Haunch retrofitting technique for seismic upgrading deficient RC frames

Abstract

Haunch retrofitting technique has been employed, primarily to stiffen the beam-column connections that controls the hierarchy of strength within the beam-column members, and avoid joint shear hinging of RC frame structures, subjected to earthquake imposed lateral loads. Shake-table tests were performed on a total of nine (09) 1:3 reduced scale two-story RC frames, including five (05) as-built and four (04) haunch retrofitted models, to develop structures’ damage scale and obtain their seismic response parameters. A representative finite element based numerical model was prepared in SeismoStruct and validated against the experimental response. A suit of seven natural accelerograms were retrieved from the PEER NGA strong ground motions database and employed for incremental dynamic analysis of structural models, in order to derive seismic fragility functions for as-built and retrofitted structures. Vulnerability curves were derived for the structures, correlating the mean damage ratio with the seismic intensity. Uniform hazard curves, obtained for candidate cities in moderate and high hazard zones, were employed to derive the structures’ loss exceedance curves for calculating the expected average annual loss. The net present value of the annual avoided repair cost was quantified, and critically compared with the retrofitting cost, to evaluate the viability of haunch retrofitting technique for seismic upgradation of deficient RC frame structures for risk mitigation.

1 Introduction

Earthquake observations, in many developing countries during recent past events, have revealed the high seismic vulnerability of deficient reinforced concrete frame structures. This is primarily due to the construction defects inherently found in these structures, consequently resulting into enormous loss of lives and economic losses (Arslan and Korkmaz 2007; Ates et al. 2013; Bal et al. 2008; Bothara and Hicyilmas 2008; Chaulagain et al. 2015; Doocy et al. 2013; Erdil 2016; Fintel 1995; Ruiz-Pinilla et al. 2016). As observed in earthquakes, and demonstrated through laboratory experiments, substandard materials (low strength concrete, reduced size and low quality re-bars), reduction in longitudinal and transverse reinforcement, inadequate anchorage of longitudinal beam reinforcement in joints and joints lacking confining ties are major factors making structure incapable of withstanding moderate-to-strong earthquake shaking, which lead to damage and early collapse of frame buildings during earthquakes (Ahmad et al. 2019; Aycardi et al. 1994; Badrashi et al. 2010; Beres et al. 1996; Bracci et al. 1995a; Calvi et al. 2002; Fintel 1995; Hakuto et al. 2000; Kuang and Wong 2006; Park 2002; Rizwan et al. 2018; Sharma et al. 2011; Yavari et al. 2013). Various, more or less costly, techniques have been proposed and experimentally validated for the seismic upgradation of deficient RC frame structures (Benavent-Climent et al. 2014; Bracci et al. 1995b; Dolce et al. 2005, 2007; Fintel 1995; Garcia et al. 2010; Ghobarah and Said 2001; Shiravand et al. 2017). Earthquake induced damages in structure if took place in the beam-column joint panels, brittle shear failure mechanism joint shear hinge form at the local level that consequently result in story mechanism at the global level due to columns hinging (Fig. 1). Haunch retrofitting technique was proposed to enhance the seismic performance of RC frames having weaker beam-column joints, where application of other conventional techniques become cumbersome and costly.

Fig. 1

Joint damageability and, consequent, collapse of structures: from left to right: 1999 Izmit earthquake in Turkey, 1999 Chi-Chi earthquake in Taiwan and 1994 Northridge earthquake in USA (Sharma 2013)

Joint panels in real structures are difficult to strengthen with the commonly adopted techniques (Engindeniz et al. 2005), and require application of an intervention that reduce shear demand on joint panels, and instead, allow beam-column members to deform inelastically under earthquake loads. To control the hierarchy of strength within the beam-column members, haunch technique was proposed for RC frames by Pampanin et al. (2006), installing a metallic haunch type element at the beam-column connections of frames, particularly, those experiencing joint shear hinging under lateral loads. A stiffer haunch to remain elastic during loading or deformable (inelastically), to yield during loading and provide supplemental energy dissipation under cyclic response, envisaged to avoid joint damage and enhance seismic performance of structure, as validated experimentally and numerically on 2D beam-column sub-assemblages and frame (Appa-Rao et al. 2013; Genesio 2012; Pampanin et al. 2006; Sharma et al. 2011, 2014; Wang et al. 2017).

However, most of these investigations were limited to the seismic performance assessment of beam-column sub-assemblages under imposed quasi-static cyclic displacement, and experimental/numerical seismic analysis of RC frames against design based earthquakes. Since, haunch intervention primarily alters the mechanism from brittle joint shear hinging to beam-column members’ yielding, at the shifted plastic hinge location, it is the later that governs the seismic resistance and demonstrates the structure’s deformability (ductility). Depending on the relative strength of beam-column members, the intended plastic hinge may form desirably in beams, in case of strong-column and weak-beam condition, but otherwise may form inevitably in columns that could lead to unfavorable soft-story global mechanism. For this reason, it is utmost important to evaluate the efficiency of haunch retrofitting technique for both seismically designed structures, but having weaker beam-column joint panels due to lack of confining ties or employing low strength concrete, and structures designed for gravity loads only. Further, the seismic assessment should also consider the economic viability of strengthening technique in both moderate and high seismic hazard regions. It is due to these reasons, cost-benefit analysis of retrofitting interventions getting more attention in recent days, to quantify the economic benefit gained over the retrofit cost for selection of appropriate strengthening schemes (Banazadeh et al. 2017; Cardone et al. 2018; Dyanati et al. 2017; Marques et al. 2018).

