Introduction
Intensive experimental and numerical research have been conducted on infilled reinforced concrete (RC) structures in the past decades in order to understand the influence of infill walls (either masonry or concrete) in the local and global behavior of frame structures [
1–
9]. However, a conclusive and reliable design approach has not been proposed yet, likely due to large uncertainties associated with unreinforced masonry (URM) properties. The RC buildings infilled with URM are common construction practice around the globe, and also one of the most common building typologies in highly seismic region potentially due to easy availability of construction material, lower construction cost and easy availability of labors and technicians.
The use of masonry infill walls in the RC frame structure can have positive and negative effects under earthquake actions. The positive contribution could be considerable increase in the global stiffness and strength capacity of the infilled RC buildings. The increase might be many folds higher relatively compared to the bare framed buildings, and if not considered in the design, it could lead to an unexpected seismic behavior of the global RC buildings [
10,
11]. This statement aligned with the findings derived from the past experimental and numerical researches [
1–
9]. Holmes [
12,
13] tests result shows that the strength of the steel frame infilled with RC walls increases by 400%, whereas it increases by 100% if infilled with brick masonry. Similarly, Bertero and Brokken [
14] concluded that the building stiffness increases from 366% to 944% depending upon the variation in the layout of the infill walls. Despite large positive contribution evidences; negative influence instigated by the irregular distribution of infill walls contribute to the structural failures (i.e., soft-storey, short-column mechanisms), observed from several post-earthquake field survey performed by Gautam et al. [
15] and also in the post-earthquake field survey conducted in Nepal after 25th April, 2015, Gorkha earthquake [
16–
19]. In addition, Varum [
11] also revealed that the infill walls along with the surrounding frames behaves monolithically in resisting the lateral forces but for low to medium magnitude earthquakes. For larger magnitude earthquakes, the structure can suffer severe damage or even collapse, due to several local and global mechanisms introduced by the infill walls. Figure 1 presents non-engineered and engineered buildings that collapsed during the Gorkha earthquake, mainly caused by the in-plane crushing and out-of-plane failure of the infill walls, thus leading soft-storey and in some cases, short-column and shear cracks in columns.
Limitation of design codes and scope of the work
To discourage the haphazard RC building construction practice, the Government of Nepal under Department of Urban Planning proposed, approved and implemented design codes since AD 2004. The present paper discussed the limitations in relation to two design codes; namely, Nepal Building Code (NBC 205: 1994) [
20] later revised as NBC 205: 2012 [
21] and NBC 201: 1994 [
22], both known as Mandatory Rule of Thumb (MRT). These guidelines provide a ready to use dimensions for various structural and non-structural and detailing of low-rise RC buildings (up to three storeys). It is generally useful for low level technicians or skilled manpower to build seismically safe buildings without consulting design engineers. As previously discussed, although the infill walls demonstrate both positive and negative influence in the global building performance, the above defined codes could not materialize its contribution in the design of RC buildings. Both NBC 205: 1994 [
20] and revised NBC 205: 2012 [
21] guidelines stated in Clause 4.1 that the frame should be designed as bare frame to resist earthquake forces excluding the influence of infill walls, but in reality, the bare frame building does not exist. NBC 201: 1994 [
22] attempts to integrate the influence of infill walls in carrying the horizontal loads by equivalent compressive strut action, modeled together with the surrounding frames (assumed as pin-jointed), as presented in Fig. 2. A limitation exist in NBC 201: 1994 [
22], where Clause 4.2 (i) stated that the infill walls with opening less than 10% of the gross panel area should only be considered in resisting seismic loads. This does not correlate with the actual RC building construction practice in Nepal, where almost 30-40% openings were usually observed, mostly in the external infill walls as illustrated in Fig. 1. In addition, these guidelines are suitable for RC buildings up to three storeys. But in reality, the owner or stakeholders utilize it only for drawing approval from the concerned authorities and later modified adding more storeys. This can be justified from recorded buildings during site survey after Gorkha earthquakes in Nepal illustrated in Fig. 1. Chaulagain et al. [
23] report also stated that most of the RC building in urban areas of Nepal were 2–6 storeys. This concludes that the past and present construction practises does not comply with both guidelines in relation to number of storeys and infill walls openings and distribution. Furthermore, Chaulagain et al. [
23] studied and published excellent work on the regular three storeys prototype building, modeled as bare frame and designed based on different design approaches. They concluded that NBC building was highly vulnerable to earthquakes. Similarly, Chaulagain et al. [
10] studied three storeys building designed based on three approaches whose structural sections were identical with NBC 205: 1994 [
20]. In this case, building analyzed as bare framed and fully infilled, and concluded that infill walls increases the stiffness and strength capacity and also the seismic performance of the building, hence, its influence should not be neglected.
Taking account all these considerations, the present study aims to investigate performance assessment of the revised MRT building, also an extension of the previous work carried out by Chaulagain et al. [
10,
23]. The primary objective of the present study is to examine the seismic performance of the prototype building whose structural sections and details were initially defined for three-storey bare frame building, which was later modified with different arrangement of infill walls (considered three cases) and finally added number of storeys (four and five storeys). In this manner, the study aims to integrate the past and present construction scenario, i.e., modification in the building, and thus attained results and conclusions expected to be beneficial to convince and make cognizant concerned authorities, stakeholders, owners and clients from likely vulnerability from building’s modifications.
