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Design of Structures to Resist the Design of Structures to Resist the Pressures and Movements of Pressures and Movements of
Expansive SoilsExpansive Soils
Robert L. Lytton
Texas A&M UniversityFoundation Performance Association
December 12, 2007
1
Acknowledgements Acknowledgements
Gyeong-Taek HongRong Luo
Charles P. AubenyRifat Bulut
Jorge A. ProzziXiaoyan Long
Anshuman ThakurEeshani Sood
2
Topics (1/2)Topics (1/2)
• Soil properties• Suction envelopes
ClimatesTrees Drainage
• Pavement designConcrete and asphalt Stabilized layers Vertical and horizontal moisture barrier
3
Topics (2/2)Topics (2/2)
• Shrinkage cracking design• Shallow slope failure• Slab-on-ground design• Drilled pier design
Lateral pressuresStresses, strains, movementsComparison with field measurement
• Retaining wall designLateral pressuresStresses, strains, movementsComparisons with measurements
4
Volume ChangeVolume Change
(Lytton, 1977)⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠
f fh 10 σ 10
i i
ΔV h σ= - log - logV h σ
γ γ
Volume–Mean Principle Stress-Suction surface
Δ Δ⎛ ⎞= ⎜ ⎟⎝ ⎠
H VfH V
⎡ ⎤Δ = ⎢ ⎥⎣ ⎦∑ i ii=1 i
Δ Δn Vf z
V
0.67 0.33 pFf = 0.5 when drying; f = 0.8 when wetting
f = − Δ
⎛ ⎞⎜ ⎟⎝ ⎠
5
Volume ChangeVolume Change
(Covar
and Lytton, 2001)
Partitioning Database on Mineral Classification
6500 Data from SSLOf National Soil Survey Center
6
Volume ChangeVolume Change
⎛ ⎞⎜ ⎟⎝ ⎠
σ h1= h1+
hθθ
γ γ
∂∂
⎡ ⎤⎢ ⎥⎣ ⎦
h 0% - 2μm= �
% -No.200 sieveγ γ
Zone III (Covar
and Lytton, 2001)
% 2%% .200c
mfNo sieve
μ−=
−
PI / %fc
LL /
%fc
(Lytton, 1994)
7
Exponential Suction Profile for Extreme Exponential Suction Profile for Extreme Wetting and Drying ConditionWetting and Drying Condition
0
2
4
6
8
10
12
14
2 3 4 5
Suction (pF)
Dept
h (ft
)
Wet
Equil.
Dry
0
2
4
6
8
10
12
14
0 0.2 0.4 0.6
Volumetric Water Content
WetDry
0
2
4
6
8
10
12
14
0 1 2 3
Vertical Movement (in)
WetDry
Fort Worth Interstate 820
⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠
e onπ nπU(Z,t) = U +U exp - Z cos 2πnt - Zα α
⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠
e onπU(Z) = U +U exp - Zα
Mitchell (1979)
MoistureActive zone
8
Volume ChangeVolume Change
(Lytton, 1977)⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠
f fh 10 σ 10
i i
ΔV h σ= - log - logV h σ
γ γ
Volume–Mean Principle Stress-Suction surface
Δ Δ⎛ ⎞= ⎜ ⎟⎝ ⎠
H VfH V
⎡ ⎤Δ = ⎢ ⎥⎣ ⎦∑ i ii=1 i
Δ Δn Vf z
V
0.67 0.33 pFf = 0.5 when drying; f = 0.8 when wetting
f = − Δ
⎛ ⎞⎜ ⎟⎝ ⎠
9
Lateral Pressure CoefficientsLateral Pressure Coefficients
(Lytton et al., 2006)
01 sin ' 1 sin '1 sin ' 1 sin '
ndK ek
φ φφ φ
⎛ ⎞⎛ ⎞− += ⎜ ⎟⎜ ⎟+ −⎝ ⎠⎝ ⎠
Conditions Ko (after McKeen, 1981) e d k n
Cracked 0 0 0 0 1
Drying (Active) 1/3 1 0 0 1
Equilibrium (at rest) 1/2 1 1 0 1
Wetting (withinmovement active zone) 2/3 1 1 0.5 1
Wetting (belowmovement active zone) 1 1 1 1 1
Swelling near surface(passive earth pressure) 3 1 1 1 2
(after Holtz and Kovacs, 1981)
