Civl2210 2008 Notes

10/9/2008

1

Golder Geomechanics Centre

CIVL2210 Fundamentals of Soil Mechanics

Professor David WilliamsDr Dorival Pedroso

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Topics

Soil classificationSoil phase (solids/water/air) relationshipsPrinciple of effective stressPore water pressureSeepage through soilsSoil strength testing and theoriesSoil consolidation testing and settlement theories

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n Soil consolidation testing and settlement theoriesFailure conditions in soilsClay mineralogy

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Lecture/Tutorial/Practical Schedule

Week Lectures Tutorials Practicals

1 L1: Introductory slide showL1: Soil classification

L2: Soil phase relationships

2 L3: Principle of effective stressL4: Pore water pressure

T1: Definitions and classification

P1: Visual classification &P2:Atterberg limits3 L5: Seepage through soils T2: Pore pressure &

effective stress

4 L5: Seepage through soils T3: Darcy’s Law

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n 5: Seepage t oug so s 3: a cy s aw

5 L5: Seepage through soils T4: Seepage

6 L6: Strength testing and theories T4: Seepage P3: Laboratory compaction &P4: Field density and CBR

7 L6: Strength testing and theories T5: Shear strength

8 L7: Strength testing and theories T5: Shear strength

9 L7: Consolidation testing andtheories

T6: Consolidation

10 L7: Consolidation testing andtheories

T6: Consolidation P5: Unconfined compression &P6: Consolidation

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Lecture/Tutorial/Practical Schedule

Week Lectures Tutorials Practicals

MID-SEMESTER BREAK

11 L8: Failure conditions in soil masses

Practice Exam P5: Unconfinedcompression and vane shear &P6: Consolidation

12 L9: Clay mineralogy T7: Lateral earthpressures

13 Revision Revision

EXAMINATION PERIOD

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Schedule

LECTURESFrom 10:00 to 11:50 am on Tuesdays in 63-348

TUTORIALSFrom 2:00 to 3:50 pm on Thursdays in 42-216

PRACTICALS

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From 2:00 to 4:00 pm on Mondays, Tuesdays, Wednesdays and Fridays in 48C-SOILS LAB

ASSESSMENTEnd of semester (multiple choice) exam:Tutorials:Completion of Practicals:

65%20%15%

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1 Soil Classification

1.1 Particle Size Distribution AnalysisParticle size limits:

Boulders > 200 mm

Cobbles 60-200 mm

Gravel 2-60 mmCoarse-grained

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Obtain distribution of sand size and coarser by sievingObtain distribution of silt and clay size by sedimentation (hydrometer), or laser

Sand 0.06-2 mm

Silt 0.002-0.06 mm

Clay < 0.002 mm

Fine-grained(can’t see or feel particles)

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1 Soil Classification (cont.)

1.2 Atterberg LimitsOf material passing 0.425 mm

SOILVOLUME

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Shrinkage limit, SL:

Plastic limit, PL:Liquid limit, LL:Plasticity index:

SL PL LLMOISTURE CONTENT, w

Solid Semi-solid Plastic Liquid

w at which soil reaches its minimum volumeon air drying from LL

minimum w at which soils deforms plastically

minimum w at which soil flowsPLLLI P −=

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1.2 Atterberg Limits (cont.)

Liquidity index,

Activity,

PL I

PLwI −=

massby clay %PIA =

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Emerson Class Number of a soil to assess slakability and dispersion – particularly relevant to the weathering of mine wastes on exposure

1 Low activity 1 2 Intermed. activity

4 High activity

<⎧⎪= −⎨⎪>⎩

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

Slaking

Complete dispersion Class 1 Some dispersion Class 2 No dispersion

I i t d ld d 3 di t il b ll i di till d t i b k

No slaking

Swelling Class 7 No swelling Class 8

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n Immerse moistened remoulded 3 mm diameter soil balls in distilled water in a beaker

Dispersion Class 3 No dispersion

No calcite or gypsum present

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

Dispersion Class 5 Flocculation Class 6

Calcite or gypsum present Class 4

Determination of Emerson class number of a soil

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1.3 Unified Soil ClassificationA common notation for describing soils, from which engineering properties, behaviour and use can be inferred (Lambe and Whitman, 1979):

Main SoilTypes Prefix

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

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GRAVEL predominant G

SAND predominant S

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

Inorganic CLAY Above A-line C

SILTBelow A-line

M

ORGANIC SOILS O

Fibrous soils

PEAT (no suffix) Pt

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Sub-division Suffix

Coarse-grained soils with < 5 % passing 0.06 mm

Well-graded (spread of sizes) W

Poorly-graded (uniform or gap-graded) P

Coarse-grained soils with > 12 % passing 0.06 mm

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Clay fines Above A-line C

Silt fines Below A-line M

Fine-grained soils

Low plasticity LL < 50 % L

High plasticity LL > 50 % H

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y In

dex

40

50

6

0

Dry strength and stickinessIncrease with increasingPlasticity Index, and dilatancy(permeability) decreases.

