Abstract
Many artificial intelligence-based predictive techniques have been developed for assessing elastic modulus (E) of rocks using results of simple rock index tests. However, most of them are related to artificial neural networks (ANNs). On the other hand, developing a feasible and easy-to-use model is still of interest more specifically when the datasets of the developed models are based on new experimental data. This study investigates the workability of tree-based techniques including random forest (RF), AdaBoost, extreme gradient boosting, and CatBoost. Utilization of the aforementioned techniques in developing predictive models of E for weak rock samples is relatively new. Nevertheless, for model construction, a suitable database obtained from laboratory experiments on different weak rock types, i.e., marl, siltstone, claystone, and limestone, was prepared. Input parameters of the tree-based model comprises rock index tests which are simple, cheap, and available in any geotechnical laboratory. Then, the aforementioned tree-based models were designed and tuned. Level of performance prediction was assessed using a ranking system which was based on statistical indices such as coefficient of determination (R2), mean absolute error (MAE), and variance account for (VAF). Overall, RF model was able to make a prediction results close to the measured elastic moduli of weak rock samples in laboratory. Additionally, using 30 extra sets of data, the proposed predictive model was validated. R2, MAE, and VAF of the validation data were 0.91, 0.597, and 91, respectively which confirm the feasibility of the proposed model in assessing the elastic modulus of weak rocks during site investigation phase.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abdi Y, Garavand AT, Sahamieh RZ (2018) Prediction of strength parameters of sedimentary rocks using artificial neural networks and regression analysis. Arab J Geosci 11:587
Acar MC, Kaya B (2020) Models to estimate the elastic modulus of weak rocks based on least square support vector machine. Arab J Geosci 13:590. https://doi.org/10.1007/s12517-020-05566-6
Aladejare AE, Alofe ED, Onifade M et al (2021) Empirical estimation of uniaxial compressive strength of rock: database of simple, multiple, and artificial intelligence-based regressions. Geotech Geol Eng 39:4427–4455
Armaghani DJ, Harandizadeh H, Momeni E et al (2022a) An optimized system of GMDH-ANFIS predictive model by ICA for estimating pile bearing capacity. Springer, Netherlands
Armaghani DJ, Harandizadeh H, Momeni E (2022b) Load carrying capacity assessment of thin-walled foundations: an ANFIS–PNN model optimized by genetic algorithm. Eng Comput 38(Suppl 5):4073–4095. https://doi.org/10.1007/s00366-021-01380-0
Armaghani DJ, Mohamad ET, Momeni E, Narayanasamy MS (2015) An adaptive neuro-fuzzy inference system for predicting unconfined compressive strength and Young’s modulus: a study on Main Range granite. Bull Eng Geol Environ 74:1301–1319
Armaghani DJ, Momeni E, Asteris P (2020) Application of group method of data handling technique in assessing deformation of rock mass. Metaheuristic Comput Appl 1:1–18
Armaghani DJ, Yagiz S, Mohamad ET, Zhou J (2021) Prediction of TBM performance in fresh through weathered granite using empirical and statistical approaches. Tunn Undergr Sp Technol 118:104183
Asteris PG, Mamou A, Hajihassani M et al (2021) Soft computing based closed form equations correlating L and N-type Schmidt hammer rebound numbers of rocks. Transp Geotech 29:100588
