Passive Force-Deflection Behavior

for Skewed Abutments

Kyle Rollins, Aaron Marsh, Bryan Franke,

Katie Palmer and Jaycee Smith

Civil & Environmental Engineering

Brigham Young University

FHWA Pooled Fund Sponsors

Utah DOT – Lead Agency

Oregon DOT

Montana DOT

California DOT

New York DOT

Minnesota DOT

FHWA

Background

Passive Pressure for non-skewed abutments (Maroney (1995),

Duncan and Mokwa (2001), Rollins and Sparks (2002), Rollins and

Cole (2006), Lemnitzer et al (2009)

Passive force best estimated using log-spiral method

Peak passive force mobilized at displacement of 0.03H to 0.05H

Hyperbolic curve best represents passive force-displacement curve

PP

Background

Unclear: Effect of skew on passive force

PP

Skewed Bridge Abutment Overview

≈ 40% of 600,000 bridges in US are skewed

Current AASHTO design code does not

consider any effect of skew on passive force

Observations of poor performance of skewed

bridges

Shamsabadi et al. 2006

Damage to Skewed Integral Abutments

(Steinberg & Sargand, 2010)

Earthquake Damage to Skewed Bridges

(Paine, Chile)

Top Bridge

Skewed Abutment

Bottom Bridge

Top Bridge

Bridge decks have rotated and

bridge was demolished

Bottom Bridge

Bridge deck was offset and was

eventually demolished

Top Bridge

Bridge remained in service after

the earthquake

Damage rate for skewed bridges was twice that of

non-skewed bridges (Toro et al 2013)

Passive Force From Inertia

Passive force contributes to resistance

Using smaller passive force (lower Kp)

may be conservative

Passive Force from Lateral Spreading

Passive force often drives displacement

Selection of smaller passive force (lower Kp)

may be unconservative

Liquefaction

Driving Force on Skewed Abutments

Interaction of Forces on Bridge Abutment

Deck Length, L

Skew Angle, θ

PL

PL

Numerical Analysis of Skewed Abutments

(5th NSC, Shamsabadi et al., 2006)

23 m (75 ft) wide abutment with 2.4 m (8 ft) high backwall

Results of Numerical Analysis

(5th NSC, Shamsabadi et al., 2006)

Objectives

1. Determine static passive force-displacement curves for

skewed abutments from large-scale tests

2. Provide comparisons of behavior of skewed abutments

with that of normal abutments.

3. Evaluate the effect of wingwalls on skewed abutment

response.

4. Develop design procedures for calculating passive

force-displacement curves and shear-displacement or

skewed abutments.

“One good test is worth a

thousand expert opinions.”

Werner Von Braun

Designer of Saturn V Moon Rocket

Healthy Skepticism for Tests

A theory is something nobody believes,

except the person who proposed it.

An experiment (test) is something

everybody believes,

--Albert Einstein

performed it

except the person who

Initial Laboratory Testing

Test Layout

No Skew

Plan view:

Elevation view:

1.22 m (4 ft)

0.6 m (2 ft)

Test Procedure

Plan view:

Elevation view:

Test Procedure

Plan view:

Elevation view:

Test “Abutment”

15°

Test “Abutment”

30°

Test “Abutment”

45°

Displacement: 60 mm 2.5” (0.10H) Load measurements:

• Longitudinal

• Vertical

• Transverse

Rollers Below Base of “Abutment”

Surface Failure Rupture - 30º Skew

30º

Backfill Soil Properties

Gradation and Strength

Property Value Classification SP or A-1-b

Cu 3.7

Cc 0.7

Rc 98%

γ 17.8 kN/m3

ϕ 46º

33.2º

Passive Force-Displacement Curves

Reduction Factor for Skew Effects

Rskew= PP(skew)/Pp (No-skew)

where Rskew is a function of skew angle, and wall width is

equal to non-skewed (projected) width.

