Show every point on the graph and the numbers ,for easy to understand

Here are the calculated values, which will be our plotting points:

• Draw a horizontal axis (x-axis) and label it "Moisture Content ($w$ %)". Choose a scale that covers the range from approximately 8% to 22%. For example, each major grid line could represent 1% moisture content.

• Draw a vertical axis (y-axis) and label it "Dry Unit Weight ($\gamma_{dry}$ $kN/m^3$)". Choose a scale that covers the range from approximately $15.5 \, \text{kN/m}^3$ to $17.0 \, \text{kN/m}^3$. For example, each major grid line could represent $0.1 \, \text{kN/m}^3$.

• Now, plot each data point from the table on your graph:

  • Point 1: ($w=9.9\%$, $\gamma_{dry}=15.89 \, \text{kN/m}^3$)
  • Point 2: ($w=10.5\%$, $\gamma_{dry}=16.08 \, \text{kN/m}^3$)
  • Point 3: ($w=12.1\%$, $\gamma_{dry}=16.41 \, \text{kN/m}^3$)
  • Point 4: ($w=13.8\%$, $\gamma_{dry}=16.70 \, \text{kN/m}^3$)
  • Point 5: ($w=15.1\%$, $\gamma_{dry}=16.79 \, \text{kN/m}^3$)
  • Point 6: ($w=17.4\%$, $\gamma_{dry}=16.64 \, \text{kN/m}^3$)
  • Point 7: ($w=19.4\%$, $\gamma_{dry}=16.27 \, \text{kN/m}^3$)
  • Point 8: ($w=21.2\%$, $\gamma_{dry}=15.86 \, \text{kN/m}^3$)

• Once all points are plotted, draw a smooth curve that connects these points. This curve should rise to a peak and then fall, forming a bell-like shape.

a)

• Locate the highest point on the smooth curve you just drew. This is the peak of the compaction curve.
• From this peak, draw a horizontal line to the y-axis. The value where it intersects the y-axis is the maximum dry unit weight ($\gamma_{d,max}$). You should read approximately $16.79 \, \text{kN/m}^3$.
• From the same peak, draw a vertical line down to the x-axis. The value where it intersects the x-axis is the optimum moisture content (OMC). You should read approximately $15.1\%$.

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 the maximum dry unit weight: $$0.95 \times \gamma_{d,max} = 0.95 \times 16.79 \, \text{kN/m}^3 = 15.95 \, \text{kN/m}^3$$
• Locate $15.95 \, \text{kN/m}^3$ on the y-axis.
• Draw a horizontal line from $15.95 \, \text{kN/m}^3$ across to the left side of your compaction curve.
• Where this horizontal line intersects the curve (on the "dry" side, before the peak), draw a vertical line straight down to the x-axis.
• Read the value on the x-axis where this vertical line lands. This is the moisture content required. You should read approximately $10.09\%$.

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