Abstract
Soil is a heterogeneous medium and due to this, the parameters on which soil slope stability depends, are having high variability, which makes the analysis a complex problem. To take into account the variability in soil parameters, the current research approach is shifting from deterministic approach to probabilistic approach. This paper describes the application of three soft-computing techniques including multivariate adaptive regression spline (MARS), Gaussian process regression (GPR) and functional network (FN) to study the soil slope reliability based on slope stability. The stability of a soil slope of a given height depends on shear strength parameters c (cohesion), ϕ (angle of shearing resistance) and ϒ (unit weight), which are taken as input variables and Factor of Safety of soil slope (FOS) as the output. Also the model performance was assessed using various performance indices i.e. NS, RMSE, VAF, MAE, RSR, Bias Factor, PI, R2, Adj. R2, MAPE, GPI, LMI, U95, tstat and β. The results of the analyses showed that MARS model outperformed GPR and FN models. Therefore, MARS model can be used as a reliable soft computing technique for analyzing soil slope stability.
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References
Abraham A, Steinberg D (2001) Is neural network a reliable forecaster on earth? A MARS query! In: Lecture notes in computer science (including subseries lecture notes in artificial intelligence and lecture notes in bioinformatics). Springer, pp 679–686
Adamowski J, Chan HF, Prasher SO, Ozga-Zielinski B, Sliusarieva A (2012) Comparison of multiple linear and nonlinear regression, autoregressive integrated moving average, artificial neural network, and wavelet artificial neural network methods for urban water demand forecasting in Montreal, Canada. Wiley Online Libr. https://doi.org/10.1029/2010WR009945
Anderson TW, Darling DA (1952) Asymptotic theory of certain, goodness of fit criteria based on stochastic processes. Ann Math Stat 23:193–212. https://doi.org/10.1214/aoms/1177729437
Armaghani DJ, Mirzaei F, Shariati M, Trung NT, Shariati M, Trnavac D (2020) Hybrid ann-based techniques in predicting cohesion of sandy-soil combined with fiber. Geomech Eng 20:191–205. https://doi.org/10.12989/gae.2020.20.3.191
Armstrong JS, Collopy F (1992) Error measures for generalizing about forecasting methods: empirical comparisons. Int J Forecast 8:69–80. https://doi.org/10.1016/0169-2070(92)90008-W
Babu GLS, Srivastava A (2007) Reliability analysis of allowable pressure on shallow foundation using response surface method. Comput Geotech 34:187–194. https://doi.org/10.1016/j.compgeo.2006.11.002
Babu GLS, Srivastava A (2010) Reliability analysis of earth dams. J Geotech Geoenviron Eng 136:995–998. https://doi.org/10.1061/(asce)gt.1943-5606.0000313
Baecher GB, Christian JT (2003) Reliability and statistics in geotechnical engineering. J Wiley
Behar O, Khellaf A, Mohammedi K (2015) Comparison of solar radiation models and their validation under Algerian climate—the case of direct irradiance. Energy Convers Manag 98:236–251. https://doi.org/10.1016/j.enconman.2015.03.067
Castillo E, Cobo A, Gutiérrez JM, Pruneda E (1999) Working with differential, functional and difference equations using functional networks. Appl Math Model 23:89–107. https://doi.org/10.1016/S0307-904X(98)10074-4
Castillo E, Gutiérrez JM, Cobo A, Castillo C (2000) Some learning methods in functional networks
Cheng Y (2003) Location of critical failure surface and some further studies on slope stability analysis. Comput Geotech 30:255–267
Cho SE (2010) Probabilistic assessment of slope stability that considers the spatial variability of soil properties. J Geotech Geoenviron Eng 136:975–984. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000309