CHLow plasticity

High plasticity

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Liquid Limit

Plas

ticity

0 10 20 30 40 50 60 70 80 90 100

0

10

20

30

CL

OHorMH

OLorML

CL

MLCL-ML

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1.4 Engineering Use ChartBased on Unified Soil ClassificationRelates engineering parameters (strength, compressibility and permeability when compacted, and workability) applied to dams, canals, foundations and roads1 = highly desirable, 14 = highly undesirable(Lambe and Whitman, 1979)

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1.5 Other Classification SystemsOther 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)

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2 Phase (solids/water/air) Relationships

UnitsVoid ratio: -

VOLUMES WEIGHTSPROPORTIONS BY

VOLUME WEIGHT

VVeV

=

e

1w1

AV

WV

SV SWWW

0 Air

Water

Solids

AV

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Porosity: -

Relative density: -

Moisture content: %

Degree of saturation: %

SV

1V

T

V enV e

= =+

max

max minR

e eDe e

−=

−

100W

S

WwW

= ⋅

100W

A W

VSV V

= ⋅+

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

Measurable? Typical valuesVoid ratio: No 3 (slurry) to 0.33

VOLUMES WEIGHTSPROPORTIONS BY

VOLUME WEIGHT

VVeV

=

e

1w1

AV

WV

SV SWWW

0 Air

Water

Solids

VV

void

s

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( y)

Porosity: No 0.75 (slurry) to 0.33

Relative density: Yes 30 to 65%

Moisture content: Yes 100 to 5%

Degree of saturation: No 0 (dry) to 100%

SV

1V

T

V enV e

= =+

max

max minR

e eDe e

−=

−

100W

S

WwW

= ⋅

100W

A W

VSV V

= ⋅+

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UnitsTotal unit weight: kN/m3

Unit weight of water: kN/m3

TT

T

WV

γ =

9.81Wγ =

11 W

w Ge

γ+= ⋅ ⋅

+

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Effective unit weight: kN/m3

Dry unit weight: kN/m3

Specific gravity: -

' T Wγ γ γ= −

SD

T

WV

γ =

S

S W

WGV γ

=⋅

1 1T

WG

w eγ γ= = ⋅+ +

G w S e⋅ = ⋅

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Measurable? Typical valuesTotal unit weight: Yes (if regular) 15 to 20 kN/m3

Unit weight of water: kN/m3 Yes 9.81 kN/m3

TT

T

WV

γ =

9.81Wγ =

11 W

w Ge

γ+= ⋅ ⋅

+

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Effective unit weight: Yes 5 to 10 kN/m3

Dry unit weight: Yes (if regular) 0.5 to 20 kN/m3

Specific gravity: Yes 1.3 (coal) to 2.7to 19.3 (gold)

' T Wγ γ γ= −

SD

T

WV

γ =

S

S W

WGV γ

=⋅

1 1T

WG

w eγ γ= = ⋅+ +

G w S e⋅ = ⋅

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3 Principle of Effective Stress

3.1 Force, pressure, and stress (review)

=p FA

-F FA

pAiA

ExternalforceInternal

pressure

→=σ

dA 0lim dF

dA

Internalstress

Observedarea

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Pressure and stressdepend on Area

Pressure and stress vary on Space

There are at least x and ycomponents of stress (in 2D)

pAii

A

A σAx

σAy = 0

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3 Principle of Effective Stress (cont.)

3.1 Force, pressure, and stress (cont.)

Pressure and stress are better related with material mechanical changes (damage, failure, stretching, …) than forces

F F=

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A

σ V

Ground =AV

A

p FA

AA

=BV

B

p FA

AB

<<

σ H

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3 Principle of Effective Stress

σwu

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wσ σ' = - u

Grains

Water

Air

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wσ σ' = - u

σ

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Analogy

σwu

σ'

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3 Principle of Effective Stress (cont.)Hydromechanicalanalogy for load-sharing and consolidationa) Physical exampleb) Hydromechanical

analogc) Load applied

with valve closedd) Piston moves as

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)water escapes

e) Equilibrium with no further flow

f) Gradual transfer of load

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Effective stress σ’ is taken by the soil skeleton

In a water-saturated soil:where σ is the total stress (weight of everything above a particular point, including water), uw is the pore water pressure

' = −σ σ wu

σwu

σ'

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In a dry soil:

Changes in σ’ 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)

' =σ σσ

σ'

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The total vertical stress σV 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

4 Geostatic Stresses

water table

γ T

ground

a

σV

at A

=σ γVA T a?=σ HA

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γ SAT

b

A

c

depth z

at B

at C

at A

C

= + γσ σVC VA SAT c?=σ HC

= + γσ σVB VA SAT b?=σ HB

?σ HA

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Sand shear strength is proportional to σ’:where is the angle of internal friction of the sand.

