Mathematical Description and Complete Solution of the Critical State in the Shear Band of Granular Soil

HUANG Wenxiong; CUI Xian

doi:10.21656/1000-0887.440295

Volume 45 Issue 3

Mar. 2024

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HUANG Wenxiong, CUI Xian. Mathematical Description and Complete Solution of the Critical State in the Shear Band of Granular Soil[J]. Applied Mathematics and Mechanics, 2024, 45(3): 287-294. doi: 10.21656/1000-0887.440295

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Mathematical Description and Complete Solution of the Critical State in the Shear Band of Granular Soil

doi: 10.21656/1000-0887.440295

HUANG Wenxiong^,,
CUI Xian

College of Mechanics and Materials, Hohai University, Nanjing 210098, P.R.China

Received Date: 2023-09-28
Rev Recd Date: 2023-11-23
Publish Date: 2024-03-01

Abstract

Abstract

High-order continuum models are needed for properly capturing the post-failure mechanical responses of soils involving shear bands. Through analysis on the evolution of shear band in granular soils based on a previously proposed micropolar hypoplastic model, a governing equation for the shear band in the critical state was obtained, which is a special nonlinear ordinary differential equation satisfied by the Cosserat angular velocity. A concise derivation of the governing equation was conducted. The properties of the governing equation, the range of the chief parameter and the approach to the solution were mainly discussed. An energy balance equation was formulated as a complementary condition for the determinant of the problem through analysis on the mechanical properties of the shear band. Then, the complete solutions, including the shear-band thickness factor, the stress distribution, the strain rate components, and the shear velocity, were obtained through numerical integration. The shear band thickness factor is particularly useful in determination of the micro-strength parameter of the constitutive model.
- shear band,
- micropolar hypoplastic model,
- critical state,
- nonlinear ordinary differential equation,
- complete solution

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References(15)

References

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