# A Novel Hybrid Soft Computing Model Using Random Forest and Particle Swarm Optimization for Estimation of Undrained Shear Strength of Soil

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## Abstract

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## 1. Introduction

## 2. Case Study and Data Collection

#### 2.1. Description of the Study Area

#### 2.2. Data Used

#### 2.2.1. Output (Undrained Shear Strength of Soil)

#### 2.2.2. Input Variables

## 3. Methods Used

#### 3.1. Random Forest

#### 3.2. Particle Swarm Optimization (PSO)

_{best}) in search space and the whole swarm best position (G

_{best}). The particle position and velocities are computed as follows:

_{1,}and m

_{2}correspond to the cognitive, social effect, and inertia parameters, respectively; n

_{1}and n

_{2}indicate arbitrary numbers with the range of [0, 1]; ${p}_{best,i}^{t}$ and ${g}_{best,i}^{t}$ symbolize the best position of particle i and swarm, respectively.

#### 3.3. Dataset Splitting

#### 3.4. Modeling and Hyperparameters Tuning

#### 3.5. RF Model Assessment

## 4. Results and Discussion

#### 4.1. Influence of Training Set Size (TSS)

#### 4.2. Hyperparameters Tuning

#### 4.3. Predictive Capability of the Models

#### 4.4. Sensitivity Analysis of Input Parameters

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Poulos, H.G. Design of reinforcing piles to increase slope stability. Can. Geotech. J.
**1995**, 32, 808–818. [Google Scholar] [CrossRef] - Liu, Y.-J.; Wang, T.-W.; Cai, C.-F.; Li, Z.-X.; Cheng, D.-B. Effects of vegetation on runoff generation, sediment yield and soil shear strength on road-side slopes under a simulation rainfall test in the Three Gorges Reservoir Area, China. Sci. Total Environ.
**2014**, 485, 93–102. [Google Scholar] [CrossRef] [PubMed] - Hettiarachchi, H.; Brown, T. Use of SPT blow counts to estimate shear strength properties of soils: Energy balance approach. J. Geotech. Geoenviron. Eng.
**2009**, 135, 830–834. [Google Scholar] [CrossRef] - Motaghedi, H.; Eslami, A. Analytical approach for determination of soil shear strength parameters from CPT and CPTu data. Arab. J. Sci. Eng.
**2014**, 39, 4363–4376. [Google Scholar] [CrossRef] - Cha, M.; Cho, G.-C. Shear strength estimation of sandy soils using shear wave velocity. Geotech. Test. J.
**2007**, 30, 484–495. [Google Scholar] - Garven, E.; Vanapalli, S. Evaluation of empirical procedures for predicting the shear strength of unsaturated soils. In Unsaturated Soils 2006, Fourth International Conference on Unsaturated Soils, Carefree, AZ, USA, 2–6 April 2006; American Society of Civil Engineers: Reston, VA, USA, 2006; pp. 2570–2592. [Google Scholar]
- Kim, B.-S.; Shibuya, S.; Park, S.-W.; Kato, S. Application of suction stress for estimating unsaturated shear strength of soils using direct shear testing under low confining pressure. Can. Geotech. J.
**2010**, 47, 955–970. [Google Scholar] [CrossRef] - Ohu, J.O.; Raghavan, G.; McKyes, E.; Mehuys, G. Shear strength prediction of compacted soils with varying added organic matter contents. Trans. ASAE
**1986**, 29, 351–355. [Google Scholar] [CrossRef] - Tiwari, B.; Marui, H. A new method for the correlation of residual shear strength of the soil with mineralogical composition. J. Geotech. Geoenviron. Eng.
**2005**, 131, 1139–1150. [Google Scholar] [CrossRef] - Vilar, O.M. A simplified procedure to estimate the shear strength envelope of unsaturated soils. Can. Geotech. J.
**2006**, 43, 1088–1095. [Google Scholar] [CrossRef] - Huang, B.; Qiu, M.; Lin, J.; Chen, J.; Jiang, F.; Wang, M.