Fragility analysis of masonry infill R.C. frame using incremental dynamic approach

The current study aims to investigate damage assessment of the RC frames with brick masonry infill (BMI). The effects of near-source ground motions (GMs) are considerably predominant in the seismic response of the structure as related to far-source ground motion due to their forward directivity plus long period. The near-source ground motion is characterized by enormous everlasting ground translation, strong peak ground acceleration (PGA), and a very low-frequency pulse. The Indian codes have not yet incorporated the influence of near-source GM into their design response spectra. Hence, IDA curves that represent ground motion uncertainty have been established for ten near-field ground motion records. Further, the fragility curves have been constructed to envisage progressive damage to the structure. The spectral acceleration-based fragility curves for the ten-story RC frames without BMI, with BMI, and with the open ground story are developed. It is proved that the BMI frame shows better performance during seismic motions. The probability of damage for the collapse prevention state is reduced for frames with BMI, and with open-ground story frames as compared to a frame without BMI.


Introduction
Fragility curves are the valuable approach for assessing seismic risk and estimating structural system losses.They depict the chance of reaching or surpassing a damage condition to the extent of the seismic damage to the structure.According to existing Indian Codes, seismic performance evaluations of structures are obtained by conventionally adopted 'strength-based technique'.This technique is deterministic and does not consider the uncertainties and variability associated with the estimation of seismic response and cannot interpret the progressive collapse of the structures.The failures in past earthquakes have shown that research in seismic analysis has to be intended on the evaluation of the susceptibility of the structure by a probabilistic approach.However, many researchers have already investigated and presented empirical and analytical approaches for developing fragility curves for risk management purposes through a probabilistic approach.Su R.K.L. and Le C.L. ( 2013) presented a coefficient-based approach for developing fragility plots for low-rise RC buildings with masonry infill.Dolsek and Fajfar (2008) suggested a very easy and straightforward probabilistic technique for assessing the seismic behaviour of RC frames with brick masonry infill utilizing incremental dynamic analysis with simplified incremental N2 analysis.The research, however, was restricted to four-story structures.Patil V.S. and Tande S.N. (2017) studied the effect of brick infill on ten-story RC frames by varying the percentage of brick infill to 0%, 50% and 100% by using twenty GMs and illustrated that infill enhance structure's resistance against the seismic loads.Phadnis P.P. and Karjinni V.V. (2019) developed capacity spectrum-based fragility curves and demonstrated that the RC frames with masonry infill and appropriate configuration of shear walls have enhanced performance in the seismic event in all modes of various damage levels.Liu C., et al. (2022) estimated the seismic performance targets in terms of the inter-story drift ratio obtained from the extensive literature survey of experimental results.Then, they applied four limit states to assess the failure pattern of masonry infill RC frame structures.Kaveh A., et al. (2020) proved that the proposed optimization method to select GMs and to develop fragility curves is efficient and time-saving with respect to conventional method.Somala S.N. (2022) performed a fragility analysis of existing bridge abutments by imposing future probable seismic events on California faults, as per the Uniform California Earthquake Rupture Forecast (UCERF) utilizing the artificial GM from Southern and Northern California.
The effects of near-source GMs are considerably predominant in the seismic behaviour of the structure as related to far-source GM due to their forward directivity for a plus long period.The near-source GM is characterized by enormous everlasting ground translation, strong PGA, and a very low-frequency pulse (Moniri H., 2017).Hence, the cumulative influences of far-fault GMs are small.At the lower levels of the frame, these ground vibrations cause additional damage.The effect of near-source GMs is more significant for 'soft' and 'weak' story frames (Madan and Hashmi, (2014)).Near-field GMs give rise to a directivity phenomenon.Therefore, uni-lateral and bi-lateral seismic events of identical extent are simulated with an efficient configuration of leading and backward directivity locations.Saha S., et al. (2022) plotted fragility curves to explore the consequence of spatial heterogeneity of near-field GMs.The unpredictability in origin features leads to spatial inconsistency in the nature of near-field GM intensities, which affects the damage probability of the structure during fragility analysis.Such uncertainty in fragility curves of low-rise structures was quantified by Veggalam S., et al. (2021) by using several directivity instances.Fragility plots can be obtained as a function of the actual length from fault in the near-field.Consequently, Karthik Reddy K.S. K., et al. (2022) developed fragility curves by taking into consideration a suite of situations parallel to the strike of the fault, and an additional suite normal to the strike of the fault at several lengths.However, the Indian codes have not yet incorporated the influence of near-source ground motion into their design response spectra.
Hence, in the present paper, the influence of BMI on ten-story RC frames is studied by developing fragility curves which are established by imposing ten near-source ground motion records through Incremental Dynamic Analysis (IDA).The spectral acceleration-based fragility curves for the ten-story RC frames without BMI, with BMI, and with the open ground story are generated for FEMA356-2000 specified damage states.

