Seismic performance evaluation of masonry infill R.C. frame considering soil-structure interaction

The structural damage due to recent seismic events in Nepal has led to a dire need for studies considering soil-structure interaction (SSI) as the majority of designers still adopt conventional design principles. These damages may be the result of the conventional fixed base method’s failure to take into account the underlying soil properties. Post Mw\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M_w$$\end{document} 7.8 Gorkha earthquake, revised Nepal National Building code NNBC 105:2020 has classified soil types based on the rigidity of the soil. A comparative analysis is carried out using linear-static and nonlinear static (Pushover) analysis considering the fixed and flexible base of a masonry infill RC frame. The seismic performance parameter evaluated for a target inelastic drift of 2% are in terms of their fundamental time period, peak floor displacement, inter-storey drift ratio (IDR), ultimate load carrying capacity and yield mechanism. The consideration of SSI drastically influenced the fundamental time period, peak floor displacement and IDR with decreasing rigidity of soil. The fixed base structure exhibited a higher ultimate load-carrying capacity than the flexible base structure for all soil types. The masonry infill dissipated the seismic energy by the failure of the majority of struts. Furthermore, the post-yield behaviour of all models highlighted that the damage level of RC frame and masonry infill elements were higher for fixed base.


Introduction
The Himalayan region is one of the most seismically active regions as can be seen from previous earthquakes [1][2][3]. Nepal, which occupies a third of the Himalayan region, has the highest risk of frequent earthquakes [4]. The prime reason attributed to such high seismicity is the continuous movement between the Indian and the Eurasian plate. The intense compression at the boundary has resulted in different geological features such as faulting and folding. Nearly 90% of its land area is under moderate-to-severe seismic hazards [5]. It can be inferred that the occurrence of moment magnitude M w 8 or higher earthquakes are very likely to occur in the Himalayan arc [6]. Despite the high vulnerability, most of the structures constructed are based on old technology and even the newly constructed RCC buildings are poorly detailed and lack the required ductility to resist such high inertia forces. Consequently, the destruction caused by earthquakes becomes several times more than usual. The 2015 Gorkha Earthquake which was a shallow earthquake having a focal depth of 15 km occurred near the Main Central Thrust (MCT) with a Maximum Modified Mercalli Intensity scale of IX [7]. This pushed researchers across the globe for parametric study and large-scale retrofitting and strengthening efforts.
Thus, the seismic design code in Nepal was revised post-Gorkha earthquake, providing the designers with four types Prajwol Karki and Shuvam Pyakurel have contributed equally to this work.
5 Page 2 of 12 of soil for seismic design, i.e. Hard soil (Type-A), Medium soil (Type-B), Soft soil (Type-C) and Very soft soil (Type-D) [8]. But as in many codes in developing nations, it provides little information on the SSI technique to evaluate the seismic performance of structures. Studies on the interaction between soil and structures have revealed that a structure supported on flexible soil may respond differently from a structure supported on a rigid base [9]. This disparity exists for a variety of reasons, one being the dynamic behaviour of soil that significantly alters the input seismic waves at the foundation levels ultimately resulting in the variation of the fundamental time period of the building [10,11] and the other being dissipation of some of the vibrational energy of the flexibly mounted structure through radiation of stress waves in the soil [12]. Regardless of these findings, current research on SSI mainly focuses on structures with significant importance such as nuclear power plants, and study lacks in the field of commercial design approach of SSI [12]. Furthermore, the drift and ductility needs are distributed more uniformly along the height of the structures when SSI effects are taken into consideration since SSI can influence the yield mechanism of the pre-specified plastic hinges in comparison to its fixed-base counterpart [13]. Thus, the effect of SSI seems to be rather significant relative to fixed-base where the translation along the structure's orthogonal axis and rocking interaction affects the response.
Some of the earliest soil structure interaction effects trace back to the nineteenth century [14] and since then it has been rapidly evolving. Under the effect of seismic waves, the assessment of soil structure interaction can play a significant role in the response of the building. This is because the underlying soil on account of its material characteristics alters the ground motion at the soil foundation interface. Subsequently, the dynamic response of the structures gets modified. Previous studies concluded that considering the soil structure interaction effects leads to a change in modal response and an increase in damping, thus reducing the elastic deformation and leading to a more economical design [15]. Whereas, some have proposed that the beneficial effects of SSI are limited [16].
Introducing SSI directly into the current codes where inelastic behaviour is not accounted for directly [17] will result in uneconomical design due to the drift limitations in the seismic design codes. So, a better procedure where the plastic behaviour is accounted for seems necessary. Pushover analysis, also known as nonlinear static analysis, is one such analysis method which has advantages in near to accurate prediction of structural behaviour and the response of different structural elements under a major earthquake [18]. The pushover analysis requires less computational capability in comparison to other rigorous analysis techniques resulting in quicker results which can be adopted for commercial design.

