Creep constitutive model of logarithmic fractal structure derivative of deep hard brittle rock

LIU Yipin; LIU Wenbo; ZHANG Shuguang; HUANG Xiang; LI Yingbo; ZHAO Shutian

doi:10.12454/j.jsuese.202400928

您当前的位置：

首页 >

文章列表页 >

Creep constitutive model of logarithmic fractal structure derivative of deep hard brittle rock

更新时间：2025-05-20

- Creep constitutive model of logarithmic fractal structure derivative of deep hard brittle rock
- Advanced Engineering Sciences Pages: 1-12(2025)
- 作者机构：
  
  1.中铁十九局集团轨道交通工程有限公司，北京100176
  2.广西岩土力学与工程重点实验室，桂林理工大学，桂林，541004
  3.广西绿色建材与建筑工业化重点实验室，桂林理工大学，桂林，541004
  4.深圳铁路投资建设集团有限公司，广州深圳，518035
- 作者简介：
- 基金信息：
- DOI：10.12454/j.jsuese.202400928
  CLC： TU45
- Received：09 November 2024，
  
  Published Online：19 May 2025，
- 稿件说明：
移动端阅览
刘轶品,刘文博,张树光等.深部硬脆性岩石对数分形结构导数的蠕变本构模型[J].工程科学与技术,

LIU Yipin,LIU Wenbo,ZHANG Shuguang,et al.Creep constitutive model of logarithmic fractal structure derivative of deep hard brittle rock[J].Advanced Engineering Sciences,XXXX,XX(XX):1‒12.
刘轶品,刘文博,张树光等.深部硬脆性岩石对数分形结构导数的蠕变本构模型[J].工程科学与技术, DOI：10.12454/j.jsuese.202400928.

LIU Yipin,LIU Wenbo,ZHANG Shuguang,et al.Creep constitutive model of logarithmic fractal structure derivative of deep hard brittle rock[J].Advanced Engineering Sciences,XXXX,XX(XX):1‒12. DOI： 10.12454/j.jsuese.202400928.

摘要

为了更好地预测围岩在荷载长期作用下的变形规律以及反映围岩蠕变变形的机制，在蠕变模型的推导过程中引入Hausdorff导数，将线性的牛顿黏壶转化为非线性的黏壶，建立了考虑对数分形结构导数的变时间分形维数黏壶。同时，采用变时间分形维数的对数分形结构导数黏壶将非线性黏壶进行优化，进而将改进后的非线性黏壶串联改进后的西原模型，得到一种变时间分形维数的对数分形结构导数岩石蠕变本构模型。结果表明：该模型曲线与试验曲线具有较好地吻合度，尤其是在非破坏荷载作用下，岩石的模型曲线与试验曲线的基本重合且相关性系数均在0.95以上，在破坏荷载作用下岩石的模型曲线与试验曲线在加速蠕变变形阶段出现了较为明显的偏离，但是总体的吻合度和相关系系数都很高。同时，该模型可以很好地描述蠕变变形全过程，也较好弥补西原蠕变模型不能对加速蠕变变形特性描述的缺点，故可以认为该模型的构建过程是正确的和合理的。

Abstract

Objective

In the field of geotechnical engineering

it has always been a key issue to deeply explore the deformation law of surrounding rock under long-term load and accurately reveal its creep deformation mechanism.

Methods

In order to achieve this goal

in the rigorous derivation of the creep model

the mathematical tool of Hausdorff derivative is innovatively introduced. It can skillfully transform the traditional linear Newton's dashpot into a nonlinear dashpot. This transformation is of great significance

because in practical engineering

the deformation characteristics of surrounding rock often show significant nonlinear characteristics

and traditional linear dashpots are difficult to accurately describe. By introducing the Hausdorff derivative

the variable time fractal dimension dashpot considering the logarithmic fractal structure derivative is successfully constructed. The model is further optimized

and the nonlinear dashpot is deeply improved by using the logarithmic fractal structure derivative dashpot with variable time fractal dimension. This optimization method fully considers the dynamic influence of time factor on fractal dimension

so that the dashpot can be more suitable for the actual deformation behavior of surrounding rock under complex time history. On this basis

