Planar Discontinuities Research Articles

Exploring joint orientation effects on rock wedge stability: Experimental and discrete element analysis

The primary objective of this study was to examine and analyze the sliding behavior of rock wedge slopes with the interaction of three joint sets, considering the influence of plunge angles, included wedge angles between joints, and gravity conditions. The discontinuity planes with varying dip directions relative to the wedge's plunge direction were analyzed. The stability assessment of wedge failure was initially reviewed, explicitly focusing on limit equilibrium (LE) analysis and in-house physical tests. Centrifuge tests and discrete element analysis using the 3DEC software were then performed to explore the factors influencing the failure characteristics of the slopes. Additionally, two mitigation strategies were proposed to enhance the stability of the rock wedge slopes. The key findings include the significant impact of plunge angle on wedge slope stability compared to the included wedge angle between joints, the strong effect of gravitational conditions on the collapsing ratio of wedge units, and the higher risk posed by wedge slopes with discontinuity planes dipping out of the slope. The numerical simulation results highlighted the importance of considering joint spacing in slope stability assessments. Mitigation methods such as fixing key wedge blocks were found to effectively reduce the wedge collapsing ratio and improve rock slope stability under more realistic stress levels. This study provides valuable insights for formulating prevention and mitigation strategies, useful for enhancing safety and reducing the potential damage caused by rock wedge failure events.

Impact of discontinuity data acquisition methods on rockfall susceptibility assessment using high-resolution 3D point cloud

This research evaluates the influence of various discontinuity data acquisition methods on three-dimensional rockfall susceptibility assessments, employing a high-resolution 3D point cloud of the Špičunak rock slope in Croatia. Discontinuity mapping was conducted utilising manual and semi-automated methods. Manual mapping was done in open-source software CloudCompare, while semi-automated mapping was done using Discontinuity Set Extractor and two CloudCompare plug-ins, qFacet Fast Marching and qFacet Kd-Tree algorithm. Significant differences were observed between the methods in terms of the number of identified discontinuity planes, sets, mean orientation values, and weighted densities associated with specific sets. Based on the mapping results, three-dimensional rockfall susceptibility maps were generated. The 3D rockfall susceptibility assessment employed a Kinematic Hazard Index (KHI) for planar, wedge, and flexural toppling failure mechanisms, which determines the percentage of discontinuity planes that meet the geometrical conditions specific to each type of failure. The findings underscore that the mapping results greatly affect the 3D rockfall susceptibility assessment, impacting the identification of potential rockfall source areas. The study emphasizes the importance of integrating manual and semi-automated mapping for reliable 3D rockfall susceptibility assessment. Additionally, this study evaluated the effect of varying the number of discontinuity orientation input data on rockfall susceptibility by comparing nine scenarios, each involving a reduction in the number of discontinuity orientation data. The results indicate that accurate discontinuity mapping is more critical than the sheer number of mapped discontinuities for reliable rockfall susceptibility assessment. Therefore, prioritizing the precise determination of discontinuity set numbers and their associated weighted densities is essential for reliable susceptibility evaluations.

Simulation research on blasting of an open pit mine slope considering elevation conditions and slope shape factors

This study established a numerical model that considers elevation conditions and slope shape factors by the modified Sadovsky formula to analyze the vibration attenuation law of open-pit slopes under blasting vibration conditions. The blasting excavation of a slope in a certain open-pit mine in Yunfu, Guangdong, is selected as an example. Using a numerical model that considers elevation conditions and slope shape factors by the modified Sadovsky formula, a triangular pulse load was utilized to approximate the time-history characteristics of explosion vibration with FLAC3D software. The simulation results showed the radiation range of the blasting vibration seismic wave. By comparison with field monitoring data, the numerical model that considers the slope shape factor had a relative error of ∼10%, while the numerical model that disregards the slope shape factor had a relative error of ∼15%. The relative accuracy of the calculation results of the new numerical model is higher and closer to the actual attenuation law of blasting particle vibration speed, providing more reliable results for slope stability assessment. The peak particle velocities obtained from the numerical simulation results were generally higher than the field monitoring data. These discrepancies might be attributed to the use of simplified models that disregard the discontinuous structural planes within the rock mass. This study provides an important reference for the stability assessment of open-pit slopes under blasting vibration conditions, offering guidance for improving slope stability assessment and related engineering practices.

