Keywords: Foundation settlement; Spatially random soil; Probabilistic analysis; Random Finite element method


The prediction of settlement in a traditional design approach usually uses a deterministic value of
modulus of elasticity (E), which is estimated as an average value by testing the soil at selected locations.
However, these deterministic properties of soil may not represent the actual properties of soil and site
condition. Due to numerous sources of uncertainty, the properties of soil mass are spatially varying and
anisotropic in the natural field condition. In this study, a random finite element method (RFEM) is used to
evaluate the reliability of settlement of the strip footing on spatially random soil. Modulus of elasticity is
the only considered random parameter. For this purpose, 2000 spatially random realizations of E-field are
generated using Monte Carlo Simulation. Each of these realizations of heterogeneous soil profile is passed
to FEM to analyze the settlement of footing. The final settlement results measured in all these realizations
are then statistically evaluated and compared. The results of analysis show that the mean and standard
deviation of the footing settlement are increased with increasing spatial correlation length. The large value
of isotropic correlation length led to an increase in the mean settlement value by more than 25% as
compared with the deterministic settlement calculations. Also, it is concluded that the rate of increase of
settlements for anisotropic correlation length is lower than the one under isotropic condition.


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Al-Bittar, T., & Soubra, A.-H. (2014). Probabilistic
analysis of strip footings resting on spatially
varying soils and subjected to vertical or
inclined loads. Journal of Geotechnical and
Geoenvironmental Engineering, 140(4),
Beacher, G. B., & Ingra, T. S. (1981). Stochastic
FEM in settlement predictions. Journal of
Geotechnical and Geoenvironmental
Engineering, 107(ASCE 16179).
Bowles, J. E. (1987). Elastic Foundation Settlements
on Sand Deposits. Journal of Geotechnical
Engineering, 113(8), 846–860.
Chenari, R. J., Roshandeh, S. P., & Payan, M. (2019).
Stochastic analysis of foundation immediate
settlement on heterogeneous spatially random
soil considering mechanical anisotropy. SN
Applied Sciences, 1(7), 660.
Fenton, G. A, & Griffiths, D. V. (2002). Probabilistic
foundation settlement on spatially random soil.
Journal of Geotechnical and
Geoenvironmental Engineering, 128(5), 381–
Fenton, Gordon A, & Vanmarcke, E. H. (1990).
Simulation of random fields via local average
subdivision. Journal of Engineering
Mechanics, 116(8), 1733–1749.
Huang, L.-C., Huang, S., & Liang, Y. (2018).
Probabilistic Settlement Analysis of Granular
Soft Soil Foundation in Southern China
Considering Spatial Variability. Granularity in
Materials Science, 25.
Jimenez, R., & Sitar, N. (2009). The importance of
distribution types on finite element analyses of
foundation settlement. Computers and
Geotechnics, 36(3), 474–483.
Kenarsari, A. E., & Chenari, R. jamshidi. (2015).
Probabilistic settlement analysis of shallow
foundations on heterogeneous soil stratum
with anisotropic correlation structure. In
IFCEE 2015 (pp. 1905–1914).
Paice, G. M., Griffiths, D. V, & Fenton, G. A. (1994).
Influence of spatially random soil stiffness on
foundation settlements. In Proceedings of the
Conference on Vertical and Horizontal
Deformations of Foundations and
Embankments, 628–639.
Poulos, H. G., & Davis, E. H. (1974). Elastic
solutions for soil and rock mechanics (Issue
BOOK). John Wiley.
Resendiz, D., & Herrera, I. (1969). A probabilistic formulation of settlement control design.
Proceedings of the 7th International
Conference on Soil Mechanics and
Foundation Engineering, Mexico City,
Mexico, Sociedad Mexicana de Mecánica de
Suelos, August, 217–225.
Smith, I. M., Griffiths, D. V., & Margetts, L. (2013).
Programming the finite element method. John
Wiley & Sons.
Vanmarcke, E. (2010). Random fields: analysis and
synthesis. World Scientific.
Wu, T. H., & Kraft, L. M. (1967). The probability of
foundation safety. Journal of the Soil
Mechanics and Foundations Division, 93(5),
Zeitoun, D. G., & Baker, R. (1992). A stochastic
approach for settlement predictions of shallow
foundations. Geotechnique, 42(4), 617–629.
How to Cite
AHMED, R. H., & HUSSAIN, M. S. (2021). PROBABILISTIC SETTLEMENT ANALYSIS OF STRIP FOOTING ON SPATIALLY RANDOM SOIL. Journal of Duhok University, 23(2), 617-629. Retrieved from