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Geomechanics 255 (610.255). Geomechanics Group School of Civil & Resource Engineering The University of Western Australia Part 2: Soil Strength Professor Martin Fahey . Outline. Shearing behaviour of sand (cohesionless soil) friction dilatancy

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geomechanics 255 610 255

Geomechanics 255 (610.255)

Geomechanics Group

School of Civil & Resource EngineeringThe University of Western Australia

Part 2: Soil Strength

Professor Martin Fahey

outline
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.

soil strength angle of internal friction f
Soil Strength: Angle of Internal Friction f'

N

N

N

R

f'

F

F

F

F

f': Angle of internal friction; m: coefficient of friction

tan f' = m = F/N

f'

f'

f': Angle of repose of sand heap

f': Angle of plank when block slides

principle of effective stress
Principle of Effective Stress

N

Water pressure u

F

N

F

F

Note: As u ® s (i.e. s' ® 0)strength (t) ® 0 (liquefaction)

other versions at uwa
Other Versions at UWA

Pneumatic jack (computer controlled) to apply vertical load

Load cells

Direct Via Lever

Hangers for load

direct shear tests on sand
Direct Shear Tests on Sand

D, M, L: Dense, Medium, Loose

relative density density index i d
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)

(obtained by vibration under load)

1 or 100%

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

0

Loosest (stable) state (emax, or rdmin)(obtained by pouring with funnel)

apparent cohesion in sand
Apparent Cohesion in Sand

Mohr-Coulomb Failure Criterion: tf = c' + s' tan f'

  • Failure surface is actually curved
  • Straight line through tests results at s' 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'

saw tooth model of dilation
"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
stress ratio dilation relationship taylor
Stress-Ratio Dilation Relationship (Taylor)

Peak stress ratio (tan f'peak)

DENSE

Stress ratio (t/s'n)

"Constant volume" stress ratio (tan f'cv)

LOOSE

dy/dx = 0

DENSE

dx

dy

Vertical displacement y (vol. strain)

Point of max. slope (nmax)

dy/dx = 0

LOOSE

dy/dx negative, increasing towards zero

critical state concept
Critical State Concept
  • When sheared, state of soil tends to migrate to a unique line in t - s' - e space. This is called the critical state line (CSL).
  • CSL has same gradient as NC line (l)
dilation depends on density and stress level
Dilation depends on density and stress level

Critical State Line (CSL)

At low stress, even loose samples may dilate

LOOSE

Void ratio e

At high stress, even dense samples may contract

DENSE

Normal effective stress s'n (or mean effective stress p')

relative density corrected for stress level

n

p' (kPa)

º

10

100

1,000

10,000

0.2 (20%)

3.2º

0.5º

-2.3 (?)

I

0.5 (50%)

17.1º

10.2º

3.3º

D

0.8 (80%)

(30.9º ?)

19.9º

8.8º

Relative Density Corrected for Stress Level
  • For plane strain, Bolton found that:
    • nmax (º) = 6 IR for plane strain
    • f´max – f´cv = 0.8 nmax
    • f´max – f´cv 5 Irº
  • For triaxial conditions
    • Must define 'dilatancy' in general as
        • where ev is volumetric strain = e1 + e2 + e3.
        • e1 is the major principal strain (generally ea in triaxial tests)
        • (negative sign, because expansion - I.e. dilation - is negative by normal sign convention, but want 'dilatancy' to be positive)

-2.2º (?)

drained undrained shear strength
Drained & Undrained Shear Strength

Shear stress t

Drained strength sd

f'cv

Undrained strength su

Undrained strength su

Drained strength sd

s'n

Void ratio e

Positive pore pressure reduces effective stress

Suction increases effective stress

Dilation

Undrained testÞ no volume change allowed

Loose states

eo

Dense states

Contraction

CSL

Normal effective stress s'n (or mean effective stress p')

triaxial test

Fa

scell

Area,A

scell

u

scell

Fa

Triaxial Test

The triaxial test enablesa variety of stress or strain controlled tests to be carried out on cylindrical soil specimens.

