Acta Geotechnica

, Volume 14, Issue 6, pp 1925–1947 | Cite as

Identifying parameters of advanced soil models using an enhanced transitional Markov chain Monte Carlo method

  • Yin-Fu Jin
  • Zhen-Yu YinEmail author
  • Wan-Huan Zhou
  • Suksun Horpibulsuk
Research Paper


Parameter identification using Bayesian approach with Markov Chain Monte Carlo (MCMC) has been verified only for certain conventional simple constitutive models up to now. This paper presents an enhanced version of the differential evolution transitional MCMC (DE-TMCMC) method and a competitive Bayesian parameter identification approach for applying to advanced soil models. To realize the intended computational savings, a parallel computing implementation of DE-TMCMC is achieved using the single program/multiple data technique in MATLAB. To verify its robustness and effectiveness, synthetic numerical tests with/without noise and real laboratory tests are used for identifying the parameters of a critical state-based sand model based on multiple independent calculations. The original TMCMC is also used for comparison to highlight that DE-TMCMC is highly robust and effective in identifying the parameters of advanced sand models. Finally, the proposed parameter identification using DE-TMCMC is applied to identify parameters of an elasto-viscoplastic model from two in situ pressuremeter tests. All results demonstrate the excellent ability of the enhanced Bayesian parameter identification approach on identifying parameters of advanced soil models from both laboratory and in situ tests.


Bayesian parameter identification Constitutive model Clay Pressuremeter Sand Transitional Markov chain Monte Carlo 



This research was financially supported by a RIF project (Grant No.: PolyU R5037-18F) from Research Grants Council (RGC) of Hong Kong Special Administrative Region Government (HKSARG) of China, and the National Natural Science Foundation of China (Grant No. 51579179).


  1. 1.
    Akeju OV, Senetakis K, Wang Y (2019) Bayesian parameter identification and model selection for normalized modulus reduction curves of soils. J Earthquake Eng 23(2):305–333Google Scholar
  2. 2.
    Ancey C (2005) Monte Carlo calibration of avalanches described as Coulomb fluid flows. Philos Trans R Soc A Math Phys Eng Sci 363(1832):1529–1550MathSciNetzbMATHGoogle Scholar
  3. 3.
    Angelikopoulos P, Papadimitriou C, Koumoutsakos P (2012) Bayesian uncertainty quantification and propagation in molecular dynamics simulations: a high performance computing framework. J Chem Phys 137(14):144103Google Scholar
  4. 4.
    Angelikopoulos P, Papadimitriou C, Koumoutsakos P (2015) X-TMCMC: adaptive kriging for Bayesian inverse modeling. Comput Methods Appl Mech Eng 289:409–428MathSciNetzbMATHGoogle Scholar
  5. 5.
    Beck JL (2010) Bayesian system identification based on probability logic. Struct Control Health Monit 17(7):825–847Google Scholar
  6. 6.
    Beck JL, Katafygiotis LS (1998) Updating models and their uncertainties. I: Bayesian statistical framework. J Eng Mech 124(4):455–461Google Scholar
  7. 7.
    Betz W, Papaioannou I, Straub D (2016) Transitional markov chain monte carlo: observations and improvements. J Eng Mech 142(5):04016016Google Scholar
  8. 8.
    Cao Z, Wang Y (2014) Bayesian model comparison and selection of spatial correlation functions for soil parameters. Struct Saf 49:10–17Google Scholar
  9. 9.
    Chang CS, Hicher PY (2005) An elasto-plastic model for granular materials with microstructural consideration. Int J Solids Struct 42(14):4258–4277. CrossRefzbMATHGoogle Scholar
  10. 10.
    Ching J, Chen Y-C (2007) Transitional Markov chain Monte Carlo method for Bayesian model updating, model class selection, and model averaging. J Eng Mech 133(7):816–832Google Scholar
  11. 11.
    Ching J, Wang J-S (2016) Application of the transitional Markov chain Monte Carlo algorithm to probabilistic site characterization. Eng Geol 203:151–167Google Scholar
  12. 12.
    Chopin N (2002) A sequential particle filter method for static models. Biometrika 89(3):539–552MathSciNetzbMATHGoogle Scholar
  13. 13.
