Numerical Modelling of Multi-directional Earthquake Loading and Its Effect on Sand Liquefaction

Earthquakes generate multi-directional ground motions, two components in the horizontal direction and one in the vertical. Nevertheless, the effect of vertical motion on site response analysis has not been the object of extensive research. The 2010/2011 Canterbury sequence of seismic events in New Zealand is a prime example among other earlier field observations strongly corroborating that the vertical acceleration may have a detrimental effect on soil liquefaction. Consequently, this study aims to provide insight into the influence of the input vertical motion on sand liquefaction. For this reason, two ground motions, with very different frequency contents, are used as the input excitations. Non-linear elasto-plastic plane strain fully coupled effective stress-based finite element analyses are conducted to investigate the occurrence of liquefaction in a hypothetical fully saturated Fraser River Sand deposit. The results indicate that the frequency content of the input motion is of utmost importance for the response of sands to liquefaction when the vertical loading is considered

The importance of accurate time-integration in the numerical modelling of P-wave propagation

The numerical dissipation characteristics of the Newmark and generalised-α time-integration schemes are investigated for P-wave propagation in a fully saturated level-ground sand deposit, where higher frequencies than those for S-waves are of concern. The study focuses on resonance, which has been shown to be of utmost importance for triggering liquefaction due to P-waves alone. The generalised-α scheme performs well, provided that the time-step has been carefully selected. Conversely, the dissipative Newmark method can excessively damp the response, changing radically the computed results. This implies that a computationally prohibiting small time-step would be required for Newmark to provide an accurate solution

CONTAIN D11 : integrated final results and conclusions

Carbon capture and storage is a technology capable of reducing CO2 outputs on a large scale; the concept usually requires CO2 to be removed from post-combustion flue gases and sequestered in geological formations. Depleted gas fields constitute “the most important storage type for the UK” and will provide a large and important potential future offshore storage capacity (DECC, 2012). Over the last 4 years, the CONTAIN research project has focussed on the geomechanical behaviour of depleted hydrocarbon fields in response to injection with CO2, combining a modelling and experimental approach with the public perceptions of CCS into three work packages. The project has provided a better understanding of the hydromechanical impacts of depletion on caprocks and the effect of subsequent CO2 injection, in order to assist with the implementation of CCS in this type of reservoir. Work package 1 outlined a phenomenological approach to assessing possible deformation during operation. Focus was placed on rock mechanics and transport experiments on material from the geologies of target formations in the North Sea, providing information that could be incorporated into numerical simulations. Work package 2 expanded this understanding by considering fractured caprock. Numerical modelling was used to study the deformation of an initially intact caprock caused by the depletion of an underlying reservoir during oil extraction. Deformation and flow were geomechanically modelled in three dimensions using a fully coupled poroelastic model, incorporating discrete fractures and faults into the caprock. Work package 3 offered new and valuable insight on future public awareness campaigns aimed at gaining acceptance of CCS. Qualitative expert interviews have been used, a CCS expert survey and a public survey across four countries to gain an understanding of perceptions of CCS risks and benefits, and has allowed for comparison of views on CCS between experts and public. In addition, the work package has explored the impact of different message framings on CCS attitudes. The findings of each work package are summarised in this report, with each work package represented by a report chapter. A synthesis of the findings and discussion of the work as a whole follows

A case study of liquefaction: demonstrating the application of an advanced model and understanding the pitfalls of the simplified procedure

The complexity of advanced constitutive models often dictates that their capabilities are only demonstrated in the context of model testing under controlled conditions. In the case of earthquake engineering and liquefaction in particular, this restriction is magnified by the difficulties in measuring field behaviour under seismic loading. In this paper, the well documented case of the Canterbury Earthquake Sequence in New Zealand, for which extensive field and laboratory data are available, is utilised to demonstrate the accuracy of a bounding surface plasticity model in fully-coupled finite element analyses. A strong motion station with manifestation of liquefaction and the second highest peak vertical ground acceleration during the Mw 6.2 February 2011 event is modelled. An empirical assessment predicted no liquefaction for this station, making this an interesting case for rigorous numerical modelling. The calibration of the model aims at capturing both the laboratory tests and the field measurements in a consistent manner. The characterisation of the ground conditions is presented, while, to specify the bedrock motion, the records of two stations without liquefaction are deconvolved and scaled to account for wave attenuation with distance. The numerical predictions are compared to both the horizontal and vertical acceleration records and other field observations, showing a remarkable agreement, also demonstrating that the high vertical accelerations can be attributed to compressional resonance. The results provide further insights into the underperformance of the simplified procedure

Vertical ground motion and its effects on liquefaction resistance of fully saturated sand deposits

