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Development of empirical correlations for limit equilibrium methods of slope stability analysis

Abstract

Determining the safety factor by limit equilibrium methods is based on different assumed slip surfaces and equilibrium equations for forces and moments to be satisfied. The safety factor can be predicted using empirical correlations instead of going through lengthy calculations. In this paper, empirical equations between the factor of safety (FS), unit weight (γ), cohesion (c), internal friction angle (φ), slope angle (α), and height of the slope (H) have been proposed for Spencer’s, Morgenstern-Price, Janbu’s simplified, Bishop’s simplified, and Lowe-Karafiath methods. Data of 50 slopes having homogeneous soil strata with non-identical shearing strength parameters, containing different geometries and the water table below the base of the slope, have been selected to determine FS using Slope-W and for the development of correlations using SPSS software. Unit weight, cohesion, friction angle, slope angle, and height of the slope vary from 11.5 to 21 (kN/m3), 0 to 137 (kPa), 0 to 39 (°), 11 to 78 (°), and 3.5 to 22 (m), respectively. Multiple regression analyses were performed on Slope-W outcomes, and equations for the prediction of FS were formulated. Validation of the proposed FS equations was done both internally and externally as well. The validation graphs are drawn between Slope-W FS versus developed equations for FS of each method. The correlations are helpful for the calculation of FS to have a quick prediction of failure of a slope, and ultimately preventive measures can be taken. The regression constant (R2) values for Spencer’s, Morgenstern-Price, Janbu’s simplified, Bishop’s simplified, and Lowe-Karafiath methods are 0.940, 0.940, 0.922, 0.932, and 0.935, respectively.

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Data availability

Data used to support this study’s findings is accessible from the author upon request.

Abbreviations

FS:

Factor of safety

LEMs:

Limit equilibrium methods

SM:

Spencer’s method

MP:

Morgenstern-Price method

JS:

Janbu’s simplified method

BS:

Bishop’s simplified method

LK:

Lowe and Karafiath method

FSSW :

Factor of safety using Slope-W

FSSM SW :

Factor of safety for Spencer’s method using Slope-W

FSMP SW :

Factor of safety for Morgenstern-Price method using Slope-W

FSJS SW :

Factor of safety for Janbu’s simplified method using Slope-W

FSBS SW :

Factor of safety for Bishop’s simplified method using Slope-W

FSLK SW :

Factor of safety for Lowe and Karafiath method using Slope-W

FSSM P :

Predicted factor of safety for Spencer’s method

FSMP P :

Predicted factor of safety for Morgenstern-Price method

FSJS P :

Predicted factor of safety for Janbu’s simplified method

FSBS P :

Predicted factor of safety for Bishop’s simplified method

FSLK P :

Predicted factor of safety for Lowe and Karafiath method

SPSS:

Statistical product and service solution

R2 :

Regression constant

R:

Correlation coefficient

SEE:

Standard error of estimate

ANOVA:

Analysis of variance

N:

Normal force component

W:

Weight of a slice

τa :

Available shear strength

τr :

Required shear strength

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Funding

The research discussed in this paper was financially supported by China's National Natural Science Foundation (Project no. 51909139) and the Taishan Scholar Foundation of Shandong Province, China (Award no. tsqn201812009).

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Correspondence to Ji-Peng Wang.

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The authors declare that they have no competing interests.

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Responsible editor: Zeynal Abiddin Erguler

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Moawwez, M.A., Wang, JP. & Hussain, M.A. Development of empirical correlations for limit equilibrium methods of slope stability analysis. Arab J Geosci 14, 2020 (2021). https://doi.org/10.1007/s12517-021-08375-7

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Keywords

  • Factor of safety
  • Unit weight
  • Cohesion
  • Internal friction angle
  • Regression analysis
  • Slope-W