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

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

www.enganalytics.com

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


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


iiv Δz%SΔzερ

FREE-FIELD HEAVE PREDICTION

FREE-FIELD HEAVE PREDICTIONby Oedometer Method

Terminology and notation for oedometer tests


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


i%iv ΔzSΔzερ


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


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


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


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


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)


PIER HEAVE PREDICTION

Typical pier and grade beam

foundation system

DAMAGE FROM EXPANSIVE SOILS

Pier

Diagonal Crack


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


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


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


Adjustment in pier heave

initial-no force on pier

soil heave-upward force on pier

soil heave-upward force on pier


Soil failure and shear strain

Strength envelopes for slip and soil failure modes


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


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


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


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 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


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)


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.


QUESTIONS?

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Documents

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