Clay shear strength is given by:

is also proportional to σ’, the constant of proportionality dependent on the over-consolidation ratio (OCR):

' tanτ σ φ= ⋅

or 'uc cτ =

τ

φτ

τ

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( )

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

constant (typically 0.25)' NC

τσ

⎛ ⎞ = ≈⎜ ⎟⎝ ⎠

( )' '

m

OC NC

OCRτ τσ σ

⎛ ⎞ ⎛ ⎞≈ ⋅⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

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In soils of high permeability (sands and gravels), any excess u induced by an applied stress generally dissipates instantaneously, with the applied stress (σ) transferring instantaneously to the soil skeleton (σ’) → DRAINED BEHAVIOUR

Quick conditions or liquefaction are an exception. Here the rate of stress application is more rapid than the rate of drainage possible, σ’ ≤ 0, and seepage stresses exceed the strength of the soil

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n seepage stresses exceed the strength of the soil

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 (σ’) → UNDRAINED SHORT TERM AND DRAINED LONG TERM BEHAVIOUR. Refer to water-bed analogy (Lambe and Withman, 1979)

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4 Pore Water Pressure

4.1 Hydrostatic Pore Water PressureHydrostatic pore water pressure increases in proportion to the depth below the water table:

PORE WATER PRESSURE, u

Water table

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DEPTH, z

W Wu zγ= ⋅

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Hydrostatic pore water pressure uw increases in proportion to the depthz below the water table: (γw = 9.81 kN.m3)

4 Geostatic Stresses (cont.)

water table

ground

uw

0=WAu

= ⋅γ WW Wu z

? at A

Unsaturatedsoil mechanics

Assumption

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b

c

depth z

at B

at CC

= γ WWCu c

B

= γWWBu b

Aat A ng

thC

ompr

essi

bilit

yPe

rmea

bilit

y

The effective vertical stress σ’V at a given depth in the soil profile is the difference between total stress and water pressure


water table

ground

= −σ σ V WA AV A' u

0K≈σ σHA VA' '

σV’

at A

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n A 0Kσ σHA VA

depth z

at B

at C

at A

B

= −σ σ V WB BV B' u

0K≈σ σHB VB' '

C

= −σ σ V WC CV C' u

0K≈σ σHC VC' '

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Summary:1) The total vertical stress σV 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.

2) The total vertical stress σV 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

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n weight.

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 σ’V at a given depth in the soil profile is the difference between total stress and water pressure

= ⋅σ γV T z

= −σσ V V W' u = ⋅σ σ0H VK' '

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4 Pore Water Pressure (cont.)

4.2 Pore water suctionPore 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 and increases above the water table

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n and below the water table, and increases above the water tableThe 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

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4 Pore Water Pressure (cont.)4.2 Pore water suction (cont.)

PORE WATER PRESSURE, uNet evaporation Net percolation

CLAY

SILT

SAND

Water table~1 m

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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.

DEPTH, z

Hydrostatic (No flow)

W Wu zγ= ⋅

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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 deformation and

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n common practice to ignore solute 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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Typical suction variations:

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Effects of covers and trees on suction:

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Volume versus suction versus moisture content:

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Soil Water Characteristic (Moisture Retention) Curves:

25

30

35

40

CO

NTE

NT

(%) Drying curve

Re-wetting curve

MMC @ AEV

AEV

Near-saturated MMC@ test density

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0

5

10

15

20

25

0.01 0.1 1 10 100 1000 10000 100000 1000000

MIN

ING

MO

ISTU

RE

C

SUCTION (kPa)

MMC @ AEV

Residual suction

Slope beyond AEV,representing water storage

capacity and ease of dewatering

"Oven-dry"

Hysteresis betweendrying and re-wetting

Suction @ AEV

Residual MMC

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5 Seepage5.1 Saturated (or near-saturated) Seepage

5.1.1 Darcy’s law:(S > 85%, which applies in many cases)

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 applies since flow is in

Aikq ..−=

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gthe direction of decreasing head.

For fine grained soils, k may be characterised by:

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 + velocity head ( for laminar flow).

beak .=

)/( wu γ02/2 ≈gv

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5 Seepage (cont.)

5.1.2 k of stratified soils (layers )

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

For horizontal flow (parallel to the strata), i is constant:

nlll ,.., 22

nn

n

klklkllllk

/..//..

2211

21

++++++

=

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n (p ),

n

nn

lllklklklk

++++++

=....

21

2211

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5 Seepage (cont.)5.2 Laboratory Permeability Testing

5.2.1 Saturated permeability testingFor m/s (clean sands and gravels), use a constant head permeameter.

For m/s (silts and clays), use a falling head permeameter.

410 −>k

47 1010 −− << k

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For m/s (clays), use indirect methods such as an oedometer test.

Typical values of (Fang, 1990)

Partially saturated 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.

k

k

710 −<k

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5 Seepage (cont.)

5.2.1 Saturated permeability tests (cont.)

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5 Seepage (cont.)

5.2.2 Constant head permeameter (Head, 1982):

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5 Seepage (cont.)

5.2.3 Falling head permeameter (Head, 1982):

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5 Seepage (cont.)

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:

wvv mck γ..=

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5 Seepage (cont.)

5.3 Field Measurement of PermeabilityFor coarse grained soils and fractured rock use pumping tests.

Unconfined flow (Cedergren, 1977):

1 22 2

2 1

l n ( / )q r rkh hπ

⎛ ⎞= ⋅ ⎜ ⎟−⎝ ⎠

( r2 / r1 )

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5 Seepage (cont.)

5.3 Field Measurement of Permeability (cont.)

Confined flow:

where q is the volumetric flow rate pumped from the well, and are the radii from the well to the observation boreholes 1 and 2, and are the total heads at the observation boreholes 1 and 2,

d D i h hi k f h fi d if

⎟⎟⎠

⎞⎜⎜⎝

⎛−

⋅=12

21 )/ln(2 hh

rrD

qkπ

1r2r

1h 2h

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n and D is the thickness of the confined aquifer.

