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On the evaluation of internal stability of gap-graded soil: a status quo review

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Abstract

Internal instability is a phenomenon of fine particle redistribution in granular materials under the seepage action and consequent change in the soil’s internal structure and hydraulic and mechanical properties. It is one of the primary causes of failures of sand-gravel foundations and embankment dams. The criteria establishment is considered the key to solving the erosion problems, so the existing internal stability criteria need a review and classification to study the recent development trends in soil seepage and erosion. Therefore, this paper aims at reviewing the internal stability factors of gap-graded soil with a focus on the internal erosion mechanism and internal stability evaluation based on geometric and hydraulic criteria. Firstly, the paper compared the effect of several commonly used geometric criteria for gap-graded soil evaluation, such as particle size, fine content, void ratio, and fractal dimension. Furthermore, it provided a hydraulic criteria overview and analyzed the effects of the hydraulic gradient, hydraulic shear stress, confining pressure, and pore velocity on internal erosion. The geometric–hydraulic coupling methods were introduced, with a detailed elaboration of the erosion resistance index method based on accumulated dissipated energy. The capabilities and limitations of these criteria were discussed throughout the paper. It was found that combined Kezdi’s criterion and Kenney and Lau’s criterion is more reliable to evaluate internal stability of soil. The gap-graded soil with fine particle content higher than 35% is not necessarily internally stable. Finally, the energy-based method (erosion resistance index method) can effectively reproduce the total amount of erosion mass and the final spatial distribution of fine particles and identifies erosion. The review's outcome can be used as a basis to evaluate the internal erosion risk for gap-graded soils. The evaluation methods discussed here can help identify the zones of relatively high erosion potential.

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Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Abbreviations

d 5 , d 15 , d 20 , d 60 , d 90 :

5%, 15%, 20%, 60%, 90% Mass passing of a soil

d 15c :

Diameter of the 15% mass passing in the coarse part

d 85f :

Diameter of the 85% mass passing in the fine part

F :

Mass fraction of particles finer than d

H :

Mass fraction between grain size d and 4d

C u :

Coefficient of uniformity

d 0 :

The average diameter of the model of the capillary tube

D c35 :

Controlling constriction for coarser fraction from CSD by surface area technique

d 85 , SA :

Representative size for finer fraction from PSD by surface area technique

VRF:

Void filling ratio

D m :

Particle size fractal dimension

CSD:

Cumulative constriction size distribution

G r :

Gap ratio

d f :

Division diameter between finer and coarser particles

d eq :

Equivalent particle diameter

d 1, d 2 :

The representative sizes of the coarse fraction and the fine fraction respectively

\(d_{50}^{c}\) :

Size of particle corresponding to 50% passing of coarse fraction

\(P_{{\text{f}}}\) :

Mass passing at \(d_{{\text{f}}}\)

i cr :

The critical gradient of heave

i ch :

The critical gradient of the initiation of suffusion

G s :

Specific gravity

Φ:

The internal friction angle of soil

A :

A reduction factor for the effective stress

α′ :

The correction factor of the particle shape, taking 1 for spheres and 1.7 for natural soils

β :

A coefficient (= 3.5)

h f :

Depth of soil specimen (mm)

A b :

Base area of soil column (mm2)

q si :

Frictional resistance to a discrete soil layer (kPa)

A si :

The circumferential area

\(P\left( {d_{0} } \right)\) :

Is the cumulative volume content of diameter d0

u cr :

The critical pore velocity of particle incipient motion

\(\rho^{\prime }\) :

The underwater density of the particles

\(\mu\) :

The kinematic viscosity coefficient of water

K :

The hydraulic conductivity

\(\overline{\sigma }_{{{\text{vm}}}}^{\prime }\) :

The normalized average vertical effective stress value

\(\sigma_{t0}^{\prime }\) :

The effective stress at the top of the soil layer

\(\sigma_{b0}^{^{\prime}}\) :

The effective stress at the base of the soil layer

\(\gamma_{{\text{d}}}\) :

The dry unit weight of the soil

\(V_{{{\text{BS}}}}\) :

The blue methylene value

I α :

Erosion resistance index

E flow(t):

The total energy during the total duration t of

P flow(Δt):

The total flow power for the duration Δt

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Funding

The authors are grateful for the support of the National Natural Science Foundation for Excellent Young Scientists of China (51922088) and program 2022TD-01 for Shaanxi Provincial Innovative Research Team.

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Authors and Affiliations

  1. State Key Laboratory of Eco-Hydraulics in Northwest Arid Region, Xi’an University of Technology, Xi’an, 710048, China

    Zengguang Xu & Yan Ye

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  1. Zengguang Xu
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  2. Yan Ye
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Correspondence to Zengguang Xu.

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The authors declare that there is no conflict of interest.

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Informed consent was obtained from all individual participants included in the study. All authors read and approved the final manuscript.

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I certify that this manuscript is original and has not been published and will not be submitted elsewhere for publication while being considered by “Natural Hazards”. And the study is not split up into several parts to increase the quantity of submissions and submitted to various journals or to one journal over time. Results were presented clearly, honestly, and without fabrication, falsification or inappropriate data manipulation. No data, text, or theories by others are presented as if they were our own.

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Cite this article

Xu, Z., Ye, Y. On the evaluation of internal stability of gap-graded soil: a status quo review. Nat Hazards 113, 63–102 (2022). https://doi.org/10.1007/s11069-022-05317-8

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  • DOI: https://doi.org/10.1007/s11069-022-05317-8

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