Geomechanics and Engineering

  • 제39권2호
  • /
  • Pages.143-155
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  • 2024
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  • 2005-307X(pISSN)
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  • 2092-6219(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Fractional model and deformation of fiber-reinforced soil under traffic loads

  • Jiashun Liu (School of Civil Engineering, Liaoning Technical University) ;
  • Kaixin Zhu (School of Civil Engineering, Chongqing University) ;
  • Yanyan Cai (Tunnel and urban underground space engineering technology research center, Huaqiao University) ;
  • Shuai Pang (School of Civil Engineering, Liaoning Technical University) ;
  • Yantao Sheng (School of Civil Engineering, Liaoning Technical University)
  • 투고 : 2024.08.14
  • 심사 : 2024.09.27
  • 발행 : 2024.10.25
⟨ 이전 논문 다음 논문 ⟩

초록

Traffic-induced cyclic loading leads to the rotation of principal stresses within pavement foundations, challenging accurate simulation with conventional triaxial testing equipment. To investigate the deformation characteristics of fiber-reinforced soil under traffic loads and to develop a fractional-order model to describe these deformations. A series of hollow cylinder torsional shear tests were conducted using the GDS-SSHCA apparatus. The effects of fiber content, load frequency, cyclic deviatoric stress amplitude, and cyclic shear stress amplitude on soil deformation were analyzed. The results revealed that fiber content up to 3% enhances soil resistance to deformation, while higher fiber content reduces it. Axial cumulative plastic deformation decreases with higher load frequencies and increases with higher cyclic stresses. The study also found that principal stress rotation exacerbates soil deformation. A fractional integral model based on the Riemann-Liouville operator was developed to describe the axial cumulative plastic strain, with its validity confirmed by supplementary tests. This model provides a scientific basis for understanding foundation deformation under traffic loading and contributes to the development of dynamic constitutive soil models.

키워드

과제정보

This work was supported by the National Natural Science Foundation of China (Grant No. 52374091, 52104088, 51978292), the China Postdoctoral Science Foundation (Grant No. 2022M713383), the Open Research Fund of State Key Laboratory of Geomechanics and Geotechnical Engineering (Grant No. SKLGME022021), the Foundation of Liaoning province Department of Education (Grant No. LJKZ0361) and. The authors gratefully acknowledge the helpful comments made by the reviewers.

