Generalized Lower-Bound Bearing Capacity Analysis of Shallow Inverted Triangular-Based Strip Footings
Publication: International Journal of Geomechanics
Volume 22, Issue 10
Abstract
This paper pertains to the finite-element lower-bound bearing capacity analysis of inverted triangular-based strip footings (ITBFs). The solutions are obtained by the construction of a linear stress field that satisfies all the equations of equilibrium, which is the same as that developed by Lysmer in 1970; however, they were modified in conjunction with a nonlinear programming technique (active set algorithm) to isolate the optimal solution. Studies have been conducted on the convergence of the solutions (by varying the number of triangular elements), and the extensibility of the chosen stress field was confirmed by extending the mesh and comparing the solutions that were obtained. Parametric studies were carried out by varying the cone apex angle (β), for relevant soil properties and different values of the coefficients of earthquake acceleration [horizontal (αh) and vertical (αv)]. A close examination of the obtained results shows that they were as expected and were similar to those of conical footings.
Get full access to this article
View all available purchase options and get full access to this article.
References
Azzam, W. R., and A. M. Nasr. 2015. “Bearing capacity of shell strip footing on reinforced sand.” J. Adv. Res. 6 (5): 727–737. https://doi.org/10.1016/j.jare.2014.04.003.
Basudhar, P. K. 1976. “Some applications of mathematical programming techniques to stability problems in geotechnical engineering.” Ph.D. thesis, Dept. of Civil Engineering, Indian Institute of Technology Kanpur.
Basudhar, P. K. 2008. “Application of optimization and other evolutionary techniques in geotechnical engineering.” In Proc., 12th Int. Conf. on Computer Methods and Advances in Geomechanics, 133–145. Goa, India: International Association for Computer Methods & Advances in Geomechanics (IACMAG).
Basudhar, P. K., M. R. Madhav, and A. J. Valsankar. 1981. “Sequential unconstrained minimization in the optimal lower bound bearing capacity analysis.” Indian Geotech. J. 11 (1): 42–55.
Basudhar, P. K., and D. N. Singh. 1994. “A generalized procedure for predicting optimal lower bound breakout factors of strip anchors.” Géotechnique 44 (2): 307–318. https://doi.org/10.1680/geot.1994.44.2.307.
Basudhar, P. K., and S. K. Srivastava. 2003. “A comparative study of lower bound limit loads of strip footings using linear and nonlinear programming techniques.” In Proc., Symp. on Advances in Geotechnical Engineering, Kanpur: Indian Institute of Technology.
Basudhar, P. K., A. J. Valsankar, and M. R. Madhav. 1979. “Optimal lower bound of passive earth pressure using finite elements and nonlinear programming.” Int. J. Numer. Anal. Methods Geomech. 3 (4): 367–379. https://doi.org/10.1002/nag.1610030405.
Bottero, A., R. Negre, J. Pastor, and S. Turgeman. 1980. “Finite element method and limit analysis theory for soil mechanics problems.” Comput. Methods Appl. Mech. Eng. 22 (1): 131–149. https://doi.org/10.1016/0045-7825(80)90055-9.
Brinch Hansen, J. A. 1970. “Revised and extended formula for bearing capacity.” Danish Geotechnical Institute, Bulletin No. 28: 5–11.
Cassidy, M. J., and G. T. Houlsby. 2002. “Vertical bearing capacity factors for conical footings on sand.” Géotechnique 52 (9): 687–692. https://doi.org/10.1680/geot.2002.52.9.687.
Chakraborty, M., and J. Kumar. 2015. “Bearing capacity factors for a conical footing using lower- and upper-bound finite elements limit analysis.” Can. Geotech. J. 52 (12): 2134–2140. https://doi.org/10.1139/cgj-2014-0507.
Chakraborty, M., and J. Kumar. 2016. “The size effect of a conical footing on Nγ.” Comput. Geotech. 76: 212–221. https://doi.org/10.1016/j.compgeo.2016.03.010.
Chen, W.-F. 1975. Limit analysis and soil plasticity. Amsterdam, Netherlands: Elsevier.
Cheng, Y. M., and C. K. Lau. 2008. Slope stability analysis and stabilization: New methods and insight. London: CRC Press.
Choudhury, D., and K. S. Subba Rao. 2005. “Seismic bearing capacity of shallow strip footings.” Geotech. Geol. Eng. 23 (4): 403–418. https://doi.org/10.1007/s10706-004-9519-9.
Drucker, D. C. 1953. “Limit analysis of two and three-dimensional soil mechanics problems.” J. Mech. Phys. Solids 1 (4): 217–226. https://doi.org/10.1016/0022-5096(53)90001-5.
EN 1997-1: 2004. Eurocode 7: Geotechnical design. Part 1: General rules. CEN.
Fox, R. L. 1971. Optimization methods for engineering design. Boston: Addison-Wesley.
Ghosh, P., and D. Choudhury. 2011. “Seismic bearing capacity factors for shallow strip footings by pseudo-dynamic approach.” Disaster Adv. 4 (3): 34–42.
Harr, M. E. 1966. Foundation of theoretical soil mechanics. New York: McGraw-Hill.
