Transcript Offshore Geomechanics Notes

Geomechanics 255 (610.255)
Geomechanics Group
School of Civil & Resource Engineering
The University of Western Australia
Part 2: Soil Strength
Professor Martin Fahey
1
Outline
• Shearing behaviour of sand (cohesionless soil)
– friction
– dilatancy
– concept of critical state (critical void ratio)
• Shearing behaviour of clays (cohesive soil)
– critical state concept for clayey soils
– drained and undrained shear strength in triaxial tests
– relationship between pore pressure change in undrained tests, and
volume change in drained tests
The aim is to show that the shearing behaviour of all soils (sands and clays) can be presented within the unified
framework of Critical State Soil Mechanics. This links the volume change behaviour in drained shearing with
the pore pressure changes that occur when drainage is not able to occur. For sands, undrained behaviour
generally can only occur when the boundary conditions prevent – otherwise, shearing is generally slow enough to
allow any pore pressures (positive or negative) that tend to occur to dissipate as the shearing progresses. (The
exception may be very fast loading, as in an earthquake, or where the scale of the problem is very large, as with
very large offshore gravity platforms). On the other hand, the permeability of clay soils is so low that it is very
difficult to apply loads slowly enough for drained conditions to apply, and hence many problems involving
applying loads to clayey soils deal with the undrained shear strength.
2
Soil Strength: Angle of Internal Friction f'
N
N
N
F
f'
R
F
F
F
f': Angle of internal friction; m: coefficient of friction
tan f' = m = F/N
f'
f'
f': Angle of plank when block slides
f': Angle of repose of sand heap
3
Principle of Effective Stress
N
Water pressure u
F
N
F
At failure:
F   N  u . A  tan f 
F  N  u. A 

tan f 
A
A
    n  u  tan f 
   n tan f 
     u  effective stress
F
Note: As u  (i.e. ' 0)
strength () 0
(liquefaction)
4
Direct Shear Box Apparatus
5
Other Versions at UWA
Pneumatic jack
(computer
controlled) to apply
vertical load
Load cells
Direct Via Lever
Hangers for load
6
Behaviour of Sand in Direct Shear Box
7
Direct Shear Tests on Sand
D, M, L: Dense, Medium, Loose
8
Direct Shear Box: Summary of Results
9
Relative Density – Density Index (ID)
Absolute value of soil density not so important – what
matters is how dense is the soil relative to its maximum
possible value and its minimum possible value
ID
Densest possible state (emin, or rdmax) 1 or 100%
(obtained by vibration under load)
Density index ID (relative
density) –
where density lies in the range
min. to max. or rather where void ratio lies
between loosest (emax) and
densest (emin) state
ID 
emax  e
emax  emin
Loosest (stable) state (emax, or rdmin)
(obtained by pouring with funnel)
0
ID (%)
0 – 15
15 – 35
35 – 65
65 – 85
85 – 100
State
Very loose
Loose
Medium
Dense
Very dense
10
Apparent Cohesion in Sand
Mohr-Coulomb Failure Criterion: f
= c' + ' tan f'
• Failure surface is actually
curved
• Straight line through tests
results at ' of 40, 60 and
80 kPa implies a cohesion
intercept (c') of 10 kPa
• This implies a strength at
zero effective stress: NOT
CORRECT
“Apparent cohesion” c'
11
"Saw-tooth" Model of Dilation
• Dilation has effect of
increasing the apparent
friction angle on interface
above the true value (f'cv)
• Apparent friction angle from
sawtooth model:
f'peak = f'cv + n
• Dilation angle = n
• Observed relationship:
f'peak  f'cv + 0.8 n (Bolton)
• Collapsing material (negative
dilation) shows friction angle
less than f'cv
12
Vertical displacement y
(vol. strain)
Stress ratio (/'n)
Stress-Ratio Dilation Relationship (Taylor)
Peak stress ratio (tan f'peak)
DENSE
"Constant volume"
stress ratio (tan f'cv)
LOOSE
DENSE
dy/dx = 0
tan f   tan f cv 
dx
dy
Point of max. slope (nmax)
dy/dx = 0
LOOSE
dy/dx negative, increasing towards zero
dy
dx
 dy 
tan f peak
 tan f cv   