the improved nonlinear d

ashpot is connected in series with the improved Nishihara model. The Nishihara model has a certain foundation in describing the creep characteristics of rock

but it has limitations. And the improved nonlinear dashpot can make up for its shortcomings. Through the organic combination of the two

a new logarithmic fractal structure derivative rock creep constitutive model with variable time fractal dimension is obtained.Results and Discussions　After a large number of experimental data verification

the model shows excellent performance. The model curve and the test curve show a high degree of agreement. Especially under the action of non-destructive load

the model curve of rock is almost perfectly coincident with the test curve. After calculation

the correlation coefficient is above 0.95

which indicates that the model can accurately simulate the creep behavior of rock under normal working conditions. Under the action of failure load

although the model curve of rock deviates obviously from the test curve in the stage of accelerated creep deformation

on the whole

the coincidence degree is still high

and the correlation coefficient is also maintained at a considerable level. This shows that the model can reflect the deformation trend of rock to a certain extent even under extreme conditions.In order to obtain the clear physical meaning of the introduced parameters

the sensitivity analysis of the parameters is carried out. Under the action of the same time

the greater the parameter αve

the greater the creep deformation value and the rate of decay creep deformation also increases

which may be that α

is closely related to the microstructure and physical process inside the rock. From the microscopic point of view

the larger α

means that some factors inside the rock make it more prone to deformation. Under the action of the same time

the larger the parameter α

the attenuation creep deformation almost coincides

but the accelerated creep stage appears in advance

reflecti

ng that the rock damage accumulation rate is accelerated

and the nonlinear characteristics of the creep curve are more and more obvious. This phenomenon profoundly reflects the acceleration of rock damage accumulation rate. The advance of the accelerated creep stage means that the damage process inside the rock is carried out faster

and the damage mechanisms such as the expansion and confluence of microcracks and the crushing of mineral particles accelerate under the action of α

.At the same time

it is worth mentioning that the model can describe the whole process of rock creep deformation in a complete and detailed manner

covering various stages such as initial creep

steady-state creep and accelerated creep. In contrast

the traditional Nishihara creep model cannot effectively describe the accelerated creep deformation characteristics

and the new model makes up for this defect well. Moreover

the model shows strong universality in the description of creep deformation law of different types of rocks. Whether it is hard red sandstone

its internal mineral particles are closely arranged

and the deformation is relatively slow and stable under load. Or relatively soft green mud shale

affected by interlayer sliding and mineral composition differences

creep deformation shows complex and changeable characteristics. The model can accurately capture its unique creep characteristics.

Conclusions

Through a large number of experimental fitting of different rock samples

it is found that the model parameters can be reasonably adjusted according to the mineral composition and mechanical properties of the rock. Therefore

it accurately reflect the creep deformation law of various rocks under different load conditions. This feature makes the model can be widely used in the prediction of most rock creep deformation laws. In deep buried tunnel projects

such as deep buried tunnel projects

in the face of complex geological conditions of different rock strata combinations

it can provide accurate surrounding rock deformation prediction data for the design of supporting structures. Based on the comprehensive performance

it can be fully determined that the construction process of the model is scientific and reasonable. It also provides a reliable and powerful tool for the prediction and analysis of surrounding rock deformation in geotechnical engineering. It is expected to be widely used in practical engineering to improve the safety and reliability of engineering design and construction.

关键词

Keywords

references

Hu Kun , Zhao Lunyang , Li Pengfei , et al . Micromechanical damage model for the brittle–ductile transition in deep hard rock [J ] . Advanced Engineering Sciences , 2024 , 56 ( 3 ): 11 – 20 . DOI: 10.12454/j.jsuese.202300634 http://dx.doi.org/10.12454/j.jsuese.202300634

胡坤 , 赵伦洋 , 李鹏飞 , 等 . 深部硬岩脆–延性转化行为的细观损伤模型 [J ] . 工程科学与技术 , 2024 , 56 ( 3 ): 11 – 20 . DOI: 10.12454/j.jsuese.202300634 http://dx.doi.org/10.12454/j.jsuese.202300634

