Terzaghi’s one-dimensional consolidation — basic assumptions: Which set of assumptions correctly represents Terzaghi's classical 1D consolidation theory for saturated soils?

Introduction / Context:
Terzaghi’s one-dimensional consolidation theory provides a practical framework to predict time-dependent settlement of saturated clays under vertical loading. The theory simplifies complex soil behavior through a set of assumptions that enable a diffusion-type equation linking excess pore pressure and time.

Given Data / Assumptions:

• Clay layer is homogeneous, isotropic, and fully saturated.
• Flow is one-dimensional and vertical.
• Water and soil grains are taken as incompressible relative to the voids volume change.
• Darcy’s law holds for flow at the prevailing gradients.

Concept / Approach:
These assumptions lead to the classical consolidation equation where the coefficient of consolidation governs the rate of excess pore-pressure dissipation. Deformation results from a decrease in void ratio as water is expelled; lateral strains are constrained in the 1D idealization, focusing on vertical strains and settlement.

Step-by-Step Solution:

Verification / Alternative check:
Oedometer tests are interpreted using this framework to estimate the coefficient of consolidation and preconsolidation pressure for design.

Why Other Options Are Wrong:
Each listed statement is one of the required assumptions; none is incorrect when viewed within the simplified 1D framework.

Common Pitfalls:
Applying the model to heavily overconsolidated clays or structured soils without judgment; ignoring secondary compression which the basic theory does not capture explicitly.

Final Answer:
All the above