黄土非线性应力–应变新模型及对比研究

New nonlinear stress-strain model for loess and its comparative research

目前,黄土的应力应变曲线只能根据其形态类型选择不同的数学模式来描述,为实现描述应力应变数学模式的统一,提出了一种新的非线性模型,并给出了各参数的确定方法。通过应用新模型与现行主要的非线性模型(邓肯–张双曲线模型、指数模型、驼峰曲线模型),同时对结构性黄土常规三轴试验所得的各种类型的应力应变曲线进行模拟,并经与实测应力应变数据点对比研究表明:新模型表达式比驼峰曲线描述软化型应力应变曲线的精度高;同样新模型比邓肯–张双曲线模型、指数模型描述硬化型应力应变曲线的精度也高,说明此非线性新模型既可描述应变强硬化型也可描述应变弱硬化型应力应变曲线;既可描述应变强软化型也可描述应变弱软化型应力应变曲线。通过新模型对经典实例应力应变曲线的描述,进一步说明新模型具有良好的适应性。新模型为形态各异的应力应变曲线提供了一个统一的数学模型。

At present, the stress-strain curve of loess can only be described by using different mathematical models according to its morphological type. To achieve a unified description of the stress-strain mathematical model, a new nonlinear model is proposed, and the method for determining each parameter is also given. The various types of stress-strain curves of structural loess which are obtained from conventional triaxial tests are simulated by applying the new model and the current main nonlinear models （Duncan-Chang hyperbolic model, exponential model and model of camelback curve）, and then they are compared with the measured stress-strain data points. The result shows that the expression of the new model can make a more accurate description for the softening stress-strain curve than that of the hump curve. Similarly, the new model describes the hardening stress-strain curve more accurately in comparison with the Duncan-Chang hyperbolic model and the exponential model, which indicates that the new nonlinear model can describe the strong hardening stress-strain curve and the weak hardening curve, and can also describe the strong softening curve and the weak softening curve. Meanwhile, based on the description of stress-strain curves of the classic example by the new model, it is shown that the new model has excellent adaptability. The proposed model provides a unified mathematical model for the stress-strain curves of different shapes.