Static analysis of laterally loaded piles by complementary functions method
Yıl 2025,
Cilt: 14 Sayı: 1, 1 - 1
Ahmad Reshad Noorı
,
Zahraa Razzaq Kareem Alhachami
,
Bilge Sultan Demirtaş
,
Suleiman Khatrush
Öz
In this study, the Complementary Functions Method (CFM) is applied for the static analysis of laterally loaded piles. The canonical equations governing the phenomenon are obtained according to the classic beam theory and simplified to an initial value problem by CFM. The material of the pile is assumed to be isotropic homogeneous and the geometrical properties in the cross-section are considered as uniform. The spring model representing the soil behavior is taken as linear and nonlinear. The effect of boundary conditions on displacements and internal forces are investigated by solving pile problems as free- and fixed-head. The effect of the values of the lateral bearing coefficient and the bearing constant for sandy soils on the flexural behavior of laterally loaded piles is presented parametrically. The obtained results are compared with the results of previous studies and found to be in agreement.
Kaynakça
- A. B. Huang, C. K. Hsueh, M. W. O’Neill, S. Chern and C. Chen, Effects of construction on laterally loaded pile groups. Journal of Geotechnical and Geoenvironmental Engineering, 127(5), 385-397, 2001. https://doi.org/10.1061/(ASCE)1090-0241(2001)127:5(385).
- B. Tak Kim, N. K. Kim, W. Jin Lee and Y. Su Kim, Experimental load transfer curves of laterally loaded piles in Nak-Dong River sand. Journal of Geotechnical and Geoenvironmental Engineering, 130(4), 416-425, 2004.https://doi.org/10.1061/(ASCE)10900241(2004)130:4(416).
- B. D. Wesselink, J. D. Murff, M. F. Randolph, I. L. Nunez and A. M. Hyden, Analysis of centrifuge model test data from laterally loaded piles in calcareous sand. Engineering for Calcareous Sediments, 261-270, 1988. https://doi.org/10.1201/9781003211433-35.
- X. Tang and M. Yang, Analysis of laterally-loaded piles in weathered rock slopes based on p-y curve method. International Journal of Geotechnical Engineering, 14(7), 809-819, 2020. https://doi.org/10.1080/19386362.2018.1498199.
- C.C. Fan and J. H. Long, Assessment of existing methods for predicting soil response of laterally loaded piles in sand. Computers and Geotechnics, 32(4), 274-289, 2005. https://doi.org/10.1016/ j.compgeo.2005.02.004.
- M. Achmus, Design of axially and laterally loaded piles for the support of offshore wind energy converters. Proceedings of the Indian Geotechnical Conference GEOtrendz-2010, pp. 16-18, Mumbai, India, 2010.
- Y. Kim and S. Jeong, Analysis of soil resistance on laterally loaded piles based on 3D soil–pile interaction. Computers and Geotechnics, 38(2), 248-257, 2011. https://doi.org/ 10.1016/j.compgeo.2010.12.001.
- D. Basu, R. Salgado and M. Prezzi, A new model for analysis of laterally loaded piles. Geo-Frontiers 2011, American Society of Civil Engineers, 122-131, Reston, VA, 2011. https://doi.org/ 10.1061/41165(397)14.
- A. Ekici, Three dimensional finite element modeling for the laterally loaded passive pile behavior. Master Thesis, Middle East Technical University, Ankara, Türkiye, 2013.
- M. Heidari, H. El Naggar, M. Jahanandish and A. Ghahramani, Generalized cyclic p–y curve modeling for analysis of laterally loaded piles. Soil Dynamics and Earthquake Engineering, 63, 138-149, 2014. https://doi.org/10.1016/j.soıldyn.2014.04.001.
- M. Khari, K.A. Kassim and A. Adnan, Development of p-y curves of laterally loaded piles in cohesionless soil. The Scientific World Journal, 2014, 1-8, 2014. https://doi.org/10.1155/2014/917174.
- B. Fatahi, S. Basack, P. Ryan, W. H. Zhou and H. Khabbaz, Performance of laterally loaded piles considering soil and interface parameters. Geomechanics and Engineering, 7(5), 495-524, 2014. https://doi.org/10.12989/gae.2014.7.5.495.
- A. L. Rishitha, Numerical modelling of laterally loaded single pile. Ph.D. Thesis, Indian Institute of Technology Hyderabad, Telangana, India, 2015.
