Unstable Zone Research Articles

Developing a Technology for Driving Mine Workings with Combined Support and Friction Anchors in Ore Mines

This study summarizes the experience of conducting and maintaining mining operations in unstable zones in mines in Kazakhstan, assessing the mining and geological technical conditions of their operation under difficult mining and geological conditions. A field study and analytical modeling with an assessment of the stability of the boundary mass using the Barton mining method enabled the development of a technology for sinking mining operations with combined fasteners and friction anchors in ore mines.

Direct Interdental Wiring as Alternative Method in the Treatment of Mandibular Fracture at Inaccessible War Zone: A Case Report

The Region of Tombouctou is considered as one of landlocked regions in Mali, unstable war zone. The frequency of mandibular fracture becomes more than usual in the last years with lack of oral and maxillofacial team; limited complementary exams; and limited surgical tools. In purpose to reduce; to fix fracture line; and to restore function of maxillofacial areas, we decided to practice direct interdental wiring as alternative method for the treatment of limited displacement of mandibular fractures. Direct interdental wiring in Intermaxillary fixation for closed reduction in the mandibular fracture is rarely used today.

Numerical investigation on effect of non-parallelism on natural transition in boundary layers around underwater axisymmetric bodies

For both fluid mechanics and practical engineering problems, it is important to study the effect of non-parallelism on the natural transition in boundary layers around underwater axisymmetric bodies. This paper develops the method of harmonic linearized Navier–Stokes (HLNS) equations for such boundary layers. The method can be used to study the evolution of small disturbances considering the non-parallelism of the basic flow. Based on the results of the HLNS equations, the transition positions of the boundary layers are predicted by the eN method. Because traditional linear stability theory (LST) neglects non-parallelism, the difference between the results using the HLNS method and those given by LST represents the effects of non-parallelism. Numerical calculations are performed for five classical forebody shapes, and the effect of non-parallelism is identified. (i) At each streamwise location, non-parallelism suppresses low-frequency disturbances while promoting high-frequency ones. The influence on high-frequency disturbances is more obvious. (ii) The effect of non-parallelism on the neutral curve focuses on the region near the critical instability position. Non-parallelism slightly delays the critical instability position for most forebody shapes and pushes the unstable zone toward the high-frequency direction while broadening its frequency bandwidth. (iii) The streamwise range at each growth-rate level is widened, implying that non-parallelism destabilizes the boundary layers. (iv) The transition occurs earlier, indicating that non-parallelism promotes the transition. (v) Non-parallelism shifts the dangerous frequency band toward the high-frequency direction. (vi) Non-parallelism enhances the wall pressure fluctuations (WPF) in the unstable laminar zone.

Monitoring Salt Domes Used for Energy Storage With Microseismicity: Insights for a Carbon‐Neutral Future

AbstractUnderground storage in geologic formations will play a key role in the energy transition by providing low‐cost storage of renewable fuels such as hydrogen. The sealing qualities of caverns leached in salt and availability of domal salt bodies make them ideal for energy storage. However, unstable boundary shear zones of anomalous friable salt can enhance internal shearing and pose a structural hazard to storage operations. Considering the indistinct nature of internal salt heterogeneities when imaged with conventional techniques such as reflection seismic surveys, we develop a method to map shear zones using seismicity patterns in the US Gulf Coast, the region with the world's largest underground crude oil emergency supply. We developed and finetuned a machine learning algorithm using tectonic and local microearthquakes. The finetuned model was applied to detect microearthquakes in a 12‐month long nodal seismic dataset from the Sorrento salt dome. Clustered microearthquake locations reveal the three‐dimensional geometry of two anomalous salt shear zones and their orientations were determined using probabilistic hypocenter imaging. The seismicity pattern, combined with borehole pressure measurements, and cavern sonar surveys, shows the spatiotemporal evolution of cavern shapes within the salt dome. We describe how shear zone seismicity contributed to a cavern well failure and gas release incident that occurred during monitoring. Our findings show that caverns placed close to shear zones are more susceptible to structural damage. We propose a non‐invasive technique for mapping hazards related to internal salt dome deformation that can be employed in high‐noise industrial settings to characterize storage facilities.

