Machine learning (ML) models are increasingly applied in rock mechanics. However, purely data-driven approaches trained on limited experimental data can often exhibit physically unrealistic results, such as violating established physical laws, which undermines their reliability. To address this, we introduce a Physics-Informed Machine Learning (PIML) approach utilizing XGBoost to predict the stress wave transmission coefficient (T) across realistic rock joints. Our model was developed using a dataset from 279 Split Hopkinson Pressure Bar (SHPB) tests conducted on granite samples replicating 80 unique natural joint morphologies. We integrated known physical constraints directly into the modeling process: (1) boundedness of T within [0, 1] enforced through logit and sigmoid transformations, and (2) hard monotonicity constraints ensuring T consistently increases with joint matching coefficient (JMC) and decreases with aperture (e). To ensure the model generalizes to unseen joint morphologies, we employed a rigorous Nested Leave-One-Group-Out (LOGO) cross validation strategy. The con-strained XGBoost model achieved R2 of 0.761 and demonstrated a statistically significant 20.55% reduction in Mean Absolute Error (MAE) compared to a Ridge Regression baseline. Post-hoc analyses using Partial Dependence and Individual Conditional Expectation plots confirmed that the model’s predictions are not only accurate but also physically realistic and interpretable. This PIML approach successfully guarantees physically consistent predictions and reaffirms the dominant influence of contact area parameters on stress wave transmission.
1 August 2021 in International Journal of Rock Mechanics and Mining Sciences
The shear strength of the rock discontinuities under different shear rates is of great importance to evaluate the stability of rock mass engineering, which is remarkably influenced by the size effects induced by both the length and the undulated amplitude of discontinuities. An advanced shear strength criterion taking into account the size and the shear rate simultaneously was proposed. There is an advantage of the dimension unity in terms of the new shear strength criterion in comparison to previous related empirical equations. Additionally, it can be degraded into the International Society for Rock Mechanics (ISRM)-suggested Barton shear strength empirical equation on the peak shear strength of the rock discontinuities. Then, based on a new dynamic direct shear testing device on rock joints, the granite discontinuities with various lengths (200 mm to 1000 mm) and undulated amplitudes (3 mm to 23 mm) were designed to conduct direct shear tests under different low shear rates (0 mm/s to 1 mm/s) to verify the involved empirical equations. It was found that the results predicted by the new shear strength criterion agreed well with the experimental results. It was proved that the new shear strength criterion had a better applicability to characterize the shear strength of the rock discontinuities.
Conventionally, the evaluation of shear failure of discontinuities in rocks and other geomaterials has been conducted under static shear loading. In such methods, the shear failure behaviors of rock discontinuities are significantly influenced by loading velocities. To evaluate the shear failure process under dynamic loading, in this paper, we propose a new experimental methodology by taking advantages of recently available high-speed optical and mechanical measurement techniques. The methodology utilizes the Hopkinson bar to apply impact loading, and the diagnostics include a dynamic stress wave acquisition system, a digital image correlation (DIC) system, and an acoustic emission (AE) monitoring system. To improve the accuracy of the DIC analysis, an advanced digital speckle pattern and an updated water transfer printing are used to obtain the optimized and consistent speckle pattern. A flexible piezoelectric film sensor is first introduced to acquire AE signals in order to locate AE events accurately. A dynamic impact shear experiment indicates that the normal stress has a significant effect on the peak shear stress of rock discontinuities and the peak shear stress itself is rate dependent. The displacement field along shear directions is quantified using the DIC method, and the initial AE source locations during the impact shear process are determined using the AE monitoring system. We thus conclude that the dynamic impact shear system can systematically characterize the dynamic impact shear process with quantitative details and can further be implemented to study other dynamic impact failure behaviors of rock discontinuities under in situ stresses.