Fragility Analysis of Masonry Infill R.C. Frame Using Incremental Dynamic Approach

doi:10.21203/rs.3.rs-2872511/v1

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 damage state is reduced for frames with BMI, and with open-ground story frames as compared to a frame without BMI.

Nonlinear modelling

Incremental dynamic analysis

Fragility analysis

Brick masonry infill

Equivalent strut

Probability of damage

Fragility curves are a 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 can't 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. R.K.L. Su and C.L. Le (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. V.S. Patil and S.N. Tande (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. P.P. Phadnis and V.V. Karjinni (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. C. Liu, 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. S.N. Somala (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 (H. Moniri, 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. S. Saha, 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 S. Veggalam (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, K.S.K. Karthik Reddy, 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).

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

A 10-story R.C. framed structure 16mx16m in the plan is considered for the production of fragility plots as represented in Fig. 2(a). For the proposed example building, first, a linear dynamic analysis is performed for the determination of forces and moments in various frame elements.

3.1 Dimensions and Material Properties

The external and internal wall thickness is considered equal to 230mm. The slab is treated as a stiff diaphragm with a thickness of 150mm. The height of each story is 3m. The loads applied are as follows: A dead load of terrace water-proofing is 1.0kN/m²and the floor finish at all other floors is 1.0kN/m². The live load is equal to 1.5kN/m² on the roof and 3.0kN/m² 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 2 (b) shows the RC frame without infill i.e. bare frame (BF). In Fig. 2 (c), 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. 2 (d), 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.

Table 1

Material properties
Sr. No.	Material	Grade	Specified Compressive Strength (f_ck)	Yield Tensile Strength	Ultimate Tensile Strength	Elastic Modulus
1.	Concrete	M25	25 N/mm²	3.11N/mm²	3.11 N/mm²	25000N/mm²
2.	Rebar	Fe415	---	415 N/mm²	485 N/mm²	2.0×10⁵ N/mm²

The nonlinear material data is incorporated by using Mander’s model and Park’s model for concrete and reinforcement respectively (J.B. Mander, et al., 1988). Mander’s stress-strain curve uses yield tensile strength of concrete as (7.5√f_c^’ in psi = 451.62 psi = 3.11 N/mm²). For plain concrete, tensile yielding is not observed w.r.t. 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.

Table 2

Reinforcement details in Columns
Column	Size in mm	Main Reinforcement	Shear Reinforcement	Remark
C1	500 x 500	14–25 #	8 # @ 150c/c	Up to story 3
C2	450 x 450	12–20 #	8 # @ 150c/c	Story 3 to 6
C3	450 x 450	8–16 #	8 # @ 150c/c	Story7 to 8
C4	400 x 400	8–16 #	8 # @ 150c/c	Story 9 to 10

Table 3

Beams Detailing
Beams	Size in mm	Main steel		Shear Reinforcement	Remark
Beams	Size in mm	At top	At bottom	Shear Reinforcement	Remark
B1	300 x 450	4–16 #	4–16 #	8 # @ 250c/c	Up to story 5
B2	300 x 450	3–16 #	4–16 #	8 # @ 250c/c	Story 6 to 10

3.2 Nonlinear modelling of frame elements

3.2.1 Nonlinear modelling of frame elements

Beams and columns are modelled as a link element, assigning associated nonlinear properties. 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. M. Inel and H.B. Ozmen (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), P.P. Phadnis and V.V. Karjinni (2019) and P.P. Phadnis (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. For geometric nonlinearity, the P-delta effect is also considered.

3.2.2 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. Ininclusionof 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 the specific type of study like 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 as Wael El-Dakhakhni, et al. (2004) and K.M. Mosalam, et al. (2015), have proposed a multi-strut approach model. However, the single strut approach proposed by Smith and Carter (1970), and FEMA 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, 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 20kN/m² and 4200N/mm² 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,

$${w}_{ds}= 0.175{\alpha }_{h}^{-0.4}{L}_{ds}$$

1

Where,

$${\alpha }_{h}=h\left(\sqrt[4]{\frac{{E}_{m}tsin\theta }{4{E}_{f}{I}_{c}h}}\right)$$

2

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.

Table 4

Dimensions of Diagonal Strut
Story	Dimensions of Diagonal Strut
Up to Story 3	230mm x 545mm
Story 3 to 8	230mm x 525mm
Story 9 to 10	230mm x 505mm

A pin-connected link element has been assigned as a strut by replacing the BMI using dimensions depicted in Table 4 and pin-connected at both ends.

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 EQ.s (3) and (4).

For bare frame:

$${T}_{a}=0.075{h}^{0.75}$$

3

For brick masonry infill frame and open ground storey frame buildings

$${T}_{a}=\frac{0.09h}{\sqrt{d}}$$

4

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.

Table 5

Fundamental time period
Building Model	Fundamental Time period (sec) obtained from
Building Model	Software analysis	IS: 1893–2016 Part 1 empirical formulae
BF	1.46	0.961
BMIF	0.783	0.675
OGS	0.854	0.675

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 (IDA) is a promising approach that has recently risen to meet the needs of performance-based 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 S_a(T1,5%) accord more consistent outcomes than any other IM. [R.P. Dhakal, et al. (2007)]. The seismic response of the smaller fundamental period structure is controlled by S_a(T1)which reveals both ground and structural response [N. Luco and C.A. Cornell (2007)], hence it is used as an IM in the present research. The structural responses subjected to horizontal loads like base shear, extreme drift value, and extreme inter-story drift can be indicated with reference to Damage Measure (DM). The selection of DM is governed by the objective of the analysis, for example, lateral deformations and inter-story drifts are the utmost general for dynamic analysis [T.L. Kravasilis, et al. (2006), X. Ramao, et al. (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 and Cornell (2002), 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.

