Now plot and indicate the following information on the graph and show the working

• Draw a horizontal axis (x-axis) and label it "Moisture Content ($w$ %)". Scale it from approximately 8% to 22%.
• Draw a vertical axis (y-axis) and label it "Dry Unit Weight ($\gamma_{dry}$ $kN/m^3$)". Scale it from approximately $15.5 \, \text{kN/m}^3$ to $17.0 \, \text{kN/m}^3$.

• Carefully mark each of the 8 coordinate points on your graph.
• Draw a smooth curve connecting these points. The curve should rise, reach a peak, and then fall. This is your compaction curve.

a)

• Identify the peak: Visually locate the highest point on the smooth compaction curve. This point represents the maximum dry unit weight.
• Read $\gamma_{d,max}$: From this peak, draw a horizontal line to the y-axis. The value where it intersects is the maximum dry unit weight. $$\gamma_{d,max} \approx 16.79 \, \text{kN/m}^3$$
• Read OMC: From the same peak, draw a vertical line down to the x-axis. The value where it intersects is the optimum moisture content. $$\text{OMC} \approx 15.1\%$$

The maximum dry unit weight is $\boxed{\text{16.79 kN/m}^3}$ and the optimum moisture content is \boxed{\text{15.1%}}.

b)

• Calculate 95% of $\gamma_{d,max}$: $$0.95 \times 16.79 \, \text{kN/m}^3 = 15.95 \, \text{kN/m}^3$$
• Locate on y-axis: Find $15.95 \, \text{kN/m}^3$ on the y-axis.
• Draw horizontal line: From $15.95 \, \text{kN/m}^3$ on the y-axis, draw a horizontal line to the left until it intersects the compaction curve.
• Draw vertical line: From this intersection point on the curve, draw a vertical line straight down to the x-axis.
• Read moisture content: The value where this vertical line intersects the x-axis is the required moisture content. $$\text{Required moisture content} \approx 10.09\%$$

The moisture content required to achieve 95% of $\gamma_{d,max}$ is approximately \boxed{\text{10.09%}}.