Geomechanics and Engineering

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Influence of moisture content on main mechanical properties of expansive soil and deformation of non-equal-length double-row piles: A case study

  • Wei, Meng (State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu University of Technology) ;
  • Liao, Fengfan (State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu University of Technology) ;
  • Zhou, Kerui (State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu University of Technology) ;
  • Yan, Shichun (State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu University of Technology) ;
  • Liu, Jianguo (China Railway Eryuan Engineering Group. Co. Ltd) ;
  • Wang, Peng (Sichuan Institute of Building Research. Co. Ltd)
  • Received : 2021.06.01
  • Accepted : 2022.06.07
  • Published : 2022.07.25
⟨ Previous Next ⟩

Abstract

The mechanical properties of expansive soil are very unstable, highly sensitive to water, and thus easy to cause major engineering accidents. In this paper, the expansive soil foundation pit project of the East Huada Square in the eastern suburb of Chengdu was studied, the moisture content of the expansive soil was considered as an important factor that affecting the mechanics properties of expansive soil and the stability of the non-equal-length double-row piles in the foundation pit support. Three groups of direct shear tests were carried out and the quantitative relationships between the moisture content and shear strength τ, cohesion c, internal friction angle φ were obtained. The effect of cohesion and internal friction angle on the maximum displacement and the maximum bending moment of piles were analyzed by the finite element software MIDAS/GTS (Geotechnical and Tunnel Analysis System). Results show that the higher the moisture content, the smaller the matrix suction, and the smaller the shear strength; the cohesion and the internal friction angle are exponentially related to the moisture content, and both are negatively correlated. The maximum displacement and the maximum bending moment of the non-equal length double-row piles decrease with the increase of the cohesion and the internal friction angle. When the cohesion is greater than 33 kPa or the internal friction angle is greater than 25.5°, the maximum displacement and maximum bending moment of the piles are relatively small, however, once crossing the points (the corresponding moisture content value is 24.4%), the maximum displacement and the maximum bending moment will increase significantly. Therefore, in order to ensure the stability and safety of the foundation pit support structure of the East Huada Square, the moisture content of the expansive soil should not exceed 24.4%.

Keywords

Acknowledgement

This work was sponsored by the National Natural Science Foundation of China (No. 41572358).

References

  1. Adamian, A., Safari, K.H., Sheikholeslami, M., Habibi, M., AlFurjan, M. and Chen, G. (2020), "Critical temperature and frequency characteristics of GPLs-reinforced composite Doubly curved panel", Appl. Sci., 10(9), 3251. https://doi.org/10.3390/app10093251.
  2. Ahmed, R.A., Fenjan, R.M. and Faleh, N.M. (2019), "Analyzing post-buckling behavior of continuously graded FG nanobeams with geometrical imperfections", Geomech. Eng., 17(2), 175-180. https://doi.org/10.12989/gae.2019.17.2.175.
  3. Al-Furjan, M., Dehini, R., Khorami, M., Habibi, M. and won Jung, D. (2020a), "On the dynamics of the ultra-fast rotating cantilever orthotropic piezoelectric nanodisk based on nonlocal strain gradient theory", Compos. Struct., 112990. https://doi.org/10.1016/j.compstruct.2020.112990.
  4. Al-Furjan, M., Fereidouni, M., Habibi, M., Abd Ali, R., Ni, J. and Safarpour, M. (2020b), "Influence of in-plane loading on the vibrations of the fully symmetric mechanical systems via dynamic simulation and generalized differential quadrature framework", Eng. with Comput., 1-23. https://doi.org/10.1007/s00366-020-01177-7
  5. Al-Furjan, M., Fereidouni, M., Sedghiyan, D., Habibi, M. and Won Jung, D. (2020c), "Three-dimensional frequency response of the CNT-Carbon-Fiber reinforced laminated circular/annular plates under initially stresses", Compos. Struct., 257, 113146. https://doi.org/10.1016/j.compstruct.2020.113146.
  6. Al-Furjan, M., Habibi, M., Shan, L. and Tounsi, A. (2021), "On the vibrations of the imperfect sandwich higher-order disk with a lactic core using generalize differential quadrature method", Compos. Struct., 257, 113150. https://doi.org/10.1016/j.compstruct.2020.113150.
  7. Al-Furjan, M., Habibi, M., won Jung, D. and Safarpour, H. (2020d), "Vibrational characteristics of a higher-order laminated composite viscoelastic annular microplate via modified couple stress theory", Compos. Struct., 113152. https://doi.org/10.1016/j.compstruct.2020.113152.
  8. Al-Furjan, M., Moghadam, S.A., Dehini, R., Shan, L., Habibi, M. and Safarpour, H. (2020e), "Vibration control of a smart shell reinforced by graphene nanoplatelets under external load: Semi-numerical and finite element modeling", Thin-Wall. Struct., 107242. https://doi.org/10.1016/j.tws.2020.107242.
  9. Al-Furjan, M., Oyarhossein, M.A., Habibi, M., Safarpour, H. and Jung, D.W. (2020f), "Frequency and critical angular velocity characteristics of rotary laminated cantilever microdisk via twodimensional analysis", Thin-Wall. Struct., 157, 107111. https://doi.org/10.1016/j.tws.2020.107111.
  10. Ali, A., Zhang, C., Bibi, T., Zhu, L., Cao, L., Li, C. and Hsiao, P.-C. (2022), "Investigation of five different low-cost locally available isolation layer materials used in sliding base isolation systems", Soil Dyn. Earthq. Eng., 154, 107127. https://doi.org/10.1016/j.soildyn.2021.107127.
  11. Alias, R., Kasa, A. and Taha, M. (2014), "Particle size effect on shear strength of granular materials in direct shear test", Int. J. Civil Environ. Eng., 8(11), 1144-1147. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000931.
  12. Alipour, M., Torabi, M.A., Sareban, M., Lashini, H., Sadeghi, E., Fazaeli, A., Habibi, M. and Hashemi, R. (2020), "Finite element and experimental method for analyzing the effects of martensite morphologies on the formability of DP steels", Mech. Based Des. Struct., 48(5), 525-541. https://doi.org/10.1080/15397734.2019.1633343.
  13. Allam, O., Draiche, K., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H., Mahmoud, S., Bedia, E.A. and Tounsi, A. (2020), "A generalized 4-unknown refined theory for bending and free vibration analysis of laminated composite and sandwich plates and shells", Comput. Concrete, 26(2), 185-201. https://doi.org/10.12989/cac.2020.26.2.185.