Liu Wenbo , Zhang Shuguang , Chen Lei , et al . Research on rock accelerated creep model based on statistical damage principle [J ] . Chinese Journal of Geotechnical Engineering , 2020 , 42 ( 9 ): 1696 – 1704 . DOI: 10.11779/CJGE2020 09014 http://dx.doi.org/10.11779/CJGE202009014

刘文博 , 张树光 , 陈雷 , 等 . 基于统计损伤原理的岩石加速蠕变模型研究 [J ] . 岩土工程学报 , 2020 , 42 ( 9 ): 1696 – 1704 . DOI: 10.11779/CJGE2020 09014 http://dx.doi.org/10.11779/CJGE202009014

Wang You , Liu Xiaohui , Hu Ankui , et al . Crack propagation characteristics of deep marble under triaxial compression [J ] . Advanced Engineering Sciences , 2024 , 56 ( 3 ): 21 – 31 . DOI: 10.12454/j.jsuese.202300477 http://dx.doi.org/10.12454/j.jsuese.202300477

王悠 , 刘晓辉 , 胡安奎 , 等 . 深埋大理岩三轴压缩渐进破坏裂纹扩展特征 [J ] . 工程科学与技术 , 2024 , 56 ( 3 ): 21 – 31 . DOI: 10.12454/j.jsuese.202300477 http://dx.doi.org/10.12454/j.jsuese.202300477

Zhang Liangliang , Wang Xiaojian . Research on viscoelastic-plastic damage creep model of rock [J ] . Chinese Journal of Geotechnical Engineering , 2020 , 42 ( 6 ): 1085 – 1092 . DOI: 10.11779/CJGE 202006012 http://dx.doi.org/10.11779/CJGE202006012

张亮亮 , 王晓健 . 岩石黏弹塑性损伤蠕变模型研究 [J ] . 岩土工程学报 , 2020 , 42 ( 6 ): 1085 – 1092 . DOI: 10.11779/CJGE 202006012 http://dx.doi.org/10.11779/CJGE202006012

Sun Ziwan , Zhang Zetian , Zhang Ru , et al . Acoustic emission characteristics and damage constitutive model of roof sandstone during direct tensile failure [J ] . Advanced Engineering Sciences , 2024 , 56 ( 4 ): 173 – 181 . DOI: 10.15961/j.jsuese.202300145 http://dx.doi.org/10.15961/j.jsuese.202300145

孙紫琬 , 张泽天 , 张茹 , 等 . 顶板砂岩直接拉伸破坏声发射特征及损伤本构模型 [J ] . 工程科学与技术 , 2024 , 56 ( 4 ): 173 – 181 . DOI: 10.15961/j.jsuese.202300145 http://dx.doi.org/10.15961/j.jsuese.202300145

Li Dejian , Liu Xiaolin , Han Chao . Variable-order fractional damage creep model based on equivalent viscoelasticity for rock [J ] . Rock and Soil Mechanics , 2020 , 41 ( 12 ): 3832 – 3839 . DOI: 10.16285/j.rsm.2020.0419 http://dx.doi.org/10.16285/j.rsm.2020.0419

李德建 , 刘校麟 , 韩超 . 基于等效黏弹性的变阶分数阶岩石损伤蠕变模型 [J ] . 岩土力学 , 2020 , 41 ( 12 ): 3832 – 3839 . DOI: 10.16285/j.rsm.2020.0419 http://dx.doi.org/10.16285/j.rsm.2020.0419

Wu F , Zhou X H , Ying P , et al . A study of uniaxial acoustic emission creep of salt rock based on improved fractional-order derivative [J ] . Rock Mechanics and Rock Engineering , 2022 , 55 ( 3 ): 1619 – 1631 . DOI: 10.1007/s00603-02 1-02741-3 http://dx.doi.org/10.1007/s00603-021-02741-3

Yang Juntao , Song Yanqi , Ma Hongfa , et al . A creep constitutive model of salt rock considering hardening and damage effects [J ] . Rock and Soil Mechanics , 2023 , 44 ( 10 ): 2953 – 2966 . DOI: 10.16285/j.rsm.202 2.0803 http://dx.doi.org/10.16285/j.rsm.2022.0803

