Rock Mechanics Letters

Tensile strength is one of the most important characteristics of rock masses that could govern the stability of rock structures. Due to difficulties in its direct measurements, indirect methods such as the Brazilian test have been developed to assess the tensile strength of laboratory-scale rock material. This study considers the effect of loading contact angle on the indirect tensile strength of rock-like disks by adopting experimental and discrete element methods. Several experimental specimens made of synthetic materials were examined under diametrical loading, and consequently, a numerical model using PFC3D was calibrated accordingly. Then, the impacts of the loading contact angle (θ) on the tensile strength, failure pattern, and contact force chain were investigated in detail. The results indicated that as θ increases from 0°, suggested by ASTM, to 90°, the tensile state is dominated at the specimen center, whereas for angles greater than 90°, the dominant stress state changed to compression. Also, while σxx (tensile stress) at the center of the disk did not change for θ below 40°, the σyy (compressive stress) and σzz (out-of-plan normal stress) increased after θ =30°. The analysis of developed cracks suggested that when θ is lower than 30°, the percentage of tensile and shear cracks were constant (80% and 20%, respectively). As the loading contact angle increased, tensile cracks decreased, whereas the other increased. By analyzing the failed specimens, three categories of crack patterns and two categories of contact force chains were identified.

In part II of this study, a second method for the prediction of the crack initiation stress was sug-gested. The new technique is based on an elementary mathematical calculus theory. Particularly, the one that supports that the points where the second derivative of a function is equal to zero can be considered as possible inflection points of the function. The proposed Second Derivative meth-od fulfilled all the necessary criteria, that were mentioned in part I, so that it can further advance the research field. The method was applied to ten rock specimens, specifically eight marbles and two vesicular basalts, that were subjected to uniaxial compressive tests. The predicted crack initi-ation stresses from the new method were compared with those obtained from the established techniques of the existing literature. The new method had very close results with all other utilized methods for the marbles, thus meaning that the proposed Second Derivative technique can accu-rately and consistently determine the onset of stable crack growth for that rock type. On the con-trary, the new method displayed a poor correlation with the other techniques for the two basalts, hence indicating that further tests need to be conducted in the future for that rock type.

The Vajont Landslide, one of the most catastrophic events in history, has been extensively studied for over 60 years. Navigating the extensive Vajont literature presents challenges due to the volume of information, persistent questions, ongoing controversies, and even unreliable information. This review offers a novel synthesis by identifying the most influential hypotheses through the lens of updated geomorphological reconstructions, evolving interpretations of the sliding surface, and conflicting assumptions. It highlights how certain long-held assumptions may have led to biased conclusions, presents a concise dataset of key geotechnical parameters, and stresses the need for future analyses that integrate rainfall and reservoir effects over time, account for possible progressive strength degradation, and revisit slope stability under more realistic boundary conditions. By clarifying closed questions and spotlighting persistent uncertainties, this paper aims to guide future research and reframe understanding of the Vajont landslide.

In part I of this study, the great practical importance of the onset of stable crack growth was out-lined, since several researchers have supported that it can serve as a more realistic estimation of the in-situ spalling strength of the rock mass, in comparison with the more frequently used uniaxi-al compressive strength. Moreover, a short review was also provided regarding the empirical techniques that have been proposed in the last six decades for the prediction of the crack initiation stress. The main criticism of each method was also mentioned. Subsequently, a new method was proposed, based on the Trapezoid Rule, an elementary calculus approximation technique. The lat-ter technique possesses a strong and robust physical explanation, easy application, and complete objectiveness. The Trapezoid Rule method was applied to ten rock specimens, eight marbles and two vesicular basalts, that were subjected to uniaxial compressive tests. The results of the newly suggested method were compared to those obtained using the established methods of the existing literature. Ultimately, it displayed exceptionally close results with all other methods for the ten specimens, thus indicating that it can accurately and consistently predict the crack initiation stress for the two rock types.

