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中文摘要：
根据Riemann-Liouville分数阶微积分理论,借鉴经典元件组合的建模思路,提出了统一采用基于分数阶微积分形式表达的四元件非线性黏弹塑性流变模型,给出了该模型的本构方程及蠕变方程,其中可分别通过调整分数阶次β1和β2来有效控制蠕变第Ⅰ、Ⅱ阶段和第Ⅲ阶段的蠕变变形速率。比较了该模型对于已有数据的预测能力,结果表明该模型与已有的理论模型具有相同的预测精度,能有效反映岩石3个阶段的蠕变特性,当应力较低时反映出瞬变蠕变和稳定蠕变,应力超过岩石长期强度时反映出加速蠕变。同时,该模型中软体元件的运用起到了减少元件个数及参数的效果。
英文摘要：
Based on an expression with a fractional calculus form, a new four-element nonlinear viscoelasto-plastic rheological model was proposed, by using the Riemann-Liouville fractional calculus theory and drawing ideas from the classic element combination modeling. The constitutive equation and creep equation of the model were given, in which the creep strain rate at the first, second and third stages can be effectively controlled by adjusting creep parameters/3~ and/32, respectively. The prediction of the model on existed data was ex- amined,and the result showed that the nonlinear rheological model can effectively describe three steps of rock creep with comparable prediction accuracy to existed theoretical models. It was found that in a lower stress level,the model can reflect the primary creep and steady creep ,while if the stress level exceeds the long-term rock strength, the model will reflect the accelerated creep. Meanwhile, the use of the soft elements plays a role to reduce the element number and parameters in the model.
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