网纹红土分数阶应力松弛模型

网纹红土松弛特性具有非线性。基于分数阶微积分理论,探讨了能更准确描述网纹红土松弛非线性特性和全过程的FVMS(Fractional Voigt and Maxwell model in series)松弛模型和FVMP(Fractional Voigt and Maxwell model in parallel)松弛模型及其理论解,进而应用提出的模型对三轴松弛试验实测数据进行反演,讨论了分数阶阶数的敏感性,并与西原模型和Burgers模型进行对比分析。研究结果表明,建立的四元件分数阶松弛本构模型应用于网纹红土应力松弛特性分析是有效可行的,模型灵活且精度更高,参数确定简便,发现分数阶阶数对应力松弛量的影响较大,但其对FVMS模型和FVMP模型松弛速率的影响不同,为实际工程长期稳定性分析提供了参考。

The fractional order relaxation model of net-like red soil

The characteristics of stress relaxation in net-like red soil are nonlinear.Based on the fractional derivative theory,new relaxation models of FVMS (Fractional Voigt and Maxwell model in series) and FVMP (Fractional Voigt and Maxwell model in parallel) were set up here to better characterize the whole phase and nonlinear characteristics of relaxation in net-like red soil,and analytical solutions of the models were also presented.The proposed models were further adopted to simulate the measured data of triaxial stress relaxation tests.Moreover,the sensitivity of the proposed models and comparisons with Nishihara model and Burgers model were conducted.The results indicate that the proposed four-element models utilized to describe the characteristics of stress relaxation of net-like red soil can lead to higher precision and are more simpler to specify model parameters relative to other models;the influences of the fractional order on the amount of stress relaxation is larger for the FVMS model and FVMP model,but are different on the relaxation rate.They provide a reference for the long-term stability analysis of practical engineering.