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).

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5 Seepage (cont.)

5.4 Seepage Flow5.4.1 1-D flow

For upward vertical flow in sands, the quick condition is given by:

5.4.2 2-D flowAssuming homogeneous and isotropic conditions within the

0'≤vσ

1≈−=

w

wsaturatedcriticali

γγγ

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n seepage zone, and both the soil particles and pore water to be incompressible, the CONTINUITY EQUATION is given by:

where and 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:

0=∂∂

+∂∂

zv

xv zx

0=∂∂

+∂∂

zh

xh

xv zv

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5 Seepage (cont.)

5.4.2 2-D flow (cont.)The Laplace Equation may be solved by:

Graphical means using FLOW NETELECTRICAL 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:

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n NUMERICAL TECHNIQUES:For anisotropic conditions, the STEADY STATE SEEPAGE EQUATION is given by:

where and are the total heads in the x and z directions, respectively, and and are the coefficients of permeability in the x and z directions, respectively.

0=∂∂⋅+

∂∂⋅

zhk

xhk z

zx

x

xh zhxk zk

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5 Seepage (cont.)

5.5 Flow Nets – RulesSets of flow lines (average trajectories of seepage) and equipotentiallines (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:

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n 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).

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5 Seepage (cont.)

5.5 Flow Nets (cont.)

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5 Seepage (cont.)


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5 Seepage (cont.)


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5 Seepage (cont.)


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5 Seepage (cont.)


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5 Seepage (cont.)


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5 Seepage (cont.)5.5 Flow Nets (cont.)

The flow through the seepage zone is given by:

where 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.Th ithi th d f th t t th id f th

NMhkq ⋅Δ⋅=

hΔ

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n The u within the seepage zone reduces from that at the side of the 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:

where and are the widths of the flow tubes in materials of and , respectively (refer to examples from Cedergren, 1977).

1w 2w 1k2k

2

1

2

1

kk

ww

=

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5 Seepage (cont.)


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5 Seepage (cont.)


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5 Seepage (cont.)


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5 Seepage (cont.)


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n

For anisotropic soils, flow nets may be used with a transformed scale (refer to examples from Cedergren, 1977):

and xkkx

x

z ⋅=' xzkkNMhq ⋅⋅Δ=

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5 Seepage (cont.)


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5 Seepage (cont.)


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5 Seepage (cont.)

5.6 Special Cases5.6.1 Local effects of seepage stresses

Quick conditions can occur in sands if seepage stresses render

This can be avoided by decreasing i (increase l using a cut-off and/or decrease h by dewatering) and/or by increasing by surcharging.

0' ≤vσ

'vσ

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n Seepage stresses can cause have in clays, and, in the extreme may facilitate piping.

5.6.2 Flow through discontinuous rockThe 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.

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5 Seepage (cont.)

5.7 Unsaturated Seepage5.7.1 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

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n 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.

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5 Seepage (cont.)

5.7 Unsaturated Seepage (cont.)5.7.1 Partially saturated permeability (cont.)

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5 Seepage (cont.)

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

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n 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.

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5 Seepage (cont.)

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

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n of loops different for each maximum 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.

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5 Seepage (cont.)

5.7.2 Suction/Moisture Content Characteristic (cont.)

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Soil Water Characteristic (Moisture Retention) Curves:

25

30

35

40

CO

NTE

NT

(%) Drying curve

Re-wetting curve

MMC @ AEV

AEV

Near-saturated MMC@ test density

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n

0

5

10

15

20

25

0.01 0.1 1 10 100 1000 10000 100000 1000000

MIN

ING

MO

ISTU

RE

C

SUCTION (kPa)

MMC @ AEV

Residual suction

Slope beyond AEV,representing water storage

capacity and ease of dewatering

"Oven-dry"

Hysteresis betweendrying and re-wetting

Suction @ AEV

Residual MMC

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5 Seepage (cont.)

5.7.3 Unsaturated seepageSurface evaporation, a surface cover, steady state infiltration, and tress have different effects on the suction profile (Fredlund and Rahardjo, 1993).

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5 Seepage (cont.)

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

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n

this induces unsaturated seepage through the relatively free-draining bund; Williams, 1992).

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6 Strength Testing and Theories

6.1 Strength Testing6.1.1 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 tests (for ) and shear reversal tests' 'c φ

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n Consolidated-drained tests (for ), and shear reversal tests (for residual shear strength ) 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).

, c φ, R Rc φ

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6.1 Strength Testing (cont.)6.1.1 Direct shear test (cont.)

6 Strength Testing and Theories (cont.)

N

F

F appliedforce

surface ofshear

N

F

F

reaction

displacement

movement

Stre

n

start of test 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.

soil specimen surface ofsliding length = breadth = L

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6.1 Strength Testing (cont.)6.1.1 Direct shear test (cont.) N

F

F

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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

N

F

F

Stre

n 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 pre-determined shear plane occurs, eg. slope instability.

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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.

N

F

F

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n 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.

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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.

N

F

F

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n 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.

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6.1 Strength Testing (cont.)6.1.2 Vane shear test

The four-bladed cruciform vane is pushed into soft cohesive soil and then rotated.

The torque required to rotate the cylinder of soil enclosing the vane is measured, from which the undrained shear strength of the soil is

appliedtorque

D

D

H

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n undrained shear strength of the soil is calculated.

