14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF...

74
Slide 1 of 74 Revised 03/2014 14.330 SOIL MECHANICS Consolidation FUNDAMENTALS OF CONSOLIDATION CLAY SAND SAND DEPTH (Vertical Stress Increase) CONSOLIDATION: Volume change in saturated soils caused by the expulsion of pore water from loading. Saturated Soils: causes u to increase immediately Sands: Pore pressure increase dissipates rapidly due to high permeability. Clays: Pore Pressure dissipates slowly due to low permeability. after Figure 7.1a. Das FGE (2005).

Transcript of 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF...

Page 1: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 1 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

FUNDAMENTALS OF CONSOLIDATION

CLAY

SAND

SAND

DEPTH

(Vertical Stress Increase) CONSOLIDATION:Volume change in saturated soils caused by the expulsion of pore water from loading.

Saturated Soils:

causes u to increase immediately

Sands: Pore pressure increase dissipates rapidly due to high permeability.

Clays: Pore Pressure dissipates slowly due to low permeability.

after Figure 7.1a. Das FGE (2005).

Page 2: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 2 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

CLAY

SAND

SAND

DEPTH

(Vertical Stress Increase)

after Figure 7.1a. Das FGE (2005).

At Time of Initial Loading (t = 0)

Pore water takes initial change in vertical loading (u) since

water is incompressible

Soil skeleton does not see initial loading

Variation in Total, Pore water, and Effective Stresses in Clay Layer

Figure 7.1b. Das FGE (2005)

FUNDAMENTALS OF CONSOLIDATION

Page 3: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 3 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

CLAY

SAND

SAND

DEPTH

(Vertical Stress Increase)

after Figure 7.1a. Das FGE (2005).

Between time t = 0 to t = ∞

Pore water increase due to initial loading dissipates

Soil skeleton takes loading as pore pressure decreases

Variation in Total, Pore water, and Effective Stresses in Clay Layer

Figure 7.1c. Das FGE (2005)

FUNDAMENTALS OF CONSOLIDATION

Page 4: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 4 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

CLAY

SAND

SAND

DEPTH

(Vertical Stress Increase)

after Figure 7.1a. Das FGE (2005).

At time t = ∞

Pore water increase due to initial loading completely dissipated

(u = 0)

Soil skeleton has taken loading. Effective stress increase now equals

vertical stress increase '

Variation in Total, Pore water, and Effective Stresses in Clay Layer

Figure 7.1e. Das FGE (2005)

FUNDAMENTALS OF CONSOLIDATION

Page 5: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 5 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

CLAY

SAND

SAND

DEPTH

(Vertical Stress Increase)

after Figure 7.1a. Das FGE (2005).

THE SPRING ANALOGY

(a)Initial

Loading

Water takes load

Soil (i.e. spring) has

no load

(b)Dissipationof Excess

Water Pressure

Water dissipating

Soil starts to take load

(c)Final

Loading

Water dissipated

Soil has load

FUNDAMENTALS OF CONSOLIDATION

Page 6: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 6 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

ConsolidometerFigure 7.2. Das FGE (2005)

D2435-11 Standard Test Methods for One-Dimensional Consolidation Properties of Soils Using Incremental Loading

ONE DIMENSIONAL (1D) CONSOLIDATION TEST

Page 7: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 7 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

Figure E-1 USACE EM1110-1-1904.

ShearTrac II DSS Equipment(Courtesy of Geocomp Corporation)

1D CONSOLIDATION TEST EQUIPMENT

Page 8: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 8 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

Figure 7.4. Das FGE (2005).

1D CONSOLIDATION TESTINGLOAD INCREMENT DATA

THREE STAGES

Stage I: Initial CompressionPrimarily caused by preloading.

Stage II: Primary ConsolidationExcess pore water pressuredissipation and correspondingsoil volume change.

Stage III: Secondary ConsolidationOccurs after excess porewater pressure dissipation.Due to plastic deformation/readjustment of soil particles.