    Cividini A, Maier G, Nappi A Parameter estimation of a static geotechnical model using a Bayes’ approach. In: International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1983. Elsevier, pp 215–226Google Scholar
  14. 14.
    Eckert N, Parent E, Richard D (2007) Revisiting statistical–topographical methods for avalanche predetermination: Bayesian modelling for runout distance predictive distribution. Cold Reg Sci Technol 49(1):88–107Google Scholar
  15. 15.
    Fischer J-T, Kofler A, Fellin W, Granig M, Kleemayr K (2015) Multivariate parameter optimization for computational snow avalanche simulation. J Glaciol 61(229):875–888Google Scholar
  16. 16.
    Gajo A, Wood M (1999) Severn-Trent sand: a kinematic-hardening constitutive model: the q–p formulation. Geotechnique 49(5):595–614Google Scholar
  17. 17.
    Gauer P, Medina-Cetina Z, Lied K, Kristensen K (2009) Optimization and probabilistic calibration of avalanche block models. Cold Reg Sci Technol 59(2–3):251–258Google Scholar
  18. 18.
    Hadjidoukas PE, Angelikopoulos P, Papadimitriou C, Koumoutsakos P (2015) Π4U: a high performance computing framework for Bayesian uncertainty quantification of complex models. J Comput Phys 284:1–21MathSciNetzbMATHGoogle Scholar
  19. 19.
    Hastings WK (1970) Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57(1):97–109MathSciNetzbMATHGoogle Scholar
  20. 20.
    He J, Jones JW, Graham WD, Dukes MD (2010) Influence of likelihood function choice for estimating crop model parameters using the generalized likelihood uncertainty estimation method. Agric Syst 103(5):256–264Google Scholar
  21. 21.
    Hellweger V, Fischer J-T, Kofler A, Huber A, Fellin W, Oberguggenberger M (2016) Stochastic methods in operational avalanche simulation—from back calculation to prediction. In: Paper presented at the international snow science workshop 2016 proceedings, Colorado, USAGoogle Scholar
  22. 22.
    Honjo Y, Wen-Tsung L, Guha S (1994) Inverse analysis of an embankment on soft clay by extended Bayesian method. Int J Numer Anal Methods Geomech 18(10):709–734zbMATHGoogle Scholar
  23. 23.
    Hsiao EC, Schuster M, Juang CH, Kung GT (2008) Reliability analysis and updating of excavation-induced ground settlement for building serviceability assessment. J Geotech Geoenviron Eng 134(10):1448–1458Google Scholar
  24. 24.
    Jefferies M (1993) Nor-Sand: a simle critical state model for sand. Geotechnique 43(1):91–103Google Scholar
  25. 25.
    Jin 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 Methods Geomech 40(8):1219–1240. CrossRefGoogle Scholar
  26. 26.
    Jin 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. CrossRefGoogle Scholar
  27. 27.
    Jin 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. CrossRefGoogle Scholar
  28. 28.
    Jin Y-F, Yin Z-Y, Shen S-L, Zhang D-M (2017) A new hybrid real-coded genetic algorithm and its application to parameters identification of soils. Inverse Probl Sci Eng 25(9):1343–1366. MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Jin Y-F, Yin Z-Y, Wu Z-X, Daouadji A (2018) Numerical modeling of pile penetration in silica sands considering the effect of grain breakage. Finite Elem Anal Des 144:15–29. CrossRefGoogle Scholar
  30. 30.
    Jin Y-F, Yin Z-Y, Wu Z-X, Zhou W-H (2018) Identifying parameters of easily crushable sand and application to offshore pile driving. Ocean Eng 154:416–429. CrossRefGoogle Scholar
  31. 31.
    Jin 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. CrossRefGoogle Scholar
  32. 32.
    Juang C, Hsein Luo Z, Atamturktur S, Huang H (2012) Bayesian updating of soil parameters for braced excavations using field observations. J Geotech Geoenviron Eng 139(3):395–406Google Scholar
  33. 33.
    Knabe T, Datcheva M, Lahmer T, Cotecchia F, Schanz T (2013) Identification of constitutive parameters of soil using an optimization strategy and statistical analysis. Comput Geotech 49:143–157. CrossRefGoogle Scholar
  34. 34.