Asteris PG, Rizal FIM, Koopialipoor M et al (2022) Slope stability classification under seismic conditions using several tree-based intelligent techniques. Appl Sci 12:1753
Basser H, Karami H, Shamshirband S et al (2015) Hybrid ANFIS–PSO approach for predicting optimum parameters of a protective spur dike. Appl Soft Comput 30:642–649
Behzadafshar K, Sarafraz ME, Hasanipanah M et al (2019) Proposing a new model to approximate the elasticity modulus of granite rock samples based on laboratory tests results. Bull Eng Geol Environ 78:1527–1536
Beiki M, Majdi A, Givshad A (2013) Application of genetic programming to predict the uniaxial compressive strength and elastic modulus of carbonate rocks. J Rock Mech Min Sci 63:159–169
Bejarbaneh BY, Bejarbaneh EY, Fahimifar A et al (2018) Intelligent modelling of sandstone deformation behaviour using fuzzy logic and neural network systems. Bull Eng Geol Environ 77:345–361
Breiman L (2001) Random forests. Mach Learn 45:5–32
Chen T, Guestrin C (2016) Xgboost: a scalable tree boosting system. Proceedings of the 22nd ACM SIGKDD international conference on knowledge discovery and data mining. Association for Computing Machinery, pp 785–794
Ding W, Nguyen MD, Mohammed AS et al (2021) A new development of ANFIS-Based Henry gas solubility optimization technique for prediction of soil shear strength. Transp Geotech 29:100579
Dorogush AV, Ershov V, Gulin A (2018) CatBoost: gradient boosting with categorical features support. arXiv Prepr. arXiv181011363
Freund Y, Schapire RE (1997) A decision-theoretic generalization of on-line learning and an application to boosting. J Comput Syst Sci 55:119–139
Friedman JH (2001) Greedy function approximation: a gradient boosting machine. Ann Stat 29:1189–1232
Ghanizadeh AR, Ghanizadeh A, Asteris PG et al (2022) Developing bearing capacity model for geogrid-reinforced stone columns improved soft clay utilizing MARS-EBS hybrid method. Transp Geotech 38:100906
Gokceoglu C, Zorlu K (2004) A fuzzy model to predict the uniaxial compressive strength and the modulus of elasticity of a problematic rock. Eng Appl Artif Intell 17:61–72
Harandizadeh H, Armaghani D, Asteris PGGA (2021) TBM performance prediction developing a hybrid ANFIS-PNN predictive model optimized by imperialism competitive algorithm. Neural Comput Appl. https://doi.org/10.1007/s00521-021-06217-x
Hasanipanah M, Monjezi M, Shahnazar A et al (2015) Feasibility of indirect determination of blast induced ground vibration based on support vector machine. Measurement 75:289–297
He B, Armaghani DJ, Lai SH (2023) Assessment of tunnel blasting-induced overbreak: A novel metaheuristic-based random forest approach. Tunn Undergr Sp Technol 133:104979
Huat CY, Moosavi SMH, Mohammed AS et al (2021) Factors influencing pile friction bearing capacity: proposing a novel procedure based on gradient boosted tree technique. Sustainability 13:11862
ISRM (2007) The complete ISRM suggested methods for rock characterization, testing and monitoring: 1974-2006. Ulusay, R. and Hudson, J.A., Eds., Ankara
Kamran M (2021) A state of the art catboost-based T-distributed stochastic neighbor embedding technique to predict back-break at dewan cement limestone quarry. J Min Environ 12:679–691. https://doi.org/10.22044/jme.2021.11222.2104
Khandelwal M, Singh TN (2011) Predicting elastic properties of schistose rocks from unconfined strength using intelligent approach. Arab J Geosci 4:435–442
