Comparison of Analytical Solutions with Finite Element Solutions for Ultimate Bearing Capacity of Strip Footings

Abstract:

The finite element method is used to compute the ultimate bearing capacity of a fictitious strip footing resting on the surface of c-φ weightless soils and a real strip footing buried in the c-φ soils with weight. In order to compare the numerical solutions with analytical solutions, the mainly existing analytical methods are briefly introduced and analyzed. To ensure the precision, most of analytical solutions are obtained by the corresponding formulas rather than table look-up. The first example shows that for c-φ weightless soil, the ABAQUS finite element solution is almost identical to the Prandtls closed solutions. Up to date, though no closed analytical solution is obtained for strip footings buried in c-φ soils with weight, the numerical approximate solutions obtained by the finite element method should be the closest to the real solutions. Apparently, the slip surface disclosed by the finite element method looks like Meyerhofs slip surface, but there are still some differences between the two. For example, the former having an upwarping curve may be another log spiral line, which begins from the water level of footing base to ground surface rather than a straight line like the latter. And the latter is more contractive than the former. Just because these reasons, Meyerhofs ultimate bearing capacity is lower than that of the numerical solution. Comparison between analytical and numerical solutions indicates that they have relatively large gaps. Therefore, finite element method can be a feasible and reliable method for computations of ultimate bearing capacity of practical strip footings.

• Periodical: Applied Mechanics and Materials (Volumes 353-356)
• Pages: 3294-3303
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.353-356.3294
• Online since: August 2013
• Authors: Zi Hang Dai*, Xiang Xu
• Keywords: C-φ Soils with Weight, C-φ Weightless Soil, Finite Element Method (FEM), Strip Footing, Ultimate Bearing Capacity, Upwarping Curve

References

[1] K. Terzaghi. Theoretical soil mechanics[M]. New York: John Wiley and Sons Inc., (1943).

[2] G.G. Meyerhof. The ultimate bearing capacity of foundations[J]. Geotechnique, 1951, 2 (4): 301–332.

[3] L. Prandtl. Über die härte plastischer körper nachrichten von der geselschaft der wissenschaften zu göttingen[J]. Math Phys Klasse, 1920, 12 (1): 74–85 (in German).

[4] L. Prandtl. Über die eindrigungsfestigkeit (härte) plastischer baustoffe und die festigkeit von Schneiden[J]. Zeitschrift fur Angewandte Mathematik und Mechanik, Berlin, 1921, 1 (1): 15–20 (in German).

DOI: 10.1002/zamm.19210010102

[5] W. F. Chen. Limit analysis and soil plasticity[M]. Amsterdam: Elsevier, (1975).

[6] A.H. Soubra. Upper-bound solutions for bearing capacity of foundations[J]. Journal of Geotechnical and Geoenvironmental Engineering, 1999, 125 (1): 59–68.

DOI: 10.1061/(asce)1090-0241(1999)125:1(59)

[7] V.V. Sokolovskii. Statics of granular media[M]. Oxford: Pergamon Press, (1965).

[8] A.D. Cox. Axially symmetric plastic deformation in soils II-indentations of ponderable soils[J]. International Journal of Mechanic Sciences, 1962, 4 (5): 371–380.

DOI: 10.1016/s0020-7403(62)80024-1

[9] Xueyan ZHANG. Prandtl and Terzaghi bearing capacity formulas of a strip footing solved by slip-line method of plasticity[J]. Journal of Tianjin University, 1987, 20 (2): 22–29 (in Chinese).

[10] M. Hjiaj, A.V. Lyamin, L.S. Sloan. Bearing capacity of a cohesive-frictional soil under non-eccentric inclined loading[J]. Computers and Geotechnics, 2004, 31 (6): 491–516.

DOI: 10.1016/j.compgeo.2004.06.001

[11] S. Frdman, H.J. Burd. Numerical studies of bearing capacity factor Nγ[J]. Journal of Geotechnical and Geoenvironmental Engineering, 1997, 123 (1): 20–29.

[12] Xingchong CHEN, Xi ZHU. 3D elasto-plastic FEM analysis of ultimate bearing capacity for bridge pier foundation[J]. Journal of Lanzhou Railway Institute, 1998, 17 (1): 1–5 (in Chinese).

[13] S.W. Perkins, C.R. Madson. Bearing capacity of shallow foundations on sand: a relative density approach[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2000, 126 (6): 521–530.

DOI: 10.1061/(asce)1090-0241(2000)126:6(521)

[14] Qingguo HU, Keneng ZHANG, Junsheng YANG. Finite element analysis of ultimate bearing capacity of strip footing above Karst cave[J]. Journal of Central South University of Technology, 2005, 36 (4): 694-697 (in Chinese).

[15] D. Loukidis, T. Charkraborty, R. Salgado. Bearing capacity of strip footings on purely frictional soil under eccentric inclined loads[J]. Canadian Geotechnical Journal, 2008, 45 (6): 768–787.

DOI: 10.1139/t08-015

[16] Dunping LIU, Minghua ZHAO, Xinjun ZOU. Analysis of the ultimate bearing capacity of subgrade by element-free Galerkin method[J]. Journal of Hunan University (Natural Sciences), 2008, 35 (1): 26–30 (in Chinese).

[17] Weixue KONG, Yingren ZHENG, Shangyi ZHAO. Finite element analysis for the bearing capacity of foundations and its application in bridge engineering[J]. China Civil Engineering Journal, 2005, 38 (4): 97–102 (in Chinese).

[18] K. Terzaghi, R. B. Peck. Soil mechanics in engineering practice[M]. New York: John Wiley and Sons Inc., (1967).

[19] Zhujiang SHEN. Theoretical soil mechanics[M]. Beijing: China Water Power Press, 2000 (In Chinese).

[20] J.B. Hansen. A general formula for bearing capacity[M]. Taastrup: Danish Geotechnical Institute, (1961).

[21] J.B. Hansen. A revised and extended formula for bearing capacity[M]. Taastrup: Danish Geotechnical Institute, (1970).

[22] A.S. Vesic. Analysis of ultimate loads of shallow foundations[J]. Journal of the Soil Mechanics and Foundations Division, ASCE, 1973, 99 (1): 45–73.

DOI: 10.1061/jsfeaq.0001846

[23] A.S. Vesic. Bearing Capacity of Shallow Foundations[J]. In: Winterkorn H F, Fang H Y ed. Foundation Engineering Handbook. New York: Van Nostrand Reinhold Company, 1975: 121–147.

[24] G.G. Meyerhof. Some recent research on the bearing capacity of foundations[J]. Canadian Geotechnical Journal, 1963, 1 (1): 16–26.

[25] A.M. Hanna, G.G. Meyerhof. Design charts for ultimate bearing capacity of foundations on sand overlying soft clay[J]. Canadian Geotechnical Journal, 1980, 17 (2): 300–303.

DOI: 10.1139/t80-030