In this paper, the geometry of borehole forced by two-dimensional stress was studied based on classical rock mechanics. The relation between horizontal principal stress and geometrical parameters of deformed circular borehole was established. The new prediction model of horizontal stress was deduced based on the above quantitative relation. Additionally, the stress computation was realized based on elliptical parameters of borehole. Subsequently, the feasibility and scientificity of the calculation method of horizontal principal stress were further confirmed via an experiment of borehole deformation based on borehole deformation. The feasibility and applicability of the method were verified based on actual drilling data in Xinjiang Province. The results demonstrated that the geometric shape of circular borehole after deformation was elliptical under the action of planar two-dimensional stress, and the horizontal principal stress could be expressed by the elliptic geometric parameters after deformation. The shape structure of the circular borehole under the action of non-uniform horizontal principal stress was elliptical, and the horizontal principal stress calculated using the parameters of the elliptical shape structure was directly proportional to the loading load. Larger the borehole diameter, smaller was the error of the method. The results provide new insights for in-situ measurement and inversion of deep horizontal in-situ stress.

Abstract The integration of artificial intelligence (AI) into blasting operations has demonstrated significant improvements in precision, safety, and operational efficiency. By leveraging AI algorithms to optimize blast design, monitor field conditions, and analyze fragmentation data, more informed decision-making is achieved. In small-scale mining, safe and efficient blasting practices are critical to protecting workers, maximizing resource extraction, and minimizing environmental impacts. This study first reviews the applications, advantages, and limitations of various AI techniques used in predicting blast performance and environmental effects, with specific attention to the overlooked impact of multicollinearity and the absence of explicit mathematical expressions in many soft computing models. In the experimental section, an imperialist competitive algorithm (ICA)-optimized artificial neural network (ANN) model is developed to predict the percentage of oversized material produced by small-scale blasting. Field data, including blast parameters and rock strength, were collected from a dolomite quarry in Akoko, Edo State, Nigeria. Fragmentation analysis was conducted using WipFrag 4.0 software across 48 blast rounds, using the primary crusher gape as the decision threshold. Input parameter selection was guided by multicollinearity analysis to ensure robust modeling. Evaluation metrics such as root-mean-square error (RMSE), correlation coefficient (R²), mean absolute percentage error (MAPE), variance accounted for (VAF), Nash–Sutcliffe efficiency (NSE), and performance index (PI) confirmed that the ICA-ANN model significantly outperformed the standard ANN. While the conventional ANN model underestimated oversize by 14.7%, the ICA-ANN achieved a lower prediction error of 2.7%. The proposed model offers a practical and accurate tool for predicting oversized fragmentation in small-scale rock engineering scenarios, contributing to improved blasting efficiency and sustainability in the mining sector.

Creep is a time-dependent plastic deformation that occurs in materials subjected to sustained underground stresses. This phenomenon is particularly significant in rocksalt, where understanding its behavior is critical due to its direct impact on mining operations and the long-term stability of underground structures. This study investigates the creep behavior of rocksalt from the Khewra Mine, located in Pakistan, through a combination of laboratory testing and numerical analysis. Triaxial creep tests were conducted on selected samples from the Khewra Salt Mine, and the resulting data were incorporated into a numerical model. Due to limited resources, certain parameters were assumed based on data from the Asse Mine in Germany. A symmetrical single-pillar model was developed in FLAC3D to simulate the mechanical response, using dilatancy and failure strength criteria to evaluate the pillar's utilization factor. The simulation results indicate the early formation of micro-fractures throughout the pillar, while macro-fractures gradually develop along its outer boundary over time. Zones between 3.4 and 4.1 meters from the center show significantly high tensile stresses, suggesting potential instability and risk of failure at the pillar's edges. These findings highlight the need for a more comprehensive investigation of the mechanical properties and creep behavior of Khewra rocksalt to ensure safe and sustainable mining practices.

Heterogeneity of natural rock mass differs from most other engineering materials. Although the heterogeneity, such as macroscopic fracture, potentially contributes to the deformability of rock mass, evidence for macroscopic heterogeneity from field studies has been circumstantial. We present the results of field drilling energy experiment on the rock mass of tuff, limestone and marble types that shows the evidence for the rock mass deformability from macroscopic heterogeneity caused by fracture, reflecting borehole macroscopic heterogeneity associated with drill energy. The experimental results show that the macroscopic heterogeneity is expected to vary linearly with the fracture frequency, and depends on rock types and drilling energy. The contributions of macroscopic heterogeneity for deformability of rock mass have undergone a leading role.