- K. Thieken, M. Achmus and K. Lemke, A new static p‐y approach for piles with arbitrary dimensions in sand. Geotechnik, 38(4), 267-288, 2015. https://doi.org/10.1002/gete.201400036.
- H. Lin, L. Ni, M. T. Suleiman and A. Raich, Interaction between laterally loaded pile and surrounding soil. Journal of Geotechnical and Geoenvironmental Engineering, 141(4), 04014119, 2014. https://doi.org/10.1061/(asce)gt.1943-5606.0001259.
- J. M. Mayoral, J .M. Pestana and R. B. Seed, Multi-directional cyclic p–y curves for soft clays. Ocean Engineering, 115, 1-18, 2016. https://doi.org/10.1016/j.oceaneng.2016.01.033.
- A. E. Haiderali and G. Madabhushi, Evaluation of curve fitting techniques in deriving p–y curves for laterally loaded piles. Geotechnical and Geological Engineering, 34(5), 1453-1473, 2016. https://doi.org/10.1007/s10706-016-0054-2.
- B. K. Gupta and D. Basu, Analysis of laterally loaded short and long piles in multilayered heterogeneous elastic soil. Soils and Foundations, 57(1), 92-110, 2017. https://doi.org/10.1016/j.sandf.2017.01.007.
- D. F. Turello, F. Pinto and P. J. Sánchez, Analysis of lateral loading of pile groups using embedded beam elements with interaction surface. International Journal for Numerical and Analytical Methods in Geomechanics, 43(1), 272-292, 2019. https://doi.org/10.1002/nag.2863.
- S. Stacul and N. Squeglia, Analysis method for laterally loaded pile groups using an advanced modeling of reinforced concrete sections. Materials. 11(2), 300, 2018. https://doi.org/10.3390/ma11020300.
- S. Nie, X. Zou and Q. He, A modified p-y curve method for offshore pile foundations under cyclic lateral loading in soft clay. Proceedings of the 2nd International Symposium on Asia Urban GeoEngineering, 485-496 Singapore, 2018. https://doi.org/10.1007/978-981-10-6632-0_37.
- D. Rathod, K. Muthukkumaran and T. G. Sitharam, Effect of slope on p-y curves for laterally loaded piles in soft clay. Geotechnical and Geological Engineering, 36(3), 1509-1524, 2018. https://doi.org/10.1007/s10706-017-0405-7.
- H. Li, L. Tong, S. Liu, H. Liu and M. Zhang, Construction and verification of a unified p–y curve for laterally loaded piles. Bulletin of Engineering Geology and the Environment, 77(3), 987-997, 2018. https://doi.org/10.1007/s10064-017-1111-7.
- S. H. Baek, J. Kim, S. H. Lee and C. K. Chung, Development of the cyclic p–y curve for a single pile in sandy soil. Marine Georesources & Geotechnology, 36(3), 351-359, 2018. https://doi.org/10.1080/1064119X.2017.1318986.
- W. Peng, M. Zhao, Y. Xiao, C. Yang and H. Zhao, Analysis of laterally loaded piles in sloping ground using a modified strain wedge model. Computers and Geotechnics, 107, 163-175, 2019. https://doi.org/10.1016/j.compgeo.2018.12.007.
- P. S. O. Kardogan, N. S. Isik, M. I. Onur and S. Bhattacharya, A study on the laterally loaded pile behaviour in liquefied soil using p-y method. IOP Conference Series: Materials Science and Engineering, 471, 042015, 2019. https://doi.org/10.1088/1757-899X/471/4/042015.
- B. Yuan, M. Sun, Y. Wang, L. Zhai, Q. Luo and X. Zhang, Full 3D displacement measuring system for 3d displacement field of soil around a laterally loaded pile in transparent soil. International Journal of Geomechanics, 19(5), 04019028, 2019. https://doi.org/10.1061/(ASCE)GM.19435622.0001409.
- S. Li, J. Yu, M. Huang and C. F. Leung, Application of T-EMSD based p-y curves in the three-dimensional analysis of laterally loaded pile in undrained clay. Ocean Engineering, 206, 107256, 2020. https://doi.org/10.1016/j.oceaneng.2020.107256.
