Literature Review of Estimating the Bearing Capacity of Rough Footings by the Stress Characteristic Lines Method

Document Type : Propagative Article

Authors

1 Department of Civil Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran

2 Geotechnical Engineering Research Center, International Institute of Earthquake Engineering and Seismology (IIEES), Tehran, Iran

Abstract

The footing of all buildings will be located on the ground. Thus, civil engineers are always faced with the problem of estimating the bearing capacity of shallow foundations. So far, various analytical and numerical methods such as stress characteristic lines method, limit equilibrium method, lower and upper boundary limit analysis methods, as well as finite difference and finite element methods, have been utilized to evaluate the bearing capacity of shallow foundations.
In the meantime, the stress characteristic method, also known as the “slip-line method”, has been shown to be an efficient and useful technique for solving the bearing capacity problem due to its simplicity, high speed in calculations, and no need for neither meshing nor complex soil behavior models. These advantages attracted the attention of many researchers over the past three decades to the stress characteristic lines method.
Obviously, the bearing capacity of footings would be reduced, if they are subjected to seismic loadings or if they are located on slopes or adjacent to them. On the other hand, experimental as well as numerical studies reported in the literature revealed that the roughness of the footing would have an important effect on its bearing capacity. Hence, estimating the bearing capacity of a footing taking into consideration the roughness of its contact surface constitutes one of the important issues in foundation engineering, which of course has been studied only by a small number of researchers.
This paper intends to review the most important works reported in the literature concentrated on the estimation of the bearing capacity of rough shallow foundations by the stress characteristic lines method. We wanted to find the answer to the question that how different researchers considered the roughness factor in evaluating the bearing capacity of footings by the stress characteristic lines method? For this purpose, firstly the mathematical formulation of the stress characteristics method was briefly reviewed. After that, the numerical algorithm of implementing this method to estimate the bearing capacity of smooth as well as rough footings, the corresponding boundary conditions, and calculation procedure for determining the bearing capacity coefficients ๐‘๐‘, ๐‘๐‘ž, and ๐‘๐›พ were discussed. Various techniques for taking into consideration the roughness factor, especially their assumptions, were investigated and compared with the smooth footing case.
An important point to keep in mind when calculating the bearing capacity of rough footing is the non-uniformity of the contact pressure inclination. Various researchers employed different assumptions and obtained quite different results. Some researchers considered uniform roughness by regarding different inclination for the contact pressure along the soil-footing interface or by placing a non-plastic curved wedge immediately beneath the footing. Some other researchers adopted the non-uniform roughness and solved the roughness problem by assigning a non-plastic curved wedge under the footing, or by considering it as a line and two types of parabolic equations, or even without regarding any pre-assumption failure pattern. The influences of these assumptions and methods on estimating the bearing capacity of rough footings were investigated in detail and discussed. Finally, the most important challenges ahead in evaluating the bearing capacity coefficients of rough footing by the stress characteristic lines method were summarized and explained.