Page 9: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 9 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

VOID RATIO-PRESSURE PLOTS

Figure 7.5. Das FGE (2005)

s

v

s

v

s

vo H

HAHAH

VVe Initial Void Ratio (eo):

Page 10: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 10 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

sHHe 1

1

11

Figure 7.6. Das FGE (2005)

Figure 7.5. Das FGE (2005)

Change in Void Ratio due to 1st

Loading (e1):

New Void Ratio after 1st

Loading:11 eee o

@ End of Load 1

VOID RATIO-PRESSURE PLOTS

Page 11: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 11 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

sHHe 2

2

22

Figure 7.6. Das FGE (2005)

Figure 7.5. Das FGE (2005)

Change in Void Ratio due to 2nd

Loading (e2):

New Void Ratio after 2nd Loading:

sHHee 2

12

@ End of Load 2

VOID RATIO-PRESSURE PLOTS

Page 12: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 12 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

Figure 7.7. Das FGE (2005).

Final e – log ´ plots consist of results of numerous load & unload

incrementsTwo Definitions of Clays based on Stress History:

Normally Consolidated (NC):The present overburden pressure (a.k.a. effective in-situ stress) is the most the soil has ever seen.

Overconsolidated Clay (OC):The present overburden pressure is less than the soil has experienced in the past. The maximum effective past pressure is called the preconsolidation pressure (´c) or Maximum Past Pressure (´vm)

VOID RATIO-PRESSURE PLOTS

Page 13: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 13 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

DETERMINATION OF MAXIMUM PAST PRESSURE(´c or ´vm)

Figure 7.8. Das FGE (2005).

Graphical Method(Casagrande, 1936)

1. Visually identify point of minimum radius of curvature on e-log ´curve (i.e. Point a).

2. Draw horizontal line from Point a(i.e. Line ab).

3. Draw Line ac tangent to Point a.4. Draw Line ad bisecting Angle bac.5. Project the straight line portion of

gh on e-log ´ curve to intersect Line ad. This intersection (Point f) is the maximum past pressure (a.k.a. preconsolidation pressure).

Page 14: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 14 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

OVERCONSOLIDAITON RATIO (OCR)

Figure 7.8. Das FGE (2005).

(´c or ´vm)

cOCRWhere:

´c (a.k.a. ´vm) = PreconsolidationPressure (a.k.aMaximum Past Pressure).

´ = Present Effective Vertical StressGeneral Guidelines:

NC Soils: 1 ≤ OCR ≤ 2OC Soils : OCR > 2

Possible Causes of OC Soils:Preloading (thick sediments, glacial ice); fluctuations of GWT, underdraining, lightice/snow loads, desiccation above GWT,secondary compression.

Page 15: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 15 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

EFFECTS OF SAMPLE DISTURBANCE

OC Clays - Figure 7.10. Das FGE (2005)

NC and OC soils of low to medium sensitivity will experience disturbance due to remolding. This changes the consolidation characteristics of the 1D consolidation tests.

)(

)(

remoldedu

dundisturbeut q

qS Sensitivity (St) Where qu = Unconfined Compressive Strength

NC Clays - Figure 7.9. Das FGE (2005)

Virgin Compression Curve – Consolidation Curve Insitu (i.e. w/o disturbance)

Page 16: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 16 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

Reconstruction of Virgin Consolidation Curves (EM 1110-1-1904)

Figure 3-12. EM 1110-1-1904 Settlement Analysis.

EFFECTS OF SAMPLE DISTURBANCE

Page 17: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 17 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

Reconstruction of Virgin Consolidation Curves (EM 1110-1-1904)Table 3-6. EM 1110-1-1904 Settlement Analysis.

EFFECTS OF SAMPLE DISTURBANCE

Page 18: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 18 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

Reconstruction of Virgin Consolidation Curves (EM 1110-1-1904)Table 3-6. EM 1110-1-1904 Settlement Analysis.

EFFECTS OF SAMPLE DISTURBANCE

Page 19: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 19 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

SETTLEMENT FROM 1D PRIMARY CONSOLIDATION

Figure 7.11. Das FGE (2005)

ASASHHAVVV ppo )(1Where:

V = Volume, Vo = Initial Volume, V1 = Final Volume, Sp = Primary Settlement

At End of Primary Consolidation = ´

Page 20: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 20 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

vvvop VVVASV 1

oo

os e

AHe

VV

11Figure 7.11. Das FGE (2005).