 dx  max
 dy 
 dy 
tan n    ; tan n   
 dx 
 dx  max
13
Critical State Concept
• When sheared, state of soil tends to
migrate to a unique line in  - ' - e
space. This is called the critical state
line (CSL).
• CSL has same gradient as NC line (l)
14
Dilation depends on density and stress level
Critical State Line (CSL)
LOOSE
Void ratio e
At low stress, even loose
samples may dilate
At high stress, even
dense samples may
contract
DENSE
Normal effective stress 'n (or mean effective stress p')
15
Relative Density Corrected for Stress Level
• For plane strain, Bolton found that:
I R  I D 10  loge p   1
– nmax (º) = 6 IR for plane strain
– f´max – f´cv = 0.8 nmax
– f´max – f´cv  5 Irº
p' is the mean effectives stress (kPa)
I D is the density index defined as
• For triaxial conditions
ID 
emax  e
emax  emin
– Must define 'dilatancy' in general as
 d e v  – where ev is volumetric strain = e1 + e2 + e3.
 
  e is the major principal strain (generally e in triaxial tests)
1
a
 d e1 
– (negative sign, because expansion - I.e. dilation - is negative by
normal sign convention, but want 'dilatancy' to be positive)
 d ev 
 
  0.3I R
 d e1 
nº
ID
p' (kPa)
10
100
1,000
0.2 (20%)
3.2º
0.5º
-2.3 (?)
0.5 (50%)
17.1º
10.2º
3.3º
0.8 (80%)
(30.9º ?)
19.9º
8.8º
10,000
-2.2º (?)
16
Drained & Undrained Shear Strength
Shear stress 
Drained strength sd
f'cv
Undrained strength su
Undrained strength su
Drained strength sd
'n
Suction increases
effective stress
eo
Dense states
Positive pore pressure
reduces effective stress
Contraction
Undrained test
no volume
change allowed
Dilation
Void ratio e
Loose states
CSL
Normal effective stress 'n (or mean effective stress p')
17
Triaxial Test
Loading frame
Loading ram
External LVDT
Top cell
The triaxial test enables a variety
of stress or strain controlled tests to
be carried out on cylindrical soil
specimens.
Fa
Internal load cell
cell
Top "O" rings
Top cap
Top porous disc
Area, A
Membrane
Phosphor bronze springs
Sample
cell
Strain gauges
u
Cell shroud
Bottom porous disc
Triaxial pedestal
Bottom "O" rings
Top drainage
To air-water interface cylinder
Bottom drainage
cell
Fa
18
One of the UWA Triaxial Systems
Axial motor drive
system
Cell cover lowered
once sample in place
Sample goes here
Cell pressure controller
Control and data
logging system
Sample, enclosed in rubber
membrane, with axial strain
measuring devices attached
19
Triaxial Test: Background
• Direct shear test useful, but limited
– Know only 1 normal stress ('n), don't know horizontal normal stresses
– Failure plane pre-defined - must coincide with the shear box
• Triaxial test still limited:
– vertical and horizontal directions still principal directions
– horizontal stress equal in all directions
– “true triaxial” test would allow different '1, '2, '3 on three faces of
cubical sample
– even more general - allow shear stresses to be applied to the three faces
'v (='1)
'h
(='2)
'h
(='3)
Triaxial
'v
'1
'2
'3
“True triaxial” ('1'2 '3)
hv
'h
'h
“Simple shear”
20
Triaxial Test: Conduct of Test
• Almost always use saturated samples (using high
backpressure uo to achieve full saturation)
• Almost always consolidate the sample to some
stress state (in situ stresses often) before carrying
out the strength test
