Civl2210 2008 Notes

Compressibility
Golder Geomechanics Centre
Permeability
10/9/2008
Topics
`
Soil classification
Soil phase (solids/water/air) relationships

Principle of effective stress
`
`
`
Soil strength testing and theories

Soil consolidation testing and settlement theories
Failure conditions in soils
Clay mineralogy
Stren
ngth
CIVL2210 Fundamentals of Soil

Mechanics
Pore water pressure

Seepage through soils
L1: Introductory slide show

L1: Soil classification
L2: Soil phase

relationships
L3: Principle of effective stress

L4: Pore water pressure
T1: Definitions and

classification
L5: Seepage through soils
T2: Pore pressure &

effective stress
5: Seepage tthrough
oug so
soilss
L5:
T3:
3: Darcys
a cy s Law
aw
L5: Seepage through soils
T4: Seepage
L6: Strength testing and theories T4: Seepage
L6: Strength testing and theories T5: Shear strength
L7: Strength testing and theories T5: Shear strength
L7: Consolidation testing and

theories
T6: Consolidation
10
L7: Consolidation testing and

theories
T6: Consolidation
P1:Visual
classification &
P2:Atterberg limits
TUTORIALS
` From 2:00 to 3:50 pm on Thursdays in 42-216
PRACTICALS
` From 2:00 to 4:00 pm on Mondays, Tuesdays, Wednesdays and
Fridays in 48C-SOILS LAB
ASSESSMENT
` End of semester (multiple choice) exam:
` Tutorials:
` Completion of Practicals:
Week Lectures
Tutorials
Practicals
MID-SEMESTER BREAK
11
L8: Failure conditions in soil

masses
Practice Exam
12
L9: Clay mineralogy
T7: Lateral earth

pressures
13
Revision
P5: Unconfined
compression and
vane shear &
P6: Consolidation
Revision
EXAMINATION PERIOD
P5: Unconfined
compression &
P6: Consolidation
Compressibility
LECTURES
` From 10:00 to 11:50 am on Tuesdays in 63-348
Lecture/Tutorial/Practical Schedule
P3: Laboratory
compaction &
P4: Field density and
CBR
Schedule
`
Permeability
Stren
ngth
Practicals
Permeability
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ngth
Permeability
Compressibility
Stren
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Tutorials
1 Soil Classification
`
1.1 Particle Size Distribution Analysis

` Particle size limits:
Boulders
> 200 mm
Cobbles
60-200 mm
Gravel
Stren
ngth
Week Lectures
Compressibility
Lecture/Tutorial/Practical Schedule
Compressibility
Permeability
Professor David Williams

Dr Dorival Pedroso
Sand
Silt
Clay
65%
20%
15%
2-60 mm
0.06-2 mm
0.002-0.06 mm
< 0.002 mm
Coarse-grained
g
Fine-grained
(cant see or feel particles)
Obtain distribution of sand size and coarser by sieving

Obtain distribution of silt and clay size by sedimentation (hydrometer),
or laser
1.2 Atterberg Limits

` Of material passing 0.425 mm
Semi-solid
SL
Plastic
Liquid
PL
LL
MOISTURE CONTENT, w
Shrinkage limit, SL:
w at which soil reaches its minimum volume

on air drying from LL
Plastic limit, PL:

Liquid limit, LL:
Plasticity index:
minimum w at which soils deforms plastically
No slaking
Some dispersion Class 2
No dispersion
Swelling Class 7
No swelling Class 8
I
Immerse
moistened
i t d remoulded
ld d 3 mm diameter
di
t soilil balls
b ll iin di
distilled
till d water
t in
i a beaker
b k
Dispersion Class 3
Compressibility
Slaking
Activity,
A=
w PL
IP
IL =
IP
% clay by mass
Low activity
Intermed. activity
High activity
Emerson Class Number of a soil to assess slakability and dispersion

particularly relevant to the weathering of mine wastes on exposure
No dispersion
No calcite or gypsum present
1 Soil Classification (cont.)

`
1.3 Unified Soil Classification

` A common notation for describing soils, from which engineering
properties, behaviour and use can be inferred (Lambe and Whitman,
1979):
Main Soil Types
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ngth
Compressibility
Liquidity index,
Immerse air-dried 2 mm to 4 mm dia. crumbs of soil in distilled water in a beaker
Stren
ngth
I P = LL PL
Complete dispersion Class 1
1.2 Atterberg Limits (cont.)
<1
= 1 2
> 4
minimum w at which soil flows
Permeability
Stren
ngth
SOIL
VOLUME
Solid
Compressibility
Permeability
Permeability
Stren
ngth
Compressibility
Permeability
10/9/2008
Prefix
Coarse-grained soils ( < 50 % passing 0.06 mm)

GRAVEL predominant
SAND predominant
Fine-grained soils ( > 50 % passing 0.06 mm)

Inorganic CLAY
Calcite or gypsum present Class 4
SILT
ORGANIC SOILS
Make up 1:5 soil/water suspension in a test tube and shake
Above A-line
Below A-line
C
M
O
Fibrous soils
Dispersion Class 5
PEAT (no suffix)
Flocculation Class 6
Pt
Permeability
Sub-division
Suffix
Coarse-grained soils with < 5 % passing 0.06 mm

Well-graded (spread of sizes)
Poorly-graded (uniform or gap-graded)
Coarse-grained soils with > 12 % passing 0.06 mm

Clay fines
Above A-line
Silt fines
Below A-line
Compressibility
Stren
ngth
Stren
ngth
Compressibility
Permeability
Determination of Emerson class number of a soil
Fine-grained soils
Low plasticity
LL < 50 %
High plasticity
LL > 50 %
Permeability

`
Compressibility
40
High plasticity
CH
Stren
ngth
30
20
Plasticityy Index
50
Dry strength and stickiness

Increase with increasing
Plasticity Index, and dilatancy
(permeability) decreases.
Low plasticity
CL
CL-ML
0
10
1.4 Engineering Use Chart

` Based on Unified Soil Classification
` Relates engineering parameters (strength, compressibility and
permeability when compacted, and workability) applied to dams,
canals, foundations and roads
` 1 = highly desirable, 14 = highly undesirable
` (Lambe and Whitman, 1979)
OH
or
MH
CL
10
Stren
ngth
Compressibility
60
Permeability
10/9/2008
OL
or
ML
ML
20
30
40
50
60
70
80
90
100
Permeability
1.5 Other Classification Systems

` Other classification systems include those directed towards specific
applications, such as road design and agriculture (Fang, 1990)
` There are classification systems based on specific engineering
properties, such as strength (for clays) or relative density (for sands)
WEIGHTS
VA
0
WW
Water
WS
Solids
VW
VS
Air
Void ratio:
e=
VV
VS
Porosity:
n=
VV
e
=
VT 1 + e
Relative density:
DR =
Moisture content:
w=
Degree of saturation: S =
Units
-
Permeability
2 Phase (solids/water/air) Relationships (cont.)
VV
VOLUMES
WEIGHTS
VA
0
WW
VW
VS
PROPORTIONS BY
VOLUME
WEIGHT
voids
VOLUMES
`
Stren
ngth
Stren
ngth
VA
PROPORTIONS BY
VOLUME
WEIGHT
Compressibility
2 Phase (solids/water/air) Relationships
Air
Solids
WS
Void ratio:
e=
VV
VS
Porosity:
n=
VV
e
=
VT 1 + e
Relative density:
DR =
WW
100
WS
Moisture content:
w=
VW
100
V A + VW
Degree of saturation: S =
emax e
emax emin
Water
Stren
ngth
Compressibility
Permeability
Stren
ngth
Compressibility
Compressibility
Permeability
Liquid Limit
w
1
Measurable? Typical values