Where:Vvo = Initial Void Volume, Vv1 = Final Void Volume

At End of Primary Consolidation = ´

Where:e = Change in Void Ratio

sv eVV

Where:e0 = Initial Void Ratio

SETTLEMENT FROM 1D PRIMARY CONSOLIDATION

Page 21: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 21 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

ee

AHeVASVo

sp

1

Figure 7.11. Das FGE (2005).

At End of Primary Consolidation = ´

or

vo

p

op

ee

HS

eeHS

1

1

Therefore:

Where:v = Vertical Strain

SETTLEMENT FROM 1D PRIMARY CONSOLIDAITON

Page 22: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 22 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

Where:

Cc = Slope of Field VirginConsolidation Curve

= Compression Index

Cs (or Cr) = Slope of ReboundCurve

= Swell Index

´vm = Maximum Past Pressure

´o = Initial Vertical EffectiveStress

VOID

RAT

IO

´v (Log Scale)

Cc

CsorCr

eo

~0.4eo

Virgin ConsolidationLine

´vm = ´o

NC Clay

SETTLEMENT FROM 1D PRIMARY CONSOLIDATION

Page 23: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 23 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

VOID

RAT

IO

´v (Log Scale)

Cc

CsorCr

eo

~0.4eo

´vm= ´o

NC Clay

o

ocp e

HCS

log1 0

Settlement (Sp) using Void Ratio

´

Virgin ConsolidationLine

ef

Where:Sp = SettlementH = Height of Soil Layer´vm = Final Vertical Effective

Stress= o´ - Current Vertical

Effective Stress´ = Change in Vertical

Effective Stressf´ = Final Vertical Effective

Stressef = Final Void Ratio´f

SETTLEMENT FROM 1D PRIMARY CONSOLIDATION

Page 24: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 24 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

Where:

Cc = Slope of Field VirginConsolidation Curve

= Compression Index

Cs (or Cr) = Slope ofRebound Curve

= Swell Index

´vm = Maximum PastPressure

´o = Initial Vertical EffectiveStress

VOID

RAT

IO

´v (Log Scale)

Cc

CsorCr

eo

´o

~0.4eo

Same Slope as Cr

´vmor´c

OC ClayVirginConsolidationLines

SETTLEMENT FROM 1D PRIMARY CONSOLIDATION

Page 25: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 25 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

VOID

RAT

IO

´v (Log Scale)

Cc

CsorCr

eo

´vmor´c

´o

~0.4eo

Same Slope as Cr

o

oc

o

vmrp e

HCeHCS

log

1log

1 00

Settlement (Sp) using Void Ratio

Where:

Sp = SettlementH = Height of Soil Layer´ = Change in Vertical

Effective Stresso´ = Initial Vertical Effective

Stressf´ = Final Vertical Effective

Stressef = Final Void Ratio

´

ef

´f

OC ClaySETTLEMENT FROM 1D PRIMARY CONSOLIDATION

Page 26: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 26 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

nc WC 0115.0

Compression Index (Cc) Estimates from Other Laboratory Tests

)25(006.01.0)1( noc WeC

)10(007.0 LLCc

)10(009.0 LLCc

Soil Cc Equation Reference

Undisturbed ClaysTerzaghi & Peck (1967)

Disturbed ClaysOrganic Soils, Peat

EM 1110-1-1904Clays

Varved ClaysUniform Silts 20.0cC

)13(01.0 LLCc

nc WC 012.0

)35.0(15.1 oc eC

SETTLEMENT FROM 1D PRIMARY CONSOLIDATION

Page 27: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 27 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

Compression Index (Cc) Estimates from Other Laboratory Tests

sc GLLC

100

2343.0

Soil Cc Equation Reference

Clays Rendon-Herrero (1983)

Clays Nagaraj & Murty (1985)

38.22.1 1141.0

s

osc G

eGC

Where:

Gs = Specific Gravity of SolidsLL = Liquid Limit (in %)Wn = Natural Water Contenteo = Initial Void Ratio

SETTLEMENT FROM 1D PRIMARY CONSOLIDATION

Page 28: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 28 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

Compression Index (Cc) Estimates from Other Laboratory Tests

sc GLLC

100

2343.0

Soil Cc Equation Reference

Clays Rendon-Herrero (1983)

Clays Nagaraj & Murty (1985)

38.22.1 1141.0

s

osc G

eGC

SETTLEMENT FROM 1D PRIMARY CONSOLIDATION

Page 29: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 29 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

10002000 3000 4000 5000 6000900800700600500

Vertical Effective Stress 'v (psf)

0.96

0.98

1

1.02

1.04

1.06

1.08

1.1

1.12

VOID

RA

TIO

(e)

EXAMPLE: SETTLEMENT FROM VIRGINCONSOLIDATION CURVES

GIVEN:

OC CH layer

o´ = 855 psf

vm´ = 1460 psf

´ = 1005 psf

eo = 1.1

Height of CH Layer = 10 ft

Figure 1. Example of Virgin Consolidation Curves.

