Question

In a plate load test on clay soil, the ratio of ultimate bearing capacity of footing to the ultimate bearing capacity of plate is

• A. 2
• B. 1.5
• C. 1
• D. 2.5

Hint:

In geotechnical engineering, the bearing capacity of clay in undrained conditions (short-term loading) is independent of footing size because it depends on the undrained shear strength (\( c_u \)), which is a material property. This is why plate load test results on clay can be directly applied to larger footings without scaling. In contrast, for granular soils like sand, bearing capacity increases with footing size due to the influence of the friction angle.

Answer 1

The Correct Option is C

Step 1: Identify the given data.
The question asks for the ratio of the ultimate bearing capacity of a footing to the ultimate bearing capacity of the plate in a plate load test on clay soil. The options provided are:
(1) 2
(2) 1.5
(3) 1
(4) 2.5
We need to determine the correct ratio based on geotechnical principles.
Step 2: Recall the concept of a plate load test and bearing capacity in clay.
A plate load test is used to determine the ultimate bearing capacity of soil by loading a small plate (typically 30 cm to 75 cm in size) until failure. The ultimate bearing capacity (\( q_u \)) is the maximum load per unit area the soil can sustain before failure. In clay soils, the bearing capacity is primarily governed by the soil’s undrained shear strength (\( c_u \)), as clay exhibits cohesive behavior under short-term loading (undrained conditions).
Step 3: Determine the bearing capacity relationship for clay.
For a footing or plate on clay, the ultimate bearing capacity can be estimated using the bearing capacity equation for cohesive soils (Terzaghi’s theory or Skempton’s method for undrained conditions):
\[ q_u = c_u N_c + \gamma D_f \] Where:
\( c_u \): Undrained shear strength of clay
\( N_c \): Bearing capacity factor (depends on the shape and depth of the footing)
\( \gamma \): Unit weight of soil
\( D_f \): Depth of the footing
In a plate load test, the plate is typically placed at the surface (\( D_f = 0 \)), so the term \( \gamma D_f \) is zero. Thus:
\[ q_u = c_u N_c \] The key question is how \( N_c \) varies between the plate and the footing, and whether the bearing capacity changes with size in clay.
Step 4: Analyze the effect of size on bearing capacity in clay.
In clay soils (under undrained conditions), the ultimate bearing capacity is independent of the size of the footing or plate. This is because:
The bearing capacity depends on \( c_u \), which is a material property of the clay and does not vary with size.
The bearing capacity factor \( N_c \) for a given shape (e.g., square or circular) is the same for both the plate and the footing in undrained conditions, as long as the depth and shape factors are similar.
For surface footings on clay, Skempton’s \( N_c \) for a square or circular footing is approximately 5.14 to 6 (depending on the shape), but the value is the same for both the plate and the footing.
Thus, the ultimate bearing capacity \( q_u \) is the same for the plate and the footing:
\[ q_{u,\text{footing}} = q_{u,\text{plate}} \] The ratio of the ultimate bearing capacity of the footing to the plate is:
\[ \frac{q_{u,\text{footing}}}{q_{u,\text{plate}}} = 1 \] (Note: This is different for granular soils like sand, where bearing capacity increases with size due to scale effects and the influence of the friction angle. However, in clay, the undrained shear strength governs, and there is no size effect.)
Step 5: Compare with the given options.
2 (Option 1) would suggest the footing has twice the bearing capacity, which is not true for clay.
1.5 (Option 2) also suggests a size effect, which doesn’t apply in undrained clay.
1 (Option 3) matches our conclusion that the bearing capacity is the same for both the plate and the footing.
2.5 (Option 4) is too high and not applicable.
The correct ratio is 1.
Step 6: Select the correct option.
Based on the analysis, the ratio of the ultimate bearing capacity of the footing to the plate in a plate load test on clay soil is 1.
The correct option is (3). \[ \boxed{1} \]