Friction coefficient, as a parameter of mechanical state, plays a crucial role in the shear failure of rocks in the field of Earth sciences. This paper investigates the frictional characteristics and anisotropy of rock by analyzing the coefficient of variation of the friction coefficient (f) and the anisotropy index of rock friction coefficients Af. Rotational friction tests were conducted using cylindrical granite against square samples of granite, sandstone, and andesite in three directions to analyze the relationship between the friction coefficient and various drilling parameters. This study reveals the variations in the friction coefficient and notable changes in the friction coefficient’s anisotropy. The results indicate a correlation between the alignment of turning points during the frictional stage and the rock strength. During the experiment, the friction coefficient undergoes cyclic variation before gradually stabilizing. The anisotropy of rotational friction follows the order: granite > andesite > sandstone, suggesting that the higher rock strength corresponds to greater frictional anisotropy. The rotational friction control coefficient C is derived and linked to the rotational friction stage. The duration of effective contact between rock surfaces and directional cutting efficiency are the primary factors contributing to anisotropy. The results offer practical implications for drilling design and seismic risk assessment in anisotropic rock formations.

The utilization of blasting has been prevalent in mining and civil engineering domains due to its cost-effectiveness and affordability as a method for fracturing rock. The achievement of an ideal blast results in the most effective fragmentation while ensuring safety, cost-effectiveness, and environmental sustainability. In developing blast efficiency model, this study considered uniaxial compressive strength (UCS), spacing, hole depth, stemming length, point load index, powder factor, charge weight and burden. The model was trained by artificial neural network (ANN) and linear multivariate regression (LMVR) using 85 production datasets. After training four-layer ANN architecture 8-4-1 was found to be optimum. The prediction accurateness of two developed models was analysed using mean square error (MSE), performance index (PI), variance accounted for (VAF), root mean square error (RMSE), and co-efficient of determination (R2). The obtained values of performance parameters reveals ANN model to be more accurate as compared to the LMVR model. The ANN and LMVR model have R2 value of 90.9% and 56.3%. The optimized model was employed to achieve the optimal blast design for high strength granite to enhance blast efficiency. The test data result was utilized to optimize the blast parameters, including spacing, stemming length, burden, charge length, and charge. The values chosen for these parameters were 1.8 m, 1.8 m, 1.5 m, 157.17 kg, and 1.35 kg/m3, respectively, based on the optimum model.

To study the variations in the damping ratio of rock at different frequencies, an external excitation test and a cyclic loading test were designed, and the relationship between the damping ratio of rock and the frequency under conditions of low and high frequency was determined. The damping mechanism was analyzed from the viewpoints of structure and lithology. The results show that: (1) On the basis of the method used for calculating the damping ratio of soil, a new method for calculating the damping ratio of rock was proposed, which is more suitable for the stress–strain curve of rock. (2) The damping ratio of rock increased with frequency at low frequency but decreased at high frequency, which indicated that there is a peak value in the curve of changes in the damping ratio with frequency. (3) The damping ratio of sandstone was greater than that of granite, which was explained from the viewpoint of the structure and the formation conditions of the rocks. From the viewpoint of the source of viscosity, it was explained why the damping ratio first increased and then decreased with an increase in frequency.

In this paper, 114 uniaxial compressive strength tests were carried out on specimens of veined gneiss with diameters ranging from 14 mm to 100 mm. The main objective of the study was to investigate the influence of the specimen size on the strength behavior of this metamorphic, heterogeneous rock. This size effect results in an increase in strength from small 14-mm diameter specimens up to 50-mm diameter specimens. Thereafter, a mild decrease in results is observed from 50-mm to 100-mm diameter specimens, in line with traditionally considered size-effect approaches. The findings generally agree with previous studies on size effects in sedimentary and igneous rocks, suggesting that metamorphic rocks may also tend to follow the Unified Size-Effect Law (USEL), accounting for general and reverse size-effects in strength. Nevertheless, some variability observed in the results, mainly attributed to inherent heterogeneity of the studied rock could influence how clearly this ascending-descending trend is captured by the model.