Research objective
In context of Nepal, for commercial design approach, nonlinearity of RC frame elements and masonry infill, in-plane stiffness of masonry infill and interaction of soil underneath its foundation are neglected as the structures are mostly modelled as bare frames with fixed base. So, the main objective of this study is to overcome these issues by modelling the masonry infill as a single equivalent compression strut and flexible base as an equivalent spring having its underlying soil and foundation properties for all soil types specified in NNBC 105:2020 (hard soil, medium soil, soft soil, and very soft soil). Linear static and nonlinear static analysis are performed to compare parameters of seismic performance in terms of their fundamental time period, peak floor displacement, inter-storey drift ratio (IDR), failure mechanism and ultimate load carrying capacity.

Details of study frame
A G+9 storey unreinforced masonry infill moment resisting R.C. frame structural system with geometric irregularity is considered in this research. For detail analysis, the interior bay is represented by a shaded region as shown in Fig. 1a and is considered as the study frame. The elevation of the study frame is represented in Fig. 1b

Masonry strut
Despite their contribution to the structural performance and behaviour during an earthquake, infill walls are considered to be non-structural components. It addition to its lateral support to the structure, it also changes the structure's force distribution mechanism and failure mode, which must be precisely calculated in order to mitigate future risks and damages [19]. The change in strength and stiffness of the RC frame due to the consideration of masonry infill causes variation in the response of the structures as it may introduce soft or weak storey mechanism in addition to torsional effects due to the irregularities [20,21]. To account for the action of the masonry infill, the infill of the frame has been modelled as equivalent masonry compressive strut. The modulus of elasticity of the masonry infill is calculated from Eq. (1) [22].
Where, E m is the modulus of elasticity of masonry and f m ' is the prism strength of masonry taken as 4 Mpa [23]. Figure 3 shows the solid unreinforced masonry infill panel, effective in resisting the lateral forces. Out of many options available for modelling of masonry infill, single equivalent diagonal compression strut is adopted having elastic in-plane stiffness represented with width a from Eq. (2) [23].
Where h col is the column height between centre lines of beams, r inf is the diagonal length of the infill panel. A Pauley and Priestley [24] provided the diagonal compressive force as Eq. (4) E me and E fe are the expected modulus of elasticity of infill and frame material, respectively, t inf is defined as the thickness of the infill panel and equivalent strut, I col as the moment of inertia of the column whereas h if corresponds to the height of the infill panel, finally, the angle between the infill height and the infill length is symbolized by . The width of the equivalent single strut is calculated to be 1167 mm while the diagonal compressive force is 800 kN.

Soil-structure interaction
Methods to include soil structure behaviour include direct analysis and substructure approach. The direct analysis approach is rather simpler; however, it does not render the complete picture and incorporation of kinematic interaction is challenging [25,26]. Furthermore, soil structure interaction may increase the ductility demand. Numerous techniques have been developed to model soil and its associated properties and one of the simplest methods involves springs at the soil foundation interface. In this paper, the spread footings are considered as rigid and uniform soil deposit is assumed. The values for shear wave velocity ( V s ) and Poisson's ratio ( ) are taken from EC-8 [27] and USACE [28]. Other variables such as modulus of elasticity ( E ) and shear modulus ( G ) are given in Table 1.
Individual Springs associated with each degree of freedom are attached to each foundation element. The characteristics of the underlying soil are calculated as translational and rotational springs from Table 2. To evaluate the collective response of the two-dimensional frame structure, the foundation and its underlying soil, the soil characteristics are modelled as translational and rotational spring as per Eq. (5) to (15) [26,29].
Where, K x is the translational spring along the x-axis, K z is the translational spring along the z-axis, and K yy is the rotational spring about the y-axis. x , z and yy are the embedment correction factors while x , z and yy are the dynamic stiffness modifiers for translational spring along x-axis, z-axis and rocking about y-axis, respectively. Using these Eqs. (5) to (15), the values for spring stiffness are calculated for various foundation sizes in all considered soil type as shown in Table 3.