Discontinuity Measurement for Slope Failure Analysis with Structure from Motion Method Using Drone on A Slope in Hargowilis, Kokap District, Kulon Progo Regency, D.I. Yogyakarta Province

Abstract The measurement of the discontinuity area is one of the important data to determine the slope failure kinematics. Discontinuity measurement can be done by geological compass measurements, but only limited to areas that can be reached and safe. Methods that can help measure the discontinuity plane is Structue from Motion techniques. This method uses raw data in the form of outcrop photos that are processed into point clouds to be processed into a 3-dimensional model. This model is used to measuring the position of the discontinuity plane digitally with a FACETS plug-in by CloudCompare software. FACETS plug-in performs a measurements automatically with the Kd-Nearest algorithm for two sides of of the outcrop. Side-1 has a dimension about 60 meter length and 25 meter height with slop face direction to the east an Side-2 has a dimensions about 25 meter length and 20 meter height, facing south. Side-1 kinematic analysis showing 8.97% of falilure mechanism are oblique. Meanwhile, wedge sliding are the most possible slope failure type happen ini Side-2 with 27,05% chance.

Study of Weathering and Rock Mass Quality using the Geological Strength Index (GSI) method on the Tuntun mine road Banggai Regency Central Sulawesi Province

Abstract The mining road in the Tuntun area of Banggai Regency, Central Sulawesi Province has experienced a landslide. The mining road mitigation engineering is a concern for the sustainability of road use. The study area is composed of peridotite rocks which are included in the Ophiolite (Ku) rock formation, where these rocks undergo a very strong deformation process by showing the fractured rock conditions. The Study of Weathering and Rock Mass Quality Using the Geological Strength Index (GSI) Method on this mine road is the focus of this research. The Geological Strength Index (GSI) is a rock mass classification system developed to assist the inaccurate Rock Mass Rating System (RMR) in determining the quality of rock masses that have very poor conditions or have undergone very strong rock deformation. using the GSI value by using two quantitative parameters, namely the condition of the discontinuity plane and the density of the discontinuity plane. The value of the Geological Strength Index (GSI) at location points 1, 2, 3, 4 and 5 is 32,17,12,2, 33.4 and 23. The rock mass value indicates that the rock mass quality in the study area has poor rock mass quality. to very bad. The results of this investigation become a reference in the method of handling slopes on mining roads.

Studi Skala Efek Pada Uji Kuat Tekan Uniaksial Terhadap Batulempung Formasi Pulau Balang dan Formasi Balikpapan Di Samarinda

Rock mass is a volume of rock consisting of rock material in the form of minerals, texture, composition and also consisting of discontinuous planes, forming a material and interconnected with all elements as a unit. The rock mass itself is composed of several intact rocks which basically have isotropic, continuous and homogeneous properties. However, the conditions found in the field are different, namely anisotropic, discontinuous and heterogeneous. These properties will certainly influence the test results in the uniaxial test. There are several factors that influence the results of uniaxial rock tests, one of which is the scale effect. The purpose of this test is to determine and analyze the effect of rock sample size on the uniaxial compressive strength value of claystone. This rock testing was carried out at the Mineral and Coal Technology Laboratory and the rock sampling locations were in Palaran District, Samarinda City and in North Samarinda District, Samarinda City. In this uniaxial compressive strength test, 3 side widths with different lengths will be used. After carrying out the uniaxial compressive strength test, the average uniaxial compressive strength test value was obtained in each formation, such as the Balang Island formation, the average rock compressive strength test value was 1.68 Mpa and the Balang formation, the average rock compressive strength test value was 3.10. Mpa. Based on these results, it can be concluded that the larger the sample size, the smaller the rock compressive strength test value tends to be.

