摘要
目的为了研究冻土的两种应力-应变数学模型产生拟合误差的原因.方法引入强度因子的概念,建立模型特征方程对传统双曲线和指数曲线应力-应变模型的数学局限性进行分析.结果研究表明,两种传统模型的数学特征方程均不独立;在初始切线模量和最终强度分别相同的情况下,双曲线模型的强度因子大于指数曲线模型的强度因子,双曲线模型的收敛速度小于指数模型的收敛速度.结论传统冻土双曲线和指数曲线应力-应变模型的拟合误差是由其各自的数学模型缺陷造成的,合理的应力-应变模型的数学特征方程应相对独立.
In order to properly understand the mathematical model of stress-strain relationships of frozen soil, strength index is defined and employed to establish mathematical property sets of two traditional stressstrain models, namely hyperbolic model and exponential model. Theoretical deficiencies of the two models are revealed by the mathematical property sets. Mathematical proof shows that the mathematical property sets of the two models are both inconsistent, and strength index of hyperbolic model is bigger than that of exponential model under the condition that they have the same initial tangent modulus and the same final strengths, respectively. At the same time, rate of convergence of hyperbolic model is smaller than that of exponential model. Fitted errors of the two models are induced by their own mathematical deficiencies, and reasonable stress-strain model for frozen soil should have relatively independent mathematical property set to overcome the mathematical deficiencies of the hyperbolic model and exponential model.
出处
《沈阳建筑大学学报（自然科学版）》
EI
CAS
2008年第3期398-401,共4页
Journal of Shenyang Jianzhu University：Natural Science
基金
中科院冻土工程国家重点实验室开放基金项目(SKLFSE200603)
国家自然科学基金项目(40672183)
关键词
冻土
应力-应变模型
强度因子
数学特征方程
frozen soil
stress-strain model
strength index
mathematical property set
