Calculating Footing Settlement from Plate Load Test in Cohesive Soil

The question asks us to determine the expected settlement of a square footing in cohesive soil based on the results of a plate load test conducted in the same soil under similar loading conditions.

The plate load test is a common method used to estimate the bearing capacity and settlement characteristics of soil. When using the results of a plate load test to predict the settlement of a footing, the relationship between the plate settlement and the footing settlement depends significantly on the type of soil.

Settlement Calculation for Cohesive Soil

For cohesive soils (like clay), the relationship between the settlement of a test plate (\(\text{S}_\text{p}\)) and the settlement of a footing (\(\text{S}_\text{f}\)) under the same intensity of loading is primarily proportional to the ratio of their sizes. The formula used for this prediction in cohesive soils is:

\[\text{S}_\text{f} = \text{S}_\text{p} \times \left(\frac{\text{B}_\text{f}}{\text{B}_\text{p}}\right)\]

Where:

• \(\text{S}_\text{f}\) = Settlement of the footing
• \(\text{S}_\text{p}\) = Settlement of the test plate
• \(\text{B}_\text{f}\) = Size (width or side) of the footing
• \(\text{B}_\text{p}\) = Size (width or side) of the test plate

Applying the Given Data

From the question, we are given the following information:

• Settlement of the plate, \(\text{S}_\text{p} = 2\) cm
• Size of the plate, \(\text{B}_\text{p} = 35\) cm
• Size of the square footing, \(\text{B}_\text{f} = 85\) cm
• Soil type: Cohesive soil

Step-by-Step Calculation of Footing Settlement

Using the formula for cohesive soil, we can calculate the expected settlement of the footing:

Substitute the given values into the formula:

\[\text{S}_\text{f} = 2 \text{ cm} \times \left(\frac{85 \text{ cm}}{35 \text{ cm}}\right)\]

Simplify the fraction \(\frac{85}{35}\):

Both 85 and 35 are divisible by 5.

\[\frac{85}{35} = \frac{85 \div 5}{35 \div 5} = \frac{17}{7}\]

Now, substitute the simplified fraction back into the formula:

\[\text{S}_\text{f} = 2 \text{ cm} \times \left(\frac{17}{7}\right)\]

Perform the multiplication:

\[\text{S}_\text{f} = \frac{2 \times 17}{7} \text{ cm} = \frac{34}{7} \text{ cm}\]

Calculate the decimal value:

\[\text{S}_\text{f} \approx 4.857 \text{ cm}\]

Rounding to two decimal places, the settlement is approximately 4.86 cm. Comparing this with the given options, the closest value is 4.85 cm.

Conclusion

Based on the plate load test results in cohesive soil, the estimated settlement of the 85 cm square footing under the same loading conditions is approximately 4.85 cm.