Geomechanics and Engineering

Techno-Press (테크노프레스)
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Analytical and ANN-based models for assessment of hunchback retaining walls: Investigating lateral earth pressure in unsaturated backfill

  • Sivani Remash Thottoth (Department of Civil Engineering, IIT(ISM) Dhanbad) ;
  • Vishwas N Khatria (Department of Civil Engineering, IIT(ISM) Dhanbad)
  • Received : 2024.05.04
  • Accepted : 2024.07.23
  • Published : 2024.08.10
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Abstract

This study investigates the behaviour of hunchback retaining walls supporting unsaturated sandy backfill under active earth pressure conditions. Utilizing a horizontal slice method and a unified effective stress methodology, the influence of various factors on lateral earth pressure, including the position of the hunch along the wall, friction angles, and wall heights, is explored. The results suggest that relocating the hunch position from close to the wall's top to near its base leads to a significant decrease (ranging from 54% to 81%) in lateral earth pressure. However, as the hunch position transitions from near the top to mid-height, the point of application of active thrust shifts upward initially, then slightly downward as the hunch position approaches the toe. Notably, the reduction in lateral earth pressure is more pronounced for shorter wall heights and higher friction angles. Building upon these findings, an Artificial Neural Network (ANN)-based model is developed to accurately predict the lateral earth pressure coefficient and point of application, achieving R2 values of 0.94 and 0.93, respectively. In addition, an analytical model based on Coulomb's earth pressure theory is presented and compared with ANN models. These models are anticipated to assist designers and practitioners in optimizing hunchback retaining walls for unsaturated backfill.

Keywords

References

  1. Abdollahi, M., Vahedifard, F., Abed, M. and Leshchinsky, B.A. (2021), "Effect of tension crack formation on active earth pressure encountered in unsaturated retaining wall bBackfills", J. Geotech. Geoenviron. Eng., 147:. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002434.
  2. Acharyya, R., Dey, A. and Kumar, B. (2020), "Finite element and ANN-based prediction of bearing capacity of square footing resting on the crest of c-φ soil slope", Int. J. Geotech. Eng., 14, 176-187. https://doi.org/10.1080/19386362.2018.1435022.
  3. Afsharpour, S., Payan, M., Chenari, R.J., Ahmadi, H. and Fathipour, H. (2022), "Bearing capacity of strip footings on unsaturated soils under combined loading using LEM", Geomech. Eng., 31(2), 223-235. https://doi.org/10.12989/gae.2022.31.2.223.
  4. Agarwal, E., Pain, A., Mukhopadhyay, T., Metya, S. and Sarkar, S. (2022), "Efficient computational system reliability analysis of reinforced soil-retaining structures under seismic conditions including the effect of simulated noise", Eng. Comput., 38, 901-923. https://doi.org/10.1007/s00366-020-01281-8.
  5. Amjad Raja, M.N., Abbas Jaffar, S.T., Bardhan, A. and Shukla, S.K. (2023), "Predicting and validating the load-settlement behavior of large-scale geosynthetic-reinforced soil abutments using hybrid intelligent modeling", J. Rock Mech. Geotech. Eng., 15, 773-788. https://doi.org/10.1016/j.jrmge.2022.04.012.
  6. Aroni Hesari, S., Javankhoshdel, S., Payan, M. and Jamshidi Chenari, R (2022), "Pseudo-static internal stability analysis of geosynthetic-reinforced earth slopes using horizontal slices method", Geomech. Geoeng., 17, 1417-1442. https://doi.org/10.1080/17486025.2021.1940316.
  7. Bahmani Tajani, S., Fathipour, H., Payan, M., Jamshidi Chenari, R. and Senetakis, K. (2023), "Temperature-dependent lateral earth pressures in partially saturated backfills", Eur. J. Environ. Civ. Eng., 27, 3064-3090. https://doi.org/10.1080/19648189.2022.2125911.
  8. Bardhan, A., Samui, P., Ghosh, K., Gandomi, A.H. and Bhattacharyya, S. (2021), "ELM-based adaptive neuro swarm intelligence techniques for predicting the California bearing ratio of soils in soaked conditions", Appl Soft Comput., 110, 107595. https://doi.org/10.1016/j.asoc.2021.107595.