-K.; Ge, H.; Huang, Y. Correlation between shear strength and soil physicochemical properties of different weathering profiles of the non-eroded and collapsing gully soils in southern China. J. Soils Sediments
**2019**, 19, 3832–3846. [Google Scholar] [CrossRef] - Zhai, Q.; Rahardjo, H.; Satyanaga, A.; Dai, G. Estimation of unsaturated shear strength from soil–water characteristic curve. Acta Geotech.
**2019**, 14, 1977–1990. [Google Scholar] [CrossRef] - Leong, E.-C. Soil-water characteristic curves-Determination, estimation and application. Jpn. Geotech. Soc. Spec. Publ.
**2019**, 7, 21–30. [Google Scholar] [CrossRef][Green Version] - Bui, D.T.; Nhu, V.-H.; Hoang, N.-D. Prediction of soil compression coefficient for urban housing project using novel integration machine learning approach of swarm intelligence and multi-layer perceptron neural network. Adv. Eng. Inform.
**2018**, 38, 593–604. [Google Scholar] - Chen, W.; Wang, Y.; Cao, G.; Chen, G.; Gu, Q. A random forest model based classification scheme for neonatal amplitude-integrated EEG. Biomed. Eng. Online
**2014**, 13, S4. [Google Scholar] [CrossRef][Green Version] - Chou, J.-S.; Pham, A.-D. Enhanced artificial intelligence for ensemble approach to predicting high performance concrete compressive strength. Constr. Build. Mater.
**2013**, 49, 554–563. [Google Scholar] [CrossRef] - Koopialipoor, M.; Fallah, A.; Armaghani, D.J.; Azizi, A.; Mohamad, E.T. Three hybrid intelligent models in estimating flyrock distance resulting from blasting. Eng. Comput.
**2019**, 35, 243–256. [Google Scholar] [CrossRef][Green Version] - Koopialipoor, M.; Ghaleini, E.N.; Tootoonchi, H.; Armaghani, D.J.; Haghighi, M.; Hedayat, A. Developing a new intelligent technique to predict overbreak in tunnels using an artificial bee colony-based ANN. Environ. Earth Sci.
**2019**, 78, 165. [Google Scholar] [CrossRef] - Pham, B.T.; Bui, D.T.; Prakash, I.; Dholakia, M. Hybrid integration of Multilayer Perceptron Neural Networks and machine learning ensembles for landslide susceptibility assessment at Himalayan area (India) using GIS. Catena
**2017**, 149, 52–63. [Google Scholar] [CrossRef] - Samui, P. Prediction of friction capacity of driven piles in clay using the support vector machine. Can. Geotech. J.
**2008**, 45, 288–295. [Google Scholar] [CrossRef][Green Version] - Shahin, M.A.; Jaksa, M.B.; Maier, H.R. Recent advances and future challenges for artificial neural systems in geotechnical engineering applications. Adv. Artif. Neural Syst.
**2009**, 2009, 5. [Google Scholar] [CrossRef] - Dao, D.V.; Adeli, H.; Ly, H.-B.; Le, L.M.; Le, V.M.; Le, T.-T.; Pham, B.T. A Sensitivity and Robustness Analysis of GPR and ANN for High-Performance Concrete Compressive Strength Prediction Using a Monte Carlo Simulation. Sustainability
**2020**, 12, 830. [Google Scholar] [CrossRef][Green Version] - Pham, B.T.; Avand, M.; Janizadeh, S.; Phong, T.V.; Al-Ansari, N.; Ho, L.S.; Das, S.; Le, H.V.; Amini, A.; Bozchaloei, S.K. GIS Based Hybrid Computational Approaches for Flash Flood Susceptibility Assessment. Water
**2020**, 12, 683. [Google Scholar] [CrossRef][Green Version] - Pham, B.T.; Prakash, I.; Dou, J.; Singh, S.K.; Trinh, P.T.; Tran, H.T.; Le, T.M.; Van Phong, T.; Khoi, D.K.; Shirzadi, A. A novel hybrid approach of landslide susceptibility modelling using rotation forest ensemble and different base classifiers. Geocarto Int.
**2019**, 1–25. [Google Scholar] [CrossRef] - Pham, B.T.; Bui, D.T.; Prakash, I.; Nguyen, L.H.; Dholakia, M. A comparative study of sequential minimal optimization-based support vector machines, vote feature intervals, and logistic regression in landslide susceptibility assessment using GIS. Environ. Earth Sci.
