Study on One-Dimensional Large Deformation Consolidation of Soil considering Liquid Phase Inertia

Classical consolidation theory ignores the influence of soil liquid phase acceleration. This paper considers the influence of liquid phase acceleration on the stress balance equation during the consolidation of soil, obtains the one-dimensional equation governing quasi-hydrostatic consolidation under large deformation with the consideration of the inertia of the liquid phase, and solves the governing equations by finite element method. The calculation results show that the liquid phase inertia effect of the soil will cause excess pore pressure in the soil, obviously increasing in the initial stage of consolidation, and the self-weight of soil exerts an influence on the excess pore pressure at the later stages of consolidation. The liquid phase inertia effect parameter Dc determines the strength of the liquid phase inertia effect. A larger Dc value results in a larger increase in the excess pore pressure, and the later the liquid phase inertial effect occurs, the longer the duration is. In the large strain consolidation analysis, especially at the initial stage of consolidation, it is necessary to consider the liquid phase inertia effect of the soil.

Tutorial: Spectral bandwidth extension — Invention versus harmonic extrapolation

Various postprocessing methods can be applied to seismic data to extend the spectral bandwidth and potentially increase the seismic resolution. Frequency invention techniques, including phase acceleration and loop reconvolution, produce spectrally broadened seismic sections but arbitrarily create high frequencies without a physical basis. Tests in extending the bandwidth of low-frequency synthetics using these methods indicate that the invented frequencies do not tie high-frequency synthetics generated from the same reflectivity series. Furthermore, synthetic wedge models indicate that the invented high-frequency seismic traces do not improve thin-layer resolution. Frequency invention outputs may serve as useful attributes, but they should not be used for quantitative work and do not improve actual resolution. On the other hand, under appropriate circumstances, layer frequency responses can be extrapolated to frequencies outside the band of the original data using spectral periodicities determined from within the original seismic bandwidth. This can be accomplished by harmonic extrapolation. For blocky earth structures, synthetic tests show that such spectral extrapolation can readily double the bandwidth, even in the presence of noise. Wedge models illustrate the resulting resolution improvement. Synthetic tests suggest that the more complicated the earth structure, the less valid the bandwidth extension that harmonic extrapolation can achieve. Tests of the frequency invention methods and harmonic extrapolation on field seismic data demonstrate that (1) the frequency invention methods modify the original seismic band such that the original data cannot be recovered by simple band-pass filtering, whereas harmonic extrapolation can be filtered back to the original band with good fidelity and (2) harmonic extrapolation exhibits acceptable ties between real and synthetic seismic data outside the original seismic band, whereas frequency invention methods have unfavorable well ties in the cases studied.