Question 4.11: Interpreting Fall Cone Data. The results of a fall cone test...

Interpreting Fall Cone Data.
The results of a fall cone test are shown in the table below.

Cone mass 80-gram cone
Penetration (mm) 5.5 7.8 14.8 22 32
Water content (%) 39 44.8 52.5 60.3 67

Determine (a) the liquid limit, (b) the plastic limit, (c) the plasticity index, and (d) the liquidity index if the natural water content is 46%.

Strategy: Make a plot of water content versus penetration, both at logarithmic scale. Use the data to make your plot, then extract the liquid limit (water content on the liquid state line corresponding to 20 mm). Find the water content difference between the two liquid state lines at any fi xed penetration. Use this value to determine the plastic limit from Equation (4.20)

Equation (4.20) : PL=C(2)^{m}

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Step 1: Plot the data.
See Figure E4.11.

Step 2: Extract the liquid limit.

LL = 60%

Step 3: Determine the plastic limit.
The best-fi t straight line for the 80-gram cone is Y=23.6X^{0.3} where Y is water content and X is penetration. Therefore, C = 23.6 and m = 0.3. From Equation (4.20):

PL=C(2)^{m}=23.6(2)^{0.3}=29\, %

Step 4: Determine PI.

PI = LL – PL = 60 – 29 = 31%

Step 5: Determine LI.

LI=\frac{w-PL}{PI}=\frac{46-29}{31}=0.55
step 1 figure e4.11

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