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
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August 2012
DAMAGE FROM EXPANSIVE SOILS
Photo of Shear Failure in South Side of Pier at N7
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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FREE-FIELD HEAVE PREDICTION
ρ  ε v  Δz i  %S  Δz i
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FREE-FIELD HEAVE PREDICTION
by Oedometer Method
Terminology and notation for oedometer tests
FREE-FIELD HEAVE PREDICTION
Determination of Heave Index, CH
Vertical stress states in soil profile
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FREE-FIELD HEAVE PREDICTION
Stress Paths Under Different Loading Conditions
S%
S
E
D
K
A
s’CS
LOG s’
s’CV
CH C
S
0
C
L
Cc
B
M
J
s’i ho
s’i1
s’i2
H
hC1
0’
G
P
F
N
LOG h
FREE-FIELD HEAVE PREDICTION
Determination of Heave Index, CH
S%
S
E
D
CH
M
CS
0
C
L
Cc
J
K
s 'i
s 'i1
B
s 'C V
LO G
'
H
h C1
'
G
P
s 'i2
A
s 'C S
ho
F
N
LO G
h
FREE-FIELD HEAVE PREDICTION
Calculations of Design Heave
B
C
S%
PER C EN T SW ELL
S%
C O N S O L ID A T IO N -S W E L L
TEST DATA
(S%)z
0
A
σ‘vo
H
S

log σ
%
'
'
 log σ
cv
i
 σ' 


S
 C log  cv 
%
H
 σ' 
 i 
CH
D
C
CONSTANT
VO LUM E
TEST DATA
s 'i
A P P L IE D S T R E S S ,
s 'C V
s ' (L O G
SCALE)
s C' S
FREE-FIELD HEAVE PREDICTION
Determination of Heave Index, CH
ρ  ε v  Δz i  S %  Δz i
CH 
S%
log σ' cv  log σ' i

S%
 σ' cv 
log 

σ'
 i 
 σ' cv 
(ε v ) z  ( S % ) z  C H log 

 σ' vo  z 
ρ oi  C H
 σ' cv 
 Δz i log 



σ'
 vo z 
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FREE-FIELD HEAVE PREDICTION
Determination of Heave Index, CH
Data from Method A of the ASTM D4546-08 Standard
12
V e rtic a l s tra in ,%
C o lla p s e (-)
S w e ll (+ )
10
8
6
4
2
0
-2
-4
-6
-8
0
100
200
300
400
500
V e rtic a l S tre s s , kP a (1 kP a = 2 0 .9
600
lb
ft
)
2
700
FREE-FIELD HEAVE PREDICTION
Determination of Heave Index, CH
Method A data from the Standard plotted in semi-log form
FREE-FIELD HEAVE PREDICTION
Determination of Heave Index, CH
Method A data from the Standard plotted in semi-log form
FREE-FIELD HEAVE PREDICTION
Relationship between s′cv and s′cs
Logarithmic Form:
log σ' cv  log σ' i  λ(logσ'
cs
 log σ' i )

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
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FREE-FIELD HEAVE PREDICTION
Relationship between s′cv and s′cs
Histograms of the λ values determined using the logarithmic form
12
10
Claystone (STD Deviation = 0.14)
All Soil Types (STD Deviation = 0.17)
Frequency
8
6
4
2
0
0 - 0.05 0.05 0.15
0.15 0.25
0.25 0.35
0.35 - 0.45 0.45
0.55
Lambda Value
0.55 0.65
0.65 0.75
0.75 0.85
0.85 0.95
PIER HEAVE PREDICTION
Typical pier and
grade beam
foundation system
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DAMAGE FROM EXPANSIVE SOILS
Diagonal Crack
Pier
PIER HEAVE PREDICTION
Rigid Pier Analysis
Rigid Pier Analysis
Pdl
U  D  Pdl  0
L  Z AD

P dl 
1 

α
σ
Z

1 cv
AD
f s 
πd 
Pmax  Pdl  f u Z AD πd
U
D
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PIER HEAVE PREDICTION
Elastic Pier Analysis
Normalized Pier Heave vs. L/ZAD
Straight Shaft
Ref: Poulos & Davis (1980)
Nelson & Miller (1992)
Nelson, Chao & Overton (2007)
Belled Pier
PIER HEAVE PREDICTION
Elastic Pier Analysis
Normalized Force vs. L/ZAD
Straight Shaft
Ref: Poulos & Davis (1980)
Nelson & Miller (1992)
Nelson, Chao & Overton (2007)
Belled Pier
PIER HEAVE PREDICTION
APEX Method
Analysis of Piers in EXpansive soils
PIER HEAVE PREDICTION
APEX Method
The field equations with soil swelling
ε rr 
ε θθ 
ε zz 
1
E
1
E
1
E
σ rr
 v σ θθ  σ zz
  ε iso
σ θθ
 v σ zz  σ rr
  ε iso
σ zz
 v σ rr  σ θθ
  ε iso
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 PREDICTION
APEX Method
Interface Conditions
Ft  k(H
p
-U t)
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
soil boundary
conditions
pier-soil boundary
conditions
PIER HEAVE PREDICTION
APEX Method
Adjustment in pier heave
initial-no force
on pier
soil heave-upward
force on pier
soil heave-upward
force on pier
PIER HEAVE PREDICTION
APEX Method
Soil failure and shear strain
Strength envelopes for slip and soil failure modes
PIER HEAVE PREDICTION
APEX Method
APEX Input

