Principles of Geotechnical Enginee...

9th Edition
Braja M. Das + 1 other
ISBN: 9781305970939



Principles of Geotechnical Enginee...

9th Edition
Braja M. Das + 1 other
ISBN: 9781305970939
Textbook Problem

A 18-ft thick clay layer in the field (drained on one side) is normally consolidated. When the pressure is increased from 0.75 ton/ft2 to 1.5 ton/ft2, the void ratio decreases from 1.12 to 0.98. The hydraulic conductivity, k, of the clay during the above loading range was found to be 4.3 × 10–7 cm/sec.

  1. a. How long (in days) will it take for the clay layer to reach 70% consolidation?
  2. b. What is the settlement at that time (that is, at 70% consolidation)?


To determine

Calculate the time taken to reach 70% consolidation for the clay layer.


Given information:

The thickness of the clay layer (H) is 18ft.

The degree of consolidation (U) is 70%.

The pressure (σ1) is 0.75ton/ft2.

The pressure (σ2) is 1.5ton/ft2.

The void ratio (e1) is 1.12.

The void ratio (e2) is 0.98.

The hydraulic conductivity of the clay (k) is 4.3×107cm/sec.


Consider the unit weight of water (γw) is 62.4lb/ft3.

  Calculate the change in void ratio (Δe) as shown below.


  Substitute 1.12 for e1 and 0.98 for e2.


  Calculate the change in pressure (Δσ) as shown below.


Substitute 0.75ton/ft2 for σ1 and 1.5ton/ft2 for σ2.


Calculate the average void ratio (eav) as shown below.


  Substitute 1.12 for e1 and 0.98 for e2.


Calculate the coefficient of compressibility (av) using the relation.


Substitute 0.14 for Δe and 0.75ton/ft2 for Δσ.


Calculate the coefficient of volume compressibility (mv) using the relation.


Substitute 0


To determine

Calculate the consolidation settlement at 70% consolidation.

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