A Framework for In Situ Rock UCS Assessment and Full‐Hole Strength Inversion Integrating MWD Signals and Symbolic Regression Strategies
Source abstract
Abstract
ABSTRACT Accurate in situ estimation of uniaxial compressive strength (UCS) is essential for safe geotechnical and mining operations, yet traditional coring followed by laboratory testing rarely supports rapid strength profiling. This study develops a UCS assessment framework based on measurement while drilling (MWD) signals to provide a lightweight prediction tool. Field drilling totaling 297 m provides continuous records of penetration rate, thrust, pump pressure, torque, bit rotation speed, and depth. Subsequently, symbolic regression (SR) is employed to extract functional relationships between MWD parameters and UCS. Among the compared SR models, the sparse identification of nonlinear dynamics algorithm via sequentially thresholded‐least squares (STLSQ–SINDy) achieves the most favorable balance between simplicity and predictive accuracy, with a test coefficient of determination ( R 2 ) of 0.9413 and a root mean square error (RMSE) of 5.53 MPa. Nonparametric tests and residual diagnostics further confirm its consistently superior performance under the current data conditions. To reduce the potential optimism associated with random partitioning in a small dataset, leave‐one‐hole‐out cross‐hole validation is conducted. Under this more conservative setting, STLSQ–SINDy achieves a mean test R 2 of 0.8709 ± 0.0471, indicating comparatively stable cross‐hole transferability within the five boreholes. The optimal analytical expression is then coupled with filtered MWD waveforms to reconstruct rock UCS profiles for five boreholes, which capture the stratified strength hierarchy and locate critical depth windows. Overall, this work presents a systematic application of sparse SR to field MWD data and demonstrates the potential of the MWD–SR framework for low‐cost rock strength prediction.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Rock Mechanics and Modeling · Drilling and Well Engineering · Mineral Processing and Grinding
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
School of Resources and Safety Engineering Central South University Changsha China
Funding
National Natural Science Foundation of China · Natural Science Foundation of Hunan Province · Scientific Research Foundation of Hunan Provincial Education Department
References (100+)
Show source-provided references
1. Engineering Classification of Jointed Rock Masses
2. A Geomechanics Classification System for the Rating of Rock Mass in Mine Design
3. Eberhardt E. · 2014 · 233
4. Prediction of Geomechanical Parameters Using Soft Computing and Multiple Regression Approach10.1016/j.measurement.2016.12.023 ↗
5. Unconfined Compressive Strength (UCS) Prediction in Real Time While Drilling Using Artificial Intelligence Tools10.1007/s00521-020-05546-7 ↗
6. Estimating the Uniaxial Compressive Strength of Argillites Using Brazilian Tensile Strength, Ultrasonic Wave Velocities, and Elastic Properties10.1007/s00603-020-02358-y ↗
7. Weathered Rock Characterization Using Drilling Parameters10.1139/t03-007 ↗
8. Automated Coal Seam Detection Using a Modulated Specific Energy Measure in a Monitor‐While‐Drilling Context10.1016/j.ijrmms.2014.10.012 ↗
9. An Overview on Measurement‐While‐Drilling Technique and Its Scope in Excavation Industry
10. Evaluation of Empirical Methods for Measuring the Uniaxial Compressive Strength of Rock10.1016/0148-9062(90)91001-N ↗
11. A Comparative Evaluation of Indirect Methods to Estimate the Compressive Strength of Rocks10.1007/s00603-005-0061-8 ↗
12. Correlation Between Point Load Index and Uniaxial Compressive Strength for Different Rock Types10.1007/s00603-011-0192-z ↗
13. Case Study: Using the Point Load Test to Estimate Rock Strength of Tunnels Constructed by a Tunnel Boring Machine10.1007/s10064-017-1198-x ↗
