UNSATURATED SOILS: SOME FUNDAMENTALS … 2010.pdfJ.L. Briaud –Texas A&M University. UNSATURATED...

J.L. Briaud –Texas A&M University.

UNSATURATED SOILS:

SOME FUNDAMENTALS AND

SOME APPLICATIONS

Jean-Louis BriaudPresident of ISSMGE, Professor Texas A&M University, USA

Remon AbdelmalakGeo-Engineer, Dar Al-Handasah Group, Cairo, Egypt

Xiong ZhangAssistant Professor, University of Alaska, USA


• SOME FUNDAMENTALS– SUCTION

– EFFECTIVE STRESS

– STRENGTH

– DEFORMATION

• SOME APPLICATIONS– ULTIMATE BEARING CAPACITY

– MOVEMENT

– COMPACTION

– SLABS ON GRADE

– TREES

– EARTH PRESSURES

– SLOPES


Soil State Swell Shrink

Unsaturated Yes No

Saturated Yes Yes

Saturated No Yes

GWL

THE THREE ZONES


WATER NORMAL STRESS

TENSION COMPRESSION

0

(SUCTION)

(pF )

uw (kPa)

(PORE PRESSURE)


u0

+-

hc

a aT T

Glass

Contractile

Skin

Water

- 1,000 kPa

d

Water

c

w

4 T cos αh

d γ

where T 72 mN/ m

h

Atmospheric

pressure

hgw

hcgw0 kPa

MATRIC WATER TENSION


J.L. Briaud –Texas A&M University.J.L. Briaud –Texas A&M University.

The Water Strider

Force = 72 mN/mThickness = a few Angstroms

Stress >? 20 MPa


Pure Water Salt Water

Initial state Initial state

After time t

After time t

h = Osmotic Suction

OSMOTIC WATER TENSION



Water Tension 200kPa

Water Tension 100,000kPa

WaterContractile Skin

SmectiteAl2Si4O10(OH)2

Water

QuartzSiO2

QuartzSiO2


GARNER’S STUDY (2002)

3 samples at 3 water contents sent to 8 laboratories.

WATER CONTENT, %

Sample 1

Sample 2

Sample 3

WATER TENSION

log (uw in kPa)

Sample 1

Sample 2

Sample 3

WATER TENSION, kPa

Sample 1

Sample 2

Sample 3

0 5 10 15 20 25 30 %

0 1 2 3 4 5 log kPa

0 15000 30000 45000 60000 kPa

fcifai fwi

F

At

0 0

ci wi ai

t t t t

f f fF

A A A A

'wi a aiw

t t

u a u a

A A

' w au u a


Saturated

uw 0

ua = 0

’ = - uw

Occluded Air

uw = ua

’ = - uw

S > 85%

Continuous Air

uw 0

ua = 0

’ = - auw

S < 85%

soil grain

water

soil grain

water

air

soil grain

water

air


For Unsaturated Soils

The effective stress is

σ’ = σ – α uw with α ~ S

The effective stress controls the behavior of the soil skeleton for saturated soils and for unsaturated soils (in most cases)

Shear Strength-unsaturated

' ' tan 's c

' ( ) tan 'w as c u u a

' ( )tan 's c uw a

(?)Sa

' tan Apparent Cohesionwc ua


(Lu & Likos, 2004)

α vs S


(Fredlund & Rahardjo, 1993)


SHEAR STRENGTH-example


Example calculations (unsaturated):

c = 5 kPa, φ = 30 degrees, z = 1 m,

S = 35%, uw = -1000 kPa, ua = 0

s = 5 + (20 – 0.35x(-1000)) tan 30

s = 218.6 kPa

Example calculations (saturated):