Koopialipoor M, Asteris PG, Mohammed AS et al (2022) Introducing stacking machine learning approaches for the prediction of rock deformation. Transp Geotech 34:100756
Lashkaripour GR (2002) Predicting mechanical properties of mudrock from index parameters. Bull Eng Geol Environ 61:73–77
Li C, Zhou J, Tao M et al (2022) Developing hybrid ELM-ALO, ELM-LSO and ELM-SOA models for predicting advance rate of TBM. Transp Geotech 36:100819
Majdi A, Beiki M (2010) Evolving neural network using a genetic algorithm for predicting the deformation modulus of rock masses. Int J Rock Mech Min Sci 47(2):246–253
Manouchehrian A, Sharifzadeh M, Moghadam RH, Nouri T (2013) Selection of regression models for predicting strength and deformability properties of rocks using GA. Int J Min Sci Technol 23:495–501
Marto A, Hajihassani M, Momeni E (2014) Bearing capacity of shallow foundation’s prediction through hybrid artificial neural networks. Applied mechanics and materials. Trans Tech Publ, pp 681–686
Mohamad ET, Armaghani DJ, Momeni E et al (2016) Rock strength estimation: a PSO-based BP approach. Neural Comput Appl 30:1635–1646. https://doi.org/10.1007/s00521-016-2728-3
Mohamad ET, Jahed Armaghani D, Momeni E et al (2015) Prediction of the unconfined compressive strength of soft rocks: a PSO-based ANN approach. Bull Eng Geol Environ 74:745–757. https://doi.org/10.1007/s10064-014-0638-0
Momeni E, Abdi Y (2022) Application of group method of data handling (GMDH) technique in predicting UCS of limestones. Iran J Eng Geol 15
Momeni, E., He, B., Abdi, Y., & Armaghani, D. J. (2023). Novel hybrid XGBoost model to forecast soil shear strength based on some soil index tests. CMES - Comput Model Eng Sci 136(3)
Momeni E, Nazir R, Armaghani DJ, Maizir H (2014) Prediction of pile bearing capacity using a hybrid genetic algorithm-based ANN. Measurement 57:122–131
Momeni E, Omidinasab F, Dalvand A et al (2022) Flexural strength of concrete beams made of recycled aggregates: An experimental and soft computing-based study. Sustainability 14:11769
Momeni E, Poormoosavian M, Mahdiyar A, Fakher A (2018) Evaluating random set technique for reliability analysis of deep urban excavation using Monte Carlo simulation. Comput Geotech 100:203–215
Momeni E, Poormoosavian M, Tehrani HS, Fakher A (2021a) Reliability analysis and risk assessment of deep excavations using random-set finite element method and event tree technique. Transp Geotech 29:100560
Momeni E, Yarivand A, Dowlatshahi MB, Armaghani DJ (2021b) An efficient optimal neural network based on gravitational search algorithm in predicting the deformation of geogrid-reinforced soil structures. Transp Geotech 26:100446
Moradian ZA, Behnia M (2009) Predicting the uniaxial compressive strength and static Young’s modulus of intact sedimentary rocks using the ultrasonic test. Int J Geomech 9:14–19
Murlidhar B, Bejarbaneh B, Armaghani D et al (2020) Application of tree-based predictive models to forecast air overpressure induced by mine blasting. Nat Resour Res. https://doi.org/10.1007/s11053-020-09770-9
Nazir R, Momeni E, Marsono K, Maizir H (2015) An artificial neural network approach for prediction of bearing capacity of spread foundations in sand. J Teknol 72:9–14
Ocak I, Seker SE (2012) Estimation of elastic modulus of intact rocks by artificial neural network. Rock Mech Rock Eng 45:1047–1054
Parsajoo M, Armaghani DJ, Asteris PG (2022) A precise neuro-fuzzy model enhanced by artificial bee colony techniques for assessment of rock brittleness index. Neural Comput Appl. https://doi.org/10.1007/s00521-021-06600-8