- Y. Zhang, K. H. Andersen and P. Jeanjean, Verification of a framework for cyclic p-y curves in clay by hindcast of Sabine River, SOLCYP and centrifuge laterally loaded pile tests. Applied Ocean Research, 97, 102085, 2020. https://doi.org/10.1016/j.apor.2020.102085.
- G. Chortis, A. Askarinejad, L. J. Prendergast, Q. Li and K. Gavin, Influence of scour depth and type on p–y curves for monopiles in sand under monotonic lateral loading in a geotechnical centrifuge. Ocean Engineering, 197, 106838, 2020. https://doi.org/10.1016/j.oceaneng.2019.106838.
- D. Xu, X. Xu, W. Li and B. Fatahi, Field experiments on laterally loaded piles for an offshore wind farm. Marine Structures. 69, 102684, 2020. https://doi.org/10.1016/j.marstruc.2019.102684.
- L. Zdravković, D. M. G. Taborda, D. M. Potts, D. Abadias, H. J. Burd, B. W. Byrne, K. G. Gavin, G. T. Houlsby, R. J. Jardine, C. M. Martin, R. A. McAdam and E. Ushev, Finite-element modelling of laterally loaded piles in a stiff glacial clay till at Cowden. Géotechnique, 70(11), 999-1013, 2020. https://doi.org/10.1680/jgeot.18.PISA.005.
- X. Liu, G. Cai, L. Liu, S. Liu, W. Duan and A. J. Puppala, Improved p-y curve models for large diameter and super-long cast-in-place piles using piezocone penetration test data. Computers and Geotechnics, 130, 103911, 2021. https://doi.org/10.1016/ j.compgeo.2020.103911.
- B. Yuan, Z. Li, Z. Zhao, H. Ni, Z. Su and Z. Li, Experimental study of displacement field of layered soils surrounding laterally loaded pile based on transparent soil. Journal of Soils and Sediments, 21, 3072–3083, 2021. https://doi.org/10.1007/s11368-021-03004-y
- F. M. Bhuiyan, R. Motamed, R. V. Siddharthan and D. H. Sanders, Evaluation of a unified p-y method for lateral analysis of large-diameter drilled shafts using NVShaft. Transportation Geotechnics, 36, 100813, 2022. https://doi.org/10.1016/j.trgeo.2022.100813.
- F. Çelik, A comparative analytical ınvestigation on the effects of different p-y curves for a laterally loaded single pile design in saturated sandy soil. European Journal of Science and Technology (34), 474-478, 2022. https://doi.org/10.31590/ejosat.1082906.
- L. M. Lalicata, G. M. Rotisciani, A. Desideri and F. Casini, A numerical model to study the response of piles under lateral loading in unsaturated soils. Geosciences, 12(1), 1, 2021. https://doi.org/10.3390/geoscıences12010001.
- F. M. Bhuiyan, R. V. Siddharthan and R. Motamed, Evaluation of existing p-y models for caliche based on numerical analysis of raiders stadium lateral load tests. DFI 47th Annual Conference on Deep Foundations, pp. 297–309, National Harbor, Maryland, 2022. https://doi.org/10.5281/zenodo.7187512.
- P. A. Arvan and M. Arockiasamy, Energy-based approach: analysis of a laterally loaded pile in multi-layered non-linear elastic soil strata. Geotechnics, 570-598. 2(3), 570-598, 2022. https://doi.org/10.3390/geotechnıcs2030028.
- L. Pang, C. Jiang and L. Chen, Nonlinear predictive framework of the undrained clay slope effect on the ınitial stiffness of p-y curves of laterally loaded piles by FEM. Journal of Marine Science and Engineering, 10(11), 1684, 2022. https://doi.org/10.3390/jmse10111684.
- Z. Shi, L. Liu, M. Huang, K. Shen and B. Wang, Simulation of cyclic laterally-loaded piles in undrained clays accounting for soil small-strain characteristics. Ocean Engineering, 267, 113268, 2023. https://doi.org/10.1016/j.oceaneng.2022.113268.
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- Z. R. K., Alhachamı, Tamamlayıcı Fonksiyonlar Yöntemi ile Yanal Yüklü Kazıkların Statik Analizi, Yüksek Lisans Tezi, İstanbul Gelişim Üniversitesi, İstanbul, 2023.
