Determining the Equivalent Elastic Modulus Relationship for Multi-layered Soils in Immediate Settlement Calculations of Shallow Foundations Using Combined FEM and EPR Numerical Modeling

Pirmohammadi Alishah, Farhad; Motalbian, Masoud

doi:10.22034/cpj.2025.561493.1413

Determining the Equivalent Elastic Modulus Relationship for Multi-layered Soils in Immediate Settlement Calculations of Shallow Foundations Using Combined FEM and EPR Numerical Modeling

https://doi.org/10.22034/cpj.2025.561493.1413

Volume 8, Issue 1 - Serial Number 83
April 2026

Pages 21-37

Document Type : Research Article

Authors

farhad pirmohammadi alishah

Masoud Motalbian

Department of Civil Engineering, Shab.C., Islamic Azad University, Shabestar, Iran.

Abstract

Many of the key behaviors of concrete at the nanoscale are influenced by its internal microstructure. Adopting a nanotechnology-based approach can thus play a crucial role in identifying, analyzing, and improving the microstructural performance of concrete as a nanomaterial. In this research, the effect of metal oxide nanoparticles on the compressive strength and permeability of ordinary concrete was investigated. A total of 36 cubic specimens were prepared to evaluate compressive strength, and 4 cylindrical specimens were produced to measure permeability. The cubic specimens had dimensions of 5 × 5 × 5 cm, and the cylindrical specimens were 15 × 15 cm. Tests were conducted at curing ages of 7 and 28 days. Compressive strength tests were performed with three cement contents—350, 400, and 450 kg/m³—at varying percentages of titanium dioxide (TiO₂) nanoparticles (0%, 1%, 3%, and 5%). The permeability test was conducted only on samples with 400 kg/m³ cement content, using the same nanoparticle replacement ratios (0%, 1%, 3%, and 5%). The results showed that for concretes with cement contents of 350 and 400 kg/m³, the highest compressive strength was achieved with 5% nanoparticle content at both ages. In contrast, for the 450 kg/m³ mix, the optimum nanoparticle dosage was 3%.

Furthermore, the permeability test results indicated that the addition of nanoparticles reduced concrete permeability, reaching the minimum permeability at the 3% nanoparticle content.

Keywords

Elastic foundation settlement

Equivalent soil elastic modulus

Finite element modeling

Evolutionary regression

Subjects

civil engineering

Abu-Farsakh, M. Y., & Chen, Q. (2012). Evaluation of the base/subgrade soil under repeated loading: phase II, in-box and ALF cyclic plate load tests [tech summary].

Alizadeh, M., & Gholami, M. (2020). Application of Evolutionary Polynomial Regression (EPR) for Estimating Dynamic Properties of Soil from Laboratory Tests. Soil Dynamics and Earthquake Engineering, 138, 106345.

Bahrami, S., & Mohammadi, A. (2019). Numerical Analysis of Shallow Foundation Settlement on Stratified Soil Layers Using 3D Finite Element Method. International Journal of Civil Engineering (Iran University of Science and Technology), 17(4), 501–515.

Brahma, P., & Mukherjee, S. (2010, December). A realistic way to obtain equivalent Young’s modulus of layered soil. In Indian geotechnical conference. Bombay, India (pp. 305-308).

Brinkgreve, R. B. J., Engin, E., & Swolfs, W. M. (2013). PLAXIS 3D 2013 user manual. Plaxis bv, Delft.

Chandrupatla, T., & Belegundu, A. (2021). Introduction to finite elements in engineering. Cambridge University Press.

Das, B. M., & Sivakugan, N. (2018). Principles of foundation engineering. Cengage learning.

Dhar, A., & Tarefder, R. (2011). An approximate spreadsheet integration method for foundation settlements in two-layered medium. International Journal of Geotechnical Engineering, 5(4), 437-446.

Ebid, A. M. (2021). 35 Years of (AI) in geotechnical engineering: state of the art. Geotechnical and Geological Engineering, 39(2), 637-690.

Erzin, Y., & Gul, T. O. (2014). The use of neural networks for the prediction of the settlement of one-way footings on cohesionless soils based on standard penetration test. Neural computing and applications, 24, 891-900.

HariBharghav, M., Madhav, M. R., & Padmavathi, V. (2017). Estimation of deformation moduli of reinforced foundation beds from load tests. In Indian geotech conf.

Javadi, A. A., Ahangar-Asr, A., Johari, A., Faramarzi, A., & Toll, D. (2012). Modelling stress–strain and volume change behaviour of unsaturated soils using an evolutionary based data mining technique, an incremental approach. Engineering Applications of Artificial Intelligence, 25(5), 926-933.

Karimi, B., Zare, M., & Hoseini, R. (2021). Prediction of Seepage in Earth Dams using Evolutionary Polynomial Regression (EPR) Combined with Finite Element Method (FEM). Journal of Geoenvironmental Engineering,

Pantelidis, L. (2019). The equivalent modulus of elasticity of layered soil mediums for designing shallow foundations with the Winkler spring hypothesis: A critical review. Engineering Structures, 201, 109452.

Pantelidis, L. (2021). The equivalent modulus of elasticity of soil mediums for designing shallow foundations. Geotechnical and Geological Engineering, 39(5), 3863-3873.

Sasmal, S. K., & Behera, R. N. (2021). Prediction of combined static and cyclic load-induced settlement of shallow strip footing on granular soil using artificial neural network. International Journal of Geotechnical Engineering.

Shahin, M. (2014). Artificial intelligence for modelling load-settlement response of axially loaded bored piles. Numerical Methods in Geotechnical Engineering, 491-495.

Shahin, M. A. (2015). Use of evolutionary computing for modelling some complex problems in geotechnical engineering. Geomechanics and Geoengineering, 10(2), 109-125.

[80] Shahin, M. A. (2015). "Genetic Programming for Modelling of Geotechnical Engineering Systems". In Handbook of Genetic Programming Applications (pp. 37-57). Springer International Publishing.

Yaghoubi, A., Ahmadi, S., & Karimi, B. (2023). 3D FEM Analysis of Soil-Pile-Structure Interaction considering Seismic Performance using Machine Learning Models (EPR). (Paper presented at the International Conference on Geotechnical Engineering,

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