Abstract
This study was motivated by the difficulty in determining the resilient modulus of soils using the repeated load triaxial test (RLTT) recommended by the mechanistic-empirical pavement design guide (MEPDG). An alternative means to estimate the resilient modulus of fine-grained soils has been established in the form of three models that were developed using three supervised machine-learning techniques. This includes k-nearest neighbor (KNN), multivariate adaptive regression splines (MARS), and random forest. The data utilized for the development of the models were sourced from the long-term pavement performance (LTPP) database domiciled in the Infopave database in the USA. A total of twelve routine soil properties that have significant influence on the resilient modulus of fine-grained soils were considered in this study. Results obtained from this study revealed that the three developed models (KNN, MARS, and random forest) had high prediction accuracy and high generalization ability. However, the random forest model, based on the statistical indices used to evaluate the models, gave the best prediction accuracy (R2 = 0.9312 for the testing dataset) of the three developed model. It was followed closely by the MARS model with an R2 value of 0.9057. The last model in terms of prediction accuracy was the KNN model with an R2 value of 0.8748. Furthermore, based on parameter significance assessment using the random forest model, it was revealed that the nominal maximum axial stress and confining pressure are the best predictor variables for the estimation of the resilient modulus of fine-grained soils.
Similar content being viewed by others
References
AASHTO T307-99 (2007) Standard method of test for determining the resilient modulus of soils and aggregate materials, Washington, DC
Adagbasa EG, Adelabu SA, Okello TW (2019) Application of deep learning with stratified k-fold for vegetation species discrimination in a protected mountainous region using Sentinel-2 image. Geocarto Int:21. https://doi.org/10.1080/10106049.2019.1704070
Ali N, Neagu D, Trundle P (2019) Evaluation of k-nearest neighbour classifier performance for heterogenous data sets. SN Appl ences 1. https://doi.org/10.1007/s42452-019-1356-9
Alwosheel A, van Cranenburgh S, Chorus CG (2018) Is your dataset big enough? Sample size requirements when using artificial neural networks for discrete choice analysis. J Choice Model 28:182. https://doi.org/10.1016/j.jocm.2018.07.002
Amit Y, Geman D (1997) Shape quantization and recognition with randomized trees. Neural Comp 9(7):1545–1588. https://doi.org/10.1162/neco.1997.9.7.1545
ARA, Inc (2004) ERES Consultants Division, Guide for mechanistic-empirical design of new and rehabilitated pavement structures. Transportation Research Board of the National Academies, Washington D.C
Arshad M (2018) Correlation between resilient modulus (Mr) and constrained modulus (Mc) values of granular materials. Const Build Mater 159:440. https://doi.org/10.1016/j.conbuildmat.2017.10.047
ASTM (1992) Annual book of ASTM standards, vol 04, Philadelphia
Ben Hassen H, Elaoud A, Masmoudi K (2020) Modeling of agricultural soil compaction using discrete Bayesian networks. Int J Environ Sci Technol 17(9):1–10. https://doi.org/10.1007/s13762-020-02664-6
Breiman L (1996a) Bagging predictors. Mach Learn 26(2):123–140
Breiman L (1996b) Heuristics of instability and stabilization in model selection. Annals Stat 24(6):2350–2383. https://doi.org/10.1214/aos/1032181158
Breiman L (2001) Random forests. Mach Learn 45:5–32
Bristish Standard Institute, Methods of testing soils for civil engineering purposes, London: BS 1377, Part 4 (1990).
