Fuzzy Stochastic Damage Mechanics And Fuzzy Stochastic Damage Finite Element Method Application On Geo-Engineering

Reliability theory and uncertain analysis theory have made great strides and advanced deeply during 70 years in the past. Normalization system on the basis of reliability theory has been setup upon structural designing domain at first.Upon geo-engineering, however, due to antediluvian geological evolution, uncertain analysis system and standard is, thereby, still on the way. The writer of this paper, with these quo statuses, setup on the basis of stochastic finite element method and generalized stochastic finite element method, namely, fuzzy stochastic numerical, in the dissertation fuzzy stochastic damage model by the help of conventional damage mechanics developed in structural engineering domain, by which, many prevalent cases in geo-engineering and hydraulic structural engineering are analyzed and calculated in this paper and the main achievements are the following below, 1,Stochastic variation algorithm, based on linear approximate theorem under random space ofΨ, is formulated by the help of elastic mechanics boundary numerical model's traditional variation theory, by which, studied are the corresponding mechanism and theorem on realization of elastic as well as elastic-plastic stochastic finite element method; With the comparison on conventional non-linear stochastic finite element method, the viscous-plastic random constitutional numerical model, under couple working behaviors, namely, associated flow rule and un-associated flow rule operating conditions, is setup on the basis of viscous quasi-time ratio-step under Mohr-Coulomb failure criterion; Viscous-plastic normal rigidity stochastic finite element method algorithm, based on the total strain theory, is deduced, by which, viscous-plastic random finite element method numerical constitution model is formulated here; Furthermore, with dike reclamation construction case's non-linear-stochastic characteristics analysis, the generalized uncertainty of non-linear random vector field's spatial variance on stochastic viscous-plastic strain, stochastic strain ratio's variables, displacement as well as stress under earth stuffing-work behavior is researched deeply in this paper; Foundation capacity under construction period during porous pressure sluggish drainage is analyzed by the help of viscous-plastic non-linear random finite element method algorithm with the research on dilation angle influence upon confined problem, by which studied comprehensively, under non-linear loading behavior, are foundation stratum random effective stress transmutation and stochastic features, stochastic porous pressure evolution and characteristic variables, base capacity reliability spatial distribution and development. Primary theorem on random damage mechanics researching, thereby, is formulated here.2,The fuzzy variation theorem upon fuzzy (?) space is setup here based on fuzzy decomposition theory. Furthermore, fuzzy stochastic variation algorithm on the basis of generalized uncertain space O:ξ(s, f) is fabricated according to expansioncriterion; Stochastic linear first-order approximate finite element method algorithm, based on classical random finite element theorem of stochastic variation algorithm is formulated with which local failure probability on geo-heterogeneous isotropic slope profile without discontinuous dominant sliding section is calculated here; With the fuzzy soft controlling on safety reservation of slope profile, three fuzzy membershipdistribution functions are formulated on the fuzzy domain (?) of slope profile safetycondition. Fuzzy stochastic assessment model of slope profile local failure, so, is setup in this paper by the help of extension criterion, by which, analyzed is levee body reliability of Yangtse Rive Main Dike on Southern Jingzhou zone in Central China. Fuzzy stochastic damage mechanics theoretical structure is forged in this paper. 3,Statistical distribution model on random seepage, on the basis of stochastic mathematical simulation, is setup in this paper to analyze statistical characteristics of seepage potential distribution under the influence of porous medium parameters and boundary conditions; With Monte Carlo simulation, 3 dimension anisotropic heterogeneous stable random seepage model is formulated here; Coupled with geological characteristics of main dike zone stratum, the stochastic turbulence proceeding from such comprehensive boundary conditions as break-water pile and drainage sink ditch is calculated on random seepage field as well as levee structure seeping deformation forms, with which, the comprehensive analysis numerical model on stochastic seepage field sensitivity is fabricated in this paper; By the foregoing studies, implemented is numerical model examination on statistical potential distribution of 3 dimension anisotropic