Tamamlayıcı fonksiyonlar yöntemi ile yanal yüklü kazıkların statik analizi
Yıl 2025,
Cilt: 14 Sayı: 1, 1 - 1
Ahmad Reshad Noorı
,
Zahraa Razzaq Kareem Alhachami
,
Bilge Sultan Demirtaş
,
Suleiman Khatrush
Öz
Bu çalışmada, yanal yüklü kazıkların statik analizi için Tamamlayıcı Fonksiyonlar Yöntemi (TFY) uygulanmıştır. Olayı idare eden kanonik denklemler, ince çubuk teorisine göre elde edilerek TFY ile başlangıç değer problemine indirgenmiştir. Kazığın malzemesi izotropik homojen ve kesit geometrik özellikleri ise üniform olarak kabul edilmiştir. Zemin davranışını temsil eden yay modeli lineer ve nonlineer olarak ele alınmıştır. Ele alınan kazık problemler serbest uçlu ve sabit uçlu olarak çözülerek sınır koşullarının deplasmanlar ve iç kuvvetler üzerindeki etkisi araştırılmıştır. Yanal yatak katsayısı değerlerinin ve yatak katsayısı sabitinin kumlu zeminler için alacağı değerlerinin yanal yüklü kazıkların eğilme davranışı üzerindeki etkisi parametrik olarak sunulmuştur. Elde edilen sonuçlar daha önce yapılan araştırmaların sonuçları ile karşılaştırılmıştır ve uyum içinde olduğu görülmüştür.
Kaynakça
- A. B. Huang, C. K. Hsueh, M. W. O’Neill, S. Chern and C. Chen, Effects of construction on laterally loaded pile groups. Journal of Geotechnical and Geoenvironmental Engineering, 127(5), 385-397, 2001. https://doi.org/10.1061/(ASCE)1090-0241(2001)127:5(385).
- B. Tak Kim, N. K. Kim, W. Jin Lee and Y. Su Kim, Experimental load transfer curves of laterally loaded piles in Nak-Dong River sand. Journal of Geotechnical and Geoenvironmental Engineering, 130(4), 416-425, 2004.https://doi.org/10.1061/(ASCE)10900241(2004)130:4(416).
- B. D. Wesselink, J. D. Murff, M. F. Randolph, I. L. Nunez and A. M. Hyden, Analysis of centrifuge model test data from laterally loaded piles in calcareous sand. Engineering for Calcareous Sediments, 261-270, 1988. https://doi.org/10.1201/9781003211433-35.
- X. Tang and M. Yang, Analysis of laterally-loaded piles in weathered rock slopes based on p-y curve method. International Journal of Geotechnical Engineering, 14(7), 809-819, 2020. https://doi.org/10.1080/19386362.2018.1498199.
- C.C. Fan and J. H. Long, Assessment of existing methods for predicting soil response of laterally loaded piles in sand. Computers and Geotechnics, 32(4), 274-289, 2005. https://doi.org/10.1016/ j.compgeo.2005.02.004.
- M. Achmus, Design of axially and laterally loaded piles for the support of offshore wind energy converters. Proceedings of the Indian Geotechnical Conference GEOtrendz-2010, pp. 16-18, Mumbai, India, 2010.
- Y. Kim and S. Jeong, Analysis of soil resistance on laterally loaded piles based on 3D soil–pile interaction. Computers and Geotechnics, 38(2), 248-257, 2011. https://doi.org/ 10.1016/j.compgeo.2010.12.001.
- D. Basu, R. Salgado and M. Prezzi, A new model for analysis of laterally loaded piles. Geo-Frontiers 2011, American Society of Civil Engineers, 122-131, Reston, VA, 2011. https://doi.org/ 10.1061/41165(397)14.
- A. Ekici, Three dimensional finite element modeling for the laterally loaded passive pile behavior. Master Thesis, Middle East Technical University, Ankara, Türkiye, 2013.
- M. Heidari, H. El Naggar, M. Jahanandish and A. Ghahramani, Generalized cyclic p–y curve modeling for analysis of laterally loaded piles. Soil Dynamics and Earthquake Engineering, 63, 138-149, 2014. https://doi.org/10.1016/j.soıldyn.2014.04.001.
- M. Khari, K.A. Kassim and A. Adnan, Development of p-y curves of laterally loaded piles in cohesionless soil. The Scientific World Journal, 2014, 1-8, 2014. https://doi.org/10.1155/2014/917174.