Houlsby, G. T. 1982. “Theoretical analysis of the fall cone test.” Géotechnique 32 (2): 111–118. https://doi.org/10.1680/geot.1982.32.2.111.
Houlsby, G. T., and C. M. Martin. 2003. “Undrained bearing capacity factors for conical footings on clay.” Géotechnique 53 (5): 513–520. https://doi.org/10.1680/geot.2003.53.5.513.
Kavlie, D., and J. Moe. 1971. “Automated design of frame structures.” J. Struct. Div. 97 (1): 33–62. https://doi.org/10.1061/JSDEAG.0002799.
Khan, V. 2012. “Optimal lower bound solutions of plane strain stability problems in geotechnical engineering.” M.Tech thesis, Dept. of Civil Engineering, Indian Institute of Technology Kanpur.
Khatri, V. N., and J. Kumar. 2009. “Bearing capacity factor Nγ for a rough conical footing.” Geomech. Eng. 1 (3): 205–218. https://doi.org/10.12989/gae.2009.1.3.205.
Lyamin, A. V., and S. W. Sloan. 2002. “Lower bound limit analysis using non-linear programming.” Int. J. Numer. Methods Eng. 55 (5): 573–611. https://doi.org/10.1002/nme.511.
Lysmer, J. 1970. “Limit analysis of plane problems in soil mechanics.” J. Soil Mech. Found. Div. 96 (SM4): 1311–1334. https://doi.org/10.1061/JSFEAQ.0001441.
Qiu, G., and J. Grabe. 2012. “Numerical investigation of bearing capacity due to spudcan penetration in sand overlying clay.” Can. Geotech. J. 49 (12): 1393–1407. https://doi.org/10.1139/t2012-085.
Rao, S. S. 1996. Engineering optimization: Theory and practice. 3rd ed. Hoboken, NJ: Wiley.
Singh, D. N., and P. K. Basudhar. 1993a. “A note on vertical cuts in homogeneous soils.” Can. Geotech. J. 30 (5): 859–862. https://doi.org/10.1139/t93-076.
Singh, D. N., and P. K. Basudhar. 1993b. “A note on the effect of mesh pattern on the lower-bound bearing capacity of embedded strip footings.” Int. J. Numer. Anal. Methods Geomech. 17 (10): 735–743. https://doi.org/10.1002/nag.1610171005.
Singh, D. N., and P. K. Basudhar. 1993c. “Optimal lower bound bearing capacity of strip footings.” Soils Found. 33 (4): 18–25. https://doi.org/10.3208/sandf1972.33.4_18.
Singh, D. N., and P. K. Basudhar. 1993d. “Determination of the optimal lower-bound-bearing capacity of reinforced soil-retaining walls by using finite elements and non-linear programming.” Geotext. Geomembr. 12 (7): 665–686. https://doi.org/10.1016/0266-1144(93)90033-K.
Singh, D. N., and P. K. Basudhar. 1995a. “Optimal lower-bound solutions of plane-strain metal indentation and extrusion problems.” J. Mater. Process. Technol. 49 (1–2): 75–84. https://doi.org/10.1016/0924-0136(94)01336-Y.
Singh, D. N., and P. K. Basudhar. 1995b. “The stability of a trapdoor, soils & foundation.” Jpn. Soc. Soil Mech. Found. Eng. 35 (3): 111–115.
Singh, D. N., P. K. Basudhar, and S. K. Srivastava. 1995. “Limit analysis of stability problems in geotechnical engineering: State-of-the-art.” Indian Geotech. J. 25 (3): 314–341.
Sloan, S. W. 1988a. “Lower bound limit analysis using finite elements and linear programming.” Int. J. Numer. Anal. Methods Geomech. 12 (1): 61–77. https://doi.org/10.1002/nag.1610120105.
Sloan, S. W. 1988b. “A steepest edge active set algorithm for solving sparse linear programming problems.” Int. J. Numer. Methods Eng. 26 (12): 2671–2685. https://doi.org/10.1002/nme.1620261207.
Sloan, S. W. 2008. “Limit analysis with adaptive mesh refinement.” In Proc., 8th World Congress on Computational Mechanics, 1–3. Barcelona, Spain: CIMNE.
Sokolovskii, V. V. 1960. Statics of soil media. London: Butterworths.
White, D. J., K. L. Teh, C. F. Leung, and Y. K. Chow. 2008. “A comparison of the bearing capacity of flat and conical circular foundations on sand.” Géotechnique 58 (10): 781–792. https://doi.org/10.1680/geot.2008.3781.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 22 • Issue 10 • October 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Dec 1, 2021
Accepted: Mar 14, 2022
Published online: Jul 27, 2022
Published in print: Oct 1, 2022
Discussion open until: Dec 27, 2022
ASCE Technical Topics:
- Analysis (by type)
- Computer programming
- Computing in civil engineering
- Construction engineering
- Construction methods
- Engineering fundamentals
- Field tests
- Finite element method
- Footings
- Foundation design
- Foundations
- Geomechanics
- Geotechnical engineering
- Limit analysis
- Load bearing capacity
- Methodology (by type)
- Numerical methods
- Shallow foundations
- Soil mechanics
- Soil properties
- Tests (by type)
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.