  14. Asgari, G., Payganeh, G. and Fard, K.M. (2019), "Dynamic instability and free vibration behavior of three-layered soft-cored sandwich beams on nonlinear elastic foundations", Struct. Eng. Mech., 72(4), 525-540. https://doi.org/10.12989/sem.2019.72.4.525.
  15. Bai, Y., Alzahrani, B., Baharom, S. and Habibi, M. (2020), "Semi-numerical simulation for vibrational responses of the viscoelastic imperfect annular system with honeycomb core under residual pressure", Eng. with Comput., 1-26. https://doi.org/10.1007/s00366-020-01191-9.
  16. Bakoura, A., Bourada, F., Bousahla, A.A., Tounsi, A., Benrahou, K.H., Tounsi, A., Al-Zahrani, M.M. and Mahmoud, S. (2021), "Buckling analysis of functionally graded plates using HSDT in conjunction with the stress function method", Comput. Concrete, 27(1), 73-83. https://doi.org/10.12989/cac.2021.27.1.073.
  17. Bekkaye, T.H.L., Fahsi, B., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H., Tounsi, A. and Al-Zahrani, M.M. (2020), "Porosity-dependent mechanical behaviors of FG plate using refined trigonometric shear deformation theory", Comput. Concrete, 26(5), 439-450. https://doi.org/10.12989/cac.2020.26.5.439.
  18. Boulefrakh, L., Hebali, H., Chikh, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S. (2019), "The effect of parameters of visco-Pasternak foundation on the bending and vibration properties of a thick FG plate", Geomech. Eng., 18(2), 161-178. https://doi.org/10.12989/gae.2019.18.2.161.
  19. Chen, F.X., Zhong, Y.C., Gao, X.Y., Jin, Z.Q., Wang, E.D., Zhu, F.P., Shao, X.X. and He, X.Y. (2021a), "Non-uniform model of relationship between surface strain and rust expansion force of reinforced concrete", Scientific Reports, 11(1), 1-9. https://doi.org/10.1038/s41598-021-88146-2.
  20. Chen, F., Chen, J., Duan, R., Habibi, M. and Khadimallah, M.A. (2022), "Investigation on dynamic stability and aeroelastic characteristics of composite curved pipes with any yawed angle", Compos. Struct., 115195. https://doi.org/10.1016/j.compstruct.2022.115195.
  21. Chen, F., Jin, Z., Wang, E., Wang, L., Jiang, Y., Guo, P., Gao, X. and He, X. (2021b), "Relationship model between surface strain of concrete and expansion force of reinforcement rust", Scientific Reports. 11(1), 1-11. https://doi.org/10.1038/s41598-021-83376-w
  22. Cheshmeh, E., Karbon, M., Eyvazian, A., Jung, D.w., Habibi, M. and Safarpour, M. (2020), "Buckling and vibration analysis of FG-CNTRC plate subjected to thermo-mechanical load based on higher order shear deformation theory", Mech. Based Des. Struct., 1-24. https://doi.org/10.1080/15397734.2020.1744005.
  23. Chikr, S.C., Kaci, A., Bousahla, A.A., Bourada, F., Tounsi, A., Bedia, E., Mahmoud, S., Benrahou, K.H. and Tounsi, A. (2020), "A novel four-unknown integral model for buckling response of FG sandwich plates resting on elastic foundations under various boundary conditions using Galerkin's approach", Geomech. Eng., 21(5), 471-487. https://doi.org/10.12989/gae.2020.21.5.471.
  24. Dai, H. and Safarpour, H. (2021), "Frequency and thermal buckling information of laminated composite doubly curved open nanoshell", Adv. Nano Res., 10(1), 1-14. https://doi.org/10.12989/anr.2021.10.1.001
  25. Dai, Z., Jiang, Z., Zhang, L. and Habibi, M. (2021a), "Frequency characteristics and sensitivity analysis of a size-dependent laminated nanoshell", Adv. Nano Res., 10(2), 175. https://doi.org/10.12989/anr.2021.10.2.175.
  26. Dai, Z., Zhang, L., Bolandi, S.Y. and Habibi, M. (2021b), "On the vibrations of the non-polynomial viscoelastic composite open-type shell under residual stresses", Compos. Struct., 113599. https://doi.org/10.1016/j.compstruct.2021.113599.
  27. Dong, Y., Gao, Y., Zhu, Q., Moradi, Z. and Safa, M. (2022), "TEGDQE implementation to investigate the vibration of FG composite conical shells considering a frequency controller solid ring", Eng. Anal. Bound. Elem., 138, 95-107. https://doi.org/10.1016/j.enganabound.2022.01.017.
  28. Ebrahimi, F., Habibi, M. and Safarpour, H. (2019a), "On modeling of wave propagation in a thermally affected GNP-reinforced imperfect nanocomposite shell", Eng. with Comput., 35(4), 1375-1389. https://doi.org/10.1007/s00366-018-0669-4.
  29. Ebrahimi, F., Hajilak, Z.E., Habibi, M. and Safarpour, H. (2019b), "Buckling and vibration characteristics of a carbon nanotube-reinforced spinning cantilever cylindrical 3D shell conveying viscous fluid flow and carrying spring-mass systems under various temperature distributions", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 233(13), 4590-4605. https://doi.org/10.1177/0954406219832323.
  30. Ebrahimi, F., Hashemabadi, D., Habibi, M. and Safarpour, H. (2019c), "Thermal buckling and forced vibration characteristics of a porous GNP reinforced nanocomposite cylindrical shell", Microsystem Technologies. 1-13.
  31. Ebrahimi, F., Hashemabadi, D., Habibi, M. and Safarpour, H. (2020a), "Thermal buckling and forced vibration characteristics of a porous GNP reinforced nanocomposite cylindrical shell", Microsyst. Technol., 26(2), 461-473. https://doi.org/10.1007/s00542-019-04542-9.
  32. Ebrahimi, F., Hosseini, S.H.S. and Selvamani, R. (2020b), "Thermo-electro-elastic nonlinear stability analysis of viscoelastic double-piezo nanoplates under magnetic field", Struct. Eng. Mech., 73(5), 565-584. https://doi.org/10.12989/sem.2020.73.5.565.
