Back to Soil Mechanics |
Based on part of the GeotechniCAL
reference package by Prof. John Atkinson , City University, London |
Compression and swelling results from drained loading and the pore pressure remains constant. If saturated soil is loaded undrained there will be no volume change.
Back to Compression and swelling
rearrangement of grains | |
fracture and rearrangement of grains | |
distortion or bending of grains |
On unloading, grains will not unfracture or un-rearrange, so volume change on unloading and reloading (swelling and recompression) will be much less than volume change on first loading (compression).
In compression, soil behaviour is:
Back to Compression and swelling
Isotropic:
Equal stress in all directions. Applicable to triaxial test before
shearing.
p' = (s'a + 2s'r)
/ 3
= mean stress
ev = DV
/ Vo
= volumetric strain
One-dimensional:
Horizontal strains are zero. Applicable to oedometer test and in the
ground below wide foundations, embankments and excavations.
s'z = vertical stress
ev = DV
/ Vo
= DH / Ho
= De / (1+eo)
= volumetric strain
Back to Compression and swelling
p' = (s'a + 2s'r)
/ 3
= mean stress
V = Vo - DVw
= volume
ev = DV
/ Vo = Dv / vo
= volumetric strain
v = V / Vs
= specific volume
As the mean stress p' is raised and lowered there are volumetric strains and the specific volume changes.
p'o = initial mean stress
vo = initial specific volume
Note the paths of compression, swelling and re-loading.
Back to Isotropic compression and swelling
First loading
normal compression line
OAD on the graph
v = N - l ln p'
Unloading and reloading
swelling line
BC on the graph
v = vk - k ln p'
N, l and k are
soil parameters.
vk and p'y locate the particular swelling line.
p'y is referred to as the yield stress.
If the current stress and the history of loading/unloading are known,
the current specific volume can be calculated.
Back to Equations for isotropic compression
K' = dp' / dev
v = N - l ln p'
dv / v = - l dp' / vp'
Hence K' = vp' / l (or vp' / k )
Bulk modulus K' depends on v and p'. Both of these will change during
compression or swelling and so K' is not a soil constant.
Back to Equations for isotropic compression
Typical values | wL | Ip | l |
very high plasticity clay | 80 | 50 | 0.29 |
high plasticity clay | 60 | 34 | 0.20 |
intermediate plasticity clay | 42 | 23 | 0.14 |
low plasticity clay | 30 | 12 | 0.07 |
quartz sand | 0.15 | ||
carbonate sand | 0.34 |
For clays l »
Ip / 170.
k / l is relatively
large (e.g. 0.25 - 0.35) because clay particles can bend and distort.
For sands l is relatively large due
to particles crushing (but states only reach NCL at high pressure).
k / l is relatively
small (e.g. 0.1) because sand particles crush and rearrange during first
compression.
Back to Isotropic compression and swelling
(Soil cannot usually be at a state outside the normal compression line unless it is bonded or structured).
At a state A the overconsolidation ratio is
Rp = p'y / p'a
(on NCL Rp = 1.0 and soil is normally consolidated).
Note: p'y is the point of intersection of the swelling line
through A and the NCL. This is usually close to the maximum past stress.
Back to Isotropic compression and swelling
The state at A is given by any two of
va , p'a , Rp = p'y / p'a
All states with the same Rp fall on the lines parallel with the NCL.
ln Rp = ln ( p'y / p'a )
= ln p'y - ln p'a
Many features of soil behaviour, especially shear modulus and peak strength,
increase with increasing overconsolidation.
Back to Isotropic compression: state
Vibration or compaction
(relevant to sands)
or creep
(relevant to clays)
Change of state can occur directly from A to B. Note that the yield
stress corresponding to B is larger than the yield stress corresponding to A.
Back to Isotropic compression: state
wet side of critical
(W on the graph)
vw > vc at stress p'
water content ww is larger than critical wc
· loose
· normally consolidated
or lightly overconsolidated
· compress during drained shear
dry side of critical
(D on the graph)
vd < vc at stress p'
water content wd is smaller than critical wc
· dense
· heavily overconsolidated
· dilate during drained shear
Back to Isotropic compression: state
Equivalent specific volume
vl = va + l ln p'a
Equivalent pressure
ln p'e = ( N - va ) / l
Critical pressure
ln p'c = ( G - va
) / l
If A is on the wet side of critical
ve > G
p'a / p'c > 1
If A is on the dry side of critical
ve < G
p'a / p'c < 1
Back to Compression and swelling
s'z = vertical effective stress
H = height or thickness
vertical strain = volumetric strain
ev = DH
/ Ho = De / (1+eo)
where Ho, eo and s'o
are initial values.
