A modified Nishihara model based on fractional calculus theory 
and its parameter intelligent identification

XU Guo-wen; HE Chuan; HU Xiong-yu; WANG Shi-min

doi:10.16285/j.rsm.2015.S2.017

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A modified Nishihara model based on fractional calculus theory and its parameter intelligent identification

更新时间：2026-06-25

- A modified Nishihara model based on fractional calculus theory and its parameter intelligent identification
- Vol. 36, Issue S2, Pages: 132-138(2015)
- 作者机构：
  
  西南交通大学交通隧道工程教育部重点实验室,四川,成都,610031
- 作者简介：
- 基金信息：
- DOI：10.16285/j.rsm.2015.S2.017
  CLC： TB115
- Online First：14 June 2018，
  
  Published：2015
- 稿件说明：
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XU Guo-wen, HE Chuan, HU Xiong-yu, et al. A modified Nishihara model based on fractional calculus theory and its parameter intelligent identification[J]. 2015, 36(S2): 132-138.
DOI：

XU Guo-wen, HE Chuan, HU Xiong-yu, et al. A modified Nishihara model based on fractional calculus theory and its parameter intelligent identification[J]. 2015, 36(S2): 132-138. DOI： 10.16285/j.rsm.2015.S2.017.

摘要

传统西原模型难以描述岩石的非线性加速流变特性，根据Riemann-Liouville分数阶微积分理论，采用分数阶黏壶及非线性黏塑性体NVPB(nonlinear viscoplastic body)模型，分别取代传统西原模型黏弹性体中的牛顿黏壶及黏塑性体，提出改进的西原模型，并推导出岩石在恒应力情况下的三维蠕变本构方程。模型采用基于流变阶段分解-粒子群-模拟退火算法相结合的智能算法对已有的试验数据进行反演，结果表明该模型能有效地反映岩石3个阶段的蠕变特征。通过对模型的敏感性分析发现，岩石的非线性渐变过程及加速蠕变阶段的快慢程度分别由分数阶导数的阶次及流变指数控制，传统西原模型是改进西原模型的一种特例。

Abstract

Classical Nishihara model is difficultly to describe the nonlinear acceleration rheological properties of rocks. According to Riemann-Liouville fractional calculus theory

by replacing a Newton dashpot and viscoplastic dashpot in classical Nishihara model with fractional dashpot and nonlinear viscoplastic body(NVPB) model

a modified Nishihara model is proposed and a three-dimensional constitutive equation is deduced in the case of constant stress creep state. The rheological stage decomposition- particle swarm optimization(PSO)-simulated annealing intelligent algorithms is used for data inversion on existing experimental data. The results show that the model can effectively reflect the three-stage creep characteristics of rock. Through sensitivity analysis

it is found that the nonlinear gradual process and acceleration stage of rock are controlled by order of fractional derivatives and rheological index respectively. Furthermore

it is pointed out that the classical Nishihara model is a special case of the modified Nishihara model.

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Related Institution

State Key Laboratory of Geomechanics and Deep Underground Engineering, China University of Mining and Technology

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