基于分数阶微积分理论的软土应力–应变关系

 利用分数阶微积分理论提出等应变率加载情况下的软土应力–应变关系。关系式显示应力–应变之间呈乘幂函数关系。通过大量的常规(等应变率加载情况下)三轴试验验证基于分数阶微积分理论的软土应力–应变关系，同一种土的分数阶阶数 不随围压变化并能够反映土的“软硬”程度。试验发现，初始弹模与围压呈较好的线性关系。与邓肯–张模型相比，应力–应变的乘幂关系具有明确的理论基础，这一点与邓肯–张模型纯粹基于曲线形状相似的应力–应变双曲线假设形成鲜明的区别。创新点在于将软土看作介于理想固体和理想流体之间的物质进行研究，并用分数阶微积分理论给出应力–应变关系，这在以往的研究中都没有先例。

STRESS-STAIN RELATION OF SOFT SOIL BASED ON FRACTIONAL CALCULUS OPERATORS THEORY

On the basis of the fractional calculus operator theory，the stress-strain relation of soft soil under the condition of loading with constant strain rate is proposed. The analysis results show that stress–strain of soft soil performs exponent relation，which can be proved by large amounts of triaxial tests(under constant strain rate). It is found that the order of fractional calculus keeps constant to the same kind of soil and characterize soft or hard soil. The test results show that there is a linear relationship between confining pressures and initial tangent modulus. Compared with Duncan-Chang model that hypothesizes stress-strain relation is hyperbolic in response to similar shape of experimental curve，the stress-strain relation from the fractional calculus has rigorous theoretical background. The major innovation of our researches is that the soil is considered as the matter whose behaviors are intermediate between that of the ideal solid and fluid，and it also may be the first known application of fractional calculus in soil stress-strain relation.