참고문헌

  1. Arikoglu, A. (2014), "A new fractional derivative model for linearly viscoelastic materials and parameter identification via genetic algorithms", Rheologica Acta, 53(3), 219-233. https://doi.org/10.1007/s00397-014-0758-2.
  2. ASTM. (2006), Standard Classification of Soils for Engineering Purposes (Unified Soil Classification System). West Conshohocken, PA: ASTM.
  3. An, N., Yan, C.G., Wang, Y.C. and Lan, H.X. (2014), "Experimental study on anti-erosion performance of polypropylene fiber-reinforced loess", Rock Soil Mech., 42(2), 501-510. https://doi.org/10.16285/j.rsm.2020.0879.
  4. Al-Bared, Harahap, I.S.H., Marto, A., Mohamad, H. Abad, S.V.A.N.K. and Mustaffa, Z. (2020), "Cyclic behavior of RT-cement treated marine clay subjected to low and high loading frequencies", Geomech. Eng., 21(5), 433-445. https://doi.org/10.12989/gae.2020.21.5.433.
  5. Ali1a, M., Aziz, M., Hamza1c, M. and Madni, M.F. (2020), "Engineering properties of expansive soil treated with polypropylene fibers", Geomech. Eng., 22(3), 227-236. https://doi.org/10.12989/gae.2020.22.3.227.
  6. Cai, Y., Zhao, L., Cao, Z., et al. (2017), "Experimental study on long-term dynamic characteristics of coarse-grained highway subgrade materials under cyclic loading at different frequencies", Chinese J. Rock Mech. Eng., 36(5), 1238-1246. https://doi.org/10.13722/j.cnki.jrme.2016.0947.
  7. Cai, Y.Y., Yu, J., Yu, H.S., Li, T. and Wanatowski, D. (2013), "Experimental study of deformation behaviour of sand under rotation of principal stress axes", Chinese J. Rock Mech. Eng., 32(2), 417-424. https://doi.org/10.1007/s00467-001-0757-2.
  8. Chai, J.C. and Miura, N. (2002), "Traffic-load-induced permanent deformation of road on soft subsoil", J. Geotech. Geoenviron. Eng., 128(11), 907-916. https://doi.org/10.1061/(ASCE)1090.
  9. Ding, J.W., Hu, L.M. and Zheng, W.T. (2012). "Study on simple shear tests for marine soft clay", Geotech. Investigat. Survey., 40(10), 22-26.
  10. Du, Z.B., Qian, J.G., Shi, Z.H., Guo, Y. and Huang, M. (2022), "Constitutive modeling for cyclic responses of saturated soft clay under principal stress rotation induced by wave loads", Ocean Eng. Adv., online publication. https://doi.org/10.1016/j.oceaneng.2022.111243.
  11. Fedakar, H.I., Cetin, B. and Rutherford, C.J. (2022), "Deformation characteristics of medium-dense sand-clay mixtures under a principal stress rotation", Transport. Geotech., 30, 100616. https://doi.org/10.1016/j.trgeo.2021.100616.
  12. Guo, L., Wang, J. and Cai, Y. (2013), "Undrained deformation behavior of saturated soft clay under long-term cyclic loading. " Soil Dyn. Earthq. Eng., 50, 28-37. https://doi.org/10.1016/j.soildyn.2013.01.029.
  13. Gray, D.H. and Ohashi, H. (1983), "Mechanics of fiber reinforcement in sand", J. Geotech. Eng., 109(3), 335-353. https://doi.org/10.1061/(ASCE)0733-9410(1983)109:3(335).
  14. He, Z.M., Wang, P.P. and Liu, Y.X. (2023), "Cumulative deformation prediction and microstructure change of coarse-grained soil under cyclic loading", Soil Dyn. Earthq. Eng., https://doi.org/10.1016/j.soildyn.2023.108136.
  15. Hu, P., Zhang, W.L., Yang, L.Q., Wei, C. and Zhao, Y.L. (2020), "Deformation behavior of fine sands under pure principal stress rotation", Build. Sci., 36(1), 34-40. https://doi.org/10.13614/j.cnki.11-1962/tu.2020.01.006.
  16. Hight, D.W., Symes, M.J. and Gens, A. (1984), "Undrained anisotropy and principal stress rotation in saturated sand", Geotechnique, 34(1), 355-383. https://doi.org/10.1016/0148-9062(84)90826-X.