one of the uwa triaxial systems
One of the UWA Triaxial Systems

Axial motor drive system

Cell cover lowered once sample in place

Sample goes here

Cell pressure controller

Sample, enclosed in rubber membrane, with axial strain measuring devices attached

Control and data logging system

triaxial test background
Triaxial Test: Background
  • Direct shear test useful, but limited
    • Know only 1 normal stress (s'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 s'1, s'2, s'3 on three faces of cubical sample
    • even more general - allow shear stresses to be applied to the three faces

s'v

s'v (=s'1)

s'1

thv

s'h

s'h

s'h (=s'2)

s'2

s'h (=s'3)

s'3

“True triaxial” (s'1s'2 s'3)

“Simple shear”

Triaxial

triaxial test conduct of test
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)
    • s'h = s'3 = sc - uo, and s'1 = s'v = s'h = s'3 in this stage
    • anisotropic consolidation: generally vertical stress greather than horizontal stress: increase cell pressure and apply additional vertical load
    • s'h = s'3 = sc - uo, and s'1 = s'v > s'h = s'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
stress paths in triaxial tests
Stress Paths in Triaxial Tests
  • Different stress paths in “shearing” phase:
    • keep cell pressure constant (Dsh = 0) and increase vertical stress (Dsv +)
    • keep vertical stress constant (Dsv = 0) and reduce cell pressure (Dsh -)
    • keep vertical stress constant (Dsv = 0) and increase cell pressure (Dsh +)
    • keep cell pressure constant (Dsh = 0) and reduce vertical stress (Dsv -)
    • 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 = Dsv - DshDp = (Dsv + 2Dsh)/3
    • Dsh = 0 and Dsv = +  Dq = +Dsv and Dp = +Dsv/3 Dq/Dp =3

Shearing phase

Shearing phase

q

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.

In this case, shearing starts from an anisotropic stress state, following anisotropic consolidation.

3

3

1

1

Anisotropic consolidation phase

p

p

Anisotropic consolidation phase

total and effective stress paths tsp esp

"Standard" stress path: sh constantsv increased to failure

sv increasing

sh constant

Dq = Dsv

Dp = D sv/3

Dq/ Dp = 3

Total and Effective Stress Paths (TSP, ESP)

q

TSP: Total stress path (imposed by apparatus)

ESP: Effective stress path (soil response)

3

1

(ESP)

Du (+)

B

q = q'

(b')

B'

(Du may be negative)

p, p'

p

A

p'

p' = p - Du

drained undrained strength clays
Drained & Undrained Strength (Clays)

CSL

Deviator stress q

Bd

TSP

Drained strength sd

Au , Bu

Du -

Undrained strength su

Undrained strength su

Du +

3

Ad

Undrained strength depends on p'oand OCR

Drained strength sd

ESP

1

A

B

Void ratio e

mean effective stress p'

Ad

NC line

Dilation

Undrained testÞ no volume change allowed

"Wet of critical"

B

eo

A

Contraction

OC line

Bd

"Dry of critical"

CSL

Mean effective stress p'

initial and final undrained strength
Initial and Final Undrained Strength

q

su for NC soil increases after consolidation

Tank or GBS ® Dsv

su

su after consolidation

suo

CSL

NC soil

In situ su

1

Depth (m)

p'

e

k

In situ eo

su after consolidation

e after consolidation

NCL

In situ su

su = k.z (k = 1 to 2 kPa/m)

(or su = suo + k.z)

CSL

p'

How long for strength increase to occur ???

GBS ® Dsv ® p'

staged loading undrained

Consolidation between increments

ESP in undrained loading

Staged Loading (Undrained)

q

CSL

Fully drained sd

6

su after two increments

5

4

In situ su

Dq due to total load > in situ su

® failure if applied in 1 increment

2

3

TSP

1

p'

e

1

2

In situ eo

3

4

NCL

e after two increments

5

6

CSL

p'

drained tx tests silica calc sands
Drained Tx Tests: Silica & Calc. Sands

Calc. sand (Dog's Bay)

Silica sand

Dilation

Dilation

drained undrained tx tests calc sand
Drained & Undrained Tx Tests, Calc. Sand

Dog's Bay

Dog's Bay

TSP

Drained

Undrained