Buhlmann P, Yu B (2002) Analyzing bagging. Annals Stat 30(4):927–961
Carmichael RF, StuaRT E (1985) Predicting resilient modulus: a study to determine the mechanical properties of subgrade soils. Transp Res Rec J Trans Res Board 1043:145–148
Chen X, Ishwaran H (2012) Random forests for genomic data analysis. Genomics 99:323. https://doi.org/10.1016/j.ygeno.2012.04.003
Chowdhury SMRM (2021) Evaluation of resilient modulus constitutive equations for unbound coarse materials. Const Build Mater 296:1–15. https://doi.org/10.1016/j.conbuildmat.2021.123688
Cover TM, Hart P (1967) Nearest neighbor pattern classification. IEE Trans Inf Theory 13(1):21–27
Debeer D, Strobl C (2020) Conditional permutation importance revisited. BMC Bioinform 21(307):5–30
Dietterich T (1995) Overfitting and undercomputing in machine learning. ACM Comp Surv 27(3):326–327. https://doi.org/10.1145/212094.212114
Drumm EC, Boateng-Poku Y, Johnson PT (1990) Estimations of subgrade resilient modulus from standard tests. Journal of geotechnical engineering 116(5):774–789
Efron B, Tibshirani RJ (1993) An introduction to the bootstrap. Chapman & Hall, London
Elaoud A, Chehaibi S (2011) Soil compaction due to tractor traffic. J Failure Anal Prev 11:539. https://doi.org/10.1007/s11668-011-9479-3
Elaoud A, Jalel R, Salah NB, Chehaibi S, Hassen HB (2021) Modelling of soil tillage techniques based on four cropping seasons. Arab J Geosci 14(11):1–7
Fix E, Hodges JL (1951) Discriminatory analysis. In: Non-parametric discrimination: Consistency properties, Technical report. California University, Berkeley
Flach P (2012) Machine learning: the art and science of algorithms that make sense of data, Cambridge. Cambridge University Press, UK
Forsyth D (2019) Applied machine learning. Springer Cham, USA
Friedman JH (1991) Multivariate adaptive regression splines. The annals of statistics 19(1):1–141
Friedman JH (2001) Greedy function approximation: a gradient boosting machine. Annals Stat 29(3):1189–1232. https://doi.org/10.1214/aos/1013203451
Garg SK (2011) Soil mechanics and foundation engineering. Khana publishers, Nai Sarak
Ghorbani B, Arulrajah A, Narsilio G, Horpibulsuk S, Bo MW (2020) Development of genetic-based models for predicting the resilient modulus of cohesive pavement subgrade soils. Soils Found 60:398–412
Goh ATC, Zhang W, Zhang Y, Xiao Y (2018) Determination of Earth pressure balance tunnel-related maximum surface settlement: a multivariate adaptive regression splines approach. Bull Eng Geol Environ 77:489. https://doi.org/10.1007/s10064-016-0937-8
Hanandeh S, Ardah A, Abu-Farsakh M (2000) Using artificial neural network and genetics algorithm to estimate the resilient modulus for stabilized subgrade and propose new empirical formula. Transp Geotech 24:8. https://doi.org/10.1016/j.trgeo.2020.100358
Hanittinan W (2007) Resilient modulus prediction using neural network algorithm. Doctoral thesis submitted at Ohio State University, Ohio. http://rave.ohiolink.edu/etdc/view?acc_num=osu1190140082.