Description of case study building
General description
As stated earlier that the primary objective of the present research was the vulnerability assessment of the prototype building designed based on revised NBC 205: 2012 [
21] and later modified by adding the number of storeys and different disposition of infill walls. The revised MRT guideline was only mandatory in 2015 after Gorkha earthquake, thus it was difficult to find real buildings; however, the present research finding could be used to generalize and also helps to check the adequacy of the structural section size as defined in the guideline. To meet the objective, initially a regular three-storey building was selected having three bays in the longer direction represented by
X-axis and two bays in the shorter direction represented along
Y-axis, as shown in Fig. 3. The second stage deals with the different arrangements of infill walls throughout the building. Although large arrays of infill walls configuration exists, the present research consider three arrangements, representing most built building types in urban and rural areas of Nepal. This includes building without infill walls at the ground floor (soft-storey) represented as WO-GI that resembles commercial buildings where ground floor used for storage and parking purposes; building with one complete bay without infill walls also known as irregularly infilled building and denoted by W-Irre.-I, which are commonly practised in residential building utilizing road facing side for commercial purpose; and finally the building with fully infilled represented by W-I. All the external walls were assumed to possess opening of around 30% of the gross panel area and provided at the periphery of the building, whereas the internal infill walls used as partition. The third and final stage was the investigation in the building seismic performance due to adding number of storeys. Therefore, the building was classified into three groups, i.e., 3-storey (MRT-3), 4-storey (MRT-4), and 5-storey (MRT-5) representing majority of the building types in Nepal. Altogether 12 building models considered for the study were presented in Table 1.
Geometrical and material properties
A typical layout of the prototype building along with structural dimensions and section details was presented in Fig. 3. The study considers a regular plan layout and all structural dimensions and cross-sections assumed similar for considered building groups. Each span in the longer direction (
X-axis) assumed to be equal of 3.75 m and short direction (
Y-axis) of 3.5 m. A constant inter-storey height of 2.75 m was considered, thus the total height of the MRT-3 was 8.25 m, MRT-4 was 11 m and MRT-5 was 13.75 m. In addition to the similar geometrical plan and sections, all the building groups have similar geometrical and material properties, loading conditions, same structural section sizes and reinforcement details. As previously stated, these assumptions were based on the past and present construction scenario across Nepal, as a consequence some representative damaged/collapsed RC building recorded during site survey after Gorkha earthquake, as presented in Fig. 1. The external infill walls of 230 mm thickness with 30% opening considered and located at the periphery of the building. In addition, the internal infill walls of 110 mm thickness considered and placed internally, functioning as the partition walls in the building. It is to be noted that the infill walls used consists heavy solid bricks of size 240mm × 115mm × 57 mm along with 10 mm horizontal and vertical mortar joints. The entire column sections was similar having sections 300mm×300 mm and uniform beam sections of 230mm×355 mm including 125 mm slab thickness [
21]. Depending upon the position of columns and beams, the reinforcement details were assigned as defined in the revised NBC 205: 2012 [
21], as presented in Tables 2 and 3. The position of columns was characterized as corner, intermediate and interior. Similarly, the beams were classified into two groups; namely, end and intermediate. The lateral reinforcement assumed two legged ofΦ 8 spaced 100 mm center throughout the column and beam height. All the stirrups were hooked at 45° with length of 75 mm at each end. The effective cover for columns and beams were provided with 40 and 25 mm, respectively. Furthermore, a layout and section details similar to three storeys was repeated to obtain four and five storeys building configurations.
In addition to similar geometrical layout, section and reinforcement details; the material properties for the concrete, infill walls and reinforcement, and loading conditions were also assumed similar for variable number of storeys (three, four, and five). The concrete and steel material properties obtained from NBC 205: 2012 [
21] and infill walls properties from NBC 201: 1994 [
22] and IS 1893 (Part 1): 2002 [
24] presented in Table 4. The various live loads subjected in the buildings were assigned as defined in IS 1893 (Part 1): 2002 [
24] and NBC 105: 1994 [
25], as presented in Table 5.
Numerical modeling
Vu-Bac et al. [
26] and Hamdia et al. [
27] proposed a MATLAB toolbox that can be utilized to randomly generate samples, construct the surrogate model and carry out the sensitivity analysis. In the present study, the selected buildings were modeled using SeismoStruct software [
28], which is based on finite element analysis and is capable of predicting large displacement behavior of space frames under static or dynamic loading considering material inelasticity and geometrical nonlinearities. The accuracy of the software was evaluated through the comparison between experimental and numerical results. For this, the software offers verification reports that contain large set of assumptions in the model and its validation with the experimental results through linear to nonlinear analyses. In addition, Smyrou et al. [
29] and Rodrigues et al
. [
30] also performed large set of numerical analyses and concluded that SeismoStruct results hold a good agreement with the experimental results.
