   Chapter 11, Problem 11.18P Principles of Geotechnical Enginee...

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

Solutions

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

(a)

To determine

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

Explanation

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.

Calculation:

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

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

Δe=e1e2

Substitute 1.12 for e1 and 0.98 for e2.

Δe=1.120.98=0.14

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

Δσ=σ2σ1

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

Δσ=1.50.75=0.75ton/ft2

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

eav=e1+e22

Substitute 1.12 for e1 and 0.98 for e2.

eav=1.12+0.982=2.102=1.05

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

av=ΔeΔσ

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

av=0.140.75=0.187ft2/ton

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

mv=av1+eav

Substitute 0

(b)

To determine

Calculate the consolidation settlement at 70% consolidation.

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