ORIGINAL PAPER Reliability Based Earthquake Resistant Design for Internal Stability of Reinforced Soil Structures B. Munwar Basha • G. L. Sivakumar Babu Received: 15 September 2008 / Accepted: 31 May 2011 / Published online: 24 June 2011 Ó Springer Science+Business Media B.V. 2011 Abstract This paper presents a method to evaluate reliability for internal stability of reinforced soil struc- tures 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 condi- tions, reliability indices of all the geosynthetic layers in relation to tension and pullout failure modes are deter- mined 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, sur- charge 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. Keywords Geosynthetics  Reliability  Reinforced soil  Tension failure  Pullout failure List of symbols 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 B. M. Basha Department of Civil Engineering, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110 016, India e-mail: basha@civil.iitd.ac.in; mbasha@gmail.com G. L. S. Babu (&) Department of Civil Engineering, Indian Institute of Science, Bangalore 560 012, India e-mail: gls@civil.iisc.ernet.in 123 Geotech Geol Eng (2011) 29:803–820 DOI 10.1007/s10706-011-9418-9