Geotechnical Engineering

DHARM

222 GEOTECHNICAL ENGINEERING

to diminish, the spring starts getting compressed as the piston descends consequent to expul-

sion of pore water. It is just the beginning of transient flow, simulating the phenomenon of

consolidation. The openness of the valve is analogous to the permeability of soil.

Referring to Fig. 7.19 (d), flow has occurred to the extent of dissipating 50% of the

excess pore pressure. The pore water pressure at this instant is half the initial value, i.e.,

1

2

(δP/A). This causes a corresponding increase in the stress in the spring of

1

2

(δP/A), the total

stress remaining constant at [(P/A) + (δP/A)]. This stage refers to that of “50% consolidation”.
Referring to Fig. 7.19 (e), the final equilibrium condition is reached when the transient
flow situation ceases to exist, consequent to the complete dissipation of the pore water pres-
sure. The spring compresses to a final height Hf < Hi, carrying the total stress of (P + δP)/A, all
by itself, since the excess pore water pressure has been reduced to zero, the pressure in it
having equalled the atmospheric. The system has reached the equilibrium condition under the
load (P + δP). This represents “100% consolidation” under the applied load or stress increment.
We may say that the “soil” has been consolidated to an effective stress of (P + δP)/A.
In this mechanistic model, the compressible soil skeleton is characterised by the spring

σ =

P

A

u = 0

σ=P

A

σ=+P δ

A

P

A

u = 0 +

δP

A

σ=P+

A

0

σ=+P δ

A

P

A

u = 0 +

δP

A

σ=P+

A

0

σ=+P δ

A

P

A

u = 0 + 21

δP

A

σ=+P δ

A

P

A

1

2

σ=+P δ

A

P

A

u = 0

σ=+P δ

A

P

A

Equilibrium under

load P

Equilibrium under

load P + δP

Beginning of tran-

sient flow; excess u

just starts to re-

duce and σ just

starts to increase.

t = 0, 0% consoli-

dation

Half-way of tran-

sient flow; 50% of

excess u dissi-

pated; σ increased

by^1

2

.δp

A

0 < t < tf

50% consolidation

End of transient

flow; excess u fully

dissipated; σ in-

creased to P

A

P

A

+δ

t = tf equilibrium

under load (P + δP)

100% consolidation

(a)(b)(c)(d)

Fig. 7.19 A mechanistic model for consolidation (adapted from Taylor, 1948)

Waterspring Hi

Piston

of area

A

P Valve

open

no

flow

Hi

P+ Pd

Valve

closed

Hi

P+ Pd

Valve

open

flow

just

starts

H+Hi f

P+ Pd

Valve

open

flow

occur

ring

2

Hf

P+ Pd

Valve

open

no

flow

(e)