Parsajoo M, Armaghani DJ, Mohammed AS et al (2021) Tensile strength prediction of rock material using non-destructive tests: a comparative intelligent study. Transp Geotech 31:100652. https://doi.org/10.1016/J.TRGEO.2021.100652
Pedregosa F, Varoquaux G, Gramfort A et al (2011) Scikit-learn: machine learning in Python. J Mach Learn Res 12:2825–2830
Pham BT, Nguyen MD, Nguyen-Thoi T et al (2020) A novel approach for classification of soils based on laboratory tests using Adaboost. Tree and ANN modeling. Transp Geotech 27:100508. https://doi.org/10.1016/j.trgeo.2020.100508
Prokhorenkova L, Gusev G, Vorobev A et al (2018) Catboost: unbiased boosting with categorical features. Adv Neural Inf Process Syst 2018-Decem:6638–6648
Rätsch G, Onoda T, Müller K-R (2001) Soft margins for AdaBoost. Mach Learn 42:287–320
Rezaei M (2018) Indirect measurement of the elastic modulus of intact rocks using the Mamdani fuzzy inference system. Meas J Int Meas Confed 129:319–331. https://doi.org/10.1016/j.measurement.2018.07.047
Roy DG, Singh TN (2018) Regression and soft computing models to estimate young’s modulus of CO2 saturated coals. Measurement 129:91–101
Sachpazis CI (1990) Correlating Schmidt hardness with compressive strength and Young’s modulus of carbonate rocks. Bull Int Assoc Eng Geol L’association Int Géologie L’ingénieur 42:75–83
Saedi B, Mohammadi SD, Shahbazi H (2018) Prediction of uniaxial compressive strength and elastic modulus of migmatites using various modeling techniques. Arab J Geosci 11:1–14
Shan F, He X, Armaghani DJ et al (2022) Success and challenges in predicting TBM penetration rate using recurrent neural networks. Tunn Undergr Sp Technol 130:104728
Singh R, Kainthola A, Singh TN (2012) Estimation of elastic constant of rocks using an ANFIS approach. Appl Soft Comput 12:40–45
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
Torabi-Kaveh M, Naseri F, Saneie S, Sarshari B (2015) Application of artificial neural networks and multivariate statistics to predict UCS and E using physical properties of Asmari limestones. Arab J Geosci 8:2889–2897
Wang S, Zhou J, Li C et al (2021) Rockburst prediction in hard rock mines developing bagging and boosting tree-based ensemble techniques. J Cent South Univ 28:527–542
Wang Y, Rezaei M, Abdullah RA, Hasanipanah M (2023) Developing two hybrid algorithms for predicting the elastic modulus of intact rocks. Sustainability 15(5):4230
Waqas U, Ahmed MF (2020) Prediction modeling for the estimation of dynamic elastic Young’s modulus of thermally treated sedimentary rocks using linear–nonlinear regression analysis, regularization, and ANFIS. Rock Mech Rock Eng 53:5411–5428
Yang H, Wang Z, Song K (2020) A new hybrid grey wolf optimizer-feature weighted-multiple kernel-support vector regression technique to predict TBM performance. Eng Comput. https://doi.org/10.1007/s00366-020-01217-2
Yang H, Song K, Zhou J (2022) Automated recognition model of geomechanical information based on operational data of tunneling boring machines. Rock Mech Rock Eng. https://doi.org/10.1007/s00603-021-02723-5
Yang L, Feng X, Sun Y (2019) Predicting the Young’s Modulus of granites using the Bayesian model selection approach. Bull Eng Geol Environ 78:3413–3423
Yaşar E, Erdoğan Y (2004) Estimation of rock physicomechanical properties using hardness methods. Eng Geol 71:281–288
Zhao H, Zhang L, Ren J, Wang M, Meng Z (2022) AdaBoost-based back analysis for determining rock mass mechanical parameters of claystones in goupitan tunnel, China. Buildings 12(8):1073
