Sustainable Marine Structures

Numerical Prediction of the Seismic Behavior of Offshore Skirted Foundations Accounting for the Separate Influences of Soil and Superstructure Inertia

Alaoua Bouaicha

Scientific and Technical Research Center on Arid Regions (CRSTRA), Campus of Mohamed Khider University, BP 1682 RP, Biskra 07000, Algeria

Nassima Zatar

Civil Engineering Department, Faculty of Technology, University Mostafa Benboulaid, Batna 05078, Algeria

DOI: https://doi.org/10.36956/sms.v8i2.3300

Received: 19 March 2026 | Revised: 25 May 2026 | Accepted: 1 June 2026 | Published Online: 5 June 2026

---

Abstract

The seismic behavior of skirted foundations plays a crucial role in the stability of marine and coastal structures subjected to earthquakes. This study provides an in-depth examination of the seismic bearing response of skirted foundations subjected to eccentric vertical loading, assessed through a Finite Element Limit Analysis (FELA) framework. The objective is to separately characterize the inertial contributions of the soil mass and the superstructure as functions of the horizontal seismic coefficient k_h, the relative skirt depth D/B, and the eccentricity ratio e/B. Unlike previous studies, which generally consider inertial effects in a simplified or combined manner, this work introduces a systematic and explicit separation of soil and superstructure inertia contributions for skirted foundations within a unified numerical framework, particularly under eccentric loading conditions. This approach enables a clearer distinction between local soil failure mechanisms and global structural effects, thereby improving the understanding of the seismic response of skirted foundations. The findings reveal the decisive role of skirt embedment depth, which enhances stability and delays failure, whereas increasing k_h and e/B significantly reduces the bearing capacity. The resulting three-dimensional surfaces offer a clear visualization of the combined influence of these parameters, revealing critical operational zones and stability domains of skirted foundations under seismic loading. Two new generalized analytical equations were developed for the correction factors associated under inertial effects, showing excellent agreement with the FELA results. These formulations, combined with the developed 3D surfaces, provide practical and reliable tools for optimized seismic design of skirted foundations under seismic conditions.

Keywords: Eccentric Loading; FELA; Skirted Foundations; Seismic Bearing Capacity; Soil and Superstructure Inertia

---

References

[1] Terzaghi, K., 1943. Theoretical Soil Mechanics. John Wiley & Sons: New York, NY, USA.

[2] Frydman, S., Burd, H.J., 1997. Numerical Studies of Bearing Capacity Factor Nγ. Journal of Geotechnical and Geoenvironmental Engineering. 123(1), 20–29. DOI: https://doi.org/10.1061/(ASCE)1090-0241(1997)123:1(20)

[3] Loukidis, D., Chakraborty, T., Salgado, R., 2008. Bearing Capacity of Strip Footings on Purely Frictional Soil under Eccentric and Inclined Loads. Canadian Geotechnical Journal. 45(6), 768–787. DOI: https://doi.org/10.1139/T08-015

[4] Bouaicha, A., Mabrouki, A., 2024. Failure Envelopes for Strip Footings on Sand Overlying Non-Homogeneous Clay under Combined Loading. Transportation Infrastructure Geotechnology. 11, 44–62. DOI: https://doi.org/10.1007/s40515-022-00272-0

[5] Bransby, M.F., Randolph, M.F., 1998. Combined Loading of Skirted Foundations. Géotechnique. 48(5), 637–655. DOI: https://doi.org/10.1680/geot.1998.48.5.637

[6] Hu, Y., Randolph, M.F., Watson, P.G., 1999. Bearing Response of Skirted Foundation on Non-Homogeneous Soil. Journal of Geotechnical and Geoenvironmental Engineering. 125(11), 924–935. DOI: https://doi.org/10.1061/(ASCE)1090-0241(1999)125:11(924)

[7] Yun, G., Bransby, M.F., 2007. The Undrained Vertical Bearing Capacity of Skirted Foundations. Soils and Foundations. 47(3), 493–505. DOI: https://doi.org/10.3208/sandf.47.493

[8] Selmi, M., Kormi, T., Hentati, A., et al., 2019. Capacity Assessment of Offshore Skirted Foundations under HM Combined Loading Using RFEM. Computers and Geotechnics. 114, 103148. DOI: https://doi.org/10.1016/j.compgeo.2019.103148

[9] Mana, D., Gourvenec, S., Randolph, M., 2010. A Numerical Study of the Vertical Bearing Capacity of Skirted Foundations. In Frontiers in Offshore Geotechnics II. CRC Press: Boca Raton, FL, USA. pp. 433–438.