Application of remote sensing/GIS in the appraisal of geotechnical stability of civil engineering structures in cretaceous sedimentary units in Gombe, Northeastern, Nigeria

The increasing urbanization in Gombe township has necessitated the need for a city-wide assessment of the area to ascertain its spatial geotechnical stability. In this study, the geotechnical stability of Gombe township and environs, Northeastern, Nigeria, was appraised using the geospatial approach. Four different thematic maps (lithology, lineament, elevation, and slope) were generated in a GIS environment. Weights were allocated to the subclasses of the thematic maps based on their contribution to the stability of engineering structures. The thematic maps were integrated using ArcGIS 10.3 software to generate a geotechnical stability model of the study area, which was validated through an on-site inspection of the structures in the area. The study area was delineated into three zones: unstable (17.24%), moderate (77.2%), and stable (4.74%). The moderate zones characterised by medium elevation and slope, average lineament density, and underlain by sandstones were the predominant zones in the area. However, the stable and the unstable zones predominate in the western and eastern parts of the study area respectively. The stable zones that occur in the northwestern and southwestern zones of the study area are underlain by the Kerri-Kerri Formation while the poor and unstable areasare underlain by argillaceous materials of the Pindiga Formation. The validation of the model revealed numerous cracked buildings and bridges and a failed bridge in the unstable zones. The moderate stability zones suffer a mixed fortune, having some stable structures in some parts and failing structures in other parts. The buildings in the stable zones, however, are generally devoid of structural cracks.

Empirical Stability Criteria for 3D Hierarchical Triple Systems. I. Circumbinary Planets

In this work we revisit the problem of the dynamical stability of hierarchical triple systems with applications to circumbinary planetary orbits. We derive critical semimajor axes based on simulating and analyzing the dynamical behavior of 3 × 108 binary star–planet configurations. For the first time, three-dimensional and eccentric planetary orbits are considered. We explore systems with a variety of binary and planetary mass ratios, binary and planetary eccentricities from 0 to 0.9, and orbital mutual inclinations ranging from 0° to 180°. Planetary masses range between the size of Mercury and the lower fusion boundary (approximately 13 Jupiter masses). The stability of each system is monitored over 106 planetary orbital periods. We provide empirical expressions in the form of multidimensional, parameterized fits for two borders that separate dynamically stable, unstable, and mixed zones. In addition, we offer a machine learning model trained on our data set as an alternative tool for predicting the stability of circumbinary planets. Both the empirical fits and the machine learning model are tested for their predictive capabilities against randomly generated circumbinary systems with very good results. The empirical formulae are also applied to the Kepler and TESS circumbinary systems, confirming that many planets orbit their host stars close to the stability limit of those systems. Finally, we present a REST application programming interface with a web-based application for convenient access to our simulation data set.

Integral resonant negative derivative feedback suppression control strategy for nonlinear dynamic vibration behavior model

One of the major problems in robotics research has been developing an actuator system for extremely dynamic-legged robots. High torque density and the capacity to control dynamic physical interactions are two design requirements for high-speed locomotion that are challenging for conventional actuators used in manufacturing applications to meet. To address this system and apply the desired control to reach the best stability position, the robot's foot was simulated with the Van der Pol equations, applied the required control, and studied that application. This work describes the actions of a new novel control mechanism known as the Integral Resonant Negative Derivative Feedback (IRNDF) controller, which reduces the vibration response of a double Van der Pol oscillator subjected to external excitations. This unique controller combines integral resonant control (IRC) and negative derivative feedback (NDF) controllers to provide a new controller effect for double Van der Pol oscillators. The multiple scale perturbation technique (MSPT) has been applied to solve the controlled system analytically. The MATLAB and MAPLE programs have been used to complete and clarify all of the numerical talks. The frequency response curves have been used to study the impact that altering the parameter values had on the amplitude. The controlled system vibration amplitude is governed by frequency-response equations (FREs), which have been constructed. In the vibration system, the IRC, NDF, and IRNDF controllers were compared to see which one was the best. Numerical results show that the unique IRNDF controller is the best at reducing oscillations and decreasing amplitude values. The effects of the effective parameters on the controlled system have been identified. The frequency-response equation that was derived has been used to plot the various response curves for the framework that show the stable and unstable zones when the controller is off and on. Lastly, excellent agreement between the derived numerical findings and the analytical ones was observed. Lastly, utilizing time histories and response curves to compare analytical and numerical solutions was fascinating and significant.

