Geotechnical Engineering

Consolidation

Primary consolidation settlement, the compression index, time factor and coefficient of consolidation — predicting how clays settle and how long it takes.

PART 1

Topic Breakdown & Traps

The Engineering Principle

Saturated clays settle slowly as excess pore water is squeezed out — primary consolidation. The magnitude depends on the compression index

C_{c}

and the stress increment (on a semi-log

e

–

lo g σ^{'}

plot); the rate is governed by Terzaghi's 1-D theory through the dimensionless time factor

T_{v}

and the coefficient of consolidation

c_{v}

. The drainage path

H

is the full layer thickness for single drainage but half for double drainage.

The Core Formula Matrix

Settlement:

S_{c} = \frac{C _{c} H}{1 + e _{0}} lo g_{10} \frac{σ _{0}^{'} + Δ σ}{σ _{0}^{'}}

Compression index (Terzaghi–Peck, undisturbed):

C_{c} = 0.009 (LL - 10)

Time factor:

T_{v} = \frac{c _{v} t}{H ^{2}}

;

U = 50% \Rightarrow T_{v} = 0.197

U = 90% \Rightarrow T_{v} = 0.848

Coefficient of consolidation:

c_{v} = \frac{T _{v} H ^{2}}{t}

The ‘IIT Traps’

⚠
Drainage path. For a clay layer drained top and bottom, $H$ = half the thickness — squaring the wrong $H$ quarters the time.
⚠
Logarithm base. The settlement equation uses $lo g_{10}$ , not natural log.
⚠
** $T_{v}$ values.** $0.197$ for $50%$ and $0.848$ for $90%$ are standard recall — don't interpolate linearly.

📚 Standard references

Basic and Applied Soil Mechanics — Gopal Ranjan & A.S.R. Rao · Consolidation

PART 2

Progressive 3-Tier Question Suite

Q1BASIC1 Mark · NAT

A normally-consolidated clay has liquid limit

40%

. By the Terzaghi–Peck relation, its compression index

C_{c}

is _____.

Q2MEDIUM2 Marks · NAT

3 m

thick clay layer (

C_{c} = 0.25

e_{0} = 0.8

) has its effective stress raised from

100

200 kPa

. The primary consolidation settlement is _____ mm.

Q3HARD2 Marks · NAT

4 m

clay layer, drained on both faces, reaches

50%

consolidation in

1.5 years

. Its coefficient of consolidation is _____ m²/yr.