Journal of Applied Mathematics
Volume 2013 (2013), Article ID 784583, 19 pages
Research Article

Bending Moment Calculations for Piles Based on the Finite Element Method

State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China

Received 17 March 2013; Accepted 1 June 2013

Academic Editor: Fayun Liang

Copyright © 2013 Yu-xin Jie et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Using the finite element analysis program ABAQUS, a series of calculations on a cantilever beam, pile, and sheet pile wall were made to investigate the bending moment computational methods. The analyses demonstrated that the shear locking is not significant for the passive pile embedded in soil. Therefore, higher-order elements are not always necessary in the computation. The number of grids across the pile section is important for bending moment calculated with stress and less significant for that calculated with displacement. Although computing bending moment with displacement requires fewer grid numbers across the pile section, it sometimes results in variation of the results. For displacement calculation, a pile row can be suitably represented by an equivalent sheet pile wall, whereas the resulting bending moments may be different. Calculated results of bending moment may differ greatly with different grid partitions and computational methods. Therefore, a comparison of results is necessary when performing the analysis.