**2017**, 76, 371. [Google Scholar] [CrossRef] - Pham, B.T.; Bui, D.T.; Pham, H.V.; Le, H.Q.; Prakash, I.; Dholakia, M. Landslide hazard assessment using random subspace fuzzy rules based classifier ensemble and probability analysis of rainfall data: A case study at Mu Cang Chai District, Yen Bai Province (Viet Nam). J. Indian Soc. Remote Sens.
**2017**, 45, 673–683. [Google Scholar] [CrossRef] - Sharma, L.; Singh, R.; Umrao, R.; Sharma, K.; Singh, T. Evaluating the modulus of elasticity of soil using soft computing system. Eng. Comput.
**2017**, 33, 497–507. [Google Scholar] [CrossRef] - Kalkan, E.; Akbulut, S.; Tortum, A.; Celik, S. Prediction of the unconfined compressive strength of compacted granular soils by using inference systems. Environ. Geol.
**2009**, 58, 1429–1440. [Google Scholar] [CrossRef] - Nhu, V.H.; Hoang, N.D.; Duong, V.B.; Vu, H.D.; Bui, D.T. A hybrid computational intelligence approach for predicting soil shear strength for urban housing construction: a case study at Vinhomes Imperia project, Hai Phong City (Vietnam). Eng. Comput.
**2019**, 1–14. [Google Scholar] [CrossRef] - Moavenian, M.; Nazem, M.; Carter, J.; Randolph, M. Numerical analysis of penetrometers free-falling into soil with shear strength increasing linearly with depth. Comput. Geotech.
**2016**, 72, 57–66. [Google Scholar] [CrossRef] - Pham, B.T.; Hoang, T.-A.; Nguyen, D.-M.; Bui, D.T. Prediction of shear strength of soft soil using machine learning methods. Catena
**2018**, 166, 181–191. [Google Scholar] [CrossRef] - Breiman, L. Random forests. Mach. Learn.
**2001**, 45, 5–32. [Google Scholar] [CrossRef][Green Version] - Liaw, A.; Wiener, M. Classification and regression by randomForest. R News
**2002**, 2, 18–22. [Google Scholar] - Jahed Armaghani, D.; Hajihassani, M.; Yazdani Bejarbaneh, B.; Marto, A.; Tonnizam Mohamad, E. Indirect measure of shale shear strength parameters by means of rock index tests through an optimized artificial neural network. Measurement
**2014**, 55, 487–498. [Google Scholar] [CrossRef] - Hajihassani, M.; Armaghani, D.J.; Kalatehjari, R. Applications of particle swarm optimization in geotechnical engineering: a comprehensive review. Geotech. Geol. Eng.
**2018**, 36, 705–722. [Google Scholar] [CrossRef] - Hasanipanah, M.; Noorian-Bidgoli, M.; Armaghani, D.J.; Khamesi, H. Feasibility of PSO-ANN model for predicting surface settlement caused by tunneling. Eng. Comput.
**2016**, 32, 705–715. [Google Scholar] [CrossRef] - Kalatehjari, R.; Ali, N.; Kholghifard, M.; Hajihassani, M. The effects of method of generating circular slip surfaces on determining the critical slip surface by particle swarm optimization. Arab. J. Geosci.
**2014**, 7, 1529–1539. [Google Scholar] [CrossRef] - Das, B.M.; Sobhan, K. Principles of Geotechnical Engineering; Cengage Learning: Stamford, CT, USA, 2013. [Google Scholar]
- Terzaghi, K.; Peck, R.B.; Mesri, G. Soil Mechanics; John Wiley & Sons: New York, NY, USA, 1996. [Google Scholar]
- Hong, H.; Pourghasemi, H.R.; Pourtaghi, Z.S. Landslide susceptibility assessment in Lianhua County (China): a comparison between a random forest data mining technique and bivariate and multivariate statistical models. Geomorphology
