Seismic Vulnerability Study of the Alaskan Way Viaduct:

Typical Three-Span Units

Marc Eberhard

(J. De la Colina, S. Ryter, P. Knaebel)

Lacey, Washington

Outline

• Scope of Study• Description of Typical WSDOT-Designed Unit• Analyses of WSDOT Unit

– 3D Response Spectrum– 2D Nonlinear Static

• Vulnerability Assessments of WSDOT Unit– Flexure– Shear– Anchorage– Splices– Joints– Footings

• Comparison of SED and WSDOT Typical Units

Scope of Structural Evaluation

• WSDOT and SED Typical Three-Span Sections

• Ground Motions– ATC-6 spectrum, Type III

soil with Ag = 0.25g– Site-specific spectra for

20-ft fill/20-ft tidal deposit

• Analyses– 3D Response Spectrum

Analysis– Nonlinear 2D Static

Analysis

• ATC-6-2 and Priestley Procedures for:– Flexure– Shear– Anchorage– Splices– Joints– Pile-Supported Footings

• As-Designed Unit (no deterioration or construction errors)

• Retrofit Priorities

Outside Scope

• Failure Modes– Torsion– Effect of anchorage

deficiencies on beam/slab shear capacity

– Effect of splice failure on shear resistance

– Piles– Fracture at welded lap splices– Behavior of square bars

• Procedures Developed Since 1994

• Specific Retrofit Recommendations

• Atypical Sections– North-end and South-end

single-deck structures (Bents 1-53)

– Double-deck to single-deck transition structures (e.g., outrigger bents)

– Ramps– Curve

• Interactions among three-span frames

• Variations in Properties – Material properties– Reinforcement

WSDOT Unit: Longitudinal Elevation

Interior Frame

Interior Frame

Exterior Frame

Exterior Frame

WSDOT Interior Bent: Transverse Elevation

Short Splices

No Top Reinforcement in Footings

Short Beam Bar Anchorage

Little Joint Confinement

Little Column Transverse Reinforcement

No. 3 @ 12 in.

WSDOT Interior Bent: Column Cross-Section

Analyses

• Assumed Material Properties• Description of Typical WSDOT-Designed Unit• Analyses of WSDOT Unit

– 3D Response Spectrum– 2D Nonlinear Static

• Vulnerability Assessments of WSDOT Unit:– Flexure– Shear– Anchorage– Splices– Joints– Footings

• Comparison of SED and WSDOT Typical Units

Model for Dynamic Analysis

WSDOT UNIT

Exterior Girders

Transverse Beams

Interior Stringers

Slab (Shell Elements)

Columns (Frame Elements)

0.0 0.5 1.0 1.5 2.0 2.5

Period, Seconds

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Spe

ctra

l Acc

eler

atio

n, g

20' Fill, 20' Tidal30' Fill, 30' Tidal40' Fill, 40' Tidal38' Fill, 26' TidalATC-6

Modal PeriodsFixed Base

T LPinned Base

T L

WSDOT-UNIT

Summary of Minimum Flexural C/D Ratios

Response Spectra

Direction Rec, First Story

Rec, Second Story

Rec,

Beams, Girders

ATC-6 Transverse 0.36 1.17 0.43

Longitudinal 0.31 0.92 0.75

Site-Specific Transverse 0.22 0.80 -

Longitudinal 0.22 0.59 -

Depending on site and direction, expect first-story column displacement ductility demands in the range of 2-4. Location of max. demands depends on column base-fixity. Low ductility demands in 2nd story, with exception of M+ in some beams.

WSDOT UNIT

WSDOT-INT FRAME

Two-Dimensional, Nonlinear Analysis

Total

One Exterior Frame

One Interior Frame

WSDOT-INT FRAME

Wunit = 4800 kips Vtrans/Wunit = 0.25

Force-Deflection Relationship

WSDOT-INT FRAME

Column Moments

Beam Bending Moment (first level)

WSDOT-INT FRAME

Curvature Ductility Demands at Vu (@Vmax/y, Fixed Base)

Interior Frame

3.9

0.7

0.7

0.5

0.7

1.0

1.010.0

5.6

0.2

0.8

1.0

WSDOT Unit

3.0

0.2

0.5

0.8

1.0

14.6

Exterior Frame

2.3

0.7

0.3

0.3

0.6

1.0

Unclear if first-story or beam mechanism controls. First-story controls for pinned base and for longitudinal frames.