For seismic evaluation, a total of nine shake-table tests were conducted on 1:3 reduced scale two-story RC frame structures at the Earthquake Engineering Center of UET Peshawar, under the research program led by the first author for seismic vulnerability assessment and strengthening of deficient modern RC frames in Pakistan, including as-built and haunch retrofitted models. Using natural accelerogram of 1994 Northridge earthquake, incremental multi-levels excitations’ tests were performed on models; deforming structure from elastic-to-inelastic and incipient collapse state. Seismic behavior of the models was observed, and damage scale of the respective models was developed. A finite element based numerical model, prepared in SeismoStruct, was calibrated with the experimental observations and employed for incremental dynamic analysis. Using a probabilistic nonlinear dynamic reliability based method (Ahmad et al. 2014), fragility functions were derived for both the as-built and haunch retrofitted models. The structures’ fragility functions were transformed to the vulnerability curves, correlating the mean damage ratio of the structure with the seismic intensity. To characterize the seismic hazard of candidate cities, uniform hazard curves were obtained, and employed to develop the structures’ loss exceedance curves, which were analyzed to calculate the average annual loss (AAL). The AAL obtained for both the as-built and retrofitted structure models were incorporated in the cost-benefit model to assess the economic viability of haunch retrofitting technique, in both the moderate and high seismic hazard regions.

2 Description of RC frame structures

2.1 As-built RC frame models

The present research considered low-rise reinforced concrete special moment resisting frame (SMRF) structures. In particular a two-story frame normally practiced for low-rise public buildings like hospitals, schools, apartment buildings and shopping malls. It has a regular rectangular plan of 2-bays by 1-bay with center-to-center length of 18 feet (5487 mm) and story height of 12 feet (3658 mm). The considered frame was designed using the lateral static force-based seismic design procedure given in the BCP-SP (2007), which is primarily based on the UBC-97. The structure design was carried out for the high seismic hazard (Zone 4, 0.40 g design PGA on soil type B, as per the NEHRP classification), which was detailed as per the ACI-318-05 recommendations for SMRF. The structure loading included self-weight for structural beam-column members and floor and roof slab, superimposed dead load for floor finishes and loads for partitions/contents: 40 psf (1.915 kN/m²) on the first floor and 60 psf (2.873 kN/m²) on the roof, and live load of 60 psf (2.873 kN/m²) on the first floor and 40 psf (1.915 kN/m²) on the roof. Concrete with compressive strength of 3000 psi (21 MPa) and reinforcing steel bars with yield strength of 60,000 psi (414 MPa) were considered. The structure design was carried out in the finite element based software CSI ETABS, considering all the load combinations for dead, live and earthquake loads given in the BCP-SP (2007). Figure 2 shows the typical geometric and reinforcement details of the code-conforming frame, extracted from the public type structure (Ahmad et al. 2019), while Table 1 reports details of all the five as-built models (a code-conforming and four deficient models) considered in the present research for assessment.

Fig. 2

Typical details of the code-conforming RC frame structure, SMRF detailings

Table 1 Characteristics of as-built frames (disparities in comparison to code-conforming model are highlighted)

Recent field surveys carried out in developing countries (Badrashi et al. 2010) have found number of construction defects in the existing building stock. This included the use of substandard construction materials (e.g. low strength concrete and under-sized re-bars), reduced longitudinal and transverse reinforcement in beam-column members, absence of confining ties in beam-column joint panels, using insufficient lap-splice length in plastic hinge region and not practicing 135° standard seismic hooks for transverse ties, among others.

2.2 Design of haunch retrofitting for RC frame

Avoiding joint shear hinging will require an intervention that reduces the moment demand in beam at the beam-column interface, this led to the development of haunch retrofitting technique for RC frames (Pampanin et al. 2006). The application of haunch at the beam-column connection result into opposing localized shear and bending in beam-column members at the point of haunch application, consequently lowering shear and moment demand in beam-column members at the joint interface, thus, reducing shear demand in joint panel zone (Figs. 3, 4).

Fig. 3

Modified bending moment and shear actions on haunch retrofitted beam-column sub-assemblages under lateral load

Fig. 4

Moment and shear developed in beam and column members after haunch installation. In this figure, α is angle the haunch makes with the column and d_b is the beam depth

Depending on the haunch axial stiffness, angle and position of application, the formation of plastic hinge can be enforced in beam to ensure desirable beam-sway mechanism of connection besides avoiding joint shear hinging under lateral loads. Additional less desirable mechanisms like flexure hinging of columns and undesirable mechanism like shear failure of beam and column members, if inevitable in deficient RC frames, may be prioritized, as; beam yielding, column yielding, joint shear hinging, shear failure of beam, shear failure of column, for optimum performance.