Page 30: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 30 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

Figure 1. Example of Virgin Consolidation Curves.

Sp H e1 eo

e 1.11.045 0.055eo 1.1

Sp (10 ft) 0.05511.1

Sp 0.262 ft

Sp 3.14in 314

in

10002000 3000 4000 5000 6000900800700600500

Vertical Effective Stress 'v (psf)

0.96

0.98

1

1.02

1.04

1.06

1.08

1.1

1.12

VOID

RA

TIO

(e)

1.1

1.0761.076

1.045Cc

Cs

eo

ef

'o 'vm 'f

'

EXAMPLE: SETTLEMENT FROM VIRGINCONSOLIDATION CURVES

Page 31: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 31 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

25

20

15

10

5

0

Dep

th fr

om E

xist

ing

Gro

und

Surf

ace

(ft)

0 2000

TOTAL STRESS()

25

20

15

10

5

0

25

20

15

10

5

0

0 200025

20

15

10

5

00 2000

PORE PRESSURE(u)

0 2000

0 2000

EFFECTIVE STRESS(')

0 200025

20

15

10

5

0

25

20

15

10

5

0

25

20

15

10

5

0

25

20

15

10

5

0

Depth

fromExisting

Ground

Surface (ft)

CLsat = 105 pcf

SMsat = 115 pcf

MHsat = 115 pcf

SC = 105 pcfsat = 110 pcf

B = 6 ft SQ

Q = P = 144 kips

EXAMPLE: SETTLEMENT FROM 1D TEST STRAIN RESULTS

Page 32: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 32 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

100 1000200 400 600 800 2000 4000 6000

Vertical Effective Stress 'v (psf)

50

45

40

35

30

25

20

15VE

RTIC

AL S

TRAI

N (%

)

CL LayerSample from 12 ft

EXAMPLE: SETTLEMENT FROM 1D TEST STRAIN RESULTS

Page 33: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 33 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

25

20

15

10

5

0

Dep

th fr

om E

xist

ing

Gro

und

Surf

ace

(ft)

0 2000

TOTAL STRESS()

25

20

15

10

5

0

25

20

15

10

5

0

AB

C

D

E

F

G

0

315

525

635

980

1325

1670

2015

2360

2820

0 200025

20

15

10

5

00 2000

PORE PRESSURE(u)

0 2000

0 2000

EFFECTIVE STRESS(')

0 200025

20

15

10

5

0

25

20

15

10

5

0

25

20

15

10

5

0

25

20

15

10

5

0

Depth

fromExisting

Ground

Surface (ft)

0

0

60

250

435

625

810

1000

1250

0

315

525

575

730

890

1045

1205

1360

1570

2525

1455

1250

1185

1240

1345

CLsat = 105 pcf

SMsat = 115 pcf

MHsat = 115 pcf

SC = 105 pcfsat = 110 pcf

B = 6 ft SQ

Q = P = 144 kips

CL Layer 1

CL Layer 2

'o'f

EXAMPLE: SETTLEMENT FROM 1D TEST STRAIN RESULTS

Page 34: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 34 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

100 1000200 400 600 800 2000

Vertical Effective Stress 'v (psf)

50

45

40

35

30

25

20

15

VERT

ICAL

STR

AIN

(%)

CL LayerSample from 12 ft

'o1

'f1

v1 = 6.5% = 0.065

CL Layer 1

inS

ftS

ftS

HS

p

p

p

vp

7.4

39.0

)065.0)(6(

1

1

1

111

EXAMPLE: SETTLEMENT FROM 1D TEST STRAIN RESULTS

Page 35: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 35 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