Legacy of aerosol radiative effect predominates daytime dust loading evolution

Dust radiative effect imposes pronounced perturbations on planetary boundary layer (PBL) development. In turn, the modified PBL characteristics and circulation fields regulate subsequent dust processes, which have not been explored sufficiently. In this study, parallel experiments are designed to isolate the instant, legacy and nonlinear impacts of aerosol radiative effect on daytime dust storm evolution over the Tarim Basin. During a typical dust storm event, legacy radiative effect is found to dominate dust loading dynamics and modulates mean dust burden by more than 16 % in the central basin and − 41 % in the marginal basin. Specifically, the dust column concentration increases in central regions but decreases in marginal regions. Dust aerosols cause opposite heating rate distributions and PBL structure between the central and marginal regions through altering radiative balance. Dust-induced cooling effect in the marginal regions leads to PBL suppression and attenuates entrainment mixing. Negative net heating also results in lowered potential temperature, elevated air pressure and thus increases their horizontal gradients. Accordingly, wind speeds are amplified through geostrophic and thermal wind effects, which further accelerate deposition rates, and eventually weaken dust suspension. In the central basin, dust plumes stimulate a warm mixing layer and unstable entrainment zone, which inhibit dry deposition removal and favor dust accumulation in the atmosphere. Our study highlights the importance of accounting PBL dynamics and geostrophic balance in quantifying the impacts of preceding radiative effect on subsequent dust evolution.

Shaking table study on the seismic dynamic behavior of high-speed railway subgrade with pile network composite-reinforced soil

Pile network composite structures are used in the construction of high-speed railway subgrades. There have been few studies on their seismic dynamic response, however, which has restricted the accurate evaluation of their seismic performance. In this study, a series of shaking table tests on a pile network composite-reinforced soil high-speed railway subgrade were conducted. Particle image velocimetry was used to analyze the slope motion and sensor data to evaluate the overall dynamic response characteristics of the subgrade. Findings indicate that seismic activity causes subsidence throughout the subgrade, with deformations occurring in three distinct phases depending on the input seismic amplitude from 0.1 to 0.4 g (slow increasing), 0.4–0.6 g (faster increasing), and 0.6–1.0 g (rapidly increasing). The inclusion of geogrids aids in dissipating seismic energy, thereby reducing the peak acceleration amplification along the elevation. The increased dynamic soil pressure of the subgrade is mitigated by the geogrid reinforcement, which improves local stability. Moreover, the geogrid strain escalated with greater seismic wave amplitudes, resulting in the progressive expansion of the unstable zone from the slope towards the center of the subgrade as the elevation increased.

Analytical and descriptive study of the production behavior for pilot multi-stages hydraulic fracturing wells in southeast Iraq

