Abstract
Internal erosion is a common form of damage in geomaterial structures that is caused by the migration of soil particles under a seepage flow. The geometrical characteristics of soil particles is regarded as the intrinsic factor for internal instability; thus, in this study, a network modelling technique is formulated for this purpose. The soil particles and pores are generalised into a network model according to their fractal gradations; thereafter, the percolation theory is applied to analyse this conceptual probabilistic model. The percolation and erosion backbones are simulated in the direct square bond percolation model through the extended Hoshen–Kopelman algorithm and direct electrifying algorithm. Monte Carlo experiments are conducted to analyse the internal erosion process in this network model. The extent of internal instability can be calculated quantitatively, and the deposition rate of transported particles in the mass conservation equation can be evaluated for further analysis. Compared with internal erosion tests, the percolation analytical method is in accordance with experimental results. This method provides fresh insights on the nature of internal erosion from a statistical perspective.
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Abbreviations
- C u :
-
Uniformity coefficient of soil
- r :
-
Radius of a soil particle
- r p :
-
Radius of a constriction
- r 60 :
-
Radius at a 60% accumulative mass percentage
- r 10 :
-
Radius at a 10% accumulative mass percentage
- r min :
-
Minimum size in a GSD curve
- r max :
-
Maximum size in a GSD curve
- r p min :
-
Minimum size in a CSD curve
- r p max :
-
Maximum size in a CSD curve
- r d :
-
The size dividing the soil particles into coarse and fine fractions
- p(rd):
-
Percentage of the fine fraction
- r e :
-
Eroded particle size
- p :
-
Occupied probability in a percolating system
- p c :
-
Percolation threshold at the critical state of the system
- ns(p):
-
Cluster size distribution at the occupied probability of p
- s :
-
Concentration of clusters per volume
- τ :
-
Fisher exponent in the expression of power law
- σ :
-
An unknown priori value in the semi-empirical equation
- N :
-
Number of soil particles
- N 0 :
-
The total number of soil particles
- N’(< r):
-
Number of soil particles with a size smaller than r
- D :
-
Fractal dimension of a grading curve
- D f :
-
Fractal dimension of a grading curve of the fine fraction
- D c :
-
Fractal dimension of a grading curve of the coarse fraction
- M(< r):
-
Accumulative mass of particles smaller than r
- M 0 :
-
The total mass of soil particles
- ⍴ :
-
Density of solid particles
- ρ tr :
-
Density of liquefied particles
- V(< r):
-
Accumulative volume of particles smaller than r
- V s :
-
Volume of solid particles
- V p :
-
Volume of pores
- φ :
-
Soil porosity
- λ :
-
Proportional constant of rpmax to rmax
- p(< r):
-
Percentage of particles smaller than r
- f(r):
-
Probability density of particles at the size of r
- f(rp):
-
Probability density of constrictions at the size of rp
- F(re):
-
Probability of particles sized re passing through constrictions
- v i :
-
Flow velocity
- q :
-
Volume flux term of transported particles
- q er :
-
Erosion rate with flow
- q dp :
-
Deposition rate to the soil skeleton
- ω :
-
Proportion of volume flux of transported particles to erosion rate
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Acknowledgements
The research work presented herein was funded by the National Natural Science Foundation of China (NSFC) (Grant No. 51479112). Their financial support is gratefully acknowledged.
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Li, Z., Luo, X., Bi, J. et al. Numerical modelling of internal erosion process in gravel soils based on the percolation analytical method. Environ Earth Sci 79, 358 (2020). https://doi.org/10.1007/s12665-020-09101-4
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DOI: https://doi.org/10.1007/s12665-020-09101-4