Methodology to generate fragility curve
Three phases are utilized to execute IDA and to generate fragility plots, namely pre-process, process, and post-process as depicted in Fig. 1.

Numerical study
A 10-story R.C. framed structure 16 m x 16 m in the plan is considered for the production of fragility plots as represented in Fig. 2a.For the proposed example building, first, a linear dynamic analysis is performed for the determination of forces and moments in various frame elements.

Dimensions and material properties
The external and internal wall thickness is considered equal to 230 mm.The slab is treated as a stiff diaphragm with a thickness of 150 mm.The height of each story is 3 m.The loads applied are as follows: a dead load of terrace waterproofing is 1.0 kN/m 2 and the floor finish at all other floors is 1.0 kN/m 2 .The live load is equal to 1.5 kN/m 2 on the roof and 3.0 kN/m 2 on the other floors.The response spectra specified by IS: 1893-2016 are used for analysis.The Indian seismic zone V, soil type II, and response reduction factor equal to 5 are considered for investigation according to IS: 1893-2016.Load combinations are implied as per IS: 456-2000 and IS: 1893-2016.
Figure 2b shows the RC frame without infill i.e. bare frame (BF).In Fig. 2c, to introduce the effect of brick masonry infill, the equivalent diagonal struts are assigned in the RC frame i.e. brick masonry infill frame (BMIF).In Fig. 2d, to introduce the consequence of the soft story all the infill struts of the ground story are removed and considered as the open ground storey (OGS).
The characteristics of the materials utilised in the analysis are enlisted in Table 1.
The nonlinear material data is incorporated by using Mander's model and Park's model for concrete and reinforcement respectively (Mander J.B., et al., 1988).Mander's stress-strain curve uses yield tensile strength of concrete as (7.5√f c ' in psi = 451.62psi = 3.11 N/mm 2 ).For plain concrete, tensile yielding is not observed with respect to time.Hence, the yield and ultimate tensile strength are the same for the concrete.
Tables 2 and 3 show the schedule of reinforcement in columns and beams, respectively.

Nonlinear modelling of frame elements
Beams and columns are modelled as a link element, assigning associated nonlinear properties (Kaveh A., 2014).The two approaches are available for assigning nonlinearities to the link element.The first approach is lumped plasticity approach and the second approach is distributed plasticity (or fibre-based approach).The lumped plasticity is allocated for prismatic sections.The distributed plasticity is assigned to a non-prismatic element like columns of flat slabs.Hence, lumped plasticity approach has been adopted in the present research work to assign flexural and shear nonlinearity to the beams and columns.The user-defined or code-defined (default) plastic hinges are assigned to frame elements to incorporate material nonlinearity.User-defined approaches require moment-curvature and moment-rotation analysis to estimate yield and ultimate values of rotation.Inel M. and Ozmen H.B. (2006) revealed that user-defined plastic hinges provide superior outcomes for the nonlinear analysis of RC frames.However, the analysis is complex and cumbersome, which involves the effect of compressive strength of materials and reinforcement, provided in tension zone and confinement steel percentage information.The code-specified technique is very simple.It assigns the characteristics to the hinges prescribed in FEMA 356-2000.To minimise computational efforts, in the present study the default hinges described by FEMA 356-2000 are employed.
The columns are allocated with axial force-moment interaction (P-M-M) hinges and shear hinges at the boundaries of the section as proposed by Cinitha, et al. (2012), Raju, et al. (2012), Phadnis P.P. and Karjinni V.V. (2019) and Phadnis P.P. (2022).The beams are allocated with moment (M3) hinges and shear hinges at the end regions.
To describe the finite size of joints, two rigid sectors are contemplated at the boundaries.The inclusion of plastic hinges resulted in the concentration of all nonlinearity on the faces of the joints and components.The beam part is deemed elastic between two hinges at the ends.
The non-linear behaviour is due to both non-linear material and geometry is essential to incorporate in the study (Kaveh A., et al. 2021).Hence, in this study, geometric nonlinearity, the P-delta effect is also considered along with material nonlinearity.