Christian JT, Ladd CC, Baecher GB (1994) Reliability applied to slope stability analysis. J Geotech Eng 120:2180–2207. https://doi.org/10.1061/(ASCE)0733-9410(1994)120:12(2180)
Craven P, Wahba G (1978) Smoothing noisy data with spline functions—estimating the correct degree of smoothing by the method of generalized cross-validation. Numer Math 31:377–403. https://doi.org/10.1007/BF01404567
El-Ramly H, Morgenstern NR, Cruden DM (2002) Probabilistic slope stability analysis for practice. Can Geotech J 39:665–683. https://doi.org/10.1139/t02-034
Fawcett T (2006) An introduction to ROC analysis. Pattern Recognit Lett 27:861–874. https://doi.org/10.1016/J.PATREC.2005.10.010
Friedman J (1991) Multivariate adaptive regression splines. JSTOR 19:1–67
Gao W, Karbasi M, Hasanipanah M, Zhang X, Guo J (2018) Developing GPR model for forecasting the rock fragmentation in surface mines. Eng Comput 34:339–345. https://doi.org/10.1007/s00366-017-0544-8
Grima MA, Babuška R (1999) Fuzzy model for the prediction of unconfined compressive strength of rock samples. Int J Rock Mech Min Sci 36:339–349. https://doi.org/10.1016/S0148-9062(99)00007-8
Gokceoglu C (2002) A fuzzy triangular chart to predict the uniaxial compressive strength of Ankara agglomerates from their petrographic composition. Eng Geol 66:39–51
Grbić R, Kurtagić D, Slišković D (2013) Stream water temperature prediction based on Gaussian process regression. Expert Syst Appl Elsevier 40:7407–7414
Gueymard C (2014) A review of validation methodologies and statistical performance indicators for modeled solar radiation data: towards a better bankability of solar projects. Renew Sustain Energy Rev 39:1024–1034
Jain SK, Sudheer KP (2008) Fitting of hydrologic models: a close look at the nash-sutcliffe index. J Hydrol Eng 13:981–986. https://doi.org/10.1061/(ASCE)1084-0699(2008)13:10(981)
Kisi O, Shiri J, Tombul M (2013) Modeling rainfall-runoff process using soft computing techniques. Comput Geosci 51:108–117. https://doi.org/10.1016/j.cageo.2012.07.001
Kumar R, Samui P, Kumari S (2017) Reliability analysis of infinite slope using metamodels. Geotech Geol Eng. https://doi.org/10.1007/s10706-017-0160-9
Kung GT, Juang CH, Hsiao EC, Hashash YM (2007) Simplified model for wall deflection and ground-surface settlement caused by braced excavation in clays. J Geotech Geoenviron Eng 133:731–747. https://doi.org/10.1061/(ASCE)1090-0241(2007)133:6(731)
Legates DR, McCabe GJ (1999) Evaluating the use of “goodness-of-fit” measures in hydrologic and hydroclimatic model validation. Water Resour Res 35:233–241. https://doi.org/10.1029/1998WR900018
Legates DR, McCabe GJ (2013) A refined index of model performance: a rejoinder. Int J Climatol 33:1053–1056. https://doi.org/10.1002/joc.3487
Liang R, Nusier O, Malkawi A (1999) A reliability based approach for evaluating the slope stability of embankment dams. Eng Geol 54:271–285
Moriasi DN, Arnold JG, Van Liew MW, Bingner RL, Harmel RD, Veith TL (2007) Model evaluation guidelines for systematic quantification of accuracy in watershed simulations. Trans ASABE 50:885–900. https://doi.org/10.13031/2013.23153
Phoon KK (2002) Potential application of reliability-based design to geotechnical engineering. In: Proceedings of 4th Colombian Geotechnical Seminar, Medellin, pp 1–22
Prasomphan S, Machine SM (2013) Generating prediction map for geostatistical data based on an adaptive neural network using only nearest neighbors. Int J Mach Learn Comput 2013:3
Raventos-Duran T, Camredon M, Valorso R, Mouchel-Vallon C, Aumont B (2010) Structure-activity relationships to estimate the effective Henry’s law constants of organics of atmospheric interest. Atmos Chem Phys 10:7643–7654. https://doi.org/10.5194/acp-10-7643-2010