No
3 ((slurry)
y) to 0.33
No
0.75 (slurry) to 0.33
Yes
30 to 65%
WW
100
WS
Yes
100 to 5%
VW
100
V A + VW
No
0 (dry) to 100%
emax e
emax emin
Permeability
Stren
ngth
Units
kN/m3
Total unit weight:
Unit weight of water: W = 9.81
kN/m3
Effective unit weight: ' = T W
kN/m3
Dry unit weight:
D =
=
Specific gravity:
G=
WS
VT
1+ w
Compressibility
WT
VT
1+ w
=
G W
1+ e
T =
Stren
ngth
Compressibility
Permeability
10/9/2008
kN/m3
=
Total unit weight:
Unit weight of water: W = 9.81 kN/m3
Yes
9.81 kN/m3
Effective unit weight: ' = T W
Yes
5 to 10 kN/m3
Dry unit weight:
G
W
1+ e
WS
VS W
Specific gravity:
Permeability
pAi
Pressure and stress

depend on Area
Compressibility
-F
Observed
area
dF
dA
G
W
1+ e
WS
VS W
3.1 Force, pressure, and stress (cont.)
There are at least x and y

components of stress (in 2D)
Ay = 0
A
Compressibility
Stren
ngth
uw
Ground
pV A =
AB
F
AA
<<
pV B =
F
AB
3 Principle of Effective Stress (cont.)
' = - uw
'
Grains
Air
'
AA
Ax
3 Principle of Effective Stress
Water
Pressure and stress are better related

with material mechanical changes
(damage, failure, stretching, ) than forces
Pressure and stress vary on Space
1.3 (coal) to 2.7

to 19.3 (gold)
pAii
Yes
Stren
ngth
dA 0
1+ w
Permeability
= lim
Compressibility
F
p=
A
Yes (if regular) 0.5 to 20 kN/m3
Stren
ngth
Permeability
Compressibility
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ngth
Internal
stress
Permeability
3.1 Force, pressure, and stress (review)

External
force
G=
WS
VT
G w = S e
3 Principle of Effective Stress
Internal
pressure
D =
=
G w = S e
Measurable? Typical values

WT
Yes (if regular) 15 to 20 kN/m3
VT
1+ w
=
G W
1+ e
T =
uw
Analogy
' = - uw
The total vertical stress V at a given depth in the soil profile is equal to
the weight of everything above that point, including the wet soil and
any surface water or surface loading
at A
VB = VA + SAT b
HB = ?
Permeability
Compressibility
In a water-saturated soil: ' = u w

where is the total stress (weight of everything above a particular point,
including water), uw is the pore water pressure
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ngth
uw
'=
In a dry soil:
Changes in lead to deformations and changes in strength the soil

grains and pore water are assumed to be incompressible
In a water-saturated soil, deformation on the application of stress is

directly related to the expulsion of pore water. Thus, related to
permeability (coupled phenomena)
'

`
Sand shear strength is proportional to :
= ' tan
where is the angle of internal friction of the sand.

`
Clay shear strength is given by: = cu or c '
is also proportional to , the constant of proportionality dependent

on the over-consolidation ratio ((OCR):
)
= constant (typically 0.25)

' NC
where NC is normally consolidated, OC is overconsolidated, and m is a
power, found experimentally to have a value of about 0.8:

(OCR )
' OC ' NC
at C
depth z

`
In soils of high permeability (sands and gravels), any excess u induced

by an applied stress generally dissipates instantaneously, with the
applied stress () transferring instantaneously to the soil skeleton ()
DRAINED BEHAVIOUR
Quick conditions or liquefaction are an exception. Here the rate of stress

application is more rapid than the rate of drainage possible, 0, and
seepage stresses exceed the strength of the soil
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ngth
SAT
Effective stress is taken by the soil skeleton

'
at B
VC = VA + SAT c
HC = ?
Stren
ngth
T
water table
In saturated soils of low permeability (clays), any applied stress is

initially taken as excess u. This dissipates with time and the water
(excess u) to the soil skeleton () UNDRAINED SHORT TERM AND
DRAINED LONG TERM BEHAVIOUR. Refer to water-bed analogy
(Lambe and Withman, 1979)
Permeability
VA = T a
HA = ?
Compressibility
Stren
ngth
Permeability
ground
4 Pore Water Pressure

`
4.1 Hydrostatic Pore Water Pressure

` Hydrostatic pore water pressure increases in proportion to the depth
below the water table:
PORE WATER PRESSURE, u
Water table
Stren
ngth
Compressibility
Permeability
Stren
ngth
4 Geostatic Stresses
Compressibility
Permeability
Hydromechanical
analogy for loadsharing and
consolidation
a) Physical example
b) Hydromechanical
analog
c) Load applied
with valve closed
d)) Piston moves as
water escapes
e) Equilibrium with
no further flow
f) Gradual transfer
of load
Compressibility
Compressibility
Permeability
10/9/2008
u = W zW
DEPTH, z
uw
Unsaturated
soil mechanics
Stren
ngth
uWA = 0
water table
Assumption
at A
uWB = W b
Stren
ngth
ground
Permeability
Hydrostatic pore water pressure uw increases in proportion to the depth

z below the water table: u W = W zW (w = 9.81 kN.m3)
4 Geostatic Stresses (cont.)

`
The effective vertical stress V at a given depth in the soil profile is the
difference between total stress and water pressure
Compressibility
Compressibility
Permeability
10/9/2008
V
ground
water table
at A
VB' = VB uW B
HB' K 0 VB'
at B
VA' = VA uW A
HA' K 0 VA'
at B
uWC = W c
3) The hydrostatic pore water pressure uW at a given depth in the soil

profile is equal to the height of the water table above that point
multiplied by the unit weight of water (9.81 kN.m3).
4) The effective vertical stress V at a given depth in the soil profile is

the difference between total stress and water pressure
Net evaporation
SILT
Net percolation
PORE WATER PRESSURE, u
CLAY
SAND
Stren
ngth
~1 m
Water table
Hydrostatic (No flow)

DEPTH, z
`
Permeability
Compressibility
Permeability
4.2 Pore water suction (cont.)
u = W zW
The magnitude of solute suction is a function of the total dissolved salt

concentration of the pore water. It can occur both above and below the
water table, and in an arid climate may well be of the order of 100 to
100 kPa for an expansive clay profile.
Compressibility
4.2 Pore water suction

` Pore water suction can occur in two forms:
` matric (or capillary) and;
` solute (or osmotic)
` Matric suction is readily incorporated within the effective stress
principle, and changes in matric suction will give rise to deformation
and changes in shear strength. By definition, matrix suction is zero at
and below the water table,
table and increases above the water table
` The magnitude of matric suction is a function of the soil pore size.
Sands are only capable of maintaining about 1 m height of capillary
rise above the water table. In clays, very high matrix suctions can
develop above the water table towards the ground surface. Silts are
intermediate between these extremes
' H = K 0 'V
4 Pore Water Pressure (cont.)
Compressibility
Permeability
'V = V uW

`
4.2 Pore Water Suction (cont.)

