Response of low-rise buildings under seismic ground excitation incorporating soil–structure interaction

Abstract

In the conventional design, buildings are generally considered to be fixed at their bases. In reality, flexibility of the supporting soil medium allows some movement of the foundation. This decreases the overall stiffness of the building frames resulting in a subsequent increase in the natural periods of the system and the overall response is altered. The present study considers low-rise building frames resting on shallow foundations, viz. isolated and grid foundation. Influence of soil–structure interaction on elastic and inelastic range responses of such building frames due to seismic excitations has been examined in details. Representative acceleration–time histories such as artificially generated earthquake history compatible with design spectrum, ground motion recorded during real earthquake and idealized near-fault ground motion, have been used to analyze the response. Variation in response due to different influential parameters regulating the effect of soil-flexibility is presented and interpreted physically. The study shows that the effect of soil–structure interaction may considerably increase such response at least for low-rise stiff structural system.

Introduction

The common design practice for dynamic loading assumes the building frames to be fixed at their bases. In reality, supporting soil medium allows movement to some extent due to its natural ability to deform. This may decrease the overall stiffness of the structural system and hence, may increase the natural periods of the system. Such influence of partial fixity of structures at the foundation level due to soil-flexibility in turn alters the response. On the other hand, the extent of fixity offered by soil at the base of the structure depends on the load transferred from the structure to the soil as the same decides the type and size of foundation to be provided. Such an interdependent behaviour between soil and structure regulating the overall response is referred to as soil structure interaction in the present study. In this context, a critical examination of the response spectrum curve reveals that the spectral acceleration may change considerably with change in natural period. So, such increase in lateral natural period may considerably alter the response of the building frames under seismic excitation. Such possibility is highlighted through a very limited number of case studies in a few earlier research works [1], [2]. In case of high-rise structures, i.e. for flexible systems, lateral natural period is expected to lie in the long period region of the response spectrum curve. Hence, the response is generally expected to get reduced due to an increase in lateral natural period for such systems. Thus, it is believed that the conventional practice of ignoring the effect of soil-flexibility in the process of design may lead to a conservative one. However, for low-rise buildings, generally, the lateral natural period is very small and may lie within the sharply increasing zone of response spectrum. Hence, an increase in lateral natural period due to the effect of soil–structure interaction may cause an increase in the spectral acceleration ordinate. Moreover, due to the effect of soil-flexibility, various natural frequencies may space closer leading to an increase in cross-modal coupling terms contributing to the overall seismic response. Thus, the effect of soil–structure interaction on the dynamic characteristics, at least for low-rise buildings, may be of major concern. The aim of the present study is to observe the effect of the same on seismic response of buildings under three typical kinds of ground motions viz. (a) two uncorrelated artificially generated earthquake time histories consistent with the design spectrum of Indian earthquake code [3], (b) one recorded earthquake history and (c) idealized near-fault-ground motion. Efforts have earlier been directed to study the seismic behaviour of multistoried building frames. For instance, a recent revealing investigation [4] has focused on the behaviour of a six storey and a 20-storey building with steel moment resisting frame. An exhaustive list of the same is available in NEHRP Recommended Provisions for the Development of Seismic Regulations for New Buildings [5]. However, the present effort has its significance in incorporating the effect of soil–structure interaction particularly on low-rise building frames in its real three-dimensional form. Furthermore, a wide variety of such buildings are included in the scope of the study through a systematic and detailed parametric variation to comprehend the influence of soil–structure interaction and evaluate seismic base shear realistically.

It is customary to design the structures so that they behave inelastically during strong ground shaking. Thus, it is also interesting and necessary to examine the behaviour of the structural system in the inelastic range of loading accounting for the effect of soil–structure interaction. Ductility demand and hysteretic energy demand are two crucial parameters to measure the inelastic range response of the load-resisting structural elements. Hence, an attempt has been made in the present paper to see the influence of soil–structure interaction on such demands. Idealized single storey systems with elasto-plastic material characteristics has been analyzed under the ground motions mentioned earlier. Such systems have been considered to rest on different representative soil medium. Outcome of such endeavour points out the need of accounting for the effect of soil-flexibility for realistic assessment of the inelastic range behaviour of the structural system.

