Time for 50% consolidation in a saturated clay layer with added drainage A saturated clay stratum drains at both the top and bottom and requires 16 years to reach 50% consolidation under load. If an additional permeable drainage layer is introduced at the mid-depth of the stratum, the time to reach 50% consolidation will be:

Introduction / Context:
Primary consolidation settlement in clays is governed by dissipation of excess pore water pressure. For a given degree of consolidation, the time required depends on the drainage path length. Adding drainage boundaries (e.g., sand drains or a permeable layer) shortens the path and accelerates consolidation.

Given Data / Assumptions:

• Originally, the clay layer drains from both its top and bottom surfaces.
• Time for 50% consolidation (U = 50%) in the original condition = 16 years.
• An additional drainage layer is introduced at the mid-depth (center) of the stratum.
• Coefficient of consolidation and load remain unchanged.

Concept / Approach:
For one-dimensional consolidation, time t for a given U is proportional to the square of the maximum drainage path Hdr: t ∝ Hdr^2. Initially, with double drainage at top and bottom, Hdr = H/2. After adding a drainage layer at mid-depth, each half-thickness H/2 drains to both sides, so the maximum Hdr becomes H/4.

Step-by-Step Solution:
1) Original path: Hdr,1 = H/2 → t1 = 16 years.2) New path with mid-drain: Hdr,2 = H/4.3) Time ratio: t2/t1 = (Hdr,2/Hdr,1)^2 = ( (H/4) / (H/2) )^2 = (1/2)^2 = 1/4.4) Hence t2 = 16 * 1/4 = 4 years.

Verification / Alternative check:
Using the time factor relation Tv = C_v * t / Hdr^2 for the same degree of consolidation shows that reducing Hdr by half reduces time by a factor of four.

Why Other Options Are Wrong:
2 years assumes a fourfold reduction beyond what is implied; 8 years corresponds to halving time only; 16 years ignores the benefit of the added drain.

Common Pitfalls:
Mixing total layer thickness with drainage path; forgetting that double drainage halves Hdr; assuming coefficient of consolidation changes with drainage arrangement.

Final Answer:
4 years