**2016**, 259, 105–118. [Google Scholar] [CrossRef] - Stumpf, A.; Kerle, N. Object-oriented mapping of landslides using Random Forests. Remote Sens. Environ.
**2011**, 115, 2564–2577. [Google Scholar] [CrossRef] - Archer, K.J.; Kimes, R.V. Empirical characterization of random forest variable importance measures. Comput. Stat. Data Anal.
**2008**, 52, 2249–2260. [Google Scholar] [CrossRef] - Biau, G.; Devroye, L.; Lugosi, G. Consistency of random forests and other averaging classifiers. J. Mach. Learn. Res.
**2008**, 9, 2015–2033. [Google Scholar] - Trigila, A.; Iadanza, C.; Esposito, C.; Scarascia-Mugnozza, G. Comparison of Logistic Regression and Random Forests techniques for shallow landslide susceptibility assessment in Giampilieri (NE Sicily, Italy). Geomorphology
**2015**, 249, 119–136. [Google Scholar] [CrossRef] - Eberhart, R.; Kennedy, J. A new optimizer using particle swarm theory. In Proceedings of the MHS’95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science, Nagoya, Japan, 4–6 October 1995; pp. 39–43. [Google Scholar]
- Cheng, Y.; Li, L.; Chi, S.-C.; Wei, W. Particle swarm optimization algorithm for the location of the critical non-circular failure surface in two-dimensional slope stability analysis. Comput. Geotech.
**2007**, 34, 92–103. [Google Scholar] [CrossRef] - Awad, Z.K.; Aravinthan, T.; Zhuge, Y.; Gonzalez, F. A review of optimization techniques used in the design of fibre composite structures for civil engineering applications. Mater. Des.
**2012**, 33, 534–544. [Google Scholar] [CrossRef][Green Version] - Chen, W.; Panahi, M.; Pourghasemi, H.R. Performance evaluation of GIS-based new ensemble data mining techniques of adaptive neuro-fuzzy inference system (ANFIS) with genetic algorithm (GA), differential evolution (DE), and particle swarm optimization (PSO) for landslide spatial modelling. Catena
**2017**, 157, 310–324. [Google Scholar] [CrossRef] - Qi, C.; Fourie, A.; Chen, Q.; Zhang, Q. A strength prediction model using artificial intelligence for recycling waste tailings as cemented paste backfill. J. Clean. Prod.
**2018**, 183, 566–578. [Google Scholar] [CrossRef] - Pedregosa, F.; Varoquaux, G.; Gramfort, A.; Michel, V.; Thirion, B.; Grisel, O.; Blondel, M.; Prettenhofer, P.; Weiss, R.; Dubourg, V. Scikit-learn: Machine learning in Python. J. Mach. Learn. Res.
**2011**, 12, 2825–2830. [Google Scholar] - Qi, C.; Chen, Q.; Fourie, A.; Zhang, Q. An intelligent modelling framework for mechanical properties of cemented paste backfill. Miner. Eng.
**2018**, 123, 16–27. [Google Scholar] [CrossRef] - Eberhart, R.C.; Shi, Y. Comparing inertia weights and constriction factors in particle swarm optimization. In Proceedings of the 2000 Congress on Evolutionary Computation, CEC00 (Cat. No.00TH8512), La Jolla, CA, USA, 16–19 July 2000; Volume 81, pp. 84–88. [Google Scholar]
- Van den Bergh, F.; Engelbrecht, A.P. A study of particle swarm optimization particle trajectories. Inf. Sci.
**2006**, 176, 937–971. [Google Scholar] [CrossRef] - Li-ping, Z.; Huan-jun, Y.; Shang-xu, H. Optimal choice of parameters for particle swarm optimization. J. Zhejiang Univ. Sci. A
**2005**, 6, 528–534. [Google Scholar] [CrossRef] - Qi, C.; Fourie, A.; Chen, Q.; Tang, X.; Zhang, Q.; Gao, R. Data-driven modelling of the flocculation process on mineral processing tailings treatment. J. Clean. Prod.
**2018**, 196, 505–516. [Google Scholar] [CrossRef] - Qi, C.; Ly, H.-B.; Chen, Q.; Le, T.-T.; Le, V.M.; Pham, B.T. Flocculation-dewatering prediction of fine mineral tailings using a hybrid machine learning approach. Chemosphere
**2020**, 244, 125450. [Google Scholar] [CrossRef] [PubMed] - Pham, B.T.; Le, L.M.; Le, T.-T.; Bui, K.-T.T.; Le, V.M.; Ly, H.-B.; Prakash, I. Development of advanced artificial intelligence models for daily rainfall prediction. Atmos. Res.
**2020**, 237, 104845. [Google Scholar] [CrossRef] - Dao, D.V.; Ly, H.-B.; Vu, H.-L.T.; Le, T.-T.; Pham, B.T. Investigation and Optimization of the C-ANN Structure in Predicting the Compressive Strength of Foamed Concrete. Materials
**2020**, 13, 1072. [Google Scholar] [CrossRef] [PubMed][Green Version] - Van Dao, D.; Jaafari, A.; Bayat, M.; Mafi-Gholami, D.; Qi, C.; Moayedi, H.; Van Phong, T.; Ly, H.