Question

If the actual value of the standard penetration number, SPT N measured in fine sand below the water table is 19, then the corrected value of SPT N for dilatancy is

• A. \( 15 \)
• B. \( 17 \)
• C. \( 19 \)
• D. \( 4 \)

Hint:

SPT N-values are empirical and require several corrections for accurate interpretation. Common corrections include overburden pressure correction ($N_1$) and dilatancy correction ($N'$). Dilatancy correction is specific to fine sands below the water table and reduces the N-value if it's greater than 15, accounting for the effect of excess pore water pressure during hammer blows.

Answer 1

The Correct Option is B

Step 1: Understand the context of SPT corrections.
The Standard Penetration Test (SPT) provides an N-value, which is an empirical measure of soil resistance. This N-value needs to be corrected for various factors to obtain a more representative value for design purposes. One common correction is for dilatancy, especially for fine sands below the water table.
Step 2: Recall the dilatancy correction for SPT N-value.
For fine sands below the water table, if the observed N-value (\( N_{obs} \)) is greater than 15, a dilatancy correction is applied. This correction accounts for the pore water pressure generation during driving in dense or fine sands below the water table, which can artificially increase the measured N-value.
The corrected N-value for dilatancy (\( N' \)) is given by the formula:
$$N' = 15 + \frac{1}{2} (N_{obs} - 15)$$
If \( N_{obs} \leq 15 \), then \( N' = N_{obs} \).
Step 3: Apply the correction formula using the given data.
Given the actual (observed) SPT N-value \( N_{obs} = 19 \).
Since \( N_{obs} = 19>15 \), the dilatancy correction is applicable.
Substitute \( N_{obs} = 19 \) into the formula:
$$N' = 15 + \frac{1}{2} (19 - 15)$$
$$N' = 15 + \frac{1}{2} (4)$$
$$N' = 15 + 2$$
$$N' = 17$$
Step 4: Select the correct option.
Based on the calculation, the corrected value of SPT N for dilatancy is \( 17 \).
$$\boxed{17}$$