New Instability Criterion for Stability Analysis of Homogeneous Slopes with Double Strength Reduction
Publication: International Journal of Geomechanics
Volume 20, Issue 9
Abstract
A new instability criterion based on the critical slope concept and the double strength reduction is proposed to evaluate the stability of slopes. In this method, the critical slope contour is determined by the slip-line field theory with the reduced cohesion and the internal friction angle, and the slope reaches the limit equilibrium state when it intersects with the critical slope contour at the toe of the slope. The proposed method is validated against a published case and compared with the traditional instability criterion. In addition, the calculation results regarding four slope cases revealed that the reduction ratio of soil strength derived from the proposed method is more reasonable, and the comprehensive safety factor is equal to the polar diameter method. Thus, the proposed method can be adopted to quantify the instability criterion.
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Acknowledgments
The authors are grateful to the 13th Five-Year Science and Technology Research Project of Jilin Province Education Department (No. JJKH20180450KJ).
Notation
The following symbols are used in this paper:
- c
- initial cohesion;
- c1
- reduced cohesion;
- c1*
- critical cohesion;
- E
- elastic modulus;
- F1
- reduction factor for the internal friction angle;
- F2
- reduction factor for cohesion;
- F1crit
- critical reduction factor for the internal friction angle;
- F2crit
- critical reduction factor for cohesion;
- F1crit*
- minimum critical reduction factor for the internal friction angle;
- F2crit*
- minimum critical reduction factor for cohesion;
- FS
- factor of safety;
- FS1
- factor of safety by the proposed method;
- FS2
- factor of safety by the polar diameter method;
- H
- slope height;
- i, j, l
- nature number;
- K
- reduction ratio factor;
- k*
- minimum reduction ratio factor;
- ko
- initial reduction ratio;
- Δk
- increment of ratio;
- Lmin, Lk
- trajectory of the strength reduction;
- M, Mα, Mβ,
- points on a slip line;
- Mb, Mij
- points on the critical slope contour;
- Mo
- point of initial condition;
- Mmin, Mk
- points on the marginal state line;
- N
- total number of nodes;
- N1
- number of calculation steps;
- P
- surcharge load at the top of the slope;
- Pmin
- minimum load at the top of the slope;
- x, x1, xb, xij, xα, xβ,
- abscissa values;
- Δx
- calculation step on the active zone boundary;
- y, yb, yij, yα, yβ,
- ordinate values;
- ymin
- minimum ordinate values;
- α
- alpha family slip line;
- α0
- slope angle;
- β
- beta family slip line;
- γ
- unit weight;
- θ, θb, θij, θα, θβ, , θI
- intersection angles between the maximum principal stress and the x-axis;
- μ
- mean angle between two family slip lines;
- ν
- Poisson’s ratio;
- σ, σb, σij, σα, σβ, , σI
- characteristic stresses;
- σ1
- maximum principal stress;
- φ
- initial internal friction angle;
- φ1
- reduced internal friction angle; and
- φ1*
- critical internal friction angle.
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© 2020 American Society of Civil Engineers.
History
Received: Jul 30, 2019
Accepted: Apr 28, 2020
Published online: Jul 13, 2020
Published in print: Sep 1, 2020
Discussion open until: Dec 13, 2020
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