development of 3d confinement models of circular bridge

PEER Meeting, San Francisco, 10/16/2009

Development of 3D Confinement Models of Circular Bridge Columns of Different sizes Khalid M. Mosalam, PhD, PE Professor and Vice Chair, University of California, Berkeley [email protected]

Selim Günay, Post-Doc Mohamed Aly (MS/PhD Student)

Outline

 Motivation and Objectives

 Milestones and Deliverables

 Previous Relevant Work

 Current Relevant Work

 Parametric Study

1)  Confined concrete models (internal transverse reinforcement or external jacketing) are limited to effect of axial load.

2)  A developed theoretical model focused on circular cross-sections with relatively small diameter calibrated with tests of RC circular columns with FRP jackets for different axial load eccentricities.

3)  Questions remain on the effectiveness of confinement for circular columns with large diameter.

4)  The goal is to address bridge column size effect in confinement models of concrete when it is subject to axial, shear and bending stresses using a theoretical/computational approach.

Motivation

1)  Literature review of tests and models for circular RC columns with confining media, internal and external.

2)  Theoretical model for confined RC circular sections addressing the size effect in a rigorous manner.

3)  Computational model with nonlinear 3D FEM for confined RC circular sections.

4)  Calibrate the models using past tests of circular columns of different sizes, e.g. PEER column database.

5)  Use recent tests in Japan on large size circular columns and future tests by the PI for a Caltrans project of shaking table tests (hrz. and vl. shaking).

6)  Implement a 3D constitutive model of confined RC sections, based on the 3D FE model, into OpenSees.

Objectives

1)  Focus on circular cross-sections of different sizes. 2)  Extend study to non-circular sections, e.g. using shape

efficiency factors calibrated by existing tests and 3D FEM, similar to those developed for in-span hinge regions.

3D FE mesh for nonlinear analysis Cracking at the bearing Hube, M. and Mosalam, K.M., “Experimental and Computational Evaluation of Current and Innovative In-Span Hinge Details in Reinforced Concrete Box-Girder Bridges, Part 1: Experimental Finding and Pre-Test Analysis” PEER Technical Report 2008/103, 2009.

Objectives

1)  Augment existing PEER database on columns with data from tests on confined circular columns from US and Japan.

2)  Accurate implementation of confined concrete material and section models for RC bridge columns of different sizes as extension of model by the PI in OpenSees.

Talaat, M. and Mosalam, K.M., “Computational Modeling of Progressive Collapse in Reinforced Concrete Frame Structures,” PEER Technical Report 2007/10, 2008.

Milestones and Deliverables

Previous Relevant Work

Rebar Buckling Model

Reflects the current state of the bar and tie material

,

  Buckling spans multiple ties

  Tie stiffness nearly equal along Lb

  Confined section determines tie state

  No lateral support from concrete cover

  Lb calculated at each step by minimizing critical stress (check Lb>s)

Geometry & Assumptions

Determining Buckling Stress

Strain decomposition scheme

+

  Assumed initial imperfection (δi lateral offset)   Assumed harmonic shape function   Stress-free initial shortening-stress, εbi = f(δi

2 )≈0   Imperfection amplified by loading to δ(δi, EI, σ/σcr)   Post-buckling, δ becomes excessive   Corresponding increase in εb   Resulting decrease in εs and axial stress

P=0

δi Unloaded, εt=ΔL/Lb=εbi ≈0

ΔLi P>0

δ> δi

Loaded, εt=ΔL/Lb=εs+εb

ΔL

Fiber mimics axial response of a deflected beam under axial and flexure loads

Post-Buckling Response

= Buckling-induced shortening εb=f(δ2)

Steel effective strain εs

Total (observed) strain εt=ΔL/Lb

Bar compression behavior, variable slenderness ratio Experimental Validation (1/2)

*Bae, S., Mieses, A.M. and Bayrak, O. (2005). "Inelastic Buckling of Reinforcing Bars." Journal of Structural Engineering

*

Bar cyclic behavior, slenderness ratio = 6

L/d = 6

* Rodriguez, Botero, Villa (1999). Cyclic Stress-strain Behavior of reinforcing Steel Including Effect of Buckling. Journal of Structural Eng. ASCE

Test* Analysis

Post-buckling response of uniaxial fiber mimics axial behavior of a deflected beam under axial and flexure loads

Experimental Validation (2/2)

  Constitutive material models: steel stress-strain   Confinement-sensitive bond-slip*   Compatibility of strain (strain decomposition):

  Equilibrium: Bond stress and axial stress along bar

Geometry and stress fields

*Xiao, Ma (1997) Seismic Retrofit of RC Circular Columns using Prefabricated Composite Jacketing. ASCE J. Str. Eng.

Deficient Lap Splice

+ = Bond (εbs) Steel (εse) Response(εst)

Experimental Validation

*Viwathanatepa, S. (1979). Bond Deterioration of Reinforcing Bars Embedded in Confined Concrete Blocks. PhD dissertation, Univ. of California, Berkeley.

