Abstract
This paper presents a generalized dilatancy angle equation of granular soil to cover not only the drained tests but also the undrained tests by introducing a generalized structure of soil: soil skeleton formed by soil particles and the fluid in soil voids, under the assumptions of the incompressibility of soil particles and the compressibility of the fluid in soil voids. For the drained tests, the generalized dilatancy angle equation of granular soil would be degenerated to its current dilatancy angle equation. However, for the undrained tests, the generalized dilatancy angle equation of granular soil was derived with a λ parameter that was related to the stress-strain state of soil and the nature of the fluid in soil voids. The λ parameter was determined by the initial dilatancy angles of granular soil at the onset of shearing on the same initial state of the soil in the drained and undrained tests. In addition, the generalized dilatancy angle equation of granular soil was verified for application in calculation of the dilatancy angles of sands in the drained and undrained tests.
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Abbreviations
- B f :
-
Bulk modulus of the fluid in soil voids
- B w :
-
Bulk modulus of water (Bw=2.15 GPa)
- C:
-
Intrinsic material constants of soil
- CD:
-
Consolidated Drained
- CU:
-
Consolidated Undrained
- d :
-
Dilatancy of granular soil
- dε 1 :
-
Major principal strain increment of soil
- dε v :
-
Volumetric strain increment of soil
- dε vf :
-
Volumetric strain increment of the fluid in soil voids
- dε vss :
-
Volumetric strain increment of soil skeleton formed by soil particles
- dε ev :
-
Elastic volumetric strain increment of soil
- dε evf :
-
Elastic volumetric strain increment of the fluid in soil voids
- dε evss :
-
Elastic volumetric strain increment of soil skeleton formed by soil particles
- dε evw :
-
Elastic volumetric strain increment of the water in soil voids
- dε pq :
-
Plastic deviator strain increment of soil
- dε pv :
-
Plastic volumetric strain increment of soil
- dε pvf :
-
Plastic volumetric strain increment of the fluid in soil voids
- dε pvss :
-
Plastic volumetric strain increment of soil skeleton formed by soil particles
- dγ 13 :
-
Maximum shear strain increment of soil dγ13f Maximum shear strain increment of the fluid in soil voids
- dγ 13ss :
-
Maximum shear strain increment of soil skeleton formed by soil particles
- dγ e13 :
-
Maximum elastic shear strain increment of soil
- dγ e13f :
-
Maximum elastic shear strain increment of the fluid in soil voids
- dγ e13ss :
-
Maximum elastic shear strain increment of soil skeleton formed by soil particles
- dγ p13 :
-
Maximum plastic shear strain increment of soil
- dγ p13f :
-
Maximum plastic shear strain increment of the fluid in soil voids
- dγ p13ss :
-
Maximum plastic shear strain increment of soil skeleton formed by soil particles
- dp :
-
Mean stress increment of soil
- du :
-
Excess pore water pressure increment of soil
- e 0 :
-
Initial void ratio of soil
- ε 1 :
-
Axial strain of soil
- ε v :
-
Volumetric strain of soil
- έ 1 :
-
Major principal strain rate of soil
- έ p1 :
-
Plastic major principal strain rate of soil
- έ v :
-
Volumetric strain rate of soil
- έ pv :
-
Plastic volumetric strain rate of soil
- f():
-
Function
- K ep :
-
Elastoplastic modulus of soil
- K p :
-
Plastic modulus of soil skeleton formed by soil particles
- K 0 :
-
Initial consolidated stress ratio of soil
- M :
-
Critical effective stress ratio of soil
- p :
-
Mean stress of soil
- p′:
-
Mean effective stress of soil
- q :
-
Deviator stress of soil
- u :
-
Excess pore water pressure of soil
- η :
-
Effective stress ratio of soil
- θ :
-
Dilatancy angle of soil
- θ D :
-
Dilatancy angle of soil for the drained tests
- θ U :
-
Dilatancy angle of soil for the undrained tests
- θ DI :
-
Initial dilatancy angle of the drained test
- θ UI :
-
Initial dilatancy angle of the undrained test
- λ :
-
A parameter in derivation
- μ :
-
A parameter in derivation
- σ c0 :
-
Initial confining stress of soil
- ψ :
-
State parameter of soil (Been and Jefferies 1985)
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Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant no. 41807268) and the Youth Innovation Promotion Association of Chinese Academy of Sciences — China (Grant no. 2018408).
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Yu, Fw. A generalized dilatancy angle equation of granular soil. J. Mt. Sci. 19, 1456–1463 (2022). https://doi.org/10.1007/s11629-021-7099-2
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DOI: https://doi.org/10.1007/s11629-021-7099-2