`
Changes in solute suction may give rise to deformation and changes

in shear strength. However, a change in solute suction would require
a dissolved salt differential to drive it, the solute suction would change
only slowly, and it is unlikely that the driving dissolved salt differential
would be maintained for a sufficiently long time. It is therefore
common practice to ignore solute suction-induced
suction induced deformation and
changes in shear strength.
Pore water suction is generally expressed in terms of pF units (a

logarithmic scale in which pF 3 100 kPa pressure, pF 4 1,000
kPa, and pF 5 10,000 kPa. In the seasonal suction profiles, the
lower bound line may be essentially solute suction, with the difference
between the two lines representing the seasonal variation of matrix
suction (Cameron and Walsh, 1984).
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2) The total vertical stress V due to wet soil is equal to its total unit
weight multiplied by the depth of soil above that point at that total unit
weight.
weight
= z
at C
depth z
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ngth
Summary:
` 1) The total vertical stress V at a given depth in the soil profile is
equal to the weight of everything above that point, including the wet
soil and any surface water or surface loading.
`
depth z
Compressibility
Permeability
VC' = V C uW C
HC' K 0 VC'
at C
Typical suction variations:
Effects of covers and trees on suction:
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`
Soil Water Characteristic (Moisture Retention) Curves:

40
MINING MOISTURE C
CONTENT (%)
Volume versus suction versus moisture content:
Compressibility
Permeability
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ngth
Compressibility
Permeability
Compressibility
Permeability
Compressibility
Permeability
10/9/2008
35
MMC @ AEV
Slope beyond AEV,
representing water storage
capacity and ease of dewatering
20
15
where q is the volumetric flow rate per unit time, k is the coefficient
of permeability (or hydraulic conductivity), i is the hydraulic gradient, A
is the flow cross-sectional area, and a sign
g applies since flow is in
the direction of decreasing head.
`
For fine grained soils, k may be characterised by:
Permeability
Compressibility
q = k .i. A
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ngth
Permeability
Compressibility
5.1 Saturated (or near-saturated) Seepage

` 5.1.1 Darcys law:
(S > 85%, which applies in many cases)
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ngth
Hysteresis between
drying and re-wetting
10
Residual MMC
5
Suction @ AEV
0
0.01
5 Seepage
Re-wetting curve
AEV
30
25
Drying curve
Near-saturated MMC
@ test density
0.1
"Oven-dry"
Residual suction
10
100
1000
SUCTION (kPa)
10000
100000 1000000
5 Seepage (cont.)
`
5.1.2 k of stratified soils (layers l2 , l2 ,..ln )

`
For vertical flow (perpendicular to the strata), q and A are constant:

k=
l1 + l2 + .. + ln
l1 / k1 + l2 / k 2 + .. + ln / k n
For horizontal flow (p

(parallel to the strata),
), i is constant:
k=
l1k1 + l2 k 2 + .. + ln k n
l1 + l2 + .. + ln
k = a.e b
where e is the void ratio, and a and b are constants determined by
oedometer or field testing.
`
Total head (h) = elevation head (z) + pressure head (u / w ) + velocity

head ( v 2 / 2 g 0 for laminar flow).
For 10 < k < 10

permeameter.
For k < 10 m/s (clays), use indirect methods such as an

oedometer test.
Typical values of
Partially saturated k is difficult to determine directly, since its

attempted measurement changes the degree of saturation. It may
be estimated indirectly via the suction/moisture content
characteristic of the soil, together with theory.
m/s (silts and clays), use a falling head
Permeability
5.2.1 Saturated permeability

tests (cont.)
5 Seepage (cont.)
`
5.2.3 Falling head permeameter (Head, 1982):
5.2.4 Indirect determination of k

`
For low permeability soils, k may be determined indirectly from the

results of oedometer or Rowe consolidometer tests:
k = c v .m v . w
Compressibility
5 Seepage (cont.)
`
5.3 Field Measurement of Permeability

` For coarse grained soils and fractured rock use pumping tests.
`
Unconfined flow (Cedergren, 1977):

k =
Stren
ngth
5 Seepage (cont.)
Permeability
Stren
ngth
Compressibility
5.2.2 Constant head permeameter (Head, 1982):
Stren
ngth
Permeability
Compressibility
Stren
ngth
k (Fang, 1990)
5 Seepage (cont.)
`
5 Seepage (cont.)
Compressibility
Compressibility
Permeability
Stren
ngth
5.2 Laboratory Permeability Testing

` 5.2.1 Saturated permeability testing
4
` For k > 10
m/s (clean sands and gravels), use a constant head
permeameter.
Permeability
Stren
ngth
5 Seepage (cont.)
Compressibility
Permeability
10/9/2008
l n ( r1 / r 2 )
2
2
h 2 h1
( r2 / r1 )
5.3 Field Measurement of Permeability (cont.)
Confined flow:
ln( r1 / r2 )
q
2 D h 2 h1
k =
where q is the volumetric flow rate pumped from the well, r1 and
are the radii from the well to the observation boreholes 1 and 2,
h1 and h2 are the total heads at the observation boreholes 1 and 2,
and
d D iis the
h thickness
hi k
off the
h confined
fi d aquifer.
if
Permeability
5 Seepage (cont.)
5 Seepage (cont.)
`
Compressibility
Compressibility
Permeability
10/9/2008
Stren
ngth
Stren
ngth
r2
5.4 Seepage Flow

` 5.4.1 1-D flow
` For upward vertical flow in sands, the quick condition v ' 0 is
given by:
w
icritical = saturated
1
w
` 5.4.2 2-D flow
` Assuming homogeneous and isotropic conditions within the
seepage zone, and both the soil particles and pore water to be
incompressible, the CONTINUITY EQUATION is given by:
For fine grained soils use a constant head test (infer k from the volume
of water required to maintain the head constant for a given geometry),
or a falling head test (infer k from the rate of fall of an elevated head in a
small diameter standpipe).
`
vz
vx
+
= 0
x
z
where vx and v z are the apparent (not actual) velocities
in x (horizontal) and z (vertical) directions, respectively.
In terms of total head h, the LAPLACE EQUATION is given by:
Stren
ngth
Permeability
5.4.2 2-D flow (cont.)

` The Laplace Equation may be solved by:
` Graphical means using FLOW NET
` ELECTRICAL ANALOGUE: the flow of water through soil, driven
by a head differential, being analogous to the flow of electrical
current through a conducting medium, driven by a voltage
differential.
` NUMERICAL TECHNIQUES:
` For anisotropic conditions, the STEADY STATE SEEPAGE
EQUATION is given by:
Compressibility
5 Seepage (cont.)
Stren
ngth
5 Seepage (cont.)
Compressibility
Permeability
h h
+
=0
x z
hx
h
+ kz z = 0
x
z
where hx and hz are the total heads in the x and z
directions, respectively, and k x and k z are the coefficients of
permeability in the x and z directions, respectively.
Compressibility
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ngth
5.5 Flow Nets (cont.)
Compressibility
Permeability
5 Seepage (cont.)
Stren
ngth
Permeability
kx
5.5 Flow Nets Rules

` Sets of flow lines (average trajectories of seepage) and equipotential
lines (loci of constant total head) may be drawn within a seepage
zone to form a FLOW NET of curvilinear squares.
` A permeable boundary is an equipotential line.
` An impermeable boundary is a flow line.
` Equipotential lines intersect a line of constant u (often u=0) at equal
drops in head:
` If the line of constant u is a phreatic line (and hence a flow line),
equipotentials will intersect it at right angles.
` If the line of constant u is a drain (and hence not a line flow),
intersections will not necessarily be at right angles.
` Examples of flow net construction (Cedergren, 1997).
5 Seepage (cont.)
`
Permeability
5 Seepage (cont.)
Stren
ngth
Permeability
Stren
ngth
5 Seepage (cont.)
`

` The flow through the seepage zone is given by:
M
q = k h
N
where h is the drop in total head across the seepage zone, M/N is
the flow net shape factor, M is the number of flow tubes and N is the
number of equipotential drops within the seepage zone.
` The velocity of flow varies throughout the seepage zone, the apparent
velocity increasing as the dimension of the flow net decreases.
` The
Th u within
ithi th
the seepage zone reduces
d
ffrom th
thatt att th
the side
id off the
th
seepage zone with the highest total head, according to the number of
equipotential drops to the point in question ( and rises from that at the
other side).
` Flow lines (and equipotential lines) are refracted on crossing an interface
between isotropic soils of different k:
5 Seepage (cont.)
`
Compressibility
Stren
ngth
5 Seepage (cont.)
Permeability
Stren
ngth
Compressibility
Compressibility
Permeability
5 Seepage (cont.)
Stren
ngth
Permeability
Compressibility
Stren
ngth
5 Seepage (cont.)
Compressibility
Compressibility
Permeability
10/9/2008
w1
k
= 1
w2
k2
where w1 and w 2 are the widths of the flow tubes in materials of k 1

and k 2 , respectively (refer to examples from Cedergren, 1977).
10
Permeability
5 Seepage (cont.)
Stren
ngth
Permeability
Stren
ngth
For anisotropic soils, flow nets may be used with a transformed scale
(refer to examples from Cedergren, 1977):
5 Seepage (cont.)
`
Stren
ngth
Stren
ngth
Compressibility
Compressibility
kz
x and
kx
5 Seepage (cont.)
Compressibility
Compressibility
Stren
ngth
M
kzkx
N
Stren
ngth
q = h
Permeability
Permeability
5 Seepage (cont.)
x' =
Permeability
5 Seepage (cont.)
Compressibility
Compressibility
Permeability
10/9/2008
5 Seepage (cont.)
`
5.6 Special Cases

