We present initial results from a set of three-dimensional (3D) deterministic earthquake ground motion simulations for the northern Canterbury plains, Christchurch and the Banks Peninsula region, which explicitly incorporate the effects of the surface topography. The simu-lations are done using Hercules, an octree-based finite-element parallel software for solving 3D seismic wave propagation problems in heterogeneous media under kinematic faulting. We describe the efforts undertaken to couple Hercules with the South Island Velocity Model (SIVM), which included changes to the SIVM code in order to allow for single repetitive que-ries and thus achieve a seamless finite-element meshing process within the end-to-end ap-proach adopted in Hercules. We present our selection of the region of interest, which corre-sponds to an area of about 120 km × 120 km, with the 3D model reaching a depth of 60 km. Initial simulation parameters are set for relatively high minimum shear wave velocity and a low maximum frequency, which we are progressively scaling up as computing resources permit. While the effects of topography are typically more important at higher frequencies and low seismic velocities, even at this initial stage of our efforts (with a maximum of 2 Hz and a mini-mum of 500 m/s), it is possible to observe the importance of the topography in the response of some key locations within our model. To highlight these effects we compare the results of the 3D topographic model with respect to those of a flat (squashed) 3D model. We draw rele-vant conclusions from the study of topographic effects during earthquakes for this region and describe our plans for future work.
Damage distribution maps from strong earthquakes and recorded data from field experiments have repeatedly shown that the ground surface topography and subsurface stratigraphy play a decisive role in shaping the ground motion characteristics at a site. Published theoretical studies qualitatively agree with observations from past seismic events and experiments; quantitatively, however, they systematically underestimate the absolute level of topographic amplification up to an order of magnitude or more in some cases. We have hypothesized in previous work that this discrepancy stems from idealizations of the geometry, material properties, and incident motion characteristics that most theoretical studies make. In this study, we perform numerical simulations of seismic wave propagation in heterogeneous media with arbitrary ground surface geometry, and compare results with high quality field recordings from a site with strong surface topography. Our goal is to explore whether high-fidelity simulations and realistic numerical models can – contrary to theoretical models – capture quantitatively the frequency and amplitude characteristics of topographic effects. For validation, we use field data from a linear array of nine portable seismometers that we deployed on Mount Pleasant and Heathcote Valley, Christchurch, New Zealand, and we compute empirical standard spectral ratios (SSR) and single-station horizontal-to-vertical spectral ratios (HVSR). The instruments recorded ambient vibrations and remote earthquakes for a period of two months (March-April 2017). We next perform two-dimensional wave propagation simulations using the explicit finite difference code FLAC. We construct our numerical model using a high-resolution (8m) Digital Elevation Map (DEM) available for the site, an estimated subsurface stratigraphy consistent with the geomorphology of the site, and soil properties estimated from in-situ and non-destructive tests. We subject the model to in-plane and out-of-plane incident motions that span a broadband frequency range (0.1-20Hz). Numerical and empirical spectral ratios from our blind prediction are found in very good quantitative agreement for stations on the slope of Mount Pleasant and on the surface of Heathcote Valley, across a wide range of frequencies that reveal the role of topography, soil amplification and basin edge focusing on the distribution of ground surface motion.
The influence of nonlinear soil-foundation-structure interaction (SFSI) on the performance of multi-storey buildings during earthquake events has become increasingly important in earthquake resistant design. For buildings on shallow foundations, SFSI refers to nonlinear geometric effects associated with uplift of the foundation from the supporting soil as well as nonlinear soil deformation effects. These effects can potentially be beneficial for structural performance, reducing forces transmitted from ground shaking to the structure. However, there is also the potential consequence of residual settlement and rotation of the foundation. This Thesis investigates the influence of SFSI in the performance of multi-storey buildings on shallow foundations through earthquake observations, experimental testing, and development of spring-bed numerical models that can be incorporated into integrated earthquake resistant design procedures. Observations were made following the 22 February 2011 Christchurch Earthquake in New Zealand of a number of multi-storey buildings on shallow foundations that performed satisfactorily. This was predominantly the case in areas where shallow foundations, typically large raft foundations, were founded on competent gravel and where there was no significant manifestation of liquefaction at the ground surface. The properties of these buildings and the soils they are founded on directed experimental work that was conducted to investigate the mechanisms by which SFSI may have influenced the behaviour of these types of structure-foundation systems. Centrifuge experiments were undertaken at the University of Dundee, Scotland using a range of structure-foundation models and a layer of dense cohesionless soil to simulate the situation in Christchurch where multi-storey buildings on shallow foundations performed well. Three equivalent single degree of freedom (SDOF) models representing 3, 5, and 7 storey buildings with identical large raft foundations were subjected to a range of dynamic Ricker wavelet excitations and Christchurch Earthquake records to investigate the influence of SFSI on the response of the equivalent buildings. The experimental results show that nonlinear SFSI has a significant influence on structural response and overall foundation deformations, even though the large raft foundations on competent soil meant that there was a significant reserve of bearing capacity available and nonlinear deformations may have been considered to have had minimal effect. Uplift of the foundation from the supporting soil was observed across a wide range of input motion amplitudes and was particularly significant as the amplitude of motion increased. Permanent soil deformation represented by foundation settlement and residual rotation was also observed but mainly for the larger input motions. However, the absolute extent of uplift and permanent soil deformation was very small compared to the size of the foundation meaning the serviceability of the building would still likely be maintained during large earthquake events. Even so, the small extent of SFSI resulted in attenuation of the response of the structure as the equivalent period of vibration was lengthened and the equivalent damping in the system increased. The experimental work undertaken was used to validate and enhance numerical modelling techniques that are simple yet sophisticated and promote interaction between geotechnical and structural specialists involved in the design of multi-storey buildings. Spring-bed modelling techniques were utilised as they provide a balance between ease of use, and thus ease of interaction with structural specialists who have these techniques readily available in practice, and theoretically rigorous solutions. Fixed base and elastic spring-bed models showed they were unable to capture the behaviour of the structure-foundation models tested in the centrifuge experiments. SFSI spring-bed models were able to more accurately capture the behaviour but recommendations were proposed for the parameters used to define the springs so that the numerical models closely matched experimental results. From the spring-bed modelling and results of centrifuge experiments, an equivalent linear design procedure was proposed along with a procedure and recommendations for the implementation of nonlinear SFSI spring-bed models in practice. The combination of earthquake observations, experimental testing, and simplified numerical analysis has shown how SFSI is influential in the earthquake performance of multi-storey buildings on shallow foundations and should be incorporated into earthquake resistant design of these structures.