  9. Bishop, A.W. (1959), "The principle of effective stress", Tek Ukebl, 859-863.
  10. Chandaluri, V.K., Sawant, V.A. and Shukla, S.K. (2015), "Seismic stability analysis of reinforced soil wall using horizontal slice method", Int. J. Geosynth. Gr. Eng., 1, 23. https://doi.org/10.1007/s40891-015-0025-3.
  11. Chen, W.F. and Liu, X.L. (1990), Limit analysis in soil mechanics. Amsterdam, Elsevier.
  12. Chenari, M.J., Payan, M. and Ghasemi-Fare, O. (2023), "Nonisothermal failure envelopes of strip shallow foundations resting on partially saturated clay subjected to combined inclined and eccentric loadings", Int. J. Geomech., 23(1), https://doi.org/10.1061/(ASCE)GM.1943-5622.0002596.
  13. Coulomb, C.A. (1776), "Essai sur une application des regles de maximis & minimis a quelques problemes de statique a l'architecture. l'Imprimerie", Mem. Acad. Roy. Div. Sav.
  14. Das, P.P. and Khatri, V.N. (2022), "Bearing capacity prediction of strip and ring footings embedded in layered sand", Proc. Inst. Civ. Eng. - Geotech. Eng., 1-18. https://doi.org/10.1680/jgeen.22.00071.
  15. Dey, A.K., Dey, A. and Sukladas, S. (2017), "3 N formulation of the horizontal slice method in evaluating pseudostatic method for analysis of seismic active earth pressure", Int. J. Geomech., 17, 04016037. https://doi.org/10.1061/(asce)gm.1943-5622.0000662
  16. Farshidfar, N., Keshavarz, A. and Mirhosseini, S.M. (2020), "Pseudo-static seismic analysis of reinforced soil slopes using the horizontal slice method", Arab. J. Geosci., 13. https://doi.org/10.1007/s12517-020-5269-0.
  17. Fatehi, M., Hosseinpour, I., Jamshidi Chenari, R., Payan, M. and Javankhoshdel, S. (2023), "Deterministic seismic stability analysis of reinforced slopes using pseudo-static approach", Iran J. Sci. Technol. Trans. Civ. Eng., 47, 1025-1040. https://doi.org/10.1007/s40996-022-00970-2.
  18. Fathipour, H., Bahmani Tajani, S., Payan, M., Chenari, R.J. and Senetakis, K. (2022), "Influence of transient flow during infiltration and isotropic/anisotropic matric suction on the passive/active lateral earth pressures of partially saturated soils", Eng. Geol., 310, 106883. https://doi.org/10.1016/j.enggeo.2022.106883.
  19. Fathipour, H., Payan, M. and Jamshidi Chenari, R. (2021a), "Limit analysis of lateral earth pressure on geosynthetic-reinforced retaining structures using finite element and second-order cone programming", Comput. Geotech., 134, 104119. https://doi.org/10.1016/j.compgeo.2021.104119.
  20. Fathipour, H., Payan, M., Jamshidi Chenari, R. and Senetakis, K. (2021b), "Lower bound analysis of modified pseudo-dynamic lateral earth pressures for retaining wall-backfill system with depth-varying damping using FEM-Second order cone programming", Int. J. Numer Anal. Method. Geomech., 45, 2371-2387. https://doi.org/10.1002/nag.3269.
  21. Fathipour, H., Payan, M., Safardoost Siahmazgi, A., Jamshidi Chenari, R. and Senetakis, K. (2023a), "Numerical study on the bearing capacity of strip footing resting on partially saturated soil subjected to combined vertical-horizontal-moment loading", Eur. J. Environ. Civ. Eng., 27, 1317-1350. https://doi.org/10.1080/19648189.2022.2080769.
  22. Fathipour, H., Safardoost Siahmazgi, A., Payan, M. and Jamshidi Chenari, R. (2020), "Evaluation of the lateral earth pressure in unsaturated soils with finite element limit analysis using second-order cone programming", Comput. Geotech., 125, 103587. https://doi.org/10.1016/j.compgeo.2020.103587.
  23. Fathipour, H., Siahmazgi, A.S., Payan, M., Veiskarami, M. and Jamshidi Chenari, R. (2021c), "Limit analysis of modified pseudodynamic lateral earth pressure in anisotropic frictional medium using finite-element and second-order cone programming", Int. J. Geomech., 21, 1-15. https://doi.org/10.1061/(asce)gm.1943-5622.0001924.