φ ' = 0.0016PI2 - 0.3021PI + 36.208R2 = 0.9978
0
5
10
15
20
25
30
35
40
0 20 40 60 80 100Plastic index, PI
Inte
rnal
fric
tion
angl
e, φ
'
10
Volumetric Moisture Content and Suction Volumetric Moisture Content and Suction CurvesCurves
(Lytton et al., 2006)
5
4
3
2
6
0
1
Volumetric Water Content θf θsat
Suct
ion
(pF)
D
A
S1
1
κθf
γγ
w
d
S1
pF0
=5.622+0.0041(% clay fines)
S = -20.29+0.1555(LL)-0.117(PI)+0.0684(-#200)
11
Pavement Design on Expansive Pavement Design on Expansive SoilsSoils
12
13
Pavement TreatmentsPavement TreatmentsPavement
Stabilized Soil
Inert soil
Subgrade
Barrier
Bar
rier
Pavement Section
WIDTH OF PAVEMENT,83 FT
10 FT6 FT 12 FT 12 FT 12 FT12 FT 7 FT
27 FT
14
Transverse Distribution of Vertical Transverse Distribution of Vertical MovementsMovements
d (ft)Swel
ling
Shrin
kage
(in)
-1.5
-0.5
0.5
1.5
2.5
3.5
0 10 20 30 40
Section ASection BSection C
15
Field ConditionsField Conditions
0
2
4
6
8
10
12
14
2.0 3.0 4.0 5.0
pFD
epth
(ft
Root zone
Moisture active zone
Wilting point 4.5 pFField capacity Equilibrium
πα
⎛ ⎞= ± ⎜ ⎟⎜ ⎟
⎝ ⎠0( ) exp -e
nU Z U U Z
= −e 3.5633exp( 0.0051TMI)U
16
Roadside Drainage Conditions
HillSlope
Valley
Cut
Flat
Fill
2.3 pF
Longitudinal Drainage
Lateral Slope
2.0 pF 2.0 pF
2.5 pF 2.2 pF 2.2 pF
2.6 pF 2.3 pF 2.3 pF
Thornthwaite
Moisture Index (TMI, 1948)Climatic Conditions
100 60
p
R DEFTMIE−
= R = runoff moisture depthDEF =deficit moisture depthEp
= evapotranspiration
17
Calculated Vertical MovementCalculated Vertical Movement
18
Comparison of PVR with Case Study Comparison of PVR with Case Study ResultsResults
No Treatments
2.0
0.0
2.0
Swel
l
2.0
0.0
2.0
Swel
l
(IN)
New methodPVR
Fort Worth A
Shrin
kSh
rink
Atlanta Edge
M F
Austin
Outer W
heel P
athEdgeOuter
EdgeOuter
EdgeOuter Edge
Outer
B C
19
Acceptable Predicted PerformanceAcceptable Predicted Performance
2.0
2.5
3.0
3.5
4.0
4.5
0 10 20 30
Fort Worth Interstate 820 A
SI
Time (yrs)
Flexible Pavement
60
100
140
180
0 10 20 30Time (yrs)
IRI
20
Acceptable Predicted PerformanceAcceptable Predicted Performance
60
100
140
180
0 10 20 302.0
2.5
3.0
3.5
4.0
4.5
5.0
0 10 20 30
Austin State Route 1
Rigid Pavement
SI
Time (yrs) Time (yrs)
IRI
21
Loss of Serviceability Increase of Roughness
Predicted Roughness with Time
Time (yrs)
2.5
3.0
3.5
4.0
4.5
0 10 20 30
Time (yrs)
SI IRI
Total
Soil
Traffic
Soil
60
80
100
120
140
0 10 20 30
Soil
Traffic
Total
Fort Worth Interstate 820 B
22
SUBGRADE MOVEMENTS COMPARED WITH PVR FOR A MINIMUM ACCEPTABLE TREATMENT
Flexible Pavement
Case SitesEdge
Fort Worth
A
B
C
Atlanta
Austin Main
Frontage
Outer Edge Outer
Swell
PVR
Shrink Total
New Method
0.78
0.72
0.02
(IN)
0.30
0.37
0.66
0.72
0.73
1.12
1.06
0.43
0.58
1.50
1.45
1.14
1.36
0.80
1.24
0.61
0.57
0.42
1.08
0.49
0.84
2.08
2.08
1.21
1.28
1.45
1.94
1.20
1.20
0.81
0.88
1.13
1.17
Avg. 0.67 in 1.1 in
23
Longitudinal Cracking over Expansive Longitudinal Cracking over Expansive SoilSoil
• Expansive soilExperience volumetric change when subjected to moisture variation