To design haunch retrofit scheme for the considered structures, listed in Table 1, Model 3 and Model 5 were selected, which represents the most commonly found recent constructions (Model-3) and existing structures (Model-5). Moment curvature analysis of beam and column was carried out to compute the yield moment capacity of the members. Considering an optimum value of β equal to 2.5, the minimum required length for haunch application is decided to achieve plastic hinging in beam. For a specified axial stiffness of the haunch element, the value of β can be calculated approximately using analytical formulae (Pampanin et al. 2006) or may be obtained through numerical analysis. Seismic design for the dissipating haunch requires a yieldable element, selected carefully to ensure altering damage mechanism from joint shear hinging to haunch element axial yielding and beam-column members flexure yielding. The most favorable will be to allow yielding in the beam member first, followed by haunch element yielding. Since, there is always a provision in beam moment increase beyond yield due to material overstrength, the designed haunch, corresponding to the yield moment in beam, will develop its yield strength to deform inelastically and dissipate energy through hysteretic response. The dissipating haunch will be subjected to alternate tension and compression, whereby the haunch element will undergo buckling, that will require an additional measure to control buckling e.g. encasing the dissipating haunch element in a buckling restrained tube filled with concrete, which is in principle similar to buckling restrained braces. Figure 5 show details of stiffer and dissipating haunch designed based on the analysis of connection of the considered frame, and following the aforementioned design procedure. The preliminary designed connections were modeled in the FE based nonlinear analysis software SeismoStruct for verification, which ensured beam flexure yielding under lateral loads.

Fig. 5

Details of stiffer and dissipating haunch designed for the considered frame

3 Shake table testing of as-built and retrofitted test models

3.1 Preparation of 1:3 reduced scale models

For simplicity reason and due to the fact that scaling stress–strain properties of both concrete and steel re-bar materials for model preparation are quite demanding and costly, a simple model idealization was considered in which the materials’ stress–strain properties essentially remained the same for both the prototype and models (Ahmad et al. 2019). Following the simple model idealization all the linear dimensions of beams, columns and slabs and diameter of the steel re-bars were reduced by a scale factor S_L 3. Concrete for the 1:3 reduced scale model was prepared with a mix proportion of cement, sand and 3/8 in. (9 mm) down coarse aggregate to respect the aggregate scaling requirements for concrete. The ACI concrete mix design procedure was followed for the preparation of concrete with compressive strength of 3000 psi (21 MPa) for Model-1 and 2000 psi (14 MPa) for Model-2 to Model-5. A mix proportion of 1:1.80:1.60 (cement: sand: aggregate) with a water-to-cement ratio of 0.48 is used to achieve 3000 psi (21 MPa) and mix proportion of 1:3.50:2.87 (cement: sand: aggregate) with a water-to-cement ratio of 0.80 is used to achieve 2000 psi (14 MPa).

The construction of models was carried in series under the strict supervision of site engineer. Initially special steel formworks were designed and prepared for all the components including structure’s base pad (footing), columns and slab with provisions for in-plane and transverse beams. The construction sequence included the preparation of reinforced concrete base pads 22 in. width × 15 in. depth × 8 feet length (559 mm × 381 mm × 2439 mm) for all the models one after the other, which were cured for 14 days with moist bags. It was followed by the construction of columns, construction of in-plane and transverse beams and slab monolithically for each of the model in series, which were cured for 14 days. In similar fashion the next story columns, beams and slab were constructed and cured. This way all the five models were prepared in time duration of about 4-1/2 months.

It is worth to mention that the model and prototype uses essentially the same materials type (concrete and steel re-bars), which have similar stress–strain behavior and material density (unit weight). Due to the above, the reduced scale models were subjected to gravity and seismic mass less than the required as per the similitude requirements for prototype-to-model conversion:

$$M_{r} = \frac{{M_{M} }}{{M_{P} }} = L_{r}^{2} ;\quad L_{r}^{2} = \frac{1}{{S_{L}^{2} }}$$

(1)

where M_r is the ratio of model mass M_M to prototype mass M_P, L_r is the reciprocal of linear scale factor S_L. In order to satisfy the above requirements for complete model mass simulation, the additional required mass were applied to each floor of the model, calculated following the mass simulation model of Quintana-Gallo et al. (2010):

$$M_{M1} = \frac{{M_{P} }}{{S_{L}^{2} }} - M_{M0}$$

(2)

where M_M1 is the additional floor mass for model, M_M0 is the floor mass of model. The total mass on each floor is, thus, the sum of additional mass M_M1 and M_M0. The additional floor mass (1200 kg for each floor) was simulated through two 600 kg steel blocks, prepared by stacking and welding steel plates together, which were mounted and fixed to the floor by means of fully secured ½ in. (13 mm) steel bolts.

In the present research both the rigid and deformable, energy dissipating, haunch types were considered for retrofitting of the considered deficient frames. Focus was particularly made on modifying the design scheme of stiffer haunch proposed by Sharma et al. (2014), and scheme of application on structure (i.e. haunch applied below beam, and haunch applied both below and above beam), additionally a nonlinear deformable haunch with restrained buckling was further included in the research to explore possibility of e nergy dissipation through deformable haunch that add supplemental damping to the structure, beside avoiding joint panel damage under seismic excitation. The stiffer haunch were fabricated from the steel plates whereas the dissipating haunch were fabricated and encased in stiffer circular steel tubes that were filled with concrete to avoid buckling of the deformable haunch element under compression loading. Figure 6 shows the application schemes considered herein. On average, the overall cost of haunch retrofitting per location (per haunch) is about Rs. 950.0 (≈ 10.0 USD) for the model, which can reach to about Rs. 2500 (≈ 25.0 USD) for the prototype. The indicated composite cost included cost for all material types (steel plates, welds, epoxy, nails) and accessories, and also included labor cost.