  33. Ebrahimi, F., Mohammadi, K., Barouti, M.M. and Habibi, M. (2019d), "Wave propagation analysis of a spinning porous graphene nanoplatelet-reinforced nanoshell", Waves in random Complex Media. 1-27. https://doi.org/10.1080/17455030.2019.1694729.
  34. Ebrahimi, F., Seyfi, A., Dabbagh, A. and Tornabene, F. (2019e), "Wave dispersion characteristics of porous graphene platelet-reinforced composite shells", Struct. Eng. Mech., 71(1), 99-107. https://doi.org/10.12989/sem.2019.71.1.099.
  35. Ebrahimi, F., Supeni, E.E.B., Habibi, M. and Safarpour, H. (2020c), "Frequency characteristics of a GPL-reinforced composite microdisk coupled with a piezoelectric layer", Eur. Phys. J. Plus, 135(2), 144. https://doi.org/10.1140/epjp/s13360-020-00217-x.
  36. El-Hassar, S.M., Benyoucef, S., Heireche, H. and Tounsi, A. (2016), "Thermal stability analysis of solar functionally graded plates on elastic foundation using an efficient hyperbolic shear deformation theory", Geomech. Eng., 10(3), 357-386. https://doi.org/10.12989/gae.2016.10.3.357.
  37. Esmailpoor Hajilak, Z., Pourghader, J., Hashemabadi, D., Sharifi Bagh, F., Habibi, M. and Safarpour, H. (2019), "Multilayer GPLRC composite cylindrical nanoshell using modified strain gradient theory", Mech. Based Des. Struct., 47(5), 521-545. https://doi.org/10.1080/15397734.2019.1566743.
  38. Fahsi, A., Tounsi, A., Hebali, H., Chikh, A., Adda Bedia, E. and Mahmoud, S. (2017), "A four variable refined nth-order shear deformation theory for mechanical and thermal buckling analysis of functionally graded plates", Geomech. Eng., 13(3), 385-410. https://doi.org/10.12989/gae.2017.13.3.385.
  39. Farokhian, A. and Kolahchi, R. (2020), "Frequency and instability responses in nanocomposite plate assuming different distribution of CNTs", Struct. Eng. Mech., 73(5), 555-563. https://doi.org/10.12989/sem.2020.73.5.555.
  40. Feng, J., Chen, B., Sun, W. and Wang, Y. (2021), "Microbial induced calcium carbonate precipitation study using Bacillus subtilis with application to self-healing concrete preparation and characterization", Constr. Build. Mater., 280 122460. https://doi.org/10.1016/j.conbuildmat.2021.122460
  41. Forsat, M., Musharavati, F., Eltai, E., Zain, A.M., Mobayen, S. and Mohamed, A.M. (2021), "Vibration characteristics of microplates with GNPs-reinforced epoxy core bonded to piezoelectric-reinforced CNTs patches", Adv. Nano Res., 11(2), 115-140. https://doi.org/10.12989/anr.2021.11.2.115.
  42. Gao, Y., Sun, D.A. and Wu, Y. (2018), "Volume change behaviour of unsaturated compacted weakly expansive soils", Bull. Eng. Geol. Environ., 77(2), 837-848. https://doi.org/10.1007/s10064-017-1142-0.
  43. Ghamkhar, M., Khadimallah, M.A., Iqbal, M.Z., Hussain, M., Yahya, A., Khedher, K.M., Naeem, M.N. and Tounsi, A. (2021), "Performance of FGM bilayered cylindrical shell placed on cantilever edge", Adv. Nano Res., 11(4), 339-345. https://doi.org/10.12989/anr.2021.11.4.339.
  44. Ghazanfari, A., Soleimani, S.S., Keshavarzzadeh, M., Habibi, M., Assempuor, A. and Hashemi, R. (2020), "Prediction of FLD for sheet metal by considering through-thickness shear stresses", Mech. Based Des. Struct., 48(6), 755-772. https://doi.org/10.1080/15397734.2019.1662310.
  45. Guellil, M., Saidi, H., Bourada, F., Bousahla, A.A., Tounsi, A., Al-Zahrani, M.M., Hussain, M. and Mahmoud, S. (2021), "Influences of porosity distributions and boundary conditions on mechanical bending response of functionally graded plates resting on Pasternak foundation", Steel Compos. Struct., 38(1), 1-15. https://doi.org/10.12989/scs.2021.38.1.001.
  46. Guo, J., Baharvand, A., Tazeddinova, D., Habibi, M., Safarpour, H., Roco-Videla, A. and Selmi, A. (2021a), "An intelligent computer method for vibration responses of the spinning multilayer symmetric nanosystem using multi-physics modeling", Eng. with Comput., 1-22. https://doi.org/10.1007/s00366-021-01433-4.
  47. Guo, Y., Mi, H. and Habibi, M. (2021b), "Electromechanical energy absorption, resonance frequency, and low-velocity impact analysis of the piezoelectric doubly curved system", Mech. Syst. Signal Pr., 157 107723. https://doi.org/10.1016/j.ymssp.2021.107723
  48. Habibi, M., Darabi, R., Sa, J.C.D. and Reis, A. (2021), "An innovation in finite element simulation via crystal plasticity assessment of grain morphology effect on sheet metal formability", Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, 235(8), 1937-1951. https://doi.org/10.1177/14644207211024686.
  49. Habibi, M., Ghazanfari, A., Assempour, A., Naghdabadi, R. and Hashemi, R. (2017), "Determination of forming limit diagram using two modified finite element models", Mech. Eng., 48(4), 141-144. https://doi.org/10.22060/MEJ.2016.664.
  50. Habibi, M., Hashemabadi, D. and Safarpour, H. (2019a), "Vibration analysis of a high-speed rotating GPLRC nanostructure coupled with a piezoelectric actuator", Eur. Phys. J. Plus, 134(6), 307. https://doi.org/10.1140/epjp/i2019-12742-7.
  51. Habibi, M., Hashemi, R., Ghazanfari, A., Naghdabadi, R. and Assempour, A. (2018a), "Forming limit diagrams by including the M-K model in finite element simulation considering the effect of bending", Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, 232(8), 625-636. https://doi.org/10.1177/1464420716642258.
