Primary consolidation – factors influencing time to reach a given degree of consolidation: Which statements about consolidation time are correct?
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ATime increases with increasing compressibility (higher mv → lower cv)
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BTime decreases with increasing permeability (higher k → higher cv)
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CTime increases rapidly as the drainage path length (size of soil mass) increases
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DTime is independent of the magnitude of the applied stress change (for primary consolidation at a given degree U)
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EAll of the above
Answer
Correct Answer: All of the above
Explanation
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:
Relate t to cv and Hdr: t ∝ Hdr^2 / cv.Express cv in terms of k and mv: cv ∝ k / mv.Infer trends for each parameter (Options A–C).Recognize load magnitude independence at constant cv (Option D).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