AbstractAbout AuthorsReferences
This paper evaluates the accuracy of Terzaghi’s one-dimensional consolidation theory for time-dependent settlement prediction of large-area raft foundations. At the raft foundation significant size and significant anisotropy of subsoil filtration properties (kx/ky>>1), the consolidation process acquires a manifested two-dimensional character due to pore water lateral outflow outside the loaded area. A parametric finite element study was carried out using Plaxis 2D for an axisymmetric model of the raft foundation on a clay stratum. The raft radius (R=10, 20, 30 m), clay layer thickness (H=5, 10, 20 m), and permeability anisotropy ratio (kx/ky=1, 2, 5, 10) were varied. It was found that at low R/H ratios (R/H = 0.5), increasing the anisotropy coefficient from 1 to 10 accelerates consolidation by the factor of 2.6, whereas at R/H=6, the effect of anisotropy is negligible. The limits of applicability of the one-dimensional approach were established as a function of R/H and permeability anisotropy.
A.Z. TER-MARTIROSYAN, Doctor of Sciences (Engineering), Associate Professor (This email address is being protected from spambots. You need JavaScript enabled to view it.),
V.V. RUD, Candidate of Sciences (Engineering) (This email address is being protected from spambots. You need JavaScript enabled to view it.),
P.V. SHISHKINA, Student (This email address is being protected from spambots. You need JavaScript enabled to view it.),
A.M. VAROSYAN, Student (This email address is being protected from spambots. You need JavaScript enabled to view it.)
V.V. RUD, Candidate of Sciences (Engineering) (This email address is being protected from spambots. You need JavaScript enabled to view it.),
P.V. SHISHKINA, Student (This email address is being protected from spambots. You need JavaScript enabled to view it.),
A.M. VAROSYAN, Student (This email address is being protected from spambots. You need JavaScript enabled to view it.)
National Research Moscow State University of Civil Engineering (26, Yaroslavskoe Highway, Moscow, 129337, Russian Federation)
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https://doi.org/10.22227/1997-0935.2026.2.195-206
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3. Тер-Мартиросян З.Г., Тер-Мартиросян А.З. Консолидация водонасыщенного грунта при действии циклической нагрузки // Вестник МГСУ. 2010. № 4. С. 194–197. EDN: RTSQOF
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5. Ai Z.Y., Zeng W.Z. Axisymmetric consolidation of saturated multi-layered soils with anisotropic permeability due to well pumping. Computers and Geotechnics. 2017. Vol. 92, pp. 229–239.
https://doi.org/10.1016/j.compgeo.2017.08.015
6. Chen Z.J., Feng W.Q., Yin J.H. et al. Finite element model and simple method for predicting consolidation displacement of soft soils exhibiting creep underneath embankments in 2-D condition. Acta Geotechnica. 2023. Vol. 18, pp. 2513–2528. EDN: NWIEJR. https://doi.org/10.1007/s11440-022-01741-z
7. Liu K., Chen J., Kang J. Long-term consolidation settlement behavior of piled raft foundations on soft clay considering strain rate effect. Transportation Infrastructure Geotechnology. 2025. Vol. 12. Art. 242. EDN: IQJGCR. https://doi.org/10.1007/s40515-025-00702-9
8. Ho L., Fatahi B. Analytical solution for the two-dimensional plane strain consolidation of an unsaturated soil stratum subjected to time-dependent loading. Computers and Geotechnics. 2015. Vol. 67, pp. 1–16. https://doi.org/10.1016/j.compgeo.2015.02.011
9. Liu Y., Zheng J.-J., Cao W.-Z. A closed-form solution for 2D plane strain consolidation in unsaturated soils considering the lateral semipermeable drainage boundary. Computers and Geotechnics. 2021. Vol. 140. 104435. EDN: LOZQEV. https://doi.org/10.1016/j.compgeo.2021.104435
10. Ai Z.Y., Hu Y.D. Time effect of vertically loaded piled rafts in layered cross-anisotropic viscoelastic saturated soils. Computers and Geotechnics. 2020. Vol. 119. 103384. EDN: LOXQVG.