14. Acquisition of Rock Mass Mechanical Parameters and Analysis of Surrounding Rock Deformation Characteristics in Jointed Rock Mass Tunnels10.1002/nag.70210 ↗
15. Automatic Monitoring of Rotary‐Percussive Drilling for Ground Characterization—Illustrated by a Case Example in Hong Kong10.1016/j.ijrmms.2003.12.151 ↗
16. RQD Predictions Based on Drill Performance Parameters10.1016/0886-7798(96)00024-7 ↗
17. Prediction of Uniaxial Compressive Strength, Tensile Strength and Porosity of Sedimentary Rocks Using Sound Level Produced During Rotary Drilling10.1007/s00603-011-0160-7 ↗
18. Implementing Acoustic Frequency Analysis for Development the Novel Model of Determining Geomechanical Features of Igneous Rocks Using Rotary Drilling Device10.1007/s10706-017-0433-3 ↗
19. Application of Measurement While Drilling Technology to Predict Rock Mass Quality and Rock Support for Tunnelling10.1007/s00603-019-01979-2 ↗
20. Predicting Rock Type From MWD Tunnel Data Using a Reproducible ML‐Modelling Process10.1016/j.tust.2024.105843 ↗
21. Application of Relationship Model for the Measurement While Drilling Data to Predict Rock Uniaxial Compressive Strength for Tunneling10.1007/s00603-024-03907-5 ↗
22. Influence of Rock Properties on Thrust and Torque during Rock Coring Operations: A Case Study10.1080/10916466.2023.2294158 ↗
23. Rock Fracture Identification With Measurement While Drilling Data in Down‐the‐Hole Drills10.1007/s10064-024-03561-9 ↗
24. A Rock Strength Prediction Model Utilizing Real‐Time Data from Percussion–Rotary Drilling Measurements
25. Enhancing Geotechnical Investigations Using Drilling Parameters10.1061/(ASCE)GT.1943-5606.0001836 ↗
26. Rock Strength Identification While Drilling Based on Percussive Rotary Drilling10.26599/RSM.2024.9435351 ↗
27. Numerical Modelling of Bit–Rock Fracture Mechanisms in Percussive Drilling With a Continuum Approach10.1002/nag.974 ↗
28. Discrete Element Modelling of Rock Cutting: From Ductile to Brittle Transition10.1002/nag.2362 ↗
29. Proposed Practical Methods to Estimate Rock Strength and Tooth Wear While Drilling With Roller‐Cone Bits10.1115/1.1794696 ↗
30. Upper Bound Analytic Mechanics Model for Rock Cutting and Its Application in Field Testing10.1016/j.tust.2017.12.023 ↗
31. The Anisotropy of Rock Drilling in Marble Quarry Mining Based on the Relationship between Vertical and Horizontal Drilling Rates10.1061/IJGNAI.GMENG-9658 ↗
32. A Bit–Rock Interaction Model for Rotary–Percussive Drilling10.1016/j.ijrmms.2011.05.007 ↗
33. A New Method for Determining Strength Parameters of Rock Using Digital Drilling Technology10.3389/feart.2023.1256150 ↗
34. Penetration‐Rate Performance of Roller‐Cone Bits10.2118/13259-PA ↗
35. An Estimation of Rock Strength Using a Drilling Performance Model: A Case Study in Blacktip Field10.1007/s00603-011-0142-9 ↗
36. Relationship Between Rock Uniaxial Compressive Strength and Digital Core Drilling Parameters and Its Forecast Method10.1007/s40789-020-00383-4 ↗
37. A Case Study of Drilling Process Monitoring for Geomaterial Strength Assessment Along Hydraulic Rotary Drillhole10.1007/s10064-023-03323-z ↗
38. Numerical Modelling of Frictional Sliding Induced Damage and Heating Effects on Rock With an Application to Sievers' J‐Miniature Drilling on Granite10.1002/nag.4005 ↗
39. Estimating Rock Strength Parameters Using Drilling Data10.1016/j.ijrmms.2018.02.013 ↗
40. Study on a Digital Drilling Test‐Based Rock Uniaxial Compressive Strength Measurement Method10.1007/s12517-020-5184-4 ↗
41. Uniaxial Compressive Strength Prediction Based on Measurement While Drilling Data: A Laboratory Study10.1016/j.jappgeo.2024.105499 ↗
42. Application of Specific Energy for Lithology Identification10.1016/j.petrol.2019.106402 ↗
43. Measurement, Prediction, and Modeling of the Drilling Specific Energy by Soft Rock Properties During the Drilling Operation10.1016/j.measurement.2023.113679 ↗
