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Reliability Based Earthquake Resistant Design for Internal Stability of Reinforced Soil Structures

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Abstract

This paper presents a method to evaluate reliability for internal stability of reinforced soil structures using reliability based design optimization. Using limit equilibrium method and assuming the failure surface to be logarithmic spiral, analysis is conducted to maintain internal stability against both tensile and pullout failure of the reinforcements. Properties of backfill soil and strength of the geosynthetic reinforcement are considered as random variables. For the seismic conditions, reliability indices of all the geosynthetic layers in relation to tension and pullout failure modes are determined for different magnitudes of seismic accelerations both in the horizontal and vertical directions, surcharge load and design strength of the reinforcement. The efforts have been made to obtain the number of layers, pullout length and total length of the reinforcement at each level for the desired target reliability index values against tension and pullout modes of failure. The influence of horizontal and vertical earthquake acceleration, surcharge load, design strength of the reinforcement, coefficient of variation of soil friction angle and design strength of the reinforcement on number of layers, pullout length and total length of the reinforcement needed for the stability at each level is discussed.

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Abbreviations

F :

resultant force acting along the radial line of the logarithmic spiral

FS it :

factor of safety with respect to tension failure at each level

FS ipo :

factor of safety with respect to pullout failure at each level

f X (x):

is a joint probability density function of X

g :

acceleration due to gravity

g(.):

limit state function

H :

height of reinforced soil structure (=ar 0)

k h , k v :

horizontal and vertical seismic acceleration coefficients

K :

reinforcement force coefficient needed to maintain the stability

L g :

length of the failure zone of reinforced soil at the top of wall

L a :

active reinforcement length

L ei :

pullout length of reinforcement

L t :

total length of the reinforcement required to stabilize the wall

P ri :

pullout force on the embedded reinforcement length of each layer

q :

surcharge intensity

Q :

surcharge coefficient (=2q/γH)

\( Q_{{h\_SH_{1} G}} \) :

horizontal inertial force acting on the wedge SH 1 G

Q h_q :

horizontal inertial force due to surcharge load (q)

\( Q_{{v\_SH_{1} G}} \) :

vertical inertial force acting on the wedge SH 1 G

Q v_q :

vertical inertial force due to surcharge load (q)

r 0, r 1 :

initial and final radius of the log-spiral wedge (AH 1 G)

r :

average radius of the elemental strip in the log-spiral wedge (H 1 JG)

T r :

reinforcement force needed to maintain the stability

T max :

tensile strength required at each level of reinforcement

T imax :

tensile strength required at each level of reinforcement

T u :

design strength of the reinforcement

u i :

variables in standard normal space

\( W_{{AH_{1} EK}} \) :

weight of triangular wedge AH 1 EK

W ESG :

weight of triangular wedge ESG

W KEGC :

weight of triangular wedge KEGC

W AGC :

weight of triangular wedge AGC

\( W_{{AH_{1} EK}} \) :

weight of triangular wedge AH 1 EK

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

vector of random variables representing uncertain quantities

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

vector of standard random variables representing uncertain quantities

\( \beta_{t} \,{\text{and}}\,\beta_{ipo} \) :

reliability indices against tension, pullout mode at each level of reinforcement

z :

depth of reinforcement layer under consideration

σ vi :

effective vertical stress acting on the embedded reinforcement length

γ :

unit weight of the backfill

ϕ :

friction angle of the backfill

θ 1 :

subtended angle of log-spiral wedge (AH 1 G)

θ 2 :

angle of the initial radius of the log-spiral wedge (AH 1) with horizontal

θ :

angle of the radial line of elemental strip with initial radius of the log-spiral wedge

δ :

soil-reinforcement interface friction angle

b :

\( \cos \theta_{2} - e^{{\theta_{1} \tan \phi }} \cos \left( {\theta_{1} + \theta_{2} } \right) \)

a :

\( \left[ {e^{{\theta_{1} \tan \phi }} \sin \left( {\theta_{1} + \theta_{2} } \right) - \sin \theta_{2} } \right] \)

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Authors and Affiliations

  1. Department of Civil Engineering, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, 110 016, India

    B. Munwar Basha

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

    G. L. Sivakumar Babu

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

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Basha, B.M., Babu, G.L.S. Reliability Based Earthquake Resistant Design for Internal Stability of Reinforced Soil Structures. Geotech Geol Eng 29, 803–820 (2011). https://doi.org/10.1007/s10706-011-9418-9

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  • DOI: https://doi.org/10.1007/s10706-011-9418-9

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