` 5.6.1 Local effects of seepage stresses
` Quick conditions can occur in sands if seepage stresses render
v ' 0
This can be avoided by decreasing i (increase l using a cut-off
and/or decrease h by dewatering) and/or by increasing v ' by
surcharging.
` Seepage stresses can cause have in clays, and, in the extreme
may facilitate piping.
5.6.2 Flow through discontinuous rock
` The permeability of discontinuous rock depends on the spacing,
persistence, aperture, and filling of the joints, and on the stresses
applied across the joints.
` Limestone and other water-soluble rocks can develop solution
channels which enlarge with time, increasing seepage rates.
`
11
5.7.2 Suction/Moisture Content Characteristic (cont.)
Permeability
5.7 Unsaturated Seepage (cont.)

` 5.7.1 Partially saturated permeability (cont.)
5 Seepage (cont.)
`
Compressibility
Permeability
Stren
ngth
Compressibility
5.7.2 Suction/Moisture Content Characteristic (cont.)

` Curve D was obtained by slurrying the clay at a high moisture
content, partially destroying the structure of the clay, then drying it
from pF 0 to pF 7 (oven dry).
` Curves B and D represent the limiting cases.
` Curves A and D coincide above pF 4.8.
` Curves E and F show that cycling below pF 4.8 results in a series
of loops different for each maximum suction.
suction
` Curve G is unique to the clay, representing the critical state
obtained for the clay on disturbance at any moisture content or
suction. Both the liquid and plastic limits lie on curve G.

`
Soil Water Characteristic (Moisture Retention) Curves:

40
MINING MOISTURE C
CONTENT (%)
5 Seepage (cont.)
5 Seepage (cont.)
Stren
ngth
5.7.2 Suction/Moisture Content Characteristic:

` Different suction/moisture content characteristics are obtained,
depending on the path followed, and the disturbance to the structure
of the soil.
` This is demonstrated by data for London (heavy) clay obtained by
Croney and Coleman (1954), which has a liquid limit of 77%, plastic
limit of 27% and plasticity index of 50%.
` Curve A was obtained by drying the undisturbed clay from its
natural moisture content (pF close to 0). The undisturbed clay
remains saturated to a moisture content of 22% (pF of about 4).
Further reduction in moisture content (increase in pF) is
accompanied by little reduction in volume (as water is replaced by
air in the pores)
` Curve B was obtained by subsequent wetting up of the clay, and
demonstrates some irreversible structural change on oven-drying.
Re-drying follows curve C. Subsequent wetting and drying cycles
follow curves B and C.
Permeability
Stren
ngth
Compressibility
Permeability
5 Seepage (cont.)
Stren
ngth
Permeability
Compressibility
Stren
ngth
5.7 Unsaturated Seepage

` 5.7.1 Partially saturated permeability
` The water permeability of soils decreases dramatically (by up to
several orders of magnitude) as it desaturates, desaturation
causing pore water to retreat into ever tighter menisci at the
particle contacts. The menisci are associated with the development
of soil suction, providing the basis for estimating partially saturated
permeability from the suction/moisture content characteristic of the
soil, together with theory.
` The air permeability of soils increases even more dramatically as it
desaturates.
` Fredlund and Rahardjo (1993) reproduced coefficients of air and
water permeability versus gravimetric moisture content.
Compressibility
Stren
ngth
5 Seepage (cont.)
Compressibility
Permeability
10/9/2008
35
Re-wetting curve
AEV
30
25
Drying curve
Near-saturated MMC
@ test density
MMC @ AEV
Slope beyond AEV,
representing water storage
capacity and ease of dewatering
20
15
Hysteresis between
drying and re-wetting
10
Residual MMC
5
Suction @ AEV
0
0.01
0.1
"Oven-dry"
Residual suction
10
100
1000
SUCTION (kPa)
10000
100000 1000000
12
6.1 Strength Testing (cont.)

` 6.1.1 Direct shear test (cont.)
N
F
F

Compressibility
Permeability
Stren
ngth
6 Strength Testing and Theories (cont.)

displacement
surface of
shear
reaction
F
applied
force
soil specimen
surface of
sliding
start of test
Compressibility
5.7.3 Unsaturated seepage (cont.)

` Unsaturated seepage is highly channelised, but also involves
storage. Rather than being bounded by a phreatic line (as in
saturated seepage), it is bounded by a wetting-up line, below which
the medium is not saturated (for example, unimpeded water flow
compared with tailings water flow through a coarse reject bund; the
latter seepage rate is about an order of magnitude lower due to the
tailings filter cake which forms on the upstream side of the bund, and
this induces unsaturated seepage through the relatively free-draining
bund; Williams, 1992).
Permeability
6.1 Strength Testing

` 6.1.1 Direct shear test
` The shearbox was designed originally for measuring the friction
angle of recompacted sands.
` The shearbox can also be used to measure the undrained shear
strength of clays, but the triaxial test is usually more suitable for
this purpose.
` Consolidated-drained
Consolidated drained tests (for c ', ' ),
) and shear reversal tests
(for residual shear strength cR , R ) may also be carried out using
the shearbox.
` The soil is placed in a rigid metal box, square in plan (60,100, or
300 mm in dimension), consisting of two halves.
` The lower half of the box can slide relative to the upper half when a
shear force is applied, while a yoke applies a normal force.
` The soil is forced to shear at the interface between the two halves
of the box. During shearing, the shear stress, and shear and
normal displacements are measured (Head, 1982).
Stren
ngth
Stren
ngth
Permeability
Compressibility
Stren
ngth
Stren
ngth
6 Strength Testing and Theories
Compressibility
Permeability
Stren
ngth
5.7.3 Unsaturated seepage

` Surface evaporation, a surface cover, steady state infiltration, and
tress have different effects on the suction profile (Fredlund and
Rahardjo, 1993).
Permeability
5 Seepage (cont.)
Compressibility
5 Seepage (cont.)
Compressibility
Permeability
10/9/2008
length = breadth = L
during relative displacement
The effect of large shear displacement can be obtained in an ordinary

shearbox by reversing the shearbox after initial shearing and
reshearing, repeating this a number of times to achieve a steady
(residual) shear strength (Head, 1982).
The normal stress may be removed during reversal to avoid

destroying the shear plane formed on shearing.

`
movement
N
F
F
` The large shearbox is 300mm square, requiring a specimen about
150mm thick, and is suitable for particle sizes up to 37.5mm. Such
testing is relevant to the design of embankments or earth dams
incorporating gravel fill.
The shearbox can also be used for measuring the angle of friction
developed at the interface between a soil and other materials such
as steel, concrete or rock. This is achieved by placing a block of
the other material to fill the bottom half of the shearbox and forming
the soil in the upper half of the shearbox.
Application of shearbox test:

The test is best suited to situations in which slip on a predetermined shear plane occurs, eg. slope instability.
13
applied
torque
D

` 6.1.2 Vane shear test
` The four-bladed cruciform vane is pushed into
soft cohesive soil and then rotated.
Stren
ngth
The torque required to rotate the cylinder of soil

enclosing the vane is measured, from which the
undrained shear strength of the soil is
calculated.
Permeability
Compressibility
Permeability

F
` Limitations of shearbox test:
The soil is constrained to fail along a pre-determined shear
plane.
The distribution of stresses in shear zone is not uniform.
Principle stresses rotate during shear.
Drainage cannot be controlled, except by varying the rate of
shear.
Pore water pressures cannot be measured.
The maximum shear deformation is limited by the travel of the
apparatus.
The sample contact area decreases during shearing, requiring
an area correction, except for purely frictional soils.