  52. Habibi, M., Hashemi, R., Sadeghi, E., Fazaeli, A., Ghazanfari, A. and Lashini, H. (2016), "Enhancing the mechanical properties and formability of low carbon steel with dual-phase microstructures", J. Mater. Eng. Perform., 25(2), 382-389. https://doi.org/10.1007/s11665-016-1882-1.
  53. Habibi, M., Hashemi, R., Tafti, M.F. and Assempour, A. (2018b), "Experimental investigation of mechanical properties, formability and forming limit diagrams for tailor-welded blanks produced by friction stir welding", J. Manufact. Processes, 31, 310-323. https://doi.org/10.1016/j.jmapro.2017.11.009.
  54. Habibi, M., Mohammadgholiha, M. and Safarpour, H. (2019b), "Wave propagation characteristics of the electrically GNP-reinforced nanocomposite cylindrical shell", J. Braz. Soc. Mech. Sci. Eng., 41(5), 221. https://doi.org/10.1007/s40430-019-1715-x.
  55. Habibi, M., Mohammadi, A., Safarpour, H. and Ghadiri, M. (2019c), "Effect of porosity on buckling and vibrational characteristics of the imperfect GPLRC composite nanoshell", Mech. Based Des. Struct., 811-840. https://doi.org/10.1080/15397734.2019.1701490.
  56. Habibi, M., Mohammadi, A., Safarpour, H., Shavalipour, A. and Ghadiri, M. (2019d), "Wave propagation analysis of the laminated cylindrical nanoshell coupled with a piezoelectric actuator", Mech. Based Des. Struct., 1-19. https://doi.org/10.1080/15397734.2019.1697932.
  57. Habibi, M., Safarpour, M. and Safarpour, H. (2020), "Vibrational characteristics of a FG-GPLRC viscoelastic thick annular plate using fourth-order Runge-Kutta and GDQ methods", Mech. Based Des. Struct., 1-22. https://doi.org/10.1080/15397734.2020.1779086
  58. Habibi, M., Taghdir, A. and Safarpour, H. (2019e), "Stability analysis of an electrically cylindrical nanoshell reinforced with graphene nanoplatelets", Compos. Part B: Eng., 175, 107125. https://doi.org/10.1016/j.compositesb.2019.107125.
  59. Hachemi, H., Bousahla, A.A., Kaci, A., Bourada, F., Tounsi, A., Benrahou, K.H., Tounsi, A., Al-Zahrani, M.M. and Mahmoud, S. (2021), "Bending analysis of functionally graded plates using a new refined quasi-3D shear deformation theory and the concept of the neutral surface position", Steel Compos. Struct., 39(1), 51-64. https://doi.org/10.12989/scs.2021.39.1.051.
  60. Hadji, L. and Avcar, M. (2021), "Nonlocal free vibration analysis of porous FG nanobeams using hyperbolic shear deformation beam theory", Adv. Nano Res., 10(3), 281-293. https://doi.org/10.12989/cac.2020.26.3.213.
  61. Hashemi, H.R., Alizadeh, A.A., Oyarhossein, M.A., Shavalipour, A., Makkiabadi, M. and Habibi, M. (2019), "Influence of imperfection on amplitude and resonance frequency of a reinforcement compositionally graded nanostructure", Waves Random Complex Media, 1-27. https://doi.org/10.1080/17455030.2019.1662968.
  62. He, X., Ding, J., Habibi, M., Safarpour, H. and Safarpour, M. (2021), "Non-polynomial framework for bending responses of the multi-scale hybrid laminated nanocomposite reinforced circular/annular plate", Thin-Wall. Struct., 166, 108019. https://doi.org/10.1016/j.tws.2021.108019.
  63. Hou, F., Wu, S., Moradi, Z. and Shafiei, N. (2021), "The computational modeling for the static analysis of axially functionally graded micro-cylindrical imperfect beam applying the computer simulation", Eng. with Comput., 1-19. https://doi.org/10.1007/s00366-021-01456-x.
  64. Huang, H., Huang, M., Zhang, W., Pospisil, S. and Wu, T. (2020), "Experimental investigation on rehabilitation of corroded RC columns with BSP and HPFL under combined loadings", J. Struct. Eng., 146(8), 04020157. 10.1061/(ASCE)ST.1943-541X.0002725.
  65. Huang, H., Huang, M., Zhang, W. and Yang, S. (2021a), "Experimental study of predamaged columns strengthened by HPFL and BSP under combined load cases", Struct. Infrastruct. Eng., 17(9), 1210-1227. https://doi.org/10.1080/15732479.2020.1801768.
  66. Huang, X., Hao, H., Oslub, K., Habibi, M. and Tounsi, A. (2021b), "Dynamic stability/instability simulation of the rotary size-dependent functionally graded microsystem", Eng. with Comput., 1-17. https://doi.org/10.1007/s00366-021-01399-3.
  67. Huang, X., Zhang, Y., Moradi, Z. and Shafiei, N. (2021c), "Computer simulation via a couple of homotopy perturbation methods and the generalized differential quadrature method for nonlinear vibration of functionally graded non-uniform microtube", Eng. with Comput., 1-18. https://doi.org/10.1007/s00366-021-01395-7.
  68. Huang, X., Zhu, Y., Vafaei, P., Moradi, Z. and Davoudi, M. (2021d), "An iterative simulation algorithm for large oscillation of the applicable 2D-electrical system on a complex nonlinear substrate", Eng. with Comput., https://doi.org/10.1007/s00366-021-01320-y.
  69. Issad, M.N., Fekrar, A., Bakora, A., Bessaim, A. and Tounsi, A. (2018), "Free vibration and buckling analysis of orthotropic plates using a new two variable refined plate theory", Geomech. Eng., 15(1), 711-719. https://doi.org/10.12989/gae.2018.15.1.711.
  70. Jiao, J., Ghoreishi, S.-m., Moradi, Z. and Oslub, K. (2021), "Coupled particle swarm optimization method with genetic algorithm for the static-dynamic performance of the magneto-electro-elastic nanosystem", Eng. with Comput., https://doi.org/10.1007/s00366-021-01391-x.
  71. Karami, B., Janghorban, M. and Tounsi, A. (2019a), "Galerkin's approach for buckling analysis of functionally graded anisotropic nanoplates/different boundary conditions", Eng. with Comput., 35(4), 1297-1316. https://doi.org/10.1007/s00366-018-0664-9.