The hydraulic fracturing technique is a widely used technique worldwide, making it interesting to study. This technique was applied for the first time in Iraq on a tight carbonate reservoir in the Halfaya oil field. In this field, the oil production rates, and flowing pressure were low during production periods reflecting a problem for the development plan designed to increase production using a hydraulic fracture technique. Initially, the hydraulic fracture well showed high oil-producing rates, but then, quickly experienced a high decline failing to keep a stable production rate. To address this problem, it is important to describe and analyze the behavior of pilot hydraulic fracturing wells during their production period, study the inflow performance relationship (IPR), and determine the optimum wellhead pressure above the bubble point pressure (Pb) to avoid loss of lifting energy. Furthermore, it identifies the allowable flow rate to keep stable production, investigates the effect of selecting internal tubing size, and reveals a future production procedure for hydraulic fracture wells. This study reveals that the transient inflow performance relationship observed in the production history of hydraulic fracture well in the tight carbonate reservoir and traditional inflow performance relationship concepts are not applicable. The optimum wellhead pressure for stability in production for Wells w-5 and w-55 is determined to be 750 and 580 psi with optimum rates of 800 and 450 Bbl/D, respectively. The results also showed that producing at a high flow rate may cause a depletion in the fracture potential storage without giving an opportunity for a reservoir to compensate for the produced fluid into fracturing potential storage. The internal tubing size has a passive effect on the hydraulic fracture well, as an increase in size causes an unstable flow zone. Lastly, future production procedures emphasize keeping wellhead pressures stable or increasing them if they drop. This can be accomplished by re-adjusting the choke size according to any changes observed.

Stability of a viscous liquid film flowing down an inclined plane with respect to three-dimensional disturbances

An analysis is presented for the stability of a viscous liquid film flowing down an inclined plane with respect to three-dimensional disturbances under the action of gravity and surface tension. Using momentum-integral method, the nonlinear free surface evolution equation is derived by introducing the self-similar semiparabolic velocity profiles along the flow (x- and y-axis) directions. A normal mode technique and the method of multiple scales are used to obtain the theoretical (linear and nonlinear stability) results of this flow problem, which conceive the physical parameters: Reynolds number Re, Weber number We, angle of inclination of the plane θ and the angle of propagation of the interfacial disturbances ϕ. The temporal growth rate ωi+ and second Landau constant J2, based on which various (explosive, supercritical, unconditional, subcritical) stability zones of this flow problem are categorized, contain the shape factors B and β owing to the non-zero steady basic flow along the y-axis direction. A novel result which emerges from the linear stability analysis is that for any given value of Re, We and θ, any stability that arises in two-dimensional disturbances (ϕ = 0) must also be present in three-dimensional disturbances. For ϕ = 0, there exists a second explosive unstable zone (instead of unconditional stable zone) after a certain value of Re (or θ) due to the involvement of B and β in the expression of J2. This explosive unstable zone vanishes after a certain value of ϕ depending upon the values of Re, We and θ, which confirms the stabilizing influence of ϕ on the thin film flow dynamics irrespective of the values of Re, We and θ.

Hot deformation behavior and microstructural evolution of high-carbon high-strength low alloy steel

This study investigates the hot deformation behavior, microstructural evolution, and processing map of a high-carbon high-strength low alloy steel subjected to hot compression tests in the temperature range of 850 °C–1150 °C and strain rates from 0.01 s⁻1–10 s⁻1. A highly accurate flow stress constitutive equation has been established and the activation energy of the experiment steel is 462.6 kJ/mol. Processing maps were generated to identify unstable zones, low-power dissipation zones, and optimum processing zones, accompanied by detailed discussions on corresponding microstructures and mechanical properties. The recommended hot deformation parameters at a true strain of 0.9 are temperatures from 944 °C to 1050 °C and strain rates from 0.01 s⁻1 to 0.52 s⁻1 according to the processing map. The effects of deformation temperature and strain rate on the microstructure were then investigated. It is revealed that reducing deformation temperature and increasing strain suppress the recrystallization process and the growth of recrystallized grains; while VC precipitation is suppressed under high temperatures and high strain rates.

