Optimum binder content graphs

In the Marshall mix design, specimens are prepared at binder contents that differ by 0.5% (for example, 4.5 to 6.5%) and tested for stability, flow, density and voids. Six graphs are plotted with the binder content on the X-axis.

Shape of the graphs

 Stability       Unit weight      Air voids (Vv)
   ^   .-.         ^    .-.         ^ \
   |  /   \        |   /   \        |  \
   | /     \       |  /     \       |   \___
   +-----------> % +--------------> +--------> %
   peak at B1      peak at B2        4% at B3

 Flow            VMA              VFB
   ^       /        ^ \     /       ^        /
   |     /          |  \___/        |      /
   |___/            |               |___ /

• Stability rises with the binder content to a maximum and then falls.
• Unit weight (bulk density) increases to a maximum (usually at a slightly higher binder content than the stability peak) and then decreases.
• Air voids ($V_v$) decrease steadily with more binder.
• Flow increases steadily with the binder content.
• VMA decreases to a minimum and then increases; VFB increases steadily.

Finding the OBC

1. From the graphs, read the binder content for:
   • maximum stability, $B_1$;
   • maximum bulk density, $B_2$;
   • 4% air voids (the middle of the 3-5% range), $B_3$.
2. The optimum binder content is the average:

$$\text{OBC} = \frac{B_1 + B_2 + B_3}{3}$$

3. Read the stability, flow, voids, VMA and VFB at the OBC from the graphs and check them against the specification (for example, flow 2-4 mm, $V_v$ 3-5%, VFB 65-75%). If the values are not satisfied, the mix is redesigned.

Example: $B_1 = 5.2\%$, $B_2 = 5.5\%$, $B_3 = 5.6\%$ gives OBC $= 5.43\%$ (illustrative values).