  24. Fathipour, H., Tajani, S.B., Payan, M., Chenari, R.J. and Senetakis, K. (2023b), "Impact of transient infiltration on the ultimate bearing capacity of obliquely and eccentrically loaded strip footings on partially saturated soils", Int. J. Geomech., 23. https://doi.org/10.1061/IJGNAI.GMENG-7463.
  25. Fausett, L (1994), Fundamentals of Neural Network. Prentice Hall, Hoboken.
  26. Feng, X. and Jimenez, R. (2015), "Predicting tunnel squeezing with incomplete data using Bayesian networks", Eng. Geol., 195, 214-224. https://doi.org/10.1016/j.enggeo.2015.06.017.
  27. Fredlund, D.G., Morgenstern, N.R. and Widger, R.A. (1978), "The shear strength of unsaturated soils", Can Geotech. J., 15, 313-321. https://doi.org/10.1139/t78-029.
  28. Ganesh, R. and Rajesh, S. (2021), "Analytical solution to estimate the point of application of resultant passive earth thrust against unsaturated retaining structures", Geomech. Geoeng., 16, 509-516. https://doi.org/10.1080/17486025.2019.1680880.
  29. Garson, G.D. (1991), "Interpreting neural network connection weights", AI Expert Arch., 6, 46-51
  30. Ghanbari, A. and Ahmadabadi, M. (2010), "Pseudo-dynamic active earth pressure analysis of inclined Retaining walls using horizontal slices method", Sci. Iran, 17, 118-130.
  31. Gnananandarao, T., Khatri, V.N. and Dutta, R.K. (2020), "Prediction of bearing capacity of H shaped skirted footings on sand using soft computing techniques", Arch. Mater. Sci. Eng., 103, 62-74. https://doi.org/10.5604/01.3001.0014.3356.
  32. Goh, A.T.C., Kulhawy, F.H. and Chua, C.G. (2005), "Bayesian neural network analysis of undrained side resistance of drilled shafts", J. Geotech. Geoenviron. Eng., 131, 84-93. https://doi.org/10.1061/(ASCE)1090-0241(2005)131:1(84),
  33. Hasthi, V., Nouman Amjad Raja, M., Hegde, A. and Kumar Shukla, S. (2022), "Experimental and intelligent modelling for predicting the amplitude of footing resting on geocell-reinforced soil bed under vibratory load", Transp. Geotech., 35, 100783. https://doi.org/10.1016/j.trgeo.2022.100783.
  34. Kalinli, A., Acar, M.C. and Gunduz, Z. (2011), "New approaches to determine the ultimate bearing capacity of shallow foundations based on artificial neural networks and ant colony optimization", Eng. Geol., 117, 29-38. https://doi.org/10.1016/j.enggeo.2010.10.002.
  35. Kardani, N., Bardhan, A., Gupta, S., Samui, P., Nazem, M., Zhang, Y. and Zhou, A. (2022), "Predicting permeability of tight carbonates using a hybrid machine learning approach of modified equilibrium optimizer and extreme learning machine", Acta Geotech., 17, 1239-1255. https://doi.org/10.1007/s11440-021-01257-y
  36. Khan, M.U.A., Shukla, S.K. and Raja, M.N.A. (2021), "Soil- conduit interaction: an artificial intelligence application for reinforced concrete and corrugated steel conduits", Neural Comput. Appl., 33, 14861-14885. https://doi.org/10.1007/s00521-021-06125-0.
  37. Khodkari, N., Hamidian, P., Khodkari, H., Payan, M. and Behnood, A. (2024), "Predicting the small strain shear modulus of sands and sand-fines binary mixtures using machine learning algorithms", Transp. Geotech., 44, 101172. https://doi.org/10.1016/j.trgeo.2023.101172.
  38. Kim, D., Kwon, K., Pham, K., Oh, J.Y. and Choi, H. (2022), "Surface settlement prediction for urban tunneling using machine learning algorithms with Bayesian optimization", Automat. Constr., 140, 104331. https://doi.org/10.1016/j.autcon.2022.104331.
  39. Kolathayar, S. and Ghosh, P. (2009), "Seismic active earth pressure on walls with bilinear backface using pseudo-dynamic approach", Comput. Geotech., 36, 1229-1236. https://doi.org/10.1016/j.compgeo.2009.05.015.
  40. Kolathayar, S. and Ghosh, P. (2011), "Seismic passive earth pressure on walls with bilinear backface uUsing pseudodynamic approach", Geotech. Geol. Eng., 29, 307-317. https://doi.org/10.1007/s10706-010-9377-6.