Numerical modelling
The analysis is performed for eight models of the study frame represented in Table 4. The seismic behaviour of the study frame is numerically investigated using the structural analysis software SAP2000. All members are represented as two-node frame elements with their respective axial, shear, and flexural properties with their centrelines joined at nodes. The boundary condition for beam-column joint is considered as rigid, whereas the masonry strut has pinned boundary condition at both ends. Discrete plastic hinges have been allocated to the members' predetermined positions as part of the lumped plasticity model, which has been used for nonlinear analysis. The kinematic and takeda hysteresis models are adopted for all reinforcing steel and concrete materials, respectively [30]. A detailed flow chart of the analysis process is shown in Fig. 4. Figure 5 shows an equivalent representation of RC infill frame with and without consideration of underlying soil. Shear and axial behaviour are considered as forcecontrolled action, whereas flexural behaviour is considered as deformation-controlled behaviour. Default axial force-bending moment (P-M) hinges are assigned for columns and moment-curvature (M-Φ ) hinges are assigned for beams, whereas axial hinges (P) are assigned for equivalent masonry struts. The material nonlinearity of the masonry hinge is assigned as a stress-strain curve [22].
The moment-rotation of structural members is represented by flexural hinge as shown in Fig. 6 [31]. The linear range is represented by A-B whereas B-C represents the inelastic but linear response. This inelastic range is further classified into three design criteria namely Immediate Occupancy (IO), Life Safety (LS) and Collapse Prevention (CP). C-D shows a sudden reduction in load resistance followed by D-E which represents response at further reduced resistance followed by a loss of resistance finally. The hinges assigned to the columns and beams are as per ASCE 41-17 [31].

Equivalent static method as per NNBC 105:2020
The seismic coefficient method as per NNBC 105:2020 is adopted for linear static analysis of the study frame. The code stipulates two performance requirements are met namely serviceability limit state (SLS) and ultimate limit state (ULS). The former requires the structural system to undergo limited deformations minimizing the structural and non-structural damage while the latter demands adequate resistance and energy dissipation capacity of the structural system. The seismic parameters for the study frame are given in Table 5. The load combination adopted for the limit state design is given by Eqs. (16) to (17) [8].
(16) 1.2DL + 1.5LL Where, DL is the dead load, LL is the live load and is 0.6 for storage facilities and 0.3 for non-storage facilities, a value of 0.3 has been taken for the analysis model. According to NBC 105:2020 the spectral shape factor C h (T) for various soil types can be obtained from Eq. (18) and is shown in Fig. 7. Eq. The elastic site spectra C(T) are taken as per Eq. (19).  Where, is the peak spectral acceleration normalized by PGA, T a and T c are the lower and upper periods of the flat part of the spectrum, while, K is the coefficient that controls the descending branch of the spectrum determined by interpolation between 1 and 2 for structure having period between 0.5 sec and 2.5 sec, respectively. The horizontal base shear coefficient for ULS and SLS is calculated as per Eqs. (20) and (21), respectively.
R is the ductility factor ( R =2.0), Ω u and Ω s are the overstrength factor for ULS and SLS, respectively ( Ω u =1.2 and Ω s =1.1) . C s (T) is the elastic site spectra for SLS given by Eq. (22).