  72. Karami, B., Janghorban, M. and Tounsi, A. (2019b), "On pre-stressed functionally graded anisotropic nanoshell in magnetic field", J. Braz. Soc. Mech. Sci. Eng., 41(11), 1-17. https://doi.org/10.1007/s40430-019-1996-0.
  73. Karami, B., Janghorban, M. and Tounsi, A. (2019c), "Wave propagation of functionally graded anisotropic nanoplates resting on Winkler-Pasternak foundation", Struct. Eng. Mech., 70(1), 55-66. https://doi.org/10.12989/sem.2019.70.1.055.
  74. Khadimallah, M.A., Hussain, M., Naeem, M.N., Taj, M. and Tounsi, A. (2021a), "Monitoring and control of multiple fraction laws with ring based composite structure", Adv. Nano Res., 10(2), 129-138. https://doi.org/10.12989/anr.2021.10.2.129.
  75. Khadimallah, M.A., Hussain, M., Taj, M., Ayed, H. and Tounsi, A. (2021b), "Parametric vibration analysis of single-walled carbon nanotubes based on Sanders shell theory", Adv. Nano Res., 10(2), 165-174. https://doi.org/10.12989/anr.2021.10.2.165.
  76. Kumar, Y., Gupta, A. and Tounsi, A. (2021), "Size-dependent vibration response of porous graded nanostructure with FEM and nonlocal continuum model", Adv. Nano Res., 11(1), 1-17. https://doi.org/10.12989/anr.2021.11.1.001.
  77. Lan, Z., Zhao, Y., Zhang, J., Jiao, R., Khan, M.N., Sial, T.A. and Si, B. (2021), "Long-term vegetation restoration increases deep soil carbon storage in the Northern Loess Plateau", Scientific Reports, 11(1), 1-11. https://doi.org/10.1038/s41598-021-93157-0.
  78. Li, J., Tang, F. and Habibi, M. (2020a), "Bi-directional thermal buckling and resonance frequency characteristics of a GNP-reinforced composite nanostructure", Eng. with Comput., 1-22. https://doi.org/10.1007/s00366-020-01110-y.
  79. Li, X., Wang, Y., Hu, Y., Zhou, C. and Zhang, H. (2022), "Numerical investigation on stratum and surface deformation in underground phosphorite mining under different mining methods", Front. Earth Sci., 10. https://doi.org/10.3389/feart.2022.831856.
  80. Li, Y., Li, S., Guo, K., Fang, X. and Habibi, M. (2020b), "On the modeling of bending responses of graphene-reinforced higher order annular plate via two-dimensional continuum mechanics approach", Eng. with Comput., 1-22. https://doi.org/10.1007/s00366-020-01166-w.
  81. Lin, P., Wang, Y.F., Fan, Z.X. and Huang, D.Y. (2010), "Application and analysis of retaining structure with double-row piles in soft ground excavation engineering", Chinese J. Geotech. Eng., 2, 331-334. https://doi.org/10.2134/agronmonogr44.c26.
  82. Liu, H., Shen, S., Oslub, K., Habibi, M. and Safarpour, H. (2021a), "Amplitude motion and frequency simulation of a composite viscoelastic microsystem within modified couple stress elasticity", Eng. with Comput., 1-15. https://doi.org/10.1007/s00366-021-01316-8.
  83. Liu, H. and Yin, Z. (2010), "Test study of influence of crack evolution on strength parameters of expansive soil", Rock Soil Mech., 31(3), 727-731. https://doi.org/10.1016/j.conbuildmat.2016.12.030.
  84. Liu, H., Zhao, Y., Pishbin, M., Habibi, M., Bashir, M. and Issakhov, A. (2021b), "A comprehensive mathematical simulation of the composite size-dependent rotary 3D microsystem via two-dimensional generalized differential quadrature method", Eng. with Comput., 1-16. https://doi.org/10.1007/s00366-021-01419-2.
  85. Liu, J.L., Wang, J.L. and Yuan, F.F. (2010), "Influence of layout style on soil arching effect of double-row anti-slide piles", J. Graduate School of the Chinese Academy of Sciences, 27(3), 364-369. https://doi.org/10.1177/1687814017727940.
  86. Liu, J., Shi, B., Jiang, H., Huang, H., Wang, G. and Kamai, T. (2011), "Research on the stabilization treatment of clay slope topsoil by organic polymer soil stabilizer", Eng. Geol., 117(1-2), 114-120. https://doi.org/10.1016/j.enggeo.2010.10.011.
  87. Liu, Y., Wang, C., Liu, X., Gao, R., Li, B. and Khan, K.U.J. (2021c), "Determination of embedded depth of soldier piles in pile-anchor supporting system in granite residual soil area", Geofluids, 2021. https://doi.org/10.1155/2021/5518233.
  88. Liu, Y., Wang, W., He, T., Moradi, Z. and Larco Benitez, M.A. (2021d), "On the modelling of the vibration behaviors via discrete singular convolution method for a high-order sector annular system", Eng. with Comput., 1-23.
  89. Liu, Z., Su, S., Xi, D. and Habibi, M. (2020a), "Vibrational responses of a MHC viscoelastic thick annular plate in thermal environment using GDQ method", Mech. Based Des. Struct., 1-26. https://doi.org/10.1080/15397734.2020.1784201.
  90. Liu, Z., Wu, X., Yu, M. and Habibi, M. (2020b), "Large-amplitude dynamical behavior of multilayer graphene platelets reinforced nanocomposite annular plate under thermomechanical loadings", Mech. Based Des. Struct., 1-25. https://doi.org/10.1080/15397734.2020.1815544.
  91. Lori, E.S., Ebrahimi, F., Supeni, E.E.B., Habibi, M. and Safarpour, H. (2020), "The critical voltage of a GPL-reinforced composite microdisk covered with piezoelectric layer", Eng. with Comput., 1-20. https://doi.org/10.1007/s00366-020-01004-z.
  92. Lu, N., Wang, H., Wang, K. and Liu, Y. (2021), "Maximum probabilistic and dynamic traffic load effects on short-to-medium span bridges", Comput. Model. Eng. Sci., 127(1), 345-360. https://doi.org/10.32604/cmes.2021.013792.