44. The Concept of Specific Energy in Rock Drilling10.1016/0148-9062(65)90022-7 ↗
45. Measurement While Drilling Method for Estimating the Uniaxial Compressive Strength of Rocks Considering Frictional Dissipation Energy10.1061/IJGNAI.GMENG-9877 ↗
46. Continuous Depth Profile of the Rock Strength in the Nankai Accretionary Prism Based on Drilling Performance Parameters10.1038/s41598-018-20870-8 ↗
47. Predicting Rock Unconfined Compressive Strength Based on Tunnel Face Boreholes Measurement‐While‐Drilling Data10.1007/s12205-024-2742-4 ↗
48. Robust Machine Learning Predictive Models for Real‐Time Determination of Confined Compressive Strength of Rock Using Mudlogging Data10.1007/s00603-024-03859-w ↗
49. Knowledge‐Based Machine Learning for Real‐Time Rock Strength Testing While Drilling: Bridging Simulation and Reality
50. Integration of Physics‐Based and Data‐Driven Approaches for Landslide Susceptibility Assessment10.1002/nag.4016 ↗
51. Data‐Driven Tools to Evaluate Support Pressure, Radial Displacements, and Face Extrusion for Tunnels Excavated in Elastoplastic Grounds10.1002/nag.3889 ↗
52. Comparison of Machine Learning Models for Rock UCS Prediction Using Measurement While Drilling Data10.1038/s41598-025-93111-4 ↗
53. Real‐Time Estimating Method on Rock Strength via MWD of Roofbolter and Its Application to In‐Situ Grouting Quality Evaluation10.1007/s40948-023-00630-3 ↗
54. Unsupervised Machine Learning for Data‐Driven Rock Mass Classification: Addressing Limitations in Existing Systems Using Drilling Data10.1007/s00603-024-04280-z ↗
55. Estimation of Intact Rock Uniaxial Compressive Strength Using Advanced Machine Learning10.1007/s40515-023-00357-4 ↗
56. Machine Learning Methods for Predicting the Uniaxial Compressive Strength of the Rocks: A Comparative Study10.1007/s11707-024-1101-6 ↗
57. Drilling‐Based Rock Strength Estimation: A Validated Model for Mohr–Coulomb and a New Theoretical‐Empirical Approach for Hoek–Brown Parameters10.1016/j.rineng.2025.107388 ↗
58. Predicting Rock Mass Strength From Drilling Data Using Synergistic Unsupervised and Supervised Machine Learning Approaches10.1007/s12145-025-01837-6 ↗
59. 10.1007/s40098‐025‐01337‐w10.1007/s40098‐025‐01337‐w ↗
60. Research on Rock Mechanics Parameter Prediction Based on the Frequency Spectrum Characteristics of Vibration While Drilling
61. 10.1007/s00603‐025‐05130‐210.1007/s00603‐025‐05130‐2 ↗
62. Deep Convolutional Neural Network for Fast Determination of the Rock Strength Parameters Using Drilling Data10.1016/j.ijrmms.2019.104084 ↗
63. Deep Learning for Intelligent Prediction of Rock Strength by Adopting Measurement While Drilling Data10.1061/IJGNAI.GMENG-8080 ↗
64. A Machine Learning Classification Approach to Geotechnical Characterization Using Measure‐While‐Drilling Data10.3390/geosciences15030093 ↗
65. Classification of Rock Hardness at Tunnel Faces Based on a Drilling Parameter Cloud Map and Convolutional Neural Network10.1061/JCCEE5.CPENG-6173 ↗
66. Reliable Rock Mass Classification for Tunneling: Hole‐Level MWD Data Modeling With Cost‐Sensitive Bagging
67. Development and Application of a Monitoring‐While‐Drilling System with an Optimized Machine Learning Algorithm for Lithology Identification and Rock Strength Prediction
68. Experimental Investigation on Potential Use of Drilling Parameters to Quantify Rock Strength
69. Real‐Time Rock Strength Determination Based on Rock Drillability Index and Drilling Specific Energy: An Experimental Study10.1007/s10064-021-02154-0 ↗
70. Measurement and Perception of the Rock Strength by Energy Parameters During the Drilling Operation10.1016/j.measurement.2024.114268 ↗
71. Distilling Free‐Form Natural Laws from Experimental Data10.1126/science.1165893 ↗
72. Artificial Intelligence in Physical Sciences: Symbolic Regression Trends and Perspectives10.1007/s11831-023-09922-z ↗
