WEEK 7

Compression Behaviour of Soils

10. Compression behaviour of soils

10-1. Compression in a broader sense

Compression of soil comprises the volume

reduction due to compression of constituent

materials (soil particles, pore water, pore

air, etc.) and consolidation (emigration of

pore water). In this section, we consider

only that due to consolidation. The under-

lying assumption is that the soil in

consideration is well saturated to have

very low undrained compressibility.

It is important to remember that, in soil mechanics at least, the term “compression” is

often used in a broad sense, applied to any stress path which includes increases in p’

(see the diagram). The relevance of different compression modes to practice is well

illustrated in the example of an embankment construction.

q

p′

(Pure shear)

Isotropic compression

K0-compression

Triaxial compression

In this section, we limit our focus on K0- and isotropic compression, as these are

conventionally simulated in laboratory as ‘consolidation tests’. The main objective of the

section is to understand relationships between the compressive stress and soils’ volume

changes and how they are affected by various factors.

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K0-compression

(Ohta, 2009)

Compression with

small lateral strain

allowed

Compression with

large lateral strain

allowed

Along the centre line:

10-2. Test apparatus

(i) K0-consolidation: Oedometer

An oedometer consists of a confining ring

housing a tested soil sample and a top cap

with a porous stone through which pore water

can escape. The vertical load may be applied

by dead weights, pneumatic pressure,

motor, etc.

As we have studied in Week 1, only the

vertical stress is known in an oedometer.

For the horizontal directions, we only know

that the normal strains are zero. The horizontal

stresses are expressed as K0σv’. Knowing a K0value is a big issue in soil mechanics.

There are two ways of applying

vertical loads:

(a) (Conventional) step loading

This is the simpler, classical, standard

method. Vertical loads are increased in

steps by, for example, adding dead weights.

(Potts and Zdravkovic, 2001)

vσ ′ (Increase)

steps by, for example, adding dead weights.

(b) CRS (Constant Rate of Strain) loading

The vertical strain is increased at a constant

rate by means of a powerful motor.

By measuring pore water pressure at the same

time, the e – log p’ relationship is obtained

continuously.

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vh K σσ ′=′ 0

(Increase) (Increase)

vh K σσ ′=′ 0

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1 10 100 1000 10000

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1 10 100 1000 10000

e

vσ ′ [kPa] [kPa]

Step loading CRS loading

vσ ′

(ii) Isotropic consolidation

Although isotropic consolidation is notionally

simpler than K0-consolidation, performing tests

no easier. It requires high pressure, and factors

such as membrane penetration need to be

considered.

In this week’s lecture, the compression curves

shown are all obtained for K0-conditions,

unless specified otherwise.

10-3. Sedimentation and normal consolidation of clayey soils

(i) Sedimentation Compression Curve

If soil is deposited uniformly in layers, it undergoes K0-consolidation due to overburdens

from subsequently deposited soil. So if the soil is normally consolidated (no removal of

overlying layers in the past), a relationship between in-situ e and in-situ log p’ over a soil

layer should be identical to the e - log p’ relationship obtained from oedometer tests of slurry

in laboratory. But usually it isn’t. The in-situ relationship, the Sedimentation Compression

hv σσ ′=′(Increase)

hv σσ ′=′(Increase)

hv σσ ′=′(Increase)

in laboratory. But usually it isn’t. The in-situ relationship, the Sedimentation Compression

Curve (SCC: Skempton, 1970) comes above the laboratory K0-Normal Compression Line

(K0-NCL) (Burland, 1990; Chandler, 2010). Let us have some more look.

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e

vσ ′log

Sedimentation Compression Curves of

natural clayey soils (Skempton, 1970;

reproduced from Chandler, 2010)

(ii) Intrinsic behaviour and void index

Intrinsic behaviour and void index are concepts put forward by Burland (1990).

Intrinsic behaviour:

Behaviour of reconstituted soil, consolidated from slurry prepared at least from the water

content of 1.0~1.5 times the liquid limit (wL), without ever being air- or oven-dried.

Examples of Intrinsic Compression Lines (ICL)

(Burland, 1990; reproduced from Chandler, 2010)

e – log p’ Iv – log p’

In the above diagram, the ICLs for soils with higher wL comes above those for lower wL.

Because all the ICLs are essentially just a line, they can be bundled as a single relationship

by normalisation using the void index, Iv.