– isotropic consolidation: vertical and horizontal stresses equal (increase
cell pressure only, allowing drainage against constant back pressure)
– 'h = '3 = c - uo, and '1 = 'v = 'h = '3 in this stage
– anisotropic consolidation: generally vertical stress greather than
horizontal stress: increase cell pressure and apply additional vertical load
– 'h = '3 = c - uo, and '1 = 'v > 'h = '3 in this stage
• “Shearing” phase (in the simplest test): increase
the vertical load (stress) until the sample fails
– other “stress paths” also possible - see later
21
Stress Paths in Triaxial Tests
•
Different stress paths in “shearing” phase:
1.
2.
3.
4.
5.
•
keep cell pressure constant (Dh = 0) and increase vertical stress (Dv +)
keep vertical stress constant (Dv = 0) and reduce cell pressure (Dh -)
keep vertical stress constant (Dv = 0) and increase cell pressure (Dh +)
keep cell pressure constant (Dh = 0) and reduce vertical stress (Dv -)
vary both cell pressure and vertical stress in some predetermined way, to
produce any type of stress path
Stress path in q-p space:
Dq = Dv - Dh
Dp = (Dv + 2Dh)/3
1. Dh = 0 and Dv = +  Dq = +Dv and Dp = +Dv/3  Dq/Dp =3
Shearing phase
q
Stress path: a plot showing how the stresses
vary during a test.
In this case, this is a Total Stress Path (TSP).
In this case, shearing starts from an isotropic
stress state, following isotropic
consolidation.
3
1
p
Anisotropic consolidation phase
Shearing phase
q
3
1
In this case, shearing
starts from an anisotropic
stress state, following
anisotropic
consolidation.
Anisotropic consolidation phase
p
22
Total and Effective Stress Paths (TSP, ESP)
Stress Parameters:
q
q = q'
ESP: Effective stress
path (soil response)
Du (+) B
B'
TSP: Total stress path Deviator stress: q   v   h
(imposed by apparatus) Mean effective stress:
   2 h
3
p'  v
3
1
(ESP)
(b')
Du may be negative)
"Standard" stress path:
h constant
v increased to failure
v increasing
p, p'
p'
A
p' = p - Du
p
h constant
Dq = Dv
Dp = Dv/3
Dq/ Dp = 3
23
Drained & Undrained Strength (Clays)
CSL
Deviator stress q
Bd
TSP
Drained strength sd
Au , Bu
Du
-
Ad
Drained strength sd
Du +
ESP
A
Undrained test
no volume change
allowed
Dilation
Void ratio e
eo
Ad
Undrained strength su
3
Undrained strength
depends on p'o and OCR
1
B
mean effective stress p'
B
"Wet of critical"
NC line
A
OC line
"Dry of critical"
Bd
Contraction
Undrained strength su
CSL
Mean effective stress p'
24
Initial and Final Undrained Strength
q
su for NC soil increases
Tank or GBS Dv
after consolidation
su after
consolidation
CSL
Depth (m)
e
suo
NC soil
In situ su
p'
su
1
k
In situ eo
su after
consolidation
e after
consolidation
NCL
CSL
p'
GBS Dv p'
In situ su
su = k.z (k = 1 to 2 kPa/m)
(or su = suo + k.z)
How long for strength
increase to occur ???
25
Staged Loading (Undrained)
q
CSL
Fully drained sd
6
su after two increments
5
4
In situ su
2
3
TSP
Dq due to total load > in situ su
failure if applied in 1 increment
1
p'
e
In situ eo
1
2
4
e after two increments
Consolidation
between increments
3
5
NCL
6
ESP in
undrained
loading
CSL
p'
26
Drained Tx Tests: Silica & Calc. Sands
Calc. sand
(Dog's Bay)
Dilation
Dilation
Silica sand
27
Drained & Undrained Tx Tests, Calc. Sand
Dog's Bay
Dog's Bay
TSP
Drained
Undrained
28