73. G.Romano “Model Discovery Integrating Symbolic Regression into Sparse Identification of Nonlinear Dynamics” (2024).
74. Symbolic Regression for the Determination of Joint Roughness Coefficient10.3390/mca30010017 ↗
75. Symbolic Regression Based Prediction of Anisotropic Closure in Deep Tunnels10.1016/j.compgeo.2024.106355 ↗
76. Uncertainty Quantification Based on Symbolic Regression and Probabilistic Programming and Its Application10.1016/j.mlwa.2025.100632 ↗
77. A True Triaxial Strength Criterion for Rocks by Gene Expression Programming10.1016/j.jrmge.2023.03.004 ↗
78. Modeling of Tunneling Total Loads Based on Symbolic Regression Algorithm10.3390/app11125671 ↗
79. Predicting Tunnel Water Inflow Using a Machine Learning‐Based Solution to Improve Tunnel Construction Safety10.1016/j.trgeo.2023.100978 ↗
80. From Measurement While Drilling Data to Rock Strength: a Robust LMWOA-XGBoost Model for Predicting Uniaxial Compressive Strength With SHAP Interpretability10.1016/j.eswa.2026.132535 ↗
81. Collinearity: A Review of Methods to Deal With It and a Simulation Study Evaluating Their Performance10.1111/j.1600-0587.2012.07348.x ↗
82. Variance Inflation Factor: As a Condition for the Inclusion of Suppressor Variable(s) in Regression Analysis10.4236/ojs.2015.57075 ↗
83. A Caution Regarding Rules of Thumb for Variance Inflation Factors10.1007/s11135-006-9018-6 ↗
84. Discovering Governing Equations From Data by Sparse Identification of Nonlinear Dynamical Systems10.1073/pnas.1517384113 ↗
85. Improving Physics‐Based Deterministic Tropical Cyclone Track and Intensity Model via Data‐Driven Sparse Identification of Nonlinear Dynamics10.1016/j.jweia.2024.105758 ↗
86. Constrained Sparse Galerkin Regression10.1017/jfm.2017.823 ↗
87. Sparse Identification of Nonlinear Dynamics with Control (SINDYc)
88. Ridge Regression: Biased Estimation for Nonorthogonal Problems10.1080/00401706.1970.10488634 ↗
89. Y. C.Pati R.Rezaiifar andP. S.Krishnaprasad “Orthogonal Matching Pursuit: Recursive Function Approximation With Applications to Wavelet Decomposition ” inProceedings of the 27th Asilomar Conference on Signals Systems and Computers(1993) 40–44.10.1109/ACSSC.1993.342465 ↗
90. Iterative Hard Thresholding for Compressed Sensing10.1016/j.acha.2009.04.002 ↗
91. The Horseshoe Estimator for Sparse Signals10.1093/biomet/asq017 ↗
92. The Bayesian Lasso10.1198/016214508000000337 ↗
93. McConaghy T. · 2011
94. Regressions by Leaps and Bounds10.1080/00401706.2000.10485982 ↗
95. An Enhanced Stability Evaluation System for Entry‐Type Excavations: Utilizing a Hybrid Bagging‐SVM Model, GP and Kriging Techniques10.1016/j.jrmge.2024.05.024 ↗
96. Shalev‐Shwartz S. · 201410.1017/CBO9781107298019 ↗
97. A Unifying View on Dataset Shift in Classification10.1016/j.patcog.2011.06.019 ↗
98. A Note on a General Definition of the Coefficient of Determination10.1093/biomet/78.3.691 ↗
99. Root Mean Square Error (RMSE) or Mean Absolute Error (MAE)?—Arguments Against Avoiding RMSE in the Literature10.5194/gmd-7-1247-2014 ↗
100. Summarizing Multiple Aspects of Model Performance in a Single Diagram10.1029/2000JD900719 ↗