Hastie T, Tibshirani R, Friedman J (2009) The elements of statistical learning. Springer, New York NY
Heidaripanah A, Nazemi M, Soltani F (2017) Predicting of resilient modulus of lime-treated subgrade soil using different kernels of support vector machine. Int J Geomech 17(2):1–6. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000723
Ho T (1995) Random decision forest. In: Proceedings of the 3rd International conference on document analysis and recognition, vol 14-16. IEEE, Montreal, QC, pp 278–282
Ho T (1998) The random subspace method for constructing decision forests. IEEE Trans Pattern Anal Mach Intell 20(8):832–844
Holtz WG, Gibbs HJ (1956) Engineering properties of expansive clays. Trans Am Soc Civil Eng 121(1):641–663
Ikeagwuani CC (2019) Comparative assessment of the stabilization of lime-stabilized lateritic soil as subbase material using coconut shell ash and coconut husk ash. Geotech Geol Eng 37(4):3065–3076. https://doi.org/10.1007/s10706-019-00825-0
Ikeagwuani CC (2021) Estimation of modified expansive soil CBR with multivariate adaptive regression splines, random forest and gradient boosting machine. Innov Infrast Solutions 6(199):1–16. https://doi.org/10.1007/s41062-021-00568-z
Ikeagwuani CC (2022) Prediction of factor of safety of modified expansive soil slope modeled with non-associated flow rule considering dilatancy effect. Arab J Geosci 15(1196). https://doi.org/10.1007/s12517-022-10406-w
Ikeagwuani CC, Nwonu DC (2019) Resilient modulus of lime-bamboo ash stabilized subgrade soil with different compactive energy. Geotech Geol Eng 37(4):3557–3565. https://doi.org/10.1007/s10706-019-00849-6
Ikeagwuani CC, Nwonu DC (2021) Model performance assessment in resilient modulus modelling: a multimodel approach. Road Mater Pave Des 22(10):2310–2328
Jalel R, Elaoud A, Salah NB, Chehaibi S, Ben Hassen H (2021) Modeling of soil tillage techniques using Fruchterman-Reingold. IntJ Environ Sci Technol 18:2987–2996. https://doi.org/10.1007/s13762-020-03044-w
Jang JSR (1993) ANFIS: adaptive-network-based fuzzy inference system. IEEE Trans Syst, Man Cybern 23(3):665–685. https://doi.org/10.1109/21.256541
Jang JSR, Sun CT, Mitzutani E (1997) Neuro-fuzzy and soft computing: a computational approach to learning and machine intelligence, New Delhi. Prentice Hall, India
Jekabsons G (2010) Areslab: adaptive regression splines toolbox for Matlab/Octave
Khasawneh MA, Al-jamal NF (2019) Modeling resilient modulus of fine-grained materials using different statistical techniques. Transp Geotech 21(100263). https://doi.org/10.1016/j.trgeo.2019.100263
Kim S-H, Yang J, Jeong J-H (2014) Prediction of subgrade resilient modulus using artificial neural network. KSCE J Civil Eng 18:1372. https://doi.org/10.1007/s12205-014-0316-6
Kor K, Altun G (2020) Is support vector regression method suitable for predicting rate of penetration? J Petrol Sci Eng 194:18. https://doi.org/10.1016/j.petrol.2020.107542
Koshy SA, Praveen A, Ajitha T (2021) Resilient modulus prediction of laterite soils under variable moisture levels using fuzzy logic model. Transp Infrast Geotechnol:23. https://doi.org/10.1007/s40515-021-00173-8
Lekarp F, Isacsson U, Dawson A (2000) State of the art. 1: resilient response of unbound aggregates. J Trans Eng 126(1):66–75
Li D, Selig ET (1994) Resilient modulus for fine-grained subgrade soils. J Geotech Eng 120(6):939–957
Liaw A, Wiener M (2002) Classification and regression by random forest. R News 2:18–22
Ling H, Qian C, Kang W, Liang C, Chen H (2019) Combination of support vector machine and k-fold cross validation to predict compressive strength of concrete in marine environment. Const Build Mater 206:363. https://doi.org/10.1016/j.conbuildmat.2019.02.071
LTPP, Long-term pavement performance IMS package [Dataset], Long-term Pavement Performance, 2018. [Online]. Available: https://infopave.fhwa.dot.govt/DownloadTracker/Bucket/23228.