As multifunctional structures, deep rock underground structures are built all over the world. Their lifespan is generally expected to exceed a hundred years. However, they are inexorable to rock creep which controls their lasting safety and stability. This article describes the strong factors affecting rock creep and the lasting stability of deep rock engineering, based on pertinent research works. It shows that temperature, water content, hydraulic pressure, stress level, and damage are major factors that significantly affect the creep behavior of host rocks of deep underground structures. Overall, such factors govern the creep life of rocks. Specifically, the increase in these factors causes an increase in the creep strain rate, a shortening of the steady creep phase, an acceleration of the onset of tertiary creep, and thus a shortening of the time-to-failure of rocks. This is due in particular to the fact that fluctuations in these factors disintegrate the internal structure of the rocks and make them increasingly weakened. As a result, the mechanical properties of the rocks are altered and the creep process proceeds at a higher rate than expected. Hence, the creep life of surrounding rocks is reduced, which significantly limits the prolonged stability of underground structures. Appropriate countermeasures, such as long-term monitoring, are strongly recommended.

This research aims to optimize ground support systems for underground tunnels in geologically challenging environments, specifically addressing the reduction of Fall of Ground (FOG) incidents in a gold mine in Mashava, Zimbabwe. The study integrates advanced detection and classification methodologies to enhance tunnel stability and safety. Tunnel Reflection Tomography (TRT) was employed to identify unfavorable geological structures ahead of excavation, while core logging at 20 locations on level 7 provided rock mass quality assessments using three classification systems: Bieniawski’s Rock Mass Rating (RMR), Laubscher’s Mining Rock Mass Rating (MRMR), and Barton’s Q-system. The results consistently indicated poor rock mass quality, informing the design and refinement of a robust ground support system. Fallout height data from past FOG incidents and probabilistic key block analysis using J-Block software further validated the support system's effectiveness. The findings significantly reduce collapse risks and downtime, enhancing operational safety and efficiency. This research contributes to developing practical strategies and tools for improving tunnel stability in complex geological settings, offering valuable insights for future advancements in mining support technologies. The study's necessity stems from the industry's growing demand for innovative solutions to enhance tunnel stability in adverse geological settings, particularly in regions with limited access to advanced technologies or methodologies.

This paper proposes a novel approach to rock mass characterization by adapting the coefficient of uniformity (Cu) and coefficient of curvature (Cc) from soil mechanics, redefining their mathematical formulations to align with RQD-based block size measurements. Specifically, Cu and Cc are calculated using D10, D30, and D60, derived from cumulative RQD data, while accounting for the increasing scale of block size distributions in rock masses. An illustrative case study demonstrates the application of this method, yielding insights into block size variability and heterogeneity in rock masses. The proposed coefficients enrich rock mass classification, offering enhanced quantitative tools for engineering and geological analyses.

Currently, the unified strength criterion (USC), the three-dimensional Hoek-Brown (3D H-B) criterion and the generalized unified strength theory (GUST) are the three types of typical rock strength criteria. In this paper, a comparative study of the three types of strength criteria is performed for rocks. Based on the nonlinear characteristics of rock strength on meridian and deviatoric planes, the USC can predict rock strength under triaxial stress state. The USC is composed of two failure functions on meridian and deviatoric planes. The failure surface of the USC in principal stress space satisfies smoothness and convexity. The predicted strength for five types of rock under the true triaxial tests were compared among the USC, the GUST, and the 3D H-B criterion. The results indicate that the USC can effectively reflect the influence of the intermediate principal stress on rock strength and accurately predict rock strength under both triaxial tension (σ₁=σ₂>σ₃) and triaxial compression (σ₁>σ₂=σ₃). Additionally, the conventional triaxial tests were conducted on other eight types of rock to measure the strength on meridian plane. The predicted strengths for the eight types of rock on meridian plane were compared between the USC and the original H-B, which suggests that the USC is suitable for various types of rock and provides higher accuracy.