E = modulus of elasticity

a = coeff. of adhesion
0
ZAD = design active zone

d = diameter of pier

Pdl = dead load
200
300
Clay Fill
W.Claystone
5
ρi = cumulative free-field
heave

100
Claystone
10
Depth (m)

Cumulative Free-Field Heave (mm)
0
15
D.G.C.S
20
25
30
PIER HEAVE PREDICTION
APEX Method
0
0
2
2
Depth (m)
Depth (m)
Typical APEX results
4
6
Uplift
Zone
4
6
Anchorage
Zone
8
8
10
10
-50
-25
0
25
Slip (mm)
(b)
50
Variation of Slip
Along Pier
75
100
-75
-50
-25
0
25
50
Shear Stress (kPa)
(c)
75
Shear Stress Distribution
Along Pier
100
PIER HEAVE PREDICTION
APEX Method
Typical APEX results
0
Depth (m)
2
4
6
8
10
0
50
100
150
200
Axial
TensileForce
Force(kN)
(KN)
Axial Tensil
(d)
(d)
250
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
VALIDATION OF APEX
Measured versus predicted
axial force in the concrete
pier for the CSU Test Site
PIER DESIGN CURVES
Pier heave - linear free-field heave distribution
1.0
0.9
0.8
0.7
ρp/ρo
0.6
0.5
ZAD
0.4
0.3
0.2
L/d = 20
0.1
α = 0.4
0.0
0.00
0.50
80
1.00
1.50
2.00
L/ZAD
2.50
3.00
3.50
PIER DESIGN CURVES
Pier heave - linear free-field heave distribution
1.0
0.30
0.9
0.25
0.8
0.7
0.20
0.6
ρpρ/ρ
o o
p/ρ
ZAD
0.5
0.15
ZAD
0.4
0.10
0.3
0.2
0.05
0.1
0.4
αα==0.4
0.00
0.0
0.00
1.00
0.501.501.00
1.50
2.00
L/d = 20
20
20
80
L/d80
= 20
80
80
2.00
3.00
3.50
2.50 2.50 3.00
3.50
L/Z
L/ZAD
AD
PIER DESIGN CURVES
Pier heave - nonlinear free-field heave distribution
1.0
0.9
0.8
0.7
ρp/ρo
0.6
ZAD
0.5
0.4
0.3
0.2
EA = 50
100
200
L/d = 20
0.1
L/d = 80
0.0
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25
L/ZAD
EXAMPLE FOUNDATION DESIGN
D = 300mm
0m
5m
10 m
Weathered Claystone
w = 12 %
g = 1.9 Mg/m3
gEs = 9,400 kPa
gS% = 2.0 %
gs’cs = 350 kPa
Claystone
w=9%
g = 1.8 Mg/m3
Es = 11,200 kPa
S% = 3.5 %
s’cs = 550 kPa
Sandy Claystone
w=8%
g = 1.8 Mg/m3
Es = 120,000 kPa
S% = 1.86 %
s’cs = 305 kPa
Free-field heave = 192 mm
Tolerable pier heave = 25
mm
a = 0.4
ZAD = 10 m
EXAMPLE FOUNDATION DESIGN
Cumulative heave profile for example calculation
Cumulative Heave (mm)
0
0
1
50
100
150
200
250
Weathered
Claystone
2
3
Depth (m)
4
5
Claystone
6
7
8
9
10
11
Sandy
Claystone
EXAMPLE FOUNDATION DESIGN
Example pier heave computed from APEX program
0.7
0.6
0.5
Sleeved Pier
ρp/ρo
0.4
Unsleeved Pier
0.3
0.2
(ρp/ρo)allowable = 0.13
0.1
LReq'd = 15.3 m
LReq'd = 11.4 m
0.0
4
6
8
10
12
14
Pier Length (m)
16
18
20
EXAMPLE FOUNDATION DESIGN
Rigid Pier
Elastic Pier
0m
APEX
(Uncased)
APEX (Cased)
0m
Weathered
Claystone
5m
5m
Claystone
10 m
10 m
Sandy
Claystone
L = 11.4 m
15 m
15 m
L = 15.3 m
20 m
L = 18.7 m
L = 18.0 m
20 m
Tolerable pier heave = 25 mm
25 m
25 m
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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