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Analysis of the Ultimate Bearing Capacity Law of the Shallow Foundation on the Soil-Rock Mixed Slope Based on the Finite Element Limit Method.

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Title: Analysis of the Ultimate Bearing Capacity Law of the Shallow Foundation on the Soil-Rock Mixed Slope Based on the Finite Element Limit Method.
Authors: Zeng, Yongqing1 yqzeng@hnist.edu.cn, Hu, Weidong2 11996498@hnist.edu.cn, Li, Bin1 12007030@hnist.edu.cn, Liu, Guohuang3 2360363839@qq.com, Tan, Xinyi3 3775478171@qq.com, Liu, Xiaohong2 11991491@hnist.edu.cn, Luo, Hua1 12015024@hnist.edu.cn, Gan, Wenju1 475645836@qq.com
Source: Engineering Letters. Jul2026, Vol. 34 Issue 7, p3010-3024. 15p.
Subjects: Bearing capacity of soils, Shallow foundations, Building foundations, Numerical analysis, Geotechnical engineering, Slopes (Soil mechanics), Finite element method
Abstract: Soil-rock mixed slopes are widely distributed in China; the calculation of foundation ultimate bearing capacity and slope failure mode of soil-rock mixed slopes is different from that of homogeneous slopes. This study systematically investigates the influence of slope geometric and soil-rock material parameters on the ultimate bearing capacity of shallow foundations on soil-rock mixed slopes using the finite element limit analysis method. The numerical model of the soil slope and the soil-rock mixed slope is established. The limit load was directly solved through optimization algorithms; the failure behavior and ultimate bearing capacity of soil slope and soil-rock mixed slope are investigated. The single-factor analysis method is used to study the effects of slope geometric and soil-rock material parameters on the ultimate bearing capacity of shallow foundations on soil-rock mixed slopes. Eleven influencing factors are chosen as follows: slope height H, slope gradient α, foundation width B, foundation burial depth H1, load position ratio λ, soil cohesion c1, soil internal friction angle ϕ1, block stone diameter d, block stone percentage β, block stone cohesion c2, and block stone internal friction angle ϕ2. Results revealed that the influence law of geometric parameters (slope height H, slope angle α, foundation width B, foundation burial depth H1, and load position ratio λ) and material parameters (soil cohesion c1, soil internal friction angle ϕ1, block stone diameter d, block stone percentage β, block stone cohesion c2, and block stone internal friction angle ϕ2) on the foundation's ultimate bearing capacity. The study identified ultimate bearing capacity under different parameter combinations, providing a theoretical basis for designing shallow foundations on soil-rock mixed slopes. [ABSTRACT FROM AUTHOR]
Copyright of Engineering Letters is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Analysis of the Ultimate Bearing Capacity Law of the Shallow Foundation on the Soil-Rock Mixed Slope Based on the Finite Element Limit Method.
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  Data: <searchLink fieldCode="AR" term="%22Zeng%2C+Yongqing%22">Zeng, Yongqing</searchLink><relatesTo>1</relatesTo><i> yqzeng@hnist.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Hu%2C+Weidong%22">Hu, Weidong</searchLink><relatesTo>2</relatesTo><i> 11996498@hnist.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Li%2C+Bin%22">Li, Bin</searchLink><relatesTo>1</relatesTo><i> 12007030@hnist.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Liu%2C+Guohuang%22">Liu, Guohuang</searchLink><relatesTo>3</relatesTo><i> 2360363839@qq.com</i><br /><searchLink fieldCode="AR" term="%22Tan%2C+Xinyi%22">Tan, Xinyi</searchLink><relatesTo>3</relatesTo><i> 3775478171@qq.com</i><br /><searchLink fieldCode="AR" term="%22Liu%2C+Xiaohong%22">Liu, Xiaohong</searchLink><relatesTo>2</relatesTo><i> 11991491@hnist.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Luo%2C+Hua%22">Luo, Hua</searchLink><relatesTo>1</relatesTo><i> 12015024@hnist.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Gan%2C+Wenju%22">Gan, Wenju</searchLink><relatesTo>1</relatesTo><i> 475645836@qq.com</i>
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  Data: <searchLink fieldCode="JN" term="%22Engineering+Letters%22">Engineering Letters</searchLink>. Jul2026, Vol. 34 Issue 7, p3010-3024. 15p.
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  Data: <searchLink fieldCode="DE" term="%22Bearing+capacity+of+soils%22">Bearing capacity of soils</searchLink><br /><searchLink fieldCode="DE" term="%22Shallow+foundations%22">Shallow foundations</searchLink><br /><searchLink fieldCode="DE" term="%22Building+foundations%22">Building foundations</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Geotechnical+engineering%22">Geotechnical engineering</searchLink><br /><searchLink fieldCode="DE" term="%22Slopes+%28Soil+mechanics%29%22">Slopes (Soil mechanics)</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Soil-rock mixed slopes are widely distributed in China; the calculation of foundation ultimate bearing capacity and slope failure mode of soil-rock mixed slopes is different from that of homogeneous slopes. This study systematically investigates the influence of slope geometric and soil-rock material parameters on the ultimate bearing capacity of shallow foundations on soil-rock mixed slopes using the finite element limit analysis method. The numerical model of the soil slope and the soil-rock mixed slope is established. The limit load was directly solved through optimization algorithms; the failure behavior and ultimate bearing capacity of soil slope and soil-rock mixed slope are investigated. The single-factor analysis method is used to study the effects of slope geometric and soil-rock material parameters on the ultimate bearing capacity of shallow foundations on soil-rock mixed slopes. Eleven influencing factors are chosen as follows: slope height H, slope gradient α, foundation width B, foundation burial depth H1, load position ratio λ, soil cohesion c1, soil internal friction angle ϕ1, block stone diameter d, block stone percentage β, block stone cohesion c2, and block stone internal friction angle ϕ2. Results revealed that the influence law of geometric parameters (slope height H, slope angle α, foundation width B, foundation burial depth H1, and load position ratio λ) and material parameters (soil cohesion c1, soil internal friction angle ϕ1, block stone diameter d, block stone percentage β, block stone cohesion c2, and block stone internal friction angle ϕ2) on the foundation's ultimate bearing capacity. The study identified ultimate bearing capacity under different parameter combinations, providing a theoretical basis for designing shallow foundations on soil-rock mixed slopes. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Engineering Letters is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 15
        StartPage: 3010
    Subjects:
      – SubjectFull: Bearing capacity of soils
        Type: general
      – SubjectFull: Shallow foundations
        Type: general
      – SubjectFull: Building foundations
        Type: general
      – SubjectFull: Numerical analysis
        Type: general
      – SubjectFull: Geotechnical engineering
        Type: general
      – SubjectFull: Slopes (Soil mechanics)
        Type: general
      – SubjectFull: Finite element method
        Type: general
    Titles:
      – TitleFull: Analysis of the Ultimate Bearing Capacity Law of the Shallow Foundation on the Soil-Rock Mixed Slope Based on the Finite Element Limit Method.
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            NameFull: Zeng, Yongqing
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            – D: 01
              M: 07
              Text: Jul2026
              Type: published
              Y: 2026
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