JOURNAL OF ROCK MECHANICS

JOURNAL OF ROCK MECHANICS

Experimental and Statistical Evaluation of the Subgrade Reaction Modulus of Clayey Soils from Triaxial Test Results

Document Type : Original Article

Authors
Nahid Rajaei Moghaddam 1
Hossien Tavakoli 2
Mohammad Bahrami 2
1 Faculty of Technology and Engineering, Shahid Bahonar University of Kerman, Kerman, Iran
2 Shahid Bahonar University of Kerman, Kerman, Iran
10.22034/irsrm.2025.545866.1057
Abstract
The modulus of subgrade reaction (Ks) is a fundamental parameter in the analysis and design of shallow and deep foundations, including strip footings, flexible raft foundations, and piles. Its accurate determination is particularly critical in large-scale engineering projects, where it can significantly influence both technical optimization and economic efficiency. The plate load test (PLT) is the most conventional and reliable method for evaluating Ks; however, due to its high cost and time-consuming nature, its application in practical projects is often limited. This limitation highlights the need for alternative laboratory-based approaches that are both reliable and efficient. In this study, the potential of unconsolidated undrained triaxial tests as a substitute for estimating Ks in fine-grained clayey soils is examined. A total of 52 triaxial tests and 8 PLTs were performed, and their results were statistically analyzed and compared. The findings revealed that Ks values obtained from PLTs were consistently higher than those derived from triaxial tests. Nevertheless, strong correlations were observed between Ks and several physical and mechanical soil parameters. To enhance prediction accuracy, multiple regression analysis was employed, incorporating parameters such as density, plasticity index, and moisture content. The regression model achieved a significant correlation coefficient, confirming the feasibility of estimating Ks using triaxial test data. The outcomes of this research demonstrate that triaxial testing, in addition to being more cost- and time-effective, can provide a reliable and practical alternative for estimating Ks in geotechnical design. By integrating triaxial test results with statistical modeling, this study offers an efficient approach for improving the estimation of the modulus of subgrade reaction, which can ultimately contribute to safer and more economical foundation design.
Keywords
Modulus of subgrade reaction
Triaxial test
Plate load test
Multiple regression
Soil parameters
Subjects
1.             Dutta, S.C. and R. Roy, A critical review on idealization and modeling for interaction among soil–foundation–structure system. Computers & structures, 2002. 80(20-21): p. 1579–1594.
2.             Meyerhof, G., The ultimate bearing capacity of foudations. Geotechnique, 1951. 2(4): p. 301–332.
3.             Al-Shayea, N.A., Estimating the Coefficient of Subgrade Reaction in the Laboratory Using the CBR Testing Apparatus. Arabian Journal for Science and Engineering, 2025. 50(3): p. 2123–2147.
4.             Sadrekarimi, J. and G.M. AKBARZAD, comparative study of methods for dererminaing coefficient of subgrade reaction 2009.
5.             Al-Sanad, H.A., N.F. Ismael, and R.P. Brenner, Settlement of circular and ring plates in very dense calcareous sands. Journal of geotechnical engineering, 1993. 119(4): p. 622–638.
6.             Elachachi, S.M., D. Breysse, and L. Houy, Longitudinal variability of soils and structural response of sewer networks. Computers and geotechnics, 2004. 31(8): p. 625–641.
7.             Okeagu, B. and G. Abdel-Sayed, Coefficients of soil reaction for buried flexible conduits. Journal of Geotechnical Engineering, 1984. 110(7): p. 908–922.
8.             Bowles, J.E. and Y. Guo, Foundation analysis and design. Vol. 5. 1996: McGraw-hill New York.
