Application of HDMR method to reliability assessment of a single pile subjected to lateral load

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Abstract

The paper presents an application of High Dimensional Model Representation (HDMR) to reliability assessment of a single pile subjected to lateral load. The purpose is to compare HDMR with some classical method based on response surface technique.

First 3D numerical model of the problem for finite elements computations in the ABAQUS STANDARD program has been presented. The soil model is assumed to be linear elastic. However, contacts between the sidewall and the foundation of the pile and the soil are modelled as Coulomb one with friction and cohesion.

Next the Response Surface Method is briefly reviewed in conjunction with reliability approach.

Then the High Dimensional Model Representation approach is presented. In our approach the HDMR algorithm is based on polynomial of the second degree. Finally the numerical studies have been carried out. The first series of computations demonstrate the efficiency of HDMR in comparison to neural network approach. The second series allows comparison of reliability indices resulting from three different approaches, namely neural network response surface, first-order HDMR and second-order HDMR. It has been observed that for increasing values of the length of the pile reliability indices reach similar values regardless of the method response surface applied.

Keywords:
References
  • [1] BAUER J., PUŁA W., Neural network supported response surface method with respect to reliabilitycomputations in geotechnics, Studia Geotechnica et Mechanica, 2000, 22, No. 3-4, 103-115.

  • [2] BOX G.P., DRAPER N.R., Empirical Model-Building and Response Surface, J. Wiley & Sons, New York, 1996.

  • [3] BUCHER C.G., BOURGUND U., A fast and efficient response surface approach for structural reliabilityproblems, Structural Safety, 1990, 7, 57-66.

  • [4] CHAN C.L., LOW B.K., Reliability Analysis of Laterally Loaded Piles Involving Nonlinear Soil andPile Behavior, J. Geotech. and Geoenvir. Engrg., 2009, 135(3), 431-443.

  • [5] CHOWDHURY R., RAO B., Hybrid High Dimensional Model Representation for reliability analysis, Comput. Methods Appl. Mech. Engrg., 2009, 198, 753-765.

  • [6] CHOWDHURY R., RAO B., Probabilistic Stability Assessment of Slopes Using High Dimensional ModelRepresentation, Computers and Geotechnics, 2010.

  • [7] DEMIRALP M., High Dimensional Model Representation and its application varieties, Tools for Mathematical Methods, Mathematical Research, St-Petersburg, 2003, Vol. 9, 146-159.

  • [8] DITLEVSEN O., MADSEN H.O., Structural reliability Methods, John Wiley & Sons, Chichester, 1996.

  • [9] ENGELUND S., RACKWITZ R., Experiences with experimental design schemes for failure surface estimationand reliability, Proc. 6th Speciality Conf. Probabilistic Mechanics and Structural and Geotechnical Reliability, Denver, 1992, 252-255.

  • [10] FAN C.C., LONG J.H., Assessment of existing methods for predicting soil response for laterallyloaded piles in sand, Computers and Geotechnics, 2005, 32, 274-289.

  • [11] FARAVELLI L.A., A response surface approach for reliability analysis, Journal of the Engineering Mechanics Division, ASCE, 1989, 115(12), 2763-2781.

  • [12] FENTON G.A., GRIFFITHS D.V., Bearing capacity prediction of spatially random c-φ soils, Canadian Geotechnical Journal, 2003, 40(1), 545.

  • [13] FENTON GA., GRIFFITHS D.V., Risk Assessment in Geotechnical Engineering, John Wiley & Sons, New York, 2008.

  • [14] HALDAR S., SIVAKUMAR M., BABU G.LS., Effect of soil spatial variability on the response of laterallyloaded pile on undrained clay, Computers and Geotechnics, 2008, 35, 537-547.

  • [15] HECHT-NIELSON R., Neurocomputing, Addison Wesley, Amsterdam, 1991.

  • [16] HIBBITT D., KARLSSON B., SORENSEN P., ABAQUS Keywords Manual Version 6.3 Hibbitt, Karlsson & Sorensen, Inc., USA, 2002.

  • [17] HOHENBICHLER M., GOLLWITZER S., KRUSE W., RACKWITZ R., New light on first and second-orderreliability methods, Structural Safety, 1987, 4, 267-284.