杨俊涛 , 宋彦琦 , 马宏发 , 等 . 考虑硬化和损伤效应的盐岩蠕变本构模型研究 [J ] . 岩土力学 , 2023 , 44 ( 10 ): 2953 – 2966 . DOI: 10.16285/j.rsm.202 2.0803 http://dx.doi.org/10.16285/j.rsm.2022.0803

Su Teng , Zhou Hongwei , Zhao Jiawei , et al . A creep model of rock based on variable order fractional derivative [J ] . Chinese Journal of Rock Mechanics and Engineering , 2019 , 38 ( 7 ): 1355 – 1363 . DOI: 10.13722/j.cnki.jrm e.2018.1382 http://dx.doi.org/10.13722/j.cnki.jrme.2018.1382

苏腾 , 周宏伟 , 赵家巍 , 等 . 基于变阶分数阶导数的岩石蠕变模型 [J ] . 岩石力学与工程学报 , 2019 , 38 ( 7 ): 1355 – 1363 . DOI: 10.13722/j.cnki.jrm e.2018.1382 http://dx.doi.org/10.13722/j.cnki.jrme.2018.1382

Yu Bingbing , Li Qing , Zhao Tongde , et al . Full-time nonlinear creep damage model of fractured rock mass based on stress-time double threshold [J ] . Chinese Journal of Rock Mechanics and Engineering , 2023 , 42 ( 8 ): 1928 – 1944 . DOI: 10.13722/j.cnki.jrme.202 2.1147 http://dx.doi.org/10.13722/j.cnki.jrme.2022.1147

于冰冰 , 李清 , 赵桐德 , 等 . 基于应力与时间双阈值的岩石全时态非线性蠕变损伤模型 [J ] . 岩石力学与工程学报 , 2023 , 42 ( 8 ): 1928 – 1944 . DOI: 10.13722/j.cnki.jrme.202 2.1147 http://dx.doi.org/10.13722/j.cnki.jrme.2022.1147

Cheng Aiping , Fu Zixiang , Deng Daiqiang , et al . Creep characteristics and fractional order constitutive model of cemented backfill under high and low stress levels [J ] . Journal of China University of Mining & Technology , 2023 , 52 ( 2 ): 276 – 285+299 . DOI: 10.13247/j.cnki.jcumt.20210832 http://dx.doi.org/10.13247/j.cnki.jcumt.20210832

程爱平 , 付子祥 , 邓代强 , 等 . 高低应力水平下胶结充填体蠕变特征及分数阶本构模型 [J ] . 中国矿业大学学报 , 2023 , 52 ( 2 ): 276 – 285+299 . DOI: 10.13247/j.cnki.jcumt.20210832 http://dx.doi.org/10.13247/j.cnki.jcumt.20210832

Chen Youliang , Chen Qijian , Xiao Peng , et al . A true triaxial creep constitutive model for rock considering hydrochemical damage [J ] . Chinese Journal of Theoretical and Applied Mechanics , 2023 , 55 ( 1 ): 159 – 168 . DOI: 10.6052/0459-1879-22-329 http://dx.doi.org/10.6052/0459-1879-22-329

陈有亮 , 陈奇键 , 肖鹏 , 等 . 考虑水化学损伤的岩石真三轴蠕变本构模型 [J ] . 力学学报 , 2023 , 55 ( 1 ): 159 – 168 . DOI: 10.6052/0459-1879-22-329 http://dx.doi.org/10.6052/0459-1879-22-329

Chen Wen . Fractal analysis of Hausdorff calculus and fractional calculus models [J ] . Computer-Aided Engineering , 2017 , 26 ( 3 ): 1 – 5 . DOI: 10.13340/j.cae.2017.03.001 http://dx.doi.org/10.13340/j.cae.2017.03.001

陈文 . 豪斯道夫微积分和分数阶微积分模型的分形分析 [J ] . 计算机辅助工程 , 2017 , 26 ( 3 ): 1 – 5 . DOI: 10.13340/j.cae.2017.03.001 http://dx.doi.org/10.13340/j.cae.2017.03.001