The beam and column elements were modeled as 3-D inelastic forced-based frame element type, connecting two adjacent nodes. These elements were discretized into 5 integration sections and at the equilibrium section level, the number of fibers was set 150. This fiber-based approach represents the cross-section behavior associated with uniaxial stress-strain relationship proposed by Rodrigues et al. [
30]. At the element level, the distributed plasticity approach was used to model the nonlinearities of beam-column members. The concrete uniaxial material model is based on the constitutive relationship proposed by Mander et al. [
31] and cyclic rule proposed by Martínez-Rueda and Elnashai [
32], initially programmed by Madas and Elnashai [
33] that is based on uniaxial nonlinear constant confinement model. Lateral transverse reinforcement confinement effect was incorporated by Mander et al., [
4], whereby constant confining pressure assumed throughout entire stress-strain range. Uniaxial steel model as proposed by Menegotto and Pinto [
34], coupled with isotropic hardening rules proposed by Filippou and Fenves. Bauschinger effect [
35] was considered in this model to represent the steel degradation and consequently both the concrete and steel (i.e., column stiffness) degradation under cyclic loading [
8]. It is to be noted that the present modeling strategy is based on fiber-based approach and does not consider the nonlinear shear behavior. In addition, shear failure in RC columns may occurs during seismic events and in cases, where masonry infill walls with opening possess higher potential to develop shear force and can lead to short column failure if not properly designed for shear or constructed. However, shear failure caused by the unexpected rupture of the element and total strength capacity in the elements are not examined [
36].
Mostly, three common approaches for modeling of infill walls exist; namely, detailed micro-modeling, simplified micro-modeling and macro-modeling. Each of the modeling approach has their own significance and the choices of modeling strategies depend on the need of the accuracy, available computational time and scope of the research. Therefore, it will not be justifiable to choose one modeling approach preferred over other as different application field exists for each modeling strategies. Micro modeling approach is necessary for better understanding about the local behavior of masonry structures and is applicable for structural details. Whereas, macro-model is applicable to large dimensions structures so that the stress across macro length is necessarily uniform. This method reduces the analysis time and applicable where comprise between accuracy and efficiency can be negligible. In the present study, the infill walls modeled through macro-model approach proposed by Crisafulli [
6], where six-struts model was utilized in which two pairs act as compression-tension diagonal struts that transfer the axial loads between the diagonal corners and a pair as shear struts with a shear spring to carry the shear from top to the bottom of the infill walls. The infill walls were modeled through four-node masonry panel element (inelastic infill panel element) [
28]. It consists of four internal nodes to account for the width and height of the columns and beams, respectively, whereas four dummy nodes are employed to account for the contact length between the frame and the infill panel [
28]. No special intermediate bonding at the interface between the infill walls and frame elements was assumed; hence, the forces (i.e., moment and shear forces, etc.) from infill walls were transferred only at the connecting end nodes of the column. All the masonry modes of failure are difficult to capture due to large uncertainties and complexity involved, thus in the present strut model common failure caused by shear is considered as utilized by Smyrou et al. [
29]. The diagonal strut member has same thickness as that of masonry without considering the plaster and its length equal to the diagonal length between compression corners of the frame. The effective width of the diagonal strut was estimated using the relation proposed by Holmes [
12]. The cross-section area obtained as the product of effective width and thickness of the strut. The opening in the infill walls were integrated by reducing the value of strut area by a value ranged from 30% to 40%, which is comparable as one proposed by Pinho and Elnashai [
37]. Table 6 shows the material properties adopted for the infill walls which was initially assumed and used by Chaulagain et al. [
23] and later by Rodrigues et al. [
38].
Figure 4 presents a typical representative 3-D numerical models for MRT-3 building, which includes a bare frame model and other three infilled RC models with different distribution of the infill walls, illustrating common and dominant construction typology of the area [
23,
39]. In addition, Fig. 5 and Fig. 6 demonstrates 3-D numerical models for MRT-4- and MRT-5 buildings, respectively, each with bare frame model and remaining three models provided with different orientations of infill walls. Initially, the building was modeled as bare frame, such that only the beam and column elements were assigned. The floor constraint was assigned at each floor level, such that all the nodes of the storey predicted to undergo similar displacement when acted lateral loads. Later, the bare frame model modified through the introduction of external and internal infill walls. The strut area for external infill walls in the building shorter or/and longer directions were deducted by 30%, to integrate openings for windows and doors. Similarly, the internal infill walls were assumed to be fully infilled. One of the infilled prototype buildings includes soft-storey at the ground storey. Other includes the irregular distribution of infill walls, where one complete bay in the longer direction was without infill walls. As stated earlier, the building’s longer direction was represented along the
X-axis and shorter direction along
Y-axis in the numerical model.
Threshold drift limits for different building cases
Limit states delineates the state of a particular building structure based on the predefined level of damages, such as cracking, yielding and collapse. Several researchers and various guidelines proposed and recommended threshold drift limits for various types of buildings to define the performance limit states for RC building, such as FEMA-273 (1997) [
40], SEAOCO-VISION (2000) [
41], Rossetto et al. [
42], Ghobarah [
43], etc. Both FEMA-273 [
40] and VISION [
41] proposed inter-storey drift limits for bare frame buildings only, thus the present study scope does not matches with these guidelines and hence only referred as reference. Similarly, the threshold inter-storey drift recommended by Ghobarah [
43] observed to be more conventional and conservative, as infilled RC buildings were expected to collapse for a drift above 1%, which does not seems practicable. Therefore, the present research aims to define the state of the building through the comparison of threshold drift proposed by Rossetto et al. [
42], as shown in Table 7. As observed in the table, the drift limit is applicable for large building cases, such as non-ductile MRF, infilled MRF and shear walls. The present study considers four modified building cases, thus for consistent comparison, the inter-storey drift associated with the all categories were considered.
