In this paper, the authors propose an analytical model for the prediction of the slope safety factor as a function of basic geometrical parameters (slope height H and slope angle β) and soil factors (bulk density γ, cohesion c, angle of internal friction φ, and pore water pressure coefficient ru). Research was performed by applying the statistical technique of experimental design, for which the input data were provided by stability analyses of different homogeneous slopes with a circular slip surface using the Spencer limit equilibrium method. The proposed model represents a nonlinear equation of a simpler form and higher prediction accuracy than those of the existing mathematical expressions, with predominant linear effect of the individual factors and significant influence of the two-factor interactions. Linear terms in a derived equation indicate a positive effect of c or φ and a negative effect of H, β, γ, or ru on slope stability. Because of two-factor interactions, the effect of c is highly ...

We study the activation process in large assemblies of type II excitable units whose dynamics is influenced by two independent noise terms. The mean-field approach is applied to explicitly demonstrate that the assembly of excitable units can itself exhibit macroscopic excitable behavior. In order to facilitate the comparison between the excitable dynamics of a single unit and an assembly, we introduce three distinct formulations of the assembly activation event. Each formulation treats different aspects of the relevant phenomena, including the thresholdlike behavior and the role of coherence of individual spikes. Statistical properties of the assembly activation process, such as the mean time-to-first pulse and the associated coefficient of variation, are found to be qualitatively analogous for all three formulations, as well as to resemble the results for a single unit. These analogies are shown to derive from the fact that global variables undergo a stochastic bifurcation from the stochastically stable fixed point to continuous oscillations. Local activation processes are analyzed in the light of the competition between the noise-led and the relaxation-driven dynamics. We also briefly report on a system-size antiresonant effect displayed by the mean time-to-first pulse.