CL Layer 2Sp2 H2v2

Sp2 (6 ft)(0.024)Sp2 0.14 ftSp2 1.7in

SPtotal Sp1 Sp2

SPtotal 6.4in

SPtotal 612

in100 1000

200 400 600 800 2000

Vertical Effective Stress 'v (psf)

50

45

40

35

30

25

20

15

VERT

ICAL

STR

AIN

(%)

CL LayerSample from 12 ft

'o2

'f2

v2 = 2.4% = 0.024Total Settlement

EXAMPLE: SETTLEMENT FROM 1D TEST STRAIN RESULTS

Page 36: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 36 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

12 loglog tteC

SETTLEMENT FROM SECONDARY CONSOLIDATION

Where:

C = Secondary CompressionIndex

e = Change in Void Ratiot = Time

Results of 1D Consolidation Test @ One Load Increment

Figure 7.15. Das FGE (2005).

Page 37: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 37 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

Where:

H = Height of Soil Layerep = Void Ratio @ End

of Primary Consolidationt = Time

p

s

eCC

ttHCS

1

log1

2

SETTLEMENT FROM SECONDARY CONSOLIDATION

Results of 1D Consolidation Test @ One Load Increment

Figure 7.15. Das FGE (2005).

Page 38: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 38 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

TIME RATE OF CONSOLIDATION

Clay Layer Undergoing Consolidation

Figure 7.17a. Das FGE (2005).

Theory of 1D Consolidation(Terzaghi, 1925)

Assumptions:1. The clay-water system is homogenous.2. Saturation is complete (S = 100%).3. Compressibility of water is negligible.4. Compressibility of soil grains is

negligible (but soil particles rearrange).5. Flow of water is in one direction only.6. Darcy’s Law is Valid.

Page 39: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 39 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

Flow of Water @ Point AFigure 7.17b. Das FGE (2005).

Clay Layer Undergoing Consolidation

Figure 7.17a. Das FGE (2005).

TIME RATE OF CONSOLIDATION

Page 40: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 40 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

Flow of Water @ Point AFigure 7.17b. Das FGE (2005).

dtVdxdydz

zv

ordtVdxdyvdxdydz

zvv

z

zz

z

(Rate of Water Outflow) –

(Rate of Water Inflow) =

(Rate of Volume Changes)Mathematical Equation:

Where:

V = Volume of Soil Elementvz = Velocity of flow in z direction

TIME RATE OF CONSOLIDATION

Page 41: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 41 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

Flow of Water @ Point AFigure 7.17b. Das FGE (2005).

Where:

Vs = Volume of Solidsvv = Volume of Voids

t

VeteV

tV

teVV

tV

tV

tV

dxdydz1

zuk

zuk

zhkkiv

tVdxdydz

zv

ss

sssv

2

2

w

wz

z

Using Darcy’s Law (v = ki)

Where u = excess pore pressure. From algebra:

Rate of change in V = Rate of Change in Vv

TIME RATE OF CONSOLIDATION

Page 42: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 42 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

Flow of Water @ Point AFigure 7.17b. Das FGE (2005).

te

e11

zuk

te

e1dxdydz

tV

e1dxdydz

e1VV

0t

V

tVe

teV

tV

teVV

tV

tV

o2

2

w

o

oos

s

ss

sssv

From Previous Slide

Assuming soil solids are incompressible

and

eo = Initial Void Ratio. Substituting:

Combining equations:

TIME RATE OF CONSOLIDATION

Page 43: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 43 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

o

vv

vo

v

w

vv

ow

eam

tum

tu

ea

zuk

uaae

te

ezuk

1

1

11

2

2

2

2

From Previous Slide

The change in void ratio is caused by the increase in effective stress.

Assuming linear relationship between the two:

av = Coefficient of Compressibility. Can be considered constant over

narrow pressure increases. Combining equations:

mv = Coefficient of Volume Compressibility.

TIME RATE OF CONSOLIDATION

Flow of Water @ Point AFigure 7.17b. Das FGE (2005).

Page 44: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 44 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

vwv

v

o

vv

vo

v

w

mkc

zuc

tu

eam

tum

tu

ea

zuk

2

2

2

2

1

1

From Previous Slide

Rearranging Equations:

av = Coefficient of Compressibility.mv = Coefficient of Volume Compressibility.

Where cv = Coefficient of Consolidation.