Montesinos Lopez OA, Montesinos Lopez A, Crossa J (2022) Random forest for genomic prediction, in Multivariate statistical machine learning methods for genomic prediction. Springer, Cham, pp 633–681. https://doi.org/10.1007/978-3-030-89010-0_15
Mousavi SH, Gabr MA, Borden RH (2018) Resilient modulus prediction of soft low-plasticity Piedmont residual soil using dynamic cone penetrometer. J Rock Mech Geotech Eng 10(2):323–332. https://doi.org/10.1016/j.jrmge.2017.10.007
Naser AH, Badr AH, Henedy SN, Ostrowski KA, Imran H (2022) Application of multivariate adaptive regression splines (MARS) approach in prediction of compressive strength of eco-friendly concrete. Case studies Const Mater 17:e01262. https://doi.org/10.1016/j.cscm.2022.e01262
Nazzal MD, Tatari O (2013) Evaluating the use of neural networks and genetic algorithms for prediction of subgrade resilient modulus. Int J Pave Eng 14(4):364–373. https://doi.org/10.1080/10298436.2012.671944
NCHRP (2004) Part 2, Design inputs, Guide for mechanistic-empirical design of new and rehabilitated pavement structures, NCHRP 1-37A, final report
Nguyen BT, Mohajerani A (2016) Resilient modulus of fine-grained soil and a simple tesing and calculation method for determining an average resilient modulus value for pavement design. Trans Geotech 7:59–70
Nguyen XC, Nguyen TT, La DD, Kumar G, Rene ER, Nguyen DD, Chang SW, Chung WJ, Nguyen XH, Nguyen VK (2021) Development of machine learning - based models to forecast solid waste generation in residential areas: a case study from Vietnam. Resour , Conserv Recycl 167:10. https://doi.org/10.1016/j.resconrec.2020.105381
Nwonu DC, Ikeagwuani CC (2019) Evaluating the effect of agro-based admixture on lime-treated expansive soil for subgrade material. Int J Pave Eng:1. https://doi.org/10.1080/10298436.2019.1703979
Pal M, Deswal S (2014) Extreme learning machine based modeling of resilient modulus of subgrade soils. Geotech Geol Eng 32:287. https://doi.org/10.1007/s10706-013-9710-y
Sadrossadat E, Heidaripanah A, Osouli S (2016) Prediction of resilient modulus of flexible pavement subgrade soil using adaptive neuro-fuzzy inference systems. Construction and building materials 123:235. https://doi.org/10.1016/j.conbuildmat.2016.07.008
Samadi M, Afshar MH, Jabbari E, Sarkardeh H (2020) Application of multivariate adaptive regression splines and classification and regression tress to estimate wave-induced scour depth around pile groups. Iran J Sci Technol, Trans Civil Eng. https://doi.org/10.1007/s40996-020-00364-2
Saud S, Jamil B, Upadhyay Y, Irshad K (2020) Performance improvement of empirical models for estimation of global solar radiation in India: a k-fold cross-validation approach. Sustain Energy Technol Assess 40:15. https://doi.org/10.1016/j.seta.2020.100768
Seraj A Mohammadi-Khanaposhtani M, Daneshfar R, Naseri M, Esmaeili M, Baghban A, Habibzadeh S and Eslamian S (2023) Cross-validation, in Handbook of hydroinformatics, Volume i: classic soft-computing techniques. Elsevier, pp 89–105. https://doi.org/10.1016/B978-0-12-821285-1.00021-X
Shaqlaih A, White L, Zaman M (2013) Resilient modulus modeling with information theory approach. Int J Geomech 13(4):348–389. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000221
Solanki P, Zaman M, Ebrahimi A (2009) Regression and artificial neural network modeling of resilient modulus of subgrade soils for pavement design applications. In: Gopalakrishnan K, Ceylan H, Attoh-Okine NO (eds) Intelligent and soft computing in infrastructure systems engineering. Studies in Computational intelligence, vol 259. Springer, Berlin, p 304. https://doi.org/10.1007/978-3-642-04586-8_10
Solanki P, Zaman MM, Dean J (2010) Resilient modulus of clay subgrades stabilized with lime, class C fly ash, and cement kiln dust for pavement design. J Trans Res Board 2186:101–110
