing where the aggregate-size effect comes into play. The graph demonstrates the basic water requirement prior to adjusting for combined aggregate grading, air entrainment, or other admixtures. For a desired 5-inch slump, the water content varies from about 310 pounds of water per cubic yard for 11/2-inch stone, to about 350 pounds per yard for 3/4-inch stone, to 400 pounds of water per cubic yard for 3/8-inch stone.
At any preselected ratio of water to cementitious materials (w/cm), more water is simply going to mean greater paste volume, and greater paste volume will generally lead to increased shrinkage—as shown in Figure 3.
What’s All This About w/cm?
The ratio of the weight of water to the weight of dry cementitious materials (water-cementitious materials ratio, w/cm) is a key index of the strength and durability of the paste that acts as the adhesive holding the aggregate together to form the concrete. This is best explained in Figure 4, showing our human-eye-view of ordinary concrete on the left, then magnified 100,000 times on the right.
In the picture on the right, you’ll see the strength and mechanical properties develop from the particle-to-particle bonding of the crystal-like products protruding from the hydrated grains of cement powder, while the dark void spaces in between are the passageways for transport of water, oxygen, carbon dioxide, sulfates, alkalis, and chlorides. These void spaces have their origin in the volume occupied by the water in the fresh concrete. The lower the amount of water in the fresh paste relative to the amount of cementitious materials, the less void space and the lower the permeability of the hardened concrete.
Likewise, the lower the w/cm, the higher the compressive strength, tensile strength, and modulus of elasticity. In addition to the fundamental influence of w/cm, mechanical- and durability-related properties are also influenced by overall mixture proportions and the selection of other ingredients, making it difficult to predict strength or durability on the basis of w/cm alone.
Nevertheless, ACI 211.1, Standard Practice for Selecting Proportions for Normal, Heavyweight, and Mass Concrete, cites the relationship between w/cm and 28-day compressive strength for non-air-entrained concrete, as shown in Figure 5.
The 236-psi-per-gallon line is approximately the ACI 211.1 relationship between w/cm and compressive strength. The other lines are from a series of concrete mixes produced in a ready-mix truck. In general, nearly all mixtures achieved a somewhat higher strength than predicted at any value of w/cm. This is not too surprising since the ACI data is old and modern cements are more efficient.
While there are obvious differences among the performance of the various mixtures, the data verifies the shape of the ACI strength relationship and demonstrate the fundamental principle that increasing water content for a fixed weight of cementitious material decreases the compressive strength. For the three mixes shown in Figure 5, the strength reduction due to an increase in water content ranged from 148 to 236 psi per gallon, as influenced by other mixture characteristics. Any concrete producer can keep track of w/cm and generate their own, unique materials database as a more reliable predictor than nationally published data.
The w/cm also has an impact on the permeability of hardened concrete (the rate at which pressurized liquid water can be forced through hardened concrete). The trend with any mix is rapidly escalating permeability with increasing w/cm, which leads to rapidly declining service life.
Putting It All Together
A typical concrete mixture is likely to have a total air-free paste volume in the range of 25% at the low-shrinkage end up to somewhere around 30%. If we add 2% to 8% air to cover the range from non-air-entrained to air-entrained concrete, the combined water, cementitious materials, and air bubbles can represent 27% to 38% of the volume of the concrete. The rest is the combined aggregate volume in the range of 62% to 73%.
Jim and Jay Shilstone always advocated further defining the “mortar volume fraction” as the percent of the concrete volume that includes everything except the coarse aggregate. Although the guidelines get complicated, a mortar volume fraction of 50% is about right for most mixes using clean, rounded gravels, and closer to 60% for crushed stone mixes. This is because the mortar separates the aggregate particles and rougher textures require more separation to achieve workability, pumpability, and finishability. But when mortar fractions get much higher than these general numbers, it can often be an indicator that the mix is “over-sanded,” leading to a mushy consistency that can clog the pump as much as a mix that is too rocky, and cause finishing problems besides.
To read part 2 of this article, click here.