`
Compressibility
Stren
ngth

F
` Advantages of shearbox test:
The test is relatively quick and simple.
Sample preparation is easy, particularly for sands.
The test can be used to determine residual strength and drained
strength parameters.
Large particle sizes can readily be tested in a large shearbox.
The test can be used to determine the angle of friction between
soil and other materials.

applied
torque
resisting
torque
Stren
ngth
Stren
ngth
Compressibility
Permeability
Compressibility
Permeability
10/9/2008
surface area
= DH
A repeat test immediately after remoulding the

soil by rapid rotation of the vane provides a
measure of the remoulded strength, and hence
sensitivity, of the soil (Head, 1982).
D
D

` Assuming a uniform distribution of stress is mobilised over the
cylindrical surface scribed by the vane, and that the stress
mobilised over the ends is zero at the centre rising to the same
value as that over the cylinder at the edge of the vane, the shear
strength sU may be calculated from the measured torque T using
D 2 H D3
T = sU
+
6
2
`
A vane height to diameter ratio of 2:1 generally applies, which

results in more than 90% of the resistance to rotation of the vane
coming from the vertical cylindrical surface scribed by the vane. As
a result any anisotropy can be ignored in the calculation, with the
vane providing an estimate of the shear strength acting on a
vertical plane.
Permeability
Compressibility
Stren
ngth
Stren
ngth
Compressibility
Permeability
vane blades
cylinder of soil rotated by vane

`

` 6.1.2 Vane shear test (cont.)
` Correlation between the vane shear strength and slope failures has
shown that the vane may overestimate the shear strength
mobilised in slopes. Bjerrum developed a reduction faction
related to the plasticity index of the clay (Craig, 1992). However,
this reduction factor was derived for sensitive Scandinavian clays
and has been found to not apply to clays in warmer climates.
1.2
1.0
0.8
0.6
0.4
20
40
60
80
Plasticity index
100
120
14
Stren
ngth
Stren
ngth
Permeability
Permeability

`
Compressibility
6.1 Strength Testing

` 6.1.3 Triaxial Test
` Triaxial tests
may also be
carried out in a
hydraulic stress
path cell, which
eliminates the
need for a load
frame, and,
being
hydraulically
driven, is more
amenable to
automated
control (Head,
1982).

` 6.1.3 Triaxial Test (cont.)

` The unconfined compression test is suitable for determining the
undrained strength:
(cu = 1 / 2 )
`
Stren
ngth
6 Strength Testing and

Theories (cont.)
Compressibility
Permeability

membrane
` 6.1.3 Triaxial Test
` Triaxial testing(on cylindrical soil samples) includes:
the unconfined compression test
the triaxial compression test
and the triaxial extension test.
` In a typical triaxial test the cylindrical soil sample is
located within a membrane and mounted in the
triaxial cell, housed within a load frame.
` Axial
A i l 1 and
d cellll 3 pressures may be
b applied
li d
independently.
` Initially, the estimated average in situ stress is
applied isotropically
( 1 = 3 )
` The sample is then sheared by either increasing
(compression) or decreasing (extension) 1 to
failure, holding 3 constant.
` During shearing, the stresses and strains are
measured.
` Pore water pressures, volumetric strains, and
localised small strains (lateral or axial) may also be
measured (Head, 1982).
Stren
ngth
6 Strength Testing and

Theories (cont.)
Compressibility
Compressibility
Permeability
10/9/2008
Of soil and rock samples which are capable of being formed as

self-supporting cylinders.
Triaxial compression and extension tests may be carried out as
follows:
Unconsolidated-undrained shearing (for cu , u 0 ).
Consolidated-undrained shearing (for ccu , cu 0 ).
Consolidated-undrained shearing, with pore water pressure
measurement (for c' , ' ).
Consolidated-drained shearing (for c' , ' ).
hydraulic driven:
Permeability

` Modes of failure in a triaxial compression test include barrelling,
shear plane failure, and a combination of these two (Head, 1982).
Stren
ngth
Compressibility
Stren
ngth
Compressibility
Permeability
displacement driven:

`

` The triaxial test is generally conducted on saturated samples.
` It may be necessary to apply a back-pressure to the sample, in
combination with a confining pressure to force any air into solution
and so saturate the sample prior to testing.
back-pressure of typically 200 kPa
confining
fi i pressure no more than
th about
b t 10 kPa
kP < back-pressure
b k
` Saturation is tested by measuring the B pore pressure parameter.
For full saturation, B =1, where
u = B[ 3 + A( 1 3 )] = B 3
`
plastic failure (barrelling)
brittle failure (shear plane)
intermediate type
Corrections are required to allow for the membrane, friction losses

(on the axial load piston), and change in sample area.
15
Stren
ngth

` 6.1.5 Strength testing of rocks
` Strength testing methods applied to rocks include:
the point load index (tensile) strength test
the direct shear test
the triaxial test
and the Hoek cell test (Brown, 1981).
` The principles involved are similar to those which apply to the
strength testing of soils.
Compressibility
Permeability

` 6.1.4 Unsaturated strength of clays
Undrained shear strength, Su
Stren
ngth
Suction
effect
water table
Self-weight
effect
Depth, z
Permeability
Stren
ngth
Compressibility
Permeability

` Application of triaxial test:
The test is best suited to situations in which vertical compression
and/or extension occur, eg. Building or embankment (beneath
centre) loading or basement excavation.
` Advantages of triaxial test:
Failure is not constrained to a pre-determined surface.
Th stresses
The
t
imposed
i
d iin a triaxial
t i i l test
t t are a better
b tt representation
t ti off
the in situ stresses than those applied in the shearbox test.
The applied stresses are principle stresses.
Drainage conditions can controlled and varied.
For intact clays, triaxial strength results obtained from good quality
samples agree well with field estimates of strength.
` Limitations of triaxial test:
Setting up sand samples for triaxial testing is difficult.
Triaxial strength results from small size samples give unrealistically
high estimates of strength for highly fissured clays.

`
Compressibility
6.2 Strength Theories

` 6.2.1 Idealized stress/strain behaviour
`
Stren
ngth
Compressibility
Permeability
10/9/2008
Elastic
STRESS
Permeability
Compressibility

` Rigid, perfectly plastic
STRESS
STRAIN
Elastic, perfectly plastic

`

` Non-linear elastic
STRESS
Stren
ngth
Stren
ngth
Compressibility
Permeability
STRAIN
STRAIN
`
STRESS
Non-linear elastic, work hardening
STRESS
STRAIN
STRAIN
16
Permeability
Stren
ngth
Compressibility

Non-linear elastic, work softening

` 6.2.2 Stress/strain behaviour of soils
` Typical stress/strain curves
` (i) Normally consolidated soils (loose sands and soft clays)
SHEAR
STRESS
Stren
ngth
Compressibility
Permeability
10/9/2008
STRESS
MAX
SHEAR STRAIN
(ii) Overconsolidated soils (dense sands and stiff clays)

peak (small strain)
STRAIN
ultimate (large strain)
SHEAR
STRESS
residual
(very large strain in clayey soils)
Permeability

` 6.2.3 Undrained shear strength su
` For normally consolidated (nc) soils (Skempton, 1957)
Stren
ngth
Stren
ngth
sU
' 0.11 + 0.0037 I P
V NC
`

(cont.)
Compressibility
Compressibility
Permeability
SHEAR STRAIN
where IP is the plasticity index in %.