  41. Kuo, Y.L., Jaksa, M.B., Lyamin, A.V. and Kaggwa, W.S. (2009), "ANN-based model for predicting the bearing capacity of strip footing on multi-layered cohesive soil", Comput. Geotech., 36, 503-516. https://doi.org/10.1016/j.compgeo.2008.07.002.
  42. Li, Z.W. and Yang, X.L. (2019), "Active earth pressure from unsaturated soils with different water levels", Int. J. Geomech., 19, 1-10. https://doi.org/10.1061/(asce)gm.1943-5622.0001471.
  43. Liang, W., Zhao, J., Li, Y., Zhang, C.G. and Wang, S. (2012), "Unified solution of Coulomb's active earth pressure for unsaturated soils without crack", Appl. Mech. Mater., 170-173, 755-761. https://doi.org/10.4028/www.scientific.net/AMM.170-173.755
  44. Lu, N., Godt, J.W. and Wu, D.T. (2010), "A closed-form equation for effective stress in unsaturated soil", Water Resour. Res., 46. https://doi.org/10.1029/2009WR008646
  45. Lu, N. and Griffiths, D.V. (2004), "Profiles of steady-state suction stress in unsaturated soils", J. Geotech. Geoenviron. Eng., 130, 1063-1076. https://doi.org/10.1061/(ASCE)1090-0241(2004)130:10(1063).
  46. Lu, N. and Likos, W.J. (2006), "Suction stress characteristic curve for unsaturated soil", J. Geotech. Geoenviron. Eng., 132, 131-142. https://doi.org/10.1061/(asce)1090-0241(2006)132:2(131).
  47. Maghferati, S.P., Jamshidi Chenari, R., Lajevardi, S.H., Payan, M. and Mirhosseini, S.M. (2023), "Seismic combined bearing capacity of strip footings on partially saturated soils using lower bound theorem of finite element limit analysis and second-order cone programming", Comput. Geotech., 157, 105327. https://doi.org/10.1016/j.compgeo.2023.105327
  48. Menon, V. and Kolathayar, S. (2024), "Optimizing nailing parameters for hybrid retaining systems using supervised learning regression models", Multiscale Multidiscip. Model. Exp. Des., https://doi.org/10.1007/s41939-024-00417-3
  49. Mirmoazen, S.M., Lajevardi, S.H., Mirhosseini, S.M., Payan, M. and Chenari, R.J. (2021), "Active lateral earth pressure of geosynthetic-reinforced retaining walls with inherently anisotropic frictional backfills subjected to strip footing loading", Comput. Geotech., 137, 3-4. https://doi.org/10.1016/j.compgeo.2021.104302
  50. Mirmoazen, S.M., Lajevardi, S.H., Mirhosseini, S.M., ayan, M. and Chenari, R.J. (2022), "Limit analysis of lateral earth pressure on geosynthetic-reinforced retaining structures subjected to strip footing loading using finite element and second-order cone programming", Iran J. Sci. Technol. Trans. Civ. Eng., 46, 3181-3192. https://doi.org/10.1007/s40996-021-00793-7.
  51. Momeni, E., Nazir, R., Armaghani, D.J. and Maizir, H. (2015), "Application of artificial neural network for predicting shaft and tip resistances of concrete piles", Earth. Sci. Res. J., 19, 85-93. https://doi.org/10.15446/esrj.v19n1.38712.
  52. Ngamkhanong, C., Keawsawasvong, S., Jearsiripongkul, T., Cabangon, L.T., Payan, M., Sangjinda, K., Banyong, R. and Thongchom, C. (2022), "Data-driven prediction of stability of rock tunnel heading: An application of machine learning mModels", Infrastruct., 7(11), 148. https://doi.org/10.3390/infrastructures7110148.
  53. Nguyen, H., Moayedi, H., Foong, L.K., Al Najjar, H.A>H., Jusoh, W.A.W., Rashid, A.S.A. and Jamali, J. (2020), "Optimizing ANN models with PSO for predicting short building seismic response", Eng. Comput., 36, 823-837. https://doi.org/10.1007/s00366-019-00733-0.
  54. Nguyen, T., Ly, K.D., Nguyen-Thoi, T., Nguyen, B.P. and Doan, N.P. (2022), "Prediction of axial load bearing capacity of PHC nodular pile using Bayesian regularization artificial neural network", Soils Found., 62, 101203. https://doi.org/10.1016/j.sandf.2022.101203.
