Post on 19-May-2020
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
J.L. Briaud –Texas A&M University.
• SOME FUNDAMENTALS– SUCTION
– EFFECTIVE STRESS
– STRENGTH
– DEFORMATION
• SOME APPLICATIONS– ULTIMATE BEARING CAPACITY
– MOVEMENT
– COMPACTION
– SLABS ON GRADE
– TREES
– EARTH PRESSURES
– SLOPES
J.L. Briaud –Texas A&M University.
Soil State Swell Shrink
Unsaturated Yes No
Saturated Yes Yes
Saturated No Yes
GWL
THE THREE ZONES
J.L. Briaud –Texas A&M University.
WATER NORMAL STRESS
TENSION COMPRESSION
0
(SUCTION)
(pF )
uw (kPa)
(PORE PRESSURE)
J.L. Briaud –Texas A&M University.
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.J.L. Briaud –Texas A&M University.
The Water Strider
Force = 72 mN/mThickness = a few Angstroms
Stress >? 20 MPa
J.L. Briaud –Texas A&M University.
Pure Water Salt Water
Initial state Initial state
After time t
After time t
h = Osmotic Suction
OSMOTIC WATER TENSION
J.L. Briaud –Texas A&M University.
J.L. Briaud –Texas A&M University.
Water Tension 200kPa
Water Tension 100,000kPa
WaterContractile Skin
SmectiteAl2Si4O10(OH)2
Water
QuartzSiO2
QuartzSiO2
J.L. Briaud –Texas A&M University.
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
J.L. Briaud –Texas A&M University.
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
J.L. Briaud –Texas A&M University.
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
Shear Strength-unsaturated
(Lu & Likos, 2004)
α vs S
Shear Strength-unsaturated
(Fredlund & Rahardjo, 1993)
J.L. Briaud –Texas A&M University.
SHEAR STRENGTH-example
J.L. Briaud –Texas A&M University.
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
J.L. Briaud –Texas A&M University.
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
J.L. Briaud –Texas A&M University.
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
Jean-Louis Briaud – Texas A&M University
, , ,L C Ur p q N s
up kr
THIS BEARING CAPACITY EQUATION
ALWAYS WORKS
J.L. Briaud –Texas A&M University.
i
iiii
E
ΔHΔεHS
ei+Deiei ev
’ o
v
D
’ i
’ ov
v
WEIGHT INDUCED SETTLEMENT
v
D’i’ovHi
z
P
J.L. Briaud –Texas A&M University.
J.L. Briaud –Texas A&M University.
i w
iiii
E
ΔwfHΔεHS
w
wi+
Dw
iw
i
ei+ Deiei ev
MOISTURE INDUCED MOVEMENT
w
Hi Dwiwi
z
J.L. Briaud –Texas A&M University.
J.L. Briaud –Texas A&M University.
w
wSW
DV/V
wSH
0
gw/gdShrink-Swell
Index1
J.L. Briaud –Texas A&M University.
CLASSIFICATION OF SHRINK-SWELL POTENTIAL
ACCORDING TO SHRINK-SWELL INDEX
Potential
Very High
High
Moderate
Low
Iss
> 60%
40 – 60
20 – 40
< 20%
J.L. Briaud –Texas A&M University.
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
J.L. Briaud –Texas A&M University.
i w
iiii
E
ΔwfHΔεHS
J.L. Briaud –Texas A&M University.
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
J.L. Briaud –Texas A&M University.
WATER INJECTION
J.L. Briaud –Texas A&M University.
Texas A&M University
J.L. Briaud –Texas A&M University.
FOOTINGS
J.L. Briaud –Texas A&M University.
J.L. Briaud –Texas A&M University.
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
J.L. Briaud –Texas A&M University.
J.L. Briaud –Texas A&M University.
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
J.L. Briaud –Texas A&M University.
J.L. Briaud –Texas A&M University.
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
J.L. Briaud –Texas A&M University.
J.L. Briaud –Texas A&M University.
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
J.L. Briaud –Texas A&M University.
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
J.L. Briaud –Texas A&M University.37
J.L. Briaud –Texas A&M University.38
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
J.L. Briaud –Texas A&M University.40
..
.
Tributary Load Area
..
.0
.
.0 0
.
.0 0
.
.
Leqv
Leqv
J.L. Briaud –Texas A&M University.41
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
J.L. Briaud –Texas A&M University.43
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)
J.L. Briaud –Texas A&M University.
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
J.L. Briaud –Texas A&M University.
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
J.L. Briaud –Texas A&M University.
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
J.L. Briaud –Texas A&M University.
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
J.L. Briaud –Texas A&M University.48
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)
J.L. Briaud –Texas A&M University.49
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)
J.L. Briaud –Texas A&M University.50
CROSS SECTION
PLAN VIEW
J.L. Briaud –Texas A&M University.
#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
J.L. Briaud –Texas A&M University.52
Excavation and steel - 16 July 2004
J.L. Briaud –Texas A&M University.
J.L. Briaud –Texas A&M University.
J.L. Briaud –Texas A&M University.
J.L. Briaud –Texas A&M University.
Completed Building
J.L. Briaud –Texas A&M University.57
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)
J.L. Briaud –Texas A&M University.58
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
J.L. Briaud –Texas A&M University.
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
J.L. Briaud –Texas A&M University.J.L. Briaud –Texas A&M University.
Effects of trees on adjacent buildings
No Change
Shrink
Shrink
J.L. Briaud –Texas A&M University.
J.L. Briaud –Texas A&M University.
LEGEND
(Richards)
D/H = 1
H
D
J.L. Briaud –Texas A&M University.J.L. Briaud –Texas A&M University.
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
J.L. Briaud –Texas A&M University.
RETAINING WALLS-EARTH PRESSURE
J.L. Briaud –Texas A&M University.
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)
J.L. Briaud –Texas A&M University.
RETAINING WALLS-EARTH PRESSURE
J.L. Briaud –Texas A&M University.
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)
J.L. Briaud –Texas A&M University.
RETAINING WALLS-EARTH PRESSURE
J.L. Briaud –Texas A&M University.
σah = ov – 2su ?
σph = ov + 2su ?
Not applicable because of cracking
J.L. Briaud –Texas A&M University.
RETAINING WALLS-EARTH PRESSURE
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
Shear Strength-unsaturated
' ( ) tan 'ws c u a
J.L. Briaud –Texas A&M University.