pushover analyses of two

Pushover Analyses of Two-Span Reinforced Concrete

Bridge With Piers Confined by Fiber Reinforcements

Theodoros C. Rousakis

Civil Engineering Department

Democritus University of Thrace, D.U.Th.

Xanthi, Greece

[email protected]

Zoi Th. Gronti

Civil Engineer, MSc, D.U.Th.

Xalkida, Greece

[email protected]

Abstract—The study examines analytically the effects of the

external confinement of reinforced concrete bridge piers with

different fiber reinforcements and techniques. A typical two-span

overpass bridge is retrofitted with light Carbon Fiber Reinforced

Polymer (CFRP) or Glass FRP (GFRP) or Aramide FRP (AFRP)

or Polythylene Naphthalate FRP (PENFRP) or Polyethylene

Terephthalate FRP (PETFRP) jackets or Vinylon Fiber Rope

(VFR) or Polypropylene FR (PPFR) wraps for the intermediate

piers. Also an extra light PPFR wrapping of the piers is

examined. Pushover analyses of the different 3d models of the

bridge are performed in order to assess the eight retrofit

schemes. VFR and PPFR have ultra high deformability at failure

and thus enhance remarkably the deformability of confined

concrete. FR wraps may provide far more upgraded

displacement ductility of the bridge than FRP jackets of

equivalent axial rigidity. FR retrofitted piers suppress the failure

of confined concrete (typical failure for FRP confined piers)

while they present steel bars’ fracture. Extra light PPFR

wrapping results in an enhanced bridge behavior similar to that for FRP jackets.

Keywords; bridge pier;fiber rope; confinement; pushover

I. INTRODUCTION

Fiber Reinforced Polymers (FRPs) are widely used in the retrofit of bridge piers. FRP confining sheets may upgrade remarkably the stress-strain behavior of concrete. Hence, the strengthened piers may present enhanced curvature ductility and further develop extensive inelastic deformations without significant loss of their shear strength [1,2]. High deformability FRP material reinforcements made of PEN or PET provide concrete with significant compressive axial strain at failure [6]. The studies by [3,4] investigate the confining effects of aramide or vinylon structural fiber ropes (AFR, VFR). The ropes are externally wrapped around the columns without the use of gluing resins. The ropes present very low sensitivity to local damage.

Recent results by [5] suggest that Vinylon or Polypropylene Fiber Ropes (VFR, PPFR) may provide confined concrete with ultimate axial strain up to 13%. The use of high deformability confining materials ensures that the high potential of concrete for energy dissipation is utilized. Then the failures of the reinforced concrete members are related to second order effects or to shear capacity degradation.

The study investigates the effects of the use of different confining materials and techniques for the strengthening of the intermediate piers in order to meet current codes seismic design requirements. It examines carbon or glass or aramide or polythylene naphthalate or polyethylene terephthalate FRP jacketing of piers as well as vinylon or polypropylene FR wrapping without the use of impregnating resins.

II. TWO-SPAN BRIDGE LAYOUT

The structure is a typical bridge [7] with total length of 67.66m, having two spans of 33.83m. The deck consists of 6 precast prestressed girders with 1.825m height and 2.95m spacing. The top slab has thickness of 0.205m (0.23m in the cantilever region) and is connected with the girders through shear connectors. The deck is simply supported on the abutments and on the intermediate piers through bearings allowing free sliding and rotation in every horizontal direction.

Figure 1. Layout of the piers.

SECTION12. Industrial and Civil Engineering

Advanced Research in Scientific Areas 2012

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(a) (b)

Figure 2. longitudinal section of bridge (half).

The intermediate piers consist of four single cylindrical columns with 1.067m diameter which are interconnected through a beam of 1.22m height. The piers are supported on spread footings and the abutments on piles (Figures 1 and 2).

The bridge was originally designed for vertical loads and then retrofitted to meet Eurocode standards for bridges in seismic regions. The bridge piers are strengthened through

external confinement. The paper investigates the effect of the different confining fiber reinforcements on the inelastic response of the bridge. Seven different reinforcements are considered: CFRP or GFRP or AFRP or PENFRP or PETFRP jackets and Vinylon Fiber Ropes (VFR) or Polypropylene Fiber Ropes (PPFR), in quantities (Table I) that provide equivalent stress-strain curves for confined concrete (Figure 3).