Two nodded frame elements along with four nodded plate elements with appropriate dimensions obtained using standard design are used to model three-dimensional space frames. During seismic excitations, owing to the lateral loading at floor levels, building frames experience in-plane lateral sway deformation parallel to the direction of the force. The brick in-fill within the panel tends to resist this deformation offering enough stiffness against the shortening along one of the diagonals and thus, effectively behaves like a compressive strut. This attributes significant additional lateral stiffness to the buildings [6], [7] and changes the shear distribution [8]. To incorporate this additional stiffening effect in the building frames, ‘equivalent strut approach’ [6], [7] has been used in the present study. The dimensions and properties of these diagonally placed equivalent compressive struts have been chosen from the literatures [6], [7], [9] to simulate the effect of the brick walls. However, at the locations of openings, the stiffness due to brick in-fill is not expected. But, at the same time, the frame and panel of windows/doors may provide a substantial amount of stiffness, which may compensate for the stiffness contribution of the brick in-fill if it were at the openings. It is difficult to assert, without case specific detailed investigation, as regard to the extent of such complimentary contribution in real situations as the same may depend on many factors such as size of panel, orientation of grillage, material used etc. Hence, the equivalent struts to represent the action of brick in-fill walls have been considered even at the locations of openings as a fair compromise between rigor and simplicity. Such idealization has been presented schematically in Fig. 1a and b for a typical low-rise building frame. All the building frames are analyzed with and without tie beams. In reality, tie beams, placed in the form of grids connecting the columns at the plinth level strengthen the column members by reducing the effective length of the same and the lateral stiffness of the structure is increased. This also helps to transfer the wall load of the ground storey to the column. The same has been modeled by two-nodded frame elements. Further details of structural idealization are available elsewhere [10], [11].

To analyze the inelastic range behaviour, structure has been idealized as rigid diaphragm model with three degrees of freedom at each floor level, two translations in two mutually perpendicular directions and one in-plane rotation as shown in Fig. 1c. Mass is assumed to be concentrated at the floor level and the load-resisting elements connecting the floors contribute to the stiffness only. In domestic regular buildings, load-resisting structural members are often distributed over its plan uniformly. Thus, in the present study, six element system [12] has been adopted to represent such stiffness distribution (Fig. 1d). Fifty percent of the total lateral stiffness has been distributed equally between the two edge elements, whilst the rest is assigned to the middle element. Similar systems have been adopted in many other previous studies perhaps because of its capability to represent realistic stiffness distribution [13], [14]. A bilinear elasto-plastic hysteresis model has been utilized to analyze the inelastic behaviour of the structural system. Single storey systems with various periods representative of one, two and three storey building frames have been considered. Strength has been attributed, in all cases, in proportion to the stiffness considering a feasible range of variation of response reduction factor.

Impedance functions associated with rigid massless foundations are utilized to incorporate the effect of soil–structure interaction in the analysis. Sizes of the footings are first determined on the basis of allowable bearing capacity obtained with various soil properties mentioned in Table 1 [10], [11]. The dimension of grid foundation has been arrived at on the basis of the guidelines prescribed in the literatures [15], [16]. Mass of the foundation so designed has also been properly incorporated in the analysis through consideration of consistent mass matrix. Three translational springs, two in principal horizontal directions and one in vertical, together with the rotational springs about these mutually perpendicular axes have been attached below the footings for buildings with isolated footings. Likewise, the entire grid foundation is conceived as a combination of a series of parallel foundation strips oriented in two mutually orthogonal directions resting in the same plane. Hence, springs in all six degrees of freedom have been attached to the foundation strips at centre of gravity of the same. For better understanding, such idealization has been schematically presented in Fig. 2a and b.

Comprehensive research [17], [18], [19] has been carried out to evaluate the stiffness of such springs. Closed form expressions for such spring stiffnesses as depicted in the literature [19] have been furnished in Table 2 of the present paper for the sake of convenience. The same has been adopted in the present investigation as made in the earlier studies [10], [11]. Values of shear modulus (G) for different types of soils have been evaluated using the empirical relationship G=120N^0.8 t/ft² [20] i.e. G=12916692.48N^0.8 MPa. Here, N is the number of blows to be applied in standard penetration test (SPT) of the soil; and Poisson's ratio (ν) of soil has been assumed to be equal to 0.5 for all types of clay [21] to evaluate the stiffness of the equivalent soil springs.

Variation of inertia force with the frequency of the excitation force may conveniently be accounted through considering a frequency dependent behaviour of equivalent soil springs [19], [22]. However, such influence is very difficult to incorporate in the analysis under real earthquake due to the participation of the pulses with wide frequency range in the same. Hence, such effect is not generally incorporated in the study. However, the present study, in the elastic range, examines the influence of such frequency dependent soil properties for some critical cases with a view to achieving upper and lower bound responses. Frequency dependent behaviour of equivalent soil springs is conveniently accounted by multiplying the stiffness of the soil springs with a suitable factor expressed in terms of $a_0=\omega B/V_{\text{s}}$ [19], [22], where ω is the frequency of the forcing function, B is the half of the width of the footing and V_s is the shear wave velocity in soil medium. a₀ could be determined based on the dominant eigen frequencies of the structure or based on the dominant frequency of the earthquake excitation. Consequently, the present study includes the frequency dependent soil-flexibility at a₀=0.0 and 1.5 for building frames with isolated footing. For buildings resting on grid foundation, three critical cases at a₀=0.0, 0.3 and 1.5 are considered. These cover the combinations of the highest and the lowest possible range of variation in stiffnesses of equivalent soil springs in different degrees of freedom and hence are expected to yield lower and upper boundaries of response.

With this idealization of the structure and subgrade medium, effect of soil–structure interaction on low-rise building frames has been analyzed in details.