Comparison between PA and PWI/TFM Techniques for Non-Destructive Testing of Carbon Steel Weld

The Total Focusing Method (TFM) technique is an advanced Non-Destructive Testing (NDT) Ultrasonic Testing (UT) technique well known for its representative images of high resolution. It was firstly developed together with Full Matrix Capture (FMC) acquisition which can be substituted later by Plane Wave Imaging (PWI) acquisition for its improved acquisition speed and gain reserve without lowering the image quality. For these advantages, the PWI/TFM technique is tending to be more and more widely implemented. This article presents some results of the related study on PWI/TFM technique. Starting by PWI/TFM reconstruction principles, mainly on the influences of beam steering settings and corresponding inspection coverage in predefined Region of Interest (ROI), it focuses on the comparison on the indication amplitudes of planar discontinuities between classical Phased Array (PA) technique and PWI/TFM technique.

Dynamic stress analysis of rock joints under railway loading

The proper estimation of stresses generated by the passage of a train is fundamentally important to the serviceability and longevity of railways, and yet very limited knowledge is available where the track substructure is built on a jointed rock mass. The present study introduces an analytical solution for estimating the ground stresses arising from moving wheel loads, causing a change in the three-dimensional stress state in the track formation, in relation to the stress variation with depth and along the longitudinal track section – that is, the direction of train passage. Based on 21 case histories, an array of field measurements and numerical simulations covering a wide range of freight tonnage, train speeds and different formation conditions were considered to validate the proposed analytical solution. The proposed methodology (analytical solution) was then applied to a jointed rock subgrade to determine the normal and shear stresses acting along a specific discontinuity plane. The main analytical outcome demonstrates that the orthogonal vertical and shear stresses present different and phase-shifted history plots for homogeneous ground conditions with principal stresses rotation. However, conversely for a jointed subgrade, the normal and shear stresses along the discontinuity have the same history plot pattern and are in phase. As a practical guide, the results from this study would help to define which cyclic loads should be applied in laboratory tests to simulate realistic traffic patterns of trains travelling over a jointed rock subgrade.

Modeling the failure process of rock masses using a 3D nodal-based continuous-discontinuous deformation analysis method

A three-dimensional nodal-based continuous-discontinuous deformation analysis method (3D-NCDDAM) is developed in this study for modeling the failure process of rock masses. In the 3D-NCDDAM, four-node tetrahedral elements which can be automatally generated are used to discretize the problem domain. To reduce computational cost, and effectively model the failure process of rock masses at concerned regions, the problem domain is devided into two types of regions, namely, the “non-destructive region” and “possible destructive region”. The non-destructive region is mainly used to reduce the boundary effects on the numerical results, and is regarded transitional zone in which the failure of rock masses is not considered. For the possible destructive region, artificial joint elements are inserted, and the failure of these joint elements is used to represent fracture initiation and propagation in rock masses. Additionally, the contact potential which is initially proposed in finite-discrete element method (FDEM) is incorporated into the 3D-NCDDAM to simuate the opening and slipping of discontinuous structural planes involved in rock masses’ failure process. Note that the difficultly in determing contact types in the traditional 3D discontinuous deformation analysis (3D-DDA) method is avoided in the 3D-NCDDAM. The proposed 3D-NCDDAM can be treated as a hybrid method, which inherite both the advantage of DDA method and FDEM. To validate the 3D-NCDDAM, seven numerical examples are conducted. The numerical results indicte that the 3D-NCDDAM can effectively model the failure process of rock masses in both experimental scale and engineering scale.

