Primary consolidation – factors influencing time to reach a given degree of consolidation: Which statements about consolidation time are correct?

Introduction / Context:
Predicting settlement rate requires understanding what controls the time for primary consolidation. Terzaghi’s theory relates time, permeability, compressibility, and drainage path length through the coefficient of consolidation cv and the time factor Tv.

Given Data / Assumptions:

• One-dimensional consolidation; constant cv for the stress range considered.
• Degree of consolidation U is the target (e.g., 90%).
• Double or single drainage boundary conditions define drainage path length Hdr.

Concept / Approach:
The time to reach a given U is t = Tv * Hdr^2 / cv, with cv = k / (mv * gamma_w). Thus t increases when mv increases (more compressible) or when Hdr increases (thicker layer), and decreases when k increases. For a specified U, Tv is a constant, so t is independent of the magnitude of the load increment itself (provided cv is unchanged in that range).

Step-by-Step Solution:

Verification / Alternative check:
Oedometer curves and theoretical solutions for different Hdr and k verify the trends; dimensionally, doubling Hdr quadruples t.

Why Other Options Are Wrong:

• Each statement matches Terzaghi’s formulation; excluding any would be incomplete.

Common Pitfalls:
Forgetting that cv may vary with stress level; confusing total time to final settlement (which includes secondary compression) with primary consolidation time only.

Final Answer:
All of the above