TABLE I. MECHANICAL PROPERTIES OF CONFINING MATERIALS

Parameters

Confining Materials

VFR PPFR GFRP CFRP PPFR0.08 AFRP PENFRR PETFRP

Ej (GPa) 15.9 2.25 73 240 2.25 115.2 12* 8.3*

εju 0.046 0.18 0.028 0.015 0.18 0.0324 0.0626 0.0871

σj,max (MPa) 734 405 2044 3600 405 3732 751 722

Equivalent

Thickness tj (mm) 3.02 25.37 0.7 0.21 7 4.2 3.94 5.69

ρj 0.0345 0.29 0.008 0.0024 0.08 0.048 0.045 0.065

εau 0.1 0.1 0.015 0.012 0.06 0.0205 0.0415 0.0625

*equivalent modulus of elasticity

Figure 3. Typical σ-ε curves from seismostruct for (a) equivalent CFRP, GFRP, AFRP, PENFRP, PETFRP, VFR, PPFR, (b) PPFR0.08 (ideally plastic σ-ε).



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(a)

(b)

Hence, the different confining materials provide different axial strains at failure (Table I, εau values), according to recent experimental findings [5,6]. The characteristic stress-strain curves for the FR confined concrete with fcm=21 MPa are modeled according to the study by [8] as provided in Seismostruct software [9] and are gathered in Figure 3.

III. ASSESSMENT OF AS-BUILT AND RETROFITTED BRIDGE

The inelastic mechanical performance of the bridge is assessed through inelastic static analyses (pushover) with the use of the Seismostruct software. Seismostruct accounts for material inelasticity along the member and across the section depth as well as for geometric nonlinearity. Herein, distributed inelasticity frame elements are used within the framework of Seismostruct. They are implemented with force-based finite element formulations.

The steel is modelled uniaxially according to [10] with isotropic hardening rules and implemented by [11]. The

elastomeric bearings are modelled as link elements (curve lin_sym). The bridge analytical model is presented in Figure 4.

Figure 4a presents the thorough detailing of the model that allows for extensive parametric analyses of different effects that are involved in the bridge design (3 dimensional modeling of all the different structural members). Figure 4b shows the required elements and nodes in order to describe accurately the deck and the substructure (discretization for deformed shape). Figures 5a and 5b depict the 3d bridge models for the case of strengthening with extra low Polypropylene FR confinement (PPFR0.08) for pushover X and pushover Y analysis correspondingly. The different colours of the piers’ regions denote the different performance criteria reached by the concrete (i.e. yellow for concrete cover failure), steel (i.e. magenta for steel fracture and pink for steel yielding) or the member itself (i.e. red for ultimate member chord rotation and blue for shear failure) during the ultimate analysis step.

Figure 4. Three dimensional model of the bridge in seismostruct (a). Discretization of the deck and the substructure (half, deformed shape) (b).



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(a)

(b)

Figure 5. Typical 3d model of the bridge for the case of piers confined by extra low Polypropylene FR confinement, PPFR0.08. Different colours denote the different performance criteria reached by the piers for pushover X-X’ (a) and Y-Y’ (b).