Rskew= 8x10-5θ2 – 0.018 θ + 1.0

(ASCE, J. of Bridge Engrg., Rollins and Jessee 2013)

Normalized Passive Force vs Skew, θ

(ASCE, J. of Bridge Engrg., Rollins and Jessee 2013)

Passive Force-Displacement Curves

Large Scale Field Testing

Field Test Setup - Plan View

12.75 inch Dia.

Steel Pipe Piles

11 ft wide x 5.5 ft high

Pile Cap

24 ft

22 ft

Transverse Wingwalls

2 x 4 ft Reinforced

Concrete blocks

4 ft Dia.

Bored Pile

Sheet Pile Wall Section

AZ-18

2 – 600 kip Actuators

Field Test Setup Elevation View

11 ft m wide x 5.5 ft high x 15 ft long

Pile Cap

6 ft

6.4m

4 ft Dia.

Bored Pile

Sheet Pile Wall

Section AZ-18

2 – 600 kip Actuators 12.75 inch Dia.

Steel Pipe Piles

Sand backfill properties

Poorly graded sand (SP/A-1-b) that generally falls

within ASTM C33 washed concrete sand gradation

requirements

96% relative compaction

ϕ = 41°

c = 4.6 kPa (100 lbs/ft2)

γmax = 17.5 kN/m3 (111.5lbs/ft3)

No Skew - 0° Test Setup

15° Skew Test Setup

30° Skew Test Setup

Rollers under the base of 45º wedge

45° Skew Test Setup

45° Skew Test Setup

Test completed at 3.21 in

(81.6 mm) of displacement

Test completed at 3.43 in

(87.2 mm) of displacement

Heave Geometry at Test Completion

0º Skew 45º Skew

Field Test Methodology

0 2 4 6 8

0

1,000

2,000

3,000

4,000

5,000

0

200

400

600

800

1,000

1,200

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50

Pile Cap Deflection [cm]

Longit

udin

al F

orc

e [k

N]

Longit

udin

al F

orc

e [k

ips]

Pile Cap Deflection [in]

Total Load

Baseline Resistance

Lateral Backfill

Resistance

Passive Force vs. Displacement

0 2 4 6 8 10

0

500

1,000

1,500

2,000

2,500

0

100

200

300

400

500

600

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Pile Cap Deflection [cm]

Pas

siv

e F

orc

e [k

N]

Pas

siv

e F

orc

e [k

ips]

Pile Cap Deflection [in]

0° Skew

15° Skew

30° Skew

45° Skew0.0

2H

0.0

3H

0.0

4H

0.0

5H

Passive Force Reduction Factor vs. Skew

Rskew = 8x10-05θ2 - 0.018θ + 1

R² = 0.98

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 15 30 45 60 75 90

Red

uct

ion

Fa

cto

r, R

skew

Skew Angle, [degrees]

Lab Tests

Numerical Analysis

Field Tests (This Study)

Proposed Reduction Line

Failure Geometry for Zero-Skew Test

0 1 2 3 4 5 6

-0.30

0.20

0.70

1.20

1.70

-1.0

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0 5 10 15 20

Distance from Cap Face on Line Parallel to Direction of Push [m]

Ele

vat

ion B

elow

Top o

f C

ap [

m]

Ele

vat

ion B

elow

Top o

f C

ap [

ft]

Distance from Cap Face on Line Parallel to Direction of Push [ft]

Upper Shear Plane

Lower Shear Plane

Heave

𝜙𝑚𝑒𝑎𝑠 = 41°

𝛼 = 45 − 𝜙′/2

𝜙 ≈ 40°

α

Comparison of Failure Geometries

Rankine Failure

Geometry

Log-Spiral Failure

Geometry

Ep

Interface Forces with Respect to Skew

Shear force vs. transverse displacement

0

20

40

60

80

100

120

140

160

180

200

-0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0

Ap

plie

d S

hear

Fo

rce [

kip

]

Transverse Displacement [in]

30° skew

15° skew

45º skew

Test Setup for MSE Wingwall Tests

15°

Skew 30°

Skew

Welded Wire Grid Reinforcement (SSL)