Role of Cairns–Gurevich ion distribution on nonlinear wave propagation in negatively charged dusty plasma

The study of dust-acoustic (DA) nonlinear electrostatic waves in dusty plasma is crucial for understanding plasma behavior in both astrophysical and laboratory environments. Dusty plasmas, characterized by the presence of negatively charged dust particles, exhibit complex dynamics influenced by various factors, including nonthermal electron and ion populations following Cairns–Gurevich distributions. This study addresses the problem of understanding wave propagation under these specific conditions by employing a set of fluid hydrodynamic equations for dust fluid, alongside appropriate electron and Cairns–Gurevich ion distributions, to model the dynamics and propagation of DA nonlinear electrostatic waves under specific plasma conditions with negatively charged dust particles. We derived a nonlinear Zakharov–Kuznetsov (ZK) equation to model the evolution of these waves and further transformed it into the nonlinear Schrödinger (NLS) equation to analyze rogue wave formation and identify unstable and stable zones within the plasma. We focused our analysis on the effects of key parameters, such as the nonthermal index, magnetic field strength, negative dust temperature ratio, polarization force, and density ratio, on the behavior of dust-acoustic waves (DAWs). The results demonstrated that soliton waves, explosive waves, and kink waves exhibit distinct behaviors depending on these parameters and the spatial context of Earth's magnetosphere. These findings provide new insights compared to previous studies into the conditions under which these waveforms emerge and evolve, especially in magnetized environments where earlier models were less effective at accurately characterizing or predicting wave behavior. By applying two different analytical methods, a direct integration approach and a generalized Kudryashov method, we expanded our understanding of nonlinear wave phenomena in dusty plasmas. Our results not only advance theoretical knowledge but also have practical implications for interpreting space plasma observations and guiding experimental design in plasma physics research. This study thus contributes to a more comprehensive understanding of plasma dynamics, with potential applications to astrophysical observation and laboratory plasma experimentation.

Multi-scale analysis of harmonic resonance in cylindrical bubbles under acoustic excitation

In this paper, the dimensionless oscillation equation of a cylindrical bubble is analyzed using the multi-scale method, Lyapunov stability theory, and the Routh–Hurwitz stability criterion. The corresponding second-order analytical solution and stability criterion are obtained. By examining the cases of second-order super-harmonic resonance and 1/2-order sub-harmonic resonance, the harmonic resonance characteristics of cylindrical bubbles and the influencing factors are revealed. The conclusions are summarized as follows: (1) Super-harmonic resonance can exhibit up to three solutions, along with unstable phenomena such as jump and hysteresis. Sub-harmonic resonance, however, shows at most two solutions simultaneously, without jump or hysteresis phenomena. (2) As the acoustic excitation amplitude increases, both the response amplitude and the unstable zone significantly enlarge. An increase in nonlinear coefficients can reduce the response amplitude and increase instability. (3) When the acoustic excitation amplitude reaches a certain threshold, the oscillation mode of the bubble shifts from periodic to chaotic. Under the same initial conditions, the chaos threshold for sub-harmonic resonance is higher than that for super-harmonic resonance.

Faraday instability of viscous liquid films on a heated substrate with Maxwell–Cattaneo heat flux

Faraday instability of viscous liquid films with Maxwell–Cattaneo (MC) heat flux on an infinite, heated horizontal substrate subject to vertical time-varying periodic vibration is investigated theoretically. The MC effect means that the response of the heat flux to a temperature gradient obeys a relaxation time law rather than a classical Fourier time law. Applying the classic Floquet theory to linear analysis, a recursive relation is obtained. When considering the MC effect, a new phenomenon appears at a large wave number k. The neutral stability curves branch new tongues that turn left rather than right as before, but the tongues still move up and right as the wave number increases. Furthermore, typical harmonic (H) and subharmonic (SH) alternation behavior continues to exist. Interestingly, the first tongue of a branch is H or SH, implying that there is a transition following the branches. However, near the critical wave number kc of a branch, the SH and H almost overlap. As Cattaneo number C increases, the tongue-like unstable zones of branches become wider, and the critical wave number kc of the appeared branch becomes small. As the driving frequency ω decreases, the branch tongues become elongated and the critical wave number kc of the appeared branch becomes small.