Table 6

Set of ten near-field ground motion records
GM	RSN	Event	Magnitude	R_jb(km)	PGA (g)
1	77	San Fernando	6.61	0	1.22
2	126	Gazli USSR	6.8	3.92	0.86
3	143	Tabas Iran	7.35	1.79	0.85
4	495	Nahani Canada	6.76	2.48	1.10
5	825	Cape Mendocino	7.01	0	1.49
6	864	Lander	7.28	11.03	0.27
7	1077	Northridge	6.69	7.28	0.75
8	1111	Kobe Japan	6.9	7.08	0.48
9	1602	Duzec Turkey	7.14	12.02	0.80
10	4895	Chuetsu Oki	6.8	0	1.12

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 [D. Vamvatsikos and C.A. Cornell (2002b), H. Shakib and M. Pirizadeh (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. Here, the IM values of GMs are increased in intermissions of 0.1 for IM values.

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.

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 ensuing IDA curves for maximum responses are depicted in Fig. 4.

For the BF model as shown in Fig. 4(a), IDA curves are comparatively yielded at lower values of IM [S_a(T1,5%)g < 3.5] indicating low resistance to seismic loading. The plots for BMIF and OGS models as represented in Fig. 4(b) and (c) are comparatively yielded at higher values of IM [S_a(T1,5%)g < 5 and 4 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.

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), with the results shown in table 7.

Table 7

DM and IM dispersions for the three building models
Model	DM-Dispersion (%)	IM-Dispersion(g)
BF	2.81	2.25
BMIF	0.31	1.9
OGS	0.47	2.0

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 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):

$${F}_{x}\left(X\right)=\varPhi \left(\frac{{ln}\left(X\right)-\lambda }{\beta }\right)$$

5

Where

${F}_{x}\left(X\right)$ is the probability that a GM with IM = x will lead the structure to failure,

$\varPhi$ is the standard normal cumulative distribution function (CDF),

Λ is the median of ln(IM)i.e. $\lambda =\sum _{i=1}^{N}\frac{ln{[S}_{a}({T}_{1},5\%)]}{N}$ (6)

$\beta$ is the standard deviation of ln(IM) i.e. $\beta =\sqrt{\frac{\sum _{i=1}^{N}{\left[ln\left({x}_{i}-\lambda \right)\right]}^{2}}{N-1}}$ (7)

The standard deviation for each fragility curve is determined by employing a constrained least-squares procedure. Table 8 represents the fragility curve estimated parameter for three building models.

Table 8

Fragility curve parameters
Fragility Parameters	BF			BMIF			OGS
Fragility Parameters	IO	LS	CP	IO	LS	CP	IO	LS	CP
λ	-0.941	-0.241	0.451	0.742	1.182	1.718	0.299	0.774	1.336
β	0.335	0.394	0.430	0.263	0.273	0.285	0.199	0.213	0.226

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. 5 (a), (b) and (c).

From Fig. 5, it is noticed that the BMIF and OGS models have wider fragility curves as compared to the BF model. It indicates that the inclusion of the consequence of BMI walls improves the building stiffness. However, the fragility curves for the first two damage states for the OGS model are closer than the BF model. It indicates that the OGS model was subjected to life safety damage at the earliest state as compared to the BF model.

Figure 6 represents the discrete damage probability established from the fragility curves of BF, BMIF and OGS models applying equations specified by P.P. Phadnis and V.V. Karjinni (2021).

According to Fig. 6, for a spectral acceleration equal to 2.5g, 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.

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.

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.
For the BF model, IDA curves are comparatively yielded at lower values of IM [Sa(T1,5%)g< 3.5] indicating low resistance to seismic loading. The curves for BMIF and OGS models are comparatively yielded at higher values of IM [Sa(T1,5%)g < 5 and 4 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.
The dispersion of Damage Measures (DM) in Multi IDA curves is 89% and 83% lower in brick masonry infill frame (BMIF) and open ground story brick masonry infill frame (OGS), respectively than the bare frame (BF), improving the resilience of the building reaction and resulting in design predictability.
Fragility curves for brick masonry infill frame (BMIF) revealed more resistance to collapse due to the inclusion of infill which increases lateral stiffness. While open ground story brick masonry infill frame (OGS) has shown early moderate damage due to decreased lateral stiffness at the ground story. While the bare frame (BF) model has shown early damage in moderate and severe damage states due to the least lateral stiffness.
Infill walls enhance the building's seismic resistance against the seismic loads and decrease GMs' record-to-record inconsistency and uncertainty in IDA, thus improving the robustness of the building seismic response results, which attains predictability design results.

Conflict of interest

On behalf of all authors, I (the corresponding author) declare that there is no conflict of interest.

Funds

The specific funds are not utilized for this research work.

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No competing interests reported.

Fragility Analysis of Masonry Infill R.C. Frame Using Incremental Dynamic Approach

Status:

Version 1

Abstract

Figures

1. Introduction

2. Methodology to generate fragility curve

3. Numerical study

3.1 Dimensions and Material Properties

3.2 Nonlinear modelling of frame elements

3.2.1 Nonlinear modelling of frame elements

3.2.2 Nonlinear Modelling of brick masonry infill

4. Dynamic properties of building

5. Incremental dynamic analysis

6. Fragility analysis

Conclusions

Declarations

References

Additional Declarations

Status:

Version 1