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(Burland, 1990; reproduced from Chandler, 2010)

*

1000

*

100

*

100

ee

eeIv −

−= e

vσ ′log100 kPa 1000 kPa

Iv = 0 (Soil A)

Iv = 0 (Soil B)

Iv = -1 (Soil A)

Iv = -1 (Soil B)

By re-plotting the Sedimentation

Compression Curves in the Iv – log σv’ form,the relative positions of the SCL (Sedimenta-

tion Compression Line: A line showing an

average of SCCs of many soils) with regard

to the ICL are confirmed to be higher for

many different soils.

What if soils are sedimented in a column,

in laboratory, the artificial SCC is still

different from the natural SCC. The

difference in time scales seems to matter,

leading to development of natural structure

in soil.

(Reproduced from Chandler, 2010)

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(Stallebrass et al., 2007;

Reproduced from Chandler, 2010)

(Locat & Lefebvre, 1982; Reproduced

from Leroueil & Vaughan, 1990)

10-4. Normal compression of sandy soils

The compression characteristics of sandy soils are less intensively studied than those of

clayey soils. For one thing, the amount of volumetric strain in sand involved in usual

engineering scales is not as large as that in clay. However, significant compression is

expected locally where large stress concentration is likely occur; for example, at pile tips.

An important difference in compression

characteristics between clay and sand is

that, for sand, the starting point of the

compression curves are not unique.

Without loading, you can prepare dense

and loose specimens. This is not true

(at least in realistic situations) with clay.

Note the following:

- Dense sand behaves as if over-

consolidated.

- The apparent yield stress is very high,

even if sand was not actually pre-loaded.

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(McDowell, 2002; Reproduced from

Golightly, 1990)

Dogs Bay Sand (carbonate)

(Coop, 1990)

Ham River Sand (quartz)

(Coop & Lee, 1992)

10-5. Over-consolidation

Over-consolidation allows soils denser states for a given effective stress level. We have

studied that over-consolidation leads to ‘apparent’ cohesion in soils, as represented by the

Hvorslev surface.

q

p′0p′

“Hvorslev”

surface

Apparent

cohesion

Tension

cut-off: q/p’ = 3

p′log

e

In K0-conditions, over-consolidation (or unloading) usually leads to a non-linear effective

stress path. As a result, K0-over-consolidated soil has high K0 values, sometimes in excess

of 1.0.

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hv σσ ′−′

3

2 hvpσσ ′+′

=′hσ ′

vσ ′

In passing, the equations proposed by Mayne and Kulhawy (1982) for expressing the

unloading and reloading K0 values are introduced. These are empirical equations, but

sometimes useful in interpreting in-situ data or planning laboratory tests.

K0-normal compression:

hv σσ ′−′

3

2 hvpσσ ′+′

=′hσ ′

vσ ′

K0-reloading

φ ′−= sin1K (Jaky, 1944)

K0-unloading:

(Mayne and Kulhawy, 1982)

K0-reloading:

(Mayne and Kulhawy, 1982)

Note that OCR refers to the over-consolidation ratio, defined as

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φ ′−= sin10NCK

'sin

00

φOCRKK NC=

−+=

−max

'sin1

max

00 14

3

OCR

OCR

OCR

OCRKK NC φ

v

vcOCRσσ′′

=Maximum effective vertical consolidation stress in the past

Current effective vertical consolidation stress

Example: London Clay

The London Clay is a very heavily over-consolidated clay. Note the K0 values estimated in-

situ are generally in excess of 1.0. Compare them with those for the (probably) normally-

consolidated Bothkennar Clay. Because over-consolidation leads to smaller void ratio, e,

the water content, w, is also very small. The water content can be as small as the plastic

limit, wL, and partly as a result, cracks called ‘fissures’ can develop.

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K0 profiles of London Clay at Heathrow Terminal

5 construction site (Hight et al., 2007)

Fissures in London Clay

(Hight et al., 2007) Friends and I at Heathrow T5 site

(when I was 24 years old!)

K0 profiles of Bothkennar Clay

(Nash et al., 1992)

10-6. Development of natural structure

(i) Clays

There is a feature in compression characteristics that is very commonly seen in natural

clays, whether normally consolidated or over-consolidated; the effective yield stress σ’vy is larger than the effective maximum consolidation stress σ’vc expected from the SSC or geological evidences.

vI

vσ ′log vσ ′logvcσ ′ vyσ ′ vyσ ′

ICL

SCL or SCC

vI

vcσ ′

vcvy σσ ′≈′vcvy σσ ′>′

This feature is believed to derive from

what is called a ‘natural structure’ in soils.