Zhou J, Qiu Y, Armaghani DJ et al (2020) Predicting TBM penetration rate in hard rock condition: a comparative study among six XGB-based metaheuristic techniques. Geosci Front. https://doi.org/10.1016/j.gsf.2020.09.020
Zhou Z, Hooker G (2021) Unbiased measurement of feature importance in tree-based methods. ACM Trans Knowl Discov from Data 15:1–21
Zorlu K, Gokceoglu C, Ocakoglu F et al (2008) Prediction of uniaxial compressive strength of sandstones using petrography-based models. Eng Geol 96:141–158
Acknowledgements
The authors would like to thank the anonymous reviewers for their constructive comments which enhance the quality of the paper.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing interests.
Appendix A. Dataset used in this study
Appendix A. Dataset used in this study
Sample No. | Lithology | n (%) | ρdry (gr/cm3) | VP (m/sec) | Id2 (%) | Abs (%) | E (GPa) |
|---|---|---|---|---|---|---|---|
S1 | Claystone | 56.55 | 1.95 | 1011.53 | 63.27 | 26.54 | 1.23 |
S2 | Claystone | 20.28 | 1.99 | 1491.57 | 83.52 | 10.16 | 2.12 |
S3 | Claystone | 32.84 | 1.98 | 1178.34 | 79.31 | 20.54 | 1.52 |
S4 | Claystone | 37.03 | 1.95 | 1649.43 | 83.44 | 21.19 | 3.61 |
S5 | Claystone | 22.91 | 1.96 | 1379.41 | 50.28 | 11.12 | 1.42 |
S6 | Claystone | 16.12 | 1.95 | 1436.49 | 44.25 | 8.67 | 3.15 |
S7 | Claystone | 16.77 | 1.61 | 1664.48 | 22.75 | 9.66 | 3.41 |
S8 | Claystone | 40.48 | 1.93 | 1389.12 | 85.18 | 23.12 | 1.56 |
S9 | Claystone | 30.18 | 1.99 | 1770.77 | 95.43 | 17.34 | 1.28 |
S10 | Claystone | 24.69 | 1.96 | 2195.09 | 84.58 | 14.32 | 2.64 |
S11 | Claystone | 10.93 | 2.01 | 3002.23 | 70.07 | 6.12 | 3.12 |
S12 | Claystone | 36.56 | 1.97 | 1326.43 | 75.37 | 19.08 | 1.62 |
S13 | Claystone | 27.25 | 1.90 | 1548.28 | 63.56 | 15.18 | 2.41 |
S14 | Claystone | 26.57 | 1.97 | 2089.30 | 83.82 | 15.23 | 2.15 |
S15 | Claystone | 30.35 | 1.92 | 1474.33 | 67.49 | 16.48 | 2.14 |
S16 | Claystone | 26.81 | 1.92 | 1605.84 | 69.86 | 15.12 | 2.30 |
S17 | Claystone | 26.66 | 1.88 | 1503.79 | 57.18 | 14.75 | 2.63 |
S18 | Claystone | 28.52 | 1.94 | 1656.91 | 70.14 | 15.62 | 2.23 |
S19 | Claystone | 28.09 | 1.95 | 1778.37 | 74.79 | 15.67 | 2.19 |
S20 | Claystone | 26.64 | 1.94 | 1706.65 | 70.65 | 14.87 | 2.30 |
S21 | Limestone | 11.32 | 2.32 | 2350.00 | 95.06 | 4.56 | 4.32 |
S22 | Limestone | 11.39 | 2.39 | 2430.00 | 95.76 | 3.52 | 4.51 |
S23 | Limestone | 13.75 | 2.39 | 2350.00 | 95.01 | 4.65 | 3.85 |
S24 | Limestone | 7.82 | 2.40 | 2450.00 | 95.14 | 2.51 | 4.11 |
S25 | Limestone | 10.85 | 2.38 | 2790.00 | 96.21 | 4.35 | 4.11 |
S26 | Limestone | 11.58 | 2.35 | 2660.00 | 96.54 | 3.87 | 5.32 |
S27 | Limestone | 12.32 | 2.14 | 2010.00 | 96.13 | 5.76 | 4.67 |
S28 | Limestone | 13.94 | 2.12 | 2130.00 | 96.10 | 6.58 | 3.92 |
S29 | Marl | 23.10 | 2.38 | 2060.80 | 86.00 | 11.20 | 6.54 |
S30 | Marl | 24.30 | 2.40 | 2154.10 | 85.40 | 12.30 | 8.12 |
S31 | Marl | 24.80 | 2.37 | 2090.30 | 86.40 | 10.40 | 8.62 |
S32 | Marl | 13.20 | 2.61 | 2701.60 | 87.30 | 6.30 | 9.43 |
S33 | Marl | 16.70 | 2.54 | 2665.10 | 87.90 | 7.50 | 9.23 |
S34 | Marl | 22.20 | 2.43 | 1944.00 | 85.80 | 10.80 | 9.23 |
S35 | Marl | 24.40 | 2.43 | 1887.00 | 85.70 | 12.10 | 5.25 |
S36 | Marl | 26.60 | 2.29 | 1526.34 | 85.80 | 13.00 | 5.72 |
S37 | Marl | 16.00 | 2.48 | 2592.40 | 86.50 | 5.70 | 10.45 |
S38 | Marl | 26.40 | 2.35 | 1766.70 | 84.60 | 16.40 | 7.54 |
S39 | Marl | 32.70 | 2.24 | 1245.70 | 84.40 | 15.30 | 4.23 |
S40 | Marl | 31.50 | 2.30 | 1303.60 | 84.70 | 14.00 | 5.01 |