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).

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appliedtorque

D

resistingtorque

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n

D

H

surface areaDHπ=

H

D

vane blades cylinder of soil rotated by vane

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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 may be calculated from the measured torque T using

⎛ ⎞

Us

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n

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.

2 3

2 6UD H DT sπ

⎛ ⎞⋅= ⋅ ⋅ +⎜ ⎟

⎝ ⎠

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6.1 Strength Testing (cont.)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.

μ

Stre

n and has been found to not apply to clays in warmer climates.1.2

1.0

0.8

0.6

0.40 20 40 60 80 100 120

Plasticity index

μ

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6 Strength Testing and Theories (cont.)6.1 Strength Testing (cont.)

6.1.3 Triaxial TestTriaxial testing(on cylindrical soil samples) includes:

the unconfined compression testthe triaxial compression testand 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.A i l d ll b li d

membrane

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n Axial and cell pressures may be applied independently.Initially, the estimated average in situ stress is applied isotropicallyThe sample is then sheared by either increasing (compression) or decreasing (extension) to failure, holding 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).

1 3( )σ σ=

1σ

3σ

1σ

3σ

1σ3σ

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Theories (cont.)

6.1 Strength Testing (cont.)6.1.3 Triaxial Test (cont.)

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Theories (cont.)

6.1 Strength Testing6.1.3 Triaxial Test

Triaxial tests may also be carried out in a hydraulic stress path cell, which eliminates the

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n eliminates the need for a load frame, and, being hydraulically driven, is more amenable to automated control (Head, 1982). hydraulic driven:

displacement driven:

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The unconfined compression test is suitable for determining the undrained strength:

Of soil and rock samples which are capable of being formed as self-supporting cylinders.

1( / 2 )uc σ=

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n Triaxial compression and extension tests may be carried out as follows:

Unconsolidated-undrained shearing (for ).Consolidated-undrained shearing (for ).Consolidated-undrained shearing, with pore water pressure measurement (for ).Consolidated-drained shearing (for ).

0, ≈uuc φ0, ≈cucuc φ

',' φc',' φc

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Modes of failure in a triaxial compression test include barrelling, shear plane failure, and a combination of these two (Head, 1982).

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n

plastic failure (barrelling) brittle failure (shear plane) intermediate type

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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 kPafi i th b t 10 kP b k

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n confining pressure no more than about 10 kPa < back-pressureSaturation is tested by measuring the B pore pressure parameter. For full saturation, B =1, where

Corrections are required to allow for the membrane, friction losses (on the axial load piston), and change in sample area.

( )[ ] 3313 σσσσ Δ⋅=Δ−Δ+Δ=Δ BABu

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6 Strength Testing and Theories (cont.)6.1 Strength Testing (cont.)

6.1.3 Triaxial Test (cont.)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 t i d i t i i l t t b tt t ti f

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n The stresses imposed in a triaxial test are a better representation of 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.

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6.1 Strength Testing (cont.)6.1.4 Unsaturated strength of clays

Undrained shear strength, Su

Suctioneffect

water table

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n

Depth, z

Self-weighteffect

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6.1 Strength Testing (cont.)6.1.5 Strength testing of rocks

Strength testing methods applied to rocks include:the point load index (tensile) strength testthe direct shear testthe triaxial testand the Hoek cell test (Brown, 1981).

Stre

n

The principles involved are similar to those which apply to the strength testing of soils.

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6.2 Strength Theories6.2.1 Idealized stress/strain behaviour

Elastic


Stre

n

STRAIN

STRESS

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Rigid, perfectly plastic


STRESS

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n

Elastic, perfectly plastic

STRAIN

STRAIN

STRESS

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Non-linear elastic


STRESS

Stre

n

Non-linear elastic, work hardening

STRAIN

STRAIN

STRESS

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Non-linear elastic, work softening


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STRAIN

STRESS

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6.2 Strength Theories6.2.2 Stress/strain behaviour of soilsTypical stress/strain curves

(i) Normally consolidated soils (loose sands and soft clays)


SHEARSTRESS

MAXτ

Stre

n

(ii) Overconsolidated soils (dense sands and stiff clays)

SHEAR STRAIN

peak (small strain)

ultimate (large strain)

residual

(very large strain in clayey soils)

SHEAR STRESS

SHEAR STRAIN

?

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6.2 Strength Theories6.2.3 Undrained shear strength su

For normally consolidated (nc) soils (Skempton, 1957)


' 0.11 0.0037UP

V NC

s Iσ⎛ ⎞

≈ +⎜ ⎟⎝ ⎠

Stre

n

where IP is the plasticity index in %.For overconsolidated (oc) soils

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)

( )' 'mU U

V VOC NC

s s OCRσ σ⎛ ⎞ ⎛ ⎞

≈ ⋅⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

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6.2 Strength Theories6.2.4 Soil behaviourin drained shear

For a drainedsimple shear test, Atkinson (1993) described the stress/strain


vε Dψ

D

W

peak

ultimate

'σsame

'τ

~1% >10% γ

'Pτ'Tτ

W sample initiallyon the wet side of critical

D sample initiallyon the dry side of critical

Stre

n stress/strain behaviour of soils in the following diagrams:

compression

γWψ−

(u = constant)

vδε

'σ'τ

ψ

δγ

W

D

γ

e

Te

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6.3 Mohr Circles (triaxial results)Circle centre is located at for total stresses, and at for effective stresses.


