# Determination of the displacement demand for the out-of-plane seismic response of unreinforced masonry walls for the Groningen Case

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## Abstract

This research describes the demand of a Displacement-based approach for the assessment of out-of plane behaviour of one-way vertically-spanning unreinforced masonry (URM) walls of terraced and detached houses in the Groningen Province. One of the most vulnerable components of a typical Dutch unreinforced masonry building subjected to earthquake excitation is the face-loaded walls. As the Dutch masonry walls are quite slender, this matter is of significant importance. Up to now, codes and standards evaluate the structural integrity of unreinforced masonry face-loaded walls with either force-based or displacement-based approaches. The latter present beneficial advantages, since the rocking mechanism of an out-of-plane wall is considered to be an instability problem. Particularly, for the definition of the demand (in terms of mid-height displacement for an out-of-plane unreinforced masonry wall) for the Groningen Case, it will be based on the design response outlined in New Zealand Society for Earthquake Engineering Standard (NZSEE) for the Seismic Assessment of Unreinforced Masonry Buildings. Nonetheless, a new rendition of the Shape Factor Coefficient Ci(Tp) and Height Coefficient CHi is necessary, in order to relate the design response with the genuine characteristics of Groningen seismicity. The Shape Factor or Part Coefficient indicates the interaction between the seismic responses of the structural parts and the building, while the Height Coefficient indicates the amplification of the peak ground accelaration through the height of building. The procedure towards the description of the out-of-plane seismic demand is analysed by three parts. In the first part, a series of Nonlinear Time History (NLTH) analyses are performed in single degree of freedom (SDOF) systems. In total, seven SDOF systems are modelled in Opensees. Each of them represents the equivalent SDOF system, according to Eurocode 8, of the considered structures for this research. The SDOF system characteristics as well as the ground motion records for five areas in the Groningen Province are provided from in-house studies of BAM Advies en Engineering. The ground motion records are related to the Draft NPR 9998:2017. Furthermore, two hysteresis rules for the structures are included in the Opensees Models. Hysteretic Rule 1 accounts for low-to-moderate energy dissipation, while Hysteretic Rule 2 for moderate energy dissipation. The hysteretic rules are in accordance with hysteretic behaviour of URM piers under in-plane loading. The geometry, loading conditions and mechanical properties of the piers are chosen to represent the piers in typical Dutch terraced and detached houses. These piers were tested at the Stevin Laboratory of the Delft University of Technology, which provided the data of the tests. Two specific in-plane wall specimens (COMP-2 and COMP-3) are used in this work. The Opensees parameters describing the aforementioned hysteretic rules, are calibrated according to the cyclic tests of these specimens. Next, the NLTH analyses are performed. The deliverables are the Floor Response Spectra (FRS) of each equivalent structure, per hysteretic rule, area and direction. Generally, a response spectrum is a plot that indicates the maximum response of linear oscillators with varying natural frequency or period. The oscillators are excited under the same vibration. Analogously, a FRS indicates the maximum seismic accelaration that the structural parts attract, if they are placed on the respective floor. Since a significant amount of FRS is provided from the NLTH analyses of the 1D Models, the production of Design Floor Accelaration Spectra per area is aimed. Design Floor Accelaration Spectra are “smooth” spectra that can be described by equations and act as an upper bound envelope for all the FRS produced per area. For their derivation, the Newmark-Hall method is applied to the mean Floor Response Spectra of all the structures per area. Consequently, a Design Spectrum per area is produced along with the equations that describe the Shape Factor Coefficient Ci(Tp). The Design Floor Accelaration Spectra efficiently describe the demand expressed in the response spectra of the 1D Models. Nevertheless, in some of the FRS, narrow high amplified spectra are observed with spectral values greater than the design plateau value. These cases are related to stiff structures that did not show proper plastic behaviour in direction X (“weak” direction of the structures governed by openings and rocking piers) and to all the structures in direction Y (“strong” direction of the structures governed by large shear walls), where they remain elastic, with the FRS to be bell shaped curves, highly amplified in a narrow period range around the fundamental period. This raises the necessity of examining if