No Skew - 0° Test Setup

15º Skew Test with MSE Wingwalls

Field Test with 30º Skew & MSE Walls

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0 5.0 10.0 15.0 20.0 25.0

MS

E W

ingw

all

Dis

pla

cem

ent

(in)

Distance From Pile Cap (ft)

0.24 0.83

1.72 2.73

3.18

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0 5.0 10.0 15.0 20.0 25.0

MS

E W

ingw

all

Dis

pla

cem

ent

(in)

Distance From Pile Cap (ft)

0.24 0.83

1.72 2.73

3.180º

Ske

w

3.3

5 m

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0 5.0 10.0 15.0 20.0 25.0

MS

E W

ingw

all

Dis

pla

cem

ent

(in)

Distance From Pile Cap (ft)

0.24 1.23

2.22 2.71

3.48

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0 5.0 10.0 15.0 20.0 25.0

MS

E W

ingw

all

Dis

pla

cem

ent

(in)

Distance From Pile Cap (ft)

0.24 1.23

2.22 2.71

3.48

15

º S

kew

3.3

5 m

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0 5.0 10.0 15.0 20.0 25.0

MS

E W

ingw

all

Dis

pla

cem

ent

(in)

Distance from Pile Cap (ft)

0.26 0.82

1.73 2.25

2.73 3.48

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0 5.0 10.0 15.0 20.0 25.0

MS

E W

ingw

all

Dis

pla

cem

ent

(in)

Distance from Pile Cap (ft)

0.26 1.28

2.25 2.73

3.48

30º

Skew

3.3

5 m

45º

Skew

0

0.5

1

1.5

2

Def

lect

ion

(in

) .75"

1.5"

2.25"

3.0"

3.5"

0

0.5

1

1.5

2

Def

lect

ion

(in

) .75"

1.5"

2.25"

3.0"

3.5"

11 ft

Passive Force-Displacement curves

0.0

1H

0.0

2H

0.0

3H

0.0

4H

0.0

5H

0.0 2.0 4.0 6.0 8.0 10.0

0

500

1,000

1,500

2,000

2,500

3,000

0

100

200

300

400

500

600

700

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Pile Cap Displacement, Δ [cm]

Pass

ive

Forc

e [k

N]

Pa

ssiv

e F

orc

e [k

ips]

Backwall Displacement, Δ [in]

0 Degree Skew

30 Degree Skew

15 Degree Skew

45 Degree Skew

Passive Force Reduction Factor vs. Skew

Rskew = 8x10-05θ2 - 0.018θ + 1

R² = 0.98

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 15 30 45 60 75 90

Red

uct

ion

Fa

cto

r, R

skew

Skew Angle, [degrees]

Lab Tests

Numerical Analysis

Field Tests (This Study)

Proposed Reduction Line

Geometry Effects?

Field and Lab tests involved W/H ratios of 2.0

Does this ratio impact the results?

Laboratory Wall

2 ft

4 ft

Field Wall

5.5 ft

11 ft

Field Test with 3 ft Backfill - W/H=3.7

11 ft wide x 5.5 ft high x 15 ft long

Pile Cap

3 ft

4 ft Dia. Reinforced

Concrete Shaft

12 in Dia.

Steel Pipe Piles

2- 600 kip Actuators

Passive Force-Displacement Curves

0

20

40

60

80

100

120

140

160

180

200

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

Pa

ssiv

e F

orc

e [k

ips]

Pile Cap Displacement [in]

0 Degree Skew

15 Degree Skew

30 Degree Skew

45 Degree Skew

0.01H

0.02H

0.03H

0.04H

0.05H

0.06H

0.07H

0.08H

0.09H

Passive Force Reduction Factor vs. Skew

Rskew = 8x10-05θ2 - 0.018θ + 1

R² = 0.98

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 15 30 45 60 75 90

Red

uct

ion

Fa

cto

r, R

skew

Skew Angle, [degrees]

Lab Tests

Numerical Analysis

Field Tests (This Study)

