Hardness, toughness and aggregate blend

Hardness and toughness

• Hardness is the resistance of aggregate to wear (abrasion and attrition) by the rubbing action of vehicle wheels. Test: Los Angeles abrasion test (limit about 30% for a wearing course) or the Deval attrition test.
• Toughness is the resistance of aggregate to failure by impact (sudden shock) from moving loads. Test: aggregate impact value test (AIV not more than 30% for a wearing course; 45% for base).

Aggregate blend by graphical method

Given: Aggregates P and Q with a specified grading envelope. Let $x$ be the fraction of P and $(1-x)$ the fraction of Q. At every sieve:

$$\text{Passing}_{mix} = x\,P + (1-x)\,Q$$

In the graphical method for two aggregates, the % passing of Q is marked on the left vertical axis (0% P) and that of P on the right vertical axis (100% P), and a straight line joins the two points for each sieve. The specification limits are marked on each sieve line, and the vertical band common to all the lines gives the allowable range of the proportion of P. The same range is obtained by solving for $x$ at each sieve:

$$x_{min} = \frac{L - Q}{P - Q},\qquad x_{max} = \frac{U - Q}{P - Q}$$

Common range: P between 37.5% and 62.5% (controlled by the 2.36 mm sieve), so Q is between 62.5% and 37.5%.

Best proportion: the mid-point, P : Q = 50 : 50. Check:

Answer: Aggregate P : Aggregate Q = 50 : 50 (any proportion of P between about 38% and 62% satisfies the specification, and 50% gives a gradation near the middle of the envelope).