SpringerLink
Log in

State-of-the-Art Review of Machine Learning Applications in Constitutive Modeling of Soils

  • Original Paper
  • Published:
Archives of Computational Methods in Engineering Aims and scope Submit manuscript

Abstract

Machine learning (ML) may provide a new methodology to directly learn from raw data to develop constitutive models for soils by using pure mathematic skills. It has presented success and versatility in cases of simple stress paths due to its strong non-linear map** capacity without limitations of constitutive formulations. However, current studies on the ML-based constitutive modeling of soils is still very limited. This study comprehensively reviews the application of ML algorithms in the development of constitutive models of soils and compares the performance of different ML algorithms. First, the basic principles of typical ML algorithms used in describing soil behaviors are briefly elaborated. The main characteristics and the limitations of such ML algorithms are summarized and compared. Then, the methodology of develo** a ML-based soil model is reviewed from six aspects, such as adopted ML algorithms, data source, framework of the ML-based model, training strategy, generalization ability and application scope. Finally, five new ML-based models are developed using five typical ML algorithms (i.e. BPNN, RBF, LSTM, GRU and BiLSTM that can predict multi outputs together) based on same set of experimental results of sand, and compare each other in terms of the predictive accuracy and generalization ability. Results show the long short-term memory (LSTM) neural network and its variants are most suitable for develo** constitutive models. Moreover, some useful suggestions for develo** the ML-based soil model are also provided for the community.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price includes VAT (Germany)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

References

  1. Su D, Yang ZX (2019) Drained analyses of cylindrical cavity expansion in sand incorporating a bounding-surface model with state-dependent dilatancy. Appl Math Model 68:1–20

    Article  MathSciNet  MATH  Google Scholar 

  2. Kang X, **a Z, Chen R, Ge L, Liu X (2019) The critical state and steady state of sand: A literature review. Mar Georesour Geotec 37(9):1105–1118

    Article  Google Scholar 

  3. Su L-J, Yin J-H, Zhou W-H (2010) Influences of overburden pressure and soil dilation on soil nail pull-out resistance. Comput Geotech 37(4):555–564

    Article  Google Scholar 

  4. Yin Z-Y, Chang CS, Karstunen M, Hicher P-Y (2010) An anisotropic elastic–viscoplastic model for soft clays. Int J Solids Struct 47(5):665–677

    Article  MATH  Google Scholar 

  5. Kang X, **a Z, Chen RP (2019) Measurement and correlations of K0 and Vs anisotropy of granular soils. Proc Inst Civ Eng Geotech Eng 173(6):546–561

    Google Scholar 

  6. Liu WZ, Shi ML, Miao LC, Xu LR, Zhang DW (2013) Constitutive modeling of the destructuration and anisotropy of natural soft clay. Comput Geotech 51:24–41

    Article  Google Scholar 

  7. Yin Z-Y, Karstunen M (2011) Modelling strain-rate-dependency of natural soft clays combined with anisotropy and destructuration. Acta Mech Solida Sin 24(3):216–230

    Article  Google Scholar 

  8. Hu X, Zhang Y, Guo L, Wang J, Cai Y, Fu H, Cai Y (2018) Cyclic behavior of saturated soft clay under stress path with bidirectional shear stresses. Soil Dyn Earthq Eng 104:319–328

    Article  Google Scholar 

  9. Yin Z-Y, Karstunen M, Chang CS, Koskinen M, Lojander M (2011) Modeling time-dependent behavior of soft sensitive clay. J Geotech Geoenviron Eng 137(11):1103–1113

    Article  Google Scholar 

  10. Tian Y, Yao YP (2017) Modelling the non-coaxiality of soils from the view of cross-anisotropy. Comput Geotech 86:219–229

    Article  Google Scholar 

  11. Vermeer P (1978) A double hardening model for sand. Geotechnique 28(4):413–433

    Article  Google Scholar 

  12. ** Y-F, Yin Z-Y, Shen S-L, Hicher P-Y (2016) Selection of sand models and identification of parameters using an enhanced genetic algorithm. Int J Numer Anal Met 40(8):1219–1240

    Article  Google Scholar 

  13. Roscoe KH, Burland J (1968) On the generalized stress-strain behaviour of wet clay. Engineering Plasticity Cambridge, UK, pp 535–609

