Calculation of Heave of Deep Pier Foundations By John D. Nelson, Ph.D., P.E., Hon. M. SEAGS, F. ASCE, Kuo-Chieh (Geoff) Chao, Ph.D., P.E., M. SEAGS, M.
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Calculation of Heave of Deep Pier Foundations
By
John D. Nelson, Ph.D., P.E., Hon. M. SEAGS, F. ASCE,
Kuo-Chieh (Geoff) Chao, Ph.D., P.E., M. SEAGS, M. ASCE,
Daniel D. Overton, M.S., P.E., F. ASCE,
and
Robert W. Schaut, M.S., P.E., M. ASCE
August 2012
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DAMAGE FROM EXPANSIVE SOILS
Photo of Shear Failure in South Side of Pier at N7
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Outline of Presentation
Introduction
Free-Field Heave Prediction
Pier Heave Prediction
Validation of APEX
Pier Design Curves
Example Foundation Design
Conclusions
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INTRODUCTION
Pier and grade beam foundations are a commonly used foundation type in highly expansive soils.
Existing pier design methods consider relatively uniform soil profiles, and piers with length to diameter ratios of about 20 or less.
Fundamental parameter on which foundation design is based is the “Free-Field Heave“ (i.e. the heave of the ground surface with no applied loads)
A finite element method of analysis (APEX) was developed to compute pier movement in expansive soils having: Variable Soil Profiles, Complex Wetting Profiles, Large Length-to-Diameter Ratios, and Complex Pier Configurations and Materials
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iiv Δz%SΔzερ
FREE-FIELD HEAVE PREDICTION
FREE-FIELD HEAVE PREDICTIONby Oedometer Method
Terminology and notation for oedometer tests
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FREE-FIELD HEAVE PREDICTIONDetermination of Heave Index, CH
Vertical stress states in soil profile
FREE-FIELD HEAVE PREDICTIONStress Paths Under Different Loading Conditions
C
S
S%
A
Cc
LOG h
ME
K
B
LOG s’
s’CS
s’CV
s’i2
s’i1
s’i
0’
0
J
H
P
N
F
G
L
ho hC1
DCH CS
FREE-FIELD HEAVE PREDICTION Determination of Heave Index, CH
LOG h
LOG '
S
E
D
M
L
K
B
A
P
N
'CS
'CV
'i2
'i1
Cc
hC1
C
''i
H
F
J
G
CH CS
ho
S%
0
0 D CA
B
CH
CONSTANTVOLUMETEST DATA
'i ' 'CV CS
APPLIED STRESS, ' (LOG SCALE)
CONSOLIDATION-SWELLTEST DATAS
S%
%P
ER
CE
NT
SW
ELL
FREE-FIELD HEAVE PREDICTIONCalculations of Design Heave
'iσlog'
cvσlog
%S
HC
σ‘vo
(S%)z
'iσ
'cvσ
logHC%S
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i%iv ΔzSΔzερ
FREE-FIELD HEAVE PREDICTIONDetermination of Heave Index, CH
i
cv
%
icv
%H
σ'σ'
log
S
σ'logσ'log
SC
zvo
cvHz%zv σ'
σ'logC)S()(ε
zvo
cviHoi σ'
σ'logΔzCρ
FREE-FIELD HEAVE PREDICTIONDetermination of Heave Index, CH
Data from Method A of the ASTM D4546-08 Standard
-80
-6
-4
-2
0
2
4
6
8
10
12
100 200 300 400 500 600 700
Ver
tical
str
ain,
%S
wel
l (+
)C
olla
pse
(-)
Vertical Stress, kPa (1kPa=20.9 lb ft )2
FREE-FIELD HEAVE PREDICTIONDetermination of Heave Index, CH
Method A data from the Standard plotted in semi-log form
FREE-FIELD HEAVE PREDICTIONDetermination of Heave Index, CH
Method A data from the Standard plotted in semi-log form