  93. Luo, J., Song, J., Moradi, Z., Safa, M. and Khadimallah, M.A. (2022), "Effect of simultaneous compressive and inertia loads on the bifurcation stability of shear deformable functionally graded annular fabrications reinforced with graphenes", Eur. J. Mech.-A/Solids, 104581. https://doi.org/10.1016/j.euromechsol.2022.104581
  94. Luo, Y., Zheng, H., Zhang, H. and Liu, Y. (2021), "Fatigue reliability evaluation of aging prestressed concrete bridge accounting for stochastic traffic loading and resistance degradation", Adv. Struct. Eng., 24(13), 3021-3029. https://doi.org/10.1177/13694332211017995
  95. Ma, L., Liu, X. and Moradi, Z. (2021), "On the chaotic behavior of graphene-reinforced annular systems under harmonic excitation", Eng. with Comput., 1-25. https://doi.org/10.1007/s00366-020-01210-9.
  96. Madenci, E. (2021), "Free vibration analysis of carbon nanotube RC nanobeams with variational approaches", Adv. Nano Res., 11(2), 157-171. https://doi.org/10.12989/anr.2021.11.2.157.
  97. Menasria, A., Kaci, A., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H., Tounsi, A., Bedia, E.A. and Mahmoud, S. (2020), "A four-unknown refined plate theory for dynamic analysis of FG-sandwich plates under various boundary conditions", Steel Compos. Struct., 36(3), 355-367. https://doi.org/10.12989/scs.2020.36.3.355.
  98. Merazka, B., Bouhadra, A., Menasria, A., Selim, M.M., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H., Tounsi, A. and Al-Zahrani, M.M. (2021), "Hygro-thermo-mechanical bending response of FG plates resting on elastic foundations", Steel Compos. Struct., 39(5), 631-643. https://doi.org/10.12989/scs.2021.39.5.631.
  99. Moayedi, H., Aliakbarlou, H., Jebeli, M., Noormohammadiarani, O., Habibi, M., Safarpour, H. and Foong, L. (2020a), "Thermal buckling responses of a graphene reinforced composite micropanel structure", Int. J. Appl. Mech., 12(1), 2050010. https://doi.org/10.1142/S1758825120500106.
  100. Moayedi, H., Ebrahimi, F., Habibi, M., Safarpour, H. and Foong, L.K. (2020b), "Application of nonlocal strain-stress gradient theory and GDQEM for thermo-vibration responses of a laminated composite nanoshell", Eng. with Comput., 1-16. https://doi.org/10.1007/s00366-020-01002-1.
  101. Moayedi, H., Habibi, M., Safarpour, H., Safarpour, M. and Foong, L. (2019), "Buckling and frequency responses of a graphene nanoplatelet reinforced composite microdisk", Int. J. Appl. Mech., 11(10), 1950102. https://doi.org/10.1142/S1758825119501023.
  102. Mohammadgholiha, M., Shokrgozar, A., Habibi, M. and Safarpour, H. (2019), "Buckling and frequency analysis of the nonlocal strain-stress gradient shell reinforced with graphene nanoplatelets", J. Vib. Control, 25(19-20), 2627-2640. https://doi.org/10.1177/1077546319863251.
  103. Mohammadi, A., Lashini, H., Habibi, M. and Safarpour, H. (2019), "Influence of viscoelastic foundation on dynamic behaviour of the double walled cylindrical inhomogeneous micro shell using MCST and with the aid of GDQM", J. Solid Mech., 11(2), 440-453. https://doi.org/10.22034/JSM.2019.665264.
  104. Mohammadi, M. and Rastgoo, A. (2019), "Nonlinear vibration analysis of the viscoelastic composite nanoplate with three directionally imperfect porous FG core", Struct. Eng. Mech., 69(2), 131. https://doi.org/10.12989/sem.2019.69.2.131.
  105. Moradi, Z., Davoudi, M., Ebrahimi, F. and Ehyaei, A.F. (2021), "Intelligent wave dispersion control of an inhomogeneous micro-shell using a proportional-derivative smart controller", Waves in Random and Complex Media, 1-24. https://doi.org/10.1080/17455030.2021.1926572.
  106. Najaafi, N., Jamali, M., Habibi, M., Sadeghi, S., Jung, D.w. and Nabipour, N. (2020), "Dynamic instability responses of the substructure living biological cells in the cytoplasm environment using stress-strain size-dependent theory", J. Biomolecular Struct. Dyn., 1-12. https://doi.org/10.1080/07391102.2020.1751297.
  107. Nejad, M.Z., Hadi, A. and Farajpour, A. (2017), "Consistent couple-stress theory for free vibration analysis of Euler-Bernoulli nano-beams made of arbitrary bi-directional functionally graded materials", Struct. Eng. Mech., 63(2), 161-169. https://doi.org/10.12989/sem.2017.63.2.161.
  108. Oyarhossein, M.A., Alizadeh, A.A., Habibi, M., Makkiabadi, M., Daman, M., Safarpour, H. and Jung, D.W. (2020), "Dynamic response of the nonlocal strain-stress gradient in laminated polymer composites microtubes", Scientific Reports, 10(1), 1-19. https://doi.org/10.1038/s41598-020-61855-w.
  109. Peng, L. (2011), "Relationship between shearing strength and water content of expansive soil", Soil Eng. Found., 25(4), 66. http://tgjc.whrsm.ac.cn/EN/Y2011/V25/I4/66. https://doi.org/10.3969/j.issn.1004-3152.2011.04.019
  110. Pourjabari, A., Hajilak, Z.E., Mohammadi, A., Habibi, M. and Safarpour, H. (2019), "Effect of porosity on free and forced vibration characteristics of the GPL reinforcement composite nanostructures", Comput. Math. Appl., 77(10), 2608-2626. https://doi.org/10.1016/j.camwa.2018.12.041
  111. Rabhi, M., Benrahou, K.H., Kaci, A., Houari, M.S.A., Bourada, F., Bousahla, A.A., Tounsi, A., Bedia, E.A., Mahmoud, S. and Tounsi, A. (2020), "A new innovative 3-unknowns HSDT for buckling and free vibration of exponentially graded sandwich plates resting on elastic foundations under various boundary conditions", Geomech. Eng., 22(2), 119. https://doi.org/10.12989/gae.2020.22.2.119.
  112. Sadoun, M., Houari, M.S.A., Bakora, A., Tounsi, A., Mahmoud, S. and Alwabli, A.S. (2018), "Vibration analysis of thick orthotropic plates using quasi 3D sinusoidal shear deformation theory", Geomech. Eng., 16(2), 141-150. https://doi.org/10.12989/gae.2018.16.2.141.
