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.

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.

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 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.

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.

Karst topography is extensively distributed throughout the southwestern part of China, posing considerable challenges to the safety and stability of building foundations and overall structural integrity. The unique geomorphological features associated with karst, such as sinkholes, underground rivers, and caves, greatly increase the geological uncertainties and risks during engineering construction. As a result, the infrastructure projects are highly vulnerable to subsidence, collapse, and other karst-related hazards, which may lead to serious safety incidents and significant economic losses. It is imperative to strengthen karst geological surveys and improve detection accuracy to thoroughly ascertain the distribution patterns and developmental characteristics of karst formations. By employing advanced investigation techniques and detailed data analysis, engineers can more accurately assess karst conditions and evaluate their influence on pile foundation design and construction. This includes potential adverse effects such as uneven bearing strata, groundwater erosion, and cave roof instability. The reasonable and adaptive recommendations for selecting foundation types and construction techniques can be proposed. This will provide a scientific basis for engineering design and risk mitigation, ensuring the safety, stability, and sustainability of structures in karst-affected regions.