TIME RATE OF CONSOLIDATION

Flow of Water @ Point AFigure 7.17b. Das FGE (2005).

Page 45: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 45 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

0,00,2

0,0

uutuHz

uz

dr

2

2

zuc

tu

v

Can be solved with the following boundary conditions:

Basic Differential Equation of 1DConsolidation Theory

The solution yields

vTMm

m dr

o eHMz

Muu

2

0

sin2

Clay Layer Undergoing

ConsolidationFigure 7.17a. Das FGE (2005).

TIME RATE OF CONSOLIDATION

Page 46: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 46 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

From Previous Slide

dr

vv H

tcT 2

pressure waterpore excess Initial

o

TMm

m dr

o

u

mM

eHMz

Muu v

122

sin2 2

0

Clay Layer Undergoing Consolidation

Figure 7.17a. Das FGE (2005).

Where:

TIME FACTOR

TIME RATE OF CONSOLIDATION

Page 47: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 47 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

o

z

o

zoz u

uu

uuU

1

Because consolidation progress by dissipation of excess pore pressure, the degree of consolidation

(Uz) at a distance z at any time t is:

Figure 7.18. Das FGE (2006).

TIME RATE OF CONSOLIDATION

Clay Layer Undergoing Consolidation

Figure 7.17a. Das FGE (2005).

Page 48: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 48 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

Figure 7.18. Das FGE (2006).

TIME RATE OF CONSOLIDATION

Page 49: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 49 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

vTMm

m

eM

U2

0221

ionConsolidat Primary from Layer of Settlement time at layer of Settlement

ionConsolidat of degree Average

p

t

StS

U

o

Hz

dr

p

t

u

dzuH

SSU

dr

2

021

1

Average degree of consolidation (U) for the entire depth of the clay layer at any time t is:

Where:

Substituting U for u

%)100log(933.0781.1100%

4

2

UTU

UTU

v

v

60%, For

60%, to 0% For

U can be approximated by thefollowing relationships:

TIME RATE OF CONSOLIDATION

Clay Layer Undergoing Consolidation

Figure 7.17a. Das FGE (2005).

Page 50: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 50 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

Variation of Tv with UTable 7.1 Das PGE (2006).

TIME RATE OFCONSOLIDATION

Page 51: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 51 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

Difference between Average Degree of Consolidation and MidplaneDegree of Consolidation

Figure 7.28. Das FGE (2006).

TIME RATE OF CONSOLIDATION

Page 52: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 52 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

COEFFICIENT OF CONSOLIDATION (cv)• Generally decreases as Liquid Limit (LL) increases.

• Determined from 1D Consolidation Test Lab per Load Increment.

Logarithm of Time Method(Casagrande and Fadum, 1940)

Figure 7.19 Das FGE (2006).

Square Root of Time Method(Taylor, 1942)

Figure 7.20 Das FGE (2006).

Page 53: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 53 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

Figure 7.19. Das FGE (2006).

Logarithm of Time Method1. Extend the straight line portion of primary

and secondary consolidations to intersect at Point A. Point A represents d100(Deformation at 100% primary consolidation).

2. The initial curved portion of the deformation plot versus log t is approximated to be a parabola on a natural scale. Select times t1and t2 on the curved portion such that t2 = 4t1. Let the difference of the specimen deformation between (t2 – t1) be equal to x.

3. Draw a line horizontal to DE such that the vertical distance BD is equal to x. The deformation corresponding to the line DE is d0 (Deformation at 0% primary consolidation).

COEFFICIENT OF CONSOLIDATION (cv)

Page 54: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 54 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

Logarithm of Time Method

50

2

250

50

197.0

197.0

tHc

HtcT

drv

dr

v

4. The ordinate of Point F on the consolidation curve represents the deformation at 50% primary consolidation (d50).

5. For 50% average degree of consolidation (U = 50%), Tv = 0.197 (see Table 7.1, Das FGE 2006).

or

Where:Hdr = Average longest drain path

during consolidation.Figure 7.19. Das FGE (2006).

COEFFICIENT OF CONSOLIDATION (cv)

Page 55: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 55 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

Figure 7.20. Das FGE (2006).

Square Root of Time Method1. Draw a line AB through the early portion

of the curve.

