Well-validated liquefaction constitutive models are increasingly important as non-linear time history analyses become relatively more common in industry for key projects. Previous validation efforts of PM4Sand, a plasticity model specifically for liquefaction, have generally focused on centrifuge tests; however, pore pressure transducers installed at several free-field sites during the Canterbury Earthquake Sequence (CES) in Christchurch, New Zealand provide a relatively unique dataset to validate against. This study presents effective stress site response analyses performed in the finite difference software FLAC to examine the capability of PM4Sand to capture the generation of excess pore pressures during earthquakes. The characterization of the subsurface is primarily based on extensive cone penetration tests (CPT) carried out in Christchurch. Correlations based on penetration resistances are used to estimate soil parameters, such as relative density and shear wave velocity, which affect liquefaction behaviour. The resulting free-field FLAC model is used to estimate time histories of excess pore pressure, which are compared with records during several earthquakes in the CES to assess the suitability of PM4Sand.
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.