Keywords

References

1.    Terzaghi, K. (1943) Theoretical Soil Mechanics. Wiley, New York.
2.    Taylor, D. (1948) Fundamentals of Soil Mechanics. Chapman and Hall, Limited, New York.
3.    Meyerhof, G.G. (1951) The ultimate bearing capacity of foudations. Geotechnique, 2(4), 301-332.
4.    Richards Jr, R., Elms, D.G., and Budhu, M. (1993) Seismic bearing capacity and settlements of foundations. Journal of Geotechnical Engineering, 119(4), 662-674.
5.    Farzaneh, O., Askari, F., and Ganjian, N. (2008) Three-dimensional stability analysis of convex slopes in plan view. Journal of Geotechnical and Geoenvironmental Engineering, 134(8), 1192-1200.
6.    Farzaneh, O., Askari, F. and Yeganeh Khaksar, R. (2010) Bearing Capacity of Foundations Located on Concave Slopes in Plan View Using Upper Bound Theorem. Journal of Civil and Surveying Engineering, 44(2), 215-224 (in Persian).
7.    Hjiaj, M., Lyamin, A.V., and Sloan, S.W. (2005) Numerical Limit Analysis Solutions for the Bearing Capacity Factor Nγ. International Journal of Solids and Structures, 42(5-6), 1681-1704.
8.    Lyamin, A.V. and Sloan, S.W. (2002) lower bound limit analysis using nonโ€linear programming. International Journal for Numerical Methods in Engineering, 55(5), 573-611.
9.    Lyamin, A.V. and Sloan, S.W. (2002) Upper bound limit analysis using linear finite elements and nonโ€linear programming. International Journal for Numerical and Analytical Methods in Geomecha-nics, 26(2), 181-216.
10.    Askari, F. and Farzaneh, O. (2003) Upper-bound solution for seismic bearing capacity of shallow foundations near slopes. Geotechnique, 53(8), 697-702.
11.    Kumar, J. and Khatri, V.N. (2008) Effect of footing roughness on lower bound Nγ values. International Journal of Geomechanics, 8(3), 176-187.
12.    Kumar, J. and Khatri, V.N. (2011) Bearing capacity factors of circular foundations for a general c–φ soil using lower bound finite elements limit Analysis. International Journal for Numerical and Analytical Methods in Geomechanics, 35(3), 393-405.
13.    Kumar, J. and Kouzer, K.M. (2007) Effect of footing roughness on bearing capacity factor N๏ง.  Journal of Geotechnical and Geoenvironmental Engineering, 133(5), 502-511.
14.    Lyamin, A.V., Salgado, R., Sloan, S.W., and Prezzi, M. (2007) Two-and three-dimensional bearing capacity of footings in sand. Géotechnique, 57(8), 647-662.
15.    Griffiths, D.V. (1982) Computation of bearing capacity factors using finite elements.  Geotechnique, 32(3), 195-202.
16.    Frydman, S. and Burd, H.J. (1997) Numerical studies of bearing-capacity factor Nγ. Journal of Geotechnical and Geoenvironmental Engineering, 123(1), 20-29.
17.    Loukidis, D. and Salgado, R. (2009) Bearing capacity of strip and circular footings in sand using finite elements. Computers and Geotechnics, 36(5), 871-879.
18.    Manoharan, N. and Dasgupta, S.P. (1995) Bearing capacity of surface footings by finite elements. Computers and Structures, 54(4), 563-586.
19.    Erickson, H.L. and Drescher, A. (2002) Bearing capacity of circular footings. Journal of Geotechnical and Geoenvironmental Engineering, 128(1), 38-43.
20.    Sokolovski, V.V. (1960) Statics of soil media (translated from Russian by DH Jones and AN schofield). Butterworth, London, England, 21, 369-395.
21.    Martin, C.M. (2005) Exact Bearing Capacity Calculations Using the Method of Characteristics. In: Proceedings of the IACMAG, Turin, 441-450.
22.    Kumar, J. and Mohan Rao, V.B.K. (2002) Seismic bearing capacity factors for spread foundatins. Geotechnique, 52(2), 79-88.
23.    Kumar, J. and Mohan Rao, V.B.K. (2003) Seismic bearing capacity of foundations on slops. Geotechnique, 53(3), 347-361.
24.    Kumar, J. (2009) The variation of Nγ with footing roughness using the method of characteristics. International Journal for Numerical and Analytical Methods in Geomechanics, 33(2), 275-284.
25.    Kumar, J. (2003) Nγ for rough strip footing using the method of characteristics. Canadian Geotech-nical Journal, 40(3), 669-674.
26.    Smith, C.C. (2005) Complete limiting stress solutions for the bearing capacity of strip footings on a Mohr-Coulomb soil. Géotechnique, 55(8), 607-612.
27.    Kumar, J. and Ghosh, P. (2005) Bearing capacity factor Nγ for ring footings using the method of characteristics. Canadian Geotechnical Journal, 42(5), 1474-1484.
28.    Martin, C.M. (2003) New software for rigorous bearing capacity calculations. Proc. British Geotech. Assoc. Int. Conf. on Found., Dundee, 581-592.
29.    Sun, J.P., Zhao, Z.Y., and Cheng, Y.P. (2013) Bearing capacity analysis using the method of charac-teristics. Acta Mechanica Sinica, 29(2), 179-188.