-B.; Le, T.-T.; Trinh, P.T. A spatially explicit deep learning neural network model for the prediction of landslide susceptibility. Catena
**2020**, 188, 104451. [Google Scholar] - Pham, B.T.; Phong, T.V.; Nguyen, H.D.; Qi, C.; Al-Ansari, N.; Amini, A.; Ho, L.S.; Tuyen, T.T.; Yen, H.P.H.; Ly, H.-B. A Comparative Study of Kernel Logistic Regression, Radial Basis Function Classifier, Multinomial Naïve Bayes, and Logistic Model Tree for Flash Flood Susceptibility Mapping. Water
**2020**, 12, 239. [Google Scholar] [CrossRef][Green Version] - Nguyen, V.V.; Pham, B.T.; Vu, B.T.; Prakash, I.; Jha, S.; Shahabi, H.; Shirzadi, A.; Ba, D.N.; Kumar, R.; Chatterjee, J.M. Hybrid machine learning approaches for landslide susceptibility modeling. Forests
**2019**, 10, 157. [Google Scholar] [CrossRef][Green Version] - Nguyen, M.D.; Pham, B.T.; Tuyen, T.T.; Yen, H.; Phan, H.; Prakash, I.; Vu, T.T.; Chapi, K.; Shirzadi, A.; Shahabi, H. Development of an Artificial Intelligence Approach for Prediction of Consolidation Coefficient of Soft Soil: A Sensitivity Analysis. Open Constr. Build. Technol. J.
**2019**, 13, 178–188. [Google Scholar] [CrossRef] - Dao, D.V.; Ly, H.-B.; Trinh, S.H.; Le, T.-T.; Pham, B.T. Artificial intelligence approaches for prediction of compressive strength of geopolymer concrete. Materials
**2019**, 12, 983. [Google Scholar] [CrossRef][Green Version] - Dao, D.V.; Trinh, S.H.; Ly, H.-B.; Pham, B.T. Prediction of compressive strength of geopolymer concrete using entirely steel slag aggregates: Novel hybrid artificial intelligence approaches. Appl. Sci.
**2019**, 9, 1113. [Google Scholar] [CrossRef][Green Version] - Pham, B.T.; Nguyen, M.D.; Van Dao, D.; Prakash, I.; Ly, H.-B.; Le, T.-T.; Ho, L.S.; Nguyen, K.T.; Ngo, T.Q.; Hoang, V. Development of artificial intelligence models for the prediction of Compression Coefficient of soil: An application of Monte Carlo sensitivity analysis. Sci. Total Environ.
**2019**, 679, 172–184. [Google Scholar] [CrossRef] - Nguyen, H.-L.; Pham, B.T.; Son, L.H.; Thang, N.T.; Ly, H.-B.; Le, T.-T.; Ho, L.S.; Le, T.-H.; Tien Bui, D. Adaptive network based fuzzy inference system with meta-heuristic optimizations for international roughness index prediction. Appl. Sci.
**2019**, 9, 4715. [Google Scholar] [CrossRef][Green Version] - Janizadeh, S.; Avand, M.; Jaafari, A.; Phong, T.V.; Bayat, M.; Ahmadisharaf, E.; Prakash, I.; Pham, B.T.; Lee, S. Prediction Success of Machine Learning Methods for Flash Flood Susceptibility Mapping in the Tafresh Watershed, Iran. Sustainability
**2019**, 11, 5426. [Google Scholar] [CrossRef][Green Version] - Kohestani, V.; Hassanlourad, M.; Ardakani, A. Evaluation of liquefaction potential based on CPT data using random forest. Nat. Hazards
**2015**, 79, 1079–1089. [Google Scholar] [CrossRef] - Wan, S. Entropy-based particle swarm optimization with clustering analysis on landslide susceptibility mapping. Environ. Earth Sci.
**2012**, 68. [Google Scholar] [CrossRef] - Qi, C.; Fourie, A.; Chen, Q. Neural network and particle swarm optimization for predicting the unconfined compressive strength of cemented paste backfill. Constr. Build. Mater.
**2018**, 159, 473–478. [Google Scholar] [CrossRef] - Pham, B.T.; Nguyen, M.D.; Bui, K.-T.T.; Prakash, I.; Chapi, K.; Bui, D.T. A novel artificial intelligence approach based on Multi-layer Perceptron Neural Network and Biogeography-based Optimization for predicting coefficient of consolidation of soil. Catena
**2019**, 173, 302–311. [Google Scholar] [CrossRef]

