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Evaluating the efficiency of supplementary rebar system in improving hysteretic damping of self-centering rocking walls

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Abstract

Although self-centering rocking walls have shown acceptable performance in decreasing downtime, repair cost, and continuous serviceability, their energy dissipation capacity is relatively low. This research introduces a supplementary rebar system (SRS) to improve the energy dissipation capacity of rocking walls. The advantages of this system are its high efficiency, applicability, simplicity of the installation, and easy replacement after yielding/failure. In this research, the efficiency of the proposed SRS was assessed by conducting a parametric study by considering the cross-sectional area, number, and location of the proposed SRSs as the study variables via seven numerical models. To this end, validated nonlinear finite element models were utilized. The results demonstrated that the models with the SRSs installed at the edge had higher load-carrying capacity, stiffness, and energy dissipation capacity. All the models under cyclic loading had stable flag-shaped hysteretic behavior up to a drift of 3% without significant strength loss. Employing SRSs increases the stiffness of the walls; however, by increasing ductility, the wall stiffness declines. Increasing the studied walls’ energy dissipation capacity and reaching the equivalent viscous damping of up to 17.36% demonstrate the efficiency of the proposed SRS. Moreover, as the first moment of area of the SRS increases, the models’ maximum base shear increases, and the ductility ratio and displacement amplification factor decrease. The response modification and displacement amplification factors were recommended to be 5.50 and 3.55, respectively, for rocking walls with the proposed SRS.

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Abbreviations

\({A}_{PT,i}\) :

The cross-sectional area of the ith tendon

\({A}_{ms,i}\) :

The cross-sectional area of the mild steel piece of the ith SRS

\(C\) :

Reaction force

\(c\) :

Compression length

\({C}_{d}\) :

Displacement amplification factor

\({E}_{PT,i}\) :

Modulus of elasticity of the ith tendon

\({E}_{ms,i}\) :

Modulus of elasticity of the mild steel piece of the ith SRS

\({E}_{D}\) :

Area confined by a hysteresis loop

\({F}_{y}\) :

Force corresponding to the yield strength point

\({F}_{m}\) :

Force corresponding to the peak strength point

\({F}_{1}\) :

Actual strength to the nominal strength of materials ratio

\({F}_{2}\) :

Members oversize ratio

\({F}_{3}\) :

Strain-hardening effect coefficient

\({F}_{4}\) :

Strain rate effect coefficient

\(f_{{cc}}^{\prime }\) :

Confined concrete strength

\({F}_{PT,in}\) :

Sum of the initial post-tensioning forces in tendons

\({f}_{PT,in,i}\) :

Initial stress applied to the ith tendon for the post-tensioning process

\({f}_{y,PT,i}\) :

Yield stress of the ith tendon

\({f}_{PT,i}\) :

Stress in the ith tendon

\({f}_{u,ms,i}\) :

Ultimate stress of the mild steel piece of the ith SRS

\({f}_{y,ms,i}\) :

Yield stress of the mild steel piece of the ith SRS

\({f}_{ms,i}\) :

Stress in the mild steel piece of the ith SRS

\({h}_{w}\) :

Height of the wall

\({h}_{u,i}\) :

Unbonded length of the ith tendon

\({K}_{s}\) :

Secant stiffness in the cyclic loading

\({l}_{w}\) :

Length of the wall

\({L}_{ms,i}\) :

Length of the mild steel piece of the ith SRS

\({M}_{D}\) :

Resisting moment induced by gravity load

\({M}_{PT}\) :

Resisting moment induced by tendons

\({M}_{SRS}\) :

Resisting moments induced by SRSs

\({n}_{PT}\) :

Number of post-tensioned tendons

\({n}_{SRS}\) :

Number of SRSs

\({P}_{D}\) :

Gravity load acting on the wall

\({P}_{PT}\) :

The resultant force of the tendons

\({P}_{SRS}\) :

The resultant force of the SRSs

\(R\) :

Response modification factor

\({R}_{\mu }\) :

Reduction factor due to ductility

\({R}_{S}\) :

Overstrength factor

\({R}_{R}\) :

Redundancy factor

\({t}_{w}\) :

The thickness of the wall

\(V\) :

Lateral force corresponding to wall rotation

\({V}_{max}^{+}\) :

Maximum calculated lateral loads in the considered positive direction

\({V}_{max}^{-}\) :

Minimum calculated lateral loads in the considered negative direction

\({X}_{PT}\) :

Location of the resultant force of all tendons

\({X}_{SRS}\) :

Location of the resultant force of all SRSs

\({x}_{PT,i}\) :

Distance of the ith tendon from the compressive edge of the wall

\({x}_{SRS,i}\) :

Distance of the ith SRS from the compressive edge of the wall

\(\alpha ,\beta\) :

Equivalent rectangular block constants

\({\beta }_{m}\) :

SRS moment ratio

\({\Delta }_{PT,i}\) :

Deformations of the ith tendon

\({\Delta }_{SRS,i}\) :

Deformations of the ith SRS

\({\Delta }_{0}\) :

Relative lateral displacement

\({\Delta }_{max}^{+}\) :

Maximum lateral displacement in the considered positive direction

\({\Delta }_{max}^{-}\) :

Minimum lateral displacement in the considered negative direction

\(\Delta_{u}\) :

Maximum lateral displacement

\(\Delta_{y}\) :

Yielding lateral displacement

\(\varepsilon_{PT,i}\) :

Strain in the ith tendon

\(\varepsilon_{ms,i}\) :

Strain in the mild steel piece of the ith SRS

\(\varepsilon_{u,ms,i}\) :

The ultimate strain of the mild steel piece of the ith SRS

\(\theta_{decom}\) :

Wall rotation at decompression state

\(\theta\) :

Wall rotation

\(\theta_{m}\) :

Lateral drift corresponding to the peak strength point

\(\theta_{y}\) :

Lateral drift corresponding to the yield strength point

\(\xi_{eq}\) :

Equivalent viscous damping

\(\mu\) :

Ductility ratio

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Authors and Affiliations

  1. Department of Civil Engineering, Shahrood University of Technology, Shahrood, Iran

    Maedeh Sadeghi & Farshid Jandaghi Alaee

  2. Department of Civil Engineering, University of Mazandaran, Babolsar, Iran

    Habib Akbarzadeh Bengar

  3. University of Michigan and Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai, China

    Abouzar Jafari

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  1. Maedeh Sadeghi
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  2. Farshid Jandaghi Alaee
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  3. Habib Akbarzadeh Bengar
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  4. Abouzar Jafari
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Correspondence to Farshid Jandaghi Alaee.

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Sadeghi, M., Jandaghi Alaee, F., Akbarzadeh Bengar, H. et al. Evaluating the efficiency of supplementary rebar system in improving hysteretic damping of self-centering rocking walls. Bull Earthquake Eng 20, 6075–6107 (2022). https://doi.org/10.1007/s10518-022-01421-z

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