cive.5370 experimental soil mechanics soil permeability...

Revised 03/2014

CIVE.5370 EXPERIMENTAL SOIL MECHANICSSoil Permeability

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).

Revised 03/2014


CLAY

SAND

SAND

DEPTH

(Vertical Stress Increase)


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)


Revised 03/2014


CLAY

SAND

SAND

DEPTH



Between time t = 0 to t = ∞

Pore water increase due to initial loading dissipates

Soil skeleton takes loading as pore pressure decreases


Figure 7.1c. Das FGE (2005)


Revised 03/2014


CLAY

SAND

SAND

DEPTH



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 '


Figure 7.1e. Das FGE (2005)


Revised 03/2014


CLAY

SAND

SAND

DEPTH



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


Revised 03/2014


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

Revised 03/2014


Figure E-1 USACE EM1110-1-1904.

ShearTrac II DSS Equipment(Courtesy of Geocomp Corporation)

1D CONSOLIDATION TEST EQUIPMENT

Revised 03/2014


S-450 Consolidation Device(Courtesy of Durham Geo)

Dead Weight Consolidation Load Frame(Courtesy of Durham Geo)


Revised 03/2014


Figure 10.9. Das PGE (2005)


Revised 03/2014


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.

Revised 03/2014


VOID RATIO-PRESSURE PLOTS

Figure 7.5. Das FGE (2005)

s

v

s

v

s

vo H

HAHAH

VVe Initial Void Ratio (eo):

Revised 03/2014


sHHe 1

1

11



Change in Void Ratio due to 1st

Loading (e1):

New Void Ratio after 1st

Loading:11 eee o

@ End of Load 1


Revised 03/2014


sHHe 2

2

22



Change in Void Ratio due to 2nd

Loading (e2):

New Void Ratio after 2nd Loading:

sHHee 2

12

@ End of Load 2


Revised 03/2014



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)


Revised 03/2014


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


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).

Revised 03/2014


OVERCONSOLIDATION RATIO (OCR)


(´c or ´vm)

cOCRWhere:

´c (a.k.a. ´vm) = PreconsolidationPressure (a.k.a.Maximum 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.

Revised 03/2014


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)

Revised 03/2014


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

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


Revised 03/2014


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


Revised 03/2014


SETTLEMENT FROM 1D PRIMARY CONSOLIDATION


ASASHHAVVV ppo )(1Where:

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

At End of Primary Consolidation = ´

Revised 03/2014


vvvop VVVASV 1

oo

os e

AHe

VV

11Figure 7.11. Das FGE (2005).

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


Where:e = Change in Void Ratio

sv eVV

Where:e0 = Initial Void Ratio


Revised 03/2014


ee

AHeVASVo

sp

1



or

vo

p

op

ee

HS

eeHS

1

1

Therefore:

Where:v = Vertical Strain

SETTLEMENT FROM 1D PRIMARY CONSOLIDAITON

Revised 03/2014


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


Revised 03/2014


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


Revised 03/2014


Where:

Cc = Slope of Field VirginConsolidation Curve

= Compression Index

Cs (or Cr) = Slope ofRebound Curve

= Swell Index

´vm = Maximum PastPressure

ó = Initial Vertical EffectiveStress

VOID

RAT

IO

´v (Log Scale)

Cc

CsorCr

eo

ó

~0.4eo

Same Slope as Cr

´vmorć

OC ClayVirginConsolidationLines


Revised 03/2014


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

Revised 03/2014


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


Revised 03/2014



sc GLLC

100

2343.0


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


Revised 03/2014



sc GLLC

100

2343.0


Clays Rendon-Herrero (1983)

Clays Nagaraj & Murty (1985)

38.22.1 1141.0

s

osc G

eGC


Revised 03/2014


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


Revised 03/2014


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


Revised 03/2014


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.

Revised 03/2014


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




Revised 03/2014



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


Revised 03/2014



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


Revised 03/2014



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:


Revised 03/2014


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.



Revised 03/2014


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.



Revised 03/2014


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).


Revised 03/2014


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



Where:

TIME FACTOR


Revised 03/2014


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:





Revised 03/2014




Revised 03/2014


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:




Revised 03/2014


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

TIME RATE OFCONSOLIDATION

Revised 03/2014


Difference between Average Degree of Consolidation and MidplaneDegree of Consolidation



Revised 03/2014


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).

Revised 03/2014



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)

Revised 03/2014


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).


Revised 03/2014


0.01 0.1 1 10 100 1000 10000Time (min)

200

175

150

125

100

75

50

25

0

Dia

l Rea

ding

(x 0

.000

1 in

ch)

D0 = 8

D100 = 160

D50 = (D0 + D100)/2D50 = 84

t50 = 9 min

CIVL402 Spring 2007 Sample0.5tsf Pressure - Loading

H = 0.0152 in

SAMPLE 1D CONSOLIDATION TEST RESULTS

Revised 03/2014



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


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