Strobl C, Boulesteix AL, Zeileis A et al (2007) Bias in random forest variable importance measures: illustrations, sources and a solution. BMC Bioinform 8(25):1–21. https://doi.org/10.1186/1471-2105-8-25
Su Y, Cui Y-J, Dupla J-C, Canou J (2021) Effect of water content on resilient modulus and damping ratio of fine/coarse soil mixtures with varying coarse grain contents. Transportation Geotech 26(100452):1–11. https://doi.org/10.1016/j.trgeo.2020.100452
Turki N, Elaoud A, Gabtni H, Trabelsi I, Khalfallah KK (2019) Agricultural soil characterization using 2D electrical resistivity tomography (ERT) after direct and intermittent digestate application. Arab J Geosci 12(243):1–11. https://doi.org/10.1007/s12517-019-4553-3
Vapnik VN (1995) The nature of statistical learning theory. Springer-Verlag, New York
Vapnik VN (1998) Statistical learning theory, Danvers. John Wiley & Sons, Inc, MA
Xing J, Wang H, Luo K, Wang S, Bai Y, Fan J (2019) Predictive single-step kinetic model of biomass devolatilization for CFD applications: a comparison study of empirical correlations (EC), artificial neural networks (ANN) and random forest (RF). Renew Energ 136:114. https://doi.org/10.1016/j.renene.2018.12.088
Xiong Z, Cui Y, Liu Z, Zhao Y, Hu M, Hu J (2020) Evaluating explorative prediction power of machine learning algorithms for materials discovery using k-fold forward cross-validation. Comp Mater Sci 171:12. https://doi.org/10.1016/j.commatsci.2019.109203
You H, Ma Z, Tang Y, Wang X, Yan J, Ni M, Cen K, Huang Q, Comparison of ANN(MLP), ANFIS (2017) SVM, and RF models for the online classification of heating value of burning municipal solid waste in circulating fluidized bed incinerators. Waste Manag 68:186. https://doi.org/10.1016/j.wasman.2017.03.044
Zaman M, Solanki P, Ebrahimi A, White L (2010a) Neural network modeling of resilient modulus using routine subgrade soil properties. Int J Geomech 10(1):1532–3641
Zaman M, Solanki P, Ebrahimi A, White L (2010b) Neural network modeling of resilient modulus using routine subgrade soil properties. Int J Geomech, ASCE 10:12
Zhang WG, Goh AT (2013) Multivariate adaptive regression splines for analysis of geotechnical engineering systems. Comp Geotech 48:82. https://doi.org/10.1016/j.compgeo.2012.09.016
Zhang W, Goh AT, Zhang Y (2016) Multivariate adaptive regression splines application for multivariate geotechnical problems with big data. Geotech Geol Eng 34(1):193–204
Zolfaghari AA, Taghizadeh-Mehrjardi R, Moshki AR, Malone BP, Weldeyohannes AO, Sarmandian F, Yazdani MR (2016) Using the nonparametric k-nearest neighbor approach for predicting cation exchange capacity. Geoderma 265:119. https://doi.org/10.1016/j.geoderma.2015.11.012
Acknowledgements
The authors wish to appreciate their undergraduate students, Oti Moses Chikadibia and Kalu Stephen Eke, for their immeasurable and kind assistance in sorting the dataset used for this study. More importantly, the authors also commend the Long-Term Pavement Performance Program that generously provided the data for the analysis. Lastly, the authors acknowledge the immeasurable and unquantifiable support of the Africa Center of Excellence for Sustainable power and energy development (ACE-SPED), University of Nigeria Nsukka.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare no competing interests.
Additional information
Responsible Editor: Zeynal Abiddin Erguler
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Ikeagwuani, C.C., Nweke, C.C. & Onah, H.N. Prediction of resilient modulus of fine-grained soil for pavement design using KNN, MARS, and random forest techniques. Arab J Geosci 16, 388 (2023). https://doi.org/10.1007/s12517-023-11469-z
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s12517-023-11469-z