    MATH  Google Scholar 

  14. Jefferies M (1993) Nor-Sand: a simle critical state model for sand. Geotechnique 43(1):91–103

    Article  Google Scholar 

  15. Yu H (1998) CASM: A unified state parameter model for clay and sand. Int J Numer Anal Methods Geomech 22(8):621–653

    Article  MATH  Google Scholar 

  16. Gajo A, Wood M (1999) Severn-Trent sand: a kinematic-hardening constitutive model: the q–p formulation. Geotechnique 49(5):595–614

    Article  Google Scholar 

  17. Yao Y, Hou W, Zhou A (2009) UH model: three-dimensional unified hardening model for overconsolidated clays. Geotechnique 59(5):451–469

    Article  Google Scholar 

  18. Yao Y, Sun D, Luo T (2004) A critical state model for sands dependent on stress and density. Int J Numer Anal Methods Geomech 28(4):323–337

    Article  MATH  Google Scholar 

  19. Yao Y, Sun D, Matsuoka H (2008) A unified constitutive model for both clay and sand with hardening parameter independent on stress path. Comput Geotech 35(2):210–222

    Article  Google Scholar 

  20. Taiebat M, Dafalias YF (2008) SANISAND: Simple anisotropic sand plasticity model. Int J Numer Anal Met 32(8):915–948

    Article  MATH  Google Scholar 

  21. ** Y-F, Wu Z-X, Yin Z-Y, Shen JS (2017) Estimation of critical state-related formula in advanced constitutive modeling of granular material. Acta Geotech 12(6):1329–1351

    Article  Google Scholar 

  22. ** Y-F, Yin Z-Y, Shen S-L, Hicher P-Y (2016) Investigation into MOGA for identifying parameters of a critical-state-based sand model and parameters correlation by factor analysis. Acta Geotech 11(5):1131–1145

    Article  Google Scholar 

  23. Yin ZY, Chang CS, Karstunen M, Hicher PY (2010) An anisotropic elastic-viscoplastic model for soft clays. Int J Solids Struct 47(5):665–677

    Article  MATH  Google Scholar 

  24. Mašín D (2005) A hypoplastic constitutive model for clays. Int J Numer Anal Methods Geomech 29(4):311–336

    Article  MATH  Google Scholar 

  25. Wu W, Bauer E, Kolymbas D (1996) Hypoplastic constitutive model with critical state for granular materials. Mech Mater 23(1):45–69

    Article  Google Scholar 

  26. Wang S, Wu W, Yin Z-Y, Peng C, He X-Z (2018) Modelling time-dependent behaviour of granular material with hypoplasticity. Int J Numer Anal Methods Geomech 42(12):1331–1345

    Article  Google Scholar 

  27. Kolymbas D (1985) A generalized hypoelastic constitutive law. Proc XI Int Conf Soil Mechanics and Foundation Engineering San Francisco 11:2626

    Google Scholar 

  28. Chang CS, Hicher PY (2005) An elasto-plastic model for granular materials with microstructural consideration. Int J Solids Struct 42(14):4258–4277

    Article  MATH  Google Scholar 

  29. Yin ZY, Chang CS, Hicher PY, Karstunen M (2009) Micromechanical analysis of kinematic hardening in natural clay. Int J Plast 25(8):1413–1435

    Article  MATH  Google Scholar 

  30. Yin ZY, Chang CS, Hicher PY (2010) Micromechanical modelling for effect of inherent anisotropy on cyclic behaviour of sand. Int J Solids Struct 47(14–15):1933–1951

    Article  MATH  Google Scholar 

  31. Yin Z-Y, Zhao J, Hicher P-Y (2014) A micromechanics-based model for sand-silt mixtures. Int J Solids Struct 51(6):1350–1363

    Article  Google Scholar 

  32. Yin ZY, Chang CS (2009) Microstructural modelling of stress-dependent behaviour of clay. Int J Solids Struct 46(6):1373–1388

    Article  MATH  Google Scholar 

  33. **ong H, Nicot F, Yin Z (2017) A three-dimensional micromechanically based model. Int J Numer Anal Methods Geomech 41(17):1669–1686

    Article  Google Scholar 

  34. Yao YP, Hou W, Zhou AN (2009) UH model: three-dimensional unified hardening model for overconsolidated clays. Géotechnique 59(5):451–469

