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Reliability Based LRFD Approach for External Stability of Reinforced Soil Walls

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Abstract

The main objective of reinforced soil wall design is to ensure safety and performance requirements of a wall for target reliability levels. Analysis is conducted to evaluate the external stability of reinforced soil walls. As this must be accomplished under conditions of uncertainties associated with reinforced backfill, retained backfill, foundation soil and surcharge load acting on the wall, probabilistic analyses are necessary in the development of such reliability based design for external stability of reinforced soil wall. A methodology for developing load and resistance factor design guidelines for reinforced soil walls is outlined in this paper. The potential failure mechanisms considered in the analysis are sliding failure, eccentricity failure of resultant force (or overturning failure) and bearing capacity failure. A first order reliability method is used to determine appropriate ranges for the values of the load and resistance factors. Load and resistance factors needed to maintain the stability against three modes of failure by targeting component reliability indices of 2, 2.5, 3, 3.5 and 4 are obtained for various values of coefficients of variation of friction angle of backfill and foundation soil, distributed dead load surcharge, live load surcharge and cohesion of the foundation soil.

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Abbreviations

c :

= cohesion of the foundation soil

e :

= eccentricity of the resultant force

f X (x) :

= is a joint probability density function of X

FS sli , FS b :

= factor of safety against sliding and bearing failure modes

FS e :

= factor of safety against eccentricity failure mode

DL :

= distributed dead load surcharge

g :

= acceleration due to gravity

g(.):

= limit state function

H :

= height of geosynthetic reinforced soil wall

L :

= length of the geosynthetic reinforcement

LL :

= live load surcharge

N c , N q , N γ :

= bearing capacity factors

P a :

= active earth pressure due to backfill soil

P q :

= active earth pressure due to surcharge load

K a :

= active earth pressure coefficient

q :

= surcharge load acting on the backfill soil

q u :

= ultimate bearing capacity of a shallow foundation

Q :

= surcharge coefficient

u i :

= variables in standard normal space

\( X = \{ x_{i} \}_{i = 1}^{n} \) :

= vector of random variables representing uncertain quantities

\( U = \{ u_{k} \}_{k = 1}^{n} \) :

= vector of standard random variables representing uncertain quantities

u*:

= most probable point of failure (MPP)

\( x_{i}^{*} \) :

= design variable corresponding to target reliability index

W ABFE :

= weight of the reinforced soil block ‘ABFE’

\( \sum {{\text{F}}_{\text{r}} } \) :

= sum of the horizontal resisting forces

\( \sum {{\text{F}}_{\text{d}} } \) :

= sum of the horizontal driving forces

Φ(.):

= the standard normal cumulative distribution

β t :

= target reliability index

β sli , β b :

= reliability indices against sliding and bearing failure modes

β e :

= reliability indices against overturning and eccentricity failure modes

COV :

= coefficient of variation

γ :

= unit weight of the reinforced backfill soil

γ b :

= unit weight of the foundation soil

μ i :

= mean of random variable

\( \mu_{i}^{N} \) :

= equivalent mean of non normal random variable

σ i :

= standard deviation of random variable

\( \sigma_{i}^{N} \) :

= equivalent standard deviation of non normal random variable

η i :

= load factor

Ψ i :

= resistance factor

ϕ :

= friction angle of the reinforced backfill soil

ϕ b :

= friction angle of the soil below the base slab of the retaining wall

δ :

= interface wedge friction angle between reinforced and retained backfill

δ b :

= interface friction angle between wall base and foundation soil

σ v :

= vertical stress at the base and

θ w :

= angle of slope with vertical

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Authors and Affiliations

  1. Department of Civil Engineering, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, 110016, India

    B. Munwar Basha

  2. Department of Civil Engineering, Indian Institute of Science, Bangalore, 560 012, India

    G. L. Sivakumar Babu

Authors
  1. B. Munwar Basha
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  2. G. L. Sivakumar Babu
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Correspondence to B. Munwar Basha.

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Basha, B.M., Babu, G.L.S. Reliability Based LRFD Approach for External Stability of Reinforced Soil Walls. Indian Geotech J 43, 292–302 (2013). https://doi.org/10.1007/s40098-013-0062-6

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  • DOI: https://doi.org/10.1007/s40098-013-0062-6

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