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应变硬化型岩土的三轴试验应力应变曲线能够表现出不同的弯曲程度,而应力应变曲线的弯曲程度是岩土应变硬化能力的体现,但已有的研究中还没有相应的参数来描述岩土的硬化能力。为了获得反映岩土应变硬化能力的参数,从而有助于了解岩土的塑性性能和指导土体的合理承载,根据Hollomon提出的描绘金属塑性拉伸变形的指数方程(经验公式),提出了岩土应变硬化指数理论。通过许多三轴试验,发现岩土应变硬化指数理论提出的岩土应力应变关系符合乘幂函数关系的假设能够被验证,岩土的应变硬化指数能够反映岩土的硬化能力。岩土的力学性质介于理想固体和理想流体之间,其应力应变关系既不遵守胡克定律,也不遵守牛顿黏性定律,而是遵守介于它们之间的某种关系。利用分数阶微积分理论给出了恒应变率加载情况下的土应力应变关系。关系式显示应力应变之间也呈乘幂函数关系,说明岩土分数阶应力应变关系能够为岩土应变硬化指数理论提供理论基础。
The stress-strain curves of strain-hardening geotechnical can show different bending degree, and the bending degree of stress-strain curve is the manifestation of the capacity of rock-soil strain hardening. However, there is no corresponding parameter to describe the rock Soil hardening capacity. In order to obtain the parameters that reflect the strain hardening ability of geomaterials, which can help to understand the plastic properties of geomaterials and guide the reasonable loading of soil, according to the exponential equation (empirical formula) proposed by Hollomon to describe the plastic ductility of metal deformation, Soil strain hardening index theory. Through many triaxial tests, it is found that the assumption that the relationship between stress and strain of rock and soil proposed in the theory of geostress of rock and soil accords with the power function can be verified, and the strain hardening index of rock and soil can reflect the hardening ability of rock and soil. The mechanical property of rock and soil is between the ideal solid and the ideal fluid. The stress-strain relationship of the rock and soil neither obey Hook’s law nor the Newton’s law of viscosity, but obey a certain relationship between them. Using the theory of fractional calculus, the relationship between soil stress and strain under constant strain rate loading is given. The relational expression shows that the stress-strain relationship also expresses the power function relationship, which shows that the fractional stress-strain relationship in geotechnical engineering can provide theoretical basis for the theory of strain hardening index of geotechnical engineering.