Verification of multi‐degree‐of‐freedom building modelling for seismic response prediction based on microtremor measurement

Abstract

The applicability of the proposed dynamic response model for buildings is investigated using shaking‐table tests with a four‐storey steel specimen. This approach derives the equation of motion for a multi‐degree‐of‐freedom linear building based on microtremor measurements. Under a linear assumption, the equation can estimate the seismic response accelerations, velocities, and displacements at microtremor sensor locations without the need for information about the mass, damping, stiffness matrices or need for structural design documents to estimate peak responses that are linked with seismic damages of structural and non‐structural components. The modelling is unconstrained by structural shape, composition of frames, connections of structural members, or the assumption of a rigid floor. In comparison to the previous methods assuming simple/regular building shape with standard/typical rigid floor, the proposed model is applicable to large‐scale low‐rise buildings with irregular shapes, flat expanses, and open spaces such as large atria and skylights as well. The applicability study considers two practical scenarios: natural frequencies and damping ratios based on microtremors that can be updated by an earthquake and a standard assumption for structural design. The prediction accuracy is best when the participation vector for seismic input is obtained from sensors located on the upper floors; the structure mostly exhibits elastic response; a modal system identification is applied to the seismic measurement; and local damage does not affect the global seismic response of the structure. The reason is that this method assumes that identified mode shapes do not change due to the occurrence of an earthquake.

Structural and non‐structural numerical blind prediction of shaking table experimental tests on fixed‐base and base‐isolated hospitals

“…A full-scale representation of two multi-storey steel hospital buildings, with both fixed and isolated base (Figure 1), was subjected to seismic tests on a shaking Institute for Earth Science and Disaster Prevention in Japan, that reproduce three-dimensional motions. 22,39,42 This section summarizes the information packets provided to the contestants in order to compete for modelling accuracy on structural and non-structural responses, and functional prediction. 49 The two buildings are adjacent though their dynamic behaviour differed because of an expansion joint.…”

“…22 Additional displacement sensors are used to assess damage state for the partition wall on the second floor, while accelerations of tanks, pipes and medical equipment are monitored. The shaking table experimental campaign consisted in the application of two horizontal earthquakes scaled at increasing intensity levels (ILs), defined as a percentage of the original peak ground acceleration (i.e., PGA), 22,39,42 following the application sequence reported in Table 2 along the horizontal (i.e., positive and negative for X and Y directions, respectively, shown in Figure 1) and vertical (i.e., positive for the Z direction) axes. Details of the selected earthquakes are also reported in Table 2: that is, recording station, horizontal component, testing day, peak-ground velocity (PGV) and peak-ground displacement (PGD).…”

“…These vibration periods are evaluated from spectrograms at the instant of time when the largest WTCs are resulted (Figure 5) and match well with those obtained from classical identification techniques of the modal properties carried out for the same building. 42 Comparison between real and numerical spectrograms of the fixed-base structure is also reported in Figure 5, focusing on first floor displacement time histories. Note that a satisfying level of matching accuracy is achieved for the lighter colours in the spectrograms that indicate larger magnitude of the WTCs and thus greater energy in the motion associated with that time and vibration period.…”

“…The second test structure is a full-scale base-isolated three-storey steel framed hospital building (Figures 6 and 7), adjacent to the fixed-base one. 22,39,42 In-plan configuration for the isolation level (Figure 6A) and level 3 (Figure 6D) consists of 5 One-way concrete slabs are placed at all levels, 15 cm thick for levels 1 and 2 and 60 cm thick for the isolation and top (third) levels. Rectangular RC beams are placed at the isolation level, whereas Hshaped steel beams represent the resisting system at the other levels, together with four steel columns with square hollow cross-section.…”

“…To this end, numerical structural and non-structural blind prediction of the results of a two-phase experimental campaign carried out in December 2020 at the National Research Institute for Earth Science and Disaster Prevention in Japan are used, with regard to two earthquakes scaled at different intensity levels. 22,42 A homemade C++ code is developed to account for lumped plasticity modelling of steel frame members, using a piecewise linearization of the axial load-biaxial bending moment elastic domain 43 ; while a homemade MATLAB code is implemented using the continuous wavelet transforms in combination to the complex Morlet wavelet, 44 to identify the predominant natural frequencies of the original structure, also taking into account variability of its dynamic property when inelastic deformations occur at different levels of seismic intensity. Moreover, three nonstructural components are modelled: that is, elastic single degree of freedom systems representing two tanks filled with sand (top floor); elastic beam elements for piping (third floor); five-element macro-model in order to represent the IP and OOP nonlinear response of partition walls (first floor).…”