[10] Eid, H.T., 2013. Bearing Capacity and Settlement of Skirted Shallow Foundations on Sand. International Journal of Geomechanics. 13(5), 645–652. DOI: https://doi.org/10.1061/(ASCE)GM.1943-5622.0000237

[11] Al-Aghbari, M.Y., Mohamedzein, Y.E.A., 2004. Model Testing of Strip Footings with Structural Skirts. Proceedings of the Institution of Civil Engineers - Ground Improvement. 8(4), 171–177. DOI: https://doi.org/10.1680/grim.8.4.171.41844

[12] Bouaicha, A., Boumekik, N.E.I., Mabrouki, A., 2025. Numerical Investigation of the Seismic Bearing Capacity of Offshore Skirted Foundations Installed in Sand Using Finite Element Limit Analysis. Materials Research Proceedings. 48, 161–170. DOI: https://doi.org/10.21741/9781644903414-19

[13] Sarma, S.K., Iossifelis, I.S., 1990. Seismic Bearing Capacity Factors of Shallow Strip Footings. Géotechnique. 40(2), 265–273. DOI: https://doi.org/10.1680/geot.1990.40.2.265

[14] Richards, R., Elms, D.G., Budhu, M., 1993. Seismic Bearing Capacity and Settlement of Foundations. Journal of Geotechnical Engineering. 119(4), 662–674. DOI: https://doi.org/10.1061/(ASCE)0733-9410(1993)119:4(662)

[15] Paolucci, R., Pecker, A., 1997. Seismic Bearing Capacity of Shallow Strip Foundations on Dry Soils. Soils and Foundations. 37(3), 95–105. DOI: https://doi.org/10.3208/sandf.37.3_95

[16] Cascone, E., Casablanca, O., 2016. Static and Seismic Bearing Capacity of Shallow Strip Footings. Soil Dynamics and Earthquake Engineering. 84, 204–223. DOI: https://doi.org/10.1016/j.soildyn.2016.02.010

[17] Chamekh, A., Bouaicha, A., Messai, A., 2025. Effects of Soil and Superstructure Inertia on the Seismic Bearing Capacity of Shallow Foundations under Eccentric Loading Using Finite Element Limit Analysis. Transportation Infrastructure Geotechnology. 12, 234. DOI: https://doi.org/10.1007/s40515-025-00692-8

[18] Pal, A., Ghosh, P., Majumder, M., 2017. Interaction Effect of Two Closely Spaced Skirted Strip Foundations in Cohesionless Soil Using Upper-Bound Limit Analysis. International Journal of Geomechanics. 17(2). DOI: https://doi.org/10.1061/(ASCE)GM.1943-5622.0000755

[19] Ghosh, P., Pal, A., 2019. Undrained Bearing Capacity of a Skirted Foundation Using Upper-Bound Limit Analysis. Acta Geotechnica Slovenica. 16(2), 2–11.