  • [18] ISO 2394:2000. General principles on reliability of structures. International Standard.

  • [19] KAYA H., KAPLANA M., SAYGINA H., A recursive algorithm for finding HDMR terms for sensitivityanalysis, Computer Physics Communications, 2004, 158, 106-112.

  • [20] LI G., WANG S.W., RABITZ H., Global uncertainty assessments by high dimensional model representation(HDMR), Chemical Engineering Science, 2002, Vol. 57, 4445-4460.

  • [21] LI G., RABITZ H., Regularized random-sampling high dimensional model representation (RSHDMR), Journal of Mathematical Chemistry, March 2008, Vol. 43, No. 3.

  • [22] MAGIERA R., Models and methods of mathematical statistics, GiS, Wrocław, 2007.

  • [23] MARQUARDT D.W., An algorithm for least-squares estimation of non-linear parameters, J. Soc. Indust. Appl. Math., June 1963, 11, No. 2.

  • [24] MARQUARDT D.W., Least-squares estimation of non-linear parameters computer code, NLIN2, Distribution No. 309401, IBM Share Library, August 1966.

  • [25] MATLOCK H., Correlations for design of laterally loaded piles in soft clay, Proc., Offshore Technology Conference, Houston, Texas, 1970, 577-594.

  • [26] McCLELLAND B., FOCHT J.A., Soil modulus for laterally loaded piles, Transactions of the ASCE, 1958, 123, 1049-1086.

  • [27] MUKHERJEE D., RAO B., PRASAD A.-M., Global Sensitivity Analysis of Unreinforced MasonryStructure Using High Dimensional Model Representation, Engineering Structures, April 2011, Vol. 33, No. 4, 1316−1325,.

  • [28] MUKHERJEE D., RAO B., PRASAD A., Cut-HDMR Based Fully Equivalent Operational Model forAnalysis of Unreinforced Masonry Structure, Sadhana, 2012.

  • [29] MYERS R.H., MONTGOMERY D.C., Response Surface Methodology Process and Product OptimisationUsing Design Experiments, John Wiley & Sons, New York, 1995.

  • [30] OSADA E., Geodesy, Wroclaw University of Technology, Wrocław, 2002.

  • [31] RABITZ H., OMER F., Alıs General foundations of high-dimensional model representations, Journal of Mathematical Chemistry, 1999, 25, 197-233 197.

  • [32] RACKWITZ R., Response surfaces in structural reliability, Berichte zur Zuverlässigkeitstheorie der Bauwerke, H. 67, LKI, Technische Universität München, 1982.

  • [33] RAO B., CHOWDHURY R., Factorized high dimensional model representation for structural reliabilityanalysis, Engineering Computations International Journal for Computer-Aided Engineering and Software, 2008, Vol. 25, No. 8, 708-738.

  • [34] RAO B., CHOWDHURY R., Probabilistic Analysis Using High Dimensional Model Representation andFast Fourier Transform, International Journal for Computational Methods in Engineering Science and Mechanics, 2008, 9, 342-357.

  • [35] REESE LC., Van IMPE W.F., Single Piles and Pile Groups Under Lateral Loading, Balkema, Rotterdam, 2001.

  • [36] SHORTER J.A., IP P.C., RABITZ H., An Efficient Chemical Kinetics Solver Using High DimensionalModel Representation, J. Phys. Chem. A, 1999, Vol. 103, 7192-7198.

  • [37] SIVAKUMAR M., RAO B., SATISHKUMAR S.R., The Effect of Pressure induced Hoop Stress on BiaxiallyLoaded Through wall Cracked Cylindrical Structures - A Strain Based Method, Applied Mechanics and Materials, 2012, Vol. 110-116, No. 4, 1525-1530.

  • [38] SOBOL I., Theorems and examples on high dimensional model representation, Reliability Engineering and System Safety, 2003, 79, 187-193.

  • [39] STRUREL, A Structural Reliability Analysis Program System, COMREL & SYSREL, Users Manual, RCP Consultant, Munich, 1995.

  • [40] TANDJIRIA V., TEH C.I., LOW B.K., Reliability analysis of laterally loaded piles using responsesurface methods, Structural Safety, 2000, 22(4), 335-355.

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