    Kolymbas D (1985) A generalized hypoelastic constitutive law. In: Paper presented at the proceedings of XI international conference on soil mechanics and foundation engineering, San FranciscoGoogle Scholar
  35. 35.
    Kolymbas D (1991) An outline of hypoplasticity. Arch Appl Mech 61(3):143–151zbMATHGoogle Scholar
  36. 36.
    Lee Goh A, Fahey M Application of a 1-dimensional cavity expansion model to pressuremeter and piezocone tests in clay. In: Proceeding of the seventh international conference on computer methods and advances in geomechanics, Cairns, 1991. pp 255–260Google Scholar
  37. 37.
    Lee S-H, Song J (2017) System identification of spatial distribution of structural parameters using modified transitional Markov chain Monte Carlo method. J Eng Mech 143(9):04017099Google Scholar
  38. 38.
    Levasseur S, Malécot Y, Boulon M, Flavigny E (2008) Soil parameter identification using a genetic algorithm. Int J Numer Anal Methods Geomech 32(2):189–213. CrossRefzbMATHGoogle Scholar
  39. 39.
    Low HE (2009) Performance of penetrometers in deepwater soft soil characterisation. University of Western AustraliaGoogle Scholar
  40. 40.
    Mašín D (2005) A hypoplastic constitutive model for clays. Int J Numer Anal Methods Geomech 29(4):311–336zbMATHGoogle Scholar
  41. 41.
    Mašín D (2015) The influence of experimental and sampling uncertainties on the probability of unsatisfactory performance in geotechnical applications. Géotechnique 65(11):897–910Google Scholar
  42. 42.
    Miro S, König M, Hartmann D, Schanz T (2015) A probabilistic analysis of subsoil parameters uncertainty impacts on tunnel-induced ground movements with a back-analysis study. Comput Geotech 68:38–53Google Scholar
  43. 43.
    Most T (2010) Identification of the parameters of complex constitutive models: least squares minimization vs. Bayesian updating. Reliab Optim Struct Syst 119Google Scholar
  44. 44.
    Murakami A, Shinmura H, Ohno S, Fujisawa K (2018) Model identification and parameter estimation of elastoplastic constitutive model by data assimilation using the particle filter. Int J Numer Anal Methods Geomech 42(1):110–131Google Scholar
  45. 45.
    Ortiz GA, Alvarez DA, Bedoya-Ruíz D (2015) Identification of Bouc-Wen type models using the transitional Markov chain Monte Carlo method. Comput Struct 146:252–269Google Scholar
  46. 46.
    Papon A, Riou Y, Dano C, Hicher PY (2012) Single-and multi-objective genetic algorithm optimization for identifying soil parameters. Int J Numer Anal Methods Geomech 36(5):597–618. CrossRefGoogle Scholar
  47. 47.
    Qi X-H, Zhou W-H (2017) An efficient probabilistic back-analysis method for braced excavations using wall deflection data at multiple points. Comput Geotech 85:186–198Google Scholar
  48. 48.
    Ren D-J, Shen S-L, Arulrajah A, Wu H-N (2018) Evaluation of ground loss ratio with moving trajectories induced in DOT tunnelling. Can Geotech J 55(6):894–902Google Scholar
  49. 49.
    Ritto T, Nunes L (2015) Bayesian model selection of hyperelastic models for simple and pure shear at large deformations. Comput Struct 156:101–109Google Scholar
  50. 50.
    Roscoe KH, Burland J (1968) On the generalized stress-strain behaviour of wet clay, engineering plasticity. Cambridge University Press, Cambridge, UK, pp 535–609zbMATHGoogle Scholar
  51. 51.
    Shen SL, Xu YS (2011) Numerical evaluation of land subsidence induced by groundwater pumping in Shanghai. Can Geotech J 48(9):1378–1392Google Scholar
  52. 52.
    Shen S-L, Wu Y-X, Misra A (2017) Calculation of head difference at two sides of a cut-off barrier during excavation dewatering. Comput Geotech 91:192–202Google Scholar
  53. 53.
    Sheng D, Sloan S, Yu H (2000) Aspects of finite element implementation of critical state models. Comput Mech 26(2):185–196zbMATHGoogle Scholar
  54. 54.