Fig. 6

Application schemes of haunch retrofitting of RC frames (Model 3 and Model 5, ref. Table 1)

3.2 Test setup and instrumentation

The model was lifted through a 20-ton overhead crane, placed on the shake tabletop and secured firmly by means of 18 steel bolts ½ in. (13 mm) diameter. The over-hanged portion of the base pad was placed on a specially fabricated roller support, comprised of 4-leg steel stool that was provided with 4#8 (4φ25 mm) steel rods to allow model lateral movement during testing. The test model was instrumented with six accelerometers with maximum capacity of ± 10 g and three displacement transducers with maximum capacity of 24 in. (610 mm). Two uni-axial accelerometers (front and back) were installed on each floor and base pad to record the in-plane acceleration of the model. For in-plane lateral displacement measurements, a fixed steel reference frame was erected in-lined with the model. The displacement transducers were mounted on the reference frame; the transducers’ strings were stretched by half-length of 12 in. (305 mm) and attached to each floor and base pad, keeping the table positioned at mid-way of ± 125 mm displacement.

3.3 Input excitation and loading protocols

A natural acceleration time history (accelerogram) of 1994 Northridge earthquake (horizontal component, 090 CDMG Station 24278 - PEER strong motion database, blind thrust faulr) was selected as an input excitation after careful analysis of number of accelerograms (Fig. 7). This record has maximum acceleration of 0.57 g, maximum velocity of 518 mm/s and maximum displacement of 90 mm, generated over a blind thrust fault with shallow depth of about 18 km. After the shake-table self-check run for system adjustment, the selected acceleration time history was applied to the test model with multiple excitations—5%, 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, 100% and 130% of the maximum acceleration of record, to push the structure from elastic to inelastic and severe damage state. Each of the model was tested progressively and its damage behavior was observed after every run, the tests were concluded when the test models were found in the incipient collapse state.

Fig. 7

Selected acceleration record for shake table testing

3.4 Observed behaviour of tested models

3.4.1 Observed behavior and damage evolution, as-built models

The code compliant model (Model-1) was observed with beam-sway mechanism; experiencing flexure yielding at the beam ends and slight flexure cracking at bottom end of columns on the ground story under test run with 100% intensity of excitation i.e. design level earthquake excitation. This model was able to resist 130% of Northridge record for collapse limit state exceedance, deforming to 5.30% roof drift with max. force resistance of 255 kN. Model-2 to Model-5 were observed with flexure cracking in both columns and beams and severe damages in joint panel regions under input excitation well below the design level excitation. Considering the ultimate limit state (incipient collapse state), Model-2 deformed to 5.0% drift with max. force resistance of 180 kN, Model-3 deformed to 4.77% drift with max. force resistance of 185 kN, Model-4 deformed to 3.45% drift with max. force resistance of 152 kN, Model-5 deformed to 3.92% drift with max. force resistance of 125 kN. Figures 8, 9 and 10 shows the typical damages observed in the deficient models. The use of low strength concrete lowered the structure resistance and altered the mechanism from beam-sway to column-sway and joint mechanism. In addition, the lack of confining ties in joint panel region resulted in the joint panels’ concrete cover spalling under lateral excitations well below the 100% intensity of Northridge record. Damage evolution was deduced for each tested model, describing the observed local damages in structural components correlated with lateral roof drift and base shear force. Tables 2 and 3 shows the damage evolution of Model-3 and Model-5, which were further considered for retrofitting.

Fig. 8

Observed damages in Model-3, refer Table 1 for damage evolution

Fig. 9

Observed damages in Model-5, refer Table 2 for damage evolution

Fig. 10

Observed damages in joint panel regions at the incipient collapse state

Table 2 Observed response and damage evolution of Model-3, as-built model

Table 3 Observed response and damage evolution of Model-5, as-built model

3.4.2 Observed behavior and damage evolution, haunch retrofitted models

The application of haunch at the beam-column connection altered the initial mechanism, forming flexure hinging in beams and columns at distance from the beam-column interface; the flexure cracking in beams and columns distributed over significant length (Fig. 11). However, damages were experienced also in the joint panel regions upon subjecting the structure to larger lateral displacement under extreme shaking (Fig. 12). This resulted due to the pullout of haunch from column during extreme shaking causing connection opening, which happened due to the inevitable detachment of a wedge like concrete from column due to the low strength of concrete providing lower resistance against prey out. Figure 11 and 12 shows the extent of damage observed in beam-column joint regions upon subjecting the model to extreme level shaking, and Tables 4, 5 and 6 reports the damage evolution of the retrofitted model. This damage is relatively more severe in model where haunch is applied only below the beam at the connection. Because, the strain in the longitudinal re-bars of columns at the bottom ends penetrate through the joints under tension loading, resulting in stress demand on panel zone. The shaking induced stress demand in joint panel can result into joint damage upon exceeding the joint principal tensile strength (Priestley 1997; Pampanin et al. 2002).

Fig. 11

Observed damages in deficient models retrofitted with haunch

Fig. 12

Observed damages in haunch retrofitted RC frames with different application schemes, after haunch pullout due to concrete pry-out

Table 4 Observed response and damage evolution of Model-3, haunch retrofitted, stiffer haunch applied only below the beam at the connection

Table 5 Observed response and damage evolution of Model-5, haunch retrofitted, stiffer haunch applied both below and above the beam at the connection

Table 6 Observed response and damage evolution of Model-5, haunch retrofitted, energy dissipating haunch applied both below and above the beam at the connection

4 Fragility functions and vulnerability curves

4.1 FE based structural modelling of RC frame

For inelastic modeling and seismic analysis of the considered structures, the FE based software SeismoStruct (SeismoSoft 2016; Pinho 2007), as proposed earlier (Ahmad et al. 2018), has been adopted and further extended herein for generalization, and also it is validated against further experimental shake table tests on RC frames. SeismoStruct is employed to model the considered reinforced concrete frames, idealized as an equivalent frame (Fig. 13), and provisioned with lumped plasticity hinges; at the beam-ends for re-bar slip (Rashid and Ahmad 2017), at the beam-column panels for joint shear hinge simulation. Haunches were modeled using the inelastic truss type element, connected to beams and columns through rigid links.