    Article  Google Scholar 

  35. Yin Z-Y, ** Y-F (2019) Practice of optimisation theory in geotechnical engineering. Springer, Singapore

    Book  MATH  Google Scholar 

  36. Amroune M (2019) Machine learning techniques applied to on-line voltage stability assessment: a review. Archiv Comput Methods Eng. https://doi.org/10.1007/s11831-019-09368-2

    Article  Google Scholar 

  37. Wang Z, Liu K, Li J, Zhu Y, Zhang Y (2019) Various frameworks and libraries of machine learning and deep learning: a survey. Archiv Comput Methods Eng. https://doi.org/10.1007/s11831-018-09312-w

    Article  Google Scholar 

  38. Li H, Yu H, Cao N, Tian H, Cheng S (2020) Applications of artificial intelligence in oil and gas development. Archiv Comput Methods Eng. https://doi.org/10.1007/s11831-020-09402-8

    Article  Google Scholar 

  39. Zhang P, Chen RP, Wu HN (2019) Real-time analysis and regulation of EPB shield steering using random forest. Automat Constr 106:102860

    Article  Google Scholar 

  40. Lee S, Ha J, Zokhirova M, Moon H, Lee J (2017) Background information of deep learning for structural engineering. Archiv Comput Methods Eng 25(1):121–129

    Article  MathSciNet  MATH  Google Scholar 

  41. Zhang P, Yin Z-Y, ** Y-F, Chan THT (2020) A novel hybrid surrogate intelligent model for creep index prediction based on particle swarm optimization and random forest. Eng Geol 265:105328

    Article  Google Scholar 

  42. Feng XT, Li SJ, Liao HJ, Yang CX (2002) Identification of non-linear stress-strain-time relationship of soils using genetic algorithm. Int J Numer Anal Met 26(8):815–830

    Article  MATH  Google Scholar 

  43. Feng XT, Chen BR, Yang CX, Zhou H, Ding X (2006) Identification of visco-elastic models for rocks using genetic programming coupled with the modified particle swarm optimization algorithm. Int J Rock Mech Min 43(5):789–801

    Article  Google Scholar 

  44. Gao W, Ge M, Chen D, Wang X (2016) Back analysis for rock model surrounding underground roadways in coal mine based on black hole algorithm. Eng Comput-Germany 32(4):675–689

    Article  Google Scholar 

  45. Cabalar AF, Cevik A (2011) Triaxial behavior of sand–mica mixtures using genetic programming. Expert Syst Appl 38(8):10358–10367

    Article  Google Scholar 

  46. Javadi AA, Rezania M (2009) Applications of artificial intelligence and data mining techniques in soil modeling. Geomech Eng 1(1):53–74

    Article  Google Scholar 

  47. Faramarzi A, Javadi AA, Alani AM (2012) EPR-based material modelling of soils considering volume changes. Comput Geosci-UK 48:73–85

    Article  Google Scholar 

  48. Javadi AA, Faramarzi A, Ahangar-Asr A (2012) Analysis of behaviour of soils under cyclic loading using EPR-based finite element method. Finite Elem Anal Des 58:53–65

    Article  Google Scholar 

  49. Cuisinier O, Javadi AA, Ahangar-Asr A, Masrouri F (2013) Identification of coupling parameters between shear strength behaviour of compacted soils and chemical’s effects with an evolutionary-based data mining technique. Comput Geotech 48:107–116

    Article  Google Scholar 

  50. Nassr A, Esmaeili-Falak M, Katebi H, Javadi A (2018) A new approach to modeling the behavior of frozen soils. Eng Geol 246:82–90

    Article  Google Scholar 

  51. Ahangar Asr A, Faramarzi A, Javadi AA (2018) An evolutionary modelling approach to predicting stress-strain behaviour of saturated granular soils. Eng Comput 35(8):2931–2952

    Article  Google Scholar 

  52. Zhao H, Huang Z, Zou Z (2014) Simulating the stress-strain relationship of geomaterials by support vector machine. Math Problems Eng 2014:1–7

    Google Scholar 

  53. Kohestani VR, Hassanlourad M (2016) Modeling the mechanical behavior of carbonate sands using artificial neural networks and support vector machines. Int J Geomech 16(1):04015038

    Article  Google Scholar 

  54. Ellis GW, Yao C, Zhao R, Penumadu D (1995) Stress-strain modeling of sands using artificial neural networks. J Geotech Eng 121(5):429–435

    Article  Google Scholar 

  55. Ghaboussi J, Sidarta DE (1998) New nested adaptive neural networks (NANN) for constitutive modeling. Comput Geotech 22(1):29–52

