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.
The paper discusses modelling of cyclic stress-strain behaviour of soil, in particular a simple model that can produce a desired stiffness and hysteretic damping for a given strain level as observed in laboratory testing is formulated. The unloading-reloading relationship is developed for total stress seismic site response analysis with appropriate damping at large strain. The constitutive model employs a hyperbolic equation as the backbone curve, and uses a modification of the extended Masing unloading-reloading relationship leading to correct measured modulus reduction and damping curves simultaneously. A quasi-static cyclic loading of increasing amplitude is used to demonstrate the model’s performance and its capability to allow improved modelling of the magnitude of energy dissipation based on an experimental program on native sandy soils from Christchurch, New Zealand.
This paper presents the probabilistic seismic performance and loss assessment of an actual bridge– foundation–soil system, the Fitzgerald Avenue twin bridges in Christchurch, New Zealand. A two-dimensional finite element model of the longitudinal direction of the system is modelled using advanced soil and structural constitutive models. Ground motions at multiple levels of intensity are selected based on the seismic hazard deaggregation at the site. Based on rigorous examination of several deterministic analyses, engineering demand parameters (EDP’s), which capture the global and local demand, and consequent damage to the bridge and foundation are determined. A probabilistic seismic loss assessment of the structure considering both direct repair and loss of functionality consequences was performed to holistically assess the seismi risk of the system. It was found that the non-horizontal stratification of the soils, liquefaction, and soil–structure interaction had pronounced effects on the seismic demand distribution of the bridge components, of which the north abutment piles and central pier were critical in the systems seismic performance. The consequences due to loss of functionality of the bridge during repair were significantly larger than the direct repair costs, with over a 2% in 50 year probability of the total loss exceeding twice the book-value of the structure.
Deformational properties of soil, in terms of modulus and damping, exert a great influence on seismic response of soil sites. However, these properties for sands containing some portion of fines particles have not been systematically addressed. In addition, simultaneous modelling of the modulus and damping behaviour of soils during cyclic loading is desirable. This study presents an experimental and computational investigation into the deformational properties of sands containing fines content in the context of site response analysis. The experimental investigation is carried on sandy soils sourced from Christchurch, New Zealand using a dynamic triaxial apparatus while the computational aspect is based on the framework of total-stress one-dimensional (1D) cyclic behaviour of soil. The experimental investigation focused on a systematic study on the deformational behaviour of sand with different amounts of fines content (particle diameter ≤ 75µm) under drained conditions. The silty sands were prepared by mixing clean sand with three different percentages of fines content. A series of bender element tests at small-strain range and stress-controlled dynamic triaxial tests at medium to high-strain ranges were conducted on samples of clean sand and silty sand. This allowed measurements of linear and nonlinear deformational properties of the same specimen for a wide strain range. The testing program was designed to quantify the effects of void ratio and fines content on the low-strain stiffness of the silty sand as well as on the nonlinear stress-strain relationship and corresponding shear modulus and damping properties as a function of cyclic shear strains. Shear wave velocity, Vs, and maximum shear modulus, Gmax, of silty sand was shown to be significantly smaller than the respective values for clean sands measured at the same void ratio, e, or same relative density, Dr. However, the test results showed that the difference in the level of nonlinearity between clean sand and silty sands was small. For loose samples prepared at an identical relative density, the behaviour of clean sand was slightly less nonlinear as compared to sandy soils with higher fines content. This difference in the nonlinear behaviour of clean sand and sandy soils was negligible for dense soils. Furthermore, no systematic influence of fines content on the material damping curve was observed for sands with fines content FC = 0 to 30%. In order to normalize the effects of fines on moduli of sands, equivalent granular void ratio, e*, was employed. This was done through quantifying the participation of fines content in the force transfer chain of the sand matrix. As such, a unified framework for modelling of the variability of shear wave velocity, Vs, (or shear modulus, Gmax) with void ratio was achieved for clean sands and sands with fines, irrespective of their fines content. Furthermore, modelling of the cyclic stress-strain behaviour based on this experimental program was investigated. The modelling effort focused on developing a simple constitutive model which simultaneously models the soil modulus and damping relationships with shear strains observed in laboratory tests. The backbone curve of the cyclic model was adopted based on a modified version of Kondner and Zelasko (MKZ) hyperbolic function, with a curvature coefficient, a. In order to simulate the hysteretic cycles, the conventional Masing rules (Pyke 1979) were revised. The parameter n, in the Masing’s criteria was assumed to be a function of material damping, h, measured in the laboratory. As such the modulus and damping produced by the