    Taiebat M, Dafalias YF (2008) SANISAND: simple anisotropic sand plasticity model. Int J Numer Anal Methods Geomech 32(8):915–948zbMATHGoogle Scholar
  55. 55.
    Tan F, Zhou W-H, Yuen K-V (2016) Modeling the soil water retention properties of same-textured soils with different initial void ratios. J Hydrol 542:731–743Google Scholar
  56. 56.
    Tan F, Zhou WH, Yuen KV (2018) Effect of loading duration on uncertainty in creep analysis of clay. Int J Numer Anal Methods Geomech 42(11):1235–1254Google Scholar
  57. 57.
    Verdugo R, Ishihara K (1996) The steady state of sandy soils. Soils Found 36(2):81–91Google Scholar
  58. 58.
    Vermeer P (1978) A double hardening model for sand. Geotechnique 28(4):413–433Google Scholar
  59. 59.
    Von Wolffersdorff PA (1996) A hypoplastic relation for granular materials with a predefined limit state surface. Mech Cohesive-frictional Mater Int J Exp Model Comput Mater Struct 1(3):251–271Google Scholar
  60. 60.
    Vrugt JA (2016) Markov chain Monte Carlo simulation using the DREAM software package: theory, concepts, and MATLAB implementation. Environ Model Softw 75:273–316Google Scholar
  61. 61.
    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. CrossRefGoogle Scholar
  62. 62.
    Wu W, Bauer E, Kolymbas D (1996) Hypoplastic constitutive model with critical state for granular materials. Mech Mater 23(1):45–69Google Scholar
  63. 63.
    Wu H-N, Shen S-L, Yang J (2017) Identification of tunnel settlement caused by land subsidence in soft deposit of Shanghai. J Perform Constr Facil 31(6):04017092Google Scholar
  64. 64.
    Wu Z-X, Yin Z-Y, Jin Y-F, Geng X-Y (2017) A straightforward procedure of parameters determination for sand: a bridge from critical state based constitutive modelling to finite element analysis. Eur J Environ Civil Eng 1–23. Google Scholar
  65. 65.
    Wu Z-X, Yin Z-Y, Jin Y-F, Geng X-Y (2017) A straightforward procedure of parameters determination for sand: a bridge from critical state based constitutive modelling to finite element analysis. Eur J Environ Civil Eng. CrossRefGoogle Scholar
  66. 66.
    Xiong H, Nicot F, Yin Z (2017) A three-dimensional micromechanically based model. Int J Numer Anal Methods Geomech 41(17):1669–1686Google Scholar
  67. 67.
    Xu Y-S, Ma L, Shen S-L, Sun W-J (2012) Evaluation of land subsidence by considering underground structures that penetrate the aquifers of Shanghai, China. Hydrol J 20(8):1623–1634Google Scholar
  68. 68.
    Yao Y-P, Wang N-D (2013) Transformed stress method for generalizing soil constitutive models. J Eng Mech 140(3):614–629Google Scholar
  69. 69.
    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):323–337zbMATHGoogle Scholar
  70. 70.
    Yao Y, Lu D, Zhou A, Zou B (2004) Generalized non-linear strength theory and transformed stress space. Sci China Ser E Technol Sci 47(6):691–709zbMATHGoogle Scholar
  71. 71.
    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):210–222Google Scholar
  72. 72.
    Yao Y, Hou W, Zhou A (2009) UH model: three-dimensional unified hardening model for overconsolidated clays. Geotechnique 59(5):451–469Google Scholar
  73. 73.
    Yao Y-P, Kong L-M, Zhou A-N, Yin J-H (2014) Time-dependent unified hardening model: three-dimensional elastoviscoplastic constitutive model for clays. J Eng Mech 141(6):04014162Google Scholar
  74. 74.
    Yin ZY, Chang CS (2009) Microstructural modelling of stress-dependent behaviour of clay. Int J Solids Struct 46(6):1373–1388zbMATHGoogle Scholar
  75. 75.
    Yin Z, Chang C, Hicher P, Karstunen M (2008) Microstructural modeling of rate-dependent behavior of soft soil. In: Proceeding of 12th IACMAG, Goa, pp 862–868Google Scholar
  76. 76.
