The time required for 50% consolidation can be calculated using the formula t = H²/Cv, where H is the thickness of the layer. For H = 5 m, t = (5²)/0.01 = 250 years, but for 50% consolidation, we use a factor of 0.1, leading to approximately 1 year.

Terzaghi's one-dimensional consolidation theory is widely used to estimate settlement in saturated clay due to its simplicity and effectiveness.

The vane shear test is specifically designed to measure the in-situ shear strength of cohesive soils.

Increasing the water content in a saturated clay layer typically increases settlement due to reduced effective stress and increased compressibility.

Differential settlement is primarily caused by soil heterogeneity, where different soil layers compress at different rates under load.

Settlement in clay soils is primarily due to consolidation, which is the process of volume reduction under load over time.

Sandy soils typically have a coefficient of permeability ranging from 10^-4 to 10^-2 m/s, allowing for relatively high water flow.

Foundation depth does not directly affect the shear strength of soil; rather, it influences the stress distribution and potential settlement.

Total settlement can be calculated using various methods including elastic theory, consolidation theory, and Boussinesq's equation, depending on the conditions.

The coefficient of consolidation is crucial for predicting the time rate of settlement, as it defines how quickly the soil will consolidate under load.