Fig. 13

Inelastic modeling of reinforced concrete frame for numerical analysis

The joint shear strength τ_j can be calculated using available analytical model developed based on the experimental and numerical research (Kurose 1987; Priestley 1997; Pampanin et al. 2002; Kim and LaFave 2012) for both non-seismic (gravity) and seismically designed frames. The present research adopted the analytical model proposed by Kim and LaFave (2012), which has been developed and validated against numerous experimental researches, to model the spring limit state strength and deformability capacity for the adopted multi-linear constitutive law of Sivaselvan and Reinhorn (2001), as shown in Fig. 14. Kim and LaFave (2012) have proposed a shear strength-shear deformability model that largely depends on the geometry of the joint, compressive strength of concrete, longitudinal reinforcement of beam and transverse reinforcements in joint panel region. For peak shear strength:

$$\tau_{j} ({\text{MPa}}) = \alpha_{t} \beta_{t} \lambda_{t} (JI)^{0.15} (BI)^{0.30} (f_{c}^{{\prime }} )^{0.75}$$

(3)

where α_t is the in-plane geometry parameter, which is 1.0 for interior, 0.7 for exterior and 0.4 for knee connection; η_t is the joint eccentricity parameter equal to (1 − e/b_c)^0.67; β_t is the out-of-plane geometry parameter, which is 1.0 for subassemblies with zero or one transverse beam and 1.2 for subassemblies with two transverse beams; λ_t is an adjusting factor to set the overall average of the ratio, it is equal to 1.31; f ^′ _c is the concrete compressive strength; JI = (ρ_j × f_yj)/f ^′ _c is the joint transverse reinforcement index, where ρj is the volumetric joint transverse reinforcement ratio in the direction of loading and f_yj is the yield stress of joint transverse reinforcement; BI = (ρ_b × f_yb)/f ^′ _c is the beam reinforcement index, where ρ_b is the beam reinforcement ratio and f_yb is the yield stress of beam reinforcement.

Fig. 14

Constitutive relationship for joint shear hinge. Limit states’ moments are computed for the corresponding shear using Eq. (3) and using the Sivaselvan and Reinhorn (2001) constitutive model given in SeismoStruct

The shear deformation corresponding to peak shear strength model proposed by Kim and LaFave (2012) is formulated:

$$\gamma_{j} (rad.) = \alpha_{\gamma t} \beta_{\gamma t} \eta_{\gamma t} \lambda_{\gamma t} BI(JI)^{0.30} \left( {\frac{{\tau_{j} }}{{f_{c}^{{\prime }} }}} \right)$$

(4)

where α_γt = (JPRU)^2.1 is the parameter for describing in-plane geometry, where JP represents the ratio of number of not-free in-plane surfaces around a joint panel to the total number of in-plane surfaces of the joint panel, to consider possible changes in joint shear strength according to in-plane geometry; JP is 1.0 for interior connections, 0.75 for exterior connections, and 0.5 for knee connections; η_γt is the joint eccentricity parameter equal to (1 − e/b_c)^−0.6, which is 1.0 for no eccentricity; β_γt is the out-of-plane geometry parameter, which is 1.0 for subassemblies with zero or one transverse beam and 1.4 for subassemblies with two transverse beams; λ_γt = 0.0055 is an adjusting factor to set the overall average of the ratio.

The above shear-deformation models, Eqs. (3) and (4), gives estimate of maximum shear and corresponding deformation in joint panel, shear-deformation for the other limit states can be obtained using the proposed empirically derived factors given in Table 7. The limit state’s shear stress computed was put in the Eq. (9) to calculate the corresponding limit state’s moment capacity for shear simulation hinge (Fig. 14).

Table 7 Limit state shear and deformation for joint panel, as proposed by Kim and LaFave (2012), used for constitutive law of shear-hinge simulation spring (Fig. 14)

4.2 Test and validation of the numerical modelling technique

The representative prototype of the tested RC frame is prepared in FE based software SeismoStruct (Fig. 15), following the aforementioned modeling approach to idealize the structural components (in-plane and transverse beams, columns and beam-column joint panels). Structural beam-column members’ geometric and material properties are defined for each model. Similarly, the joint limit state shear stress and deformation are calculated for each model and transformed to corresponding moment-rotation (Celik and Ellingwood 2008; Alath and Kunnath 1995; Biddah and Ghobarah 1999; Youssef and Ghobarah 2001; Lowes and Altoontash 2003). In case of code conforming model, materials’ overstrength is considered as proposed by Priestley et al. (2007). The frame was subjected to the considered imposed loading on floors and subjected to input excitation (acceleration) that was recorded at the base of the model. The response of each model was recorded in terms of roof displacement time history, peak lateral displacement and peak base shear force, and local damage mechanism (beam bar-slip and joint damage). Figure 16 shows the comparison of numerical analysis using SeismoStruct to the experimentally observed roof displacement time history response for as-built frames, Table 8 reports the comparison of numerically obtained peak displacement and peak base shear force to experimentally observed.