1 3 1 3max

' 'Radius of circle2 2

σ σ σ σ τ− −= = =

1 3( ) / 2σ σ+1 3( ' ') / 2σ σ+

τ

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n

STRAIN

STRESS

1 3 1 3 2 2

σ σ σ σ+ −

maxτ

3 1 σ σ

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6.4 Stress Paths (triaxial results)Total stress axes:

MIT:

Cambridge:


1 3 1 3, or,2 2

s tσ σ σ σ+ −= =

2 , 3 2

A R A Rp qσ σ σ σ+ −= =

Stre

n

Effective stress axes:MIT:

Cambridge:

where

1 3 1 3' ' ' '' , ' , 2

or2

s tσ σ σ σ+ −= =

' 2 ' ' '' , '3 2

A R A Rp qσ σ σ σ+ −= =

1 1 33 ' ', , , ' 'AA R Rσ σ σ σ σ σσ σ== ==

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6.4 Stress Paths (triaxialresults)

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


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6.5 Failure in Direct Shear


STRESS

τ ( , )F Nτ σ

Stre

n

NORMAL STRESS, Nσ

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6.7 Mohr-Coulomb Failure Criterion6.7.1 In direct shear

Total stresses (undrained conditions in a clay)

where is the undrained shear strength, is the undrainedfriction angle ( 0) and is the applied total normal stress.


tanf U N Ucτ σ φ= + ⋅

Uc UφNσ

Stre

n

NORMAL STRESS,

STRESS

τ ( 0)F U Ucτ φ= =

Nσ

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6.7 Mohr-Coulomb Failure Criterion6.7.1 In direct shear

Effective stresses (sands and drained clays)

where is the applied effective normal stress.An applied stress will, with time, give rise to a change in normal


'Nσ

' ' tan 'f Ncτ σ φ= + ⋅

Stre

n

pp g gstress , which will give rise to a change in shear strength given approximately by

τ

'Nσ'c

'NσΔ' tan 'F Nτ σ φΔ = Δ ⋅

FτΔ

'φ' ' tan 'f Ncτ σ φ= + ⋅

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6.7 Mohr-Coulomb Failure Criterion6.7.2 In triaxial shear

Total stresses

The failure surface will be approximately horizontal, tangential to the


21 3 tan 45 2 tan 45

2 2o oU U

Ucφ φσ σ ⎛ ⎞ ⎛ ⎞= ⋅ + + ⋅ +⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

Stre

n

pp y gMohr circle.

STRESS

Unconfined

( )0f u ucτ φ= =

σ

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6.7 Mohr-Coulomb Failure Criterion6.7.2 In triaxial shear

Effective stresses

The failure surface is drawn tangential to the Mohr circle.


21 3

' '' ' tan 45 2 ' tan 452 2

o ocφ φσ σ ⎛ ⎞ ⎛ ⎞= ⋅ + + ⋅ +⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

Stre

n

g

STRESS

σ

' ' tan 'f Ncτ σ φ= + ⋅

'φ

'c

'σ

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6.8 Soil Moduli


SHEARSTRESS

ITESE

TEURE

Stre

n

where and are the initial tangent, secant, tangent, and unload/reload moduli, respectively.

IT S TE ,E ,E ,

T S IT URE < E < E < E

SHEAR STRAIN

URE

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6.9 Stress/Strain Behaviour of Rocks and Rockfill

Different rock types


Stre

n types experience different stress-strain behaviour(Hunt, 1984).

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6.9 Stress/Strain Behaviour of Rocks and Rockfill (cont.)Fractured rock typically experiences elastoplastic (with work hardening) stress-strain behaviour (Goodman, 1989)


Stre

n

STRAIN

STRESS

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6.9 Stress/Strain Behaviour of Rocks and Rockfill (cont.)The failure criteria for rock masses typically have the following form (Brown, 1981).

6 Strength Testing and Theories (cont.)H

[M

Pa]

Bφ

Stre

n

0

SHEA

R S

TR

ENG

TH

NORMAL STRESS [MPa]

Rφ

c’

C

A

Aφ

Aσ

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6.9 Stress/Strain Behaviour of Rocks and Rockfill (cont.)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)


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STRAIN

STRESS

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6.9 Stress/Strain Behaviour of Rocks and Rockfill (cont.)


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6.9 Stress/Strain Behaviour of Rocks and Rockfill (cont.)Typical friction angles

for coal mine spoil were compared with Leps’ data by Seedsmanet al. (1988)


55

50

45

40

Average rockfill

High density, well graded,strong particles

Low density, angl

e

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n

35

30

25

10020

200 500 1000 2000Normal Stress (kPa)

y,poorly graded,weak particles Cemented

Poorly lithified

Weathered

Fric

tion

a

Compilation of the strength ofrockfill as measured in largetriaxial tests (after Leps, 1970)compared with direct shearvalues for coal mine spoil.

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6.9 Stress/Strain Behaviour of Rocks and Rockfill (cont.)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.


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7.1 Consolidation Testing7.1.1 Oedometer test

The oedometer 1-D consolidation test is used to determine the consolidation characteristics (magnitude and rate) of low permeability soils (Head, 1982).