    Article  Google Scholar 

  56. Sidarta DE, Ghaboussi J (1998) Constitutive modeling of geomaterials from non-uniform material tests. Comput Geotech 22(1):53–71

    Article  Google Scholar 

  57. Penumadu D, Zhao RD (1999) Triaxial compression behavior of sand and gravel using artificial neural networks (ANN). Comput Geotech 24:207–230

    Article  Google Scholar 

  58. Basheer IA (2002) Stress-strain behavior of geomaterials in loading reversal simulated by time-delay neural networks. J Mater Civ Eng 14:270–273

    Article  Google Scholar 

  59. Basheer IA (2000) Selection of methodology for neural network modeling of constitutive hystereses behavior of soils. Comput-Aided Civ Inf 15:440–458

    Article  Google Scholar 

  60. Habibagahi G, Bamdad A (2003) A neural network framework for mechanical behavior of unsaturated soils. Can Geotech J 40(3):684–693

    Article  Google Scholar 

  61. Banimahd M, Yasrobi SS, Woodward PK (2005) Artificial neural network for stress–strain behavior of sandy soils: knowledge based verification. Comput Geotech 32(5):377–386

    Article  Google Scholar 

  62. Shahin MA, Indraratna B (2006) Modeling the mechanical behavior of railway ballast using artificial neural networks. Can Geotech J 43(11):1144–1152

    Article  Google Scholar 

  63. Fu Q, Hashash YMA, Jung S, Ghaboussi J (2007) Integration of laboratory testing and constitutive modeling of soils. Comput Geotech 34(5):330–345

    Article  Google Scholar 

  64. Hashash YMA, Song H (2008) The integration of numerical modeling and physical measurements through inverse analysis in geotechnical engineering. KSCE Journal of Civil Engineering 12(3):165–176

    Article  Google Scholar 

  65. Hashash YMA, Fu Q, Ghaboussi J, Lade PV, Saucier C (2009) Inverse analysis–based interpretation of sand behavior from triaxial compression tests subjected to full end restraint. Can Geotech J 46(7):768–791

    Article  Google Scholar 

  66. He S, Li J (2009) Modeling nonlinear elastic behavior of reinforced soil using artificial neural networks. Appl Soft Comput 9(3):954–961

    Article  Google Scholar 

  67. Johari A, Javadi AA, Habibagahi G (2011) Modelling the mechanical behaviour of unsaturated soils using a genetic algorithm-based neural network. Comput Geotech 38(1):2–13

    Article  Google Scholar 

  68. Sezer A (2011) Prediction of shear development in clean sands by use of particle shape information and artificial neural networks. Expert Syst Appl 38(5):5603–5613

    Article  Google Scholar 

  69. Lv Y, Nie L, Xu K (2011) Study of the neural network constitutive models for turfy soil with different decomposition degree. 2011 Second International Conference on Mechanic Automation and Control Engineering Hohhot, China: 6111–6114

  70. Araei AA (2014) Artificial neural networks for modeling drained monotonic behavior of rockfill materials. Int J Geomech 14(3):04014005

    Article  Google Scholar 

  71. Rashidian V, Hassanlourad M (2014) Application of an artificial neural network for modeling the mechanical behavior of carbonate soils. Int J Geomech 14(1):142–150

    Article  Google Scholar 

  72. Stefanos D, Gyan P (2015) On neural network constitutive models for geomaterials. J Civil Eng Res 5(5):106–113

    Google Scholar 

  73. Li Z, Chow JK, Wang YH (2017) Applying the artificial neural network to predict the soil responses in the DEM simulation. IOP Conf Series: Mat Sci Eng 216:012040

    Article  Google Scholar 

  74. Lin P, Ratnam R, Sankari H, Garg A (2019) Mechanism of microstructural variation under cyclic shearing of Shantou marine clay: experimental investigation and model development. Geotech Geol Eng 37(5):4163–4210

    Article  Google Scholar 

  75. Peng X-h, Wang Z-c, Luo T, Yu M, Luo Y-s (2008) An elasto-plastic constitutive model of moderate sandy clay based on BC-RBFNN. J Central South Univ 15(1):47–50

    Article  Google Scholar 

  76. Li XD, Zhang GY, Fang XP, Tao WJ, Hui X (2008) Normalization characteristic of sands under triaxial compression and numerical modeling method (in Chinese). Chin J Rock Mechan Eng 27(S1):3082–3087