Nonlinear modelling of brick masonry infill
Infill is very stiff in its own plane and attracts a larger amount of lateral force.As infill is brittle in nature, it cracks and these cracks dissipate energy during seismic loading which is cyclic in nature.Inclusion of BMI, the initial stiffness of the frame increases but as infill cracks, the stiffness reduces abruptly.The modelling of BMI is always a challenging issue due to complex frame-infill interaction under seismic loading.Micro modelling is based on the finite element approach and is suitable for specific types of study like the modelling of frame and infill interaction, the effect of opening on the behaviour of infill etc.In the interest of the global behaviour of the building, macro modelling is the simple approach and is adopted in the present research study.When the infill is strong enough so that the sliding failure occurs in the frame, various researchers such as Wael El-Dakhakhni, et al. (2004) and Mosalam K.M., et al. (2015), have proposed a multi-strut approach model.However, the single strut approach proposed by Smith andCarter (1970), andFEMA 273 (1997) is the simplest and reasonably accurate approach of modelling the infill to estimate the lateral strength and stiffness of the infill frame.Kaushik H.B., et al. (2007), state the information used for the assessment of the width of the BMI diagonal strut.The stress-strain relation used for BMI for 1:3 mortar is as designated in Fig. 3.The unit weight and modulus of elasticity for brick masonry are 20 kN/m 3 and 4200 N/mm 2 respectively.In the present research work, BMI is modelled as a single equivalent strut technique prescribed by IS:1893-2016 and is determined by utilizing EQs. ( 1) and ( 2).
The width of the diagonal strut, where, where E m and E f are the moduli of elasticity of the materials of BMI and RC frame, I c is the M.I. of the column, t is the infill thickness, θ is the angle of the diagonal strut, L ds is the span of equivalent diagonal strut and h is the exact distance of infill from the top and bottom beam of the floor slab.
The obtained dimensions of the equivalent diagonal strut are listed in Table 4.
A pin-connected compression link element has been assigned as a strut by replacing the BMI using dimensions depicted in Table 4 and pin-connected at both ends.The nonlinearity of strut is allocated by assigning axial 'P' hinge at the centre of strut. (1)

Dynamic properties of building
Modal analysis is performed to determine the dynamic properties of example buildings in SAP 2000 software.
The time period obtained from empirical formulae from IS: 1893-2016 Part I.The fundamental translational period T a is estimated by using Eqs.( 3) and (4).
For bare frame: For brick masonry infill frame and open ground storey frame buildings where, h = height of the building in meter, d = plan dimension of the structure at the plinth height along the intended direction of earthquake shaking in meter The results obtained from software analysis and using empirical formulae from IS:1893-2016 Part I are presented in Table 5.
The fundamental natural time period for BMIF and OGS models is reduced by 46%, and 42% in comparison with the BF model for the first mode.This indicates that the inclusion of infill panels reduces the fundamental natural period due to an enhancement in stiffness.The fundamental natural time period evaluated from empirical codal specifications proves that the empirical formula results in much lesser time periods imposing more base shear on the building and exerts conservative design.