https://doi.org/10.1016/j.compgeo.2019.103384
https://doi.org/10.22227/1997-0935.2026.2.195-206
1. Nikiforova N.S., Pirogov D.D. Digital methods for predicting foundation settlements. Vestnik MGSU. 2026. Vol. 21. No. 2, pp. 195–206. (In Russian). EDN: DDTEVZ. https://doi.org/10.22227/1997-0935.2026.2.195-206
2. Тер-Мартиросян З.Г., Тер-Мартиросян А.З., Нгуен Х.Х. Консолидация и ползучесть оснований фундаментов конечной ширины // Вестник МГСУ. 2013. № 4. С. 38–51. EDN: PZIELL
2. Ter-Martirosyan Z.G., Ter-Martirosyan A.Z., Nguyen H.H. Consolidation and creep of subfoundations having finite widths. Vestnik MGSU. 2013. No. 4, pp. 38–51. (In Russian). EDN: PZIELL
3. Тер-Мартиросян З.Г., Тер-Мартиросян А.З. Консолидация водонасыщенного грунта при действии циклической нагрузки // Вестник МГСУ. 2010. № 4. С. 194–197. EDN: RTSQOF
3. Ter-Martirosyan Z.G., Ter-Martirosyan A.Z. Consolidation of saturated soil under cyclic load. Vestnik MGSU. 2010. No. 4, pp. 194–197. (In Russian). EDN: RTSQOF
4. Мосолов Г.В., Димов И.Л. Применение современных моделей грунтов при выполнении численных расчетов оснований и фундаментов резервуаров // Наука и технологии трубопроводного транспорта нефти и нефтепродуктов. 2021. Т. 11. № 3. С. 257–269. EDN: UYORNS. https://doi.org/10.28999/2541-9595-2021-11-3-257-269
4. Mosolov G.V., Dimov I.L. Application of modern soil models in numerical analysis of foundations and tanks. Nauka i Tekhnologii Truboprovodnogo Transporta Nefti i Nefteproduktov. 2021. Vol. 11. No. 3, pp. 257–269. (In Russian). EDN: UYORNS. https://doi.org/10.28999/2541-9595-2021-11-3-257-269
5. Ai Z.Y., Zeng W.Z. Axisymmetric consolidation of saturated multi-layered soils with anisotropic permeability due to well pumping. Computers and Geotechnics. 2017. Vol. 92, pp. 229–239.
https://doi.org/10.1016/j.compgeo.2017.08.015
6. Chen Z.J., Feng W.Q., Yin J.H. et al. Finite element model and simple method for predicting consolidation displacement of soft soils exhibiting creep underneath embankments in 2-D condition. Acta Geotechnica. 2023. Vol. 18, pp. 2513–2528. EDN: NWIEJR. https://doi.org/10.1007/s11440-022-01741-z
7. Liu K., Chen J., Kang J. Long-term consolidation settlement behavior of piled raft foundations on soft clay considering strain rate effect. Transportation Infrastructure Geotechnology. 2025. Vol. 12. Art. 242. EDN: IQJGCR. https://doi.org/10.1007/s40515-025-00702-9
8. Ho L., Fatahi B. Analytical solution for the two-dimensional plane strain consolidation of an unsaturated soil stratum subjected to time-dependent loading. Computers and Geotechnics. 2015. Vol. 67, pp. 1–16. https://doi.org/10.1016/j.compgeo.2015.02.011
9. Liu Y., Zheng J.-J., Cao W.-Z. A closed-form solution for 2D plane strain consolidation in unsaturated soils considering the lateral semipermeable drainage boundary. Computers and Geotechnics. 2021. Vol. 140. 104435. EDN: LOZQEV. https://doi.org/10.1016/j.compgeo.2021.104435
10. Ai Z.Y., Hu Y.D. Time effect of vertically loaded piled rafts in layered cross-anisotropic viscoelastic saturated soils. Computers and Geotechnics. 2020. Vol. 119. 103384. EDN: LOXQVG.
https://doi.org/10.1016/j.compgeo.2019.103384
For citation: Ter-Martirosyan A.Z., Rud V.V., Shishkina P.V., Varosyan A.M. Two-dimensional consolidation of raft foundation subsoil considering soil permeability anisotropy. Zhilishchnoe Stroitel'stvo [Housing Construction]. 2026. No. 4, pp. 47–52. (In Russian). https://doi.org/10.31659/0044-4472-2026-4-47-52
