Accurate wellbore trajectory prediction is of great significance for enhancing the efficiency and safety of directional drilling in coal mines. However, traditional mechanical analysis methods have high computational complexity, and the existing data-driven models cannot fully integrate non-sequential features such as stratum lithology. To solve these problems, this study proposes a parallel input gated recurrent unit (Pi-GRU) model based on the TensorFlow framework. The GRU network captures the temporal dependencies of sequence data (such as dip angle and azimuth angle), while the BP neural network extracts deep correlations from non-sequence features (such as stratum lithology), thereby achieving multi-source data fusion modeling. Orthogonal experimental design was adopted to optimize the model hyperparameters, and the ablation experiment confirmed the necessity of the parallel architecture. The experimental results obtained based on the data of a certain coal mine in Shanxi Province show that the mean square errors (MSE) of the azimuth and dip angle angles of the Pi-GRU model are 0.06° and 0.01°, respectively. Compared with the emerging CNN-BiLSTM model, they are reduced by 66.67% and 76.92%, respectively. To evaluate the generalization performance of the model, we conducted cross-scenario validation on the dataset of the Dehong Coal Mine. The results showed that even under unknown geological conditions, the Pi-GRU model could still maintain high-precision predictions. The Pi-GRU model not only outperforms existing methods in terms of prediction accuracy, with an inference delay of only 0.21 milliseconds, but also requires much less computing power for training and inference than the maximum computing power of the Jetson TX2 hardware. This proves that the model has good practicability and deployability in the engineering field. It provides a new idea for real-time wellbore trajectory correction in intelligent drilling systems and shows strong application potential in engineering applications.

Understanding rock behavior under cutting tools is critical for enhancing cutting processes and forecasting rock behavior in engineering contexts. This study examines the link between mechanical properties and indentation crater morphology of six rocks using a conical indenter until initial fracture. Through indentation testing, mechanical properties (indentation stiffness index k and hardness index HI) were assessed, and crater morphology was analyzed using a 3D laser profilometer. The rocks were categorized into three groups based on specific energy: Class I (slate, shale), Class II (sandstone, marble), and Class III (granite, gneiss). The morphological features of their indentation craters were analyzed both quantitatively and qualitatively. The linear model was used to establish the relationship between crater morphology indices and mechanical properties, with model parameters determined by linear regression. Key findings include: (1) Fracture depth, cross-sectional area, and contour roundness are independent morphological indicators, serving as characteristic parameters for crater morphology, with qualitative and quantitative analyses showing consistency; (2) Post-classification linear fitting revealed statistically significant morphological prediction models, though patterns varied across rock categories due to inherent properties like structure and grain homogeneity; (3) Classification by specific energy revealed distinct mechanical and morphological differences, with significant linear relationships established for all three indicators in Classes II and III, but only roundness showing significance in Class I (non-significant for cross-sectional area and depth). However, all significant models exhibited limited explanatory power (R² = 0.220–0.635), likely due to constrained sample sizes. Future studies should expand sample sizes to refine these findings.