Force-displacement response of in-plane loaded URM walls with a dominating flexural mode

This article presents a new mechanical model for the non-linear force-displacement response of unreinforced masonry (URM) walls developing a flexural rocking mode including their displacement capacity. The model is based on the plane section hypothesis and a constitutive law for the masonry with zero tensile strength and linear-elastic behaviour in compression. It is assumed that only the compressed part of the wall contributes to the stiffness of the wall and therefore the model accounts for a softening of the response due the reduction of the effective area. Stress conditions for limit states are proposed that characterise the flexural failure. The new model allows therefore to link local performance levels to global displacement capacities. The limit states criteria describe the behaviour of modern URM walls with cement mortar of normal thickness and clay bricks. The model is validated through comparison of local and global engineering demand parameters with experimental results. It provides good prediction of the effective stiffness, the force capacity and the displacement capacity of URM walls at different limit states.

Investigating the in-plane mechanical behavior of URM piers via DSFM

Katrin Beyer, Sarah Petry, Shenghan Zhang

In this paper we use the novel Disturbed Stress Field Model (DSFM) from Facconi et al. (2013) to model the lateral in-plane behaviour of different unreinforced masonry (URM) walls which we tested at the laboratory of the EPF Lausanne, Switzerland. The model uses the failure criterion developed by Ganz (1985) for URM and is implemented in the software VecTor 2. In the first part of this article, we show that the DSFM gives good estimates for the initial stiffness of the walls but underestimates the displacement and force capacity of our URM walls. This is due to the confinement of the mortar base joint which is confined by the wall foundation. However, we show that this phenomenon can be accounted for by replacing the compression strength of the masonry of the first brick layer by the strength of the brick itself. Using this improved model, we compare the numerical results to the experimental results with regard to displacements and strains. We show that the simplification of the masonry to a continuous material is correct when comparing the global engineering demand parameters (EDPs), e.g., force-displacement behaviour of the walls or crack pattern. However, when comparing local EDPs, e.g., strains and crack widths, significant differences can be obtained. These differences are mainly caused by the torque of the bricks inside the walls (Mann and Müller, 1982). We show that this distortion gets less important with increasing shear span and that for a wall with higher shear span the assumption of a continuous material gives reasonable results even at the local level.

2014

Force-displacement response of unreinforced masonry walls for seismic design

Sarah Petry

In regions with low to moderate seismicity, unreinforced masonry (URM) is commonly used for the construction of low to mid-rise buildings. When these structures are subjected to seismic loading, the stiff URM walls attract considerable part of the lateral forces and need therefore to be considered in seismic design and assessment. Nevertheless, the response of URM walls subjected to lateral in-plane loading is not yet fully understood and given estimates for some of the crucial design parameters are unsatisfactory (the displacement capacity and the effective stiffness). Two series of URM walls tested under lateral in-plane loading are presented. First series was built at full-scale using a typical Swiss hollow clay brick and a commercially available standard cement-based mortar. Second series represented the same walls at half-scale. During all tests, the walls were subjected to quasi-static cycles of increasing drift demands, while controlling the boundary conditions (axial load and moment restraint at the top of the walls) such to simulate the typical loading of a ground floor wall in an URM building. From the experiments several new insights on the kinematics of URM walls are drawn. For instance, it is identified that once several diagonal cracks develop in the walls, the deformation capacity of the walls is governed by the separation of the rectangular wall into two triangles. From comparison between both test series at different scales, new recommendations for the correct scaling of hollow core masonry are derived and proposed. In order to compare our own results to other existing wall tests, an existing dataset of URM walls is extended and reanalyzed. Finally, a dataset of 64 quasi-static tests on modern URM walls of different heights and masonry types is presented. The evaluation of the dataset confirms the influence of the boundary conditions on the drift capacity. Moreover, it reveals the presence of a strong size effect and an empirical equation is proposed to estimate the ultimate drift capacity while accounting for these factors. Throughout the wall tests, an optical measurement system is used to track the displacement field of the walls. This measurement was synchronized with the force measurement such that global and local engineering demand parameters of the walls could be linked. This point was crucial for the following contributions of this thesis: (i) proposition of two sets of limit states (LSs) that link local damage states to characteristic points of the global force-displacement curve of URM walls; (ii) the study of different deformation parameters for the validation of mechanical and numerical models at local level. A new mechanical model is proposed which describes the nonlinear force-displacement response of flexural dominated URM walls. For this, first, an analytical part is derived based on the plane section hypothesis and a non-tension material with a linear-elastic constitutive material law in compression. It assumes that only the compressed part of the wall contributes to the wall resistance and accounts for a softening due to the reduction of the effective area. In a second step, new criteria are developed which predict the occurrence of the previous proposed local LSs, which are then incorporated in the analytical model. The new complete mechanical model is validated through the comparison with experimental evidence yielding to good estimates for the effective stiffness and the displacement capacity.

EPFL2015

Limit states of modern unreinforced clay brick masonry walls subjected to in-plane loading

Katrin Beyer, Sarah Petry

Recent research showed that the in-plane horizontal displacement capacity of unreinforced masonry (URM) walls depends on numerous factors that are not yet captured by current empirical drift capacity models; e.g., axial stress, shear span, geometry of the walls and the material used. In order to improve the performance-based assessment of URM wall buildings, future research should aim at developing numerical and mechanical models that link the global force-displacement response of URM walls to local deformation measures such as strains. This paper addresses the behaviour of modern clay brick masonry and makes first contributions to such an endeavour by the evaluation of experimental results: first, two sets of limit states are proposed that link local damage limit states to characteristic points of the global force-displacement response of the URM wall. The two sets define limit states for walls developing a shear or a flexural mechanism respectively. Second, local deformation measures deemed suitable for the characterisation of these limit states are evaluated from optical measurement data of quasi-static cyclic wall tests. These include strains, compression zone depth and the ratio of shear to flexural deformations.

Springer Verlag2015

Force-displacement response of unreinforced masonry walls for seismic design

Sarah Petry

EPFL2015