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以往岩土体的应力–应变曲线只能根据其形态类型采用不同的数学模式来描述,且针对相应体变曲线的描述研究较少。为实现描述形态各异的应力–应变曲线及体变曲线数学模式的统一,通过分析幂函数与指数函数,提出了一个新的非线性模型——复合幂–指数模型(简称CPE模型),并给出了模型参数的确定方法。以结构性黄土为例,通过对不同含水量、不同围压常规三轴试验得到的应力–应变曲线及体变曲线进行CPE模式拟合,并分析各参数的变化规律,得到了非饱和原状黄土考虑含水量的应变软化型、考虑围压的应变硬化型应力–应变曲线CPE模型,及考虑围压的剪缩型体变曲线CPE模型,并将其计算曲线与实测曲线进行了对比,研究表明:CPE模型可描述各种型式的应力–应变曲线及不同形态的体变曲线,具有广泛的适用性和准确性,为形态各异的应力–应变曲线及体变曲线提供了一个统一的数学模型。
In the past, the stress-strain curves of rock and soil body can only be described by different mathematical models according to their morphological types, and there are few researches on the corresponding deformation curves. In order to unify the stress-strain curves and the mathematical models of body-changing curves, a new nonlinear model named compound exponential model (CPE model) is proposed by analyzing power function and exponential function The method of determining the model parameters is given. Taking structural loess as an example, CPE mode fitting was carried out on stress-strain curves and body-deformation curves obtained by conventional triaxial tests with different water contents and different confining pressures, and the variation regularities of the parameters were analyzed. Unsaturated intact loess Considering the strain softening of water content, the strain hardening stress-strain curve CPE model considering the confining pressure and the CPE model considering the confining pressure shear deformation are compared with the measured curves, and the results show that : The CPE model can describe various types of stress-strain curves and different forms of body-deformation curves, has a wide range of applicability and accuracy, provides a unified mathematical model for different stress-strain curves and body-deformation curves .