Selection of ground motion records
The vulnerability assessments of the buildings were performed using incremental dynamic analysis method. For this, larger sets of earthquake data were required, but no past recorded data were available, except 2015 Gorkha earthquake. Therefore, the present study selected a total of 21 real ground motion records from the real seismic events according to Macedo et al. [
44], that matches with the target response spectra as defined in IS 1893 (Part 1): 2002 [
24], for the zone V and medium type of the soil demonstrated in Fig. 7(a). Ram and Wang [
45] estimated PGA values at bed rocks of Nepal using a probabilistic approach. According to Ram and Wang [
45], the annual probability of exceedance of PGA values for a range of 0.07
g–0.16
g is 63%, PGA between 0.21
g and 0.6
g is 10%, and between 0.38
g and 1.1
g is 2%, for a return period of 50 years. Similarly, Shrestha [
46] predicted PGA values for the Kathmandu Valley. The study revealed that there is 2% annual probability of exceeding, 0.31
g PGA, in 50 years that is equivalent to Modified Mercalli Intensity (MMI) of VIII. Similarly, there is 10% annual probability of exceeding, a PGA of 0.18
g, having earthquakes of 50 years return period, i.e., similar to MMI of VII. In addition, an earthquake of MMI of IX that is comparable to the 1934 Nepal-Bihar earthquake, of PGA between 0.5
g and 0.55
g has 0.7% annual probability of exceedance in 50 years [
46]. Subedi and Parajuli [
47] predicated that the earthquakes of 475 year return period can have maximum PGA of 0.3
g for hard soil, 0.4
g for medium soil, and 0.5
g for soft soil. Considering all these previous researches prediction in context of Nepal, the selected earthquakes have PGA ranges between 0.08
g and 0.921
g. The selected ground motion records also matches the target spectrum having range of periods between 0.1 and 1.1 s that covers the fundamental periods of the entire modified MRT buildings.
Vulnerability assessment
Different types of analysis were performed for each building type; such as Eigen value analysis, static pushover analysis and nonlinear time history analyses. Thus obtained results were presented and interpreted with the help of inter-storey drift profile, IDA curves and fragility curves, obtained from dynamic time history analyses. The detail analysis, results and discussions were discussed in the following sections.
Eigen value analysis
The Eigenvalue analysis was performed to investigate the fundamental frequency of the buildings. The obtained first three fundamental frequencies for all building types were presented in Table 8. Although the dynamic behavior of the building changes with the introduction of the infill walls, the observed vibration modes were identical for the studied infill walls configurations, i.e., initial two vibration modes along translational and third one torsional. As expected, the infilled prototype buildings increased the fundamental frequencies almost 4 times compared to corresponding bare frame. The maximum increases can be observed for the fully infilled building, and followed by irregularly infilled and soft-storey building case. This phenomenon holds true in case of four and five storey building as well. Similarly, the increase in number of storeys decreased the fundamental frequencies and reduced by almost 25% and 50% for four and five storeys, respectively. The higher frequency corresponds to lower time period of the structure, thus attracting large seismic force particularly low rise buildings, as obtained from the site response spectra, defined in IS1893 (Part1): 2000 [
24], as shown in Fig. 7. Hence, such buildings should be properly designed and detailed to counteract the large seismic forces, a primary objective of the present study.
Static pushover analysis
The influence in base shear capacity of the building as a result of different dispositions of infill walls and due to added number of storeys were analyzed through adaptive pushover analysis, utilizing the response spectra shown in Fig. 7. Figure 8 presents capacity curves for all modified prototype buildings in both directions. The plot illustrates that addition of infill walls in the RC frame building considerably increases stiffness and strength relatively compared to the bare frame. The maximum increases can be obtained for fully infilled and minimum for soft-storey building case. The increase in stiffness for three storeys building ranges (4–20) and (4–16) times in X and Y directions, respectively. In addition, the increase in stiffness four storeys varies from (6–21) and (6–17) times in X and Y directions, respectively. Furthermore, the increase in five storey was (8–25) and (8–20) times in X and Y directions.
