journal homepage: www.elsevier.com/locate/acme Available online at www.sciencedirect.com Reliability of rigid piles subjected to lateral loads W. Pula n , A. Ro ´z ˙an ´ ski Wroclaw University of Technology, Faculty of Civil Engineering, Institute of Geotechnics and Hydrotechnics, Wybrzez ˙e Stanislawa Wyspian ´skiego 27, 50-370 Wroclaw, Poland article info Article history: Received 23 April 2012 Accepted 26 April 2012 Available online 4 May 2012 Keywords: Reliability index Response surface Soil strength parameters abstract In this paper the complete solution to the problem of random lateral bearing capacity of rigid piles has been presented. The suggested solution is based on the limit states theory approach proposed by Brinch Hansen [2]. A revised approach utilising the response surface method is proposed and compared with the solution presented in earlier papers. Both cases of non- cohesive and cohesive soils are studied. In addition, the influence of spatial averaging is also analysed. Numerical algorithms, for both cases of cohesive and cohesionless soils, have been developed in order to evaluate probability of lateral bearing capacity exceeding. As it has been demonstrated random fluctuations of soil properties can cause significant changes in the value of ultimate lateral loading determined according to the Brinch Hansen method. Series of numerical examples under consideration give some important conclusions concerning an influence of soil properties randomness on safety evaluations. & 2012 Politechnika Wroclawska. Published by Elsevier Urban & Partner Sp. z.o.o. All rights reserved. 1. Introduction Methods elaborated in this paper have been inspired by many computations carried out when the modernisation of main railway tracks in Poland has been started. In almost all cases there was a need to replace existing foundations – of over- head electrical transmission lines supports – by new founda- tions. One of possible solutions was to apply single pre-cast concrete piles as a foundations of electrical line supports (as demonstrated in Fig. 1). In many cases, due to lengths of piles and soil conditions, piles had to be considered as rigid ones. Therefore the lateral ultimate soil resistance has been con- sidered. The ultimate lateral resistance of the soil in the vicinity of a pile is not very often treated in the engineering practice. This is due to fact that majority of piles used in foundation engineering are not rigid [1]. Therefore the prob- abilistic approach, in this area, is almost forgotten in the literature. Among deterministic methods the solution pro- posed by Brinch Hansen [2] is considered as a one of the most precise, however simplified approaches elaborated by Broms [3,4] are more commonly used. The vital point in the Brinch Hansesn method is the position of the rotation centre z r of the pile under consideration (see Fig. 2). It is possible to prove that the ultimate horizontal loading H u is highly sensitive to the location of the centre of rotation z r . The rotation centre itself is subjected to random fluctuations due to inherent uncertainty of soil properties (mostly the strength para- meters) as well as uncertainty in geotechnical recognition. Therefore a probabilistic approach to this problem seems to be quite adequate. On the other hand solutions of determi- nistic problem could not be written in a closed mathematical form. Due to this difficulty standard probabilistic approaches could not be applied straightforward. A solution of the reliability problem associated with laterally loaded piles is the objective of this paper. The problem of the reliability of rigid piles subjected to lateral loads in the context of piles capacity has been discussed in earlier works [5,6]. In the papers an algorithm for evaluating reliability indices (and corresponding failure probabilities), based on the SORM method [7], was introduced. The algorithm 1644-9665/$ - see front matter & 2012 Politechnika Wroclawska. Published by Elsevier Urban & Partner Sp. z.o.o. All rights reserved. http://dx.doi.org/10.1016/j.acme.2012.04.007 n Corresponding author. Tel.: þ48 502209006; fax: þ48 713284814. E-mail address: Wojciech.Pula@pwr.wroc.pl (W. Pula). archives of civil and mechanical engineering12 (2012) 205–218