• Longitudinal crackInitiate in shrinking expansive subgradePropagate to pavement surface
24
Practice of Geogrid ReinforcementPractice of Geogrid Reinforcement
FM1915 (Milam County, Texas)
25
Practice of Lime TreatmentPractice of Lime Treatment
26
Stress Analysis on Subgrade SoilStress Analysis on Subgrade Soil
• Stress variable for saturated soil: σ-uw
•
Stress variable for unsaturated soil: σ-ua , ua -uw
•
Soil suctionThe affinity of soil for waterMatric suction: negative water pressureOsmotic suction: soluble salts in the soil water
•
Constitutive equation to estimate the volumetric strain of unsaturated soil:
⎟⎟⎠
⎞⎜⎜⎝
⎛−⎟⎟
⎠
⎞⎜⎜⎝
⎛−⎟⎟
⎠
⎞⎜⎜⎝
⎛−=
Δ
i
f
i
f
i
fh h
hVV
ππ
γσσ
γγ πσ 101010 logloglog
27
⎟⎟⎠
⎞⎜⎜⎝
⎛−⎟⎟
⎠
⎞⎜⎜⎝
⎛−⎟⎟
⎠
⎞⎜⎜⎝
⎛−=
Δ
i
f
i
f
i
fh h
hVV
ππ
γσσ
γγ πσ 101010 logloglog
where
VVΔ = volumetric strain;
ih = initial value of matric suction; fh = final values of matric suction; iσ = initial value of mean principle stress; fσ = finial value of mean principle stress; iπ = initial value of osmotic suction;
fπ = finial value of osmotic suction;
hγ = matric suction compression index;
σγ = mean principal stress compression index; and
πγ = osmotic suction compression index.
28
Without Geogrid ReinforcementWithout Geogrid Reinforcement……
Subgrade (Expansive soil)
Asphalt
CL
BaseCrack
29
With Geogrid ReinforcementWith Geogrid Reinforcement……
Subgrade (Expansive soil)
Asphalt
CL
Base
Geogrid
30
Mechanism of Geogrid ReinforcementMechanism of Geogrid Reinforcement
P P P P
Asphalt
Base
Subgrade
Travel direction Depth
31
0.000
0.020
0.040
0.060
0.080
0.100
0.120
0.140
0.160
0.180
0.200
0 400 800 1600 3200 6400 12800
Geogrid Stiffness (kN/m)
Stre
ss In
tens
ity F
acto
r (M
Pa*m
^.5)
0
10
20
30
40
50
60
70
80
90
Geo
grid
Ten
sile
Str
engt
h (k
N/m
)
Number of Crack=1
Number of Crack=2
Number of Crack=3
Number of Crack=4
Number of Crack=5
Upper Tensile Strength
Lower Tensile Strength
Geogrid Tensile Strength
32
Transverse Stress Distribution in Pavement (Full Restraint)
33
Transverse Stress Distribution in Pavement (Crack at Edge of Shoulder)
34
Transverse Stress Distribution in Pavement with Treated Layer
35
SlabSlab--onon--GroundGround DesignDesign
36
37
38
39
40
41
42
43
44
45
46
47
48
Dry Season
(-) Suction Ground Surface
Wet Season
Equilibrium
Dep
th
49
50
51
52
53
Equilibrium Soil Suction vs. TMIEquilibrium Soil Suction vs. TMI
54
55
ROOT ZONE
Crack Spacing Gets Larger with Depth
56
RUNOFF WATER
DRY LIMIT
WET LIMIT4.0
2.0
4.0
2.5
pF
SUCTION RANGEBETWEEN CRACKS
WATERSOAKSINTOSOIL 2.0
57
58
DEPTHBELOW
SOILSURFACE
CRACKING SPACING
SOURCE : MICHAEL KNIGHTPH. D. DISSERTATATION, GEOLOGYUNIVERSITY OF MELBOURNE (AUSTRALIA) 1972
59
Field to laboratory diffusion coefficient ratio (ContField to laboratory diffusion coefficient ratio (Cont’’d)d)
Rel
iabi
lity
Field α/laboratory α0
60
Drilled Pier Design Drilled Pier Design
Retaining Wall DesignRetaining Wall Design
61
Lateral Earth Pressure Concept (1/5)Lateral Earth Pressure Concept (1/5)Suction Change