As the vertical stress s'z is raised and lowered the top of the sample settles or heaves, or the layer contracts or expands.
Note that the compression-swelling-recompression curve is similar to
that for isotropic compression, but the axes used are (s'z,
e) rather than (p', v).
Back to One-dimensional compression and swelling
First loading:
normal compression line (NCL)
OAD on the graph
e = eN - Cc log s'z
Unloading and reloading:
swelling-recompression line (SRL)
BC on the graph
e = ek - Cs log s'z
· eN, Cc and Cs are soil parameters
· ek and s'y
locate a particular swelling line
If the current stress s'o and
the history of loading and unloading are known, the current void ratio
can be calculated. e.g.
eo = eN - Cc log s'y
+ Cs (s'y - s'o
)
Back to One-dimensional compression: equations
M' = Ds'z / Dev
or
E'o = Ds'z / Dez
(since eh = 0)
The reciprocal of stiffness is compressibility. The one-dimensional coefficient of compressibility is the slope of the strain/stress curve:
mv = De / (Ds'z
(1+e))
= 1 / E'o
E'o and mv apply for the normal compression line
and for swelling and recompression lines, and depend on the current state,
on the history and on the increment of loading, so they are not soil constants.
Since mv varies with s'z,
its value is often quoted for s'z
= 100kPa.
Back to One-dimensional compression and swelling
Soil cannot usually be at a state outside the normal compression line unless it is bonded or structured.
At a state A the overconsolidation ratio is
Ro = s'y / s'a
(on NCL Ro = 1.0 and soil is normally consolidated).
Note: s'y is the point of intersection
of the swelling line through A and the NCL. This is usually, but not always,
close to the maximum past stress (see change of state).
Back to One-dimensional compression and swelling
The ratio Ko = s'h / s'z is known as the coefficient of earth pressure at rest.
Ko depends on
· the type of soil
· the overconsolidation ratio (Ro)
· the loading or unloading cycle
Approximations
normally consolidated soils:
Konc » 1 - sinf'c
overconsolidated soils:
Ko » Konc ÖRo
Back to One-dimensional compression and swelling
The state at A is given by any two of
ea , s'a , Ro
= s'y / s'a
All states with the same Ro fall on the lines parallel with the NCL.
log Ro = log ( s'y
/ s'a )
= log s'y - log s'a
Many features of soil behaviour, especially shear modulus and peak strength,
increase with increasing overconsolidation.
Back to One-dimensional compression: state
Vibration or compaction
(relevant to sands)
or creep:
(relevant to clays)
Change of state can occur directly from A to B. Note that the yield
stress corresponding to B is larger than the yield stress corresponding
to A.
Back to One-dimensional compression: state
wet side of critical
(W on the graph)
ew > ec at stress s'
water content ww is larger than critical wc
· loose
· normally consolidated
or lightly overconsolidated
· compress during drained shear
dry side of critical
(D on the graph)
ed < ec at stress s'
water content wd is smaller than critical wc
· dense
· heavily overconsolidated
· dilate during drained shear
Back to One-dimensional compression: state
Equivalent void ratio
el = ea + Cc log s'a
Equivalent stress
log s'e = ( eN - ea
) / Cc
Critical stress
log s'c = ( eG - ea
) / Cc
If A is on the wet side of critical
el > eG
s'a / s'c
> 1
If A is on the dry side of critical
el < eG
s'a / s'c
< 1
Back to Compression and swelling
A lightly overconsolidated soil has a state which lies above
the CSL.
A heavily overconsolidated soil has a state which lies below
the CSL.
States lying above the CSL are said to be on the wet side
of critical.
States lying below the CSL are said to be on the dry side
of critical.
In the diagrams: va > vb, and yet since the stress at B is greater, state B is on the wet side of critical, while state A is on the dry side of critical.
Back to Compression and swelling
A lightly overconsolidated soil has a state which lies
above
the CSL.
A heavily overconsolidated soil has a state which lies
below
the CSL.
States lying above the CSL are said to be on the wet side
of critical.
States lying below the CSL are said to be on the dry side
of critical.
In the diagrams: va > vb, and yet since the stress
at B is greater, state B is on the wet side of critical, while state A
is on the dry side of critical.
Back to Wet and dry states
Stress state parameter
Ss = pa' / pc'
ln Ss = ln pa' - ln pc'
Volume state parameter
Sv = va - vc
The state parameters are related:
Sv = ln Ss
Normally consolidated state:
Sv = l ln Ss = 0
States on the wet side of critical:
Sv and ln Ss are positive
States on the dry side of critical:
Sv and ln Ss are negative