Figures 6a and 6b show the total base shear V versus intermediate pier top displacement d curve for the as-built and retrofitted bridge. The same figure includes the V-ddeck (displacement at the deck) for the case of bridge retrofitted by the PPFR0.08 confinement that shows the effect of the elastomeric bearings. The pushover X-X’ analyses suggest that the as-built bridge presents early shear failure of concrete and then of confined concrete at the base region of the piers. What follows is the fracture of the steel bar reinforcements. The retrofitted bridges reveal the effects of the different confining materials. The bridge confined with light CFRP jacket achieves a higher displacement d at a higher base shear V upon failure of the confined concrete than the as-built bridge. The use of higher deformability GFRP jacket (of the same axial rigidity with CFRP) provides the same enhanced V-d behaviour (with respect to as-built bridge) while the failure displacement of the bridge is higher (Figure 6a). The bridge confined with AFRP jacket achieves a higher displacement d upon failure of the confined concrete than the confined with GFRP or CFRP bridge. The bridge confined by PENFRP or PETFRP jackets or ultra high deformability Vinylon or Polypropylene Fiber Ropes present identical V-d response. Furthermore, the confined concrete failure is suppressed and the failure displacement of the bridge happens upon the fracture of the steel at the base region of the inner piers. The corresponding displacement is more than twice than that of the CFRP or GFRP jacketed piers. The same results come over the pushover Y-Y’ analyses. The bridge confined with light CFRP or GFRP jacket achieves almost the same displacement d with the as-built bridge but at a higher base shear V. The bridge confined with AFRP jacket achieves a higher displacement d at a higher base shear V upon

failure of the confined concrete than the confined with GFRP or CFRP bridge. The failure displacement of the bridge happens upon the fracture of the steel at the base region of the exterior pier.

The case of extra low confinement with PPFR (PPFR0.08) uses a quantity (axial rigidity) that is 0.29/0.08 = 3.65 times lower than the abovementioned retrofits. Such an equivalent CFRP or GFRP confinement leads to marginal stress-strain upgrade and thus it is not investigated. The analyses of the bridge suggest that the stress-strain curve of confined concrete of the piers that is almost ideally plastic (very weak hardening behaviour) may accelerate the fracture of the steel at the base region of the exterior piers. That failure occurs around the displacement levels of the as-built bridge. Yet, the V-d response of the bridge is identical with the one of multiple axial rigidity of confining reinforcement. Also, the failure happens around the failure of CFRP or GFRP jacketed piers. The failure chord rotation of the piers occurs in twice the displacement of the steel fracture.

The V-ddeck response in Figures 6a and 6b include the displacements of the spring elements that model the mechanical behaviour of the elastomeric bearings. The elastic stiffness of the V-ddeck response of the bridge, incorporates the combined effect of the substructure and elastomeric bearings. The pushover Y-Y’ presents a higher deviation from V-d behaviour as the double bending of the piers provides higher stiffness for the substructure.



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(a)

failure of all

bearings of all

confined concrete cases

0

2000

4000

6000

8000

10000

12000

14000

0 50 100 150 200 250 300 350 400 450 500

Displacement, d (mm)

To

tal

Bas

e S

hea

r, V

(K

N)

.

steel yielding at base, cover failure,

shear failure of two exterior piers

failure of confined concrete at base

steel fracture at base

failure chord rotation

failure of Carbon FRP

confined concrete piers case

failure of Glass FRP confined concrete piers case

fracture of steel of inner piers at base of

Polythylene Naphthalate FRP, Polyethylene

Terephthalate FRP, Vinylon and

Polypropylene FR confined concrete piers

cases

fracture of steel of exterior

piers at base for PPFR0.08

failure chord rotation of piers for PPFR0.08

PPFR0.08 confined

bridge piers

CFRP, GFRP, AFRP, PENFRP, PETFRP, VFR PPFR confined bridge piers

As-built bridge

PPFR0.08 V-ddeck

0

2000

4000

6000

8000

10000

12000

14000

0 50 100 150 200 250 300 350 400 450 500

Displacement, d (mm)

To

tal

Base

Sh

ear,

V (

KN

)

.

shear failure of exterior pier

shear failure of all piers and yielding of steel of exterior pier

yielding of steel of all piers

failure of concrete cover

fracture of steel of all piers

shear failure

of one inner

pier

failure of Glass

or Carbon FRP

confined concrete piers cases

fracture of the steel of one exterior

pier at base for PENFRP or PETFRP or VFR or PPFR

fracture of steel of all piers

As-built bridge

PPFR0.08 confined

bridge piers

CFRP, GFRP, AFRP, PENFRP,

PETFRP, VFR PPFR confined

bridge piers PPFR0.08 V-ddeck

(b)

Figure 6. Pushover curves of as-built and retrofitted bridge (CFRP, GFRP, AFRP, PENFRP, PETFRP, VFR, PPFR or PPFR0.08) for pushover X-X’ (a) and pushoverY-Y’ (b).