Proposed Reduction Line

Tests with Gravel Backfil

0 2.5 5 7.5 10

0

200

400

600

800

1000

1200

1400

1600

0

50

100

150

200

250

300

350

400

0 0.5 1 1.5 2 2.5 3 3.5 4

Horizontal Deflection [cm]

Pass

ive

Forc

e [k

N]

Pass

ive

Forc

e [k

ip]

Horizontal Deflection [in]

0 degree Skew

30 Degree Skew

45º Skew with

RC Wingwalls

45º Skew with RC Wingwalls

0º Skew with RC Wingwalls

Passive Force Reduction Factor vs. Skew

Rskew = 8x10-05θ2 - 0.018θ + 1

R² = 0.98

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 15 30 45 60 75 90

Red

uct

ion

Fa

cto

r, R

skew

Skew Angle, [degrees]

Lab Tests

Numerical Analysis

Field Tests (This Study)

Proposed Reduction Line

Summary of Results Significant decrease in passive force with increase in

skew angle.

• Numerical Analysis

• 8 Small Scale Lab Tests

• 16 Large Scale Field tests

Reduction factor proposed by Rollins and Jessee (2013)

is generally applicable for both perpendicular and

parallel (MSE) wingwall cases

Reduction factor not much affected by wall L/H ratio

Passive force typically mobilized at Δ/H ≈ 0.03 or 3%

Shear resistance mobilized in 0.2 to 0.3 inches of

transverse movement

AASHTO Design Method

73

• Bi-linear relationship

• Failure occurs at

0.01-0.05H

• Peak passive force

obtained using log

spiral method Pas

sive

Forc

e

0.01H-0.05H

PP

Log Spiral Passive Force

γ = moist unit weight

ϕ = Soil friction angle

= wall friction angle

=backfill slope angle

H= height of back wall

Kp=passive pressure

coefficient

Pp = 0.5H2 Kp

Recommended Design Procedure

for Skew Effects

PP(skew) = Rskew Pp (No-skew)

where Rskew is a given by the equation

Rskew= 8x10-5θ – 0.018 θ + 1.0

and wall width is equal to non-skewed (projected) width.

(ASCE, J. of Bridge Engrg., Rollins and Jessee 2013)

Adjustment for width & Skew

PpH = 28.5 k/ft

50 ft

= 30º

For 0º skew condition

PpH = (28.5 k/ft) (50ft) = 1425 k

Compute skew reduction factor

Rskew= 8x10-5(30)2 – 0.018 (30) + 1.0

= 0.53

For 30º skew condition

PpH = (1425 k)(0.53) = 755 k

PpH

Passive Force-Displacement

50 ft

= 30º

PpH

PpH

Displacement (in)

For a 6 ft high backwall:

Peak at 0.03H = 0.03(6 ft)(12in/ft)

= 2.2 in

2.2 in

755 k

= 755k

Shear Force-Displacement

50 ft

= 30º For a δ=28º = 0.70

T = cA + PpHtan

= 0 + (755 k) tan(28º) = 401k

PpH=755k

T

Displacement (in)

Peak at 0.25 in

0.25 in

401k

T = 401k

Bi-linear Passive Force vs. Displacement

0 2 4 6 8 10

0

500

1,000

1,500

2,000

2,500

0

100

200

300

400

500

600

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Pile Cap Deflection [cm]

Pas

siv

e F

orc

e [k

N]

Pas

siv

e F

orc

e [k

ips]

Pile Cap Deflection [in]

0° Skew

15° Skew

30° Skew

45° Skew0.0

2H

0.0

3H

0.0

4H

0.0

5H

Hyperbolic Passive Force vs. Displacement

0 2 4 6 8 10

0

500

1,000

1,500

2,000

2,500

0

100

200

300

400

500

600

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Pile Cap Deflection [cm]

Pas

siv

e F

orc

e [k

N]

Pas

siv

e F

orc

e [k

ips]

Pile Cap Deflection [in]

0° Skew

15° Skew

30° Skew

45° Skew0.0

2H

0.0

3H

0.0

4H

0.0

5H

Questions?

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