[20] Santhoshkumar, G., Ghosh, P., 2020. Ultimate Bearing Capacity of Skirted Foundation on Cohesionless Soil Using Slip Line Theory. Computers and Geotechnics. 123, 103573. DOI: https://doi.org/10.1016/j.compgeo.2020.103573

[21] Ding, H., Pan, C., Zhang, P., et al., 2022. Shaking Table Tests and Seismic Response of Three-Bucket Jacket Foundations for Offshore Wind Turbines. Journal of Ocean University of China. 21, 719–736. DOI: https://doi.org/10.1007/s11802-022-4742-7

[22] Beygi, M., Fallahi, M., Vali, R., et al., 2023. FELA-DNN Framework to Predict the Seismic Bearing Capacity of Skirted Strip Footing Built on a Non-Cohesive Slope. Soil Dynamics and Earthquake Engineering. 171, 107932. DOI: https://doi.org/10.1016/j.soildyn.2023.107932

[23] Chauhan, V.B., Singh, T., Verma, S., et al., 2025. Adaptive FELA and Machine Learning for Skirted Footing Performance under Inclined Loading. Transportation Infrastructure Geotechnology. 12, 293. DOI: https://doi.org/10.1007/s40515-025-00753-y

[24] Datta, N.V., Khuntia, S., 2026. Seismic Bearing Capacity Analysis of Skirted Footing on Cohesive-Frictional Soil Slopes. In: Bhandary, N.P., Tiwari, B., Acharya, I.P., et al. (eds.). Proceedings of GeoMandu 2024 Volume 1. Springer: Singapore. DOI: https://doi.org/10.1007/978-981-96-7921-8_17

[25] Verma, S., Datta, S., Chauhan, V.B., 2026. Seismic Bearing Capacity of Skirted Footings on Cohesive Slopes Using Limit Analysis. Proceedings of the Indian National Science Academy. DOI: https://doi.org/10.1007/s43538-026-00717-x

[26] Zhou, H., Liu, Z., Shao, J., et al., 2026. Effects of Stress Direction and Magnitude on Strength and Failure of Weakly Anisotropic Sandstone under True Triaxial Compression. Rock Mechanics and Rock Engineering. 59, 3213–3234. DOI: https://doi.org/10.1007/s00603-025-04982-y

[27] Optum Computational Engineering, 2023. OptumG2—2D Geotechnical Design & Analysis Software. Available from: https://optumce.com/optum-g2/ (cited 1 March 2026).

[28] Lai, V.Q., Shiau, J., Promwichai, T., et al., 2023. Modelling Soil Stability in Wide Tunnels Using FELA and Multivariate Adaptive Regression Splines Analysis. Modeling Earth Systems and Environment. 9, 2993–3008. DOI: https://doi.org/10.1007/s40808-022-01595-0

[29] Keawsawasvong, S., Kounlavong, K., Duong, N.T., et al., 2024. Seismic Stability Assessment of Rock Slopes Using Multivariate Adaptive Regression Splines. Transportation Infrastructure Geotechnology. 11, 2296–2318. DOI: https://doi.org/10.1007/s40515-024-00374-x

[30] Chen, X., Wang, Z., Kong, D., et al., 2025. Development of an Adaptive Meshing Upper Bound Limit Analysis Method for Large Deformation Axisymmetric Geotechnical Problems. Scientific Reports. 15, 5771. DOI: https://doi.org/10.1038/s41598-025-89033-w

[31] Tran, D.T., Shiau, J., Keawsawasvong, S., et al., 2025. Failure Envelopes of Embedded Foundations under V-H-M Loadings in Anisotropic Clays Using Optimised ANFIS Algorithms. Marine Georesources and Geotechnology. 43(10), 1900–1917. DOI: https://doi.org/10.1080/1064119X.2024.2440553

[32] Mohapatra, D., Kumar, J., 2020. Bearing Capacity of Embedded Foundations Using Quasi-Kinematic Limit Analysis. Computers and Geotechnics. 117, 103275. DOI: https://doi.org/10.1016/j.compgeo.2019.103275

[33] Conti, R., 2018. Simplified Formulas for the Seismic Bearing Capacity of Shallow Strip Foundations. Soil Dynamics and Earthquake Engineering. 104, 64–74. DOI: https://doi.org/10.1016/j.soildyn.2017.09.027

[34] Tian, Z., Liu, K., Malik, A., 2026. An Experimental Method for Turbine Rotors Based on Temperature Correction. Aerospace Science and Technology. 177, 112237. DOI: https://doi.org/10.1016/j.ast.2026.112237