Modeling permanent strains of granular soil under cyclic loading with variable confining pressure

  • Qi Sun
  • Quanyang DongEmail author
  • Yuanqiang Cai
  • Jun Wang
Research Paper


Previous experimental studies showed that variable confining pressure (VCP) promoted the development of permanent strains of granular soils in most cases and indicated VCP should not be ignored. However, existing empirical formulas do not fully account for the effect of VCP on permanent strains. Therefore, three series of cyclic triaxial tests with constant confining pressure (CCP) and VCP are performed on saturated sand at three relative densities. These tests aim at investigating the influential factors which could reflect the effect of VCP on permanent strains and should be considered in establishing the empirical formula. Test results show that an increasing initial void ratio has great effect on the permanent strains of sand. The permanent strains increase with an increase in the stress ratio of maximum deviatoric stress to average confining pressure \({{q^{\hbox{max} } } \mathord{\left/ {\vphantom {{q^{\hbox{max} } } {\sigma_{3}^{\text{av}} }}} \right. \kern-0pt} {\sigma_{3}^{\text{av}} }}\) and the length of stress path L in both CCP and VCP tests. Based on that, a four-parameter equation considering the initial void ratio, stress ratio, length of stress path, and number of loading cycles is proposed to predict the permanent strains under cyclic loading with VCP. Comparison between the measured and predicted permanent strains shows that the equation can well capture the permanent strain response in tests with CCP and VCP.


Cyclic loading Granular soil Permanent strain Variable confining pressure 

List of symbols


Constant confining pressure


Relative density after consolidation


Function of void ratio


Length of stress path


Number of loading cycles


Reference stress


Amplitude of mean principal stress


Average mean principal stress


Maximum mean principal stress


Minimum mean principal stress


Amplitude of deviatoric stress


Average deviatoric stress


Cyclic deviatoric stress


Maximum deviatoric stress


Minimum deviatoric stress


Variable confining pressure

α1, α2, α3, and α4

Parameters of the equation


Axial permanent strain


Inclination of stress path


Amplitude of confining pressure


Average confining pressure


Cyclic confining pressure



The work presented in this paper was supported by the National Natural Science Foundation of China under Grant Nos. 51608394, 51508417, and the Natural Science Foundation of Zhejiang Province Nos. LY18E080030 and LY19E080021. These financial supports are gratefully acknowledged.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Civil Engineering and Architecture, the Key Laboratory of Engineering and Technology for Soft Soil Foundation and Tideland Reclamation of Zhejiang ProvinceWenzhou UniversityWenzhouPeople’s Republic of China
  2. 2.Research Center of Coastal and Urban Geotechnical EngineeringZhejiang UniversityHangzhouPeople’s Republic of China
  3. 3.College of Civil Engineering and ArchitectureZhejiang University of TechnologyHangzhouPeople’s Republic of China

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