Pushover analysis
The philosophy of earthquake-resistant design is based on two aspects: one, that under low-intensity shaking, the structure can fulfil the seismic demand elastically. Second, under a major earthquake, the structure resists its effects  through its inelastic capacities [32]. Hence, nonlinear behaviour plays a significant role in earthquake-resistant design techniques. This not only utilizes the reserve strength of the structure but also makes the design economical. Pushover analysis as defined in FEMA 356 [23] and ATC-40 [33] is one such technique which is a popular and widely used method on account of its simplicity and applicability [34].
To arrive at desired results, modelling is one of the important parameters in pushover analysis. The structural model used must consider the nonlinear behaviour of all its members and their respective materials [20]. Hence, it is crucial to arrive at nonlinear properties of each component that indicates the strength as well as deformation capacities. Commercially available computer programs such as SAP2000 have very well implemented provisions of FEMA 356 [23] and ATC-40 [33] to perform Pushover analysis. These properties depend upon the type of detailing and construction techniques. A user has the option of either choosing the default properties or defining manually the loaddeformation behaviour of individual members based upon the different material modelling techniques [35].
In this paper, default hinge properties as per the provisions of ASCE 41-17 [31] are taken for the flexural hinge while the axial hinge for the masonry strut is as per FEMA 356 [23] in compliance with NNBC 105:2020 [8]. In general, hinges are of three types: flexural, shear and axial, these hinges are also illustrated in Fig. 5. Axial hinges are normally defined for infill frames using appropriate masonry strut modelling. For beams and columns, shear and flexural  hinges are defined. The location of plastic hinges is predefined at the end of beam-column joints to account for the actual failure mechanism during seismic excitation.

Results
Both linear static and nonlinear static analyses are carried out to compare the seismic performance of considered Masonry Infill RC frame for the fixed and flexible base. The results post-analysis is presented.

Linear static analysis
The output from the linear static analysis is discussed in terms of the fundamental time period (T) of the structure, peak floor displacement (D) and maximum inter-storey drift ratio (IDR) and reported in Table 6 The percentage change in the structure's fundamental time period is calculated to be 7.23%, 7.6%, 20.38% and 63.60% for SSI A, SSI B, SSI C and SSI D models compared to the fixed base models for the respective soil type. Likewise, Fig. 8a

Nonlinear static analysis
Nonlinear static analysis was performed for specified target drift and the following parameters in terms of lateral load carrying capacity and yield mechanism were investigated. Figure 9 shows the capacity curve for fixed and flexible RC infill frame.  Figure 10 shows the failure mechanism of the masonry infill RC frame with a fixed and flexible base for all soil types due to the formation of hinges.  Table 7 shows that 65% members have collapsed for SSI A followed by 54%, 32%, 27% and 24% members collapsed for SSI B, SSI C, SSID and FB, respectively. Also, 40% of members are near to collapse state for the SSI A model which is also the highest for this state.

Conclusion
This paper addresses the effect of soil-structure interaction for a masonry infill RC frame for all soil types as classified by NNBC 105:2020 in comparison to the fixed base frame. The substantial shift in the fundamental time period exhibited that the structure's flexibility is sensitive to the soil properties. As presented in the code-based spectra, this increment reduces the spectral acceleration. However, this does not necessarily mean the reduction of seismic demand on the structure. From the observed peak floor displacement and IDR of the SSI models, it can be inferred that these parameters are sensitive to soil properties. Current seismic design codes have limited the maximum IDR and peak floor displacement for the linear-static method. Due to the severe amplification of these parameters, it can be established that directly considering the effects of SSI in the linear-static method of analysis will lead to an uneconomical design of structures. From the post-yield behaviour, the hinge formation shows that majority of the masonry strut have collapsed prior to beam and column failure for the flexible base models. However, the frame elements exhibited higher level of damage for the fixed base model. In addition to this, the  fixed base model demonstrated the increment in ultimate load carrying capacity compared to the flexible base models. This paper demonstrates the seismic design procedure for a RC infill frame to be used for the commercial design approach to directly consider the inelastic deformation, the interaction of soil with the structure and the effects of infill. However, further studies must be carried out to make this procedure more effective. Studies relating to various aspect ratio of the foundation and the structure is of paramount interest. The effect of infill can be accounted for by other procedures such as multiple strut analogy and their effect needs observation. Furthermore, accounting for the nonlinear behaviour of the soil is a tedious task and would require a much basic approach before this can be implemented in the commercial design approach, current studies require large computational capabilities.