Incremental dynamic analysis
Incremental dynamic analysis (IDA) is a promising approach that has recently risen to meet the needs of performancebased seismic analysis.The first important phase of IDA is the choice of IM and DM.IM increased progressively with respect to the scale factor for each GM record.IMs of seismic activity are measured in terms of Peak Ground Acceleration (PGA), Peak Ground Velocity (PGV) or 1st mode spectral acceleration at 5% damping S a (T1,5%).The    2013)).Here, extreme inter-story drift is utilized as the DM as many of the design codes have prescribed different limit states based on extreme inter-story drift values.
To execute IDA and obtain consistent results, a set of GM records must be chosen.The amount of GM records to employ in nonlinear time history analysis (NLTHA) is a topic of debate.The sort of structure responses i.e. distribution or mean value of responses are essential, the accuracy of the response, the probable degree of inelastic response, and the expected estimation of collapse response are the influencing factors to decide the number of GMs.As a result, the quantity of GMs in each research differs.According to Vamvatsikos andCornell (2002a, 2002b), 10 to 20 GMs are generally adequate to predict seismic performance with acceptable precision for medium-rise buildings, whereas Haselton, et al. (2011) recommended at least 7 GMs for the IDA.In this research, 10 near-field GMs are selected as per FEMA 695P criteria and enlisted in Table 6.
The actual GMs at different places have variations in forms of PGA, frequency content and period.The next step in IDA is scaling the chosen ground motion records for definite parameters to reduce variability in capacity estimates.Many researchers (Vamvatsikos D. andCornell C.A. (2002b), Shakib H. andPirizadeh M. (2014)) and different codes of developed countries (ASCE/SEI 7-10-2007, FEMA P695-2009) have specified different techniques for scaling of GMs.In current research work, Vamvatsikos and Cornell (2002b) prescribed a 'simple technique' for the direct scaling of GMs.In this technique, normalised spectral acceleration for the fundamental mode at 5% damping is implemented.Here, designated GMs are scaled to the fundamental natural period of the buildings individually to decrease the variation between the design response spectrum and the GM response spectrum.
In IDA, nonlinear time history analysis is performed using the selected set of scaled GMs for the nonlinear structural model.The scale factor is progressively increased until the structure develops a collapse mechanism.Here, the IM values of GMs are increased in intermissions of 0.1 for IM values.
In the present work, the IM magnitudes of accelerograms are increased in the spell of 0.1 for IM values.By plotting the results of DM and IM for each GM, IDA curves along the x-direction are developed for all three building frames.The resulting IDA curves for maximum responses are depicted in Fig. 4.
The variation of the upper and lower limit of DM or IM for a selected value of IM or DM is known as dispersion.The dispersion is estimated for all three structures in the X-direction for both DM at the specified IM (= 1.0 g) and IM at the specified DM (= 4% inter-story drift), is shown in Table 7.
From Table 7, the dispersion of damage measures (DM) are less than 88.97% and 83.27% respectively in the case of BMIF and OGS as compared to BF models.The dispersion of intensity measures (IM) are less by 15.56% and 11.11% respectively for the BMIF and OGS as compared to BF models.Thus the provision of infill improves the robustness of the building responses and hence causes predictability in design.
The median (50% fractile) IDA curves for BF, OGS and BMIF models are presented in Fig. 5 to predict strength and stiffness with respect to IM.
From Fig. 5, the yielding values of IM [S a (T1,5%)g] are enlisted in Table 8.The ductility of the frames is evaluated as μ = Δ u /Δ y , where Δ u is ultimate lateral displacement and Δ y is the lateral displacement at yield and also shown in Table 8.
From Fig. 5 and Table 8, it has observed that, median IDA curve is comparatively yielded at lower values of IM [S a (T1,5%)g = 1.9] indicating low resistance to seismic loading.The median IDA plots for OGS and BMIF models as represented in Fig. 5 are comparatively yielded at higher values of IM [S a (T1,5%)g = 2.5 and 3.3, respectively] in the linear range.This yielding is observed in the BMI.With a further increase in IM, the structure loses stiffness rapidly.This is due to truss action of BMI, high axial forces developed in the columns resulting into failure of columns.From Table 8, it is demonstrated that displacement ductility of BMIF and OGS models are improved by 63.20% and 39.71%.This improvement of displacement ductility is observed because of combined action of frame and BMI.This behaviour indicates that due inclusion of BMI, the strength and artificial stiffness of the structure considerably increased in the linear range.For the OGS model, because  It is seen from Fig. 6a for BF, hinges have been generated in distributed manner first in beams and then in columns.As BMI is the weakest material, hinge development started in struts as presented in Fig. 6b and then extended to frame elements.At higher stage of seismic intensity, hinges formed in ground storey columns, also, depicting weak storey mechanism in OGS (Fig. 6c) and at the first floor level the initial failure observed in BMI and hinges of IO levels are formed in columns.

