The time-dependent failure of surrounding rock in deep engineering is essentially controlled by the evolution of microcracks, with the pre-existing fracturing state induced by excavation playing a crucial role in the subsequent time-dependent fracturing process. From the perspective of microcrack development, it is a continuous, dynamic process. Therefore, taking the microcrack propagation process as the fundamental principle, this paper proposes a novel three-dimensional (3D) time-dependent model for hard rock that can depict the entire fracturing process within a unified theoretical framework. This developed model discards the traditional tri-modal partition method based on deformation, and instead adopts an analysis approach centred on time-dependent tensile and shear fracturing. The results show that the time-dependent deformation of hard rock is the macroscopic manifestation of the progressive evolution of microcracks over time. Under true triaxial stress, the growth tendency of cracks in hard rock is orientation-dependent throughout the entire loading process. This developed model provides a mechanical explanation for key time-dependent fracture characteristics observed in true triaxial creep tests, including the anisotropy of time-dependent deformation and the preferred orientation of macroscopic failure plane, and provides a novel framework for elucidating the time-dependent failure process of hard rock.

This study investigates the influence of mean stress and Lode angle on the mechanical behavior of porous sandstone. Sandstone specimens were tested using a newly developed true-triaxial loading apparatus under five constant Lode angle conditions and seven different mean stresses, covering a transition from brittle to ductile regimes. Based on the experimental results, three types of stress-strain responses were identified, transitioning progressively from Type 1, through Type 2 to Type 3 as the mean stress increases. Type 1 response represents typical brittle behavior, characterized by prominent shear fractures. Type 2 response corresponds to the brittle-ductile transition behavior, exhibiting non-penetrating shear fractures. Type 3 response is associated with ductile behavior, characterized by no visible shear fractures. The deviatoric stress initially increases and then decreases with increasing mean stress, forming a cap surface in the meridian plane. A generalized failure criterion is subsequently developed, capable of accurately characterizing this strength response. Furthermore, the brittle-ductile transition behavior is found to be significantly dependent on the Lode angle. Finally, the brittle-ductile transition boundary is described, incorporating the dependence of Lode angle.

The ISRM-suggested Brazilian disc (BD) test using split Hopkinson pressure bar (SHPB) for dynamic rock tensile strength requires central crack initiation and stress equilibrium. This study aims to re-evaluate the critical strain rate, ensuring a valid dynamic Brazilian disc test, and to analyse the reliable dynamic tensile behaviour of granite using high-speed digital image correlation (DIC). The comparison between the measured strain obtained through high-speed DIC analysis and the strain gauge allowed for determining the optimal subset parameters used to obtain the real-time deformation field and the stress-strain curve from DIC data. Crack initiation, crack velocity, and failure process are studied to reveal the rate dependence of granites. A unified dynamic increase factor (DIF) model is proposed for the tensile strength of rocks, and the reason for the sudden drop in DIF for high strain rates is discussed. The results reveal that the upper limit of the valid strain rate, which ensures the validity of the ISRM-suggested dynamic BD test, is co-determined by the conditions of stress equilibrium and crack initiation from the centre of the disc. At higher strain rates (75 s^-1), BD test results fail to capture the actual tensile behaviour of rocks, and the potential factors influencing the critical valid strain rate (CVSr), such as sample radius and boundary crack length, should also be considered.

This study presents a novel framework for evaluating slope stability in spatially variable soils by integrating a newly developed sequential limit analysis based on the Hellinger-Reissner functional, utilizing the node-based smoothed finite element method (NS-FEM), with a newly proposed deep learning (DL) approach termed multi-downsampling hybrid Linformer-convolutional neural networks (CNNs). The NS-FEM-based mixed formulation of limit analysis (MFLA) enhances computational accuracy and convergence by smoothing strain fields and mitigating numerical discontinuities commonly encountered in standard finite element methods (FEMs). This method generates reliable datasets for stochastic simulations of slope stability under both static and seismic loading conditions. To address the computational expense of specific simulations, we propose the multi-downsampling hybrid Linformer-CNN model, a sophisticated DL architecture that employs dual parallel pathways with distinct downsampling strategies - AveragePpooling1D for medium-scale feature extraction and MaxPooling1D for coarse-scale feature extraction. Each pathway integrates one-dimensional (1D) CNNs for local feature extraction and Linformer-based self-attention mechanisms to efficiently capture global dependencies. The parallel downsampling strategies balance computational efficiency with feature granularity, enabling the model to leverage both local and global data characteristics effectively. The extracted multi-scale features are concatenated and further processed through fully connected networks (FCNs) to accurately predict the factor of safety (FoS) of slopes. Comparative analyses demonstrate that the hybrid Linformer-CNN model outperforms traditional FCN and CNN architectures, achieving robust and precise predictions with a mean absolute percentage error (MAPE) below 10 %. Additionally, the proposed framework significantly reduces computational time, highlighting the potential of integrating NS-FEM-based MFLA with advanced DL architectures for rapid and reliable slope stability assessment in geotechnical engineering.