Ray R, Kumar D, Samui P, Roy LB, Goh ATC, Zhang W (2020) Application of soft computing techniques for shallow foundation reliability in geotechnical engineering. Geosci Front 12:375–383. https://doi.org/10.1016/j.gsf.2020.05.003
Reale C, Xue J, Pan Z, Gavin K (2015) Deterministic and probabilistic multi-modal analysis of slope stability. Comput Geotech 66:172–179
Samui P, Kim D, Jagan J, Roy SS (2019) Determination of uplift capacity of suction caisson using Gaussian process regression, minimax probability machine regression and extreme learning machine. Iran J Sci Technol Trans Civ Eng 43:651–657. https://doi.org/10.1007/s40996-018-0155-7
Sephton P (2001) Forecasting recessions: can we do better on mars. Fed Reserv Bank St Louis Rev 83:39–49
Sharda VN, Prasher SO, Patel RM, Ojasvi PR, Prakash C (2008) Performance of multivariate adaptive regression splines (MARS) in predicting runoff in mid-Himalayan micro-watersheds with limited data. Hydrol Sci J 53:1165–1175. https://doi.org/10.1623/hysj.53.6.1165
Srinivasulu S, Jain A (2006) A comparative analysis of training methods for artificial neural network rainfall–runoff models. Appl Soft Comput 6:295–306. https://doi.org/10.1016/j.asoc.2005.02.002
Stone RJ (1993) Improved statistical procedure for the evaluation of solar radiation estimation models. Sol Energy 51:289–291. https://doi.org/10.1016/0038-092X(93)90124-7
Taylor KE (2001) Summarizing multiple aspects of model performance in a single diagram. J Geophys Res Atmos 106:7183–7192. https://doi.org/10.1029/2000JD900719
USACE (1997) Risk-based analysis in geotechnical engineering for support of planning studies, engineering and design. Dept Army, USACE Washington, DC
Viscarra RA, McGlynn RN, McBratney AB (2006) Determining the composition of mineral-organic mixes using UV–vis–NIR diffuse reflectance spectroscopy. Geoderma 137:70–82. https://doi.org/10.1016/j.geoderma.2006.07.004
Wang Y, Qin Z, Liu X, Li L (2019) Probabilistic analysis of post-failure behavior of soil slopes using random smoothed particle hydrodynamics. Eng Geol 261:105266. https://doi.org/10.1016/j.enggeo.2019.105266
Williams CKI (1997) Regression with gaussian processes, pp 378–382
Williams CKI, Barber D (1998) Bayesian classification with Gaussian processes. IEEE Trans Pattern Anal Mach Intell 20:1342–1351. https://doi.org/10.1109/34.735807
Willmott CJ (1981) On the validation of models. Phys Geogr 2:184–194. https://doi.org/10.1080/02723646.1981.10642213
Willmott CJ (1982) Some comments on the evaluation of model performance. Bull Am Meteorol Soc 63:1309–1313. https://doi.org/10.1175/1520-0477(1982)063%3c1309:SCOTEO%3e2.0.CO;2
Willmott CJ (1984) On the evaluation of model performance in physical geography. In: Spatial statistics and models. Springer, Netherlands, Dordrecht, pp 443–460
Yılmaz I, Yuksek AG (2008) An example of artificial neural network (ANN) application for indirect estimation of rock parameters. Rock Mech Rock Eng 41:781–795. https://doi.org/10.1007/s00603-007-0138-7
Zeroual A, Fourar A, Djeddou M (2009) Predictive modeling of static and seismic stability of small homogeneous earth dams using artificial neural network. Arab J Geosci. https://doi.org/10.1007/s12517-018-4162-6
Zhang C, Wei H, Zhao X, Liu T, Zhang K (2016) A Gaussian process regression based hybrid approach for short-term wind speed prediction. Energy Convers Manag 126:1084–1092. https://doi.org/10.1016/j.enconman.2016.08.086
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Ray, R., Choudhary, S.S. & Roy, L.B. Reliability analysis of soil slope stability using MARS, GPR and FN soft computing techniques. Model. Earth Syst. Environ. 8, 2347–2357 (2022). https://doi.org/10.1007/s40808-021-01238-w
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DOI: https://doi.org/10.1007/s40808-021-01238-w