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突变理论在湿陷性黄土微结构失稳模型中的应用

Catastrophe Theory Model Applied in Microstructural Un-stability of Collapsible Loess

【作者】 王婧

【导师】 朱彦鹏;

【作者基本信息】 兰州理工大学 , 岩土工程, 2012, 硕士

【摘要】 黄土广泛分布于我国西北、华北地区,作为地基用于各类建筑工程中己有漫长的历史。湿陷性黄土在天然低湿度下具有明显的高强度和低压缩性,一旦浸水会发生强度大幅度骤降和变形大幅度突增。建造在湿陷性黄土地基上的建筑物由于施工中或建成后使用过程中地基被水浸湿而导致建筑物沉陷甚至破坏的事故屡见不鲜。随着湿陷性黄土地区工程建设事业的发展,深入研究湿陷性黄土的湿陷性质,正确评价黄土的湿陷程度,合理控制黄土的湿陷变形,对西部的建设有着极为重要的意义。本文是从稳定性角度出发,分析了黄土湿陷的多种湿陷机理,介绍了突变理论的主要观点和不同的突变模型,借助突变理论的数学模型和计算方法运用在了湿陷性黄土微结构失稳突变过程中,对这一过程进行了模拟计算,从突变理论角度揭示出湿陷性黄土发生湿陷的变形机制和湿陷规律。本文建立了简单直观的架空空隙模型,给出了明确的模型假定条件,分别通过折迭突变模型和尖点突变模型计算了两种不同情况下的湿陷性黄土微结构模型的失稳判据,明确给出了判据的表达式,证明了当应力满足突变模型的分叉点集方程时,其相对应的孔隙的微结构将发生失稳坍塌,即黄土湿陷。由于模型的控制变量随模型的刚度系数k(含水量的函数)的改变而改变,故此计算方法再度证明出了黄土的浸水湿化是黄土发生湿陷的重要影响因素。

【Abstract】 Loess is widely distributed in northwest China, north China, as the foundation forall types of building projects has a long history. Collapsible loess has high strength andlow compression in natural low humidity. Once the flooding will occur strengthsignificant dips and deformation substantial increased greatly.Buildings built in the collapsible loess foundation because the foundation wassoaked in water during use or after the completion of construction which led to thefrequent occurrence of building subsidence or damage.With the development ofcollapsible loess construction projects, in-depth study of collapsible loess collapsiblenature of the correct evaluation of collapsibility degree of rational control of loesscollapse deformations, has a very important significance to the construction of thewestern.This article is from the stability point of view, it analyzes a variety of collapsiblemechanism of loess collapsibility, introduces the main ideas of catastrophe theory andthe different mutation model, with the mutation theory of mathematical models andcalculation methods used in collapsible loess micro-structural instability of themutation process, and the process is simulated calculation, then the simulation isrevealed the deformation mechanism and the collapsible rule of collapsible loess, fromthe perspective of catastrophe theory.In this paper, a simple and intuitive overhead gap model is established, and a clearmodel assumption is given. Then the instability criterion of collapsible loessmicrostructure model can be calculated, respectively through the fold catastrophemodel and the cusp catastrophe model. So the expression of the clear criteria is given.It can be proved that the pore of collapsible loess microstructure model wouldcollapsed, when the stress to meet the bifurcation point set equation of the catastrophemodel, that is, the loess collapsibility.Because the he model control variable with thestiffness coefficient k (the water content of function) changed, therefore the calculationmethod again proved the loess soaking wet in the loess of the collapsible importantfactors.

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