c = 5 kPa, φ = 30 degrees, z = 1 m,

S = 100%, uw = 10 kPa, ua = 0

s = 5 + (20 – 1x10) tan 30

s = 10.8 kPa


EXAMPLE OF STRESS PROFILESD

epth

,m

0

1

2

3

4

5

6

7

0 40 80

s, kPa

0 40 80 120

’, kPa

0 0.5 1

a

0 40 80 120

, kPa

Unsaturated

G.W.L

Top of

Capillary Zone

-80 -40 0

au, kPa

-400 -200 0 -100

u, kPa

Saturated by

Capillarity

Unsaturated

Saturated

1

2

3

4

5

6

7

Dep

th ,m


Jean-Louis Briaud – Texas A&M University

THIS BEARING CAPACITY EQUATION DOES

NOT WORK FOR UNSATURATED SOILS

12u c qp cN BN DNgg g


, , ,L C Ur p q N s

up kr

THIS BEARING CAPACITY EQUATION

ALWAYS WORKS


i

iiii

E

ΔHΔεHS

ei+Deiei ev

’ o

v

D

’ i

’ ov

v

WEIGHT INDUCED SETTLEMENT

v

D’i’ovHi

z

P



i w

iiii

E

ΔwfHΔεHS

w

wi+

Dw

iw

i

ei+ Deiei ev

MOISTURE INDUCED MOVEMENT

w

Hi Dwiwi

z



w

wSW

DV/V

wSH

0

gw/gdShrink-Swell

Index1


CLASSIFICATION OF SHRINK-SWELL POTENTIAL

ACCORDING TO SHRINK-SWELL INDEX

Potential

Very High

High

Moderate

Low

Iss

> 60%

40 – 60

20 – 40

< 20%


WATER CONTENT VARIATION AS A FUNCTION OF TIME

Av

era

ge

Wa

ter

Co

nte

nt

0.35

0.30

0.25

0.20

0.15

0.10

0.05

0.00Fall Winter Spring Summer Fall Winter Spring1992 1993 1993 1993 1993 1994 1994

CC = Corpus Christi (0-0.5m)

SA = San Antonio (0-0.5m)

CS = College Station (0-1.5m)

OUTSIDE = Outside the Foundation Imprint

UNDER = Under the Foundation Imprint

Time for SA and CC

Time for CS

Fall Winter Spring Summer Fall Winter Spring1993 1994 1994 1994 1994 1995 1995

CC OUTSIDESA OUTSIDE

CC UNDER

SA UNDER CS OUTSIDE


i w

iiii

E

ΔwfHΔεHS


Depth

,m

Legend

RF : Reference

W : Water injected

BM : Benchmark

1.5

2

2.5

3

0.5

1

0

Su = 179.8 kPa

wmean = 19.74 %

h = 3.41 pF

LL = 40.4, PL = 17.1

2m 2m

0.6m

Brown Silty Clay, trace fine Sand : Calcareous

gt = 20.4 kN/m3

Ew = 0.869, f = 0.39

%SW = 4.31

%<0.002= 45.5

NorthA’

W1

20m

10m

10m

RF2

W2RF1

A

BM2BM1

Su = 151.5 kPawmean = 20.73 %h = 3.42 pFLL = 51.3, PL = 22.3

Dark Gray Silty Clay : Trace Fine Sand

gt = 20.3 kN/m3

Ew = 0.752, f = 0.39%SW = 5.17%<0.002= 47.7

A A’

GWL : 4.27 m (Jun./25/99)

4.8 m (Feb./1/01)

4 m (Jul./15/01)

Site in Arlington,

Texas

Texas A&M University


WATER INJECTION


Texas A&M University


FOOTINGS



WATER CONTENT AND SUCTION vs. DEPTH

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 1 2 3 4 5

B:Boring

B1 B2

B3 B4

B5 B6

B7 B8

B9

Dep

th, m

Suction, pF

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.00 0.05 0.10 0.15 0.20 0.25 0.3