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Data collected from Porter, 1977; Reichler, 1997; Feng et al., 1998; Bonner, 1998; Fredlund, 2004; Thompson et al. 2006; and Al-Mhaidib, 2006
The types of the soils consist of claystone, weathered claystone, clay, clay fill, and sand-bentonite
l = 0.36 to 0.90 (avg = 0.62) for claystone
= 0.36 to 0.97 (avg = 0.59) for all soil types
FREE-FIELD HEAVE PREDICTIONRelationship between s′cv and s′cs
)σ'logλ(logσ'σ'logσ' log icsicv
Logarithmic Form:
FREE-FIELD HEAVE PREDICTIONRelationship between s′cv and s′cs
Histograms of the λ values determined using the logarithmic form
0
2
4
6
8
10
12
0 - 0.05 0.05 -0.15
0.15 -0.25
0.25 -0.35
0.35 -0.45
0.45 -0.55
0.55 -0.65
0.65 -0.75
0.75 -0.85
0.85 -0.95
Fre
qu
ency
Lambda Value
Claystone (STD Deviation = 0.14)
All Soil Types (STD Deviation = 0.17)
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PIER HEAVE PREDICTION
Typical pier and grade beam
foundation system
DAMAGE FROM EXPANSIVE SOILS
Pier
Diagonal Crack
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PIER HEAVE PREDICTIONRigid Pier Analysis
Rigid Pier Analysis
πd
PZσα
f
1ZL dl
ADcv1s
AD
πdZfPP ADudlmax
dlU D P 0
Pdl
U
D
PIER HEAVE PREDICTIONElastic Pier Analysis
Normalized Pier Heave vs. L/ZAD
Ref: Poulos & Davis (1980)Nelson & Miller (1992)Nelson, Chao & Overton (2007)
Straight Shaft
Belled Pier
PIER HEAVE PREDICTIONElastic Pier Analysis
Straight Shaft
Belled Pier
Normalized Force vs. L/ZAD
Ref: Poulos & Davis (1980)Nelson & Miller (1992)Nelson, Chao & Overton (2007)
PIER HEAVE PREDICTIONAPEX Method
Analysis of Piers in EXpansive soils
PIER HEAVE PREDICTIONAPEX Method
The field equations with soil swelling
isozzθθrrrr εσσσE
1ε v
isorrzzθθθθ εσσσE
1ε v
isoθθrrzzzz εσσσE
1ε v
where: eiso = isotropic swelling strain,
err, eqq, ezz = components of stress and strain in cylindrical coordinates, and
E = modulus of elasticity of the soil
PIER HEAVE PREDICTIONAPEX Method
Interface Conditions
soil boundary conditions
) U-k(HF tpt
pier-soil boundary conditions
where:
Ft = the nodal force tangent to pier,
Hp = the pier heave,
Ut = the nodal displacement tangent to pier, and
k = the parameter used to adjust shear stress
PIER HEAVE PREDICTIONAPEX Method
Adjustment in pier heave
initial-no force on pier
soil heave-upward force on pier
soil heave-upward force on pier
PIER HEAVE PREDICTIONAPEX Method
Soil failure and shear strain
Strength envelopes for slip and soil failure modes
PIER HEAVE PREDICTIONAPEX Method
APEX Input0 50 100 150 200 250
0
5
10
15
20
25
30
Cumulative Free-Field Heave (mm)
De
pth
(m
)
Clay FillW.Claystone
Claystone
D.G.C.S
E = modulus of elasticity
a = coeff. of adhesion
ρi = cumulative free-field heave
ZAD = design active zone
d = diameter of pier
Pdl = dead load
PIER HEAVE PREDICTIONAPEX Method
0
2
4
6
8
10
-50 -25 0 25 50 75 100
De
pth
(m)
Slip (mm)(b)
Variation of Slip Along Pier
Typical APEX results
0
2
4
6
8
10
-75 -50 -25 0 25 50 75 100
De
pth
(m)
Shear Stress (kPa)(c)
Anchorage Zone
UpliftZone
Shear Stress Distribution Along Pier
PIER HEAVE PREDICTIONAPEX Method
Typical APEX results
0
2
4
6
8
10
0 50 100 150 200 250
De
pth
(m)
Axial Tensil Force (kN)(d)