Fig. 15

FE based representative prototype structure prepared in SeismoStruct

Fig. 16

Roof displacement time history response of RC frames, as-built models

Table 8 Numerical to experimental prediction using FE-based software SeismoStruct

It can be observed that the numerical models predict the roof displacement time history response in a reasonable agreement to the experimentally observed response: in terms of the displacement response following the same trend, the occurrence of displacement peaks, and the alternate rise and decay in displacement response. The comparison reveal an error of about 10% in numerically predicting the lateral displacement and an error of about 5% in predicting the base shear force. In comparison to the deficient RC frames, the percentage of error is less in case of code conforming model. This reasonable prediction of global performance of RC frame structures shows soundness of the proposed modeling technique and the FE based tool SeismoStruct in simulating the dynamic seismic response of reinforced concrete frame structures experiencing beam bar-slip and joint panels damageability.

For haunch retrofitted frames, Model-3 and Model-5 are considered and provisioned with haunches in similarly fashion as discussed earlier, however considering all sources of inelasticity i.e. inelasticity in beam-column members, beam bar-slip, joint panel damageability and inelastic haunches, which were modeled as inelastic truss element. Figure 17 shows the comparison of numerically predicted to experimentally observed roof displacement response for models retrofitted with haunch. It can be observed that numerical analysis is reasonably in agreement with the experimental observation, however, in case of the Model-5 retrofitted with stiffer haunch, numerical analysis experience a permanent offset after the peak response is observed. It is due to the fact that the ground-story column experience irrecoverable plastic deformation for this model. Numerically predicted peak response is in a good agreement but with a little over prediction, also, the residual deformation observed in numerical analysis is relatively higher than the experimental, nevertheless, it is conservative for vulnerability assessment. Table 8 also reports the error in numerical to experimental prediction for roof displacement and base shear force, on average, which is about 5.23% for displacement and 2.94 for base shear force for all the models.

Fig. 17

Roof displacement time history response of RC frames, retrofitted models

4.3 Incremental dynamic seismic analysis and derivation of fragility functions

Incremental dynamic seismic analysis (IDA) technique, as proposed earlier by Vamvatsikos and Cornell (2002) for structure’s dynamic response analysis and derivation of seismic response curve, and the probabilistic-based nonlinear dynamic reliability based method (NDRM) of Ahmad et al. (2014) are considered for the derivation of fragility functions of the considered as-built and retrofitted RC frame structures. A suit of seven ground motion records were obtained from the PEER NGA strong ground motions database, having moment magnitude M_W in the range of 6–7.5 and source-to-site distance of 10–30 km. Table 9 reports the selected ground motion records, which are carefully selected taking into account the event-to-event and region-to-region variability, and being compatible with the regional tectonics. The selected ground motion records were scaled and matched to the design acceleration spectrum through wavelet-based approach incorporated in SeismoMatch (2016). The matched accelerograms were retrieved and linearly scaled up/down to multiple intensity levels for structures’ incremental seismic analysis in order to retrieve the seismic response demand parameters (roof displacement), which is correlated with the seismic intensity to derive the structures’ response curves, which are employed for the calculation of limit state probability exceedance for specified seismic intensities.

Table 9 Ground motion records extracted from the PEER NGA strong ground motions database, used for incremental dynamic seismic analysis of structures

Both for as-built and haunch retrofitted structures, two-storey representative prototype structure models were considered and numerically modeled in SeismoStruct, like-wise Fig. 15, considering detailing that of Model-3 and Model-5 and their counterpart haunch retrofitted models. Haunch applied at the connection both below and above the beam are considered for Model-5 whereas haunch applied only below the beam is considered for Model-3. Furthermore, since the hysteretic-based energy-dissipating haunch, as designed earlier, has very much similar seismic response in comparison to the stiffer haunch, thereby, only the latter is considered for onward seismic analysis and derivation of fragility functions. Both the as-built and retrofitted structures were analyzed through IDA using the selected accelerograms. Roof displacement response demand under each ground motion record was correlated with the base shear force and seismic intensity in order to derive capacity curves and seismic response curves respectively (Ahmad et al. 2014, 2018).

For derivation of fragility functions, the NDRM method requires structure-specific damage scale to calculate the limit states’ probability of exceedance. A unified procedure was adopted to develop damage scale for each structure, which specifies the limit states’ drift capacity given the structures’ idealized yield and ultimate drift capacities. Figure 18 shows the experimentally obtained force-displacement curves and the idealized bi-linear curves derived based on the energy balance criterion in order to calculate the structures’ idealized yield displacement.

Fig. 18

Lateral force-deformation response of as-built and retrofitted RC frame obtained experimentally and the idealized bi-linear force-displacement capacity curves

Upon exceedance of the yield displacement, most of the structures initiate cracking/damage in the structural components (i.e. beams, columns, joint panels). The ultimate drift capacity of structures is based on the experimentally observed maximum drift capacity at the incipient collapse limit state, essential for the collapse assessment of the structures. Additionally, code specified 2.50% allowable drift limit is also considered for all the structures that correspond to the occurrence of significant damage in the structural components, and essential for the structural performance assessment. For a target seismic intensity level, the roof displacement demand vector is obtained for the time history analysis for all the records, which is convolved with the limit-states’ roof displacement capacity obtained experimentally (Table 10).

