The Catholic Cathedral is classified as a category 1 listed heritage building constructed largely of unreinforced stone masonry, and was significantly damaged in the recent Canterbury earthquakes of 2010 and 2011. In the 2010 event the building presented slight to moderta damage, meanwhile in the 2011 one experienced ground shaking in excess of its capacity leading to block failures and partial collapse of parts of the building, which left the building standing but still posing a significant hazard. In this paper we discuss the approach to develop the earthquake analysis of the building by 3D numerical simulations, and the results are compared/calibrated with the observed damage of the 2010 earthquake. Very accurate records were obtained during both earthquakes due to a record station located least than 80 m of distance from the building and used in the simulations. Moreover it is included in the model the soil structure interaction because it was observed that the ground and foundation played an important role on the seismic behavior of the structure. A very good agreement was found between the real observed damage and the nonlinear dynamic simulations described trough inelastic deformation (cracking) and building´s performance.
Recent experiences from the Darfield and Canterbury, New Zealand earthquakes have shown that the soft soil condition of saturated liquefiable sand has a profound effect on seismic response of buildings, bridges and other lifeline infrastructure. For detailed evaluation of seismic response three dimensional integrated analysis comprising structure, foundation and soil is required; such an integrated analysis is referred to as Soil Foundation Structure Interaction (SFSI) in literatures. SFSI is a three-dimensional problem because of three primary reasons: first, foundation systems are three-dimensional in form and geometry; second, ground motions are three-dimensional, producing complex multiaxial stresses in soils, foundations and structure; and third, soils in particular are sensitive to complex stress because of heterogeneity of soils leading to a highly anisotropic constitutive behaviour. In literatures the majority of seismic response analyses are limited to plane strain configuration because of lack of adequate constitutive models both for soils and structures, and computational limitation. Such two-dimensional analyses do not represent a complete view of the problem for the three reasons noted above. In this context, the present research aims to develop a three-dimensional mathematical formulation of an existing plane-strain elasto-plastic constitutive model of sand developed by Cubrinovski and Ishihara (1998b). This model has been specially formulated to simulate liquefaction behaviour of sand under ground motion induced earthquake loading, and has been well-validated and widely implemented in verifcation of shake table and centrifuge tests, as well as conventional ground response analysis and evaluation of case histories. The approach adopted herein is based entirely on the mathematical theory of plasticity and utilises some unique features of the bounding surface plasticity formalised by Dafalias (1986). The principal constitutive parameters, equations, assumptions and empiricism of the existing plane-strain model are adopted in their exact form in the three-dimensional version. Therefore, the original two-dimensional model can be considered as a true subset of the three-dimensional form; the original model can be retrieved when the tensorial quantities of the three dimensional version are reduced to that of the plane-strain configuration. Anisotropic Drucker-Prager type failure surface has been adopted for the three-dimensional version to accommodate triaxial stress path. Accordingly, a new mixed hardening rule based on Mroz’s approach of homogeneous surfaces (Mroz, 1967) has been introduced for the virgin loading surface. The three-dimensional version is validated against experimental data for cyclic torsional and triaxial stress paths.