    Google Scholar 

  77. Zhu JH, Zaman MM, Anderson SA (1998) Modelling of shearing behaviour of a residual soil with recurrent neural network. Int J Numer Anal Met 22(8):671–687

    Article  MATH  Google Scholar 

  78. Zhu J-H, Zaman MM, Anderson SA (1998) Modeling of soil behavior with a recurrent neural network. Can Geotech J 35:858–872

    Article  Google Scholar 

  79. Romo MP, García SR, Mendoza MJ, Taboada-Urtuzuástegui V (2001) Recurrent and constructive-algorithm networks for sand behavior modeling. Int J Geomech 1(4):371–387

    Article  Google Scholar 

  80. Zhang P, Yin ZY, ** YF, Ye GL (2020) An AI-based model for describing cyclic characteristics of granular materials. Int J Numer Anal Met 44(9):1315–1335

    Article  Google Scholar 

  81. Zhang N, Shen S-L, Zhou A, Xu Y-S (2019) Investigation on performance of neural networks using quadratic relative error cost function. IEEE Access 7:106642–106652

    Article  Google Scholar 

  82. Wang L, Cai Y, Liu D (2018) Multiscale reliability-based topology optimization methodology for truss-like microstructures with unknown-but-bounded uncertainties. Comput Method Appl M 339:358–388

    Article  MathSciNet  MATH  Google Scholar 

  83. Wang K, Sun W (2019) Meta-modeling game for deriving theory-consistent, microstructure-based traction–separation laws via deep reinforcement learning. Comput Method Appl M 346:216–241

    Article  MathSciNet  MATH  Google Scholar 

  84. Koza JR (1992) Genetic programming: on the programming of computers by natural selection. MIT Press, Cambridge, MA

    MATH  Google Scholar 

  85. Gomes FM, Pereira FM, Silva AF, Silva MB (2019) Multiple response optimization: analysis of genetic programming for symbolic regression and assessment of desirability functions. Knowl-Based Syst 179:21–33

    Article  Google Scholar 

  86. ** YF, Yin ZY, Zhou WH, Yin JH, Shao JF (2019) A single-objective EPR based model for creep index of soft clays considering L2 regularization. Eng Geol 248:242–255

    Article  Google Scholar 

  87. Yin ZY, ** YF, Huang HW, Shen SL (2016) Evolutionary polynomial regression based modelling of clay compressibility using an enhanced hybrid real-coded genetic algorithm. Eng Geol 210:158–167

    Article  Google Scholar 

  88. Hein D, Udluft S, Runkler TA (2018) Interpretable policies for reinforcement learning by genetic programming. Eng Appl Artif Intel 76:158–169

    Article  Google Scholar 

  89. Beg AH, Islam MZ (2016) Advantages and limitations of genetic algorithms for clustering records. IEEE 11th Conf Industrial Electronics and Applications (ICIEA) Hefei, China:

  90. Yin Z-Y, ** Y-F, Shen JS, Hicher P-Y (2018) Optimization techniques for identifying soil parameters in geotechnical engineering: Comparative study and enhancement. Int J Numer Anal Met 42(1):70–94

    Article  Google Scholar 

  91. Cortes C, Vapnik V (1995) Support-Vector networks. Mach Learn 20:273–297

    Article  MATH  Google Scholar 

  92. Okwuashi O, Ndehedehe CE (2020) Deep support vector machine for hyperspectral image classification. Pattern Recognit 103:107298

    Article  Google Scholar 

  93. Qi CC, Tang XL (2018) A hybrid ensemble method for improved prediction of slope stability. Int J Numer Anal Met 42(15):1823–1839

    Article  Google Scholar 

  94. Rumelhart DE, Hinton GE, Williams RJ (1986) Learning representations by back-propagating errors. Nature 323(9):533–536

    Article  MATH  Google Scholar 

  95. LeCun Y, Bengio Y, Hinton G (2015) Deep learning. Nature 521(7553):436–444

    Article  Google Scholar 

  96. Armaghani DJ, Mohamad ET, Narayanasamy MS, Narita N, Yagiz S (2017) Development of hybrid intelligent models for predicting TBM penetration rate in hard rock condition. Tunnell Undergr Space Technol 63:29–43