62
Lateral Earth Pressure Concept (2/5)Lateral Earth Pressure Concept (2/5)
Suction Change
( ) ⎛ ⎞⎛ ⎞⎜ ⎟⎜ ⎟
⎝ ⎠ ⎝ ⎠
hh
σσ
2ε-1-f ti
h 0 t if
z3 hσ = k z = σ 10 -2 h 2
γγ
γ γγ
Lateral PressureDue to Suction Change
63
Lateral Earth Pressure Concept (3/5)Lateral Earth Pressure Concept (3/5)
Lateral PressureDue to Suction Change
Limited by Soil Strength
64
Lateral Earth Pressure Concept (4/5)Lateral Earth Pressure Concept (4/5)
(Small Suction Change)At Rest Earth Pressure
65
Lateral Earth Pressure Concept (5/5)Lateral Earth Pressure Concept (5/5)Zone
I
II
III
Zmp
66
UPWARDMOVEMENT
ANCHORZONE
REINFORCING
DRILLED PIER
67
68
Severe damage to a reinforced concrete columns due to differential heave, in Saudi Arabia (Al-Shamrani
and Dhowian, 2003)
69
Retaining WallsRetaining Walls
EXPANSIONPRESSURE
RESISTINGPRESSURE
70
3 –
4 ft
71
72
Horizontal Earth Pressure in Expansive Horizontal Earth Pressure in Expansive SoilsSoils
73
Zone I
Zone II
Zone III
Mov
emen
tac
tive
zone
Anc
hor z
one
Heave
Zero Swell
Zmp
Richards and Kurzeme
(1973) 4 times the overburdenJoshi and Katti
(1980) 42 psi
@ 3 ft, lab Komornik
(1962)
55 psi
@ 3 ft, labBrackely
and Sanders (1992) 12 psi
@ 3 ft, field
Horizontal Swelling Pressure Model
( )′mpz tan 45 + /2 = 5 - 7 ftφ
( )⎡ ⎤⎛ ⎞⎢ ⎥⎜ ⎟
⎝ ⎠⎢ ⎥⎣ ⎦′i
2
mp= zXZ z tan 45 +φ /2 1-H
Horizontal Active zone
Zmp
= 3 -
5 ftJoshi and Katti
(1980); Komornik
(1962);Brackely
and Sanders (1992); Symons et al. (1989)
( )′h tσ = 1- sin zφ γ
74
Mean angle of the fissure to the horizontal = 43 degree
Silckensides
occurs in soil which has PI >30, -2μm>30
Leeuhof
test site at Vereeniging, South Africa
Fissures caused by a passive failure of the soil resulting from the horizontal pressure during seasonal swelling of the clay
Williams and Jennings (1973)
0
2
4
6
8
10
12
14
16
0 5 10 15 20 25
Horizontal Pressure (psi)
Prediction197919801981Vertical
Zone I(Passive Failure)
Zone II(Passive)
Zone III(at Rest)
Zone II(Passive)
0
2
4
6
8
10
12
14
16
2 3 4 5
Suction (pF)
Dept
h (ft
)
0
2
4
6
8
10
12
14
16
0 1 2 3 4
Swelling Movement (in)
Prediction
Measured
0
2
4
6
8
10
12
14
16
0 10 20
Shear Strength (psi)
Seasonal range of suction(In situ psychrometers)
Maximum pressures measuredat four depths in 1979,1980,1981(In situ pressure cells)
Zmp
= 3.8 ft
Brackely and Sanders (1992)Natural horizontal pressures measured in field
Komornik (1962)Measured horizontal pressures in the large scale pile test
0
1
2
3
4
2 3 4
Suction (pF)
Dept
h (ft
)
0
1
2
3
4
0 2 4 6 8
Swelling (in)
Prediction
Measured
0
1
2
3
4
0 20 40 60
Horizontal Pressure (psi)
PredictionMeasuredVertical
Soil PropertiesLL
76 %PI
48 %#200
90 %-2μm
62 %
Site Kibbutz Mizra, Israel
Sand seam
Kim and O’Neill (1998)Axial behavior of the pier
Test Site Stratigraphy(NGES-UH)
Schedule of Rebar and Concretein Drilled Shaft
Kim and O’Neill (1998)Axial behavior of the pier
Bar versus Time(1 bar=100 kPa) Uplift Force versus Time
55
34
193.1 pF
3.7 pF
4.1 pF