For overconsolidated (oc) soils

` 6.2.4 Soil behaviour
in drained shear
` For a drained
simple shear test,
Atkinson (1993)
described the
stress/strain
behaviour of soils
in the following
diagrams:
sU
sU
m
' ' ( OCR )
V OC V NC
Radius of circle =
1 3
2
1 ' 3 '
2
= max
max
>10%
D
eT
D

`
6.4 Stress Paths (triaxial results)

` Total stress axes:
+3
s= 1
,
MIT:
p=
A + 2 R
3
t=
where
p' =
A '+ 2 R '
3
1 3
2
q=
Effective stress axes:

'+ 3 '
MIT:
s' = 1
,
Cambridge:
'
(u = constant)
2
STRAIN
same
compression
STRESS
1 3
ultimate
~1%
1 + 3
D sample
initially
on the dry side
of critical
'
Cambridge:
Stren
ngth
Permeability
6.3 Mohr Circles (triaxial results)

` Circle centre is located at ( 1 + 3 ) / 2 for total stresses, and
at ( 1 '+ 3 ') / 2 for effective stresses.
peak
Compressibility
Stren
ngth
Compressibility
Permeability
where OCR is the overconsolidation ratio, and m is an empirical

constant dependent on soil type, with a range from 0.68 to 0.87,
and a typical value of 0.8 (Wroth, 1984)
'
W sample
initially
on the wet side
of critical
'
P '
T '
t'=
or
A R
2
1 ' 3 '
q' =
or
A ' R '
2
A = 1 , R = 3 , A ' = 1 ', R ' = 3 '
17
6.4 Stress Paths (triaxial

results)
` Atkinson (1993) and Craig
(1992) plotted the following
typical stress paths in p-q
space and s-t space,
respectively.

`
6.5 Failure in Direct Shear
Compressibility
Permeability

(cont.)
( F , N )
Stren
ngth
Stren
ngth
Compressibility
Permeability
10/9/2008
STRESS
Permeability
6.7 Mohr-Coulomb Failure Criterion

` 6.7.1 In direct shear
` Total stresses (undrained conditions in a clay)
f = cU + N tan U
Stren
ngth
where cU is the undrained shear strength, U is the undrained

friction angle ( 0) and N is the applied total normal stress.
F = cU (U = 0)
Compressibility

` 6.7.1 In direct shear
` Effective stresses (sands and drained clays)
f = c '+ N ' tan '
Stren
ngth
Compressibility
Permeability
NORMAL STRESS, N
where N ' is the applied effective normal stress.

An applied
pp
stress will, with time, g
give rise to a change
g in normal
stress N ' , which will give rise to a change in shear strength F
given approximately by F = N ' tan '
STRESS
Permeability

` 6.7.2 In triaxial shear
` Total stresses
1 = 3 tan 2 45o +
o U
+ 2cU tan 45 +
2
2
The failure surface will be approximately

pp
y horizontal, tangential
g
to the
Mohr circle.
f = cu (u = 0 )
Compressibility

`
'
N '
c'
Stren
ngth
Stren
ngth
Compressibility
Permeability
NORMAL STRESS, N
f = c '+ N ' tan '

`

` 6.7.2 In triaxial shear
` Effective stresses
1 ' = 3 ' tan 2 45o +
'
o '
+ 2c ' tan 45 +
2
2
The failure surface is drawn tangential

g
to the Mohr circle.
f = c '+ N ' tan '
STRESS
'
STRESS
Unconfined
c'
'
18
Permeability
6.8 Soil Moduli
E IT
ES
EUR
ET
6 Strength Testing
and Theories
(cont.)
`
Stren
ngth
Stren
ngth
SHEAR
STRESS
Compressibility
Compressibility
Permeability
10/9/2008
SHEAR STRAIN
where E IT , E S , ET , and EUR are the initial tangent, secant,

tangent, and unload/reload moduli, respectively.
6.9 Stress/Strain
Behaviour of
Rocks and
Rockfill
` Different rock
types
experience
different
stress-strain
behaviour
(Hunt, 1984).
Permeability
STRESS
6.9 Stress/Strain Behaviour of Rocks and Rockfill (cont.)

` The failure criteria for rock masses typically have the following form
(Brown, 1981).
SHEAR STRENGTH
H [MPa]
Stren
ngth

` Fractured rock typically experiences elastoplastic (with work
hardening) stress-strain behaviour (Goodman, 1989)
Stren
ngth
Compressibility
Compressibility
Permeability
ET < E S < E IT < EUR
STRAIN
B
A
Permeability

` For rockfill, the peak shear strength envelope may curve
continuously, from a value of 0 at zero normal stress, with the friction
angle varying linearly with the log of the normal stress (decreasing
with increasing normal stress) (Leps, 1970)
NORMAL STRESS [MPa]

`
Stren
ngth
Compressibility
Stren
ngth
Compressibility
Permeability
STRESS
STRAIN
19
35
y,
Low density,
poorly graded,
weak particles
Weathered
100
200
1000
500
Normal Stress (kPa)
2000
7.1 Consolidation Testing

` 7.1.1 Oedometer test (cont.)
`
The oedometer may also be used in a swelling test, to determine

the swelling pressure (pressure at which no volume change
occurs) of an expansive clay.
For stiff soils, corrections may be required to allow for the

deformation of the apparatus.
Variations to the conventional test, such as the constant strain rate

test, are available. Some of these allow results to be obtained
much more rapidly.
Permeability

` In an oedometer test, a sample is cut using
the oedometer ring
t or log10 t
This ring is mounted in the oedometer cell and surrounded with

water.
Pressure is applied by means of dead weights, with each pressure

twice the previous one (or half on unloading), and with each
pressure maintained for 24 hours.
During loading and unloading, the deformation of the sample is

measured with time.
By extending the duration of particular pressure increments, the

oedometer test may be used to estimate secondary consolidation
or creep.
7 Consolidation Testing and Settlement Theories (cont.)

`
Compressibility
Stren
ngth
Permeability
Compressibility
Stren
ngth
Stren
ngth

` 7.1.1 Oedometer test
` The oedometer 1-D consolidation test is used to determine the
consolidation characteristics (magnitude and rate) of low
permeability soils (Head, 1982).
Permeability
20
Stren
ngth
Compressibility
Permeability
25
7 Consolidation Testing and Settlement Theories

`
Permeability
Poorly lithified
30
Compilation of the strength of

rockfill as measured in large
triaxial tests (after Leps, 1970)
compared with direct shear
values for coal mine spoil.
Cemented

` Seedsman et al. (1988) also found that the strength parameters
(cohesion and friction angle) of coal mine spoil depend very much on
whether they are tested dry or saturated.
Compressibility
Friction aangle
Stren
ngth
40
Compressibility

` Typical friction angles
55
for coal mine spoil were
High density, well graded,
compared with Leps
50
strong particles
data by Seedsman
Average rockfill
et al. (1988)
45
Stren
ngth

`
Compressibility
Permeability
10/9/2008

` Application of oedometer test:
`
The test is applied to the primary consolidation, swelling, and

creep of low permeability soils
The consolidation is usually due to loading imposed by

structures, embankments, and self-weight, for example.
By varying the orientation of specimens relative to their

orientation in the field, anisotropic effects can be investigated.
The test is applicable to silts and peats, even soft rocks, in

addition to clays.
20
Compressibility
Permeability
7 Consolidation Testing and Settlement Theories (cont)
Stren
ngth
Permeability
Compressibility
Stren
ngth
7.1.2 Rowe consolidometer test

` Application of Rowe cell test:
` The Rowe cell test may be applied to the same range of problems
and soils as the oedometer test, together with those situations
involving lateral drainage.
Advantages of Rowe cell test:
A range of Rowe cell diameters is available (250, 150 and 75 mm).
The hydraulic loading system used in the Rowe cell is less
susceptible to vibrational effects than the dead weights used in the
oedometer, and lends itself to automated control.
Both low (applied to a soil slurry) and high pressures are readily
applied using the hydraulic loading system.
The sample can be saturated by means of a back-pressure.
7 Consolidation Testing and Settlements Theories (cont.)