2. Draw a line AC such that OC = 1.15OB. The time value for Point D (i.e. the intersection of line AC and the data) is the square root of time for t90 (i.e. the time to 90% primary consolidation).

3. For 90% consolidation, Tv = 0.848 (see Table 7.1, Das FGE 2006).

90

2

290

90

848.0

848.0

tHc

HtcT

drv

dr

v

or

COEFFICIENT OF CONSOLIDATION (cv)

Page 56: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 56 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

SP FILL ( = 115 pcf)

SC ( = 115 pcf)

CL ( = 115 pcf)

SM ( = 115 pcf)

3ft

4ft

6ft

5ft

GIVEN: Soil Profile (NTS).2 way drainage.

REQUIRED: Determine the following:

a. The change in pore pressure in the CL layer immediately after the application of the 3 ftof SP Fill.

b. The degree of consolidation in the middle of the clay layer when the excess pore pressure (ue) is 170 psf.

c. How high would the water in a piezometer located in the middle of the layer rise above the GWT when ue = 170 psf?

d. If cv = 0.000004 ft²/sec, how long would it take to get to 25% average degree of consolidation? To U = 50%? To U = 99%?

COEFFICIENT OF CONSOLIDATION (cv)Example

Page 57: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 57 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

PRECOMPRESSION – GENERAL CONSIDERATIONSPRECOMPRESSION: Loading an area prior to placement of the planned structural loading to limit post-construction settlement. Also known as Surcharging.

Settlement caused by structural loading (Sp):

o

ocp e

HCS

log1 0

Settlement caused by structural loading and surcharging (S´p or Sp+f):

o

focfpp e

HCSS

log

1 0

Where:f = Change in vertical stress due to Fill added.

Page 58: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 58 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

Figure 7.26. Das FGE (2006).

Where:p) = Change in vertical stress due to

structural load.f) = Change in vertical stress due to

Fill added.

Where:Sp = Settlement due to structural load.Sp+f = Settlement due to structural load

and Fill.

PRECOMPRESSION – GENERAL CONSIDERATIONS

Page 59: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 59 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

)(

)()(

)(

)()(

)(

11log

1log

log

log

p

f

o

p

o

p

o

fpo

o

po

p

p

U

U

SS

U

Mathematical Equations

Definition of average Degree of Consolidation U

Substitution

Re-arranging (Eqn 7.56 Das FGE 2006)Place in graphical form

for design use(Figure 7.27 Das FGE 2006)

PRECOMPRESSION – PLANNING

Page 60: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 60 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

Figure 7.27. Das FGE (2006).

Where:

f) = Change in vertical stressdue to Fill added.

p) = Change in vertical stressdue to Structural Loading.

´o = Initial vertical effectivestress.

PRECOMPRESSION –PLANNING

Page 61: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 61 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

Figure 7.27. Das FGE (2006).

STEPS:1. Calculate primary consolidation

settlement from planned loading (Sp).2. Calculate primary consolidation

settlement from planned loading plus surcharge (Sp+f ).

3. Calculate average degree of consolidation U. Note U = Sp/Sp+f. Can also use Figure 7.27 or Eqn 7.56 (Das FGE 2006).

1. Find Tv from calculated U. To find time to when surcharge loading should be removed (i.e. t2):

v

drv

cHTt

2

2

PRECOMPRESSION –PLANNING

Page 62: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 62 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

Difference between Average Degree of Consolidation and MidplaneDegree of Consolidation

Figure 7.28. Das FGE (2006).

Removal of Surcharge may still cause net

settlement(swelling near drainage

layers, settlement @ middle)

Conservative Approach:Assume U is the midplanedegree of consolidation.

TIME RATE OF CONSOLIDATION

Page 63: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 63 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

Midplane Degree of Consolidation

Figure 7.29. Das FGE (2006).

TIME RATE OF CONSOLIDATION

Page 64: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 64 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

SURCHARGING EXAMPLESP FILL ( = 115 pcf)

SC ( = 115 pcf)

CL ( = 115 pcf)

SM ( = 115 pcf)

3ft

4ft

6ft

5ft

GIVEN: Soil Profile (NTS).2 way drainage.

REQUIRED: Determine the following:

a. If cv = 0.000004 ft²/sec, how long would it take to get to 99% average degree of consolidation?

b. If a surcharge of 4 ft of fill was placed in addition to the 3 ft of fill planned, when would you be able to remove the surcharge? Use the same value for cvgiven in a.

