Abstract
To accurately estimate the rock shear strength parameters of cohesion (C) and friction angle (φ), triaxial tests must be carried out at different stress levels so that a failure envelope can be obtained to be linearized. However, this involves a higher budget and time requirements that are often unavailable at the early stage of a project. To address this problem, faster and more inexpensive indirect techniques such as artificial intelligence algorithms are under development. This paper first aims to utilize four machine learning techniques of Gaussian process regression (GPR), support vector regression (SVR), decision trees (DT), and long-short term memory (LSTM) to develop a predictive model to estimate parameters C and φ. To this aim, 244 datasets are available in the RockData software for intact Sandstone, including three input parameters of uniaxial compressive strength (UCS), uniaxial tensile strength (UTS), and confining stress (σ3) are employed in the models. The dropout technique is used to overcome the overfitting problem in LSTM-based models. A comprehensive evaluation is adopted for the performance indices of the prediction models. In this step, the most accurate results are produced by the LSTM model (C: R2 = 0.9842; RMSE = 1.295; MAPE = 0.009/φ: R2 = 0.8543; RMSE = 1.857; MAPE = 1.4301). In the second step, we improve the performance of the proposed LSTM model by fine-tuning the LSTM hyper-parameters, using six metaheuristic algorithms of grey wolf optimization (GWO), particle swarm optimization (PSO), social spider optimization (SSO), sine cosine algorithm (SCA), multiverse optimization (MVO), and moth flame optimization (MFO). The developed models' prediction performance for predicting parameter C from high to low was PSO-LSTM, GWO-LSTM, MVO-LSTM, MFO-LSTM, SCA-LSTM SSO-LSTM, and LSTM with ranking scores of 34, 29, 24, 21, 14, 12, and 5, respectively. Also, the models' prediction performance for predicting parameter φ from high to low was PSO-LSTM, GWO-LSTM, MVO-LSTM, MFO-LSTM, SCA-LSTM SSO-LSTM, and LSTM with ranking scores of 34, 31, 23, 18, 15, 14, and 5, respectively. However, the most robust results are produced by the PSO-LSTM model. Finally, the results indicate that applying a metaheuristic algorithm to tune the hyper-parameters of the LSTM model can significantly improve the prediction results. In the last step, the mutual information test method is applied to sensitivity analysis of the input parameters to predict parameters C and φ. Finally, it is revealed that parameters σ3 and UCS have the highest and lowest impact on the parameters C and φ, respectively.
Highlights
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Employing a large dataset consists of 244 data.
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Using six ML algorithms that most of them had not been tested before for this issue.
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Applying 5-fold CV to validate the results.
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Application of feature selection to find the most effective parameters on the water inflow into tunnels.
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Recognition of the best prediction method.
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Abbreviations
- \({\sigma }_{1}\) :
-
Maximum principal stresse
- \({\sigma }_{3}\) :
-
Minimum principal stresse
- \(k\) :
-
An intermediate auxiliary parameter
- \({\sigma }_{{\mathrm{c}}_{i}\_\mathrm{fitted}}\) :
-
Fitted UCS value from regression analysis
- \(N\) :
-
Number of tests
- \({y}_{i}\) :
-
Actual value
- \({y}_{i}^{^{\prime}}\) :
-
Predicted value
- \({\overline{y} }_{i}\) :
-
Mean of actual value
- \({\overline{y} }_{i}^{^{\prime}}\) :
-
Mean of predicted value
- \(\mu \left({x}_{i}\right)\) :
-
Mean
- \(k({x}_{i},{x}_{i})\) :
-
Kernel
- \(S\) :
-
A group of samples that is not separated yet
- \({S}_{\mathrm{t}}\) :
-
A group of separated samples with true result
- \({S}_{\mathrm{f}}\) :
-
A group of separated samples with a false result
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Mahmoodzadeh, A., Mohammadi, M., Ghafoor Salim, S. et al. Machine Learning Techniques to Predict Rock Strength Parameters. Rock Mech Rock Eng 55, 1721–1741 (2022). https://doi.org/10.1007/s00603-021-02747-x
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DOI: https://doi.org/10.1007/s00603-021-02747-x