非线性模糊随机损伤研究

Studies on non-linear fuzzy stochastic damage field

为研究岩土材料非线性模糊随机损伤演变机理,建立广义非确定损伤力学模型,基于模糊随机双层数学覆盖下3种典型模糊损伤泛函,提出平面应变下服从随机β分布的各向异性初始模糊随机损伤场,及其广义FPDF(Fuzzy Probabilistic Density Function)、FCDF(Fuzzy Cumulative Distribution Function)数学模型。并基于黏-弹-塑性模糊随机初始损伤应力场模型及损伤矢量临界值算法,推导了黏-弹-塑性模糊随机损伤本构模型,及模糊随机损伤变化率指数模型方程与数字特征算法。基于土方开挖损伤增益,探讨基坑工程损伤演变及广义可靠性,结果表明:模糊随机损伤模型可根据材料强度耗散对损伤分布调整,以反映细观粒子间的凝聚或断裂造成的复杂宏观硬化-屈服-破坏-重分布-愈合等力学性征。得到结论:阶段卸载导致场内损伤增益由单汇向多汇发展,且强度指标变异累加会诱发可靠指标削减,这些规律性认识对实现全面化、精确化分析研究有重要意义。

To study the fuzzy-stochastic evolution mechanism of geo-materials＇ non-linear damage and establish generalized uncertain damage mechanics model, the anisotropic initial fuzzy-stochastic damage field submitting to β-probabilistic distribution under plane strain state was suggested, which is based on triple typical fuzzy damage function, including half depressed distribution, swing distribution, combined swing distribution under double mathematical coverages of fuzziness and randomness. FPDF（Fuzzy Probabilistic Density Function） and FCDF（Fuzzy Cumulative Distribution Function） were deduced for anisotropic initial fuzzy-stochastic damage field. The visco-elasto-plasto fuzzy-stochastic damage constitution and exponential function fuzzy-stochastic damage evolution rate as well as its probabilistic characteristics algorithm were deduced based on visco-elasto-plasto fuzzy-stochastic initial damage stress field and critical damage vector algorithm. Damage development and generalized reliability on typical foundation ditch excavation were studied based on damage-gain characteristics of earthwork excavation. These were demonstrated that fuzzy-stochastic damage-development model rationalizes damage field distribution according to material spatial strength dissipation and such complex macro-mechanical characteristics of geo-structure as hardening, yielding, failure, re-distribution of vector field, healing induced by micro-concentration and rupture of material particle were disclosed. It is concluded that the sink form on damage-gain characteristics will be transformed from single to multiple under phase unloading and strength indexes＇ variation accumulation will cause the decline of damage reliability. The conclusions achieved are helpful for realization of overall analysis and accurate simulation on geo-engineering.