Vol. 337 No. 5 (2026)
DOI https://doi.org/10.18799/24131830/2026/5/5244
Modern methods for assessing the bearing capacity of shallow foundation bases
Relevance. The engineering and geological structure of survey sites, as a rule, involves working with heterogeneous, multi-layered, weak soils, in which case classical approaches to determining the bearing capacity of the foundation can give significant errors, leading to overestimated or underestimated estimates. Aim. Comparison of traditional methods for calculating the bearing capacity of shallow foundations based on the theory of marginal soil equilibrium, with methods based on numerical analysis, as well as a demonstration of the application of a probabilistic stochastic approach in engineering geology. Methods. The calculations performed on the basis of theory of marginal soil equilibrium (calculation according to SP 22.13330.2016, Terzaghi formula) and based on numerical analysis (limit analysis in ABC, limit analysis in Optum G2, discontinuity layout optimization, random finite element method, increasing load to achieve stability loss in Plaxis). Results and conclusions. The results obtained demonstrate the significant effect of the chosen calculation method on the assessment of the bearing capacity of the soil base. With a simplified geological structure, the methods based on the theory of marginal soil equilibrium show the highest values of bearing capacity, compared with methods based on numerical analysis, varying from 1408 to 1477 kPa and from 940 to 1366 kPa, respectively. The paper shows that the surface of soil destruction in most cases lies deeper than the depth of the compressible stratum determined by the current set of rules. The use of the random finite element method illustrates the application of a probabilistic stochastic approach, on the basis of which the probability of loss of stability of the soil base is determined and a quantitative assessment of the reliability of the lithotechnical system under consideration is given.
For citation: Gorlov A.A., Fomenko I.K. Modern methods for assessing the bearing capacity of shallow foundation bases. Bulletin of the Tomsk Polytechnic University. Geo Assets Engineering, 2026, vol. 337, no. 5, pp. 53-62. https://doi.org/10.18799/24131830/2026/5/5244
Keywords:
bearing capacity, soil, uncertainty, probabilistic-stochastic approach, lithotechnical system, reliability, shallow foundation
References:
1. SP 22.13330.2016. Foundations of Buildings and Structures. Moscow, Ministry of Construction of the Russian Federation Publ., 2016. 54. p. (In Russ.)
2. Tang C., Phoon K.-K. Databases for data-centric geotechnics: geotechnical structures. Boca Raton, CRC Press, 2025. 490 p.
3. Baecher G., Christian J. Reliability and statistics in geotechnical engineering. New Jersey, NJ, USA, Publishing house of the John Wiley and Sons, 2005. 620 p.
4. Martin C. Exact bearing capacity calculations using the method of characteristics. Proceedings of the 11th International Conference IACMAG. Graz, Austria, 2005. pp. 441–450.
5. Florin V.A. Fundamentals of Soil Mechanics. Vol. 2. Leningrad, Gosstroyizdat Publ., 1961. 277 p. (In Russ.)
6. Rankine W. On the stability of loose earth. London, Philosophical transactions, 1857. pp. 9–27.
7. Prandtl L. About the Hard plastisher body. Gottingen, Nachrichten, 1920. pp. 340–350. (In Germ.)
8. Tsytovich N.A. Soil mechanics. Moscow, Vysshaya Shkola Publ., 1983. 343 p. (In Russ.)
9. Martin C. User guide for ABC – analysis of bearing capacity. London, Department of Engineering Science, University of Oxford, 2004. 77 p.
10. Pendin V.V., Fomenko I.K. Methodology of assessment and prediction of landslide hazard. Moscow, LENAND Publ., 2015. 137 p. (In Russ.)
11. Fomenko I.K., Kropotkin M.P. Comparison of probabilistic calculations in the analysis of slope stability of road embankments by finite element method. Prospects for the development of engineering surveys in construction in the Russian Federation. Materials of the Eighteenth All-Russian Scientific and Practical Conference of Survey Organizations. Moscow, 2023. pp. 19–27. (In Russ.) DOI: 10.25296/978-5-6050369-2-0-2023-12-1-328.
12. Gorlov A.A., Fomenko I.K. Stochastic calculation of foundation settlements using the random finite element method. Geotechnics, 2024, vol. XVI, no. 3, pp. 28–40. (In Russ.) DOI: 10.25296/2221-5514-2024-16-3-28-40.
13. Zerkal O.V., Fomenko I.K., Samarin E.N. Probabilistic Approach in Slope Stability Modelling: Implementation and Features. Geoecology, 2023, no. 6, pp. 26–38. (In Russ.) DOI: 10.31857/S0869780923060103.
14. Kurguzov K.V., Fomenko I.K., Sirotkina O.N. Probabilistic and statistical approaches in assessing uncertainty of lithotechnical systems. Geoecology, 2020, no. 2, pp. 80–89. (In Russ.) DOI: 10.31857/S0869780920020071.
15. Fenton G., Griffith D. Risk assessment in geotechnical engineering. NJ, USA, John Wiley and Sons. New Jersey, 2008. 480 p.
16. Lacasse S., Nadim F., Rahim A., Guttormsen T. Statistical description of characteristic soil properties. Proceedings of the Offshore Technology Conference. Houston, Texas, TX, USA, 2007. DOI: 10.4043/19117-MS. 2007.
17. Vanmarcke E. Random fields: analysis and synthesis. MIT Press, Cambridge, UK, 1983. 382 p.
18. Hutapea E., Nonaka T., Julijanto R., Sin Wong. Application of 3-D finite element analysis on settlement of tank on reclamation. Conference: International Symposium on Advances in Foundation Engineering. Singapore, 2013. pp. 179–184.
19. Terzaghi K., Peck R., Mesri G. Soil mechanics in engineering practice. 3rd ed. New Jersey, NJ, USA, John Wiley and Sons, 1996. 663 p.
20. Fomenko I.K., Zerkal O.V., Gorlov A.A., Averin I.V., Shubina D.D. Evaluation of compressible layer thickness of foundation soils in numerical modeling (for discussion). Industrial and civil engineering, 2024, no. 8, pp. 65–70. (In Russ.) DOI: 10.33622/0869-7019.2024.08.65-70.
21. Engineer Technical Letter 1110-2-547. United States Army Corps of Engineers. Engineering and Design: Introduction to Probability and Reliability Methods for Use in Geotechnical Engineering. Washington, DC, USA, Department of the Army, 1997. 14 p.