Fragility analysis
The fragility curve is the function of probabilities of damage that exceed certain limit states.Here, only GM variation is involved in plotting the fragility curves.For a specified damage limit state, a fragility plot is well prescribed by the lognormal probability density function through the EQs.( 5) to (7): where F x (X) is the probability that a GM with IM = x will lead the structure to failure, Φ is the standard normal cumulative distribution function (CDF),λ is the median of ln(IM) i.e.
is the standard deviation of ln(IM) i.e.
The standard deviation for each fragility curve is determined by employing a constrained least-squares procedure.Table 9 represents the fragility curve estimated parameter for three building models.
Three damage limit states are demonstrated Immediate Occupancy (IO), Life Safety (LS) and Collapse Prevention (CP).IO, LS and CP limit-states appeared at maximum inter-story drift on the IDA curve equal to 1%, 2% and 4% respectively as per FEMA356-2000.The fragility plots of considered three frames for three different limit states are revealed in Fig. 7a, b, c).
From Fig. 7, it is noticed that the BMIF and OGS models have wider fragility curves as compared to the BF model.
(      According to Fig. 8, for an arbitrarily selected value of spectral acceleration equal to 2.5 g, the BMIF model develops a 26% probability of no damage.The chances of no damage probability for BF and OGS models are almost 0%.The BMIF and OGS models develop 58% and 33% more concerning BF at immediate occupancy damage.While for the same spectral acceleration, the life safety damage state for the OGS model is observed to be increased by 58% due to the development of hinges in the columns of the open ground story.The collapse probability for BMIF and OGS models is 86% and 83% less than the BF model, respectively.It indicates that the inclusion of brick infill reduces the collapse prevention damage of the structures.

Conclusions
The prime objective of this research is to use near-field GMs dependent incremental dynamic analysis to demonstrate how brick infill affects the seismic fragility of a medium-rise RC building.For three ten-story RC structures, spectral acceleration-based fragility curves are generated and compared.For these three structures, 3 limit states (IO, LS and CP) are considered to determine progressive damage.The conclusions are summarized below.1.The fundamental natural time period for BMIF and OGS models is reduced by 46%, and 42% in comparison with the BF model for the first mode.This indicates that the inclusion of infill panels reduces the fundamental natural period due to an increase in stiffness.2. IDA curve of BF is comparatively yielded at lower values of IM [S a (T1,5%)g = 1.9] indicating low resistance to seismic loading.BMIF and OGS models are comparatively yielded at higher values of IM [S a (T1,5%) g = 2.5 and 3.3, respectively] in the linear range.With a further increase in IM, the structure loses stiffness rapidly.This behaviour indicates that due inclusion of infill, the strength and stiffness of the structure considerably increased in the linear range.For the OGS model, because of the soft story mechanism, the stiffness and strength of columns on the parking floor reduce and thus show poor performance as compared to the BMIF model.

Fig. 2
Fig. 2 Plan and elevations of RC frames

Fig. 3
Fig. 3 Stress-strain relation for BMI (-ve sign indicates stress-strain curve for compression)

Fig. 4 Fig. 5
Fig. 4 IDA curves of buildings in X-direction

Figure. 6
Figure.6 shows the hinge pattern for BF, BMIF and OGS for GM 5.It is seen from Fig.6afor BF, hinges have been generated in distributed manner first in beams and then in columns.As BMI is the weakest material, hinge development started in struts as presented in Fig.6band then extended to frame elements.At higher stage of seismic intensity, hinges formed in ground storey columns, also, depicting weak storey mechanism in OGS (Fig.6c) and at the first floor level the initial failure observed in BMI and hinges of IO levels are formed in columns.

Figure 8
represents the discrete damage probability established from the fragility curves of BF, BMIF and OGS models applying Eqs.(8).Probability of Complete Prevention, P[CP] = P[CP|S a ].Probability of Life Safety, P[LS] = P[CP|S a ]-P[LS|S a ].P r o b a b i l i t y o f I m m e d i a t e O c c u p a n c y, P[IO] = P[LS|S a ]-P[IO|S a ].Probability of No damage, (8) P[ND] = 100 − P IO|S a −−P LS|S a − P CP|S a Fig. 7 Fragility curves

Fig. 8
Fig.8Discrete damage probabilities at S a = 2.5 g

Table 1
Material properties

Table 4
Dimensions of Diagonal Strut

Table 5
Fundamental time period

Table 6
Set of ten near-field ground motion records

Table 8
Yield IM and ductility of frames