  17. Toyota, H. and Takada, S. (2021), "Soil element assessment of cyclic-load-induced settlement considering the combination of vertical, horizontal, and shear stresses in cohesive soil", Soils Found., https://doi.org/10.1016/j.sandf.2021.02.007.
  18. Ishihara, K. and Towhata, I. (1983), "Sand response to cyclic rotation of principal stress directions as induced by wave loads", Soils Found., 23(4), 11-26. https://doi.org/10.3208/sandf1972.23.4_11.
  19. Inam, A., Ishikawa, T. and Miura, S. (2012), "Effect of principal stress axis rotation on cyclic plastic deformation characteristics of unsaturated base course material", Soils Found., 52(3), 465-480. https://doi.org/10.1016/j.sandf.2012.05.006.
  20. Kong, Y.X., Sheng, F.F. and Wang, H.J. (2018), "Stress-dilatancy properties for fiber-reinforced sand", Chinese J. Geotech. Eng., 40(12), 2249-2256. https://doi.org/10.11779/CJGE201812012.
  21. Kuang, Y., Chen, Y. and Dong, H. (2019), "Experimental study on dynamic response of soft clay under subway train load", Railway Standard Design, 63(11), 50-55. https://doi.org/10.13238/j.issn.1004-2954.201901140002.
  22. Lade, P.V. and Kirkgard, M.M. (2000), "Effects of stress rotation and changes of b-values on cross-anisotropic behavior of natural, k0-consolidated soft clay", Soils Found., 40(6), 93-105. https://doi.org/10.3208/sandf.40.6_93.
  23. Liu, Y., Luo, Q., Yang, X., Yuan, B., Luo, L. and Lai, M. (2019), Experimental study on dynamic deformation properties of muck soil under low frequency cyclic loading", J. Vibroeng., 21(4), 1215-1226. https://doi.org/10.21595/JVE.2019.20632.
  24. Liu, Z. and Xue, J. (2022), "The deformation characteristics of a kaolin clay under intermittent cyclic loadings", Soil Dyn. Earthq. Eng., 153, 107112. https://doi.org/10.1016/j.soildyn.2021.107112.
  25. Liu, J., Ren, Y., Zhu, K., Cai, Y., Zhang, H. and Jin, J. (2023), "Dynamic characteristics of freezing-thawing aeolian soil under intermittent cyclic loading", Int. J. Geomech., 23(10), 04023171. https://doi.org/10.1061/IJGNAI.GMENG-9523.
  26. Liu, J., Zhu, K., Sheng, Y., Wang, L., Xu, Y. and Pang, S. (2024), "Deformation characteristics and noncoaxial behavior of fiber-reinforced soil under pure principal stress axis rotation", Int. J. Geomech., 24(8), 04024164. https://doi.org/10.1061/IJGNAI.GMENG-9523.
  27. Liu, J.S., Zhang, X.D., Sun, J.B., Yang, J.J. and Fang, T.J. (2018), "Experimental study on the pore pressure and deformation of saturated silty clay under K0 consolidation and principal stress axis rotation", Rock Soil Mech., 39(8), 2787-2794+2804. https://doi.org/10.16285/j.rsm.2016.2474.
  28. Lei, H., Yang, X. and Feng, S. (2023), "Softening and deformation characteristics of Tianjin soft soil under principal stress rotation induced by traffic loading", Soil Dyn. Earthq. Eng., 164, 107587. https://doi.org/10.1016/j.soildyn.2022.107587.
  29. Liu, J., Otsubo, M., Kawaguchi, Y. and Kuwano, R. (2022), "Anisotropy in small-strain shear modulus of granular materials: Effects of particle properties and experimental conditions", Soils Found., 62(1), 101-105. https://doi.org/10.1016/j.sandf.2021.101105.
  30. Liu, J.S., Zhu, K.X., Shen, Y., Cai, Y.Y., Ren, Y. and Sheng, Y.T. (2022), "Experimental investigation on the deformation and noncoaxial characteristics of fiber-reinforced aeolian soil under traffic load", Int. J. Geomech., 22(5), 04022054-1-12. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002364.
  31. Mirzababaei, M., Arulrajah, A., Haque, A., Nimbalkar, S. and Mohajerani, A. (2018), "Effect of fiber reinforcement on shear strength and void ratio of soft clay", Geosynthetics Int., 25(4), 1-35. https://doi.org/10.1680/jgein.18.00023.