  113. Safarpour, H., Ghanizadeh, S.A. and Habibi, M. (2018), "Wave propagation characteristics of a cylindrical laminated composite nanoshell in thermal environment based on the nonlocal strain gradient theory", Eur. Phys. J. Plus, 133(12), 532. https://doi.org/10.1140/epjp/i2018-12385-2.
  114. Safarpour, H., Hajilak, Z.E. and Habibi, M. (2019a), "A size-dependent exact theory for thermal buckling, free and forced vibration analysis of temperature dependent FG multilayer GPLRC composite nanostructures restring on elastic foundation", Int. J. Mech. Mater. Des., 15(3), 569-583. https://doi.org/10.1007/s10999-018-9431-8.
  115. Safarpour, H., Pourghader, J. and Habibi, M. (2019b), "Influence of spring-mass systems on frequency behavior and critical voltage of a high-speed rotating cantilever cylindrical three-dimensional shell coupled with piezoelectric actuator", J. Vib. Control. 25(9), 1543-1557. https://doi.org/10.1177/1077546319828465.
  116. Safarpour, M., Ebrahimi, F., Habibi, M. and Safarpour, H. (2020), "On the nonlinear dynamics of a multi-scale hybrid nanocomposite disk", Eng. with Comput., 1-20. https://doi.org/10.1007/s00366-020-00949-5.
  117. Setoodeh, A. and Rezaei, M. (2017), "Large amplitude free vibration analysis of functionally graded nano/micro beams on nonlinear elastic foundation", Struct. Eng. Mech., 61(2), 209-220. https://doi.org/10.12989/sem.2017.61.2.209.
  118. Shao, Y., Zhao, Y., Gao, J. and Habibi, M. (2021), "Energy absorption of the strengthened viscoelastic multi-curved composite panel under friction force", Arch. Civil Mech. Eng., 21(4), 1-29. https://doi.org/10.1007/s43452-021-00279-3.
  119. Shariati, A., Habibi, M., Tounsi, A., Safarpour, H. and Safa, M. (2020a), "Application of exact continuum size-dependent theory for stability and frequency analysis of a curved cantilevered microtubule by considering viscoelastic properties", Eng. with Comput., 1-20. https://doi.org/10.1007/s00366-020-01024-9.
  120. Shariati, A., Mohammad-Sedighi, H., Zur, K.K., Habibi, M. and Safa, M. (2020b), "On the vibrations and stability of moving viscoelastic axially functionally graded nanobeams", Materials, 3(7), 1707. https://doi.org/10.3390/ma13071707.
  121. Shariati, A., Mohammad-Sedighi, H., Zur, K.K., Habibi, M. and Safa, M. (2020c), "Stability and dynamics of viscoelastic moving rayleigh beams with an asymmetrical distribution of material parameters", Symmetry, 12(4), 586. https://doi.org/10.3390/sym12040586.
  122. Shen, Y.J., Qing, L. and Shang, Y.Q. 2008), "Effect of pile row distance on internal stress of double-row anti-slide piles [J]", Chinese J. Geotech. Eng., 7. https://doi.org/10.4028/www.scientific.net/AMR.168-170.127
  123. Shi, T., Liu, Y., Zhang, Y., Lan, Y., Zhao, Q., Zhao, Y. and Wang, H. (2022), "Calcined attapulgite clay as supplementary cementing material: thermal treatment, hydration activity and mechanical properties", Int. J. Concrete Struct. Mater., 16(1), 1-10. https://doi.org/10.1186/s40069-022-00499-8.
  124. Shokrgozar, A., Safarpour, H. and Habibi, M. (2020), "Influence of system parameters on buckling and frequency analysis of a spinning cantilever cylindrical 3D shell coupled with piezoelectric actuator", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 234(2), 512-529. https://doi.org/10.1177/0954406219883312
  125. Sobhy, M. (2017), "Hygro-thermo-mechanical vibration and buckling of exponentially graded nanoplates resting on elastic foundations via nonlocal elasticity theory", Struct. Eng. Mech., 63(3), 401-415. https://doi.org/10.12989/sem.2017.63.3.401.
  126. Soleimani-Javid, Z., Arshid, E., Khorasani, M., Amir, S. and Tounsi, A. (2021), "Size-dependent flexoelectricity-based vibration characteristics of honeycomb sandwich plates with various boundary conditions", Adv. Nano Res., 10(5), 449-460. https://doi.org/10.12989/anr.2021.10.5.449.
  127. Tahir, S.I., Chikh, A., Tounsi, A., Al-Osta, M.A., Al-Dulaijan, S.U. and Al-Zahrani, M.M. (2021a), "Wave propagation analysis of a ceramic-metal functionally graded sandwich plate with different porosity distributions in a hygro-thermal environment", Compos. Struct., 269, 114030. https://doi.org/10.1016/j.compstruct.2021.114030.
  128. Tahir, S.I., Tounsi, A., Chikh, A., Al-Osta, M.A., Al-Dulaijan, S.U. and Al-Zahrani, M.M. (2021b), "An integral four-variable hyperbolic HSDT for the wave propagation investigation of a ceramic-metal FGM plate with various porosity distributions resting on a viscoelastic foundation", Waves in Random and Complex Media, 1-24. https://doi.org/10.1080/17455030.2021.1942310.
  129. Tan, Y. and Wang, D. (2013), "Characteristics of a large-scale deep foundation pit excavated by the central-island technique in Shanghai soft clay. I: Bottom-up construction of the central cylindrical shaft", J. Geotech. Geoenviron. Eng., 139(11), 1875-1893. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000928.
  130. Tang, F., Zheng, Y. and Yang, B. (2010), "Thrust share ratios and optimization design for two-row anti-slide piles", Chinese J. Rock Mech. Eng., 29(1), 3162-3168. https://doi.org/10.1016/j.csite.2018.09.006.
  131. Ting, L., Chaosheng, T., Dan, X., Yunsheng, L., Yan, Z., Kan, W. and Bin, S. (2018), "Advance on the engineering geological characteristics of expansive soil", J. Eng. Geol., 26(1), 112-128. https://doi.org/10.13544/j.cnki.jeg.2018.01.013.
  132. Tlidji, Y., Benferhat, R., Trinh, L.C., Tahar, H.D. and Abdelouahed, T. (2021), "New state-space approach to dynamic analysis of porous FG beam under different boundary conditions", Adv. Nano Res., 11(4), 347-359. https://doi.org/10.12989/anr.2021.11.4.347.