IV. CONCLUSIONS

The study presents the comparative investigation of the effects of different confining reinforcements on the seismic behaviour of reinforced concrete bridges, through inelastic static analyses. The higher the axial deformability of the confining materials, the higher the ultimate base shear and displacement of the bridge. Fiber rope reinforcements made of

vinylon or polypropylene may provide a more effective alternative strengthening technique for bridges than CFRPs or GFRPs. High deformability PENFRP and PETFRP confinement presents similar efficiency with FRs. The displacement of FR (and PEN or PET FRP) confined piers at failure is around twice as that of bridges with CFRP or GFRP confined piers and is limited by the fracture of the steel bars. Extra light confinement of the piers with PPFR0.08 (3.65 times

failure of Aramide FRP

confined concrete piers case

failure of two exterior

Aramide FRP confined

concrete piers



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lower axial rigidity than the one that corresponds to light CFRP or GFRP confinement) results in identical V-d response of the bridge. The failure V and d values are around the ones for CFRP or GFRP confinement of 3.65 times higher axial rigidity. While CFRP or GFRP or AFRP strengthened piers fail with the crushing of confined concrete, the PPFR0.08 wrapped piers fail with the fracture of the steel bars. This failure concerns only the two exterior piers for pushover X-X’ (cantilever behaviour).

REFERENCES

[1] G. Monti, N. Nistico, S. Santini, “Design of FRP Jackets for Upgrade of Circular Bridge Piers,” Journal of Composites for Construction, Vol. 5,

No. 2, May 2001, pp. 94-101.

[2] D. Anggawidjaja, T. Ueda, J. Dai, H. Nakai, “Deformation capacity of

RC piers by new fiber-reinforced polymer with large fracture strain,” Cem Concr Compos. 2006;28:914–27

[3] T. Shimomura, N.H. Phong, “Structural Performance of Concrete

Members Reinforced with Continuous Fiber Rope,” FRPRCS-8 Conference University of Patras, Patras, Greece, July 16-18, 2007.

[4] T. Shimomura, H. Fujikawa, K.Maruyama, “MODELING OF LOAD

BEARING MECHANISM OF RC COLUMN WITH EXTERNAL CONTINUOUS FIBER ROPE UNDER REVERSED CYCLIC LOAD,”

Asia - Pacific Conference on FRP in Structures APFIS 2009, pp137-142.

[5] T.C. Rousakis, “Confinement of Concrete Columns by Fiber Rope

Reinforcements,” CICE 2012 Conference, 13 – 15 June, Rome,.

[6] Jian-Guo Dai, Yu-Lei Bai, and J.G. Teng, “Behavior and Modeling of

Concrete Confined with FRP Composites of Large Deformability,” Journal of Composites for Construction, Vol. 15, No. 6, December 1,

2011.

[7] Modjeski and Masters, Inc., “COMPREHENSIVE DESIGN EXAMPLE FOR PRESTRESSED CONCRETE (PSC) GIRDER

SUPERSTRUCTURE BRIDGE WITH COMMENTARY (Task order DTFH61-02-T-63032),” Submitted to THE FEDERAL HIGHWAY

ADMINISTRATION, November 2003.

[8] B. Ferracuti, M. Savoia, “Cyclic behaviour of FRP-wrapped columns under axial and flexural loadings,” Proceedings of the International

Conference on Fracture, Turin, Italy 2005.

[9] Seismosoft, Seismostruct programme v5.2.2 (22/08/2011).

[10] M. Menegotto, P.E. Pinto, “Method of analysis for cyclically loaded R.C. plane frames including changes in geometry and non-elastic

behaviour of elements under combined normal force and bending,” Symposium on the Resistance and Ultimate Deformability of Structures

Acted on by Well Defined Repeated Loads, International Association for Bridge and Structural Engineering, Zurich, Switzerland, 1973, pp. 15-

22.

[11] G. Monti, C. Nuti, S. Santini, “CYRUS - Cyclic Response of Upgraded Sections,” Report No. 96-2, University of Chieti, Italy 1996.



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pushover analyses of two

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