  55. Ning, L. and William, L. (2004), Unsaturated Soil Mechanics. 
  56. Nouzari, M.A., Jamshidi Chenari, R., Payan, M. and Pishgar, F. (2021a), "Pseudo-static seismic bearing capacity of shallow foundations in unsaturated soils employing limit equilibrium method", Geotech. Geol. Eng., 39, 943-956. https://doi.org/10.1007/s10706-020-01535-8.
  57. Nouzari, M.A., Jamshidi Chenari, R., Payan, M. and Pishgar, F. (2021b), "Pseudo-static seismic bearing capacity of shallow foundations in unsaturated soils employing limit equilibrium method", Geotech, Geol, Eng., 39, 943-956. https://doi.org/10.1007/s10706-020-01535-8.
  58. Olden, J.D. and Jackson, D.A. (2002), "Illuminating the "black box": a randomization approach for understanding variable contributions in artificial neural networks", Ecol. Modell., 154, 135-150. https://doi.org/10.1016/S0304-3800(02)00064-9.
  59. Payan, M., Fathipour, H., Hosseini, M., Chenari, R.J. and Shiau, J.S. (2022), "Lower bound finite element limit analysis of geostructures with non-associated flow rule", Comput. Geotech., 147, 104803. https://doi.org/10.1016/j.compgeo.2022.104803.
  60. Rahaman, O. and Raychowdhury, P. (2017), "Seismic active earth pressure on bilinear retaining walls using a modified pseudodynamic method", Int. J. Geo-Eng., 8(6). https://doi.org/10.1186/s40703-017-0040-4.
  61. Raja, M.N.A. and Shukla, S.K. (2021a), "Predicting the settlement of geosynthetic-reinforced soil foundations using evolutionary artificial intelligence technique", Geotext. Geomembranes, 49, 1280-1293. https://doi.org/10.1016/j.geotexmem.2021.04.007.
  62. Raja, M.N.A. and Shukla, S.K. (2021b), "Predicting the settlement of geosynthetic-reinforced soil foundations using evolutionary artificial intelligence technique", Geotext. Geomembranes, 49, 1280-1293. https://doi.org/10.1016/j.geotexmem.2021.04.007.
  63. Raja, M.N.A., Shukla, S.K. and Khan, M.U.A. (2022), "An intelligent approach for predicting the strength of geosyntheticreinforced subgrade soil", Int. J. Pavement Eng., 23, 3505-3521. https://doi.org/10.1080/10298436.2021.1904237.
  64. Rajesh, S. and Ganesh, R. (2022), "Analytical solution for the action of seismic active earth pressures of unsaturated backfills behind inclined walls", Lecture Notes in Civil Engineering, 17-31.
  65. Reeves, C.R. (1993), Modern heuristic techniques for combinatorial problems, McGraw-Hill, UK
  66. Sadrekarimi, A. (2010), "Pseudo-static lateral earth pressures on broken-back retaining walls", Can Geotech. J., 47, 1247-1258. https://doi.org/10.1139/T10-025.
  67. Sadrekarimi, A. (2017), "Seismic distress of broken-back gravity retaining walls", J. Geotech. Geoenviron. Eng., 143, 04016118. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001612.
  68. Sadrekarimi, A., Ghalandarzadeh, A. and Sadrekarimi, J. (2008), "Static and dynamic behavior of hunchbacked gravity quay walls", Soil Dyn. Earthq. Eng., 28, 99-117. https://doi.org/10.1016/j.soildyn.2007.05.004.
  69. Sahoo, J.P. and Ganesh, R. (2018), "Active earth pressure on retaining walls with unsaturated soil backfill", Sustain. Civ. Infrastruct., 1-19. https://doi.org/10.1007/978-3-319-63889-8_1.
  70. Sangdeh, M.K., Salimi, M., Khansar, H.H., Dokaneh, M., Zanganeh Ranjbar, P., Payan, M. and Arabani, M. (2024), "Predicting the precipitated calcium carbonate and unconfined compressive strength of bio-mediated sands through robust hybrid optimization algorithms", Transp. Geotech., 46, 101235. https://doi.org/10.1016/j.trgeo.2024.101235.
  71. Santhoshkumar, G. and Ghosh, P. (2020), "Seismic stability of a broken-back retaining wall using adaptive collapse mechanism", Int. J. Geomech., 20:04020154. https://doi.org/10.1061/(asce)gm.1943-5622.0001786.
