【作者】 王亚军；

【导师】 张我华；

【作者基本信息】 浙江大学 ， 岩土工程， 2008， 博士

【摘要】 在过去的七十多年时间可靠度理论及非确定性分析方法得到了长足的发展，以可靠度理论为基础的规范体系率先在结构设计领域形成，在岩土工程领域，非确定性分析理论体系还不是很完整。鉴于这种状况，笔者结合在结构工程领域已经得到发展的损伤力学理论，建立了以随机有限元法、广义随机有限元即模糊随机数值方法为基础的模糊随机损伤力学分析模型，对岩土工程、水工结构中普遍存在的一系列问题进行了较为深入的分析和探讨，形成的主要研究成果如下，1、基于弹性力学边值问题的经典变分原理，在随机空间ψ上推导了基于线性逼近理论的随机变分列式，进而对弹性、弹塑性随机有限元实现理论和方法做了研究；对照非线性随机有限元理论的特点，以Mohr-Coulomb破坏准则下的粘性伪时间步为基础，分别采用了“关连流动法则”、“非关连流动法则”两种工况、提出了粘塑性随机本构模型；推导并建立了基于全量理论的粘塑性常刚度随机有限元列式，形成了粘塑性随机有限元数值计算模型；继而就堤坝填筑问题的非线性随机工程特性进行了分析，对土方填筑过程中的随机粘塑性应变、随机应变率数字特征、位移及应力非线性随机矢量场的空间变异性等广义非确定性做了深入研究分析；考虑“有侧限”问题情况下膨胀角ψ的影响，利用粘塑性非线性随机有限元数值模型就施工期孔隙水压消散缓慢条件下的地基承载力进行了分析研究，对非线性变载条件下地基中随机有效应力与随机孔隙水压的发展演变及数字特征、承载力的可靠指标空间分布和发展做了探讨研究，形成了随机损伤力学的理论基础。2、基于模糊分解定理建立了模糊空间(?)((?),(?),(?))上的模糊变分理论，进而依据扩张原则在广义非确定性空间O：ξ(s，f)上提出了模糊随机变分列式；由随机变分列式在经典随机有限元理论基础上，建立了线性一次逼近随机有限元模型，对非均质各向同性岩土工程结构在没有优势方向不连续面情况下的局部破坏概率进行了分析；通过对岩土工程结构安全储备做模糊软化处理，构造了关于岩土工程结构安全状态论域(?)的三种隶属度函数，基于模糊随机变分并依据扩张原则建立了岩土工程结构局部破坏的模糊随机失效模型；在此基础上对荆南长江干堤堤身可靠度进行了讨论，奠定了模糊随机损伤力学的理论基础。3、基于随机数学模拟，提出了渗流场随机统计分布模型，分析了在土性参数、边界条件等随机影响因素下渗流场水头势的统计分布特征；结合Monte Carlo模拟，建立了三维各向异性非均质稳定随机渗流场模型；依据堤防区域内土层地质结构空间分布特性，对截渗墙、导渗沟等复杂边界的对渗流场的随机干扰和堤防的随机渗透破坏做了分析讨论，提出了三维各向异性非均质稳定随机渗流场敏感性分析模型；在此基础上结合长江荆南干堤隐蔽工程对三维各向异性非均质稳定随机渗流场统计分布及敏感性分析模型进行数值验证，所得研究成果成为渗透破坏诱发性随机损伤研究的理论基础。4、以岩石介质为依据，探讨了岩质材料裂纹开展的各向异性及随机分布特征之间内在联系；通过对模型试件做统计分析，基于Weibull函数建立了岩石材料裂纹长度的分布函数模型，基于Gaussian分布函数建立了岩石材料裂纹角度θ累积分布函数和概率密度函数模型；利用Monte-Carlo统计仿真生成岩石样本三个表面上的裂纹长度和方向角的柱状值和概率分布曲线、并借助于K-S检验，证明了在置信区间α<0.1上各向异性随机损伤变量符合Beta分布，从而基于裂纹仿真的统计信息提出了岩石材料各向异性随机损伤变量的累积分布方程和概率密度方程；在各向异性随机损伤材料的无量纲损伤弹模基础上提出了可用以估计岩体中随机损伤变量统计值的随机数字特征；基于实验物理模型建立了岩石损伤模型的有效弹性模量随机数字特征以求解随机损伤变量的平均值和标准偏差，从而可以对各向异性随机损伤分布特征进行分析研究；利用Rosenblueth方法并结合统计学理论和有限元技术实现了对岩石材料各向异性随机损伤场的数值模拟。5、在各向异性随机损伤统计模型基础上进一步分析了模糊、随机、损伤三者在[0,1]区间上的一致性，基于损伤变量的广义非确定性提出了模糊随机损伤概念模型;在分析了损伤变量的本质基础上，构造并解释了三类损伤变量模糊数，即降半分布、“秋千”分布、组合“秋千”分布，提出了实现模糊随机损伤的模糊自适应理论；依据扩展原则在随机损伤模型基础上建立了三维弹性模糊随机损伤本构模型、并借助模糊随机变分变分原理在模糊工作状态论域基础上将损伤力学进行扩展推导建立了广义弹性模糊随机有限元算法；探讨模糊随机损伤变量的同时分析了损伤变量的随机分布特性及程序实现原理，借助正交设计原理及当量正态理论，实现了模糊随机有限元可靠度分析与模糊随机损伤的同步分析；在三维弹性模糊随机损伤力学理论基础上，进一步考虑岩土材料的非线性模糊随机损伤特性，分析了开挖卸载导致的土体损伤特性，明确了基坑的损伤演变也是建立在一个广义非确定性空间O：ξ(s，f)上模糊随机损伤演化过程；定义了平面应变下各向异性模糊随机初始损伤变量，进而定义了模糊随机初始损伤有效张量；把卸除单元看作是“损伤源”，得到了凝聚损伤荷载矢量{p}，采用模糊衰减模型构造模糊随机损伤增量方程；为了构造损伤刚度矩阵及模糊随机损伤切线刚度矩阵，提出了损伤矢量极限值{Ω_u}，根据Sidoroff的弹性能量假设和Lemaitre等效应变假设，提出了粘塑性模糊随机卸荷损伤本构模型和粘塑性模糊随机损伤变化率方程，建立了较为完整的基坑开挖卸载的粘塑性模糊随机损伤力学概念模型及基础理论框架。更多还原

【Abstract】 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.更多还原