Similarly, the capacity curves also demonstrate considerable increase in base shear capacity of the building after the intrusion of infill walls, but depend upon its distribution. As expected, the maximum increase in base shear capacity was observed for the fully infilled building, almost increased by 4 and 3 times in X and Y directions, respectively. Similar increase can be detected in case of four and five storeys as well. Whereas, a slight increase in base shear capacity was recorded for soft-storey building, but comparable to the bare frame. When compared between variable storeys, no significant variation in maximum base shear capacity was observed, i.e. almost comparable, as illustrated in Fig. 8. Beside increase in stiffness and strength capacity, the infill walls reduce the deformation capability and overall ductility of the infilled buildings. The maximum base shear capacity attained for lower global drift likely due to brittle behavior of the masonry walls in comparison to RC frames. At the maximum point, infill walls predicted to contribute fully along with the surrounding RC frames behaving monolithic in resisting lateral forces. This state of the building could be expected to possess minor cracks in the infill walls, and the inter-storey drift could be around 1.2% in both directions. After attaining the maximum capacity, a steep decline in the capacity curve can be observed, also known as descending branch. This state of the building might be due to in-plane crushing and in some cases, out-of-plane of the infill walls; as a consequence infilled building potentially fails under soft-storey mechanism.
From the above discussions and observed capacity curves, it can be concluded that the variation in base shear capacity depends upon the infill walls distribution, positions and percentage of openings, and is independent to the variable number of storeys when all parameters are constant.
Nonlinear dynamic time history analysis
The seismic vulnerability of all modified prototype MRT buildings was assessed through nonlinear time history analyses. As already discussed, the selected 21 real ground motion records were suitably scaled between 0.1 and 0.5g at the interval of 0.1g, and subjected at the support as bidirectional. To determine the critical angle of incidence, thus recorded earthquakes were subjected along 0 and 90 degree. For each set of earthquake, 10 scaled IMs were acted in bidirectional, and almost 210 analyses performed for each prototype building, thus a total of 2400 analyses were carried out and results presented as follows.
Inter-storey drift profile
Influence due to different arrangements of infill walls
A representative comparative inter-storey drift profile for MRT-3, MRT-4, and MRT-5 buildings modified with various dispositions of infill walls, subjected by 5-Chi-ChiTaiwan (China) earthquake, at 0.3g PGA, was shown in Figs. 9–11, respectively. The entire plots demonstrated that soft-storey building exhibits maximum inter-storey drift (ISDmax), mainly in the ground floor and insignificant drift at the consecutive upper floors, as expected. This could potentially due to lower stiffness and strength capacity at the soft-storey compared to consecutive upper infilled storeys; as a consequence becomes much more susceptible. Whereas, bare frame model exhibits uniform drift profile, illustrating uniform distribution of global building’s stiffness and strength. Although the drift was uniformly distributed in the bare frame building, but comparable to maximum drift recorded in soft-storey model. The regular and irregular distributions of infill walls in the building not only reduced ISDmax to lower values but also uniformly distribute throughout. For this particular earthquake, the infilled frame reduced maximum drift to one tenth than soft-storey and BF in both directions. When compared between drift profiles, fully infilled building exhibits lower drift than irregularly infilled. Furthermore, the uniform drift profile attained in the infilled building highlighted the uniform distribution of stiffness and strength, but valid for low to moderate magnitude earthquakes. The ISDmax for MRT-3, MRT-4, and MRT-5 buildings without ground infill walls was approximately 2.7%, 3%, and 3.2%, respectively, in Y direction. And this ISDmax can be reduced below 0.7%, 0.5%, and 0.9%, respectively, in Y direction with the introduction of infill walls. This reveals that for this particular earthquake of specified IM, the soft-storey building could possess extensive to partial damages in relation to Table 6, where the crushing of infill walls and shear failure in some structural elements could be predicted. This state of the building after intervention of infill walls, exhibits light to moderate damages only.
Influence due to added number of storeys
Figures 12 to 15 present a representative comparative ISDmax profile for various infill walls configurations to investigate the influence of added number of storeys on the seismic response of the building. As expected, the entire plots illustrate higher building response, i.e., exhibits relatively larger ISDmax corresponding to added number of storeys except in case of bare frame building, where four storey building exhibits slightly higher drift at the upper floors than five storeys. In case of soft storey configuration, the drift increases almost by 100% and 20% in X and Y directions when storey modifies from three to five storeys. Similarly, the drift increased by more than twice in both directions for irregular infilled model when storey increased from three to five storeys. Furthermore, for fully infilled building, five storeys building exhibits higher drift almost 2 and 3 times than three storeys building. Whereas, a slight increase in drift observed when storey increased from three to four storeys. This concludes that the vulnerability increased when storeys added, particularly MRT buildings initially designed and detailed for three storeys.