numerical model could match the stress-strain behaviour observed in the laboratory over the course of this study. It was shown that the Masing parameter n, is strain-dependent and generally takes values of n ≤ 2. The model was then verified through element test simulations under different cyclic loadings. It was shown that the model could accurately simulate the modulus and the damping simultaneously. The model was then incorporated within the OpenSees computational platform and was used to scrutinize the effects of damping on one-dimensional seismic site response analysis. For this purpose, several strong motion stations which recorded the Canterbury earthquake sequence were selected. The soil profiles were modelled as semi-infinite horizontally layered deposits overlying a uniform half-space subjected to vertically propagating shear waves. The advantages and limitations of the nonlinear model in terms of simulating soil nonlinearity and associated material damping were further scrutinized. It was shown that generally, the conventional Masing criteria unconservatively may underestimate some response parameters such as spectral accelerations. This was shown to be due to larger hysteretic damping modelled by using conventional Masing criteria. In addition, maximum shear strains within the soil profiles were also computed smaller in comparison to the values calculated by the proposed model. Further analyses were performed to study the simulation of backbone curve beyond the strain ranges addressed in the experimental phase of this study. A key issue that was identified was that relying only on the modulus reduction curves to simulate the stress-strain behaviour of soil may not capture the actual soil strength at larger strains. Hence, strength properties of the soil layer should also be incorporated to accurately simulate the backbone curve.
A building boom in the 1980s allowed pre-stressed hollow-core floor construction to be widely adopted in New Zealand, even though the behaviour of these prefabricated elements within buildings was still uncertain. Inspections following the Canterbury and Kaikōura earthquakes has provided evidence of web-splitting, transverse cracking and longitudinal splitting on hollow-core units, confirming the susceptibility of these floors to undesirable failure modes. Hollow-core slabs are mainly designed to resist bending and shear. However, there are many applications in which they are also subjected to torsion. In New Zealand, hollow-core units contain no transverse reinforcement in the soffit concrete below the cells and no web reinforcement. Consequently, their dependable performance in torsion is limited to actions that they can resist before torsional cracking occurs. In previous work by the present authors, a three-dimensional FE modelling approach to study the shear flexural behaviour of precast pre-stressed hollow core units was developed and validated by full-scale experiments. This paper shows how the FE analyses have been extended to investigate the response of HC units subjected to torsional actions. Constitutive models, based on nonlinear fracture mechanics, have been used to numerically predict the torsional capacity of HC units and have been compared with experimental results. The results indicate that the numerical approach is promising and should be developed further as part of future research.
In 2010 and 2011 Christchurch, New Zealand experienced a series of earthquakes that caused extensive damage across the city, but primarily to the Central Business District (CBD) and eastern suburbs. A major feature of the observed damage was extensive and severe soil liquefaction and associated ground damage, affecting buildings and infrastructure. The behaviour of soil during earthquake loading is a complex phenomena that can be most comprehensively analysed through advanced numerical simulations to aid engineers in the design of important buildings and critical facilities. These numerical simulations are highly dependent on the capabilities of the constitutive soil model to replicate the salient features of sand behaviour during cyclic loading, including liquefaction and cyclic mobility, such as the Stress-Density model. For robust analyses advanced soil models require extensive testing to derive engineering parameters under varying loading conditions for calibration. Prior to this research project little testing on Christchurch sands had been completed, and none from natural samples containing important features such as fabric and structure of the sand that may be influenced by the unique stress-history of the deposit. This research programme is focussed on the characterisation of Christchurch sands, as typically found in the CBD, to facilitate advanced soil modelling in both res earch and engineering practice - to simulate earthquake loading on proposed foundation design solutions including expensive ground improvement treatments. This has involved the use of a new Gel Push (GP) sampler to obtain undisturbed samples from below the ground-water table. Due to the variable nature of fluvial deposition, samples with a wide range of soil gradations, and accordingly soil index properties, were obtained from the sampling sites. The quality of the samples is comprehensively examined using available data from the ground investigation and laboratory testing. A meta-quality assessment was considered whereby a each method of evaluation contributed to the final quality index assigned to the specimen. The sampling sites were characterised with available geotechnical field-based test data, primarily the Cone Penetrometer Test (CPT), supported by borehole sampling and shear-wave velocity testing. This characterisation provides a geo- logical context to the sampling sites and samples obtained for element testing. It also facilitated the evaluation of sample quality. The sampling sites were evaluated for liquefaction hazard using the industry