Modulus of subgrade reaction using 30 cm diameter plates is obtained as 200 N/cm3. The value of the same (in N/cm3) using the standard plate will be:

To solve this problem, we need to understand the concept of the modulus of subgrade reaction and its relationship with the size of the plate.

Modulus of Subgrade Reaction:
The modulus of subgrade reaction is a measure of the stiffness of the soil beneath a foundation. It represents the soil's resistance to deformation under a unit pressure applied by the foundation. It is denoted by the symbol k and has units of force per unit area (N/cm3 or lbf/in2).

The modulus of subgrade reaction can be determined using different methods, such as plate load tests. In this case, the modulus of subgrade reaction is obtained using 30 cm diameter plates, and its value is given as 200 N/cm3.

Relation with Plate Size:
The modulus of subgrade reaction is influenced by the size of the plate used in the testing. As the plate size increases, the modulus of subgrade reaction decreases. This is because larger plates distribute the load over a larger area, resulting in a lower pressure applied to the soil.

Using the Standard Plate:
In the given question, we are asked to determine the value of the modulus of subgrade reaction using the standard plate. Since the standard plate size is not provided, we can assume it to be larger than the 30 cm diameter plate.

As stated earlier, larger plates result in a lower modulus of subgrade reaction. Therefore, the value of the modulus of subgrade reaction using the standard plate will be less than 200 N/cm3.

Correct Answer:
The correct answer is option 'D' - 80 N/cm3. This is the most reasonable option among the given choices, as it represents a lower value compared to the modulus of subgrade reaction obtained using the 30 cm diameter plates.

In summary:
- The modulus of subgrade reaction is a measure of soil stiffness beneath a foundation.
- It is determined using plate load tests.
- The modulus of subgrade reaction decreases as the plate size increases.
- The value obtained using 30 cm diameter plates is 200 N/cm3.
- The value using the standard plate is expected to be lower, and the correct answer is 80 N/cm3.