B:Boring

B1 B2

B3 B4

B5 B6

B7 B8

B9

Dep

th, m

Water ContentFooting RF1 at a site

in Arlington, Texas



FOOTING MOVEMENT OVER TWO YEARS

08

/1/1

999

09

/1/1

999

10

/1/1

999

11

/1/1

999

12

/1/1

999

01

/1/2

000

02

/1/2

000

03

/1/2

000

04

/1/2

000

05

/1/2

000

06

/1/2

000

07

/1/2

000

08

/1/2

000

09

/1/2

000

10

/1/2

000

11

/1/2

000

12

/1/2

000

01

/1/2

001

02

/1/2

001

03

/1/2

001

04

/1/2

001

05

/1/2

001

06

/1/2

001

07

/1/2

001

08

/1/2

001

09

/1/2

001

40

30

20

10

0

-10

-20

-30

-40

-50

-60

Dis

pla

cem

ent,

mm

Date

RF1

RF2

W1

W2

sum

mer

fall

win

ter

spri

ng

sum

mer

fall

win

ter

spri

ng

sum

mer



RAINFALL AND TEMPERATURE

Date

08/1

/1999

09/1

/1999

10/1

/1999

11/1

/1999

12/1

/1999

01/1

/2000

02/1

/2000

03/1

/2000

04/1

/2000

05/1

/2000

06/1

/2000

07/1

/2000

08/1

/2000

09/1

/2000

10/1

/2000

11/1

/2000

12/1

/2000

01/1

/2001

02/1

/2001

03/1

/2001

04/1

/2001

05/1

/2001

06/1

/2001

07/1

/2001

08/1

/2001

09/1

/2001

Ra

infa

ll, m

m

7

6

5

4

3

2

1

0

Ave. Monthly Temperature

Ave. Monthly Rainfall

Tem

pera

ture, oC

35

30

25

20

15

10

5

0



60

40

20

0

20

40

60

Dis

pla

cem

ent,

mm

100 0 100 200 300 400 500 600 700 800

Time, days

RF1+ RF2+ W1+ W2

4

Average Measured movements

Water Content Method

PREDICTED AND MEASURED MOVEMENTS

Average of 4 Footings at a site

in Arlington, Texas


i w

iiii

E

ΔwfHΔεHS

Example of same modulus test

in lab and in field

J-L Briaud, Texas A&M University

BCD Test: Briaud Compaction Device

BCD on Proctor Mold BCD in the Field

0

10

20

30

40

50

60

0 2 4 6 8 10 12 14

Water Content (%)

Mo

du

lus (

MP

a)

.

0

4

8

12

16

20

Dry

Un

it W

eig

ht

(kN

/m3)

.

Plate Reload Modulus (MPa)

Dry Unit Weight (kN/m^3)

34

NGES Silty Sand (Mold #5)

0

10

20

30

40

0 2 4 6 8 10 12 14

Water Content (%)

Mo

du

lus (

MP

a)

0

4

8

12

16

20

Dry

Un

it W

eig

ht

(kN

/m3)

Plate Reload Modulus (MPa)

Dry Unit Weight (kN/m^3)

J-L Briaud, Texas A&M University

Modulus measured with BPT: Briaud Plate Test

J.L. Briaud –Texas A&M University.36

TYPICAL DAMAGE CAUSED

BY SHRINK-SWELL SOILS

SUMMER WINTER

SwellSwell

No changeNo Change

Shrink Shrink

39

FOUNDATION SOLUTIONS

air gap

• Stiffened Slab on Grade

• Elevated Structural Slab on Piers

• Stiffened Slab on Grade and on Piers

• Thin Post Tensioned Slab


..

.

Tributary Load Area

..

.0

.

.0 0

.

.0 0

.

.

Leqv

Leqv


Q (kN/m)

Mmax

Leqv Δ = f ( Q, EI, L)

EI

Tolerable Distortion

Δ / L = 1/480 Edge drop

Δ / L = 1/960 Edge liftACI 302

Weather Model

Moisture Diffusion Model

Soil Volume change Model

Soil- Structure Interaction Model


Daily MeanTemperature

of Arlington, Texas

0

20

40

60

80

100

08

/01

/99

10

/01

/99

12

/01

/99

02

/01

/00

04

/01

/00

06

/01

/00

08

/01

/00

10

/01

/00

12

/01

/00

02

/01

/01

04

/01

/01

06

/01

/01

08

/01

/01

10

/01

/01

(oF

)

Daily Mean Relative Humidity

of Arlington, Texas

0

20

40

60

80

100

08

/01

/99

10

/01

/99

12

/01

/99

02

/01

/00

04

/01

/00

06

/01

/00

08

/01

/00

10

/01

/00

12

/01

/00

02

/01

/01

04

/01

/01

06

/01

/01

08

/01

/01

10

/01

/01

(%

)

Daily Mean Wind Speed

of Arlington, Texas

0

2

4

6

8

10

08

/01

/99

10

/01

/99

12

/01

/99

02

/01

/00

04

/01

/00

06

/01

/00

08

/01

/00

10

/01

/00

12

/01

/00

02

/01

/01

04

/01

/01

06

/01

/01

08

/01

/01

10

/01

/01

(m/s

)