  133. Wang, X., Yang, Y., Yang, R. and Liu, P. (2022), "Experimental Analysis of Bearing Capacity of Basalt Fiber Reinforced Concrete Short Columns under Axial Compression", Coatings. 12(5), 654. https://doi.org/10.3390/coatings12050654.
  134. Wang, Z., Yu, S., Xiao, Z. and Habibi, M. (2020), "Frequency and buckling responses of a high-speed rotating fiber metal laminated cantilevered microdisk", Mech. Adv. Mater. Struct., 1-14. https://doi.org/10.1080/15376494.2020.1824284.
  135. Wei, J., Xie, Z., Zhang, W., Luo, X., Yang, Y. and Chen, B. (2021), "Experimental study on circular steel tube-confined reinforced UHPC columns under axial loading", Eng. Struct., 230, 111599. https://doi.org/10.1016/j.engstruct.2020.111599.
  136. Wu, J. and Habibi, M. (2021), "Dynamic simulation of the ultrafast-rotating sandwich cantilever disk via finite element and semi-numerical methods", Eng. with Comput., 1-17. https://doi.org/10.1007/s00366-021-01396-6.
  137. XIE, Y., Chen, Z.H. and Li, G. (2005), "Research of thermal effects on shear strength and deformation characteristics of unsaturated bentonite soils [J]", Chinese J. Geotech. Eng., 9. https://doi.org/10.1002/nag.332
  138. Xiong, Q.M., Chen, Z., Huang, J.T., Zhang, M., Song, H., Hou, X.F., Li, X.B. and Feng, Z.J. (2020), "Preparation, structure and mechanical properties of Sialon ceramics by transition metal-catalyzed nitriding reaction", Rare Metals, 39(5), 589-596. https://doi.org/10.1007/s12598-020-01385-6.
  139. Xu, H., Wang, X.Y., Liu, C.N., Chen, J.N. and Zhang, C. (2021a), "A 3D root system morphological and mechanical model based on L-Systems and its application to estimate the shear strength of root-soil composites", Soil Tillage Res., 212, 105074. https://doi.org/10.1016/j.still.2021.105074
  140. Xu, J., Lan, W., Ren, C., Zhou, X., Wang, S. and Yuan, J. (2021b), "Modeling of coupled transfer of water, heat and solute in saline loess considering sodium sulfate crystallization", Cold Regions Sci. Technol., 189 103335. https://doi.org/10.1016/j.coldregions.2021.103335.
  141. Xu, J., Wu, Z., Chen, H., Shao, L., Zhou, X. and Wang, S. (2021c), "Study on strength behavior of basalt fiber-reinforced loess by digital image technology (DIT) and scanning electron microscope (SEM)", Arabian J. Sci. Eng., 46(11), 11319-11338. https://doi.org/10.1007/s13369-021-05787-1.
  142. Xu, W., Pan, G., Moradi, Z. and Shafiei, N. (2021d), "Nonlinear forced vibration analysis of functionally graded non-uniform cylindrical microbeams applying the semi-analytical solution", Compos. Struct., 114395. https://doi.org/10.1016/j.compstruct.2021.114395.
  143. Yang, N., Moradi, Z., Khadimallah, M.A. and Arvin, H. (2022), "Application of the Chebyshev-Ritz route in determination of the dynamic instability region boundary for rotating nanocomposite beams reinforced with graphene platelet subjected to a temperature increment", Eng. Anal. Bound. Elem., 139 169-179. https://doi.org/10.1016/j.enganabound.2022.03.013.
  144. Younsi, A., Tounsi, A., Zaoui, F.Z., Bousahla, A.A. and Mahmoud, S. (2018), "Novel quasi-3D and 2D shear deformation theories for bending and free vibration analysis of FGM plates", Geomech. Eng., 14(6), 519-532. https://doi.org/10.12989/gae.2018.14.6.519.
  145. Yu, X., Maalla, A. and Moradi, Z. (2022), "Electroelastic high-order computational continuum strategy for critical voltage and frequency of piezoelectric NEMS via modified multi-physical couple stress theory", Mech. Syst. Signal Pr., 165, 108373. https://doi.org/10.1016/j.ymssp.2021.108373
  146. Zare, R., Najaafi, N., Habibi, M., Ebrahimi, F. and Safarpour, H. (2020), "Influence of imperfection on the smart control frequency characteristics of a cylindrical sensor-actuator GPLRC cylindrical shell using a proportional-derivative smart controller", Smart Struct. Syst., 26(4), 469-480. https://doi.org/10.12989/sss.2020.26.4.469.
  147. Zerrouki, R., Karas, A., Zidour, M., Bousahla, A.A., Tounsi, A., Bourada, F., Tounsi, A., Benrahou, K.H. and Mahmoud, S. (2021), "Effect of nonlinear FG-CNT distribution on mechanical properties of functionally graded nano-composite beam", Struct. Eng. Mech., 78(2), 117-124. https://doi.org/10.12989/sem.2021.78.2.117.
  148. Zhang, Y., Wang, Z., Tazeddinova, D., Ebrahimi, F., Habibi, M. and Safarpour, H. (2021), "Enhancing active vibration control performances in a smart rotary sandwich thick nanostructure conveying viscous fluid flow by a PD controller", Waves in Random and Complex Media, 1-24. https://doi.org/10.1080/17455030.2021.1948627.
  149. Zhao, Y., Moradi, Z., Davoudi, M. and Zhuang, J. "Bending and stress responses of the hybrid axisymmetric system via state-space method and 3D-elasticity theory", Eng. with Comput., 1-23. https://doi.org/10.1007/s00366-020-01242-1.
  150. Zheng, C.M., Zeng-hui, W. and Zhang, X. (2010), "Economic analysis of double-row piles in deep foundation pits in soft soils in coastal areas of Fujian Province", Chinese J. Geotech. Eng., 32(1), 317-320. https://doi.org/10.1007/s10064-016-0852-z.
  151. Zhou, C., Zhao, Y., Zhang, J., Fang, Y. and Habibi, M. (2020), "Vibrational characteristics of multi-phase nanocomposite reinforced circular/annular system", Adv. Nano Res., 9(4), 295-307. https://doi.org/10.12989/anr.2020.9.4.295.