胡其志, 王芝超, 丁志刚.基于分数阶导数的岩石蠕变本构模型研究[J].河南理工大学学报（自然科学版）,2021,40(6):163-168.

HU Q Z, WANG Z C, DING Z G.Study on the rock creep constitutive model based on fractional derivative[J].Journal of Henan Polytechnic University(Natural Science) ,2021,40(6):163-168.

基于分数阶导数的岩石蠕变本构模型研究

胡其志1, 王芝超1, 丁志刚1,2

1.湖北工业大学 土木建筑与环境学院，湖北 武汉430068;2.中交路桥南方工程有限公司，北京 101149

摘要:针对组合元件模型无法描述岩石非线性蠕变加速阶段的劣势问题，将基于分数阶理论的软体元件和弹簧元件与一个由摩擦件及牛顿黏壶并联组成的非线性黏塑性组合体串联，组成一个能较好描述岩石蠕变全过程基于分数阶导数的四元件蠕变模型。分析岩石蠕变3个过程特点，推导出四元件模型的表达式。结合锦屏水电站绿片岩、万州红层砂岩和长山盐岩的蠕变试验数据，对该分数阶模型进行拟合，发现调整分数阶模型中的分数阶数可以更好模拟岩石等速蠕变阶段的非线性渐变过程，同时该分数阶模型也能体现加速蠕变阶段岩石应变随时间发展呈现指数函数增长的特点。通过对比，认为该分数阶模型能很好模拟岩石蠕变的全过程，且模型组合简单、参数少，具有良好的实际应用价值。

关键词:分数阶导数;岩石蠕变;加速阶段;非线性;本构模型

doi:10.16186/j.cnki.1673-9787.2020040027

基金项目:国家自然科学基金资助项目（51609081）

收稿日期:2020/04/07

修回日期:2020/07/14

出版日期:2021/11/15

Study on the rock creep constitutive model based on fractional derivative

HU Qizhi1, WANG Zhichao1, DING Zhigang1,2

1.Civil Architecture and Environment， Hubei University of Technology， Wuhan 430068 ， Hubei， China;2.China Jiaotong Brige South Engineering Co.， Ltd. ， Beijing  101149 ， China

Abstract:Since the composite element model cannot describe the disadvantage of the nonlinear creep acceleration stage of the rock ， the soft element based on the fractional order theory was connected in series with the spring element and a nonlinear viscoplastic composite composed of a friction member and a Newton viscous potin parallel to form an four-element creep model based on the fractional derivative that could better describe the whole process of rock creep. The three process characteristics of rock creep were analyzed ， and the expression of the four-element model was derived. Combining the creep experiment data of green schist ， Wanzhou red bed sandstone and Changshan salt rock of Jinping Hydropower station ， the fractional order model was fitted ， and it was found that by adjusting the order of the fractional order in the fractional model ， it was possible to better simulate the nonlinear gradual change process with the constant creep velocity of rock in the creep stage ， and the fractional order model could also reflect the characteristics of the exponential function growth of the rock strain over time in the accelerated creep stage. By comparison ， it was believed that the fractional order model could well simulate the whole process of rock creep， and the model had simple combination and few parameters ， and had good practical application value.

Key words:fractional derivative;rock creep;acceleration phase;nonlinear;constitutive model

 基于分数阶导数的岩石蠕变本构模型研究_胡其志.pdf