- B. Fatahi, S. Basack, P. Ryan, W. H. Zhou and H. Khabbaz, Performance of laterally loaded piles considering soil and interface parameters. Geomechanics and Engineering, 7(5), 495-524, 2014. https://doi.org/10.12989/gae.2014.7.5.495.
- A. L. Rishitha, Numerical modelling of laterally loaded single pile. Ph.D. Thesis, Indian Institute of Technology Hyderabad, Telangana, India, 2015.
- K. Thieken, M. Achmus and K. Lemke, A new static p‐y approach for piles with arbitrary dimensions in sand. Geotechnik, 38(4), 267-288, 2015. https://doi.org/10.1002/gete.201400036.
- H. Lin, L. Ni, M. T. Suleiman and A. Raich, Interaction between laterally loaded pile and surrounding soil. Journal of Geotechnical and Geoenvironmental Engineering, 141(4), 04014119, 2014. https://doi.org/10.1061/(asce)gt.1943-5606.0001259.
- J. M. Mayoral, J .M. Pestana and R. B. Seed, Multi-directional cyclic p–y curves for soft clays. Ocean Engineering, 115, 1-18, 2016. https://doi.org/10.1016/j.oceaneng.2016.01.033.
- A. E. Haiderali and G. Madabhushi, Evaluation of curve fitting techniques in deriving p–y curves for laterally loaded piles. Geotechnical and Geological Engineering, 34(5), 1453-1473, 2016. https://doi.org/10.1007/s10706-016-0054-2.
- B. K. Gupta and D. Basu, Analysis of laterally loaded short and long piles in multilayered heterogeneous elastic soil. Soils and Foundations, 57(1), 92-110, 2017. https://doi.org/10.1016/j.sandf.2017.01.007.
- D. F. Turello, F. Pinto and P. J. Sánchez, Analysis of lateral loading of pile groups using embedded beam elements with interaction surface. International Journal for Numerical and Analytical Methods in Geomechanics, 43(1), 272-292, 2019. https://doi.org/10.1002/nag.2863.
- S. Stacul and N. Squeglia, Analysis method for laterally loaded pile groups using an advanced modeling of reinforced concrete sections. Materials. 11(2), 300, 2018. https://doi.org/10.3390/ma11020300.
- S. Nie, X. Zou and Q. He, A modified p-y curve method for offshore pile foundations under cyclic lateral loading in soft clay. Proceedings of the 2nd International Symposium on Asia Urban GeoEngineering, 485-496 Singapore, 2018. https://doi.org/10.1007/978-981-10-6632-0_37.
- D. Rathod, K. Muthukkumaran and T. G. Sitharam, Effect of slope on p-y curves for laterally loaded piles in soft clay. Geotechnical and Geological Engineering, 36(3), 1509-1524, 2018. https://doi.org/10.1007/s10706-017-0405-7.
- H. Li, L. Tong, S. Liu, H. Liu and M. Zhang, Construction and verification of a unified p–y curve for laterally loaded piles. Bulletin of Engineering Geology and the Environment, 77(3), 987-997, 2018. https://doi.org/10.1007/s10064-017-1111-7.
- S. H. Baek, J. Kim, S. H. Lee and C. K. Chung, Development of the cyclic p–y curve for a single pile in sandy soil. Marine Georesources & Geotechnology, 36(3), 351-359, 2018. https://doi.org/10.1080/1064119X.2017.1318986.
- W. Peng, M. Zhao, Y. Xiao, C. Yang and H. Zhao, Analysis of laterally loaded piles in sloping ground using a modified strain wedge model. Computers and Geotechnics, 107, 163-175, 2019. https://doi.org/10.1016/j.compgeo.2018.12.007.
- P. S. O. Kardogan, N. S. Isik, M. I. Onur and S. Bhattacharya, A study on the laterally loaded pile behaviour in liquefied soil using p-y method. IOP Conference Series: Materials Science and Engineering, 471, 042015, 2019. https://doi.org/10.1088/1757-899X/471/4/042015.
- B. Yuan, M. Sun, Y. Wang, L. Zhai, Q. Luo and X. Zhang, Full 3D displacement measuring system for 3d displacement field of soil around a laterally loaded pile in transparent soil. International Journal of Geomechanics, 19(5), 04019028, 2019. https://doi.org/10.1061/(ASCE)GM.19435622.0001409.