25 mm (#8) bar embedded in 635 mm (25”) column stub

32 mm (#10) bar embedded in 635 mm (25”) column stub

* *

  Family of stress-strain curves (σ1, ε1)

  Parametrized by

  Softening conserves fracture energy, Gfc

  Enforces lateral strain compatibility with confining material in real time

Envelope Curve*

* Binici (2003). An Analytical Model for Stress-strain Behavior of Confined Concrete. Eng. Structures. Elsevier ** Ahmad, Shah (1982). Stress-strain Curves of Concrete Confined by Spiral Reinforcement. ACI Journal. ACI

Experimental Validation**

  Unconfined cylinders

  Confined with tie spacing = s

Analysis Test

Concrete Confinement

Backbone curve

Leon-Pramono failure criterion

& : hardening & softening parameters

Effective jacket rigidity Uniaxial jacket rigidity

Lateral strain compatibility

Formulation

ε1 max σfmax

R θc

σf + d σf

σf τ

x θ Neutral Axis

dθ

dx

(a) Section (b) Strain Profile

(c) Jacket (d) Infinitesimal Jacket Element

(e) Confining Stress Distribution

y

Strain compatibility enforced HERE

Depending on location of fiber in cross-section Section Model Confined Fiber Section

Hyperbolic lateral confinement distribution along cross-section   Based on bond stress equilibrium along confining jacket   Confinement maximum at maximum compressive strain

  Confinement vanishes at neutral axis

Experimental [Lokuge et al, 2004] vs. simulated axial and lateral stress-strain response

 Unloading-reloading rules based on the work in [Lokuge et al, 2004]

 The stress-strain relationship is invariant in the principal shear space

 Modified to account for variable confinement  Modified to account for hysteretic energy-based

envelope reduction factor

Extension to Cyclic Loading

Class Map and OO Implementation

VariableConfinementMaterial UniaxialCurve

LoadingCurve

UnloadingCurve TransitionCurve

EnvelopeCurve

UniaxialMaterial

ConfinedFiberSec (2D, 3D)

HystereticDamage

SectionForceDeformation

Material

DamageModel

ParkAng

1

1

1

1

1

nfiber

1

DissipatedEnergy

New Classes Abstract Classes

Implementation

* Mosalam, Talaat, Binici (2007). A Computational Model for Reinforced Concrete Members Confined with FRP Lamina: Implementation and Experimental Validation. Composites-B: Engineering. Elsevier

Measured lateral strains along circumference match analytical confinement profile*

Normalized confining stress distribution along perimeter (converted from measured strains)


Constructed using variable-confinement envelope and lap splice models [Sheikh and Yao, 2002]

[Xiao and Ma, 1997]


chuck Jack

Load cell

LVDT

cable

Eccentricity

FRP rupture

Test Setup Specimen Geometry

Tested Specimens  4 pin-pin columns: 1 as-built, 3 CFRP-retrofitted  Axial load under fixed eccentricity  3 different eccentricity levels


22

0 500 1000 1500 0

5

10

15

20

curvature [rad/km] M

omen

t [kN

m] Specimen 2

Specimen 1

Specimen 3 Estimates loss of confinement in as-built and retrofitted columns

-.016 -.012 -.008 -.004 0 .004 .008 .012 .016 .02 0

200

400

600

800

Strain (compression positive)

Axia

l Loa

d (k

N)

Max. Lateral Strain Avg. Axial Strain

__ Pure Axial Load --- 15 mm eccentricity

Experimental Computational


Estimates fracture of FRP jacket and loss of confinement

FRP rupture

Experimental [Sheikh and Yao, 2002] and computational moment-curvature response of FRP-wrapped columns


Estimates bar buckling for different confining effects

Experimental [Henry, 1999] and computational force-deformation relationships


Specimen 415P 0.66% trans. reinf. ratio

Specimen 415S 0.33% trans. reinf. ratio

Current Relevant Work

Prototype: Plumas-Arboga Overpass

Prof. Kunnath, UC-Davis

Interlocking Circular


Full Bridge: Interlocking Spiral vs. Circular

Northridge EQ; Column Aspect Ratio (AR) = 4.0



Northridge EQ; Column Aspect Ratio (AR) = 3.0

Landers EQ, Aspect Ratio (AR) = 3.0 Prof. Kunnath, UC-Davis


Landers EQ, Aspect Ratio (AR) = 4.0


Full Bridge vs. Single Column

Northridge EQ; AR = 3.0

Northridge EQ; AR = 4.0 Prof. Kunnath, UC-Davis

• Withandwithoutmassmomentofiner1a

• AspectRa1o=2.5,3.0,3.5,4.0,4.5,5.0• BWHelementwithfibersec1on,HingelengthbyCaltrans

Parametric Study

meanofabs{(withver1cal/wover1cal)‐1}(fromtheen1rePEERNGAdatabase)

Type1 Type2

Parametric Study

AspectRa.o

AR=4.0,PacoimaDam(RSN1051)

kN

Sec

Parametric Study

CASE H (m)

D (m)

Aspect Ratio

Long Reinf. Spiral Reinf.

Long Reinf. Ratio

Spiral Reinf. Ratio

Mass (ton)

Mass Moment of Inertia

(MMI) (ton m2)

T (sec)

1 8 1.33 6 30 #29 #19 @ 160 mm 1.4% 0.54% 800 6000 1.82

2 8 2 4 44 #36 #19 @ 105 mm 1.4% 0.54% 800 6000 0.80

3 8 4 2 70 #57 #19 @ 53 mm 1.4% 0.54% 800 6000 0.20

•  Case 2 is very similar to the equivalent cross section of the

Prototye Plumas Bridge

•  Cases 1 and 3 are modified from Case 2

•  MMI from hat shaped mass configuration s.t. centroid of mass

coincides with top of column

•  Axial load level is 10% of Agf’c

•  Confined concrete section [Talaat and Mosalam, 2007]

Parametric Study

GM # Earthquake Station Component PGA (g) PGV (cm/s) PGD (cm) Epicentral

Distance (km)

1 Landers Lucerne 345 0.79 32.4 69.8 44

2 Northridge Sylmar 052 0.61 117.4 54.3 13.1

•  Ground motion 1: long duration and a far fault ground motion

•  Ground motion 2: pulse type near fault ground motion

Parametric Study

Parametric Study

Questions, Comments

development of 3d confinement models of circular bridge

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