This document discusses consolidation properties and prefabricated vertical drains. It begins by outlining Terzaghi's theory of one-dimensional consolidation, including the assumptions, equations describing pore water flow and changes in void ratio over time. It then discusses how consolidation affects drained and undrained conditions. Prefabricated vertical drains are introduced as a way to accelerate consolidation settlement by improving drainage, shown in a settlement versus time graph comparing performance with and without PVDs.

1. CONSOLIDATION &
DRAINAGE PROPERTIES
Submitted to
Professor Myoung Soo
Won
By Sanchari Halder

2. CONTENTS
 Time Rate of Consolidation
 Effect of Consolidation
 Prefabricated Vertical Drains (PVD)

3. Time Rate of Consolidation
Terzaghi (1925) proposed the first theory to consider the rate of
one-dimensional consolidation for saturated clay soils. The
mathematical derivations are based on the following six
assumptions:
1. The clay–water system is homogeneous.
2. Saturation is complete.
3. Compressibility of water is negligible.
4. Compressibility of soil grains is negligible (but soil grains
rearrange).
5. The flow of water is in one direction only (that is, in the direction
of compression).

4. Figure 1(a) shows a layer of clay of thickness 2Hdr (Note: Hdr
length of maximum drainage path) that is located between two
highly permeable sand layers.
If the clay layer is subjected to an increased pressure of Δσ,
the pore water pressure at any point A in the clay layer will
increase. For one-dimensional consolidation, water will be
squeezed out in the vertical direction toward the sand layer.
Figure 1(a): Clay layer Undergoing
consolidation;

5. Figure 1(b) shows the flow of water through a prismatic element at A. For the soil element shown,
Rate of outflow of water – Rate of inflow of water = Rate of volume change
……….(1)
……….(2)
1 & 2
……….(3)

6. During consolidation, the rate of change in the volume of the soil element is equal to the
rate of change in the volume of voids. Thus,
But (assuming that soil solids are incompressible)
an
d
…….(4)
Substitution for and Vs in Eq. (4) yields, ……… (5)
Where e0 initial void ratio.
Combining Eqs. (3) and (5)
gives,
……… (6)

7. The change in the void ratio is caused by the increase of effective stress (i.e., a
decrease of excess pore water pressure). Assuming that they are related linearly, we
have
………(7)
Combining Eqs. (6) and (7)
gives,
Where, mv = coefficient of volume compressibility =
Or, Where, cv = coefficient of
consolidation =
Thus,
…(8)

8. Eq. (8) is the basic differential equation of Terzaghi’s consolidation
theory and
can be solved with the following boundary conditions:
The solution yields, …..(9)
The time factor is a non dimensional number. Because consolidation progresses by the
dissipation of excess pore water pressure, the degree of consolidation at a distance z at
any time t is
where, uz= excess pore water pressure at time
t.
…….. (10)

9. Equations (9) and (10) c
can be combined to obtain the degree of consolidation
at any depth z. This is shown in Figure 2.
The average degree of consolidation for the entire
depth of the clay layer at any time t can be written
from Eq. (10) as
Figure2: Variation of Uz
withSubstitution of the expression for excess pore water pressure
uz given in Eq. (9) into Eq. (11) gives
……. (11)

10. The variation in the average degree of
consolidation with the non dimensional
time factor Tv , is given in Figure 3, which
represents the case where u0 is the same
for the entire depth of the consolidating
layer.
The values of the time factor and their
corresponding average degrees of
consolidation for the case presented in
Figure 3 may also be approximated by the
following simple relationship:
Figure
3:
Sivaram and Swamee (1977) gave the
following equation for U varying from 0 to
100%:

11. Effect of Consolidation:
In coarse soils (sands and gravels) any volume change resulting from a change in loading
occurs immediately; increases in pore pressures are dissipated rapidly due to high
permeability. This is called drained loading.
In fine soils (silts and clays) - with low permeability - the soil is undrained as the load is
applied. Slow seepage occurs and the excess pore pressures dissipate slowly.

12. Consolidation Effects:
After consolidation (Drained
condition)
Road
Embankment
Settlement occurs when the weight of a structure or
newly-placed fill soils compress lower, weak soft or
clayey soils. The applied load forces water out of the
clay soils, allowing the individual soil particles to
become more densely spaced.

13. Settlement Vs Time Graph
Settleme
nt
Tim
e
Consolidat
ion
Settlement
Initial
Settleme
nt Final
Settleme
nt

14. Settlement Properties for Road
Embankment:
When thin soil layers covering a large area are loaded vertically, the
compression can be assumed to be one‐dimensional.

15. Settlement Properties of Road Embankment
for using GEOSYNTHETICS:
Pavement structures commonly fall into two main, namely, flexible and rigid pavements. Such
structures just as other structures are susceptible to different type categories of distresses. In
order to minimize the deterioration of pavements, GEOSYNTHETIC reinforcement is one of the
techniques adopted to improve their performance.
Unpaved Road Design Model
Paved Road Design Model

16. The addition of a geosynthetic as a reinforcement layer within a flexible pavement section
allows the pavement to take on a larger load carrying capacity without increased surface
deformation. Utilizing a geosynthetic under the aggregate base layer of a pavement section
increases the stability of the layer.

17. Settlement Vs Time Graph for Road
Embankment
Settleme
nt
Time
With
Geosyntheticsc
Without
Geosyntheticsc
With
Geosyntheticsc
Without
Geosyntheticsc

18. Prefabricated Vertical Drains (PVD)
The vertical drain system has been used since 1930 to accelerate the
consolidation settlement process, induced by the pre-loading of normally
consolidated low-permeability soil.

19. Settlement Vs Time Graph for using PVD:

20. Thank You All….