**Figure 4.**Experimental and predicted values of shear strength using the model: (

**a**) training set, (

**b**) testing set.

No | Parameters | Min Values | Max Values | Mean Values | Standard Deviation |
---|---|---|---|---|---|

1 | Clay content (%) | 1.00 | 47.5 | 25.72 | 10.172 |

2 | Water content (%) | 23.04 | 70.74 | 48.3 | 11.73 |

3 | Specific gravity | 2.67 | 2.72 | 2.69 | 0.01 |

4 | Void ratio | 0.63 | 1.92 | 1.36 | 0.31 |

5 | Liquid limit (%) | 26.08 | 79.76 | 53.34 | 13.39 |

6 | Plastic limit (%) | 15.36 | 40.48 | 28.38 | 5.01 |

7 | Undrained total normal shear strength (kG/cm^{2}) | 0.29 | 0.57 | 0.41 | 0.06 |

No | Hyperparameters | Explanation | Range |
---|---|---|---|

1 | Max_depth | The maximum depth of DTs. | 1–20 |

2 | Min_samples_split | The minimum number of samples for the split. | 2–10 |

3 | Min_samples_leaf | The minimum number of samples at the leaf node. | 1–10 |

4 | Max_DT | The maximum number of RT models in the ensemble | 1–1000 |

5 | Max_features | The number of features considered during the selection of the best splitting | 0.4–1 |

No | Models | RMSE | |
---|---|---|---|

Training | Testing | ||

1 | RF | 0.517 | 0.480 |

2 | RF-PSO | 0.487 | 0.453 |

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## Share and Cite

**MDPI and ACS Style**

Pham, B.T.; Qi, C.; Ho, L.S.; Nguyen-Thoi, T.; Al-Ansari, N.; Nguyen, M.D.; Nguyen, H.D.; Ly, H.-B.; Le, H.V.; Prakash, I. A Novel Hybrid Soft Computing Model Using Random Forest and Particle Swarm Optimization for Estimation of Undrained Shear Strength of Soil. *Sustainability* **2020**, *12*, 2218.
https://doi.org/10.3390/su12062218

**AMA Style**

Pham BT, Qi C, Ho LS, Nguyen-Thoi T, Al-Ansari N, Nguyen MD, Nguyen HD, Ly H-B, Le HV, Prakash I. A Novel Hybrid Soft Computing Model Using Random Forest and Particle Swarm Optimization for Estimation of Undrained Shear Strength of Soil. *Sustainability*. 2020; 12(6):2218.
https://doi.org/10.3390/su12062218

**Chicago/Turabian Style**

Pham, Binh Thai, Chongchong Qi, Lanh Si Ho, Trung Nguyen-Thoi, Nadhir Al-Ansari, Manh Duc Nguyen, Huu Duy Nguyen, Hai-Bang Ly, Hiep Van Le, and Indra Prakash. 2020. "A Novel Hybrid Soft Computing Model Using Random Forest and Particle Swarm Optimization for Estimation of Undrained Shear Strength of Soil" *Sustainability* 12, no. 6: 2218.
https://doi.org/10.3390/su12062218