7 Consolidation Testing and Settlement Theories

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7 Consolidation Testing and Settlement Theories (cont.)7.1 Consolidation Testing

7.1.1 Oedometer test (cont.)In an oedometer test, a sample is cut usingthe oedometer ring

This ring is mounted in the oedometer cell and surrounded with water.

10 or logt t

h

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n

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.

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7 Consolidation Testing and Settlement Theories (cont.)

7.1 Consolidation Testing7.1.1 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.

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n 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.

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Application of oedometer test:

The test is applied to the primary consolidation, swelling, and creep of low permeability soils

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n

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.

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Advantages of oedometer test:☺ The test procedure and calibrations have been standardised

and are reproducible.☺ The test results provide a reasonable estimate of settlements

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n ☺ The test results provide a reasonable estimate of settlements, provided they are properly interpreted.

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.

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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).

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7 Consolidation Testing and Settlement Theories (cont)

7.1.2 Rowe consolidometer testApplication 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:

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n

☺ 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.

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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.

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Limitations of Rowe cell Test:The Rowe cell test is more time consuming and difficult to set up than the oedometer test.

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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:

7 Consolidation Testing and Settlements Theories (cont.)

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n 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.

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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 for a footing on a deep sand layer with a deep water table may be approximately by

( ) ( )q B mmρ ⋅≈

( )i AVρ

Stre

n

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.

( ) ( )5i AV

mmN

ρ ≈

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7.2. Settlement Theories: (cont.)7.2.2 Immediate Settlement of soils :(cont.)

Immediate settlement of clays is generally calculated using elasticity theory, using the undrained elastic parameters:

and (typically = 0.5).

For example, for a flexible footing (Bowles, 1968)

iρ

uE uv

Stre

n

where and are constants dependent on the geometry of the problem, q is the uniformly distributed applied pressure, and B is the footing width.

20 1

. (1 )i uu

q B vE

ρ μ μ= ⋅ ⋅ ⋅ −

0 1 μ μ

0 1.0.75

u

q BE

μ μ= ⋅ ⋅

0.5uv← =

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Values of and for settlement computations using previous equation (after Janbu, Bjerrum, and Kjaensli).

0 1 μ μ

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7.2. Settlement Theories: (cont.)7.2.3 Primary consolidation of clays:

Definition:Primary consolidation is the time dependent expulsion of waterfrom 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 accompanied by the expulsion of

σσ

Stre

n which dissipates with 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.

'σ

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7 Consolidation Testing and Settlements Theories: (cont.)7.2. Settlement Theories: (cont.)

7.2.4 1-D consolidation (Oedometer Test): (cont.) for a constant increment of stress

90t50t

Vc

C

Stre

n

Consider 1-D PRIMARY CONSOLIDATION over several increments of stress, including an unload/reload loop.

CC

RC

Vm

Rt Cα

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7.2.4 1-D consolidation (Oedometer Test): (cont.)For normally consolidated clays

11 0 10

0

'log'

vC

v

e e C σσ⎛ ⎞

= − ⎜ ⎟⎝ ⎠

10log 'Vσ

eCC

RC

110

0 0

'log1 '

vc C

v

H Ce

σρσ

⎛ ⎞ ⎛ ⎞= ⎜ ⎟ ⎜ ⎟+⎝ ⎠ ⎝ ⎠

Stre

n

where is the initial void ratio (corresponding to ), is the void ratio corresponding to , is the 1-D primary consolidation corresponding to the stress increment , and H is the thickness of the consolidating layer.For overconsolidated clays

0e 1e1 'vσ cρ

1 0' ' 'v vσ σ σΔ = −

0 'vσ

11 0 10

0

'log'

vR

v

e e c σσ⎛ ⎞

= − ⋅ ⎜ ⎟⎝ ⎠

0 0v⎝ ⎠ ⎝ ⎠

110

0 0

'log1 '

vc R

v

H ce

σρσ

⎛ ⎞ ⎛ ⎞= ⋅ ⋅⎜ ⎟ ⎜ ⎟+⎝ ⎠ ⎝ ⎠

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7.2. Settlement Theories: (cont.)7.2.4 1-D consolidation (Oedometer Test): (cont.)Alternatively

where is the coefficient of volume change.

'c v vm Hρ σ= ⋅Δ ⋅

vm

10log 'Vσ

eCC

RC

Stre

n

For normally consolidated clay

0.435 (1 ) '

cv

v

Cme σ

=+

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7.2. Settlement Theories: (cont.)7.2.4 1-D consolidation (Oedometer Test): (cont.)

Primary consolidation may also be estimated indirectly using elasticity theory

where is the total settlement corresponding to the drained elastic parameters and . For example, for a flexible footing (Bowles 1968)

c T iρ ρ ρ= −

Tρ'E 'v

Stre

n (Bowles, 1968)

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.

20 1

. (1 ' )'T

q B vE

ρ μ μ= ⋅ ⋅ ⋅ −

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7.2. Settlement Theories: (cont.)7.2.5 3-D effects: (cont.)