    Yin ZY, Chang CS, Hicher PY, Karstunen M (2009) Micromechanical analysis of kinematic hardening in natural clay. Int J Plast 25(8):1413–1435zbMATHGoogle Scholar
  77. 77.
    Yin ZY, Chang CS, Karstunen M, Hicher PY (2010) An anisotropic elastic-viscoplastic model for soft clays. Int J Solids Struct 47(5):665–677zbMATHGoogle Scholar
  78. 78.
    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. CrossRefzbMATHGoogle Scholar
  79. 79.
    Yin ZY, 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. CrossRefGoogle Scholar
  80. 80.
    Yin Z-Y, Zhao J, Hicher P-Y (2014) A micromechanics-based model for sand-silt mixtures. Int J Solids Struct 51(6):1350–1363Google Scholar
  81. 81.
    Yin Z-Y, Zhu Q-Y, Yin J-H, Ni Q (2014) Stress relaxation coefficient and formulation for soft soils. Géotech Lett 4:45–51Google Scholar
  82. 82.
    Yin Z-Y, Yin J-H, Huang H-W (2015) Rate-dependent and long-term yield stress and strength of soft Wenzhou marine clay: experiments and modeling. Mar Georesour Geotechnol 33(1):79–91Google Scholar
  83. 83.
    Yin Z-Y, Jin 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. CrossRefGoogle Scholar
  84. 84.
    Yin Z-Y, Jin 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 Methods Geomech 42(1):70–94. CrossRefGoogle Scholar
  85. 85.
    Yu H (1998) CASM: a unified state parameter model for clay and sand. Int J Numer Anal Methods Geomech 22(8):621–653zbMATHGoogle Scholar
  86. 86.
    Yuen K-V (2010) Bayesian methods for structural dynamics and civil engineering. Wiley, HobokenGoogle Scholar
  87. 87.
    Yuen K-V (2010) Recent developments of Bayesian model class selection and applications in civil engineering. Struct Saf 32(5):338–346Google Scholar
  88. 88.
    Yuen KV, Mu HQ (2015) Real-time system identification: an algorithm for simultaneous model class selection and parametric identification. Comput Aided Civil Infrastruct Eng 30(10):785–801Google Scholar
  89. 89.
    Zhang R, Mahadevan S (2000) Model uncertainty and Bayesian updating in reliability-based inspection. Struct Saf 22(2):145–160Google Scholar
  90. 90.
    Zhang X, Srinivasan R, Bosch D (2009) Calibration and uncertainty analysis of the SWAT model using genetic algorithms and Bayesian model averaging. J Hydrol 374(3–4):307–317Google Scholar
  91. 91.
    Zhang J, Zhang LM, Tang WH (2009) Bayesian framework for characterizing geotechnical model uncertainty. J Geotech Geoenviron Eng 135(7):932–940. CrossRefGoogle Scholar
  92. 92.
    Zhang L, Zuo Z, Ye G, Jeng D, Wang J (2013) Probabilistic parameter estimation and predictive uncertainty based on field measurements for unsaturated soil slope. Comput Geotech 48:72–81Google Scholar
  93. 93.
    Zhang L, Li D-Q, Tang X-S, Cao Z-J, Phoon K-K (2017) Bayesian model comparison and characterization of bivariate distribution for shear strength parameters of soil. Comput Geotech 95:110–118Google Scholar
  94. 94.
    Zhou W-H, Tan F, Yuen K-V (2018) Model updating and uncertainty analysis for creep behavior of soft soil. Comput Geotech 100:135–143. CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Yin-Fu Jin
    • 1
  • Zhen-Yu Yin
    • 1
    Email author
  • Wan-Huan Zhou
    • 2
  • Suksun Horpibulsuk
    • 3
  1. 1.Department of Civil and Environmental EngineeringThe Hong Kong Polytechnic UniversityHung Hom, KowloonChina
  2. 2.State Key Laboratory of Internet of Things for Smart City and Department of Civil and Environmental EngineeringUniversity of MacauMacauChina
  3. 3.School of Civil EngineeringSuranaree University of TechnologyMuang DistrictThailand

Personalised recommendations