heterogeneous stable random seepage as well as sensitivity analytical model of concealed work of Yangtse Rive Main Dike on Southern Jingzhou zone in Central China, by which, the researching feats could be translated into primary theorem of stochastic damage induced by seepage deformation.4,Natural relation between anisotropy and random distribution feature of rock-like material crack evolution is analyzed according to rock material; The crack length probabilistic cumulative distribution function as well as probabilistic density function derived from Weibull random model and the crack angle probabilistic cumulative distribution function as well as probabilistic density function derived from Gaussian random model are setup with rock-like material model stochastic statistic analysis; Column figure and probabilistic distribution table on crack length as well as direction angle from 3 dimension orthogonal sections of rock medium are generated associated with Monte-Carlo statistic emulation technology. Moreover, it is testified with KolmogorovSmirnov examination, that random anisotropic damage variables submit toβdistribution upon confidence interval ofα?0.l, with which, probabilistic cumulative distribution function as well as probabilistic density function on stochastic anisotropic damage variables of rock-like material is formulated from statistic information on crack simulation; Fabricated, based non-dimensional damage modulus of random anisotropic damage medium, are stochastic feature variables that could assess those statistic values of rock-like material stochastic damage variables; On the basis of experimental physical model, calculated are effective elastic modulus' stochastic characteristic variables of rock damage evolution model so as to formulate the expectation and even-square variance of random damage variables by which the analysis on distribution feature of stochastic anisotropic damage variables could be realized; The numerical simulation process on stochastic anisotropic damage space of rock-like material is implemented with finite element theorem by the help of Rosenblueth orthogonal analytical statistic technique.5,The primary conception model on fuzzy stochastic damage evolution, coupled with generalized uncertainty of natural damage variables, is forged in this paper when considering the consistency of fuzzy, random, damage upon interval of [0,1] based on the statistic model of stochastic anisotropic damage; With the analysis of damage variables nature, three damage variable fuzzy membership functions is setup and translated, namely, half depressed distribution, swing distribution, combined swing distribution. Fabricated is fuzzy adaptive theory to realize fuzzy stochastic damage; Elastic 3-dimension fuzzy random damage constitution model is setup here according to expansion criterion and elastic generalized fuzzy stochastic finite element method algorithm is formulated with the expanding deduction on damage mechanics on the basis of the fuzzy working status' domain conception by the help of generalized fuzzy stochastic variation theorem; Damage variables' stochastic distribution characteristics and program working mechanism is analysis with the researching on fuzzy stochastic damage variables; Fuzzy stochastic finite element method reliability analysis coupled with fuzzy stochastic damage calculation is realized by the help of orthogonal design theory and equivalent normalization theory; Furthermore, with the examination on non-linear fuzzy stochastic damage characteristics of geo-material based on the foregoing elastic 3-dimansion fuzzy stochastic damage mechanics theory, it is proved that foundation ditch excavation-inducing damage evolution should be determined as the fuzzy randomdamage development process under generalized uncertain space of O :ξ(s,f) whenconsidering the porous medium's excavation unloading damage feature; With definition of fuzzy-random anisotropic initial damage vector under plane strain condition, the fuzzy-random initial effective damage tensor is deduced; With unloaded element being defined as damage resource, the damaged-coacervation loadingvector {P} is formulated. Fuzzy stochastic damage increment function is realizedunder fuzzy damping model; The ultimate damage vector {Ω_μ} is calculated toresearch damage rigid matrix as well as fuzzy stochastic damage tangent rigid matrix. Moreover, according to Sidoroff elastic energy hypothesis and Lemaitre equivalent strain hypothesis, the viscous-plastic fuzzy stochastic unloading damage constitution model and viscous-plastic fuzzy stochastic damage ratio functions' distribution are formulated in this paper, too, by which, realized are the comprehensive fuzzy stochastic viscous-plastic damage mechanics conception constitution model on foundation ditch excavation unloading in addition to primary fuzzy-random damage mechanics theoretical structure.