---
title: "Optimum binder content graphs"
subject: "Transportation Engineering I"
chapter: 6
key: "semester_6/transportation_engineering_i:optimum-binder-content"
source: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/optimum-binder-content
site: BCT Engineering
---

# Optimum binder content graphs

Transportation Engineering I · Chapter 6: Highway Materials

- Asked in: 2079 Chaitra, 4 marks
- Video: [OPTIMUM BINDER CONTENT AS PER MS 2 & MORT&H 5th REVISION](https://www.youtube.com/watch?v=iy3jhWPB0O8) — HIGHWAY GUIDE
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/optimum-binder-content
- Whole chapter: https://www.bctengineer.com/md/semester_6/transportation_engineering_i/chapter-6

## Question

Describe using graphical sketches how one obtains the optimum binder content.

## Short answer

Plot stability, bulk density, and air voids vs binder content. Read binder content at maximum stability (B1), maximum density (B2), and 4% air voids (B3). Optimum binder content = (B1 + B2 + B3)/3, then check stability, flow, and voids meet specifications.

## Answer

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
```text
 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).

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. How does stability vary with binder content?
   A. Rises to a maximum and then falls
   B. Falls steadily
   C. Rises steadily
   D. Stays constant
   Answer: A. Peak stability gives B1. (Key point: Stability curve)

2. How do air voids vary?
   A. Increase steadily
   B. Decrease steadily with more binder
   C. Peak then fall
   D. Constant
   Answer: B. 4% voids gives B3. (Key point: Air voids curve)

3. The OBC is
   A. Binder at max flow
   B. Sum of three
   C. Average of binder contents at max stability, max density and 4% air voids
   D. Binder at min VFB
   Answer: C. OBC = (B1 + B2 + B3)/3. (Key point: OBC formula)

4. For B1 = 5.2, B2 = 5.5, B3 = 5.6, OBC is
   A. 5.6%
   B. 16.3%
   C. 5.2%
   D. 5.43%
   Answer: D. (5.2+5.5+5.6)/3 = 5.43%. (Key point: Example)

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