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.
A non-destructive hardness testing method has been developed to investigate the amount of plastic strain demand in steel elements subjected to cyclic loading. The focus of this research is on application to the active links of eccentrically braced frames (EBFs), which are a commonly used seismic-resisting system in modern steel framed buildings. The 2010/2011 Christchurch earthquake series, especially the very intense February 22 shaking, which was the first earthquake worldwide to push complete EBF systems fully into their inelastic state, generating a moderate to high level of plastic strain in EBF active links, for a range of buildings from 3 to 23 storeys in height. This raised two important questions: 1) what was the extent of plastic deformation in active links; and 2) what effect does that have to post-earthquake steel properties? This project comprised determining a robust relationship between hardness and plastic strain in order to be able to answer the first question and provide the necessary input into answering the second question. A non-destructive Leeb (portable) hardness tester (model TH170) has been used to measure the hardness, in order to determine the plastic strain, in hot rolled steel universal sections and steel plates. A bench top Rockwell B was used to compare and validated the hardness measured by the portable hardness tester. Hardness was measured from monotonically strained tensile test specimens to identify the relationship between hardness and plastic strain demand. Test results confirmed a good relationship between hardness and the amount of monotonically induced plastic strain. Surface roughness was identified as an important parameter in obtaining reliable hardness readings from a portable hardness reader. A proper surface preparation method was established by using three different cleaning methods, finished with hand sanding to achieve surface roughness coefficients sufficiently low not to distort the results. This work showed that a test surface roughness (Ra) is not more than 1.6 micron meter (μm) is required for accurate readings from the TH170 tester. A case study on an earthquake affected building was carried out to identify the relationship between hardness and amount of plastic strain demand in cyclically deformed active links. Hardness was carried out from active links shown visually to have been the most affected during one of the major earthquake events. Onsite hardness test results were then compared with laboratory hardness test results. A good relationship between hardness from onsite and laboratory was observed between the test methods; Rockwell B bench top and portable Leeb tester TH170. Manufacturing induced plastic strain in the top and bottom of the webs of hot rolled sections were discovered from this research, an important result which explains why visual effects of earthquake induced active link yielding (eg cracked or flaking paint) was typically more prevalent over the middle half depth of the active link. The extent of this was quantified. It was also evident that the hardness readings from the portable hardness tester are influenced by geometry, mass effects and rigidity of the links. The final experimental stage was application of the method to full scale cyclic inelastic tested nominally identical active links subjected to loading regimes comprising constant and variable plastic strain demands. The links were cyclically loaded to achieve different plastic strain level. A novel Digital Image Correlation (DIC) technique was incorporated during the tests of this scale, to confirm the level of plastic strain achieved. Tensile test specimens were water jet cut from cyclically deformed webs to analyse the level of plastic strain. Test results show clear evidence that cyclically deformed structural steel elements show good correlation between hardness and the amount of plastic strain demand. DIC method was found to be reliable and accurate to check the level of plastic strain within cyclically deformed structural steel elements.