IDA Curves
Influence due to different arrangements of infill walls
The IDA curves can be used for the seismic performance assessment, where the seismic demand in terms of ISDmax was plotted along the abscissa and scaled ground motions records, i.e., IMs along the ordinate. In this section, the IDA curves were plotted for the ISDmax attained from a total 42 ground motion records as discussed above, which were scaled for a range of IMs, i.e., 0.1g to 0.5g at a step of 0.1g. Figure 16(a) to 16(d) presents statistical distributions of building responses as a function of IMs for three storey building contributed by different arrangements of infill walls, and represented by the boundary of minimum, maximum and mean IDA curves. The light solid lines represent an individual IDA curve that corresponds to each subjected earthquake, illustrating variation of seismic demands with respect to the IMs. As predicted, the entire IDA plots exhibits increase in ISDmax for increase in IMs, such that building can be expected to behave elastically for lower IMs, i.e., until 0.2g PGA for bare frame and soft-storey buildings and until 0.3g PGA for fully and irregularly infilled buildings. However, in some cases, observed decrease in ISDmax, although increase in IMs, mostly in soft-storey and bare frame models. This state of the building response related to the hardening of the structural elements when acted by earthquake of large IMs, such that the building is unable to meet seismic demand. This state of the building could also be predicted to undergo partial collapse and collapse. For lower IMs, i.e., until 0.2g, a large dispersions of drift could be recorded in soft-storey and bare frame buildings relatively compared to the fully and irregularly infilled buildings. Large dispersions of building response for same IMs reveals large variations in frequency contents and recorded durations of the selected earthquakes. In addition, for a slight increase in the IMs, i.e., beyond 0.3g PGA, irregularly infilled building also demonstrates relatively comparable maximum inter-storey drift as that of bare frame and soft-storey buildings. This could potentially due to in-plane crushing and out-of-plane collapse of infill walls that results soft-storey mechanism, a dominant failure mechanism and in some cases short-column and shear failures in structural columns and so on. In case of fully infilled building, nonlinearity response becomes dominant beyond 0.4g PGA, where large numbers of subjected earthquakes are likely to cause in-plane crushing of infill walls. As a consequence, the failure of the infilled buildings under soft-storey and short-column mechanisms becomes prominent.
A better seismic performance for different orientations of infill walls can be evaluated through a more simplified approach, i.e. comparison of mean IDA curves. Figure 17 presents comparative mean IDA curves, illustrating both bare frame and soft-storey buildings exhibit comparable mean drift in both directions. Similarly, both fully and irregular infilled buildings also demonstrates relatively similar mean drift in X direction for the subjected IMs, whereas in Y-direction, the difference becomes wider beyond 0.2g PGA. The mean ISDmax obtained for three-storey building with bare frame and soft-storey, at 0.3g PGA, was almost 2.2%, and this was reduced below 1.2% with infill walls introduction throughout. This concludes that the seismic performance could be enhanced through the introduction a regular distribution of infill walls. However, the performance is highly dependent on many factors, such as workmanship, connection details between infill and frames, quality of materials, among other factors in the actual construction site. Therefore, in one hand its positive effects cannot be ignored however with the perfect knowledge that if this positive effect is considered in the design stage, additional caution are needed in the construction stage and during the life of the building.
Figure 18 (a)–18(d) presents the IDA curves for MRT-4 building with BF, WO-GI, W-Irre.-I, and W-I, respectively, in both directions. Similar to three storeys MRT building behavior, a large dispersion of building response can be recorded for the same IMs. Similarly, larger increase in inter-storey drift for lower IMs can be detected for the soft-storey and bare frame buildings, whereas in case of fully and irregular infilled building, comparatively lower drift could be detected. The inter-storey drift increases with the increase in IMs, i.e., beyond 0.3g PGA, irregularly infilled building exhibits comparable drift similar to the bare frame and soft-storey buildings. Such higher and comparable drifts could be detected in fully infilled building beyond 0.4g PGA, where the failure of buildings potentially under soft-storey mechanism is likely.
Figure 19 presents a comparative mean IDA curves for MRT-4 building with different distributions of infill walls in both directions. Similar to three storeys MRT building, both bare frame and soft-storey buildings demonstrate comparatively similar drift in both directions. Similarly, fully and irregularly infilled buildings demonstrate relatively similar drift in X direction, whereas the difference widens beyond 0.2g along Y direction. The observed mean ISDmax for MRT-4 building with BF, WO-GI, W-Irre.-I, and W-I, at 0.3g PGA, was almost 3%, 2.7%, 2%, and 2%, respectively, in both directions. When compared with Table 6, the state of both BF and WO-GI buildings could be predicted to be in extensive to partial-collapse states in both directions; whereas, irregularly and fully infilled buildings likely to possess only moderate to extensive damages.
Figure 20 presents the IDA curves for MRT-5 building with various configurations of infill walls, subjected by 42 ground motion records. For this building, a larger dispersion of inter-storey drift could be recorded, such that nonlinearity becomes dominant beyond 0.1g PGA for soft-storey and bare frame buildings. Whereas, for irregularly and fully infilled buildings, the elastic behavior could be expected until 0.2g and 0.3g, respectively, beyond which hardening becomes dominant. The former building case exhibits slightly higher drift for lower IMs and higher drift beyond 0.2g PGA, when compared between individual IDA curves. This also justifies that regularly infilled building could enhances the seismic performance than initially predicted, but in most cases for low to medium magnitude earthquakes and assumed that there is good workmanship at the site and provided good connection details between frames and infill walls.
It was difficult to generalize the conclusion through the individual IDA curves as discussed above; therefore, the comparative mean IDA curves were plotted to compare between different infill walls configurations, as illustrated in Fig. 21. The plot demonstrates that both bare frame and soft-storey buildings demonstrate similar mean ISDmax until 0.2g in both directions. Remarkably, the difference widens and more distinct mean ISDmax was recorded beyond 0.3g PGA in both directions, such that revealing soft-storey building as the most vulnerable building. Similarly, for irregularly and fully infilled buildings, both illustrates relatively similar mean IDA curves in X direction; whereas, more distinct can be observed beyond 0.1g, such that the former one illustrates higher drift compared to the latter one. The mean ISDmax for MRT-5 building with BF, WO-GI, W-Irre.-I and W-I, at 0.3g PGA, was approximately 4%, 3.5%, 2.5%, and 2.4%, respectively. This shows that both BF and WO-GI buildings likely partial collapse and collapse states, whereas, the building could be in moderate to extensive damage states with throughout distribution of infill walls.
