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Quantification of variability of shear and interface shear parameters of soils and its application to stability of veneer cover slopes

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Abstract

The stability of soil slopes is governed by the shear strength parameters including cohesion (c) and angle of internal friction (\(\phi\)). Stability also depends on the interface shear strength parameters including interface cohesion (\(c_{0}\)) and interface friction angle (\(\delta\)) between soil and non-woven geotextile. The suitability of using normal and lognormal distributions for the reliability analysis accounting for the variability of these parameters is verified. A novel framework is developed in the present study to provide the most suitable probability density functions for c, \(\phi\), \(c_{0}\), and \(\delta\). A database of 16, 55, 60, 40, and 48 sample points is compiled from the experimental studies reported on ϕ for sands, and c and \(\phi\) for clays, silty clays, clayey sands, and silty sands, respectively. Considering non-woven geotextile (NWGT) as interface material, experimental data points of 37, 47, and 26 for \(c_{0}\) and \(\delta\) are collected, respectively, for sands, clays, and silty clays. This study optimizes the mean and standard deviation such that the errors related to the percentile, quantile, and cumulative distribution function (CDF) are minimum and thereby provide the optimum probability density functions (PDF). The best PDFs obtained from this study to represent c, \(\phi\), \(c_{0}\), and \(\delta\) for silty clays are inverse Gaussian, Gumbel minimum, normal, and Gumbel minimum distributions, respectively. The reliability index of the veneer cover system, considering the sliding and uplifted floating failures resulting from a clogged drainage layer (i.e., silty clay) is evaluated considering these optimized PDFs. This study depicts that choosing inappropriate PDFs significantly overestimates or underestimates the probability of failure when there is a high degree of variability.

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Data availability

All data generated or analyzed during this study are included in this published article [and its supplementary information files]

Code availability

All steps for the implementation of code are provided in this published article.

Abbreviations

c :

Cohesion (kPa)

c 0 :

Interface cohesion (kPa)

COV :

Coefficient of variation

FS ds :

Factor of safety against direct sliding failure

FS uf :

Factor of safety against uplifted floating failure

\(F\left( x \right)\) :

CDF of generated random variables

\(F\left( {x^{*} } \right)\) :

CDF of experimental data

\(g_{ds} \left( x \right)\) :

Performance function for direct sliding failure

\(g_{uf} \left( x \right)\) :

Performance function for uplifted floating failure

h :

Thickness of cover soil layer (m)

h w :

Vertical height of seepage in the drainage layer of veneer cover system (m)

H :

Height of MSW landfill (m)

L :

Slope length of cover soil (m)

\(n_{b}\) :

Number of bins

N :

Number of data points

\(P_{f}\) :

Percentile function

\(P_{f\_ds}\) :

Probability of failure by direct sliding

\(P_{f\_uf}\) :

Probability of failure by uplifted floating

\(Q_{f}\) :

Quantile function

\(r_{c\phi }\) :

Correlation coefficient between cohesion (c) and internal friction angle (\(\phi\)) of soils

\(X^{*}\) :

Experimental data

\(X_{pf}\) :

Polynomial fit of experimental data

\(\beta_{ds}\) :

Reliability index against direct sliding

\(\beta_{uf}\) :

Reliability index against uplifted floating

\(\gamma_{sat}\) :

Saturated unit weight of cover soil (kN/m3)

δ :

Interface friction angle (o)

\(\varepsilon_{CDF}\) :

CDF error

\(\varepsilon_{P - P}\) :

Percentile-percentile error

\(\varepsilon_{Q - Q}\) :

Quantile–quantile error

\(\mu\) :

Mean of a random variable

\(\sigma\) :

Standard deviation

\(\phi\) :

Angle of internal friction (o)

\(\theta\) :

Slope angle of veneer cover soil (o)

\(\Phi\) :

Standard normal distribution function

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Funding

The study gratefully acknowledges the financial support received from the Ministry of Education, Government of India.

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  1. Department of Civil Engineering, Indian Institute of Technology Hyderabad, Kandi, 502285, India

    Dabbiru Soujanya & B. Munwar Basha

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  1. Dabbiru Soujanya
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Contributions

All authors contributed to the study’s conception and design. Material preparation, data collection, and analysis were performed by DS and BMB. The first draft of the manuscript was written by DS and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to B. Munwar Basha.

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Soujanya, D., Basha, B.M. Quantification of variability of shear and interface shear parameters of soils and its application to stability of veneer cover slopes. Environ Earth Sci 82, 453 (2023). https://doi.org/10.1007/s12665-023-11143-3

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