Daily Acumulative Rainfall

of Arlington, Texas

0

20

40

60

80

100

08

/01

/99

10

/01

/99

12

/01

/99

02

/01

/00

04

/01

/00

06

/01

/00

08

/01

/00

10

/01

/00

12

/01

/00

02

/01

/01

04

/01

/01

06

/01

/01

08

/01

/01

10

/01

/01

(mm

/day

)

Input Weather Data (FAO 56)

../../Short Course Shrink-Swell 2005/My Documents/FondSup-Paris/FondSup2003/simulation_presentaion1.xls


m

y

y

x

1.5 L

L0.5L

40 Columns of equal

width elements20 Columns of elements with

bias 1.1

25 C

olumn

s of e

lemen

ts wi

th

bias 1

.1

Edge Lift Mound

Cente

r Line

( Line

of sy

mmetr

y)

Foundation slab

Edge Lift Case

140 Abaqus simulations covering manyweather, soil, and structure parameters


Edge Drop Case

140 Abaqus simulations covering manyweather, soil, and structure parameters

m

y

y

x

1.5 L

L0.5L

40 Columns of equal

width elements20 Columns of elements with

bias 1.1

25 C

olumn

s of e

lemen

ts wi

th

bias 1

.1

Edge Drop Mound

Cente

r Line

( Line

of sy

mmetr

y)

Foundation slab


Soil mound and foundation elevations

-0.01

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0 1 2 3 4 5 6 7 8

x- coordinate (m)

y- c

oord

inat

e (m

)

Initial Mound Elev.

Final Mound Elev.

Final Found Elev

Bending moments and shearing forces

-60

-40

-20

0

20

40

60

80

100

120

140

0 1 2 3 4 5 6 7 8

x- coordinate (m)

V (

kN

) or

M (

kN

.m)

Shearing Force, V

Bending Moment, M


SOIL WEATHER INDEX Isw

Isw = Iss H ΔlogUedge

ΔlogUedge = 0.5 ΔlogUff

Iss = shrink-swell index = wsw – wsh (e.g. 0.2)

H = depth of shrink-swell movement (e.g. 3m)

ΔlogUff = change in water tension in the free field due to

weather (e.g. 1.4)

ΔlogUedge = change in water tension at the edge of the

foundation and at the soil surface (e.g. 0.7)

Isw = 0.2 x 3 x 0.7 = 0.42


Water Tension based design charts (Edge drop)

Leqv design chart (Edge drop)

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

0 0.2 0.4 0.6 0.8 1 1.2

Iss. H. DUedge (m)

Leq

v (

m)

deq=0.63 m

deq=0.51 m

deq=0.38 m

deq=0.25 m

deq=0.13 m

2

2

max

eqvqLM

Iss H ΔlogUedge (m)


Leqv design chart (Edge drop)

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

0 0.1 0.2 0.3 0.4 0.5 0.6

H. Dwedge (m)

Leq

v (

m)

deq=0.63 m

deq=0.51 m

deq=0.38 m

deq=0.25 m

deq=0.13 m

2

2

max

eqvqLM

Water content based design charts (Edge drop)


CROSS SECTION

PLAN VIEW


#4@16" OCEW

0.1 m

1.05 m

3-#6

#3 TIES @ 24" C-C

2-#5

6 MIL POLY

0.3 m

3-#6

51


Excavation and steel - 16 July 2004


Completed Building


Soil movement log

0

3

6

9

12

15

-0.005 0 0.005 0.01 0.015

Movements (m)D

epth

(ft)

Corner Ext movement ( Sept - Oct )

Center Ext movement ( Sept - Oct )

Corner Ext movement ( Sept - Dec )

Center Ext movement ( Sept - Dec )

Corner Ext movement ( Sept - Feb05 )

Center Ext movement ( Sept - Feb05 )

Corner Ext movement ( Sept 04 - Apr05 )

Center Ext movement ( Sept 04- Apr 05 )

MOVEMENT (m)

DE

PT

H (

0.3

m)


