Behaviour of two-way spanning walls subjected to out-of-plane loading by numerical analysis

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Unreinforced masonry (URM) buildings are vulnerable when subjected to out-of-plane dynamic loading, especially under as earthquakes. Within the masonry building, the wall spanning in the direction perpendicular to the seismic loading is the most critical component. Damage to these walls (out-of-plane failure) frequently leads to the partial or global collapse in the URM building structures, especially if the wall is a load-bearing wall. Boundary conditions and overburden load drastically influence the response of out-of-plane loaded walls. Two-way spanning walls that are restrained on three or four sides show a larger force capacity compares to one-way spanning walls, which are only restrained at top and bottom. Nevertheless, the studies on the behavior of two-way spanning walls are limited. This thesis aims to understand the two-way bending behavior of unreinforced masonry walls subjected to out-of-plane loading employing numerical analysis. A three-dimensional model using a shell element is adopted. Cracking is modeled with a continuum damage approach by comparing the isotropic model, namely the rotating smeared cracking approach (TSRC), and an orthotropic model, namely the engineering masonry model (EMM). The effect of the top boundary condition on the response of the two-way spanning walls is examined by considering case studies: four sides restrained wall with overburden load, and three sides restrained wall without overburden load. Both the walls are vertically connected with the pier (or return wall) with an alternate row of headers providing full moment restraint. The description concerning the seismic behavior of the two-way spanning wall made based upon the analysis carried out incorporating different loadings types like the uniform, mode proportional loading, time history, and cyclic loading. The orthotropic material model is better in evaluating the response of the two-way spanning wall as compared to the isotropic material model if the proper support condition is specified. The difference in response using either material model is visible at the onset of cracking. The response of the two-way spanning wall under monotonic increasing load using EMM demonstrates walls have a displacement capacity to sustaining a relatively constant load, whereas the TSRC fails to capture this behavior. Due to high non-linearity because of cracking in the elements, the solution becomes non-convergent, and a solid statement regarding the ultimate displacement capacity of the wall can not be made. However, based on the results from static analysis using EMM, a two-way spanning wall have sufficient displacement capacity well over the wall thickness. The displacement capacity signifies the wall can deform in the out-of-plane direction without failure and is beneficial, especially during an earthquake event. In two-way spanning walls, both the peak load and initial stiffness of the walls is enhanced by higher pre-compression and top lateral support. It is found both experimentally and numerically, as precompression increases flexural and shear resistance capacity of the wall to resist the out-of-plane load. Furthermore, in the wall restrained on three sides, the crack pattern is initiated at the main-wall and pier connection, representing the head-joint cracking, leading to changing the behavior from two-way to one-way. While in the wall restrained on four sides, the cracking is initiated at the top and bottom support, therefore the wall can sustain the load both via horizontal bending along the vertical edge. Furthermore, the influence of top rotation fixity on the crack pattern in four sides restrained wall demonstrates the change in crack pattern without significant difference in the force-displacement plot. Therefore, it is vital to know the proper boundary condition in the wall to help in identifying the weakest link and suggest the necessary strengthening location. To predict the dynamic behavior of the two-way spanning wall by alternative load application is studies using static, non-linear time history, and cyclic analysis. The analysis of the wall with uniform monotonic increasing load fails to capture the post-crack behavior. Whereas, under the application of mode-proportional loading and using the material properties as stated in the case study, the initial stiffness and peak load is significantly lower, because of the applied load pattern. Therefore, the material properties are calibrated to match the initial stiffness and peak load but fail to provide information regarding peak load and ultimate displacement capacity. Using the original material properties, the outcome of the non-linear time history (NLTH) gives reasonable prediction in response up to the pre-crack run as compared to the case study. The four sides restrained wall shows very stiff response with very few cracks initiations to dissipate energy in the wall while rapid degradation in the three sides restrained wall is found, which attributed to the brittle response with wall top reaching the larger out-of-plane displacement. Due to non-linearity (follows from cracking), irrespective of the material model, the outcomes of NLTH analysis fails to capture the crack and post-crack behavior. Therefore, the material model needs improvement in tension and cohesion softening to better account for non-linearity in the time-history analysis. Due to the limitation of the NLTH analysis, cyclic analysis with increasing magnitude of load cycles was carried out to replicate the dynamic response. The outcomes give a fair indication of material degradation (based on energy dissipation) and crack formation but fail to capture the displacement capacity. Furthermore, the contribution of mode-II fracture energy in the overall energy degradation is significant for three sides restrained wall but not in four sides restrained wall. Due to top support, and increased shear strength capacity of the wall due to pre-compression load. Analyzing the two-way spanning wall under different loading shows the asymmetric response in the positive (toward pier) and negative (away from pier) displacement directions (with a 36% difference in force capacity). This asymmetry is arisen due to the presence of the return wall at the vertical junction. Finally, the combination of static (with uniform load) and cyclic analysis provides a reliable indication of wall force degradation of the two-way spanning wall. It can be used as a substitute for NLTH analysis. However, no solid statement regarding displacement capacity can be made based on the non-convergence in the numerical analysis. Furthermore, the crack pattern observes under different loading shows the damage is primarily influenced by boundary conditions rather than the type of loading. Based on the outcome of the thesis work, further studies are needed to improve the convergent behavior of the numerical analyses to gain information on the displacement capacity of two-way spanning walls subject to out-of-plane loading. Additionally, it becomes interesting to explore the use of micro-modeling to understand the crack propagation in the masonry wall, and to exploring different anisotropic model such as the Rankine-Hill model, or to
explore the implementation of strain rate dependent constitutive model (mainly used for impact loading) to understand the dynamic behavior in NLTH analysis.