Study on stability evaluation of goaf based on AHP and EWM—taking the northern new district of Liaoyuan city as an example

Throughout the history of coal mining in all countries of the world, large areas of goaf have been left behind, and sudden collapses and surface subsidence of large areas of goaf may occur, especially for mining areas with long mining cycles. The northern new district of the Liaoyuan mining area has been subjected to nearly half a century of mining activities, accompanied by a gradual accumulation of disasters, which have occurred frequently in recent years. In order to assess the stability of the goaf in the study area, this paper proposes a hybrid decision-making multi-factor integrated evaluation method. The distribution of underground goafs was determined using geophysical exploration techniques (seismic survey and transient electromagnetic method) and geological drilling exploration. First, an evaluation index system was established based on the specifications of the goaf, the ecological and geological environment, and the mining conditions; the system included 14 indicators. Two weight calculation methods, AHP-EWM, were employed to determine the comprehensive weight of each indicator by combining subjective and objective weights on the basis of improved game theory. Subsequently, the fuzzy comprehensive evaluation method was utilised to complete the stability rating of each block in the study area, and MapGIS and ArcGIS were employed to complete the drawing of the stability zoning map of the northern new district goaf. The study area was divided into three zones of stability, basic stability and instability, according to the critical value. These zones accounted for 23.03%, 36.45% and 40.52% of the total area of the study area, respectively. The comprehensive on-site investigation revealed a decrease in the size and number of collapse pits and the rate of damage to the houses from the unstable zone to the stable zone. This indicates that the results of the division are consistent with the actual situation. The classification results are consistent with the actual ground disaster situation, thus verifying the rationality and validity of the evaluation method. The results indicate that the stability of the study area is generally at the lower middle level.

Linear stability analysis of compressible boundary layer over an insulated wall using compound matrix method: Existence of multiple unstable modes for Mach number beyond 3

The linear spatial stability of a parallel two-dimensional (2D) compressible boundary layer on an adiabatic plate is investigated by considering both 2D and three-dimensional (3D) disturbances. The compound matrix method is employed here, for the first time, for compressible flows, which, unlike other conventional techniques, can efficiently eliminate the stiffness of the equations governing the spectral amplitudes. The method is first validated with published results in the literature corresponding to spatial and temporal instability of flows ranging from low subsonic to high supersonic Mach numbers (M), which shows a good match depending upon the proper choice of free-stream temperature and the wall dispersion relation. Subsequently, flow compressibility effects and the spanwise variation of disturbances are also investigated for M ranging from low subsonic to high supersonic cases (from M = 0.1 to 6). Mack (AGARD Report No. 709, 1984) reported the existence of two unstable modes for M > 3 from viscous calculations (the so-called “second mode”) that subsequently fuse to create only one unstable zone when M increases. Our calculations show a series of higher-order unstable modes for M > 3 in addition to the findings of Ma and Zhong [“Receptivity of a supersonic boundary layer over a flat plate. Part 1. Wave structures and interactions,” J. Fluid Mech. 488, 31–78 (2003)], where such higher-order modes for supersonic boundary layers are all noted to be spatially stable. The number and the frequency extent of the corresponding unstable zones increase with an increase in M beyond 3 while propagating downstream at a higher speed than those corresponding to incompressible, subsonic, and low supersonic (M < 2) cases.

Shear-imposed falling film on a vertical moving plate with disrupted time-reversal