The presence of rock mass fractures has always been a subject of study for the prevention and control of related natural disasters. To understand the effects of different dip angles and horizontal distances on crack development, numerical simulation experiments on Brazilian disks under uniaxial compression were con-ducted using the PFC2D particle flow program. A function module was utilized to monitor the expansion and quantity of cracks. The numerical simulation results under 0° conditions were in good agreement with the experimental results, validating the rationality of the numerical simulation. The simulation results indicate that: under single fracture conditions with different dip angles, samples with angles between 30° and 60° produced typical wing-shaped cracks. At 0°, cracks propagat-ed through the center of the fracture, while at 90°, cracks initiated from the tip of the fracture and propagated through the sample. The peak stress and the number of cracks in the samples first decreased and then increased with the increase of the dip angle, reaching a maximum at 90°. For samples with double fractures and varying horizontal distances, all produced wing-shaped cracks. Their peak stress and the number of cracks increased monotonically with the increase in distance, reaching a maximum at a distance of 30mm. The experimental results confirmed that the PFC2D program can effectively simulate the process of crack initiation and development, and the research findings provide a reference for correctly understanding the fracture mechanics of fractured rock masses.

The determination of reserved deformation is typically based on referring to relevant codes or the engineering analogy method, lacking a certain theoretical approach. The purpose of this study is to provide a theoretical basis for determining reserved deformation and to analyze the variation law of the surrounding rock affected by reserved deformation. Considering the reserved deformation under the condition of asymmetric load, the expression of optimal reserved deformation, the expression of support resistance reflecting the strength of surrounding rock, the strength of support material and the magnitude of in situ stress, the displacement expression of surrounding rock are derived by approximate solution based on the classical elastic–plastic theory. Numerical simulation software is used to simulate the displacement expression of the surrounding rock considering the reserved deformation and the expression of the optimum reserved deformation under the condition of asymmetric load. The results of the numerical simulation were compared with those of the analytical solutions, and the analytical results show that the errors between the two are within 12% and that the consistency is good.

The block caving is one of the most commonly used methods in underground mining of massive, low/high grades, and deep deposits. As a result of undercutting, caving occurs and propagates toward the upper part of the ore block. It is essential to predict the height of caved ore and its volume based on shape of the caved zone to make an economic decision. This paper describes the mechanism of height of the caving zone development. Consequently, four new mathematical models (prismatic, parabolic, cubic, and hemispheric) are proposed to estimate the height of this caving zone. The results are compared with the existing approaches. The proposed methods have proven that the height of caving zone has a linear relationship with the uniaxial tensile and compressive strengths and the height of undercut as well. Also, the height of the caving zone has a negative exponential relationship with unit weight of undercut roof materials and its expansion factor. The Height of the caving zone of the prismatic model is 1.5 times higher than the parabolic model and 1.3 times higher than the hemispheric model. The cubic model estimates the lowest height of the caving zone (0.3 times the height estimated by the prismatic model). The average height of the caving zone, taking the average unit weight of 27 KN/m3 into account, is about 69.4 times the tensile strength, 5.8 times the uniaxial compressive strength of the rock mass, and 18.8 times the height of the undercut.

Dimension stone and terrazzo are quarried rocks following specific dimensions, generally huge in tonnage than ore minerals. Dimension stone and Terrazo resource development opportunities in the Tigray Region, Ethiopia, are studied regarding their potential to make dimension and terrazzo, geology and deposit nature, physio-mechanical properties, rock petrography, and opportunity for exploitation. The granite and marble are quarried as dimension stones and they meet the quality parameters of the rocks, which include, being durable, easy to quarry, work, cut, and polish. It was conducted through the integration of new geological descriptions, interpretation of thin sections, and physico-mechanical tests. Both surface and quarry rock samples were used for the study. 15 from granite and 15 from marble deposits in total 30 samples were used for petrographic analysis and physico-mechanical tests. Based on petrographic and physicomechanical results, granite is harder than marble this may be due to silicates being less dissolved than carbonates. The accessory minerals in both granite and marble deposits limit the quality of the deposits as being impurities. The integrated results indicate that the marble and granite deposits in the area are good in quality and quantity. In addition, they are geologically widespread, technologically do not need sophisticated technology and economically they do not need huge investment and have less effect upon the environment. Diamond wire saws and diamond belt saws separated the dimension stone, which are oblate to curved in shape with 1m width. In the area, investment has been at a relatively low stage more investment will significantly increase production of the dimension stone for local usage, export, and economic growth of the region.