  32. Metzler, R. and Nonnenmacher, T.F. (2003), "Fractional relaxation processes and fractional rheological models for the description of a class of viscoelastic materials", Int. J. Plast., 19(7), 941-959. https://doi.org/10.1016/S0749-6419(02)00087-6.
  33. Monismith, C.L., Ogawa, N. and Freeme, C.R. (1975), "Permanent deformation characteristics of subgrade soils due to repeated loading", Transport. Res. Record J. Transport. Res. Board, (537), 1-17. http://onlinepubs.trb.org/Onlinepubs/trr/1975/537/537-001.pdf.
  34. Nakata, Y., Hyodo, M. and Murata, H. (1998), "Flow deformation of sands subjected to principal stress rotation", Soils Found., 38(2), 115-128. https://doi.org/10.3208/sandf.38.2_115.
  35. Okonta, F.N. and Nxumalo, S.P. (2022), "Strength properties of lime stabilized and fibre reinforced residual soil", Geomech. Eng., 28(1), 35-48. https://doi.org/ 10.12989/gae.2022.28.1.035.
  36. Prabakar, J. and Sridhar, R.S. (2002), "Effect of random inclusion of sisal fibre on strength behaviour of soil", Constr. Build. Mater., 16(2), 123-131. https://doi.org/10.1016/S0950-0618(02)00008-9.
  37. Qian, J.G., Wang, Y.G., Zhang, J.F. and Huang, M.S. (2013), "Undrained cyclic torsion shear tests on permanent deformation responses of soft saturated clay to traffic loadings", Chinese J. Geotech. Eng., 35(10), 1790-1798. https://doi.org/CNKI:SUN:YTGC.0.2013-10-005. 10-005
  38. Qian, J. G., Du, Z. B., Lu, X. L., Gu, X. and Huang, M. (2019), "Effects of principal stress rotation on stress-strain behaviors of saturated clay under traffic-load-induced stress path", Soils Found., 59(1), 41-55.
  39. Qian, J.G., Li, S. Y., Gu, X.Q. and Zhang, J. (2019), "A unified model for estimating the permanent deformation of sand under a large number of cyclic loads", Ocean Eng., 181, 293-302. https://doi.org/10.1016/j.oceaneng.2019.03.051.
  40. Rong, D.Z., Sheng, C.S., Zeng, H. and Cheng, Q. (2021), "Evaporation process and tensile behavior of fiber-reinforced rammed earth", Chinese J. Geotech. Eng., 43(4), 670-678. https://doi.org/10.11779/CJGE202104009.
  41. Ren, H.P., Liu, X.Z. and Xuan, M.M. (2021), "Study of cumulative plastic deformation of compacted silt under cyclic loading", Rock Soil Mech., 42(4), 1045-1055. https://doi.org/10.16285/j.rsm.2020.1198.
  42. Shen, Y., Tao, M.A., Wang, X. and Du, W.H. (2016), "An experimental study of the deformation and strength characteristics of soft clay under principal stress axis rotation caused by traffic load", Rock Soil Mech., https://doi.org/10.16285/j.rsm.2016.06.006.
  43. Sakai, A., Samang, L. and Miura, N. (2008), "Partially-drained cyclic behavior and its application to the settlement of a low embankment road on silty-clay", J. Jap. Geotech. Soc., 43(1), 33-46. https://doi.org/10.3208/sandf.43.33.
  44. Shang, Y.J. and Yao, Z.M. (2017), "Fractional order component model for accumulative deformation of clay under rotation of principal stress axes", Mech. Eng., 39(3), 268-273. https://doi.org/10.6052/1000-0879-16-313.
  45. Shen, Y., Du, W., Xu, J., Rui, X. and Liu, H. (2021), "Non-coaxiality of soft clay generated by principal stress rotation under high-speed train loading", Acta Geotechnica, (8). https://doi.org/10.1007/s11440-021-01242-5.
  46. Sujatha, E.R., Geetha, A.R., Jananee, R. and Karunya, S.R. (2018), "Strength and mechanical behaviour of coir reinforced lime stabilized soil", Geomech. Eng., 16(6), 627-634. https://doi.org/10.12989/gae.2018.16.6.627.