We propose a mathematical model to study the stability and dynamics of a shear-imposed thin film flow on a vertical moving plate, incorporating the influence of odd viscosity. This odd viscosity effect is vital in conventional fluids when there is a disruption in time-reversal symmetry. Our motivation to study the dynamics with odd viscosity arises from recent studies (Kirkinis & Andreev, vol. 878, 2019, pp. 169–189; Chattopadhyay & Ji, vol. 455, 2023, pp. 133883) where the odd viscosity effectively reduces flow instabilities under different scenarios. Utilizing a long wave perturbation method, we derive a nonlinear evolution equation at the liquid–air interface, which is influenced by the motion of the vertical plate, imposed shear, odd viscosity, and inertia. We first perform a linear stability analysis of the model to get firsthand information on various flow parameters. Three distinct conditions for the vertical plate, quiescent, upward-moving, and downward-moving, are considered, accounting the imposed shear and odd viscosity. Additionally, employing the method of multiple scales, we conduct a weakly nonlinear stability analysis for the traveling wave solution of the evolution equation and explore its bifurcation analysis. The bifurcation analysis reveals the existence of subcritical unstable and supercritical stable zones for crucial flow parameters: odd viscosity, imposed shear, and motion of the vertical plate. Both linear and weakly nonlinear stability analyses demonstrate that the destabilizing effect induced by the upward motion of the vertical plate can be alleviated by applying uphill shear, while the destabilizing effect of downhill shear can be mitigated when the vertical plate is in a downward motion. Moreover, we define an eigenvalue problem that mirrors the Orr–Sommerfeld (OS) model for analyzing normal modes and identifying the critical Reynolds number. We investigate the dynamics of surface waves through numerical solutions of the OS eigenvalue problem using the Chebyshev spectral collocation method. We observe the consistent enhancement of stabilization in the presence of odd viscosity. In the low to moderate Reynolds number range, vertical plate motion and odd viscosity show similar behavior in OS analysis, while imposed shear exhibits distinct changes. The Benney-type model does not agree with the OS problem when the Reynolds number is moderate with or without the three key parameters: vertical plate motion, imposed shear, and odd viscosity. However, when the Reynolds number is low with or without the three key parameters: vertical plate motion, imposed shear, and odd viscosity, the Benney-type model agrees with the OS. Further, numerical simulations of the evolution equation corroborate the results obtained from linear stability, weakly nonlinear stability, and OS analyses. Finally, the Hopf bifurcation analysis of the fixed point reveals that the wave speed is influenced by both the motion of the plate and the imposed shear while it remains independent of odd viscosity.

Enhancing stability graphs for stope design in deep metal mines using machine learning

Stope structural parameters, which are human-controllable, directly impact the safety and economics performance of underground mineral extraction. Current stope design still relies heavily on empirical methods such as stability graphs, due to the complex nature of rock masses and varied stope failure mechanisms. This study aims to enhance stability graphs with machine learning techniques. Firstly, a dataset of 980 records from unsupported stopes was compiled, representing perhaps the largest dataset of its kind so far in the literature. This was achieved through extensive literature review and the collation of an additional 289 records from Chinese mines which were previously not included. An analysis of data reveals that over 90 % of the records fall within a stability coefficient of 0–100 and a hydraulic radius of 0–20 m. Secondly, a stability graphs optimization process was established using Python, eliminating the subjectivity of partitioning. Nine supervised machine learning algorithms were employed and trained to test their performance in partitioning form and predicting accuracy. It was found that the neural network algorithm demonstrated the best overall performance. At last, a neural network with the Keras framework was used to establish a new multilayer perceptron model to generate safety factor probability curves, which were then used to construct the stability graph. To facilitate practical use, mathematical functions fitting safety factor curves within the unstable zone were further formulated. Compared with other empirical stability graphs, our new approach allows designers to more efficiently and reliably select safety factors to determine the stability state according to site specific conditions and technical support systems, thereby providing enhanced guidance for stope design.

Reliability and landslide consequence analysis of long heterogeneous soil infrastructure slopes: A parallel computing investigation

Long infrastructures, like flood defense levees, built upon diverse soils, often face complex landslide failures. Risk assessments for such structures involve evaluating slope stability reliability and potential landslide consequences. Historically, embankment slope reliability and failure assessments focused on shorter sections due to computational limitations. This study, however, delves into a longer 3D soil slope section, 100 times the height, using the random finite element method to analyse the size or length effect. It conducts a parametric study varying the soil strength’s horizontal correlation length to understand slope failure initiation in heterogeneous soils. In contrast to prior work, this paper emphasises several facets: the realised factor of safety (FOS) distribution, quantification of discrete unstable zones and failures, and the size impact on the reliability and landslide consequences of long embankment slopes. Findings indicate the Weibull distribution better fits the realised FOS, aiding in predicting long embankment slope system reliability when combined with the weakest link theory. While multiple failures are possible for very long soil embankment slopes, observations suggest a greater likelihood of a single localised failure despite this potential.