Kim and O’Neill (1998)Axial behavior of the pier
0
2
4
6
8
10
12
14
0.0 1.0 2.0
Swelling (in)
Prediction
Measured
0
2
4
6
8
10
12
14
0 5 10
Horizontal Pressure (psi)
Prediction
Vertical
0
2
4
6
8
10
12
14
-0.6 -0.4 -0.2 0.0 0.2
Pile Movement (in)
Prediction
Measured
0
2
4
6
8
10
12
14
0 50 100 150
Axial Stress (psi)
Prediction
Measured
0
2
4
6
8
10
12
14
2.5 3.5 4.5
Suction (pF)
Dept
h (ft
)
Case Study of Bending Behavior of the PierUneven Wetting with Same Initial Condition
0
2
4
6
8
10
12
2.0 2.5 3.0 3.5 4.0
Suction (pF)
Dep
th (f
t)
0 5 10
Active Zone (ft)2.0 2.5 3.0 3.5 4.0
Suction (pF)0 2 4
Swelling (in)0 2 4
Swelling (in)
( )tan 45 / 2mpZ φ′⋅ +
NGES-UH Site (Kim and O’Neill, 1998)
0 10 20
Horizontal (psi)-20 -10 0
Horizontal (psi)-10 0 10
Shear Stress (psi)
-10 0 10
Shear Stress (psi)
NGES-UH Site (Kim and O’Neill, 1998)
Case Study of Bending Behavior of the PierUneven Wetting with Same Initial Condition
-4.0 -2.0 0.0
Deflection (in)-200 -100 0 100
Lateral Load (lb)
Prediction
At Rest
-40000 -20000 0 20000 40000
Bending Moment (lb-in)-2000 -1000 0 1000 2000
Shear Force (lb)
Case Study of Bending Behavior of the PierUneven Wetting with Same Initial Condition
NGES-UH Site (Kim and O’Neill, 1998)
83
Retaining Wall DesignRetaining Wall Design
Katti et al. (1979)Measured horizontal pressures in the large scale retaining wall test
Black cotton soil, IndiaLL
81.5 %
PI
38.3 %#200
96.0 %
-2μm
56.0 %
3 months saturation
0
1
2
3
4
5
6
7
8
2 3 4
Suction (pF)
Dep
th (f
t)
0
1
2
3
4
5
6
7
8
0 2 4 6
Swelling Movement (in)
Prediction
Measured
0
1
2
3
4
5
6
7
8
0 20 40 60
Horizontal Pressure (psi)
PredictionMeasuredVertical
Air
dry
initi
al c
ondi
tion
100%
Sat
urat
ion
Katti et al. (1979)Measured horizontal pressures in the large scale retaining wall test
Case Study of Bending Behavior of the Retaining Wall
0
2
4
6
8
10
12
2.5 3.0 3.5 4.0
Suction (pF)
Dept
h (ft
)
2.5 3.0 3.5 4.0
Suction (pF)0 1 2
Swell (in)
-10 -5 0
Horizontal (psi)0 5 10
Horizontal (psi)0 1 2
Swell (in)
NGES-UH Site (Kim and O’Neill, 1998)
-150 -50 50
Lateral Load (lb)
0
2
4
6
8
10
12
-10 -5 0
Deflection (in)-50000 0 50000
Bending Moment (lb-in)-2000 0 2000
Shear Force (lb)
NGES-UH Site (Kim and O’Neill, 1998)
Case Study of Bending Behavior of the Retaining Wall
89
Topics (2/2)Topics (2/2)
• Shrinkage cracking design• Shallow slope failure• Slab-on-ground design• Drilled pier design
Lateral pressuresStresses, strains, movementsComparison with field measurement
• Retaining wall designLateral pressuresStresses, strains, movementsComparisons with measurements
88
Topics (1/2)Topics (1/2)
• Soil properties• Suction envelopes
ClimatesTrees Drainage
• Pavement designConcrete and asphalt Stabilized layers Vertical and horizontal moisture barrier
Design of Structures to Resist the Design of Structures to Resist the Pressures and Movements of Pressures and Movements of
Expansive SoilsExpansive Soils
Robert L. Lytton
Texas A&M UniversityFoundation Performance Association
December 12, 2007