S41 | Marl | 19.60 | 2.39 | 2156.80 | 86.50 | 10.80 | 9.32 |
S42 | Marl | 20.30 | 2.42 | 2165.40 | 86.30 | 10.10 | 8.34 |
S43 | Marl | 25.30 | 2.98 | 1476.40 | 84.40 | 13.90 | 4.38 |
S44 | Marl | 26.83 | 2.34 | 1739.07 | 85.90 | 12.37 | 7.23 |
S45 | Marl | 21.33 | 2.43 | 2226.05 | 86.30 | 9.77 | 11.04 |
S46 | Marl | 17.95 | 2.44 | 2412.35 | 87.55 | 9.30 | 9.26 |
S47 | Marl | 16.75 | 2.52 | 2577.90 | 87.30 | 7.70 | 10.23 |
S48 | Marl | 21.30 | 2.39 | 2259.60 | 86.15 | 9.35 | 10.56 |
S49 | Marl | 19.95 | 2.41 | 2161.10 | 86.40 | 10.45 | 7.32 |
S50 | Marl | 22.33 | 2.40 | 2135.40 | 86.00 | 10.27 | 8.21 |
S51 | Marl | 32.10 | 2.27 | 1274.65 | 84.55 | 14.65 | 6.50 |
S52 | Marl | 23.70 | 2.39 | 2107.45 | 85.70 | 11.75 | 8.37 |
S53 | Marl | 26.83 | 2.34 | 1739.07 | 85.90 | 12.37 | 7.64 |
S54 | Marl | 19.25 | 2.80 | 2233.40 | 86.35 | 9.60 | 13.23 |
S55 | Marl | 19.60 | 2.60 | 2197.25 | 86.38 | 10.03 | 10.32 |
S56 | Marl | 19.13 | 2.46 | 2436.80 | 86.70 | 9.07 | 9.76 |
S57 | Siltstone | 29.92 | 2.05 | 1520.36 | 62.78 | 14.54 | 3.56 |
S58 | Siltstone | 30.14 | 2.05 | 1289.44 | 64.88 | 15.12 | 2.51 |
S59 | Siltstone | 16.84 | 2.02 | 2421.30 | 33.40 | 9.56 | 4.01 |
S60 | Siltstone | 25.34 | 2.05 | 1798.32 | 28.46 | 12.34 | 2.08 |
S61 | Siltstone | 23.24 | 2.02 | 1472.99 | 66.82 | 11.13 | 2.15 |
S62 | Siltstone | 16.73 | 2.03 | 2134.24 | 75.65 | 8.32 | 4.31 |
S63 | Siltstone | 36.24 | 2.03 | 1608.10 | 75.14 | 20.23 | 2.67 |
S64 | Siltstone | 40.14 | 2.05 | 1345.63 | 76.55 | 22.54 | 2.09 |
S65 | Siltstone | 42.90 | 2.00 | 1123.45 | 72.08 | 19.45 | 1.12 |
S66 | Siltstone | 42.55 | 2.09 | 1278.12 | 45.12 | 18.86 | 1.41 |
S67 | Siltstone | 8.44 | 2.20 | 2197.11 | 79.76 | 3.45 | 3.89 |
S68 | Siltstone | 5.44 | 2.19 | 2196.69 | 63.54 | 2.65 | 3.32 |
S69 | Siltstone | 46.83 | 2.14 | 1410.63 | 53.99 | 22.12 | 1.25 |
S70 | Siltstone | 18.20 | 2.07 | 2195.09 | 68.30 | 8.76 | 2.12 |
S71 | Siltstone | 19.11 | 2.06 | 3186.71 | 81.99 | 10.34 | 3.34 |
S72 | Siltstone | 15.73 | 2.02 | 2315.37 | 77.06 | 8.65 | 2.54 |
S73 | Siltstone | 17.56 | 2.00 | 2254.23 | 54.73 | 10.15 | 2.67 |
S74 | Siltstone | 18.25 | 2.01 | 1547.00 | 61.13 | 10.73 | 2.56 |
S75 | Siltstone | 26.08 | 2.01 | 1387.32 | 90.48 | 15.65 | 2.32 |
S76 | Siltstone | 26.07 | 2.00 | 1591.53 | 61.20 | 14.54 | 3.76 |
S77 | Siltstone | 15.00 | 2.09 | 1841.58 | 53.42 | 7.65 | 2.23 |
S78 | Siltstone | 15.77 | 2.02 | 2325.94 | 73.45 | 8.12 | 3.11 |
S79 | Siltstone | 16.61 | 2.05 | 2601.56 | 61.51 | 9.65 | 3.43 |
S80 | Siltstone | 39.42 | 2.03 | 1315.65 | 74.07 | 22.05 | 1.30 |
S81 | Siltstone | 7.21 | 2.02 | 3250.45 | 75.77 | 3.43 | 3.81 |
S82 | Siltstone | 9.10 | 2.00 | 3123.12 | 73.24 | 5.12 | 1.65 |
S83 | Siltstone | 16.01 | 2.06 | 2756.34 | 43.12 | 9.13 | 2.51 |
S84 | Siltstone | 20.73 | 2.06 | 1675.32 | 81.27 | 12.54 | 3.86 |
S85 | Siltstone | 11.71 | 1.95 | 2874.32 | 47.37 | 5.23 | 3.67 |
S86 | Siltstone | 17.46 | 2.62 | 2300.41 | 44.73 | 8.67 | 3.56 |
S87 | Siltstone | 32.05 | 2.00 | 1143.56 | 52.17 | 18.34 | 1.45 |
S88 | Siltstone | 12.17 | 2.01 | 2891.21 | 74.08 | 7.32 | 3.27 |
S89 | Siltstone | 11.57 | 2.05 | 2956.42 | 57.21 | 6.34 | 3.64 |
S90 | Siltstone | 18.25 | 2.06 | 2474.87 | 64.22 | 10.13 | 2.85 |
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
Abdi, Y., Momeni, E. & Armaghani, D.J. Elastic modulus estimation of weak rock samples using random forest technique. Bull Eng Geol Environ 82, 176 (2023). https://doi.org/10.1007/s10064-023-03154-y
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10064-023-03154-y