  72. Shahgholi, M., Fakher, A. and Jones, C.J.F.P. (2001), "Horizontal slice method of analysis", Geotechnique, 51, 881-885. https://doi.org/10.1680/geot.2001.51.10.881.
  73. Shahrokhabadi, S., Vahedifard, F., Ghazanfari, E. and Foroutan, M. (2019a), "Earth pressure profiles in unsaturated soils under transient flow", Eng. Geol., 260, 105218. https://doi.org/10.1016/j.enggeo.2019.105218.
  74. Shahrokhabadi, S., Vahedifard, F., Ghazanfari, E. and Foroutan, M. (2019b), "Earth pressure profiles in unsaturated soils under transient flow", Eng. Geol., 260, 105218. https://doi.org/10.1016/j.enggeo.2019.105218.
  75. Stanier, S. and Tarantino, A. (2010), "Active earth force in 'cohesionless' unsaturated soils using bound theorems of plasticity", Unsaturated Soils. CRC Press, 1081-1086.
  76. Terzaghi, K. (1943), Theoretical Soil Mechanics, John Wiley & Sons, Inc., Hoboken, NJ, USA
  77. Thottoth, S.R., Das, P.P. and Khatri, V.N. (2024a), "Prediction of compression capacity of under-reamed piles in sand and clay", Multiscale Multidiscip. Model. Exp. Des., https://doi.org/10.1007/s41939-023-00331-0.
  78. Thottoth, S.R., Khatri, V.N., Kolathayar, S., Keawsawasvong, S. and Lai, V.Q. (2024b), "Optimizing seismic earth pressure estimates for battered retaining walls using numerical methods and ANN", Geotech. Geol. Eng., 42, 3307-3329. https://doi.org/10.1007/s10706-023-02731-y
  79. Vahedifard, F., Leshchinsky, B.A., Mortezaei, K. and Lu, N. (2015), "Active earth pressures for unsaturated retaining structures", J. Geotech. Geoenviron. Eng., 141(11), 236. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001356.
  80. Vo, T. and Russell, A.R. (2014), "Slip line theory applied to a retaining wall-unsaturated soil interaction problem", Comput. Geotech., 55, 416-428. https://doi.org/10.1016/j.compgeo.2013.09.010.
  81. Wang, L., Sun, D. and Li, L. (2019), "3D stability of partially saturated soil slopes after rapid drawdown by a new layer-wise summation method", Landslides, 16, 295-313. https://doi.org/10.1007/s10346-018-1081-2.
  82. Wang, L., Sun, D., Yao, Y., Wu, L. and Xu, Y. (2020), "Kinematic limit analysis of three-dimensional unsaturated soil slopes reinforced with a row of piles", Comput. Geotech., 120, 103428. https://doi.org/10.1016/j.compgeo.2019.103428.
  83. Xiao, F. and Zhao, Z. (2019), "Evaluation of equivalent hydraulic aperture (EHA) for rough rock fractures", Can Geotech. J., 56, 1486-1501. https://doi.org/10.1139/cgj-2018-0274.
  84. Yang, X.L. and Chen, H. (2021), "Seismic analysis of 3D active earth pressure for unsaturated backfill.", Transp. Geotech., 30, 100593. https://doi.org/10.1016/j.trgeo.2021.100593.
  85. Zhang, C., Zhao, J., Zhang, Q. and Xu, F. (2010), "Unified solutions for unsaturated soil shear strength and active earth pressure", Experimental and Applied Modeling of Unsaturated Soils. American Society of Civil Engineers, Reston, VA, 218-224
  86. Zhang, W., Wu, C., Zhong, H., Li, Y. and Wang, L. (2021), "Prediction of undrained shear strength using extreme gradient boosting and random forest based on Bayesian optimization", Geosci. Front, 12(1), 469-477. https://doi.org/10.1016/j.gsf.2020.03.007.
  87. Zhao, L.H., Luo, Q., Li, L., Yang, F. and Yang, X.L. (2009), "The upper bound "Calculation of Passive Earth Pressure Based on Shear Strength theory of unsaturated soil", Slope Stability, Retaining Walls, and Foundations. American Society of Civil Engineers, Reston, VA, 151-157.
  88. Zurada, J.M. (1992), Introduction to Artificial Neural Systems. West Group.