This study proposes an alternative calculation mode for stresses on the slip surface(SS).The calculation of the normal stress(NS)on the SS involves examining its composition and expanding its unknown using the Taylor ...This study proposes an alternative calculation mode for stresses on the slip surface(SS).The calculation of the normal stress(NS)on the SS involves examining its composition and expanding its unknown using the Taylor series.This expansion enables the reasonable construction of a function describing the NS on the SS.Additionally,by directly incorporating the nonlinear Generalized Hoke-Brown(GHB)strength criterion and utilizing the slope factor of safety(FOS)definition,a function of the shear stress on the SS is derived.This function considers the mutual feedback mechanism between the NS and strength parameters of the SS.The stress constraints conditions are then introduced at both ends of the SS based on the spatial stress relation of one point.Determining the slope FOS and stress solution for the SS involves considering the mechanical equilibrium conditions and the stress constraint conditions satisfied by the sliding body.The proposed approach successfully simulates the tension-shear stress zone near the slope top and provides an intuitive description of the concentration effect of compression-shear stress of the SS near the slope toe.Furthermore,compared to other methods,the present method demonstrates superior processing capabilities for the embedded nonlinear GHB strength criterion.展开更多
This paper analyzes Bernoulli’s binary sequences in the representation of empirical nonlinear events,analyzing the distribution of natural resources,population sizes and other variables that influence the possible ou...This paper analyzes Bernoulli’s binary sequences in the representation of empirical nonlinear events,analyzing the distribution of natural resources,population sizes and other variables that influence the possible outcomes of resource’s usage.Consider the event as a nonlinear system and the metrics of analysis consisting of two dependent random variables 0 and 1,with memory and probabilities in maximum finite or infinite lengths,constant and equal to 1/2 for both variables(stationary process).The expressions of the possible trajectories of metric space represented by each binary parameter remain constant in sequences that are repeated alternating the presence or absence of one of the binary variables at each iteration(symmetric or asymmetric).It was observed that the binary variables X_(1)and X_(2)assume on time T_(k)→∞specific behaviors(geometric variable)that can be used as management tools in discrete and continuous nonlinear systems aiming at the optimization of resource’s usage,nonlinearity analysis and probabilistic distribution of trajectories occurring about random events.In this way,the paper presents a model of detecting fixed-point attractions and its probabilistic distributions at a given population-resource dynamic.This means that coupling oscillations in the event occur when the binary variables X_(1)and X_(2)are limited as a function of time Y.展开更多
基金Project(52278380)supported by the National Natural Science Foundation of ChinaProject(2023JJ30670)supported by the National Science Foundation of and Technology Major Project of Hunan Province,China。
文摘This study proposes an alternative calculation mode for stresses on the slip surface(SS).The calculation of the normal stress(NS)on the SS involves examining its composition and expanding its unknown using the Taylor series.This expansion enables the reasonable construction of a function describing the NS on the SS.Additionally,by directly incorporating the nonlinear Generalized Hoke-Brown(GHB)strength criterion and utilizing the slope factor of safety(FOS)definition,a function of the shear stress on the SS is derived.This function considers the mutual feedback mechanism between the NS and strength parameters of the SS.The stress constraints conditions are then introduced at both ends of the SS based on the spatial stress relation of one point.Determining the slope FOS and stress solution for the SS involves considering the mechanical equilibrium conditions and the stress constraint conditions satisfied by the sliding body.The proposed approach successfully simulates the tension-shear stress zone near the slope top and provides an intuitive description of the concentration effect of compression-shear stress of the SS near the slope toe.Furthermore,compared to other methods,the present method demonstrates superior processing capabilities for the embedded nonlinear GHB strength criterion.
文摘This paper analyzes Bernoulli’s binary sequences in the representation of empirical nonlinear events,analyzing the distribution of natural resources,population sizes and other variables that influence the possible outcomes of resource’s usage.Consider the event as a nonlinear system and the metrics of analysis consisting of two dependent random variables 0 and 1,with memory and probabilities in maximum finite or infinite lengths,constant and equal to 1/2 for both variables(stationary process).The expressions of the possible trajectories of metric space represented by each binary parameter remain constant in sequences that are repeated alternating the presence or absence of one of the binary variables at each iteration(symmetric or asymmetric).It was observed that the binary variables X_(1)and X_(2)assume on time T_(k)→∞specific behaviors(geometric variable)that can be used as management tools in discrete and continuous nonlinear systems aiming at the optimization of resource’s usage,nonlinearity analysis and probabilistic distribution of trajectories occurring about random events.In this way,the paper presents a model of detecting fixed-point attractions and its probabilistic distributions at a given population-resource dynamic.This means that coupling oscillations in the event occur when the binary variables X_(1)and X_(2)are limited as a function of time Y.