`
7.2 Settlement Theories:

` 7.2.1 Compaction of soils:
` Definition:
Compaction is the expulsion of air from a soil by mechanical
means. It generally occurs instantaneously.
` 7.2.2 Immediate settlement of soils:
` Definition:
In a sand, the majority of the settlement under an applied stress
occurs immediately.
In a clay, the immediate settlement under an applied stress
occurs under constant volume conditions.
Permeability
Compressibility
7.1 Consolidation Test: (cont.)

` 7.1.2 Rowe consolidometer test:
` The Rowe consolidation cell may be used to determine the
consolidation characteristics (magnitude and rate) of low
permeability soils, but in addition to testing vertical drainage can
also test lateral drainage (Head, 1982).
Stren
ngth
Permeability
Limitations of oedometer test:

The results of the oedometer test often under-estimate the rate
of settlement.
In the conventional oedometer test there is no means of
controlling drainage, nor of measuring pore water pressures.
7 Consolidation Testing and Settlements Theories (cont.)

`
Advantages of Rowe Cell Test (cont.)

Loading can be applied by means of a membrane (uniform
pressure) or by means of a rigid plate (uniform deformation).
Drainage can be controlled.
Pore water pressures can be measured.
The volume of water expelled from the cell can be measured.
Deformation of the hydraulic loading system is negligible.
Limitations of Rowe cell Test:

The Rowe cell test is more time consuming and difficult to set up
than the oedometer test.
Compressibility
Stren
ngth
Compressibility
Advantages of oedometer test:

The test procedure and calibrations have been standardised
and are reproducible.
The test results provide a reasonable estimate of settlements
settlements,
provided they are properly interpreted.
Stren
ngth
Permeability

Compressibility
Stren
ngth
Permeability
10/9/2008
7 Consolidation Testing and Settlements Theories: (cont.)

`
7.2. Settlement Theories: (cont.)

` 7.2.2 Immediate Settlement of soils :(cont.)
Immediate settlement of sands is generally calculated using
empirical methods. For example, using the Parry (1977) method,
the average immediate settlement ( i ) AV for a footing on a deep
sand layer with a deep water table may be approximately by
( i ) AV
qB
(mm)
5N
where q is the uniformly distributed applied pressure in MPa, B is

the footing width in m, and N is the Standard Penetration Test blow
count for 300mm penetration.
If the water table is located at the footing base level, the average
immediate settlement may be up to twice that calculated using the
above expression.
21
Stren
ngth
For example, for a flexible footing (Bowles, 1968)
q.B
(1 vu2 )
Eu
q.B
= 0.750 1
Eu
i = 0 1
Permeability

` 7.2.2 Immediate Settlement of soils :(cont.)
` Immediate settlement i of clays is generally calculated using
elasticity theory, using the undrained elastic parameters:
Eu and vu (typically = 0.5).
Values of 0 and 1
for settlement
computations using
previous equation
(after Janbu,
Bjerrum, and
Kjaensli).
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Compressibility
Compressibility
Permeability
10/9/2008
vu = 0.5
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Permeability

` 7.2.3 Primary consolidation of clays:
` Definition:
Primary consolidation is the time dependent expulsion of water
from low permeability saturated soils (clays) subjected to an
applied stress .
The applied is initially taken by the pore water as excess u,
which dissipates with time
time, accompanied by the expulsion of
water and the transfer of stress from the pore water (u) to the
soils skeleton ( ' ).
` 7.2.4 1-D consolidation (Oedometer Test):
` Where the thickness of the consolidating layer is thin compared
with the dimension of the loaded area, or where lateral strain is
prevented, as in the oedometer test, 1-D consolidation applies.
` For each increment of stress, settlement/time data are recorded.
Compressibility

` 7.2.4 1-D consolidation (Oedometer Test): (cont.) for a constant
increment of stress
t50 t90
cV
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ngth
Compressibility
Permeability
where 0 and 1 are constants dependent on the geometry of the

problem, q is the uniformly distributed applied pressure, and B is
the footing width.
tR
`
Consider 1-D PRIMARY CONSOLIDATION over several increments

of stress, including an unload/reload loop.
CC
CR

` 7.2.4 1-D consolidation (Oedometer Test): (cont.)
` For normally consolidated clays
'
e1 = e0 CC log10 v1
v0 '
H
v1 '
c =
CC log10
+
1
e
0
v0 '
e
CC
CR
log10 'V
where e0 is the initial void ratio (corresponding to v 0 ' ), e1 is the void

ratio corresponding to v1 ', c is the 1-D primary consolidation
corresponding to the stress increment ' = v1 ' v 0 ', and H is the
thickness of the consolidating layer.
For overconsolidated clays
'
e1 = e0 cR log10 v1
v0 '
H
v1 '
cR log10
+
1
e
0
v0 '
c =
Compressibility
Permeability

`

` Alternatively
c = mv v ' H
`
where mv is the coefficient of volume change.
For normally consolidated clay
e
CC
CR
log10 'V
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ngth
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ngth
Compressibility
Permeability
mV
mv =
0.435 Cc
(1 + e) v '
22
c = T i
Stren
ngth
where T is the total settlement corresponding to the drained

elastic parameters E ' and v ' . For example, for a flexible footing
(Bowles 1968)
(Bowles,
T = 0 1

7.2.5 3-D effects: (cont.)
where oed is the oedometer c and is a correction factor

dependent on the pore pressure parameter A and degree of
overconsolidation (Scott, 1969;Fang, 1990 ).

`
7.2.5 3-D effects: (cont.)
Permeability
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ngth

` 7.2.6 Rate of 1-D primary consolidation (Terzaghi):
` Diffusion equation for 1-D primary consolidation
2u u
=
z 2 t
k
cv =
w mv
cv
t or log10 t
where cv is the coefficient of consolidation.
The solution of the diffusion equation introduces the non-dimensional

time factor
c t
Tv = v 2
D
`
`
`
where D is the maximum vertical drainage path length.

For 1-way vertical drainage D=H
For 2-way vertical drainage D=H/2
Permeability
Compressibility
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ngth
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ngth
Permeability
Compressibility
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ngth
( c )3 D = oed
Compressibility

` 7.2.5 3-D effects: (cont.)
` Skempton and Bjerrum method:
7.2.5 3-D effects:

` Where the thickness of the consolidating layer is thick compared
with the dimension of the loaded area, lateral strain will be
significant and must be allowed for.
Compressibility
Permeability
q.B
(1 v '2 )
E'
Compressibility

` Primary consolidation may also be estimated indirectly using
elasticity theory
Permeability
Stren
ngth
Compressibility
Permeability
10/9/2008

`

` Degree of consolidation
U=
ct H
=
cf
1
H
=
u1 dz
1
H
1
H
1
H
ut dz
u1 dz
( v ui ) dz
ui dz
where ct is the consolidation at time t, ct is the final

consolidation, ui is the initial excess pore water pressure, and ut is
the excess pressure at time t.
23
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ngth


`

` Laboratory determination of cv :
(time) fit
7.3 Creep of Soils and Rockfill:

` Definition
` Creep of low permeability soils and rockfill is a catch-all to cover
the long term settlement which is not described by theory, and is
often poorly understood.
` Creep s is the characterised by approximately constant
settlement per log cycle of time.
tR
s = D C log10
Compressibility

`
7.3 Creep of Soils and Rockfill: (cont.)

