A large-scale shaking table test was performed to study the dynamic response of slopes parallel to geological bedding (bedding slopes) and slopes that cross-cut geological bedding (counter-bedding slopes). The test results show that the acceleration amplification coefficients increase with increasing elevation and, when the input earthquake amplitude is greater than 0.3 g, both bedding and counter-bedding slopes begin to show nonlinear dynamic response characteristics. With increasing elevation, the displacement of the bedding slope surface increases greatly. Conversely, the displacement of the counter-bedding slope surface increases first and then decreases; the slope develops a bulge at the relative elevation of 0.85. The displacement of the bedding slope surface is greater than that of the counter-bedding slope. The counter-bedding slope is more seismically stable compared with the bedding slope. Based on the Hilbert-Huang transform and marginal spectrum theories, the processes that develop dynamic damage of the bedding and counter-bedding slopes are identified. It is shown that the dynamic failure mode of the bedding slope is mainly represented by vertical tensile cracks at the rear of the slope, bedding slide of the strata along the weak intercalation, and rock collapse from the slope crest. However, the dynamic failure mode of the counter-bedding slope is mainly represented by staggered horizontal and vertical fissures, extrusion of the weak intercalation, and breakage at the slope crest.

A novel full Eulerian fluid-elastic membrane coupling method on the fixed Cartesian coordinate mesh is proposed within the framework of the volume-of-fluid approach. The present method is based on a full Eulerian fluid-(bulk) structure coupling solver (Sugiyama et al., J. Comput. Phys., 230 (2011) 596-627), with the bulk structure replaced by elastic membranes. In this study, a closed membrane is considered, and it is described by a volume-of-fluid or volume-fraction information generally called VOF function. A smoothed indicator (or characteristic) function is introduced as a phase indicator which results in a smoothed VOF function. This smoothed VOF function uses a smoothed delta function, and it enables a membrane singular force to be incorporated into a mixture momentum equation. In order to deal with a membrane deformation on the Eulerian mesh, a deformation tensor is introduced and updated within a compactly supported region near the interface. Both the neo-Hookean and the Skalak models are employed in the numerical simulations. A smoothed (and less dissipative) interface capturing method is employed for the advection of the VOF function and the quantities defined on the membrane. The stability restriction due to membrane stiffness is relaxed by using a quasi-implicit approach. The present method is validated by using the spherical membrane deformation problems, and is applied to a pressure-driven flow with the biconcave membrane capsules (red blood cells).

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Abstract. In this paper, we shall establish the well-posedness of a mathematical model for a special class of electrochemical power device -lithium-ion battery. The underlying partial differential equations in the model involve a (mix and fully) coupled system of quasi-linear elliptic and parabolic equations. By exploring some special structure, we are able to adopt the well-known Nash-MoserDeGiorgi boot strap to establish suitable a priori supremum estimates for the electric potentials. Using the supremum estimates, we apply the Leray-Schauder theory to establish the existence and uniqueness of a subsystem of elliptic equations that describe the electric potentials in the model. We then employ a Schauder fix point theorem to obtain the local (in time) existence for the whole model. We also consider the global existence of a modified 1-d governing system under additional assumptions. In particular, we are able to derive uniform a priori estimates depending only on the existence time T , including the supremum estimates for electric potentials and growth and decay estimates for the concentration c. Using the uniform estimates, we prove that the modified system has a solution for all time t > 0.