The elastic behaviour of granular materials is non-linear, in that the small-strain tangent stiffness depends on the stress level. The elastic moduli typically vary as power functions of the mean stress. Simple models of this nonlinearity can result in behaviour that violates the laws of thermodynamics. To guarantee that an elasticity model is thermodynamically acceptable it must be possible to derive the elastic behaviour from a free energy potential (or alternatively from a complementary energy potential). In this paper elasticity models are derived that allow for variation of elastic moduli as power functions of mean stress, while guaranteeing thermodynamic acceptability. The important issue of the dependence of secant stiffness on strain amplitude (a phenomenon related to dissipation processes in the soil) is acknowledged but not addressed here.
Abstract.The geomagnetic observatory of Juriquilla Mexico, located at longitude -100.45 • and latitude 20.70 • , and 1946 m a.s.l., has been operational since June 2004 compiling geomagnetic field measurements with a three component fluxgate magnetometer. In this paper, the results of the analysis of these measurements in relation to important seismic activity in the period of 2007 to 2009 are presented. For this purpose, we used superposed epochs of Discrete Wavelet Transform of filtered signals for the three components of the geomagnetic field during relative seismic calm, and it was compared with seismic events of magnitudes greater than M s > 5.5, which have occurred in Mexico. The analysed epochs consisted of 18 h of observations for a dataset corresponding to 18 different earthquakes (EQs). The time series were processed for a period of 9 h prior to and 9 h after each seismic event. This data processing was compared with the same number of observations during a seismic calm. The proposed methodology proved to be an efficient tool to detect signals associated with seismic activity, especially when the seismic events occur in a distance (D) from the observatory to the EQ, such that the ratio D/ρ < 1.8 where ρ is the earthquake radius preparation zone. The methodology presented herein shows important anomalies in the Ultra Low Frequency Range (ULF; 0.005-1 Hz), primarily for 0.25 to 0.5 Hz. Furthermore, the time variance (σ 2 ) increases prior to, during and after the seismic event in relation to the coefficient D1 obtained, principally in the Bx (N-S) and By (E-W) geomagnetic components. Therefore, this paper proposes and develops a new methodology to extract the abnormal signals of the geomagnetic anomalies related to different stages of the EQs.
An elastoplastic framework to account for the volumetric behavior of unsaturated soils is proposed herein. The proposed equation is based on the effective stress principle and results in a unifying framework for the volumetric behavior for both saturated and unsaturated soils. The results of the proposed equation are compared with experimental results published by different researchers. These comparisons show that the equation is adequate to account for wetting–drying and net stress loading–unloading paths. In addition, the collapse upon wetting phenomenon can be simulated and the critical state for unsaturated soils coincides with the proposed volumetric framework. This analysis confirms that the effective stress principle can be applied to the volumetric behavior of unsaturated soils.
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