Predicting the effective stress parameter of unsaturated soils using adaptive neuro-fuzzy inference system

Document Type : Article


1 Department of Civil and Environmental Engineering, Shiraz University of Technology, Shiraz, Iran.

2 School of Civil and Environmental Engineering, University of Technology, Sydney (UTS).


The effective stress parameter (χ) is applied to obtain the shear strength of unsaturated soils. In this study, two adaptive neuro-fuzzy inference system (ANFIS) models, including SC-FIS model (created by subtractive clustering) and FCM-FIS model (created by Fuzzy c-means (FCM) clustering), are presented for prediction of χ and the results are compared. The soil water characteristic curve fitting parameter (λ), the confining pressure, the suction and the volumetric water content in dimensionless forms are used as input parameters for these two models. Using a trial and error process, a series of analyses were performed to determine the optimum methods. The ANFIS models are constructed, trained and validated to predict the value of χ. The quality of the ANFIS prediction ability was quantified in terms of the determination coefficient (R2), Root Mean Square Error (RMSE) and Mean Absolute Error (MAE). These two ANFIS models are effectively able to predict the value of χ with reasonable values of R2, RMSE and MAE. Sensitivity analysis was used to acquire the effect of input parameters on χ prediction, and the results revealed that the confining pressure and the volumetric water content parameters had the most influence on the prediction of χ.