Influence due to added number of storeys
The vulnerability of the prototype MRT building was investigated in this section due added number of storeys and the recorded mean IDA curves were presented in Figs. 22(a)–22(d) representing bare frame, soft-storey, irregular infilled, and fully infilled buildings, respectively. The entire plots demonstrated that the vulnerability (in terms of inter-storey drift) increases with added number of storeys when compared to same IM. For the considered infill walls arrangements, the IDA plots demonstrated similar behavior of mean IDA curves. In each configuration, all considered storeys exhibits approximately similar mean drift until 0.1g PGA and the difference widens with the increase in the IMs. The four storeys model always exhibit intermediate building response between three and five storeys buildings. The mean IDA curves for bare frame and soft-storey building, at 0.3g PGA, shows that vulnerability increased almost twice, when modified from three to five storeys. Similarly, the vulnerability increased by almost 50%, when modified from three to four storeys buildings. Similarly, in case of both irregularly and fully infilled buildings, at 0.3g PGA, the mean drift increases by more than twice for storey varied from three to five. And, when changed from three to four storeys, both infilled buildings exhibits drift almost 100% higher than three storey mean drift. This result shows that fully and irregularly infilled cases could also be the worst scenario for higher IMs as the susceptibility increased largely due to increase in number of storeys.
Fragility Curves
The fragility curve is a statistical tool that helps to understand vulnerability of building typology. In other words, the fragility of a structure is defined as the probability of exceeding a given damage state conditional to a certain curve of the intensity measure which accounts for the record-record variability. Here, fragility curves were developed considering
ISDmax as a building response parameter, obtained from nonlinear dynamic time history analyses. The states of damages for IMs were compared with inter-storey drift threshold proposed by Rossetto and Elnashai [
42] as presented in Table 6. The vertical dotted line, at 0.3
g PGA, represents the 475 years return period earthquakes that was considered as a boundary to compute the probability of occurrence of each damage states.
Influence due to different arrangements of infill walls
The present study demonstrates and discusses the influence of distribution of infill walls (BF, WO-GI, W-Irre.-I and W-I) on the seismic performance of the prototype MRT building considering higher damage states, such as extensive, partial-collapse, and collapse. Figure 23 presents the fragility curves for three storeys MRT building. The entire plots demonstrate that soft-storey building as the most susceptible, as expected. Remarkably, both W-Irre.-I and W-I buildings display relatively similar conditional probability of exceedance. The probability of exceeding collapse, at 0.3g PGA, for MRT-3 with BF, WO-GI, W-Irre.-I and W-I was approximately 12%, 16%, 9%, and 8%, respectively. Although no significant failure probability can be reduced for extensive damage, but in case of partial collapse and collapse, the failure probability can be reduced below halves when the building was fully and irregularly infilled.
In a similar manner, Fig. 24 presents comparative fragility curves for MRT-4 building to investigate the influence of arrangement of infill walls. It was observed that soft-storey building likely to have higher failure probability for same PGA, which was expected. For extensive damage, both bare frame and soft-storey, and fully and irregularly infilled buildings have relatively similar probability of exceedance. With the distribution of infill walls throughout, the extensive damage, at 0.3g PGA, can only be reduced by 20%, whereas partial collapse and collapse was reduced by almost 80% and 50%, respectively.
Furthermore, Fig. 25 presents the comparative fragility curves for the MRT-5 building, illustrating the level of failure probability that can be reduced with infill walls introduction throughout. At 0.3g PGA, the extensive damage could be reduced by almost 35% and 15% when fully and irregularly infilled, respectively. In case of partial-collapse, both soft-storey and bare frame buildings, and fully and irregularly infilled buildings have almost same failure probability. Furthermore, the entire building configurations have reasonably similar failure probability, such that the failure can be reduced by only 3% for infilled building compared to soft-storey. This reveals that the vulnerability of building to collapse for MRT-5 is comparable for all considered infill walls configurations. Hence, the infill walls do not have significance effect in resisting building collapse for five storey building.
Influence due to added number of storeys
This section intends to determine the variation in failure probability as a result of increase in the number of storeys, initially designed for three storeys. Figure 26 presents the fragility curve for the bare frame building. As expected, the maximum failure probability increased with the added number of storeys. For extensive damage, both four and five storeys buildings have almost similar failure probability, increased by almost 10% than three storeys. In case of partial-collapse, the failure probability was almost doubled when increased from three to five storeys. Finally, the probability of collapse was increased by almost 10% and 20%, when storey increased to four and five storeys, respectively.
