Scaling laws for quasi-static granular sand at critical state

FEI Jianbo; TANG Hao; JIE Yuxin; CHEN Xiangsheng

doi:10.11779/CJGE20230435

Volume 46 Issue 9

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Chinese Journal of Geotechnical Engineering > 2024 > 46(9): 1831-1839. > DOI: 10.11779/CJGE20230435

FEI Jianbo, TANG Hao, JIE Yuxin, CHEN Xiangsheng. Scaling laws for quasi-static granular sand at critical state[J]. Chinese Journal of Geotechnical Engineering, 2024, 46(9): 1831-1839. DOI: 10.11779/CJGE20230435

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Scaling laws for quasi-static granular sand at critical state

FEI Jianbo^{1, 2, 3,},
TANG Hao^{1, 2, 3},
JIE Yuxin^{4, 5, 6},
CHEN Xiangsheng^{1, 2, 3}

1.
State Key Laboratory of Intelligent Geotechnics and Tunnelling, Shenzhen University, Shenzhen 518060, China
2.
Key Laboratory of Coastal Urban Resilient Infrastructures (Shenzhen University), Ministry of Education, Shenzhen 518060, China
3.
College of Civil and Transportation Engineering, Shenzhen University, Shenzhen 518060, China
4.
State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China
5.
Key Laboratory of Hydrosphere Sciences of the Ministry of Water Resources, Tsinghua University, Beijing, 100084, China
6.
Department of Hydraulic Engineering, Tsinghua University, Beijing 100084, China

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Received Date: May 17, 2023
Available Online: April 18, 2024

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Abstract

Abstract

The critical state theory of soils describes the correspondence between effective stress, shear strength and soil density. Numerous soil mechanics experiments have also revealed a correlation between soil strength and loading rate. Considering that the granular matter is the actual medium of natural soils, a quasi-static inertia number is proposed, i.e., Q=ϕ₀[ln(I)+α], for the granular soils considering the particle volume fraction. Based on the classical triaxial test data of soils, the scaling laws of quasi-static deforming sand at the critical state from the perspective of granular physics are explored, and a simple linear relationship i.e., μ=ξQ, is found between the friction coefficient and the quasi-static particle inertia number. The newly established scaling laws can quantitatively describe the influences of the volume fraction, shear rate, confining pressure and particle size on the frictional properties of sand when reaching the critical state. In addition, to quantify the volumetric deformation laws of sand under quasi-static shear, a correlation is obtained between the particle volume fraction ϕ at the critical state and the quasi-static inertia number Q. In attempt to characterize the scaling laws of the three-dimensional stress state, a new dimensionless number (i.e., the intermediate principal stress number) is defined to reveal the influences of the intermediate principal stress on the frictional properties. Thus, the scaling laws are extended.
- granular material,
- critical state,
- scaling law,
- Cambridge model,
- sand

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Scaling laws for quasi-static granular sand at critical state

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