Skempton and Bjerrum method:

( )3c oedDρ μ ρ

−= ⋅

Stre

n

where is the oedometer and is a correction factor dependent on the pore pressure parameter A and degree of overconsolidation (Scott, 1969;Fang, 1990 ).

oedρcρ μ

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7.2.5 3-D effects: (cont.)

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7.2.5 3-D effects: (cont.)

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7.2.6 Rate of 1-D primary consolidation (Terzaghi):Diffusion equation for 1-D primary consolidation

2

2vu uc

z t∂ ∂

=∂ ∂

10 or logt t

h

vw v

kcmγ

=⋅

Stre

n

where is the coefficient of consolidation.The solution of the diffusion equation introduces the non-dimensional time factor

where D is the maximum vertical drainage path length.For 1-way vertical drainage D=HFor 2-way vertical drainage D=H/2

vc

2v

vc tTD⋅

=

w vmγ ngth

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7.2. Settlement Theories: (cont.)7.2.6 Rate of 1-D primary consolidation (Terzaghi):

Degree of consolidation

10 0

10

1 1

1

H H

tct

Hcf

u dz u dzH HU

u dzH

ρρ

⋅ − ⋅= =

⋅

∫ ∫

∫

Stre

n

where is the consolidation at time t, is the final consolidation, is the initial excess pore water pressure, and is the excess pressure at time t.

0H ∫

0

0

1 ( )

1

H

v i

H

i

u dzH

u dzH

σ − ⋅=

⋅

∫

∫ctρ ctρ

tuiu

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7.2. Settlement Theories: (cont.)7.2.6 Rate of 1-D primary consolidation (Terzaghi):The relationship between and is a function of the assumed initial pore water pressure distribution and the maximum drainage path length (Craig, 1992).

vT U

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Laboratory determination of :(time) fit

vc10log

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Laboratory determination of :(time) fit

vc

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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 is the characterised by approximately constant settlement per log cycle of time.

sρ

Stre

n

where is the coefficient of secondary consolidation, and is the reference time.

< 0.001 for OC clays0.005 for NC clays, increasing to0.02 with increasing organic content0.02 – 0.1 for Pt

10logsR

tD Ctαρ

⎛ ⎞= ⋅ ⋅ ⎜ ⎟

⎝ ⎠

Cα

Cα≈

≈

Rt

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7.3 Creep of Soils and Rockfill: (cont.)For rockfill, the 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 value may range from 0.01 to 0.04 (Seedsman and Williams, 1987).

Cα

Cα

Stre

n

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8 Failure Conditions in Soil Masses

8.1 Stress States8.1.1 At rest state

where and are the horizontal and vertical effective stresses, respectively, and is the at rest earth pressure coefficient.For normally consolidated soils

' 'h o vkσ σ= ⋅

'hσ 'vσok

Stre

n

where is the effective angle of internal friction of the soil. Typically is in the range 0.4 to 0.6.

For overconsolidated soils, is typically 1.

where n is an empirical constant dependent on soil type.

1 sin 'ok φ−

'φ

0( )OCk ≥

0 0( ) ( ) ( )nOC NCk k OCR⋅

0( )NCk

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8 Failure Conditions in Soil Masses (cont.)

8.1 Stress States (cont.)8.1.2 Active and passive failure statesRankine active earth pressure coefficient:

is typically about 0.33, and develops at relatively small lateral

1 sin '1 sin 'Ak φ

φ−

=+

Ak

Stre

n

yp y p ydilation.Rankine passive earth pressure coefficient:

is typically about 3.0, and requires substantial lateral compression to be fully mobilised.

A

1 sin ' 11 sin 'P

A

kK

φφ

+= =

−

Pk

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8.1 Stress States (cont.)8.1.2 Active and passive failure states

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8.1 Stress States (cont.)8.1.3 Critical StatesThe 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 as shown in the following diagrams (Atkinson 1993)

Stre

n the void ratio, as shown in the following diagrams (Atkinson, 1993)

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8.1 Stress States (cont.)8.1.3 Critical States

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8 Failure Conditions in Soil Masses (cont.)8.1 Stress States (cont.)

8.1.3 Critical StatesThe CSL is given by

(Mohr- Coulomb failure criterion, with effective cohesion c’= 0)

' ' tan 'f f cτ σ φ= ⋅

10log 'f c fe e C σΓ= − ⋅

Stre

n

where the subscript denotes ultimate failure conditions at the critical state, and is the friction angle at the critical state. defines the position of the CSL, in the same way as 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.

10f c fΓ

f

0eeΓ'cφ

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9 Clay MineralogyGranular 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.

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Fig. 1.1 Single grain structure

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9 Clay Mineralogy (cont.)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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Fig. 1.2 Clay minerals: basic units

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9 Clay Mineralogy (cont.)

The principal clay minerals, kaolinite, illite and montmorillonite, have the structures (Craig, 1992)

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Fig. 1.2 Clay minerals: basic units

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9 Clay Mineralogy (cont.)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

( )

Stre

n 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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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 short-range van der Waals forces. Like charges repel, Net repulsion leads to face-to-face orientation, a dispersed structure. Net attraction leads to edge-to-face or edge-to-edge orientation, a flocculated structure

Stre

n to edge to face or 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).

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Fig. 1.4 Clay structures: (a) dispersed, (b) flocculated, (c) bookhouse, (d) turbostratic, (e) example of a natural clay.

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Civl2210 2008 Notes