Figure 27 presents the comparative fragility curves for the soft-storey building influenced by the added number of storeys. The entire plots show relatively comparable failure probability for considered all storeys. For extensive damage, all the variable storeys have peak exceedance, at 0.3g PGA. The probability of partial-collapse increased by almost 15% and 25% when storey increased to four and five, respectively. Furthermore, the probability of collapse, at 0.3g PGA, was increased by almost 5% and 20% when storey was increased to four and five, respectively.
Figure 28 presents the comparative fragility curves for irregularly infilled building influenced by the added number of storeys. Both four and five storeys buildings have almost same probability of failure, such that the failure probability increased by almost 30% than three storeys. In case of partial-collapse, at 0.3g PGA, five and four storeys buildings increased the susceptibility by about 55% and 20%, respectively. Furthermore, the probability of collapse, at 0.3g PGA, increased nearly by 80% and 30% corresponding to five and five storeys, respectively.
Furthermore, the comparative fragility curves for the fully infilled building to examine the probability of exceeding the damages with respect to the added number of storeys were presented in Fig. 29. No significant vulnerability could be observed for extensive damage, where both three and four storeys have almost similar probability of failure. For the four and five storeys buildings, the failure probability for partial-collapse, at 0.3g PGA, was increased by almost 25% and 50%, respectively. Whereas, in case of total collapse: the failure probability, at 0.3g PGA, was increased by almost 60% and 40% when storey was increased to five and four storeys, respectively.
Conclusions
The prototype MRT building initially designed and detailed for three storeys were later modified with added number of storeys and also different configurations of infill walls throughout to investigate the seismic performance of the building before and after the modifications. The various findings obtained from linear to nonlinear dynamic time history analyses can be drawn as follows:
1) Application of infill walls found to increase the fundamental frequencies by almost 4 times compared to bare frame building. In addition, the frequencies decreased with the increase in the number of storeys, and reduced by almost 25% and 50% for four and five storeys, respectively.
2) Infilled frame increased global building stiffness, such that it increases for three, four and five storeys by almost (4–20), (6–21), and (8–25) times than bared frame.
3) Addition of infill walls also increases the strength capacity but lower the deformation capability. The increase in strength was maximum for fully infilled building, increased nearly by 4 and 3 times than bare frame in X and Y directions, respectively. The maximum base shear capacity and its profile do not change with the increase in number of storeys.
4) A steep decline in base shear capacity was observed for infilled building after attaining maximum capacity. This is potentially due to in-plane crushing and out-of-plane failure of the infill walls, and the lateral force was expected to be resisted by the bare frame structures.
5) Large drift is concentrated in a single storey in case of soft-storey building, thus leading to the failure of structure under soft-storey mechanism. This failure mechanism can be minimized or largely eliminated with intervention of infill walls throughout. Infill walls not only reduced the inter-storey drift, but also uniformly distribute drift throughout the storey. Thus, infill walls can be predicted to evenly distribute building’s global stiffness and strength.
6) The attained inter-storey drift for soft-storey building with variable number of storeys, at 0.3g PGA, for typical earthquake was 2.7%–3.2% and was reduced to 0.7%–0.9% after fully infilled. However, this is true for lower IMs, until 0.3g PGA, after which infilled RC building could be expected to fail under soft-storey mechanism, short-column and in some cases, shear cracks in frame elements.
7) When storey increased from three to five in case of soft-storey building configuration, the inter-storey drift increased almost by 100% and 20% in X and Y directions, respectively. The drift increased by more than twice in both directions for irregularly infilled and (2–3) times in case of fully infilled buildings. Whereas, only a slight increase in inter-storey drift was attained when storey increased from three to four storeys.
8) The increase in IMs increases the seismic demand (i.e. increases the inter-storey drift), but maximum increases occurred in soft-storey and bare frame buildings than fully and irregularly infilled buildings for same IM. This holds true until seismic demand exceeds the capacity of the building. And after demand exceeds capacity, the building exhibits lower drift even for the increase in IMs. This state of the building can be expected to have hardening and collapse of the building becomes dominant.
9) The larger scattering of the inter-storey drift observed with added number of storeys. In case of fully infilled, the three storeys building behaves elastically until 0.4g PGA, whereas in case of five storeys, behaves elastically until 0.2g PGA. This concludes that vulnerability increases with the increase in the number of storeys and holds true for all configurations.
10) In case of lower damage states, the conditional probability of failure does not improve significantly with the different arrangement of infill walls. However, in case of three storeys building, the partial-collapse and collapse states, at 0.3g PGA, reduced below halves for fully and irregular infilled. For four storeys, the partial-collapse and collapse damage was reduced by almost 80% and 50%, respectively. Furthermore, for the five storeys, the extensive damage reduced by almost 35% and 15% for fully and irregular infilled buildings, respectively.
11) For the bare frame and soft-storey buildings, the probability of exceeding does not change significantly when increased in storeys from three to five. However, the vulnerability increased in case of irregularly infilled building, where the partial-collapse probability increased by almost 55% and 20% for five and four storeys. Similarly, the collapse probability increased by 80% and 30% for five and three storeys. Similar conclusions could be obtained for fully infilled building, where the failure portability of partial-collapse, at 0.3g PGA, increased by almost 25% and 50% for four and five storeys, respectively and total collapse by 60% and 40% for four and five storeys, respectively.
Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature
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