  47. Tong, Z.X., Zhang, J.M., Yu, Y.L. and Zhang, G. (2010), "Drained deformation behavior of anisotropic sands during cyclic rotation of principal stress axes", J. Geotech. Geoenviron. Eng., 136(11), 1509-1518. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000378.
  48. Tang, L.S., Chen, H.K., Sun, Y.L., Zhang, Q.H. and Liao, H.R. (2018), "Traffic-load-induced dynamic stress accumulation in subgrade and subsoil using small scale model tests", Geomech. Eng., 16(2), 113-124. https://doi.org/10.12989/gae.2018.16.2.113.
  49. Vu, A.T. (2021), "Shear strength behaviour of coral gravelly sand subjected to monotonic and cyclic loading", Geomech. Eng., 25(2), 89-98. https://doi.org/10.12989/gae.2021.25.2.089.
  50. Wang, Q., Zhong, X., Su, Y., et al. (2016), "Study on dynamic deformation characteristics of loess in Lanzhou subway under dynamic load", Modern Tunn. Technol., 53(6), 137-142. https://doi.org/10.13807/j.cnki.mtt.2016.06.019
  51. Wang, Y.K., Gao, Y., Guo, L., Cai, Y., Li, B. and Qiu, Y. (2017), "Cyclic response of natural soft marine clay under principal stress rotation as induced by wave loads", Ocean Eng., 129, 191-202. https://doi.org/10.1016/j.oceaneng.2016.11.031.
  52. Weng, X.L., Hao, L.I., Shang, X.W. and Jia, Y. (2019), "Deformation properties of remolded loess under cyclic loading", J. Traffic Transport. Eng., 19(3), 10-18. https://doi.org/10.19818/j.cnki.1671-1637.2019.03.002.
  53. Wu, T.Y., Guo, L., Cai, Y.Q. and Wang, J. (2017), "Deformation behavior of K0-consolidated soft clay under traffic load-induced stress paths", Chinese J. Geotech. Eng., 39(5), 859-867. https://doi.org/10.11779/CJGE201705010.
  54. Xiao, J., Jang, C.H., Wei, K. and Xu, S. (2014), "Effects of principal stress rotation on the cumulative deformation of normally consolidated soft clay under subway traffic loading", J. Geotech. Geoenviron. Eng., 140(4), 1-9. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001069.
  55. Yang, Z.X., Li, X.S. and Yang, J. (2007), "Undrained anisotropy and rotational shear in granular soil", Geotechnique, 57(4), 371-384. https://doi.org/10.1680/geot.2007.57.4.371.
  56. Yang, Y.H., Cheng, S.G., Gu, J.Y. and Hu, X.H. (2011), "Triaxial tests research on strength properties of the polypropylene fiber reinforced soil", Proceedings of the IEEE International Conference on Multimedia Technology (ICMT), Hangzhou, China. https://doi.org/10.1109/ICMT.2011.6003219
  57. Yao, Z.M., Huang, M.S. and Cao, J. (2012), "Cumulative deformation of saturated soft clay subjected to cyclic rotation of principal stress axis", Chinese J. Geotech. Eng., 34(6), 1005-1012.
  58. Zhao, F.T. and Zheng, Y.W. (2022), "Shear strength behavior of fiber-reinforced soil: Experimental investigation and prediction model", Int. J. Geomech., 22(9), 04022146. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002502.
  59. Zhang, X., Zhao, C. and Zhai, W. (2019), "Importance of load frequency in applying cyclic loads to investigate ballast deformation under high-speed train loads", Soil Dyn. Earthq. Eng., 120, 28-38. https://doi.org/10.1016/j.soildyn.2019.01.023.
  60. Zhu, K.X. (2023), "Research on mechanical properties of fiber fiber-reinforced aeolian soil considering the main stress direction", Liaoning Technical University. https://doi.org/10.27210/d.cnki.glnju.2023.000759.
  61. Zhong, Z., Wang, S., Liu, X., Wu, B. and Chen, B. (2021), "Influences of principal stress rotation (PSR) on the cumulative deformation of remoulded loess with different water contents under traffic loading", Eur. J. Environ. Civil Eng., 25(12), 2301-2316. https://doi.org/10.1080/19648189.2019.1626289.