out-of-plane walls can potentially be subjected to these greater accelarations indicated by the narrow high amplified spectra. Therefore, the incorporation of a set of out-of-plane walls in the Opensees Models is decided, in order to compare their actual NLTH out-of-plane responses with their design responses ph. For the definition of the design response, the produced Shape Factor Coefficient Ci(Tp) for the Groningen Case is used. Hence, the second part of this research deals with the extended 1D Models, which are described as two degree of freedom mass-spring systems (2DOF systems). In the extended 1D Models, the nonlinear springs are in series and portray the hysteresis of the buildings and the out-of-plane walls. The hysteretic behaviour of the out-of-plane walls in the Opensees Models are calibrated to the experimental test of one-way spanning, double-clamped out-of-plane wall specimen COMP-7, performed at the Stevin Laboratory of the Delft University of Technology. Twelve wall configurations are considered, as a result of the 4 boundary conditions in the edges of one-way spanning walls presented in NZSEE Norm and 3 considered overburden loads (5 kN, 15 kN and 30 kN). The sensitivity studies in Opensees indicate that the design responses are larger than the NLTH responses for the non-failing walls and predict the failure when it is indicated in the NLTH responses. As a result, the Shape Factor Coefficient Ci(Tp) satisfies also the cases in which the FRS present higher values than the design plateau value. In the third part of the research, NLTH analyses are carried out in a 3D Model that resembles four two storey terraced houses with rigid diaphragms. The finite element method (FEM) software that is used for the NLTH analyses is ANSR-II and the Macro-element based modelling approach is adopted. ANSR-II allows the definition of nonlinear membrane elements to model the structural components. For shear walls and spandrels, specific in-plane backbone curves and hysteresis profiles are provided, being in agreement with the provisions of NZSEE Norm and Draft NPR 9998:2017. Regarding the in-plane rocking piers, no hysteresis is involved. However, the rocking capacity is in accordance with the Norms mentioned above. Triaxial excitations of the 3D Model with 11 sets of ground motions per area are performed in ANSR-II, following the requirements of Annex F of Draft NPR 9998:2017. From the NLTH analyses, the Floor Response Spectra are produced for each of the two floors of the 3D Model. These FRS are compared with the Design Floor Accelaration Spectra derived from the simplified 1D Models. A good predictabilty of the Response Spectra from the Design Spectra is found. Moreover, the Height Coefficient CHi is obtained as the ratio of the Peak Floor Accelaration (PFA) over the Peak Ground Accelaration (PGA). Linear regression analysis related to PFA/PGA ratios in the two floor levels of the structure is implemented per direction and area. The output is the linear equation describing the height effect as a function of height h. This equation has the same format with the one describing the Height Coefficient in NZSEE Norm, hence they are directly comparable. Similar to the 1D Models and for analogous purposes, sensitivity studies of one-way vertically-spanning out-of-plane walls in ANSR-II are conducted. The variation of the walls is retained the same. The out of plane walls in the 3D Model are modelled as beam elements that can rock out of their plane. The behaviour of these beam elements under dynamic excitation in ANSR-II is described by elastic loading and unloading, so no hysteresis is introduced. That is a major difference compared with the Opensees Models. In spite of that, the behaviour of the out-of-plane beam elements in ANSR-II is based on the rigid bodies assumption and rocking mechanism of an out-of-plane wall according to Nonlinear Kinematic Analysis (NLKA). In fact, a good agreement is observed between the capacity curves of the considered out-of-plane walls in ANSR-II and the capacity curves derived from the NLKA method. The results of the sensitivity studies in ANSR-II lead to same conclusions as the ones derived from the sensitivity studies in Opensees Models. That enhances the ability of the Shape Factor Coefficient Ci(Tp) and the Height Coefficient CHi to provide the appropriate design response. As an overall conclusion, it is stated that the Shape Factor Coefficient Ci(Tp) and the Height Coefficient CHi produced in this thesis, can be used for the definition of the displacement demand of one-way spanning out of-plane walls for the Groningen Case, using the displacement-based methodology described in NZSEE Norm. The deliverables serve all the possible factors and parameters that distinguish the characteristics of the Dutch scenario. As the number of the Opensees Models is already satisfying, it is recommended to carry out NLTH analyses in more 3D Models. It is believed that this would further raise the consistency of the deliverables.