Han Yang , Tan Yuehu , Li Erbing , et al . Unsteady Burgers creep model for rock and its parameter identification [J ] . Engineering Mechanics , 2018 , 35 ( 3 ): 210 – 217 . DOI: 10.6052/j.issn.1000-4750.2017.01.0025 http://dx.doi.org/10.6052/j.issn.1000-4750.2017.01.0025

韩阳 , 谭跃虎 , 李二兵 , 等 . 岩石非定常Burgers蠕变模型及其参数识别 [J ] . 工程力学 , 2018 , 35 ( 3 ): 210 – 217 . DOI: 10.6052/j.issn.1000-4750.2017.01.0025 http://dx.doi.org/10.6052/j.issn.1000-4750.2017.01.0025

Wang Yanyan , Sheng Dongfa . Study on the whole process of rock creep considering damage based on Burgers model [J ] . Chinese Quarterly of Mechanics , 2019 , 40 ( 1 ): 143 – 148 . DOI: 10.15959/j.cnki.0254-0053.2 019.01.016 http://dx.doi.org/10.15959/j.cnki.0254-0053.2019.01.016

汪妍妍 , 盛冬发 . 基于Burgers模型考虑损伤的岩石蠕变全过程研究 [J ] . 力学季刊 , 2019 , 40 ( 1 ): 143 – 148 . DOI: 10.15959/j.cnki.0254-0053.2 019.01.016 http://dx.doi.org/10.15959/j.cnki.0254-0053.2019.01.016

Pu Zhicheng , Cao Ping , Zhang Chunyang , et al . Variable parameters nonlinear creep damage model of rock with consideration of aging,damage,and deterioration [J ] . Engineering Mechanics , 2017 , 34 ( 6 ): 17 – 27 . DOI: 10.6052/j.issn.1000-4750.2015.12.0967 http://dx.doi.org/10.6052/j.issn.1000-4750.2015.12.0967

蒲志成 , 曹平 , 张春阳 , 等 . 考虑时效损伤劣化的变参数非线性蠕变损伤模型 [J ] . 工程力学 , 2017 , 34 ( 6 ): 17 – 27 . DOI: 10.6052/j.issn.1000-4750.2015.12.0967 http://dx.doi.org/10.6052/j.issn.1000-4750.2015.12.0967

Xue Dongjie , Lu Lele , Yi Haiyang , et al . A fractional Burgers model for uniaxial and triaxial creep of damaged salt-rock considering temperature and volume-stress [J ] . Chinese Journal of Rock Mechanics and Engineering , 2021 , 40 ( 2 ): 315 – 329 . DOI: 10.13722/j.cnki.jrme.2020.0734 http://dx.doi.org/10.13722/j.cnki.jrme.2020.0734

薛东杰 , 路乐乐 , 易海洋 , 等 . 考虑温度和体积应力的分数阶蠕变损伤Burgers模型 [J ] . 岩石力学与工程学报 , 2021 , 40 ( 2 ): 315 – 329 . DOI: 10.13722/j.cnki.jrme.2020.0734 http://dx.doi.org/10.13722/j.cnki.jrme.2020.0734

Qi Yajing , Jiang Qinghui , Wang Zhijian , et al . 3D creep constitutive equation of modified Nishihara model and its parameter identification [J ] . Chinese Journal of Rock Mechanics and Engineering , 2012 , 31 ( 2 ): 347 – 355 . DOI: CNKI:SUN:YSLX.0.2012-02-017 http://dx.doi.org/CNKI:SUN:YSLX.0.2012-02-017

齐亚静 , 姜清辉 , 王志俭 , 等 . 改进西原模型的三维蠕变本构方程及其参数辨识 [J ] . 岩石力学与工程学报 , 2012 , 31 ( 2 ): 347 – 355 . DOI: CNKI:SUN:YSLX.0.2012-02-017 http://dx.doi.org/CNKI:SUN:YSLX.0.2012-02-017