Table 10 Damage scales developed for as-built and retrofitted structures

The limit state exceedance probability is computed using the first order reliability method (FORM) approximation (Der Kiureghian 2005) and considering both the demand and capacity lognormally distributed. The limit state probability of exceedance can be calculated as:

$$P_{f} = \varPhi ( - RI)$$

(5)

where P_f is the probability of exceedance, calculated for a specified limit state; Φ is the standard normal cumulative distribution function and RI is the reliability index, calculated using the FORM approximation:

$$RI = \frac{{\lambda_{R} - \lambda_{S} }}{{\sqrt {\zeta_{R}^{2} } + \zeta_{S}^{2} }}$$

(6)

$$\lambda_{R} = \ln (\mu_{R} ) - 0.5\zeta^{2}$$

$$\zeta = \sqrt {\ln (1 + \delta_{R}^{2} )}$$

$$\delta_{R} = \frac{{\sigma_{R} }}{{\mu_{R} }}$$

where μ is the mean value, δ is the coefficient of variation, ζ is the logarithmic standard deviation, λ is the median value, the subscript R represents capacity while S represents demand. These parameters will be obtained for both the demand and the capacity to calculate reliability index RI and the limit state exceedance probability P_f using Eq. (5). Similarly, P_f will be calculated for multiple seismic intensity levels for the limit states, which is correlated with the seismic intensity to derive fragility functions. Figures 19 and 20 shows the derived fragility functions for the considered RC frames, as-built and haunch retrofitted.

Fig. 19

Fragility functions for Model-3. From top to bottom: as-built (left) and haunch-retrofitted applied below the beam (right), and fragility functions comparison

Fig. 20

Fragility functions for Model-5. From top to bottom: as-built (left) and haunch-retrofitted applied below the beam (right), and fragility functions comparison

The fragility functions of both the as-built and retrofitted structures are somewhat comparable for idealized yield limit state damage state but very distinct for code-specified drift limit state. The former is because of the fact that both the as-built and retrofitted structures respond almost similarly in the elastic state but in the inelastic state the as-built RC frames exceed the code-specified drift limit earlier than the retrofitted frames. The later is because of the fact that the haunch retrofitting technique stiffens the beam-column joint and increase the lateral stiffness and strength of structures that consequently retard the damageability of joint under seismic excitation and reduce the probability of exceedance of code drift limit state. However for Model 3, the probability of exceedance of incipient collapse limit state is also very much similar to the as-built structure. It is due to the fact that onset of cracking in the joint panel zones progress damage rapidly in joint panels in case the haunch is applied only below the beam. In case of Model 5, the application of haunch both below and above the beam retard the joint panel damageability, thereby, reduce the probability of exceedance of code drift limit and incipient collapse limit state, particularly in moderate to high seismic intensity. In case of very high seismic intensity, the limit states probability of exceedance of retrofitted structure becomes comparable to as-built structure, and the benefit of haunch retrofit technique cannot be seen in very high seismic intensity (Fig. 23). It is due to the fact that the haunch primarily stiffen the beam-column connection and shift the plastic hinge from joint shear hinging to beam-column member hinging, however, due to non-seismic design nature of beams and columns this doesn’t cause appreciable increase in seismic resistance under very high seismic intensity. Nevertheless, the haunch technique will significantly enhance structure performance under moderate to strong ground shaking.

Fragility functions are extended to derive structures’ vulnerability curve, correlating the mean damage ratio (MDR) of structure with the seismic intensity. The MDR is calculated by analyzing the structural fragility functions for a specified level of seismic intensity i.e. a given level of intensity is considered for which the damage statistics are retrieved, analyzing the fragility functions, that quantify the fraction of building stock in a given damage state e.g. pre-yield, post-yield (pre- and post-code drift limit state) and collapse. The structural-damage to monetary-loss model developed by Bal et al. (2008) is used to transform the structural damage statistics to MDR:

$$MDR_{i} = \sum\limits_{i = 1}^{n} {\sum\limits_{j = 1}^{m} {DS_{j} \times RCR_{j} } }$$

(7)

where MDR_i is the structure mean damage ratio for a specified seismic intensity level i, DSj (DS1, DS2, DS3) is the fraction of structure in a given damage state j, calculated from the fragility functions for a specified seismic intensity, RCR_j (RCR₁ = 0.33, RCR₂ = 1.05, RCR₃ = 1.04) is the repair cost ratio (RCR) of structure for a specified damage state, defined as per the model of Bal et al. (2008). The derived MDR is correlated with the seismic intensity to develop vulnerability curves (Fig. 21). For Model 3, the application of haunch reduce the MDR over the whole range of seismic intensity, whereas for Model 5, the haunch application reduce the MDR particularly in the range of moderate to high seismic intensity.

Fig. 21

Vulnerability curves derived for as-built and haunch retrofitted RC frames

5 Cost-benefit analysis of haunch retrofitting

The PBEE time-based assessment procedure is included to assess the performance of the retrofitting technique, quantifying the seismic performance of structures in terms of average annual loss (AAL). If calculated for both the as-built and retrofitted structures, the annual avoided expenditure due to retrofitting can be quantified, which is summed over the specified life of structure and converted to net present value that is critically compared with the cost of retrofit to assess its viability:

$$NPV = A\left\{ {\frac{{1 - \frac{1}{{(1 + i)^{t} }}}}{i}} \right\}$$

(8)

$$A = AAL_{Retrofitted} - AAL_{{As{ - }Built}}$$

where NPV is the net present value of the annual avoided expenditure due to the use of retrofit, i is the interest rate (internal rate of return), t is the time span over which the assessment is carried out (equal to intended life of a structure). Given the site seismic hazard, presented in terms of seismic hazard curve specifying the annual probability of exceedance of seismic intensity, and the structure’s MDR that specify the RCR correlated with the seismic intensity, both are related to calculate the AAL. For a specified time period (intended life of structure), if the calculated value of NPV is larger than the cost of retrofit, there is economic benefit in retrofitting the structure, because the annual avoided cost is greater than the cost of the retrofit.