` For rockfill, the C value can vary over a wide range, depending on
the placement density, trafficking of the material, and the potential
for the material to breakdown on exposure.
` For loose dumped mine waste rock, the C value may range from
0.01 to 0.04 (Seedsman and Williams, 1987).
Stren
ngth
Permeability
Stren
ngth

` Laboratory determination of cv :
log10 (time) fit
Permeability
Stren
ngth
Permeability
Compressibility
Stren
ngth
Compressibility
Compressibility
Permeability
Stren
ngth

` The relationship between Tv and U is a function of the assumed initial
pore water pressure distribution and the maximum drainage path
length (Craig, 1992).
Permeability
Compressibility
Compressibility
Permeability
10/9/2008
where C is the coefficient of secondary consolidation, and t R is

the reference time.
< 0.001 for OC clays
0.005 for NC clays, increasing to
C
0.02 with increasing organic content
0.02 0.1 for Pt
24
h ' = ko v '
where h ' and v ' are the horizontal and vertical effective stresses,
respectively, and ko is the at rest earth pressure coefficient.
For normally consolidated soils
where
Stren
ngth
ko 1 sin '
Permeability
8.1 Stress States

` 8.1.1 At rest state
Compressibility
8 Failure Conditions in Soil Masses (cont.)
kA =
' is the effective angle of internal friction of the soil. Typically
k P is typically about 3.0, and requires substantial lateral compression

to be fully mobilised.
Compressibility
8.1 Stress States (cont.)

` 8.1.3 Critical States
Permeability
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ngth
Compressibility
Permeability

` The critical state of soils is that reached after strains of at least 10%,
and is associated with turbulent flow (laminar flow exists at residual
strength) (Atkinson, 1993).
` At the critical state (defined by the critical state line or CSL), there is a
unique relationship between the shear stress, the normal stress, and
the void ratio,
ratio as shown in the following diagrams (Atkinson,
(Atkinson 1993)

`

` The CSL is given by
f ' = f ' tan c '

`
(Mohr- Coulomb failure criterion, with effective cohesion c= 0)
e f = e Cc log10 f '
Stren
ngth
Permeability
Compressibility
Stren
ngth
Compressibility
Permeability
Stren
ngth

` 8.1.2 Active and passive failure states

`
1 + sin '
1
=
1 sin ' K A
where n is an empirical constant dependent on soil type.

`
1 sin '
1 + sin '
k A is typically
yp
y about 0.33, and develops
p at relatively
y small lateral
dilation.
Rankine passive earth pressure coefficient:
kP =
( k0 ) NC is in the range 0.4 to 0.6.

For overconsolidated soils, ( k0 )OC is typically 1.
(k0 )OC (k0 ) NC (OCR ) n

`

` 8.1.2 Active and passive failure states
` Rankine active earth pressure coefficient:
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ngth
8 Failure Conditions in Soil Masses
Compressibility
Permeability
10/9/2008
where the subscript f denotes ultimate failure conditions at the

critical state, and c ' is the friction angle at the critical state. e
defines the position of the CSL, in the same way as e0 defines the
position of the normal consolidation line (NCL).
The state of a soil initially wet of critical (that is, above critical or
normally consolidated) or that of a soil initially dry of critical (that is,
below critical or overconsolidated) moves towards the critical state
(either compressing or dilating from opposite sides of the CSL) during
shearing.
25
9 Clay Mineralogy (cont.)

`
Compressibility
Stren
ngth
The principal clay minerals, kaolinite, illite and montmorillonite, have

the structures (Craig, 1992)
Compressibility
Permeability
Fig. 1.2 Clay minerals: basic units
Stren
ngth
Permeability
Fig. 1.1 Single grain structure

`
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ngth
Double layer refers to the negatively charged particle surface and the
dispersed layer of cations.
Absorbed water is held around a clay mineral particle by hydrogen
bonding and hydration of the cations.
Attraction between adjacent clay mineral particles is due to shortrange van der Waals forces. Like charges repel, Net repulsion leads
to face-to-face orientation, a dispersed structure. Net attraction leads
to edge
edge-to-face
to face or edge
edge-to-edge
to edge orientation, a flocculated structure
(Craig, 1992).
In natural clays, particles stack, resulting in bookhouse and
turbostractic equivalents to dispersed and flocculated single particles
(Craig, 1992).
Permeability
Compressibility
Kaolinite consists of silica and alumina sheets, held together fairly tightly
by hydrogen bonding, allowing very limited isomorphous substitution of
silicon and aluminium. Kaolinite is the most stable (and most
weathered) clay mineral.
Illite consists of alumina sheets between two silica sheets, these groups
held together fairly weakly due to (non-exchangeable) potassium ions
between them. There is partial substitution of aluminium by magnesium
and iron, and of silicon by aluminium.
Montmorillonite has the same basic structure as illite, but with water
and (exchangeable)
(
) cations other than potassium between groups,
resulting in very weak bonding and the potential for considerable swell in
the presence of water. There is partial substitution of aluminium by
magnesium. Montmorillonite is the least stable (and least weathered)
clay mineral.
The surfaces of clay mineral particles carry residual negative charges,
mainly as a result of isomorphous substitution by atoms of lower valency,
and also due to disassociation of hydroxyl ions. These result in weak
attractions for cations in the water in the voids between particles
(replaceable by other cations by cation exchange), forming a dispersed
layer around the particles, with cation concentration decreasing with
increasing distance.
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ngth
Permeability
Fig. 1.2 Clay minerals: basic units
Compressibility
Chemical weathering of minerals in the parent rock (due to the action of water,
especially acid or alkaline water, oxygen and carbon dioxide) results in the
formation of groups of crystalline particles of colloidal size (<0.002mm), known as
clay minerals. Most clay minerals are platey, having a high specific surface (high
surface area to mass ratio), with the result that their properties are influenced
significantly by surface forces. The basic structural units of most clay minerals
consist of silica tetrahedrons and aluminium octahedrons (Crais, 1992), with
different bonding between units.
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ngth
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ngth
Granular soils assume a single grain structure, in which adjacent

particles are in direct contact, without there being any bond or cohesion
between them (Craig, 1992). The structure may be loose, medium dense
or dense, depending on the state of packing.
Permeability
Compressibility
9 Clay Mineralogy
Compressibility
Permeability
10/9/2008
Fig. 1.4 Clay structures: (a) dispersed, (b) flocculated, (c) bookhouse, (d) turbostratic,
(e) example of a natural clay.
26

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Compressibility

Golder Geomechanics Centre

Soil phase (solids/water/air) relationships

Soil strength testing and theories

Failure conditions in soils

CIVL2210 Fundamentals of Soil

Pore water pressure

L1: Introductory slide show

L2: Soil phase

L3: Principle of effective stress

T1: Definitions and

L5: Seepage through soils

T2: Pore pressure &

L5: Seepage through soils

L6: Strength testing and theories T4: Seepage

L6: Strength testing and theories T5: Shear strength

L7: Strength testing and theories T5: Shear strength

L7: Consolidation testing and

L7: Consolidation testing and

L8: Failure conditions in soil

L9: Clay mineralogy

T7: Lateral earth

1.1 Particle Size Distribution Analysis

Professor David Williams

Obtain distribution of sand size and coarser by sieving

1.2 Atterberg Limits

Shrinkage limit, SL:

w at which soil reaches its minimum volume

Plastic limit, PL:

minimum w at which soils deforms plastically

Some dispersion Class 2

Emerson Class Number of a soil to assess slakability and dispersion

No calcite or gypsum present

1 Soil Classification (cont.)

1.3 Unified Soil Classification

Immerse air-dried 2 mm to 4 mm dia. crumbs of soil in distilled water in a beaker

1 Soil Classification (cont.)

Complete dispersion Class 1

1.2 Atterberg Limits (cont.)

minimum w at which soil flows

1 Soil Classification (cont.)

1 Soil Classification (cont.)

Coarse-grained soils ( < 50 % passing 0.06 mm)

Fine-grained soils ( > 50 % passing 0.06 mm)

Calcite or gypsum present Class 4

Make up 1:5 soil/water suspension in a test tube and shake

PEAT (no suffix)

Coarse-grained soils with < 5 % passing 0.06 mm

Poorly-graded (uniform or gap-graded)

Coarse-grained soils with > 12 % passing 0.06 mm

1 Soil Classification (cont.)

1 Soil Classification (cont.)

Determination of Emerson class number of a soil

1 Soil Classification (cont.)

1 Soil Classification (cont.)

Dry strength and stickiness

1.4 Engineering Use Chart

1.5 Other Classification Systems

2 Phase (solids/water/air) Relationships (cont.)