Su Yan , Zhang Xiangdong , Zhou Linlin . Study on constitutive model of fractional creep damage of rock [J ] . Journal of Hebei University of Engineering:Natural Science , 2020 , 37 ( 1 ): 19 – 23 . DOI: 10.3969/j.issn.1673-9469.2020.0 1.004 http://dx.doi.org/10.3969/j.issn.1673-9469.2020.01.004

苏彦 , 张向东 , 周林林 . 岩石分数阶蠕变损伤本构模型研究 [J ] . 河北工程大学学报:自然科学版 , 2020 , 37 ( 1 ): 19 – 23 . DOI: 10.3969/j.issn.1673-9469.2020.0 1.004 http://dx.doi.org/10.3969/j.issn.1673-9469.2020.01.004

Xiao Shiwu , Zhou Xiong , Hu Xiaoling , et al . Linear rheological solid model with fractional derivative and its application [J ] . Engineering Mechanics , 2012 , 29 ( 10 ): 354 – 358 . DOI: 10.6052/j.issn.1000-4750.2011.01.0064 http://dx.doi.org/10.6052/j.issn.1000-4750.2011.01.0064

肖世武 , 周雄 , 胡小玲 , 等 . 分数阶导数线性流变固体模型及其应用 [J ] . 工程力学 , 2012 , 29 ( 10 ): 354 – 358 . DOI: 10.6052/j.issn.1000-4750.2011.01.0064 http://dx.doi.org/10.6052/j.issn.1000-4750.2011.01.0064

Liu Kaiyun , Xue Yongtao , Zhou Hui . A nonlinear viscoelastic-plastic creep model of soft rock with unsteady parameters [J ] . Journal of China University of Mining & Technology , 2018 , 47 ( 4 ): 921 – 928 . DOI : 10.13247/j.cnki.jcumt.00 0905 http://dx.doi.org/10.13247/j.cnki.jcumt.000905

刘开云 , 薛永涛 , 周辉 . 参数非定常的软岩非线性黏弹塑性蠕变模型 [J ] . 中国矿业大学学报 , 2018 , 47 ( 4 ): 921 – 928 . DOI: 10.13247/j.cnki.jcumt.00 0905 http://dx.doi.org/10.13247/j.cnki.jcumt.000905

Liu J , Jing H , Meng B , et al . A four-element fractional creep model of weakly cemented soft rock [J ] . Bulletin of Engineering Geology and the Environment , 2020 ,( 2 ): 5569 – 5 584 . DOI: 10.1007/s10064-020-01869-w http://dx.doi.org/10.1007/s10064-020-01869-w

Liu Wenbo . Research on constitutive model and rheological characteristics of loading and unloading damage of deep sandstone [D ] . Fuxin : Liaoning Technical University , 2020 . DOI: 10.27210/d.cnki.glnju.2020.000018 http://dx.doi.org/10.27210/d.cnki.glnju.2020.000018

刘文博 . 高应力作用下砂岩加卸载损伤本构模型及流变特性研究 [D ] . 阜新 : 辽宁工程技术大学 , 2020 . DOI: 10.27210/d.cnki.glnju.2020.000018 http://dx.doi.org/10.27210/d.cnki.glnju.2020.000018

Views

下载量

CNKI被引量

Alert me when the article has been cited

提交

Tools

Publicity Resources

Creep Characteristics of Fractured Sandstone Under the Coupling Action of Axial Compression and Hydraulic Pressure

Numerical Analysis on Deformation of Reservoir Landslides Considering Coupling Effect of Seepage and Creep

Experimental Study of Shear Creep Characteristic of Moraine Soil in Dadu River Bridge in Luding

Resarch on Unloading Modulus for Salt Rock Damage Testing

Related Author

Defeng LIU

Pengtao LIU

Zhenyue ZHANG

Yinlong XI

Xiuwei CHAI

Li WANG

Shimei WANG

Gao LI

Related Institution

School of Resources & Safety Eng., Wuhan Inst. of Technol.

Hubei Research and Design Inst. of Chemical Industry

Lab. of Geological Hazards on Three Gorges Reservoir Area, Ministry of Education, China Three Gorges Univ., Yichang

Sichuan Highway Planning, Survey, Design and Research Inst. Ltd.

Chongqing Branch, Changjiang River Scientific Research Inst.

⁰