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Limit Equilibrium Analyses for Internal Design of Geosynthetic Reinforced Slopes: Influence of Potential Failure Surface and Strength Distribution

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Abstract

The paper presents results from a computer code, based on limit equilibrium analyses, able to quantify earth pressure coefficients for the internal design of geosynthetic reinforced soil structures and identify the potential failure surfaces. Failure mechanisms assuming bilinear or logarithmic spiral failure surfaces are considered. The influence of the potential failure surface and geosynthetic strength distribution on the earth pressure coefficient is analysed. Required reinforcement tensile strengths calculated by the developed program are compared with values published in the literature. To further evaluate the capabilities of limit equilibrium analyses, the numerical modelling of a geosynthetic reinforced steep slope, designed at ultimate limit state conditions (FS = 1), is also presented. Good agreement was achieved between the potential failure surfaces predicted by limit equilibrium analyses and those obtained with numerical modelling.

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Abbreviations

FS:

Factor of safety (dimensionless)

H:

Height of structure (m)

H:

Horizontal component of inter-wedge force (Fig. 1 and Eq. (1)) (kN)

Fig. 1
figure 1

Two-Part wedge failure mechanism

Full size image
Kreq :

Equivalent earth pressure coefficient (dimensionless)

\( {\text{K}}_{\rm req}^{\rm uniform} \) :

Equivalent earth pressure coefficient for uniform distribution of reinforcement (dimensionless)

N:

Resultant force of normal stresses over the failure surface (kN)

Pa :

Required force for equilibrium (kPa)

r:

Radius of log spiral surface (m)

S:

Resultant force of shear stresses over the failure surface (kN)

Sv,i :

Contributory height for the ith layer (m)

Ti :

Required strength for reinforcement layer, i (kN/m)

Tmax :

Maximum reinforcement tensile force (kN/m)

V:

Vertical component of inter-wedge force (kN)

W:

Weight of failure mass (kN)

XC :

Horizontal coordinate of the centre of gravity (failure mass) (m)

XP :

Horizontal coordinate of the pole (m)

Ya :

Elevation of Pa application point (above the base) (m)

YC :

Vertical coordinate of the centre of gravity (failure mass) (m)

YP :

Vertical coordinate of the pole (m)

β:

Slope angle (°)

δ:

Friction angle between the soil and the wall facing (º)

εsmax :

Maximum soil shear strain (dimensionless)

ϕ:

Soil internal friction angle (°)

ϕd :

Design value of internal friction angle of backfill (°)

γ:

Backfill unit weight (kN/m3)

λ:

Inter-wedge mobilized shear stress ratio (dimensionless)

θ:

Angle between the radius, r, and a vertical line (Fig. 2 and Eq. (4)) (°)

Fig. 2
figure 2

Log spiral failure mechanism

Full size image
σav :

Available stress (kPa)

σv,i :

Vertical stress at the depth of reinforcement layer, i (kPa)

σreq :

Required stress (kPa)

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Acknowledgments

The authors would like to thank the financial support of Portuguese Science and Technology Foundation (FCT) and FEDER, Research Project FCOMP-01-0124-FEDER-009750 - PTDC/ECM/100975/2008.

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Authors and Affiliations

  1. Faculty of Engineering, University of Porto, R. Dr. Roberto Frias, 4200-465, Porto, Portugal

    Castorina Silva Vieira & Maria de Lurdes Lopes

  2. National Laboratory of Civil Engineering, Av. do Brasil, 1700-066, Lisbon, Portugal

    Laura M. Caldeira

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  1. Castorina Silva Vieira
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  2. Maria de Lurdes Lopes
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  3. Laura M. Caldeira
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Correspondence to Castorina Silva Vieira.

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Vieira, C.S., Lopes, M.L. & Caldeira, L.M. Limit Equilibrium Analyses for Internal Design of Geosynthetic Reinforced Slopes: Influence of Potential Failure Surface and Strength Distribution. Geotech Geol Eng 31, 1123–1135 (2013). https://doi.org/10.1007/s10706-013-9639-1

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