5.1 Derivation of seismic hazard curve

Two candidate cities are selected to assess probabilistically the benefit of haunch retrofitting scheme for the considered deficient RC frames. The city of Muzaffarabad, which is in the highest seismic zone (Zone 4, as per the BCP-2007) that was once devastated in 2005 Mw 7.6 Kashmir earthquake, and the city of Jhelum, which is in the moderate seismic zone (Zone 2B, as per the BCP-2007) that have experienced moderate to strong earthquakes. Since, the current building code of Pakistan specifies only the design level ground motions for the region. A classical probabilistic seismic hazard analysis (PSHA) technique was adopted, and that including the most up-to-date developments in procedure (Cornell 1968; Reiter 1999; Gutenberg and Richter 1956; McGuire 2004; Abrahamson 2000; Bommer and Stafford 2009; CRISIS 2007), available catalogue (Zare et al. 2014; USGS, ISC, NGDC, Ambraseys and Douglas 2004; Ambraseys 2000; Kale and Akkar 2003; Scherbaum et al. 2009) and seismic sources (PMD 2007; BCP-SP 2007), to obtain ground motions for various return periods and construct seismic hazard curve (Fig. 22).

Fig. 22

Uniform seismic hazard curve derived for Muzaffarad (left) and Jhelum (right), using classical PSHA procedure

5.2 Calculation of average annual loss and cost-benefit analysis

To calculate the AAL, for a specified seismic intensity, the MDR of structures are retrieved from the vulnerability curve and correlated with the corresponding annual probability of exceedance of seismic intensity, to derive loss exceedance curves (Fig. 23). Haunch retrofitting shift the loss exceedance curve towards the ordinate, which is due to the reduction of mean damage ratio for a specified ground motion, that reduce the area under the loss exceedance curve. For a given structure, the AAL is calculated by integrating the loss exceedance curve, using the Simpson’s rule and numerical integration to estimate AAL:

$$AAL = \sum\limits_{i \to \infty } {\left( {\frac{{APE_{i + 1} - APE_{i} }}{6}} \right) \times (MDR_{i} + 4MDR_{i + 0.5} + MDR_{i + 1} )}$$

(9)

where APE is the annual probability of exceedance of ground motion and MDR is the mean damage ratio, MDR_i+0.5 is approximated as the average of the MDR_i+1 and MDR_i. Table 11 reports the average annual loss computed for both Model-3 and Model-5 (as-built and haunch retrofitted) in both high and moderate hazard regions i.e. Muzaffarabad, which is Zone 4 (design PGA, 0.40 g on rock site) and Jhelum, which is in Zone 2B (design PGA, 0.20 g on rock site), as per the BCP-SP (2007). The AAL computed are incorporated in Eq. (8), to calculate the net present value over the next 50 years. An interest rate of 6% and time span of 50 years are considered. It can be observed that the application of haunch, either applied only below the beam or both above and below the beam, tremendously reduce the average annual loss of the structures.

Fig. 23

Loss exceedance curves derived for both as-built and haunch retrofitted models for Muzaffarad (left) and Jhelum (right)

Table 11 Average annual loss computed for as-built and haunch retrofitted models over the next 50 years (design life of a structure)

6 Conclusions

The experimental shake table tests conducted on nine 1:3 reduced scale RC frames (five as-built and four haunch retrofitted) demonstrated that steel haunch applied either only below the beam or both below and above the beam can significantly enhance the seismic performance of deficient RC frames. The haunch retrofit primarily cause increase in the structure stiffness and strength and to some extent in the structural deformability (nevertheless ductility is enhanced). This increase is relatively more in case the haunches are applied both below and above the beam. The retrofitting shifts the initial damages from joint panel zones to beam and column members and retards the joint panel damages, particularly against moderate to strong excitation. The retrofit also enabled the structures to limit the deformation demand under similar imposed excitation.

The FE based modeling technique using SeismoStruct, as proposed earlier for the inelastic modeling of deficient RC frames with joint shear hinging and beam re-bars slip, which was further extended herein for modeling of haunch retrofitted models. It has shown better performance in simulating the roof displacement response of the structures (both as-built and haunch retrofitted) and predicted the peak roof displacement and peak base shear force demand very reasonably; an average error of 5% in peak displacement prediction and less than 3% error in predicting the peak base shear force, this demonstrates the efficiency of the modeling technique and SeismoStruct software.

The seismic fragility functions derived herein revealed that the haunch retrofitting technique largely reduce the probability of exceedance of code-drift limit states under seismic excitations, which indicates that the haunch retrofitting technique is promising in enhancing the seismic performance of structures, particularly under moderate and strong earthquake shaking. Further, the derived vulnerability curves (MDR versus seismic intensity) show a significant reduction in the repair cost ratio of the structure for a specified ground motion. Similarly, the haunch retrofit technique cause a shift in the loss exceedance curve and reduce the area underneath that result in the reduction of the average annual loss (AAL) of the retrofitted structure. The reduced AAL due to retrofitting bring savings in the annual average loss by avoiding a significant portion of the annual losses. This is further demonstrated through the calculation of the net present value of annual avoided loss over the design life of a structures (i.e. 50 years in present case), which was compared with the retrofit cost that resulted in the cost-benefit ratio of larger than 1.0, indicating the economic benefit of the proposed upgradation, demonstrating the economic viability of haunch retrofitting technique for seismic risk mitigation.