Pseudo-static internal stability analysis of geosynthetic-reinforced earth slopes using horizontal slices method

ABSTRACT

In this study, the well-established pseudo-static approach along with the horizontal slices method (HSM) is employed to investigate the seismic internal stability of geosynthetic-reinforced earth slopes. Previous simple HSM analyses were based on a primary assumption stating that the normal inter-slice forces are exerted on the mid-length of horizontal sections. However, this simplifying assumption could give rise to substantial errors in the calculation of design parameters, specifically in the case of high seismic excitations or low soil strength parameters. To address this deficiency, a balancing moment is considered as a new variable to account for the corresponding eccentricity. In the current HSM, two sets of unknown variables, including horizontal inter-slice forces and shear forces along failure surface, are determined using the well-known λ coefficient and the Mohr-Coulomb failure criterion. In this new technique, the traditional ‘5N-1ʹ type of HSM analysis is reduced to a robust and rigorous ‘3N’ one with the same predictive capability. The influence of various parameters, including soil characteristics, slope geometry and different earthquake coefficients are rigorously examined. Moreover, a number of useful graphs is provided to help engineers in the preliminary seismic design of geosynthetic-reinforced earth slopes.

KEYWORDS:

• Seismic internal stability
• geosynthetic-reinforced slopes
• horizontal slices method (HSM)
• slip surface
• pseudo-static approach

Nomenclature

$a_h,a_v$ Horizontal and vertical seismic acceleration, respectively

c Cohesion of backfill soil

$c_{eq}$ Equivalent cohesion of backfill soil for the constant parameter of $c/\gamma H$

$c_f$ Mobilized cohesion of backfill soil

$d_i$ Thickness of all slices (equally spaced reinforcement layers)

$D_i$ Tributary distance of layer i (distance between layers i and i+1)

$E$ Young’s modulus

FS Factor of safety

g Gravity acceleration

H Height of slope

${\mathrm{H}}_i,{\mathrm{H}}_{i+1}$ Horizontal inter-slice forces at top and bottom of the ith slice, respectively

i Number index of the slices

$k_h,k_v$ Horizontal and vertical seismic coefficient, respectively

K Normalized total tension force in geosynthetic layers

$l_i$ Length of slip surface in the ith slice

$L_c$ Length of top chord of an arbitrary slip wedge

$L_C$ Critical length of reinforcement

${\mathrm{M}}_i,{\mathrm{M}}_{i+1}$ Balancing inter-slice moment at top and bottom of the ith slice, respectively

N Number of slices

$N_i$ Normal force on the ith slice

$S_i$ Shear force on the ith slice

T Total tension force in reinforcement layers per unit length of slope

$T_i$ Tension force of the ith slice’s reinforcement

${\mathrm{V}}_i,{\mathrm{V}}_{i+1}$ Vertical inter-slice force at the top and bottom of the ith slice, respectively

$W_i$ Weight of the ith slice

$X_{Gi}$ X coordinate of the gravity center of the ith slice

$X_i$ X coordinate of the lower corner of the ith slice on the slip surface

${\mathrm{X}}_{v}i,{\mathrm{X}}_{vi+1}$ X coordinate of exertion point of ${\mathrm{V}}_{i}and{\mathrm{V}}_{i+1}$, relative to midpoint of ith slice edge

$Y_{Gi}$ Y coordinate of the gravity center of the ith slice

$Y_i$ Y coordinate of the lower corner of the ith slice on the slip surface

$Z_i$ Vertical distance of the ith slice reinforcement from the top of slope

${\alpha }_i,{\theta }_i$ Horizontal and vertical angle of the ith slice edge, respectively

${\alpha }_{Lc}$ Angle of linear slip surface with horizontal line

${\alpha }_S$ An arbitrary slip surface angle between ${\alpha }_{Lc}$ and $90°$

β Slope angle

γ Unit weight of backfill soil

ε Value of Σ$F_X$ of the last slice, as the verification equation

λ Unknown coefficient in Morgenstern and Price method; constant for all slices

υ Poisson’s ratio

φ Friction angle of backfill soil

${\phi }_f$ Mobilized friction angle of backfill soil

Abbreviation

HSM Horizontal slices method

LA Limit analysis

LEM Limit equilibrium method

RSS Reinforced soil slopes

Supplementary material

Supplemental data for this article can be accessed here.

Disclosure Statement

No potential conflict of interest was reported by the author(s).