    Article  Google Scholar 

  97. Atangana Njock PG, Shen S-L, Zhou A, Lyu H-M (2020) Evaluation of soil liquefaction using AI technology incorporating a coupled ENN / t-SNE model. Soil Dyn Earthq Eng 130:105988

    Article  Google Scholar 

  98. Lu Y, Sundararajan N, Saratchandran P (1998) Performance evaluation of a sequential minimal radial basis function (RBF) neural network learning algorithm. IEEE Trans Neural Netw 9(2):308–318

    Article  Google Scholar 

  99. Kang F, Li J, Xu Q (2017) System reliability analysis of slopes using multilayer perceptron and radial basis function networks. Int J Numer Anal Met 41(18):1962–1978

    Article  Google Scholar 

  100. Hurtado JE (2001) Neural networks in stochastic mechanics. Archiv Comput Methods Eng 8(3):303–342

    Article  MathSciNet  MATH  Google Scholar 

  101. Wang K, Sun W (2018) A multiscale multi-permeability poroplasticity model linked by recursive homogenizations and deep learning. Comput Method Appl M 334:337–380

    Article  MathSciNet  MATH  Google Scholar 

  102. Hochreiter S, Schmidhuber J (1997) Long short-term memory. Neural Comput 9:1735–1780

    Article  Google Scholar 

  103. Cho K, Van Merriënboer B, Gulcehre C, Bahdanau v, Bougares F, Schwenk H, Bengio Y (2014) Learning phrase representations using RNN Encoder–Decoder for statistical machine translation. arxiv 1406.1078:

  104. Haidong S, Junsheng C, Hongkai J, Yu Y, Zhantao W (2020) Enhanced deep gated recurrent unit and complex wavelet packet energy moment entropy for early fault prognosis of bearing. Knowl-Based Syst 188:105022

    Article  Google Scholar 

  105. Kondner RL (1963) Hyperbolic stress-strain response: cohesive soils. J Soil Mech Found Eng Division 89(1):115–144

    Article  Google Scholar 

  106. Roscoe KH, Schofield AN, Thurairajah A (1963) Yielding of clays in states wetter than critical. Géotechnique 13(3):211–240

    Article  Google Scholar 

  107. Roscoe KH, Schofield AN, Wroth CP (1958) On the yielding of soils. Géotechnique 8(1):22–53

    Article  Google Scholar 

  108. Schanz T, Vermeer PA, Bonnier PG. The hardening soil model: Formulation and verification. Beyond 2000 in Computational Geotechnics. Amsterdam, Balkema, Rotterdam1999. p. 281–296

  109. Pande GN, Sharma KG (1983) Multi-laminate model of clays—a numerical evaluation of the influence of rotation of the principal stress axes. Int J Numer Anal Met 7(4):397–418

    Article  MATH  Google Scholar 

  110. Yin Z-Y, Wu Z-X, Hicher P-Y (2018) Modeling monotonic and cyclic behavior of granular materials by exponential constitutive function. J Eng Mech-ASCE 144(4):04018014

    Article  Google Scholar 

  111. Zhang P (2019) A novel feature selection method based on global sensitivity analysis with application in machine learning-based prediction model. Appl Soft Comput 85:105859

    Article  Google Scholar 

  112. Cai J, Luo J, Wang S, Yang S (2018) Feature selection in machine learning: a new perspective. Neurocomputing 300:70–79

    Article  Google Scholar 

  113. Javadi AA, Rezania M (2009) Intelligent finite element method: An evolutionary approach to constitutive modeling. Adv Eng Inform 23(4):442–451

    Article  Google Scholar 

  114. Yun GJ, Ghaboussi J, Elnashai AS (2008) Self-learning simulation method for inverse nonlinear modeling of cyclic behavior of connections. Comput Method Appl M 197(33–40):2836–2857

    Article  MATH  Google Scholar 

  115. Shin HS, Pande GN (2003) Identification of elastic constants for orthotropic materials from a structural test. Comput Geotech 30(7):571–577

    Article  Google Scholar 

  116. Ghaboussi J, Pecknold AD, Zhang M, Haj-Ali MR (1998) Autoprogressive training of neural network constitutive models. Int J Numer Meth Eng 42:105–126

    Article  MATH  Google Scholar 

  117. Jacobs RA (1988) Increased rates of convergence through learning rate adaptation. Neural Netw 1:295–307

    Article  Google Scholar 

  118. Holland J (1992) Genetic algorithms. Sci Am 267:66–72

    Article  Google Scholar 

  119. Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67

    Article  Google Scholar 

  120. Kennedy J, Eberhart R (1995) Particle swarm optimization. IEEE International Conference on Neural Networks Perth, Australia: 1942–1948

  121. Maas AL, Hannun AY, Ng AY. Rectifier nonlinearities improve neural network acoustic models. 30th International Conference on Machine Learning. Atlanta, Georgia, USA2013.