Mitchell (1976) defined ‘structure’ as

Structure = Fabric + Bonding

Once loaded beyond the yield

stress, the natural structure is destroyed

and the compression curve approaches

the ICL.

It is debatable if this effect has really

anything to do with actual bonding

(i.e. cementation). The true mechanism

of natural structure is not fully understood,

so the vague word ‘structure’ has come

to be used to describe anything that is not

seen in laboratory-prepared samples.

Now, let us take time to think what

practical implications this feature has.

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Example: Boom Clay (Chandler, 2010)

vcvy σσ ′≈′vcvy σσ ′>′

(ii) Sands

A similar feature of natural structure is also seen in sands. Coop and his co-workers have

performed many high-pressure compression tests to see the effect in uncemented, weakly

cemented and strongly cemented natural sands (including sandstones).

Cemented carbonate sand (Coop & Atkinson, 1993)

K0-compressionIsotropic compression

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Strongly cemented sand

(Cuccovillo & Coop, 1997)

Strongly cemented sand

(Cuccovillo & Coop, 1999)

References

Burland, J. B. (1990) “On the compressibility and shear strength of natural clays,”

Geotechnique 40(3) 329–378.

Chandler, R.J. (2010) “Stiff sedimentary clays: geological origins and engineering

properties,” Geotechnique 60(12) 891-902.

Coop, M.R. (1990) “The mechanics of uncemented carbonate sands,” Geotechnique 40(4)

607-626.

Coop, M. R. & Atkinson, J. H. (1993) “The mechanics of cemented carbonate sands,”

Geotechnique 43(1) 53-67.

Coop, M.R. and Lee, (1993) “The behaviour of granular soils at elevated stresses,”

Proceedings of Wroth Memorial Symposium: Predictive Soil Mechanics, Thomas Telford,

London, 86-198.

Cuccovillo, T. and Coop, M. R. (1997) “Yielding and prefailure behaviour of structured

sands,” Geotechnique 47(3) 491-508.

Cuccovillo, T. and Coop, M.R. (1999) “On the mechanics of structured sands,”

Geotechnique 49(6) 741-760.

Golightly, C.R. (1990) “Engineering properties of carbonate sands,” PhD Dissertation,

Bradford University.

Hight, D. W., Gasparre, A., Nishimura, S., Minh, N. A., Jardine, R. J. and Coop, M. R.

(2007) “Characteristics of the London Clay from the Terminal 5 site at Heathrow Airport,”

Geotechnique 57(1) 3–18.

Jaky, J. (1944) “The coefficient of earth pressure at rest,” J. of the Union of Hungarian

Engineers and Architects, 355-358 (in Hungarian).Engineers and Architects, 355-358 (in Hungarian).

Leroueil, S. and Vaughan, P.R. (1990) “The general and congruent effects of structure in

natural soils and weak rocks,” Geotechnique 40(3) 467-488.

Locat, J. and Lefebvre, G. (1985) “The compressibility and sensitivity of an artificially

sedimented clay soil: the Grande-Baleine marine clay, Quebec,” Marine Geotechnol. 6(1)

1-27.

Mayne, P.W. and Kulhawy, F.H. (1982): “K0-OCR relationships in soil,” Journal of

Geotechnical Engineering Division, ASCE, 108(GT6) 851-872.

McDowell, G. (2001) “On the yielding and plastic compression of sand,” Soils and

Foundations 42(1) 139-145.

Mitchell, J.K. (1976): “Fundamentals of soil behavior,” John Wiley & Sons, Inc.

Nash, D. F. T., Powell, J. J. M. & Lloyd, I. M. (1992) “Initial investigations of the soft clay

test site at Bothkennar,” Geotechnique 42(2) 163-181.

Ohta, H. (2009) “Settlement of embankments”, The Monthly Bulletin of Japanese

Geotechnical Society, 57(3) 46-53.

Potts, D.M. and Zdravkovic, L. (2001) “Finite element analysis in geotechnical engineering:

Application,” Thomas Telford, London.

Skempton, A.W. (1970) “The consolidation of clays by gravitational compaction,” Q. J.

Geol.

Soc. London 125, 373–412.

Stallebrass, S. E., Atkinson, J. H. and Masin, D. (2007) “Manufacture of samples of

overconsolidated clay by laboratory sedimentation,” Geotechnique 57(2) 249–253.

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