Main Subjects

1. Fredlund, D.G. and Morgenstern, N.R. Stress state variables for unsaturated soils", Journal of Geotechnical and Geoenvironmental Engineering, 103(5), pp. 447-466 (1977). 2. Terzaghi, K., Theoretical Soil Mechanics, London: Chapman and Hall Limited: John Wiley and Sons, Inc. New York (1943). 3. Croney, D., Coleman, J.D., and Black, W.P.M., Studies of the Movement and Distribution of Water in Soil in Relation to Highway Design and Performance, Transport and Road Research Laboratory (1958). 4. Bishop, A.W. The principle of e_ective stress", published in Teknisk Ukeblad, 106(39), pp. 859-863 (1959). 3156 H. Rahnema et al./Scientia Iranica, Transactions A: Civil Engineering 26 (2019) 3140{3158 5. Richards, B. The signi_cance of moisture ow and equilibria in unsaturated soils in relation to the design of engineering structures built on shallow foundations in Australia", In: Symposium on Permeability and Capillarity, ASTM, Atlantic City, NJ. Richards, L.A (1966). 6. Aitchison, G.D. Moisture equilibria and moisture changes in soils beneath covered areas: a symposium in print", Engineering Concepts of Moisture Equilibria and Moisture Changes in Soils, Statement of the review panel, G.D. Aitchison, Ed., 8(1), pp. 7-21 (1965). 7. Khalili, N. and Khabbaz, M. A unique relationship of chi for the determination of the shear strength of unsaturated soils", Geotechnique, 48(5), pp. 681-687 (1998). 8. Lu, N. and Likos, W.J., Unsaturated Soil Mechanics, John Wiley & Sons (2004). 9. Fredlund, D., Morgenstern, N., and Widger, R. The shear strength of unsaturated soils", Canadian Geotechnical Journal, 15(3), pp. 313-321 (1978). 10. Escario, V. and Saez, J. The shear strength of partly saturated soils", Geotechnique, 36(3), pp. 453-456 (1986). 11. Vanapalli, S., Fredlund, D., Pufahl, D., and Clifton, A. Model for the prediction of shear strength with respect to soil suction", Canadian Geotechnical Journal, 33(3), pp. 379-392 (1996). 12. Fredlund, D.G., Xing, A., Fredlund, M.D., and Barbour, S. The relationship of the unsaturated soil shear to the soil-water characteristic curve", Canadian Geotechnical Journal, 33(3), pp. 440-448 (1996). 13. Kayadelen, C. Estimation of e_ective stress parameter of unsaturated soils by using arti_cial neural networks", International Journal for Numerical and Analytical Methods in Geomechanics, 32(9), pp. 1087- 1106 (2008). 14. Ajdari, M., Habibagahi, G., and Ghahramani, A. Predicting e_ective stress parameter of unsaturated soils using neural networks", Computers and Geotechnics, 40, pp. 89-96 (2012). 15. Johari, A., Nakhaee, M., and Habibagahi, G. Prediction of unsaturated soils e_ective stress parameter using gene expression programming", Scientia Iranica, 20(5), pp. 1433-1444 (2013). 16. Jang, J.-S. ANFIS: adaptive-network-based fuzzy inference system", Systems, Man and Cybernetics, IEEE Transactions on, 23(3), pp. 665-685 (1993). 17. Kar, S., Das, S., and Ghosh, P.K. Applications of neuro fuzzy systems: A brief review and future outline", Applied Soft Computing, 15, pp. 243-259 (2014). 18. Gokceoglu, C., Yesilnacar, E., Sonmez, H., and Kayabasi, A. A neuro-fuzzy model for modulus of deformation of jointed rock masses", Computers and Geotechnics, 31(5), pp. 375-383 (2004). 19. Kalkan, E., Akbulut, S., Tortum, A., and Celik, S. Prediction of the uncon_ned compressive strength of compacted granular soils by using inference systems", Environmental Geology, 58(7), pp. 1429-1440 (2009). 20. Kayadelen, C., Ta_sk_ran, T., Gunayd_n, O., and Fener, M. Adaptive neuro-fuzzy modeling for the swelling potential of compacted soils", Environmental Earth Sciences, 59(1), pp. 109-115 (2009). 21. Cobaner, M. Evapotranspiration estimation by two di_erent neuro-fuzzy inference systems", Journal of Hydrology, 398(3), pp. 292-302 (2011). 22. Sezer, A., Goktepe, A., and Altun, S. Adaptive neurofuzzy approach for sand permeability estimation", Environ Eng Manag J, 9(2), pp. 231-238 (2010). 23. Ikizler, S.B., Vekli, M., Dogan, E., Aytekin, M., and Kocabas, F. Prediction of swelling pressures of expansive soils using soft computing methods", Neural Computing and Applications, 24(2), pp. 473- 485 (2012). 24. Doostmohammadi, R. Cyclic swelling estimation of mudstone using adaptive network-based fuzzy inference system", Middle-East Journal of Scienti_c Research, 11(4), pp. 517-524 (2012). 25. Cabalar, A.F., Cevik, A., and Gokceoglu, C. Some applications of adaptive neuro-fuzzy inference system (ANFIS) in geotechnical engineering", Computers and Geotechnics, 40, pp. 14-33 (2012). 26. Zoveidavianpoor, M. A comparative study of arti_- cial neural network and adaptive neurofuzzy inference system for prediction of compressional wave velocity", Neural Computing and Applications, 25(5), pp. 1-8 (2014). 27. Zadeh, L.A. Fuzzy sets", Information and Control, 8(3), pp. 338-353 (1965). 28. Jang, J.S.R. and Gulley, N., Fuzzy Logic Toolbox: User's Guide, The Mathworks", Inc (2000). 29. Mamdani, E.H. and Assilian, S. An experiment in linguistic synthesis with a fuzzy logic controller", International Journal of Man-Machine Studies, 7(1), pp. 1-13 (1975). 