- S. Li, J. Yu, M. Huang and C. F. Leung, Application of T-EMSD based p-y curves in the three-dimensional analysis of laterally loaded pile in undrained clay. Ocean Engineering, 206, 107256, 2020. https://doi.org/10.1016/j.oceaneng.2020.107256.
- Y. Zhang, K. H. Andersen and P. Jeanjean, Verification of a framework for cyclic p-y curves in clay by hindcast of Sabine River, SOLCYP and centrifuge laterally loaded pile tests. Applied Ocean Research, 97, 102085, 2020. https://doi.org/10.1016/j.apor.2020.102085.
- G. Chortis, A. Askarinejad, L. J. Prendergast, Q. Li and K. Gavin, Influence of scour depth and type on p–y curves for monopiles in sand under monotonic lateral loading in a geotechnical centrifuge. Ocean Engineering, 197, 106838, 2020. https://doi.org/10.1016/j.oceaneng.2019.106838.
- D. Xu, X. Xu, W. Li and B. Fatahi, Field experiments on laterally loaded piles for an offshore wind farm. Marine Structures. 69, 102684, 2020. https://doi.org/10.1016/j.marstruc.2019.102684.
- L. Zdravković, D. M. G. Taborda, D. M. Potts, D. Abadias, H. J. Burd, B. W. Byrne, K. G. Gavin, G. T. Houlsby, R. J. Jardine, C. M. Martin, R. A. McAdam and E. Ushev, Finite-element modelling of laterally loaded piles in a stiff glacial clay till at Cowden. Géotechnique, 70(11), 999-1013, 2020. https://doi.org/10.1680/jgeot.18.PISA.005.
- X. Liu, G. Cai, L. Liu, S. Liu, W. Duan and A. J. Puppala, Improved p-y curve models for large diameter and super-long cast-in-place piles using piezocone penetration test data. Computers and Geotechnics, 130, 103911, 2021. https://doi.org/10.1016/ j.compgeo.2020.103911.
- B. Yuan, Z. Li, Z. Zhao, H. Ni, Z. Su and Z. Li, Experimental study of displacement field of layered soils surrounding laterally loaded pile based on transparent soil. Journal of Soils and Sediments, 21, 3072–3083, 2021. https://doi.org/10.1007/s11368-021-03004-y
- F. M. Bhuiyan, R. Motamed, R. V. Siddharthan and D. H. Sanders, Evaluation of a unified p-y method for lateral analysis of large-diameter drilled shafts using NVShaft. Transportation Geotechnics, 36, 100813, 2022. https://doi.org/10.1016/j.trgeo.2022.100813.
- F. Çelik, A comparative analytical ınvestigation on the effects of different p-y curves for a laterally loaded single pile design in saturated sandy soil. European Journal of Science and Technology (34), 474-478, 2022. https://doi.org/10.31590/ejosat.1082906.
- L. M. Lalicata, G. M. Rotisciani, A. Desideri and F. Casini, A numerical model to study the response of piles under lateral loading in unsaturated soils. Geosciences, 12(1), 1, 2021. https://doi.org/10.3390/geoscıences12010001.
- F. M. Bhuiyan, R. V. Siddharthan and R. Motamed, Evaluation of existing p-y models for caliche based on numerical analysis of raiders stadium lateral load tests. DFI 47th Annual Conference on Deep Foundations, pp. 297–309, National Harbor, Maryland, 2022. https://doi.org/10.5281/zenodo.7187512.
- P. A. Arvan and M. Arockiasamy, Energy-based approach: analysis of a laterally loaded pile in multi-layered non-linear elastic soil strata. Geotechnics, 570-598. 2(3), 570-598, 2022. https://doi.org/10.3390/geotechnıcs2030028.
- L. Pang, C. Jiang and L. Chen, Nonlinear predictive framework of the undrained clay slope effect on the ınitial stiffness of p-y curves of laterally loaded piles by FEM. Journal of Marine Science and Engineering, 10(11), 1684, 2022. https://doi.org/10.3390/jmse10111684.
- Z. Shi, L. Liu, M. Huang, K. Shen and B. Wang, Simulation of cyclic laterally-loaded piles in undrained clays accounting for soil small-strain characteristics. Ocean Engineering, 267, 113268, 2023. https://doi.org/10.1016/j.oceaneng.2022.113268.
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