Response Spectra

Direction C/D(Fixed)

C/D(Pinned)

ATC-6 Transverse 1.07 0.75

Longitudinal 1.43 0.97

Site-Specific Transverse 0.64 0.53

Longitudinal 0.89 0.70

cu=0.005 corresponds to low level of damage. Depending on site and base fixity, expect low to moderate level of flexural damage. Unlikely to lead to catastrophic collapse of unit.

WSDOT UNIT

Flexural Failure C/D Ratios

Shear Failure

Vi

Vf

i f

Initial

Final

Displacement Ductility

Case A

Case B

Case C

= 2 = 4

Shear Failure (Min. C/D Ratios)

Story Direction C/D(=2)

C/D(=4)

First Transverse 2.28 1.23

Longitudinal 2.64 1.34

Second Transverse 0.95 0.51

Longitudinal 1.39 0.70

First-story columns probably OK, but margin of safety is small at large ductility demands. Second story columns OK as long first story is not strengthened. Could check with updated shear-strength procedures

WSDOT UNIT

Anchorage

AsfyTuslfT sts 5.1

• Assume hooked bars are OK

• Follow Priestley (1992) recommendations (No method available to account for square bars in SED Unit).

• Bar development OK if splitting failure suppressed

• If not ……

ls

ls

ls

ls

5.0)^'(4 cfft

Ts/Tu

ls

ls

ls

ls

0.8-0.9

0.9-1.3

1.4

0.8-1.3

Bottom reinforcing bars of first-level beams have the most critical anchorage conditions. Consequences on vulnerability (e.g., shear resistance) unclear. Also need to look at development of top-story column bars through joint.

Lap Splices

ATC-6-2

(rcs)

Priestley

(Mb/My)

Priestley

(Mb/Mu)

First Story 0.02-0.04 1.2 1.0

Second Story

0.05-0.15 1.2 1.0

• Short (20-22 Db)

• Poorly confined

• Located at base of first- and second-story columns

Bottom splice critical, because even if Priestley procedure is correct, deformation demands will be large. Top splice probably OK. (Interaction with joint?)

Joints

• Priestley (1992) suggests limit on maximum tensile stress of 3.5(f’c)^.5 to prevent joint cracking. Others limit shear stress.

• Did not consider results of recent tests by Stanton and Lehman (2000)

• Calculate:

• with and without slab reinforcement

• at ultimate conditions and using forces from nonlinear analysis

• Neglect interaction with splice

• Assume only part of joint is effective

Joint Effective Areas Girder

Beam Column

Effective Joint Area

Interior Interior Exterior Beam

Girder

Column Exterior

Effective Joint Area

Depth

Girder

Beam

Column

Effective

Joint

Area

Interior

Exterior

Beam

Girder

ColumnInterior

Exterior

Effective

Joint

Area

Transverse

Longitudinal

Normalized Joint Stresses (Transverse)

Similar for interior and exterior WSDOT frames

2.7

8.32.7

6.5

Normalized vult

Normalized Joint Stresses (Longitudinal)

5.0 4.6 4.6 5.0

5.08.78.75.2

Normalized vult

1.2 2.3 2.5 2.6

5.57.97.74.6

Normalized vnonl

WSDOT Unit, including slab reinforcement

Joint shear cracking is expected in transverse direction (1st and 2nd level) and in longitudinal direction (1st level only). Cracking does not necessarily lead to collapse.

Footings

F1

F5

F4F3

F2

P

Mu• Flexure

• Shear (ACI-ASCE 426)

• Anchorage

• Joints (3.5(f’c)^.5)

Footings C/D Ratios

C/D min

Transverse

C/D min

Longitudinal

Flexure 0.9 on My

1.1 on Mu

1.3 on My

1.6 on Mu

Shear 0.31 0.53

Anchorage of Starter Bars

0.99 0.91

Joints 0.60 0.70

Using conservative criteria, it appears that the WSDOT footings are vulnerable to shear failure. Detailed analyses and testing might change that diagnosis. Few footings have failed during earthquakes.

Priorities for Retrofitting

Location Failure Mode

Likelihood Consequence Cost

1st-Story Splices

Flexure

Shear

1

?

2

1

1

1

Joints Diag. Tens. 2 1 3

Columns Flexure

Shear

2

2-3

4

1

1-2

2

Footings Shear 2* 2 3

2nd-Story Splices

Flexure 4 2 2

* Modified