30. Takagi, T. and Sugeno, M. Fuzzy identi_cation of systems and its applications to modeling and control", Systems, Man and Cybernetics, IEEE Transactions on, 1, pp. 116-132 (1985). 31. Tsukamoto, Y. An approach to fuzzy reasoning method", Advances in Fuzzy Set Theory and Applications, 137, p. 149 (1979). 32. Rumelhart, D.E. and McClelland, J.L., Parallel Distributed Processing, Cambridge, MA, MIT Press: IEEE (1988). 33. Hashemi Jokar, M. and Mirasi, S. Using adaptive neuro-fuzzy inference system for modeling unsaturated soils shear strength", Soft Computing, 22(13), pp. 1-18 (2017). 34. Steinhaus, H. Sur la division des corp materiels en parties", Bull. Acad. Polon. Sci, 4(12), pp. 801-804 (1956). H. Rahnema et al./Scientia Iranica, Transactions A: Civil Engineering 26 (2019) 3140{3158 3157 35. Bezdek, J.C., Pattern Recognition With Fuzzy Objective Function Algorithms, Kluwer Academic Publishers (1981). 36. Chiu, S.L. A cluster estimation method with extension to fuzzy model identi_cation", In Proceedings of 1994 IEEE 3rd International Fuzzy Systems Conference, IEEE, pp. 1240-1245 (1994). 37. Chiu, S. Fuzzy model identi_cation based on cluster estimation", Journal of Intelligent and Fuzzy Systems, 2(3), pp. 267-278 (1994). 38. Yager, R.R. and Filev, D.P. Generation of fuzzy rules by mountain clustering", Journal of Intelligent and Fuzzy Systems, 2(3), pp. 209-219 (1994). 39. Dunn, J.C. A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters", J. Cybernet., 3(3), pp. 32-57 (1973). 40. Rahardjo, H., Heng, O.B., and Choon, L.E. Shear strength of a compacted residual soil from consolidated drained and constant water content triaxial tests", Canadian Geotechnical Journal, 41(3), pp. 421-436 (2004). 41. Lee, I.-M., Sung, S.-G., and Cho, G.-C. E_ect of stress state on the unsaturated shear strength of a weathered granite", Canadian Geotechnical Journal, 42(2), pp. 624-631 (2005). 42. Rassam, D.W. and Williams, D.J. A relationship describing the shear strength of unsaturated soils", Canadian Geotechnical Journal, 36(2), pp. 363-368 (1999). 43. Khalili, N., Geiser, F., and Blight, G. E_ective stress in unsaturated soils: review with new evidence", International Journal of Geomechanics, 4(2), pp. 115- 126 (2004). 44. Miao, L., Liu, S., and Lai, Y. Research of soil-water characteristics and shear strength features of Nanyang expansive soil", Engineering Geology, 65(4), pp. 261- 267 (2002). 45. Thu, T.M., Rahardjo, H., and Leong, E.-C. E_ects of hysteresis on shear strength envelopes from constant water content and consolidated drained triaxial tests", Unsaturated Soils, pp. 1212-1222 (2006). 46. Rampino, C., Mancuso, C., and Vinale, F. Experimental behaviour and modelling of an unsaturated compacted soil", Canadian Geotechnical Journal, 37(4), pp. 748-763 (2000). 47. Russell, A.R. and Khalili, N. A bounding surface plasticity model for sands exhibiting particle crushing", Canadian Geotechnical Journal, 41(6), pp. 1179-1192 (2004). 48. Russell, A. and Khalili, N. A uni_ed bounding surface plasticity model for unsaturated soils", International Journal for Numerical and Analytical Methods in Geomechanics, 30(3), pp. 181-212 (2006). 49. Bishop, A.W. and Blight, G.E. Some aspects of e_ective stress in saturated and partially saturated soils", Geotechnique, 13(3), pp. 177-197 (1963). 50. Gath, I. and Geva, A.B. Unsupervised optimal fuzzy clustering", Pattern Analysis and Machine Intelligence, IEEE Transactions on, 11(7), pp. 773-780 (1989). 51. Pal, N.R. and Bezdek, J.C. On cluster validity for the fuzzy c-means model", Fuzzy Systems, IEEE Transactions on, 3(3), pp. 370-379 (1995). 52. Krishnapuram, R. and Freg, C.-P. Fitting an unknown number of lines and planes to image data through compatible cluster merging", Pattern Recognition, 25(4), pp. 385-400 (1992). 53. Kaymak, U. and Babuska, R. Compatible cluster merging for fuzzy modelling", Fuzzy Systems, 1995. International Joint Conference of the Fourth IEEE International Conference on Fuzzy Systems and The Second International Fuzzy Engineering Symposium., Proceedings of 1995 IEEE Int, 2(1), pp. 897-904 (1995). 54. Alvarez Grima, M. and Babu_ska, R. Fuzzy model for the prediction of uncon_ned compressive strength of rock samples", International Journal of Rock Mechanics and Mining Sciences, 36(3), pp. 339-349 (1999). 55. Pradhan, B., Sezer, E.A., Gokceoglu, C., and Buchroithner, M.F. Landslide susceptibility mapping by neuro-fuzzy approach in a landslide-prone area (Cameron Highlands, Malaysia)", Geoscience and Remote Sensing, IEEE Transactions on, 48(12), pp. 4164-4177 (2010). 56. Monjezi, M., Ghafurikalajahi, M., and Bahrami, A. Prediction of blast-induced ground vibration using arti _cial neural networks", Tunnelling and Underground Space Technology, 26(1), pp. 46-50 (2011). 57. Smith, G.N., Probability and Statistics in Civil Engineering: An Introduction, Collins London (1986). 58. Jang, J.S.R. and Gulley, N. Fuzzy logic toolbox user's guide", The Mathworks Inc, Natick (2000).