Page 65: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 65 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

GROUND MODIFICATION FOR CONSOLIDATIONSAND DRAINS

Section ViewFigure 10.38. Das PGE (2006).

Plan View – Triangular SpacingFigure 10.38. Das PGE (2006)

Reduction Drainage Path =Reduction in Drainage Time

rw = Sand Drain Radiusde = Effective Diameter

Page 66: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 66 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

Figure 10.39. Das PGE (2006).

1

23

4

5

STEPS

Sand Drain Installation: Auger Method(Kirmani, 2004)

1. Place auger at drain location.2. Screw auger to selected depth.3. Rotate auger at selected depth to remove soil.4. Inject sand while auger is extracted.5. Complete sand drain to working platform level.

GROUND MODIFICATION FOR CONSOLIDATIONSAND DRAINS

Page 67: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 67 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

Conceptual ConceptCourtesy of www.americanwick.com

Figure 7.31. Das FGE (2006).

Courtesy ofwww.americandrainagesystems.com

GROUND MODIFICATION FOR CONSOLIDATIONPREFABRICATED VERTICAL DRAINS (PVD’S) (A.K.A. WICK DRAINS)

Page 68: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 68 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

Courtesy of www.nilex.com

Courtesy of www.nilex.com

Courtesy of www.americandrainagesystems.com

GROUND MODIFICATION FOR CONSOLIDATIONPREFABRICATED VERTICAL DRAINS (PVD’S) (A.K.A. WICK DRAINS)

Page 69: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 69 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

Plan View – Sand DrainTriangular Spacing

Figure 7.30. Das FGE (2006).

wo

hvr

e

vrr

w

e

rr

eekc

dtcT

rdn

nnn

nnm

mTU

)1(

2

413)ln(

1

8exp1

2

2

2

2

2

Ur = Average Degree of Radial Consolidation

Barron (1948)

de = Effective Diameterrw = Sand Drain Radius

cvr = Coefficient of Radial ConsolidationTr = Time Factor for Radial Consolidation

kh = Coefficient of Horizontal PermeabilityTr = Time Factor for Radial Consolidationeo = Initial Void Ratio

GROUND MODIFICATION FOR CONSOLIDATIONRADIAL CONSOLIDATION

Page 70: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 70 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

TIME RATE OF RADIAL CONSOLIDATIONVariation of Tr with U - Table 7.3 Das PGE (2006).

Page 71: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 71 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

TIME RATE OF RADIAL CONSOLIDATIONVariation of Tr with U - Table 7.3 Das PGE (2006).

Page 72: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 72 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

Sand

Clay

Sand

Dra

in

Vertical and Radial DrainageCourtesy of www.nhi.fhwa.dot.gov

Drainage

)1)(1(1, vrrv UUU Where:

Uv,r = Average Degree of Consolidationdue to Vertical & Radial Drainage

Uv = Average Degree of Consolidationdue to Vertical Drainage

Ur = Average Degree of Consolidationdue to Radial Drainage

GROUND MODIFICATION FOR CONSOLIDATIONAVERAGE DEGREE OF CONSOLIDATION DUE TO VERTICAL & RADIAL DRAINAGE

Page 73: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 73 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

CONSOLIDATION MONITORINGSETTLEMENT PLATES

Insitu Soil Layerto be Monitored

Fill Layer SettlementPlate Base(Plywood or Steel)

Rod Protection(Typically PVC Pipe)

Settlement Rod(Steel)

General Concept Standard Plan Detail(Courtesy of Iowa DOT)

Page 74: 14.330 SOIL MECHANICS Consolidation FUNDAMENTALSOF ...faculty.uml.edu/ehajduk/Teaching/14.330/documents/14.3302014Consolidation.pdfRevised 03/2014 Slide 3of 74 14.330 SOIL MECHANICS

Slide 74 of 74Revised 03/2014

14.330 SOIL MECHANICSConsolidation

Settlement Platforms

Permanent Fill

Soft Clay Vertical Drain

Surcharge

DrainageBlanket

Piezometers

Firm Soil

Not to Scale

Inclinometers

SURCHARGING INSTRUMENTATION EXAMPLE

Courtesy of www.nhi.fhwa.dot.gov