Sub-level caving (SLC) is a mass mining method suitable for large, steeply dipping orebodies. The particle size distribution (PSD) of blasted material affects material flow through the stope. Improving blast-induced fragmentation can enhance draw point extraction, increasing ore recovery, reducing dilution, and lowering costs in loading and crushing. Numerical simulations using the Mechanistic Blasting Model (MBM) explored these improvements. MBM simulates the explosive loading, rock fracturing, and dynamic explosive gas effects. It addresses uneven explosive distribution from fan-shaped blast holes and complex broken ground conditions. The simulations used Ernest Henry Mine (EHM) data to define the baseline blast design and rock mass and compared field and modelled fragmentation sizes for varying explosive densities and burden sizes. Then, MBM simulations incorporated different rock mass fracture densities, tensile strengths and in-situ stresses, and further blast design changes in the blasthole diameter and charge spacings. A total of 34 scenarios were modelled. Multivariate regression analysis identified key parameters, and new regression models for P20, P50, and P80 passing sizes were developed and validated against the EHM and MBM simulation data. Additional simulations confirmed that while regression predictive models were slightly less accurate, they provided efficient predictions with acceptable accuracy.

Cemented paste backfill (CPB) is a key material in underground mining, providing essential ground support while aiding in tailings management. However, current research has overlooked the combined effects of horizontal rockwall closure stress and vertical self-loading stress, referred to as multiaxial stress, on the CPB's consolidation behavior and its mechanical properties development. Understanding and assessing these effects is critical because they directly affect the stability and performance of CPB structures. In this study, a novel multiaxial compressive stress curing and monitoring apparatus was used to simulate two horizontal rockwall closure scenarios with a consistent backfilling rate, under both drained and undrained conditions. Key parameters assessed included unconfined compressive strength (UCS), deformation during curing, stress-strain behavior, and modulus of elasticity. The results highlight that rockwall closure, combined with vertical stress, plays a pivotal role in the consolidation behavior of CPB, significantly affecting key mechanical properties. Higher horizontal stress from faster rockwall closure intensified compression during curing, leading to reduced porosity, enhanced particle rearrangement, and accelerated consolidation. This intensified consolidation leads to notable improvements in mechanical properties, including increased UCS, enhanced stiffness, and a higher modulus of elasticity, indicating improved load-bearing capacity. Moreover, the interaction between multiaxial stress and drainage conditions influenced stress-strain behavior and deformation, with drained conditions promoting earlier plasticity and higher peak stresses. These findings underscore the critical influence of multiaxial stress, combined with drainage conditions, on CPB performance, offering valuable insights for optimizing CPB design in underground mining applications.

The instability of composite coal-rock structures can easily trigger severe dynamic disasters, such as rockbursts. The application of electric potential (EP) method shows promise for disaster prediction and accurate identification of coal-rock interfaces. In this study, uniaxial compression experiments were conducted to monitor the EP spatiotemporal response of fine sandstone-coal and coarse sandstone-coal combined samples. EP distribution contour maps and three-dimensional (3D) EP models were utilized to explore the failure mechanisms and identify the interface state. Then the relationship between EP response and force field was examined through numerical simulations. An EP-based multifractal method was utilized to predict rock failure. Results show that the intensity and polarity of EPs differ between coal and rock but are correlated with stress state. The progressive failure features of two types of combined samples differ, triggering distinct EP responses. In the EP contour maps, the EP level increases with increasing height, and a low-intensity signal band appears around the interface before failure. When failure occurs, the EP field changes, and the low-intensity signal band becomes distorted. The 3D EP models effectively visualize the progressive failure of combined samples and clearly identify the interface location, similar to acoustic emission (AE) location. The evolution of force chain field is closely related to EP generation, and sparse strong force chain fields leads to a significant increase in EP level. Furthermore, the EPs display multifractal features, with precursory information being reflected inΔα and Δf. This study provides new ideas for early-warning of composite coal-rock and coal-rock interface identification.

The phase-field method (PFM) has emerged as a robust tool for fracture simulation; however, applying this technique to rock materials poses significant challenges, particularly in accurately modeling the propagation of multiple cracks in the presence of complex three-dimensional (3D) mixed-mode loading involving tensile, tensile-shear, and compressive-shear cracks. To address these limitations, this study aims to introduce an enhanced PFM that integrates frictional effects and Lode angle dependence while unifying the volumetric deviatoric (VD) and spectral decomposition (SD) methods. The proposed model incorporates a modified driving force for 3D compressive-shear cracks by embedding a triple shear energy strength (TSES) criterion within the energy decomposition framework. This refinement guarantees that crack behavior remains physically realistic under compression-dominated loading while effectively preserving well-established tensile fracture mechanisms. The validation of the numerical implementation is also conducted through both analytical verification against theoretical solutions and 3D finite element simulations of fissured rock and heterogeneous specimens. Furthermore, numerical case studies demonstrate the model's ability to effectively capture the 3D propagation of multiple cracks and replicate realistic true 3D mechanical responses. The findings present valuable insights and practical guidelines for the application of PFM in rock engineering.