Calculation of Heave of Deep Pier Foundations

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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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i
i
v
Δz
%S
Δz
ε
ρ




FREE
-
FIELD HEAVE PREDICTION

FREE
-
FIELD HEAVE PREDICTION

by
O
edometer Method

Terminology and notation for
oedometer

tests

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FREE
-
FIELD HEAVE PREDICTION

Determination of Heave Index, C
H

Vertical stress states in soil profile

FREE
-
FIELD HEAVE PREDICTION

Stress Paths Under Different Loading Conditions

C

S

S
%

A

C
c

LOG h

M

E

K

B

LOG
s


s

CS

s

CV

s

i2

s

i1

s

i

0’

0

J

H

P

N

F

G

L

h
o

h
C1

D

C
H

C
S

FREE
-
FIELD HEAVE PREDICTION


Determination of Heave Index, C
H

LOG
h
LOG

'
S
E
D
M
L
K
B
A
P
N
s
'
CS
s
'
CV
s
'
i2
s
'
i1
C
c
h
C1
C

'
s
'
i
H
F
J
G
C
H
C
S
h
o
S
%
0
0
D
C
A
B
C
H
CONSTANT
VOLUME
TEST DATA
s
'
i
s
'
s
'
CV
CS
APPLIED STRESS,
s
' (LOG SCALE)
CONSOLIDATION-SWELL
TEST DATA
S
S
%
%
PERCENT SWELL
FREE
-
FIELD HEAVE PREDICTION

Calculations of Design Heave

'
i
σ
log
'
cv
σ
log
%
S
H
C


σ‘
vo

(S
%
)
z












'
i
σ
'
cv
σ
log
H
C
%
S
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i
%
i
v
Δz
S
Δz
ε
ρ




FREE
-
FIELD HEAVE PREDICTION

Determination of Heave Index, C
H










i
cv
%
i
cv
%
H
σ'
σ'
log
S
σ'
log
σ'
log
S
C










z
vo
cv
H
z
%
z
v
σ'
σ'
log
C
)
S
(
)
(
ε










z
vo
cv
i
H
oi
σ'
σ'
log
Δz
C
ρ
FREE
-
FIELD HEAVE PREDICTION

Determination of Heave Index, C
H

Data from Method A of the ASTM D4546
-
08 Standard


-8
0
-6
-4
-2
0
2
4
6
8
10
12
100
200
300
400
500
600
700
Vertical strain,%
Swell (+)
Collapse (-)
Vertical Stress, kPa (1kPa=20.9
lb
ft
)
2
FREE
-
FIELD HEAVE PREDICTION

Determination of Heave Index, C
H

Method A data from the Standard plotted in
semi
-
log
form

FREE
-
FIELD HEAVE PREDICTION

Determination of Heave Index, C
H

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 PREDICTION

Relationship between
s

cv

and
s

cs

)
σ'
log
λ(logσ'
σ'
log
σ'

log
i
cs
i
cv



Logarithmic Form:

FREE
-
FIELD
HEAVE PREDICTION

Relationship 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
Frequency
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 PREDICTION

Rigid
Pier Analysis

Rigid Pier Analysis











πd
P
Z
σ
α
f
1
Z
L
dl
AD
cv
1
s
AD
πd
Z
f
P
P
AD
u
dl
max


dl
U D P 0
  
P
dl

U

D

PIER HEAVE
PREDICTION

Elastic
Pier Analysis

Normalized Pier
H
eave
vs.
L/Z
AD



Ref: Poulos & Davis (1980)

Nelson & Miller (1992)

Nelson, Chao & Overton (2007)


Straight Shaft

Belled Pier

PIER HEAVE
PREDICTION

Elastic Pier Analysis

Straight Shaft

Belled Pier

Normalized Force vs
.
L/Z
AD



Ref: Poulos & Davis (1980)

Nelson & Miller (1992)

Nelson, Chao & Overton (2007)


PIER HEAVE
PREDICTION

APEX Method

A
nalysis
of
P
iers in
EX
pansive

soils

PIER HEAVE
PREDICTION

APEX Method

The field equations with soil swelling





iso
zz
θθ
rr
rr
ε
σ
σ
σ
E
1
ε




v




iso
rr
zz
θθ
θθ
ε
σ
σ
σ
E
1
ε




v




iso
θθ
rr
zz
zz
ε
σ
σ
σ
E
1
ε




v
where:
e
iso

= isotropic
swelling strain,

e
rr
,
e
qq
,
e
zz

= components of stress and strain in
cylindrical coordinates, and

E = modulus
of elasticity of the soil







PIER HEAVE
PREDICTION

APEX Method

Interface Conditions

soil boundary
conditions

)
U
-
k(H
F
t
p
t

pier
-
soil
boundary
conditions

where:

F
t

= the nodal force
tangent to
pier,

H
p

= the pier
heave,

U
t

= the nodal
displacement tangent
to
pier,
and

k
= the parameter used to
adjust shear stress

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

0
5
10
15
20
25
30
0
100
200
300
Depth
(m)

Cumulative
Free
-
Field
Heave (mm)

Clay Fill

W.Claystone


Claystone




D.G.C.S


E = modulus of elasticity


a

=
coeff
. of adhesion


ρ
i

= cumulative free
-
field
heave


Z
AD

= design active zone


d = diameter of pier


P
dl

= dead load


PIER HEAVE
PREDICTION

APEX Method

0
2
4
6
8
10
-
50
-
25
0
25
50
75
100
Depth (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
Depth (m)
Shear Stress (kPa)
(c)
Anchorage
Zone
Uplift
Zone
Shear Stress Distribution
Along Pier

PIER HEAVE
PREDICTION

APEX Method

Typical APEX results

0
2
4
6
8
10
0
50
100
150
200
250
Depth (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
ρ
p
/
ρ
o
L/Z
AD
80
L/d
= 20
Z
AD
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
ρ
p
/
ρ
o
L/Z
AD
80
L/d
= 20
Z
AD
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
ρ
p
/
ρ
o
L/Z
AD
80
L/d
= 20
80
80
20
20
α
= 0.4
Z
AD
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
ρ
p
/
ρ
o
L/Z
AD
L/d = 80
L/d
= 20
E
A
= 50
200
100
Z
AD
PIER DESIGN CURVES

Pier heave
-

nonlinear free
-
field heave distribution

EXAMPLE FOUNDATION DESIGN

Weathered
Claystone

Claystone

Sandy
Claystone

0 m

5 m

10 m

Z
AD

= 10 m

D = 300mm

Free
-
field heave = 192 mm

T
olerable pier heave = 25
mm

a

㴠=⸴.



w = 12 %

g
= 1.9 Mg/m3

g
E
s

= 9,400
kPa

g
S
%

= 2.0 %

g
s

cs

= 350
kPa

w = 9 %

g
= 1.8 Mg/m3

E
s

= 11,200
kPa

S
%

= 3.5 %

s

cs

= 550
kPa

w = 8 %

g
= 1.8 Mg/m3

E
s

= 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
Depth (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
ρ
p
/
ρ
o
Pier Length (m)
(
ρ
p
/
ρ
o
)
allowable
= 0.13
Unsleeved
Pier
L
Req'd
= 11.4 m
Sleeved
Pier
L
Req'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 Pier

0 m

5 m

10 m

15 m

20 m

25 m

Rigid Pier

L = 18.7 m


T
olerable 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?





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oint

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