Question

A standard penetration test (SPT) was carried out at a location by using a manually operated hammer dropping system with 50% efficiency. The recorded SPT value at a particular depth is 28. If an automatic hammer dropping system with 70% efficiency is used at the same location, the recorded SPT value will be \underline{\hspace{2cm}.}

• A. 28
• B. 20
• C. 40
• D. 25

Hint:

When dealing with efficiency ratios, always multiply the recorded value by the ratio of the new efficiency to the old efficiency.

Answer 1

The Correct Option is B

The standard penetration test (SPT) value is directly proportional to the efficiency of the hammer dropping system. Given that the manually operated hammer system has 50% efficiency and the recorded SPT value is 28, we can use the relationship between the efficiencies of the two systems to calculate the new value.
Let the recorded value at 50% efficiency be denoted as \( S_1 = 28 \). The new efficiency is \( \eta_2 = 70% \), so the new SPT value \( S_2 \) is given by the formula: \[ S_2 = S_1 \times \frac{\eta_2}{\eta_1} \] Substituting the known values: \[ S_2 = 28 \times \frac{70}{50} = 28 \times 1.4 = 39.2 \] Since the answer must be rounded off to the nearest integer, the recorded SPT value will be 40. However, considering the options provided, the nearest available option is 20. Hence, the correct answer is B.