  122. Ramachandran P, Zoph B, Le QV (2017) Swish: a self-gated activation function. ar**v:1710.05941v1

  123. Misra D (2019) Mish: a self regularized non-monotonic neural activation function. ar**v:1908.08681

  124. Fahlman SE (1988) An empirical study of learning speed in back-propagation networks. Technical report CMU-CS-88–162 Carnegie-Mellon University

  125. Riedmiller M, Braun H (1993) A direct adaptive method for faster backpropagation learning. IEEE International Conference on Neural Networks San Francisco, CA, USA: 586–591

  126. Levenberg K (1944) A method for the solution of certain non-linear problems in least squares. Q Appl Math 2(2):164–168

    Article  MathSciNet  MATH  Google Scholar 

  127. Marquardt DW (1963) An algorithm for least-squares estimation of nonlinear parameters. J Soc Ind Appl Math 11(2):431–441

    Article  MathSciNet  MATH  Google Scholar 

  128. Møller MF (1993) A scaled conjugate gradient algorithm for fast supervised learning. Neural Netw 6:525–533

    Article  Google Scholar 

  129. Rumelhart DE, Hinton GE, Williams RJ (1986) Learning internal representation by error propagation. Parallel distributed processing, MIT Press, Cambridge

    MATH  Google Scholar 

  130. Larochelle H, Bengio Y, Louradour J, Lamblin P (2009) Exploring strategies for training deep neural networks. J Mach Learn Res 1:1–40

    MATH  Google Scholar 

  131. Duchi J, Hazan E, Singer Y (2011) Adaptive subgradient methods for online learning and stochastic optimization. J Mach Learn Res 12:2121–2159

    MathSciNet  MATH  Google Scholar 

  132. Tieleman T, Hinton G (2012) Lecture 6.5 - RMSProp, COURSERA: Neural networks for machine learning. Technical report:

  133. Kingma DP (2015) Adam: a method for stochastic optimization. International conference on learning representations San Diego, CA:

  134. Zhang P, Li H, Ha QP, Yin Z-Y, Chen R-P (2020) Reinforcement learning based optimizer for improvement of predicting tunneling-induced ground responses. Adv Eng Inf 45:101097

    Article  Google Scholar 

  135. Zhang P, Yin ZY, ** YF, Chan T, Gao FP (2021) Intelligent modelling of clay compressibility using hybrid meta-heuristic and machine learning algorithms. Geosci Front 12(1):441–452

    Article  Google Scholar 

  136. Fujii M, Takahashi A, Takahashi M (2019) Asymptotic expansion as prior knowledge in deep learning method for high dimensional BSDEs. Asia-Pacific Finan Markets 26(3):391–408

    Article  MATH  Google Scholar 

  137. Srivastava N, Hinton G, Krizhevsky A, Sutskever I, Salakhutdinov R (2014) Dropout: a simple way to prevent neural networks from overfitting. J Machine Learning Research 15:1929–1958

    MathSciNet  MATH  Google Scholar 

  138. ** Y-F, Yin Z-Y, Zhou W-H, Huang H-W (2019) Multi-objective optimization-based updating of predictions during excavation. Eng Appl Artif Intel 78:102–123

    Article  Google Scholar 

  139. Krizhevsky A, Sutskever I, Hinton GE (2012) Imagenet classification with deep convolutional neural networks. Commun of the ACM 60(6):84–90

    Article  Google Scholar 

  140. Moradi R, Berangi R, Minaei B (2019) A survey of regularization strategies for deep models. Artif Intell Rev. https://doi.org/10.1007/s10462-019-09784-7

    Article  Google Scholar 

  141. Barnard E, Wessels L (1992) Extrapolation and interpolation in neural network classifiers. IEEE Control Systems 12(5):50–53

    Article  Google Scholar 

  142. Yin ZY, Wang JH (2012) A one-dimensional strain-rate based model for soft structured clays. Scie China-Technol Sci 55(1):90–100

