Let's evaluate each of the statements one by one:
Statement (P): "While designing a shallow footing in sandy soil, monsoon season is considered for critical design in terms of bearing capacity."
This statement is True. During the monsoon season, the water table in sandy soils can rise, which impacts the bearing capacity of shallow footings. The presence of water can reduce the effective stress in the soil, leading to a reduced bearing capacity. Therefore, it is critical to consider the effects of the monsoon season during design.
Statement (Q): "For slope stability of an earthen dam, sudden drawdown is never a critical condition."
This statement is False. Sudden drawdown refers to a rapid decrease in the water level behind a dam, which can reduce the water pressure on the downstream slope and cause the dam to become unstable. A sudden drawdown can indeed be a critical condition for slope stability, as it may lead to excessive pore water pressures and increase the likelihood of slope failure. Therefore, the statement is incorrect.
Statement (R): "In a sandy sea beach, quicksand condition can arise only if the critical hydraulic gradient exceeds the existing hydraulic gradient."
This statement is True. Quicksand occurs when the upward flow of water through sand exceeds the downward force of gravity, creating a condition where the sand behaves like a liquid. This happens when the critical hydraulic gradient (the minimum gradient required to induce quicksand conditions) exceeds the existing hydraulic gradient. Thus, the statement is correct.
Statement (S): "The active earth thrust on a rigid retaining wall supporting homogeneous cohesionless backfill will reduce with the lowering of water table in the backfill."
This statement is True. The active earth thrust on a retaining wall depends on the soil's effective stress, which is influenced by the water table. When the water table is lowered, the pressure exerted by the water on the soil (known as the hydrostatic pressure) decreases, reducing the total active earth pressure on the wall. Therefore, the statement is correct.
Conclusion:
- (P) is True,
- (Q) is False,
- (R) is True,
- (S) is True.
Thus, the correct answer is (C).