Soil liquefaction has been extensively investigated over the years with the aim to understand its fundamental mechanism and successfully remediate it. Despite the multi-directional nature of earthquakes, the vertical seismic component is largely neglected, as it is traditionally considered to be of much lower amplitude than the components in the horizontal plane. The 2010–2011 Canterbury earthquake sequence in New Zealand is a prime example that vertical accelerations can be of significant magnitude, with peak amplitudes well exceeding their horizontal counterparts. As research on this topic is very limited, there is an emerging need for a more thorough investigation of the vertical motion and its effect on soil liquefaction. As such, throughout this study, uni- and bidirectional finite-element analyses are carried out focusing on the influence of the input vertical motion on sand liquefaction. The effects of the frequency content of the input motion, of the depth of the deposit and of the hydraulic regime, using variable permeability, are investigated and exhaustively discussed. The results indicate that the usual assumption of linear elastic response when compressional waves propagate in a fully saturated sand deposit does not always hold true. Most importantly post-liquefaction settlements appear to be increased when the vertical component is included in the analysis

An energy-based interpretation of sand liquefaction due to vertical ground motion

In several recent earthquakes, high vertical ground accelerations accompanied by liquefaction were observed. Downhole records have also shown that large vertical accelerations do not necessarily originate from the source, but rather get amplified towards the ground surface. Given the advantages of energy-based interpretation of liquefaction triggering due to S-waves, this approach is used together with finite element analyses to investigate vertical motion amplification and ensuing liquefaction. The results show the importance of the post-resonance response cycles, while hysteretic damping based on total stresses, accounting for the water in the pores, is shown to be very low, explaining the observed amplification

Liquefaction modelling of a strong motion station in Christchurch, New Zealand

Advanced constitutive models can replicate several aspects of soil behaviour, but, due to their complexity and number of parameters, they need more sophisticated and realistic validation under general loading conditions. When modelling liquefaction phenome na, the lack of field monitoring data means that model testing, such as centrifuge experiments, is often used as benchmark for the numerical analyses. The 2010 - 2011 Canterbury earthquake sequence in New Zealand was recorded by a number of strong motion sta tions at various distances from the earthquake epicentre. Additionally, an extensive field and laboratory program me has since become available, adequately describing the geological, geotechnical and hydro geo logical conditions in the area. As such, the perf ormance of a two - surface bounding surface plasticity constitutive model for sands, calibrated based on site - specific laboratory data, is assessed using field evidence of a strong motion station in fully - coupled effective stress - based finite element analyse s. As the real stratigraphy is complex , with layers of silts and clays between the sandy strata, a simpler cyclic non - linear elastic model , which can adequately incorporate the basic aspects of dynamic soil behaviour, is also used to model the non - liquefia ble strata. To specify the input ground motion at the base of the deposit , the recorded ground surface motion at a site with no evidence of liquefaction is deconvolve d and compared with the outcrop predictions of a New Zealand - specific gr ound motion predic tion equation . The numerical results are compared with the recorded horizontal ground surface acceleration time - history of the 22 nd February 2011 seismic event , exhibiting very good agreement

The effect of irregular seismic loading on the validity of the simplified liquefaction procedures

Soil liquefaction has been one of the major hazards for civil engineering projects relating to earthquakes. The simplified liquefaction procedure which is used to assess liquefaction susceptibility in practice is still based on semi-empirical methods. These rely on the assumption that irregular seismic motions can be represented fully by an equivalent number of cycles of uniform stress amplitude, which is based on the peak acceleration measured at ground surface. Most methodologies used to calculate the equivalent number of cycles are based on Miner's damage concept developed for the fatigue analysis of metals. Several researchers have questioned the validity of this concept, as soils have a highly non-linear response. The present work investigates numerically the concept of the equivalent uniform amplitude cycles. Effective stress-based non-linear finite element analyses are performed with a modified bounding surface plasticity model that allows to realistically simulate liquefaction, reproducing the cyclic strength of sands accurately. The seismic response of a 15 m deep uniform level-ground sand deposit is simulated with full hydro-mechanical coupling to establish the benchmark extent of liquefaction zone. In parallel, the analyses are repeated assuming drained conditions to compute the irregular time-histories, which are then converted to an equivalent number of uniform amplitude cycles. The constant amplitude series are then applied in single element simple shear test simulations, with initial conditions those corresponding to the 7 m depth in the deposit. The results in terms of the predicted triggering of liquefaction are contrasted to the predictions of the fully coupled benchmark analyses at the corresponding depth to assess the validity of the Seed et al. (1975) methodology, based on Miner's cumulative damage concept