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Study on the Fractional‐Order Creep Constitutive Model of Rock Considering Chemical–Stress–Seepage Damage.

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Title: Study on the Fractional‐Order Creep Constitutive Model of Rock Considering Chemical–Stress–Seepage Damage.
Authors: Zhao, Shutian1,2 (AUTHOR), Zhang, Shuguang1,2 (AUTHOR) guilinligong753@163.com, Zhao, Junkang1,2 (AUTHOR), Liu, Wenbo1,2 (AUTHOR), Sun, Xiaodong3 (AUTHOR), Li, Yingbo3 (AUTHOR), Liu, Yipin4 (AUTHOR)
Source: Fatigue & Fracture of Engineering Materials & Structures. Oct2026, Vol. 49 Issue 10, p4446-4462. 17p.
Subject Terms: *Damage models, *Elastic modulus, *Rock mechanics, *Rock deformation, *Corrosion & anti-corrosives
Abstract: Accurate characterization of rock creep under coupled chemical–stress–seepage conditions is essential for deep rock stability. A three‐dimensional fractional‐order creep constitutive model is developed. Chemical, stress, and seepage damage are quantified by elastic modulus degradation, the Kachanov evolution, and permeability–pore‐pressure gradient evolution and combined into a total damage variable. This variable is introduced into an Abel‐type fractional dashpot, and the governing equation is converted into an explicit time‐power series form through the Riemann–Liouville integration and the Beta function. The model is extended to three‐dimensional stress states and validated by step‐loading triaxial creep tests under varied pH, seepage pressure, and stress levels. Results show that stronger corrosion, higher seepage pressure, and higher stress increase the fractional order and time‐power coefficients, reduce viscosity, and promote accelerating creep. Fitting gives coefficients of determination R2 > 0.85, supporting long‐term deformation prediction and stability assessment of rock masses under coupled multi‐field environments. Highlights: Three‐dimensional fractional‐order creep model couples chemical, stress, and seepage damage.Total damage links modulus degradation, the Kachanov law, and seepage evolution.Explicit time‐power series solution was derived with damage‐embedded viscosity. [ABSTRACT FROM AUTHOR]
Database: Academic Search Index
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  – Url: https://resolver.ebsco.com/c/fiv2js/result?sid=EBSCO:asx&genre=article&issn=8756758X&ISBN=&volume=49&issue=10&date=20261001&spage=4446&pages=4446-4462&title=Fatigue & Fracture of Engineering Materials & Structures&atitle=Study%20on%20the%20Fractional%E2%80%90Order%20Creep%20Constitutive%20Model%20of%20Rock%20Considering%20Chemical%E2%80%93Stress%E2%80%93Seepage%20Damage.&aulast=Zhao%2C%20Shutian&id=DOI:10.1111/ffe.70376
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Items – Name: Title
  Label: Title
  Group: Ti
  Data: Study on the Fractional‐Order Creep Constitutive Model of Rock Considering Chemical–Stress–Seepage Damage.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Zhao%2C+Shutian%22">Zhao, Shutian</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Zhang%2C+Shuguang%22">Zhang, Shuguang</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> guilinligong753@163.com</i><br /><searchLink fieldCode="AR" term="%22Zhao%2C+Junkang%22">Zhao, Junkang</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Liu%2C+Wenbo%22">Liu, Wenbo</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Sun%2C+Xiaodong%22">Sun, Xiaodong</searchLink><relatesTo>3</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Li%2C+Yingbo%22">Li, Yingbo</searchLink><relatesTo>3</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Liu%2C+Yipin%22">Liu, Yipin</searchLink><relatesTo>4</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Fatigue+%26+Fracture+of+Engineering+Materials+%26+Structures%22">Fatigue & Fracture of Engineering Materials & Structures</searchLink>. Oct2026, Vol. 49 Issue 10, p4446-4462. 17p.
– Name: Subject
  Label: Subject Terms
  Group: Su
  Data: *<searchLink fieldCode="DE" term="%22Damage+models%22">Damage models</searchLink><br />*<searchLink fieldCode="DE" term="%22Elastic+modulus%22">Elastic modulus</searchLink><br />*<searchLink fieldCode="DE" term="%22Rock+mechanics%22">Rock mechanics</searchLink><br />*<searchLink fieldCode="DE" term="%22Rock+deformation%22">Rock deformation</searchLink><br />*<searchLink fieldCode="DE" term="%22Corrosion+%26+anti-corrosives%22">Corrosion & anti-corrosives</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Accurate characterization of rock creep under coupled chemical–stress–seepage conditions is essential for deep rock stability. A three‐dimensional fractional‐order creep constitutive model is developed. Chemical, stress, and seepage damage are quantified by elastic modulus degradation, the Kachanov evolution, and permeability–pore‐pressure gradient evolution and combined into a total damage variable. This variable is introduced into an Abel‐type fractional dashpot, and the governing equation is converted into an explicit time‐power series form through the Riemann–Liouville integration and the Beta function. The model is extended to three‐dimensional stress states and validated by step‐loading triaxial creep tests under varied pH, seepage pressure, and stress levels. Results show that stronger corrosion, higher seepage pressure, and higher stress increase the fractional order and time‐power coefficients, reduce viscosity, and promote accelerating creep. Fitting gives coefficients of determination R2 > 0.85, supporting long‐term deformation prediction and stability assessment of rock masses under coupled multi‐field environments. Highlights: Three‐dimensional fractional‐order creep model couples chemical, stress, and seepage damage.Total damage links modulus degradation, the Kachanov law, and seepage evolution.Explicit time‐power series solution was derived with damage‐embedded viscosity. [ABSTRACT FROM AUTHOR]
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=asx&AN=196829091
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1111/ffe.70376
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 17
        StartPage: 4446
    Subjects:
      – SubjectFull: Damage models
        Type: general
      – SubjectFull: Elastic modulus
        Type: general
      – SubjectFull: Rock mechanics
        Type: general
      – SubjectFull: Rock deformation
        Type: general
      – SubjectFull: Corrosion & anti-corrosives
        Type: general
    Titles:
      – TitleFull: Study on the Fractional‐Order Creep Constitutive Model of Rock Considering Chemical–Stress–Seepage Damage.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Zhao, Shutian
      – PersonEntity:
          Name:
            NameFull: Zhang, Shuguang
      – PersonEntity:
          Name:
            NameFull: Zhao, Junkang
      – PersonEntity:
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            NameFull: Liu, Wenbo
      – PersonEntity:
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            NameFull: Sun, Xiaodong
      – PersonEntity:
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            NameFull: Li, Yingbo
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            NameFull: Liu, Yipin
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          Dates:
            – D: 01
              M: 10
              Text: Oct2026
              Type: published
              Y: 2026
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            – Type: issn-print
              Value: 8756758X
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              Value: 49
            – Type: issue
              Value: 10
          Titles:
            – TitleFull: Fatigue & Fracture of Engineering Materials & Structures
              Type: main
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