Axial Tensile Force (KN)
(d)Axial Force Distribution
VALIDATION OF APEX
Case I Manufacturing Building in Colorado, USA
Case II Colorado State University (CSU) Expansive Soil Test Site
VALIDATION OF APEX
Soil heave distribution for Cases I and II
Case I Manufacturing Building
Case II CSU Expansive Soil Test Site
VALIDATION OF APEX
Elevation survey data in hyperbolic form compared with heave computed by APEX for Manufacturing Building
Measured versus predicted axial force in the concrete pier for the CSU Test Site
VALIDATION OF APEX
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50
ρp/ρ
o
L/ZAD
80
L/d = 20
ZAD
α = 0.4
PIER DESIGN CURVES
Pier heave - linear free-field heave distribution
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50
ρp/ρ
o
L/ZAD
80
L/d = 20
ZAD
α = 0.4
PIER DESIGN CURVES
0.00
0.05
0.10
0.15
0.20
0.25
0.30
1.00 1.50 2.00 2.50 3.00 3.50
ρp/ρ
o
L/ZAD
80
L/d = 20
8080
2020
α = 0.4
ZAD
Pier heave - linear free-field heave distribution
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25
ρp/ρ
o
L/ZAD
L/d = 80
L/d = 20
EA = 50
200100
ZAD
PIER DESIGN CURVES
Pier heave - nonlinear free-field heave distribution
EXAMPLE FOUNDATION DESIGN
Weathered Claystone
Claystone
Sandy Claystone
0 m
5 m
10 m
ZAD = 10 m
D = 300mm
Free-field heave = 192 mm
Tolerable pier heave = 25 mm
a = 0.4
w = 12 %
g = 1.9 Mg/m3gEs = 9,400 kPagS% = 2.0 %gs’cs = 350 kPa
w = 9 %
g = 1.8 Mg/m3
Es = 11,200 kPa
S% = 3.5 %
s’cs = 550 kPa
w = 8 %
g = 1.8 Mg/m3
Es = 120,000 kPa
S% = 1.86 %
s’cs = 305 kPa
EXAMPLE FOUNDATION DESIGN
Cumulative heave profile for example calculation
0
1
2
3
4
5
6
7
8
9
10
11
0 50 100 150 200 250
Dep
th (m
)Cumulative Heave (mm)
Weathered Claystone
Claystone
Sandy Claystone
EXAMPLE FOUNDATION DESIGN
Example pier heave computed from APEX program
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
4 6 8 10 12 14 16 18 20
ρp/ρ
o
Pier Length (m)
(ρp/ρo)allowable = 0.13
Unsleeved Pier
LReq'd = 11.4 m
Sleeved Pier
LReq'd = 15.3 m
EXAMPLE FOUNDATION DESIGN
0 m
5 m
10 m
15 m
20 m
25 m
Weathered Claystone
Claystone
Sandy Claystone
L = 15.3 m
APEX(Uncased)
L = 18.0 m
Elastic Pier0 m
5 m
10 m
15 m
20 m
25 m
Rigid Pier
L = 18.7 m
Tolerable pier heave = 25 mm
L = 11.4 m
APEX (Cased)
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CONCLUSIONS
The rigid pier method assumes equilibrium of the pier, and hence, no pier movement, providing an overly conservative design.
The elastic pier method allows for some tolerable amount of pier heave. However, it is limited to use in simplified soil profiles and uniform piers.
The APEX program is a versatile and robust method of analysis.
APEX allows for pier analysis within complex soil profiles where soil properties and/or water contents vary with depth.
APEX generally predicts lower pier heave values, and shorter design lengths than other methods.
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QUESTIONS?
Engineering Analytics, Inc.
1600 Specht Point Rd., Ste. 209
Fort Collins, Colorado 80525 USA
Phone: 970-488-3111 Fax: 970-488-3112www.enganalytics.com
Email: jnelson@enganalytics.com
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