Perimeter average level vs. Interior average level

-0.003

-0.002

-0.001

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0 30 60 90 120 150 180 210 240 270

Time (days)

Re

lati

ve

ele

va

tio

ns

in

(m

)

Perimeter average level

Interior average level

Difference (per-int)

SLAB MOVEMENT over 1 YEAR


COST

Foundation with 1.05 m deep beams: 100 $/m2

Foundation with 0.52 m deep beams: 60 $/m2

Completed Building: 1600 $/m2

Increase in cost: 40 $/m2 or40/1600 = 2.5% of building cost

Slab stiffness increased 8 times (1.05/0.52)3


Effects of trees on adjacent buildings

No Change

Shrink

Shrink


LEGEND

(Richards)

D/H = 1

H

D


Zm

= M

ax

. R

oo

t D

ep

th +

2 f

t

Typical Wet

suction profile: initial

suction profile

Eq

uil

ibri

um

su

cti

on

Final driest suction

profile with tree roots

Effects of tree root on adjacent buildings


RETAINING WALLS-EARTH PRESSURE


σah = Ka (ov+ Δv) – 2c Ka0.5 + auw

σah = Ka (ov+ Δv) – 2c Ka0.5 + auw (1-Ka)

where:

σah is the total active earth pressure

Ka is the active earth pressure coefficient

c is the effective stress cohesion intercept of the soil at depth z

ov is the initial vertical effective stress at depth z

Δv is the change in vertical effective stress at depth z

(due to load at the surface of the retained side)

a is the ratio of water over total pore area

(use 0 for unsaturated soils or soils in the capillary zone,

and 1 for saturated soils under the GWT)

uw is the water stress (pore water pressure if saturated)




σph = Kp (ov+ Δv) + 2c Kp0.5 + auw

σph = Kp (ov+ Δv) + 2c Kp0.5 + auw (1-Kp)

where:

σph is the total passive earth pressure

Kp is the passive earth pressure coefficient

c is the effective stress cohesion intercept of the soil at depth z

ov is the initial vertical effective stress at depth z

Δv is the change in vertical effective stress at depth z

(due to load at the surface of the retained side)

a is the ratio of water over total pore area

(use 0 for unsaturated soils or soils in the capillary zone,

and 1 for saturated soils under the GWT)

uw is the water stress (pore water pressure if saturated)




σah = ov – 2su ?

σph = ov + 2su ?

Not applicable because of cracking



Zone 1

Zone 1

Zone 1

Swelling Pressure

Passive Pressure

At Rest or Active Pressure

Lytton, 2008

1. Loss of suction over time

2. Progressive failure and low

residual friction angle

Shallow

1 to 3 m

Roughly Planar

Slip Surface

Typical apparent strength

Su = 15 to 35 kPa

Moisture Migration into Intact Slope

Moist Condition on

Surface (say u = 2 pF)

Suction as Compacted

u = 3.5-4 pF

Darcy's Law:

dhv = k

dx

0 0

Unsaturated k

k hk =

h

+

Mitchell (1979)

e0 0 0 0

d (log h)dh / hv = k h k h

dx dx

Unsteady Flow Equation

2

2

0 0 w

d

u uα

x t

Sk h γα

0.434 γ

10u = log h

0

20

40

60

80

100

0 20 40 60 80 100

Cra

ck S

pac

ing (

cm)

Crack Depth (cm)

Crack Spacing versus Depth (Knight, 1972)

Pore Pressure Distribution

-

+z

Hydrostatic

Increase with

Depth z

Suction at Surface, u0

Moisture Migration into Cracked Slope

0 0.5 1 1.5

Suct

ion (

pF

)

Distance (meters)

Wetted

Crack

Surface

Wetted

Crack

Surface

Time = 10 yrs

3

1

0.3

0.1

1

5

2

3

4

Moisture Infiltration from Wetted Crack Surfaces

Wet Crack Surface Wet Crack Surface


' ( ) tan 'ws c u a

UNSATURATED SOILS: SOME FUNDAMENTALS … 2010.pdfJ.L. Briaud –Texas A&M University. UNSATURATED...

Documents

Transcript of UNSATURATED SOILS: SOME FUNDAMENTALS … 2010.pdfJ.L. Briaud –Texas A&M University. UNSATURATED...