standard empirical procedures, and showed good correlation to observations made following the 22 February 2011 earthquake. However, the empirical method over-predicted liquefaction occurrence during the preceding 4 September 2010 event, and under-predicted for the subsequent 13 June 2011 event. The reasons for these discrepancies are discussed. The response of the GP samples to monotonic and cyclic loading was measured in the laboratory through triaxial testing at the University of Canterbury geomechanics laboratory. The undisturbed samples were compared to reconstituted specimens formed in the lab in an attempt to quantify the effect of fabric and structure in the Christchurch sands. Further testing of moist tamped re- constituted specimens (MT) was conducted to define important state parameters and state-dependent properties including the Critical State Line (CSL), and the stress-strain curve for varying state index. To account for the wide-ranging soil gradations, selected representative specimens were used to define four distinct CSL. The input parameters for the Stress-Density Model (S-D) were derived from a suite of tests performed on each representative soil, and with reference to available GP sample data. The results of testing were scrutinised by comparing the data against expected trends. The influence of fabric and structure of the GP samples was observed to result in similar cyclic strength curves at 5 % Double Amplitude (DA) strain criteria, however on close inspection of the test data, clear differences emerged. The natural samples exhibited higher compressibility during initial loading cycles, but thereafter typically exhibited steady growth of plastic strain and excess pore water pressure towards and beyond the strain criteria and initial liquefaction, and no flow was observed. By contrast the reconstituted specimens exhibited a stiffer response during initial loading cycles, but exponential growth in strains and associated excess pore water pressure beyond phase-transformation, and particularly after initial liquefaction where large strains were mobilised in subsequent cycles. These behavioural differences were not well characterised by the cyclic strength curve at 5 % DA strain level, which showed a similar strength for both GP samples and MT specimens. A preliminary calibration of the S-D model for a range of soil gradations is derived from the suite of laboratory test data. Issues encountered include the influence of natural structure on the peak-strength–state index relationship, resulting in much higher peak strengths than typically observed for sands in the literature. For the S-D model this resulted in excessive stiffness to be modelled during cyclic mobility, when the state index becomes large momentarily, causing strain development to halt. This behaviour prevented modelling the observed re- sponse of silty sands to large strains, synonymous with “liquefaction”. Efforts to reduce this effect within the current formulation are proposed as well as future research to address this issue.
The Canterbury Earthquake Sequence (CES) of 2010-2011 caused widespread liquefaction in many parts of Christchurch. Observations from the CES highlight some sites were liquefaction was predicted by the simplified method but did not manifest. There are a number of reasons why the simplified method may over-predict liquefaction, one of these is the dynamic interaction between soil layers within a stratified deposit. Soil layer interaction occurs through two key mechanisms; modification of the ground motion due to seismic waves passing through deep liquefied layers, and the effect of pore water seepage from an area of high excess pore water pressure to the surrounding soil. In this way, soil layer interaction can significantly alter the liquefaction behaviour and surface manifestation of soils subject to seismic loading. This research aimed to develop an understanding of how soil layer interaction, in particular ground motion modification, affects the development of excess pore water pressures and liquefaction manifestation in a soil deposit subject to seismic loading. A 1-D soil column time history Effective Stress Analysis (ESA) was conducted to give an in depth assessment of the development of pore pressures in a number of soil deposits. For this analysis, ground motions, soil profiles and model parameters were required for the ESA. Deconvolution of ground motions recorded at the surface during the CES was used to develop some acceleration time histories to input at the base of the soil-column model. An analysis of 55 sites around Christchurch, where detailed site investigations have been carried out, was then conducted to identify some simplified soil profiles and soil characteristics. From this analysis, four soil profiles representative of different levels of liquefaction manifestation were developed. These were; two thick uniform and vertically continuous sandy deposits that were representative of sites were liquefaction manifested in both the Mw 7.1 September 2010 and the Mw 6.3 February 2011 earthquakes, and two vertically discontinuous profiles with interlayered liquefiable and non-liquefiable layers representative of sites that did not manifest liquefaction in either the September 2010 or the February 2011 events. Model parameters were then developed for these four representative soil profiles through calibration of the constitutive model in element test simulations. Simulations were run for each of the four profiles subject to three levels of loading intensity. The results were analysed for the effect of soil layer interaction. These were then compared to a simplified triggering analysis for the same four profiles to determine where the simplified method was accurate in predicting soil liquefaction (for the continuous sandy deposits) and were it was less accurate (the vertically discontinuous deposits where soil layer interaction was a factor).