9.             Naeini, S., R. Ziaie Moayed, and F. Allahyari, Subgrade reaction modulus (Ks) of clayey soils based on field tests. Journal of Engineering Geology, 2014. 8(1): p. 2021–2046.
10.          Kang, S.-S., H.-Y. Kim, and B.-A. Jang, Correlation of in situ modulus of deformation with degree of weathering, RMR and Q-system. Environmental earth sciences, 2013. 69(8): p. 2671–2678.
11.          Amini Ahidashti, R. and A. Hadad, Estimation of the Coefficient of Subgrade Reaction using Small-Strain Stiffness. Amirkabir Journal of Civil Engineering, 2015. 47(2): p. 67–79.
12.          Salari, P., et al., Evaluating the Subgrade Reaction Modulus Variations with Soil Grains Shape in Coarse-Grained Soils Using Genetic Algorithm. Open Journal of Geology, 2020. 10(2): p. 111–123.
13.          Dinçer, İ., Models to predict the deformation modulus and the coefficient of subgrade reaction for earth filling structures. Advances in Engineering Software, 2011. 42(4): p. 160–171.
14.          Puri, A., et al., Determining Additional Modulus of Subgarde Reaction Based on Tolerable Settlement for the Nailed-slab System Resting on Soft Clay. International Journal of Civil and Environmental Engineering (IJCEE)-IJENS, 2012. 12(03).
15.          Asakereh, A. and M. Mossafa, Numerical Investigation of Subgrade Reaction Coefficient in Sand Soils of Bandar Abbas City. Journal of Structural Engineering and Geo-Techniques, 2017. 7(2): p. 15–26.
16.          Barmenkova, E.V. and A.V. Matveeva, Calculation of plates of variable rigidity on elastic foundation with variable coefficient of subgrade reaction. Procedia Engineering, 2015. 111: p. 97–102.
17.          Alva García, F.J., L. Medina García, and M.M. de Farias, Numerical estimation of the subgrade reaction modulus of a horizontally loaded piled raft. Revista de la construcción, 2024. 23(3): p. 538–553.
18.          Khaiiatali, S., et al., Estimation of the subgrade reaction modulus using field and numerical analysis methods. Journal of Civil Engineering and Structures, 2024. 8(1): p. 1–7.
19.          Koltuk, S. Effect of soil-foundation interaction on the modulus of subgrade reaction. in MATEC Web of Conferences. 2024. EDP Sciences.
20.          Koltuk, S. and S. Topçu, Determination of Subgrade Reaction Modulus Considering the Relative Stiffnesses of Soil–Foundation Systems. Applied Sciences, 2025. 15(9): p. 4714.
21.          Salem, L.A., A.M. Shaban, and R.R. Almuhanna. Predicting subgrade reaction modulus of sand soils using dynamic cone penetrometer. in AIP Conference Proceedings. 2024. AIP Publishing LLC.
22.          Zarazvand, B. and J. Frankovska, Determining the modulus of subgrade reaction for piled raft foundations by numerical modelling, in Geotechnical Engineering Challenges to Meet Current and Emerging Needs of Society. 2024, CRC Press. p. 971–974.
23.          Hafeznia , M.R., Introduction to Research Methodology in Humanities. 2001, Tehran: Organization for the Study and Compilation of University Humanities Books(In Persian).
24.          Habibpour, K. and R. Safari, Comprehensive Guide to Using SPSS in Survey Research (Quantitative Data Analysis). Tehran. 2014, Loya Publications (In Persian).
25.          Vafaian, M., Rock Mechanics. 1932, Yazd: Iran University of Science and Technology, 87(In Persian).
26.          Das, B.M., Sivakugan , N., Principles of Foundation Engineering. Ninth Edition. 2019, Cengage Learning, Inc., USA.
27.          Taherzade Dorbaty, M.H.a.H., Forecasts of p-y curve of PLT, in International Conference of Civil Engineering, Architecture and urban sustainable development. 2013, 27 and 28 November 2013: Tabriz, Iran(In Persian).
28.          Ajallonnieyan, R., and Sedaghat, M, application of In-Situ tests in geotechnical. 2015, Publications (SID): Khatam Construction Headquarters (In Persian).
JOURNAL OF ROCK MECHANICS
Volume 9, Issue 2
Summer 2025
Pages 1-16