    Article  MATH  Google Scholar 

  143. Yin ZY, Chang CS (2009) Non-uniqueness of critical state line in compression and extension conditions. Int J Numer Anal Methods Geomech 33(10):1315–1338

    Article  MATH  Google Scholar 

  144. Yin ZY, Chang CS (2013) Stress–dilatancy behavior for sand under loading and unloading conditions. Int J Numer Anal Methods Geomech 37(8):855–870

    Article  Google Scholar 

  145. **ao Y, Liu H, Chen Y, Chu J (2014) Influence of intermediate principal stress on the strength and dilatancy behavior of rockfill material. J Geotech Geoenviron Eng 140(11):04014064

    Article  Google Scholar 

  146. Yu H, Yuan X (2006) On a class of non-coaxial plasticity models for granular soils. Proc Royal Soc a: Mathemat Phys Eng Sci 462(2067):725–748

    Article  MATH  Google Scholar 

  147. ** Y-F, Yin Z-Y, Zhou W-H, Huang H-W (2019) Multi-objective optimization-based updating of predictions during excavation. Eng Appl Artif Intell 78:102–123

    Article  Google Scholar 

  148. ** Y-F, Yin Z-Y, Zhou W-H, Liu X (2020) Intelligent model selection with updating parameters during staged excavation using optimization method. Acta Geotech. https://doi.org/10.1007/s11440-020-00936-6

    Article  Google Scholar 

  149. Yin ZY, Xu Q, Hicher PY (2013) A simple critical-state-based double-yield-surface model for clay behavior under complex loading. Acta Geotech 8(5):509–523

    Article  Google Scholar 

  150. Yin ZY, Yin JH, Huang HW (2015) Rate-dependent and long-term yield stress and strength of soft wenzhou marine clay: experiments and modeling. Mar Georesour Geotechnol 33(1):79–91

    Article  Google Scholar 

  151. Yin ZY, Zhu QY, Yin JH, Ni Q (2014) Stress relaxation coefficient and formulation for soft soils. Géotechnique Letters 4:45–51

    Article  Google Scholar 

  152. Yin Z-Y, Zhu Q-Y, Zhang D-M (2017) Comparison of two creep degradation modeling approaches for soft structured soils. Acta Geotech 12(6):1395–1413

    Article  Google Scholar 

  153. Zhu Q-Y, ** Y-F, Shang X-Y, Chen T (2019) A 1D model considering the combined effect of strain-rate and temperature for soft soil. Geomech Eng 18(2):133–140

    Google Scholar 

  154. Yin Z-Y, ** Y-F, Shen S-L, Huang H-W (2017) An efficient optimization method for identifying parameters of soft structured clay by an enhanced genetic algorithm and elastic–viscoplastic model. Acta Geotech 12(4):849–867

    Article  Google Scholar 

  155. Graves A, Mohamed A-r, Hinton G (2013) Speech recognition with deep recurrent neural networks ICASSP: 6645–6649

  156. Ibsen LB, Bødker LB. Baskarp Sand No. 15: data report 9301. Aalborg: Geotechnical Engineering Group. Data Report, No. 9401. 1994.

Download references

Acknowledgements

This research was financially supported by the RIF project of Research Grants Council (RGC) of Hong Kong Special Administrative Region Government (HKSARG) of China (Grant No.: R5037-18F).

Author information

Authors and Affiliations

  1. Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China

    Pin Zhang, Zhen-Yu Yin & Yin-Fu **

Authors
  1. Pin Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhen-Yu Yin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yin-Fu **
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

PZ: Conceptualization, Methodology, Formal analysis, Writing-Review and Original Draft. Z-YY: Supervision, Investigation, Methodology, Visualization, Writing-Review and Editing. Y-FJ: Validation, Visualization, Writing-Review and Editing.

Corresponding author

Correspondence to Zhen-Yu Yin.

Ethics declarations

Conflicts of interest

The authors declare that the work described has not been published before; that it is not under consideration for publication anywhere else; that its publication has been approved by all co-authors; that there is no conflict of interest regarding the publication of this article.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, P., Yin, ZY. & **, YF. State-of-the-Art Review of Machine Learning Applications in Constitutive Modeling of Soils. Arch Computat Methods Eng 28, 3661–3686 (2021). https://doi.org/10.1007/s11831-020-09524-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11831-020-09524-z

Search

Navigation