Analytical modeling of interface behavior in reinforced concrete

Analytical modeling of interface behavior in reinforced concrete jacketed members Georgia E. Thermou, Civil Engineer, MSc, DIC, Ph. D Candidate DUTh Supervised by Professors: SJ Pantazopoulou, AS Elnashai, A. Karabinis Mid-America Earthquake Center Seminar Series Wednesday May 12 th 2004 Demokritus University of Thrace Imperial College of Science, Technology and Medicine

Performance of Structures in Earthquakes 2/22 Demokritus University of Thrace

Why retrofitting is important? Ø Socio-economic issues - Direct effect on market place and community Ø 95% of existing buildings stock have been designed with out-of-date codes Ø Seismic risk mitigation programs 3/22 Demokritus University of Thrace

Design Approaches Old generation of codes Direct design Μc, u Μb Μc, u + Μc, b + Μb = 0 Current codes Capacity design Μ’c, u Μb, max Μ’c, b Μ’c, u + Μ’c, b + Μb, max = 0 Μ’c, u = Mc, u∙Μb, max/Mb Μ’c, b = Mc, b∙Μb, max/Mb 4/22 Demokritus University of Thrace

Framework for Seismic Rehabilitation (1) • Rehabilitation Objectives Earthquake Performance Level Collapse Inelastic Range Very Rare (970 years) Life Safety Serviceability Rare (475 years) (for New Construction) cti ve nti a l Ob /H jec aza Sa tiv rdo fet e us y Ob C jec riti tiv cal e se Occasional (72 years) Ob je Collapse Prevention Es Near Collapse Unacceptable Performance Ba sic Life Safety Ductility Operational Strength Stiffness Fully Operational Frequent (43 years) Lateral Load Earthquake Design Level Elastic Range Deflection [SEAOC, 1995] 5/22 Demokritus University of Thrace

Framework for Seismic Rehabilitation (2) • Selection of the retrofit scheme Technical & Socio-economic issues ü Structural compatibility ü Workmanship ü Materials/Technology ü Quality control ü Foundation system ü Duration of work ü Structural irregularities ü Functionality ü Cost vs importance • Level of intervention 6/22 Demokritus University of Thrace

Framework for Seismic Rehabilitation (3) • Retrofit Strategy Design Parameters Stiffness Strength Ductility Base shear Stiffness, Strength Ductility enhancement Stiffness & Strength enhancement & Ductility enhancement rehabilitated structure ΔV existing structure ΔV Δu Δu Roof displacement 7/22 Demokritus University of Thrace

Rehabilitation Schemes for RC Structures Intervention Techniques Local Global • Injection of cracks • RC jacketing • Shotcrete (Gunite) • Addition of RC walls • Steel Plate Adhesion • External buttresses • Steel Jacketing • Steel bracing • FRP Jacketing • Base isolation Selective • Stiffness-only • Strength-only • Ductility-only 8/22 Demokritus University of Thrace

Reinforced Concrete Jacketing 9/22 (1) Demokritus University of Thrace

Reinforced Concrete Jacketing Side Jacketing 10/22 (2) Local intervention Demokritus University of Thrace

Fibre Reinforced Polymers (FRPs) Jacketing Beams Columns Shear strengthening* * Triantafillou 11/22 TC, 1998, ACI Struct. J. , 95(2), 107 -115 Demokritus University of Thrace

Effect of Retrofit on Global Response Accurate assessment of the retrofitted structure Base shear Accurate modeling at local level ΔV Δu Roof displacement 12/22 FRPs Jacketing RC Jacketing Demokritus University of Thrace

Monolithic Approach ξtot Addition of RC Jacket prioritizing of failure modes M Composite section Ideal behavior Δφ φc ´ φtot ΔΜ φc Aim: flexural failure φ Premature failure 13/22 Demokritus University of Thrace

Analytical Model: slip at the interfaces Composite section 14/22 Monolithic approach Analytical modeling Demokritus University of Thrace

Estimation of Crack Spacing Stresses at mid-crack Stresses at crack N. A. ft, o hc fms, o τ fcrs, o h 1 fcrs, n fms, n c/2 Shear Flow: τ = (nn∙fb, n∙π∙db, n) / btot Crack Spacing: c=(2∙ft, o∙hc∙btot)/(no∙fb, o∙π∙db, o+ τ∙btot) 15/22 Demokritus University of Thrace

Shear Transfer Mechanisms Aggregate interlock vci (1) Clamping τ = μ∙σlat + vci fy Dowel action Fd Fd Fd σlat fy Total shear force V = τ∙A+n∙Fd Fd 16/22 Fd Fd Α=l∙bnew (shear area) n: number of dowels Demokritus University of Thrace

Shear Transfer Mechanisms (2) Shear stress supply: Frictional resistance* Dowel resistance** τu Fd, scrit τ1 Fd 1 τ2 Fd 2 s 1 s 2 su s 1 s 2 τu = 0. 44 ∙(fc 2∙σc)1/3 * Tassios Fdu = 1. 3∙db 2∙(fsy∙fc)1/2 & Vintzileou, 1987, J. of Struct. Eng. , ASCE, 113(4), 411 -428 ** Vintzileou 17/22 su & Tassios, 1987, ACI Struct. Journal, 84(1): 18 -30 Demokritus University of Thrace

Presentation of the Algorithm (1) Shear stress demand: ΣF’ 1 ΣF’ 2 L A B jacket v 1 ΣF’i ΣF 2 core v 2 B A ΣF 1 ΣF’ 3 c/2 ΣF 3 jacket c vi=ΣFi/(bnew∙c/2) 18/22 Demokritus University of Thrace ΣFi

Presentation of the Algorithm (2) Define curvature φ Modify longitudinal strain gradient in order to obtain section equilibrium Estimate slip at top and bottom interfaces, s 1 & s 2 (analytical approach) Calculate the shear stresses, τ΄1 & τ΄2 making use of the shear stress resistance model Perform dual section analysis in order to obtain vertical shear stresses, τ1 & τ2 Compare τ1 & τ2 with the corresponding τ΄1 & τ΄2. Is equilibrium established? ΝΟ The algorithm aims at establishing equilibrium: • of the entire cross-section • between shear stress demand shear stress supply YES Check section equilibrium. Is section equilibrium satisfied? ΝΟ YES Calculate the axial, shear and moment resultant 19/22 Demokritus University of Thrace

Analytical Results Experimental work of Rodriguez & Park* S 1 & S 2: old type columns (New Zealand Code late 50’s), ρc=2. 05%, Φ 6/265 SS 1: repaired/strengthened column SS 2: strengthened column SRi=Ki SMi *Rodriguez & Park, 1994, ACI Struct. Journal, 91(2): 150 -159 20/22 Κi≈70% Demokritus University of Thrace

Conclusions Analytical modeling of the interface behavior in RC jacketed members* • Design diagrams for RC jacketed members • Accurate modeling at local level Retrofitting *Thermou GE, Pantazopoulou SJ & Elnashai AS. Structures Congress 2004, Nashville, Tennessee 2004. Paper No 349. 21/22 Demokritus University of Thrace

Acknowledgements This research project was funded by the European Research Project SPEAR (Seismic Performance Assessment and Rehabilitation), Contract Number G 6 RD-CT-2001 -00525) through Imperial College of Science, Technology and Medicine, London. 22/22 Demokritus University of Thrace