unsaturated soils: some fundamentals … 2010.pdfj.l. briaud –texas a&m university....

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

THE THREE ZONES

WATER NORMAL STRESS

TENSION COMPRESSION

(SUCTION)

uw (kPa)

(PORE PRESSURE)

a aT T

Contractile

- 1,000 kPa

4 T cos αh

where T 72 mN/ m

Atmospheric

pressure

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

h = Osmotic Suction

OSMOTIC WATER TENSION

Water Tension 200kPa

Water Tension 100,000kPa

WaterContractile Skin

SmectiteAl2Si4O10(OH)2

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

ci wi ai

t t t t

f f fF

A A A A

'wi a aiw

u a u a

' w au u a

Saturated

ua = 0

’ = - uw

Occluded Air

uw = ua

’ = - uw

S > 85%

Continuous Air

ua = 0

’ = - auw

S < 85%

soil grain

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

' 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

0 40 80

s, kPa

0 40 80 120

’, kPa

0 0.5 1

0 40 80 120

Unsaturated

Top of

Capillary Zone

-80 -40 0

au, kPa

-400 -200 0 -100

u, kPa

Saturated by

Capillarity

Unsaturated

Saturated

Jean-Louis Briaud – Texas A&M University

THIS BEARING CAPACITY EQUATION DOES

NOT WORK FOR UNSATURATED SOILS

12u c qp cN BN DNgg g

Jean-Louis Briaud – Texas A&M University

, , ,L C Ur p q N s

THIS BEARING CAPACITY EQUATION

ALWAYS WORKS

ΔHΔεHS

ei+Deiei ev

’ ov

WEIGHT INDUCED SETTLEMENT

D’i’ovHi

ΔwfHΔεHS

ei+ Deiei ev

MOISTURE INDUCED MOVEMENT

Hi Dwiwi

gw/gdShrink-Swell

Index1

CLASSIFICATION OF SHRINK-SWELL POTENTIAL

ACCORDING TO SHRINK-SWELL INDEX

Potential

Very High

Moderate

40 – 60

20 – 40

WATER CONTENT VARIATION AS A FUNCTION OF TIME

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

ΔwfHΔεHS

Legend

RF : Reference

W : Water injected

BM : Benchmark

Su = 179.8 kPa

wmean = 19.74 %

h = 3.41 pF

LL = 40.4, PL = 17.1

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’

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 A&M University

WATER INJECTION

Texas A&M University

FOOTINGS

WATER CONTENT AND SUCTION vs. DEPTH

0 1 2 3 4 5

B:Boring

Suction, pF

0.00 0.05 0.10 0.15 0.20 0.25 0.3

B:Boring

Water ContentFooting RF1 at a site

in Arlington, Texas

FOOTING MOVEMENT OVER TWO YEARS

RAINFALL AND TEMPERATURE

Ave. Monthly Temperature

Ave. Monthly Rainfall

ture, oC

100 0 100 200 300 400 500 600 700 800

Time, days

RF1+ RF2+ W1+ W2

Average Measured movements

Water Content Method

PREDICTED AND MEASURED MOVEMENTS

Average of 4 Footings at a site

in Arlington, Texas

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 2 4 6 8 10 12 14

Water Content (%)

Plate Reload Modulus (MPa)

Dry Unit Weight (kN/m^3)

NGES Silty Sand (Mold #5)

0 2 4 6 8 10 12 14

Water Content (%)

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

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

Q (kN/m)

Leqv Δ = f ( Q, EI, L)

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

Daily Mean Relative Humidity

of Arlington, Texas

Daily Mean Wind Speed

of Arlington, Texas

Daily Acumulative Rainfall

of Arlington, Texas

Input Weather Data (FAO 56)

40 Columns of equal

width elements20 Columns of elements with

bias 1.1

s of e

bias 1

Edge Lift Mound

r Line

( Line

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

40 Columns of equal

width elements20 Columns of elements with

bias 1.1

s of e

bias 1

Edge Drop Mound

r Line

( Line

Foundation slab

Soil mound and foundation elevations

0 1 2 3 4 5 6 7 8

x- coordinate (m)

Initial Mound Elev.

Final Mound Elev.

Final Found Elev

Bending moments and shearing forces

0 1 2 3 4 5 6 7 8

x- coordinate (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 0.2 0.4 0.6 0.8 1 1.2

Iss. H. DUedge (m)

deq=0.63 m

deq=0.51 m

deq=0.38 m

deq=0.25 m

deq=0.13 m

eqvqLM

Iss H ΔlogUedge (m)

Leqv design chart (Edge drop)

0 0.1 0.2 0.3 0.4 0.5 0.6

H. Dwedge (m)

deq=0.63 m

deq=0.51 m

deq=0.38 m

deq=0.25 m

deq=0.13 m

eqvqLM

Water content based design charts (Edge drop)

CROSS SECTION

PLAN VIEW

#4@16" OCEW

1.05 m

#3 TIES @ 24" C-C

6 MIL POLY

Excavation and steel - 16 July 2004

Completed Building

Soil movement log

-0.005 0 0.005 0.01 0.015

Movements (m)D

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)

Perimeter average level vs. Interior average level

-0.003

-0.002

-0.001

0 30 60 90 120 150 180 210 240 270

Time (days)

Perimeter average level

Interior average level

Difference (per-int)

SLAB MOVEMENT over 1 YEAR

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

LEGEND

(Richards)

D/H = 1

Typical Wet

suction profile: initial

suction profile

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

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

Unsaturated k

k hk =

Mitchell (1979)

e0 0 0 0

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

Unsteady Flow Equation

Sk h γα

0.434 γ

10u = log h

0 20 40 60 80 100

Crack Depth (cm)

Crack Spacing versus Depth (Knight, 1972)

Pore Pressure Distribution

Hydrostatic

Increase with

Depth z

Suction at Surface, u0

Moisture Migration into Cracked Slope

0 0.5 1 1.5

Distance (meters)

Wetted

Surface

Wetted

Surface

Time = 10 yrs

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....

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