30.    Bolton, M.D. and Lau, C.K. (1993) Vertical bearing capacity factors for circular and strip footings on Mohr-Coulomb Soil. Canadian Geotechnical Journal, 30(6), 1024-1033.
31.    Martin, C.M. (2004) ABC-analysis of bearing capacity v1.0. Software and documentation. http://www.eng.ox.ac.uk/civil/people/cmm/software/abc. Accessed 14 Dec 2014.
32.    Casablanca, O., Cascone, E., and Biondi, G. (2016). The static and seismic bearing capacity factor Nγ for footings adjacent to slopes. Procedia Engineering, 158, 410-415.
33.    Cascone, E. and Casablanca, O. (2016). Static and seismic bearing capacity of shallow strip footings. Soil Dynamics and Earthquake Engineering, 84, 204-223.
34.    Kamalian, M., Behnia, C., Lotfizadeh, M., and Rastegar, A. (2011) Considerations about load inclination effect on seismic bearing capacity factors of strip foundations. Journal of Civil and Surveying Engineering, 45(4), 495-504 (in Persian).
35.    Kamalian, M., Goldasteh, M., Amoli, R., and Rahmani, I. (2013) Estimation of seismic bearing capacity coefficients of strip foundations adjacent to the top of slops by the stress characteristic method. Sharif Journal of Civil Engineering,        29-2(3), 81-90 (in Persian).
36.    Kamalian, M. (2014) Estimation of Seismic Bearing Capacity of Strip Foundations on Slopes by the Stress Characteristic Method. Research Report, International Institute of Earthquake Engineering and Seismology (IIEES) 6309-p.93-1 (in Persian).
37.    Kamalian, M. (2007) Estimation of Friction Effect on Seismic Bearing Capacity of Strip Foundations by the Characteristic Method. Research Report, International Institute of Earthquake Engineering and Seismology (IIEES) 6118-p.89-4 (in Persian).
38.    Jahanandish, M. and Keshavarz, A. (2005) Seismic bearing capacity of foundations on reinforced soil slopes. Geotextiles and Geomembranes, 23(1), 1-25.
39.    Keshavarz, A., Jahanandish, M., and Ghahramani, A. (2011) Seismic bearing capacity analysis of reinforced soils by the method of stress characteristics. IJST, Transactions of Civil Engineering, 35, 185-197.
40.    Ames, W.F. (1992) Numerical Methods for Partial Differential Equations. Boston: Academic Press.
41.    Booker, J.R. and Davis, E.H. (1977) 'Stability analysis by plasticity theory'. In: Desai CS, Christian JT (Eds), Numerical Methods in Geotechnical Engineering. McGraw Hill, New York, 719-748.
42.    Larkin, L.A. (1968) Theoretical bearing capacity of very shallow footings. Journal of the Soil Mecha-nics and Foundations Division, 94(6), 1347-1360.
43.    James, R.G. and Bransby, P. (1970) Experimental and theoretical investigations of a passive earth pressure problem. Geotechnique, 20(1), 17-37.
44.    Graham, J. (1971) Calculation of passive pressure in sand. Canadian Geotechnical Journal, 8(4), 566-578.
45.    Lee, I.K. and Herington, J.R. (1972) A theoretical study of the pressures acting on a rigid wall by a sloping earth or rockfill. Geotechnique, 22(1), 1-26.
46.    Behnia, C. and Tabatabai, A.M. (1988) 'Plastic Equilibrium'. In: Soil Mechanics, 1, (Ed.) Tehran University Pub. Co., Tehran, 357-408 (in Persian).
47.    Behnia, C. and Tabatabai, A.M. (1989) 'Surface Footings'. In: Soil Mechanics, 2, (Ed.) Tehran University Pub. Co., Tehran, 185-257 (in Persian).
48.    Lundgren, H. and Mortensen, K. (1953) Determination by the theory of plasticity of the bearing capacity of continuous footings on sand. In: Proceedings of the Third International Conference on Soil Mechanics and Foundation Engineering, Zürich, Switzerland, 409-412.
49.    Michalowski, R. (1997) An estimate of the influence of soil weight on bearing capacity using limit analysis. Soils and Foundations, 37(4), 57-64.
50.    Hill, R. (1950) The Mathematical Theory of Plasticity. Clarendon Press: Oxford University, London.
51.    Ahmadi, S., Kamalian, M., and Askari, F. (2020) Evaluation of the static bearing capacity coefficients of rough strip footing using the stress characteristics method. Int. J. Civ. Eng., 19, 155-165.
52.    Ahmadi, S., Kamalian, M. and Askari, F., (2020) Considerations on bearing capacity factors of rough strip footing using the stress characteristics method. Iran J. Sci. Technol. Trans. Civ. Eng., 1-11.
Bulletin of Earthquake Science and Engineering
Volume 7, Issue 4 - Serial Number 25
January 2021
Pages 147-161

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History

  • Receive Date: 17 April 2021
  • Accept Date: 17 April 2021

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