A method for analyzing discontinuities characterization using the integration of underground drift point cloud with 3DEC software

The geometric statistical characteristics of rock mass discontinuities, such as mean trace length and intensity, cannot be measured directly and require the use of statistical tools (such as sampling lines, sampling windows, and drilling) for analysis. In this paper, we propose a method for extracting discontinuity characteristics using the 3DEC software in three-dimensional (3D) drift models (3DM). Specifically, we introduce the Surface Disk Discontinuity Model (SDDM) as a representation model for planar and linear discontinuities identified in point clouds. By importing the 3DM and SDDM into 3DEC and utilizing a multi-circular window, we calculate the mean trace lengths and two-dimensional (2D) intensity (P21). Additionally, we propose a method to estimate the three-dimensional (3D) intensity (P32), which provides a more comprehensive reflection of the discontinuous characteristics in different spatial orientations. To validate the proposed method, we apply it to the underground drift of the Jiapigou gold mine in Jilin Province to extract the geometric statistical characteristics of discontinuities. The results demonstrate that our method successfully captures the orientation, trace length, and P32 characteristics of four dominant discontinuity groups in the study area. This approach proves to be an effective technique for utilizing 3D laser scanning to obtain accurate discontinuity characteristics of rock mass.

Rockfall Analysis from UAV-Based Photogrammetry and 3D Models of a Cliff Area

The application of Unmanned Aerial Vehicles (UAVs), commonly known as drones, in geological, geomorphological, and geotechnical studies has gained significant attention due to their versatility and capability to capture high-resolution data from challenging terrains. This research uses drone-based high-resolution photogrammetry to assess the geomechanical properties and rockfall potential of several rock scarps within a wide area of 50 ha. Traditional methods for evaluating geomechanical parameters on rock scarps involve time-consuming field surveys and measurements, which can be hazardous in steep and rugged environments. By contrast, drone photogrammetry offers a safer and more efficient approach, allowing for the creation of detailed 3D models of a cliff area. These models provide valuable insights into the topography, geological structures, and potential failure mechanisms. This research processed the acquired drone imagery using advanced geospatial software to generate accurate orthophotos and digital elevation models. These outputs analysed the key factors contributing to rockfall triggering, including identifying discontinuities, joint orientations, kinematic analysis of failures, and fracturing frequency. More than 8.9 × 107 facets, representing discontinuity planes, were recognised and analysed for the kinematic failure modes, showing that direct toppling is the most abundant rockfall type, followed by planar sliding and flexural toppling. Three different fracturation grades were also identified based on the number of planar facets recognised on rock surfaces. The approach used in this research contributes to the ongoing development of fast, practical, low-cost, and non-invasive techniques for geomechanical assessment on vertical rock scarps. In particular, the results show the effectiveness of drone-based photogrammetry for rapidly collecting comprehensive geomechanical data valid to recognise the prone areas to rockfalls in vast regions.

A computationally efficient approach to automatically extract rock mass discontinuities from 3D point cloud data

Geometric characterization of discontinuity planes in rock masses is an essential practice in rock engineering. Analysis of 3D point cloud data of exposed rock surfaces acquired by remote sensing techniques is becoming widespread due to its benefits such as quality and quantity of the data. In this study, we propose a computationally efficient workflow to extract planar discontinuities from point cloud data automatically. The proposed workflow includes voxel-grid downsampling as a preprocessing step to smooth the point cloud, forming a covariance matrix and applying singular value decomposition to estimate normal vectors, primary clustering to assign the normal vectors to a cluster, secondary clustering to separate individual discontinuity planes in each set, and plane fitting using RANSAC to extract the orientation and location of each discontinuity plane. The proposed workflow's ability to accurately extract discontinuities and calculate their orientations in a computationally efficient procedure was demonstrated through the analysis of two case studies of rock face point clouds.

Probability-Based Design of Reinforced Rock Slopes Using Coupled FORM and Monte Carlo Methods

The efficiency of the first-order reliability method (FORM) and the accuracy of Monte Carlo simulations (MCS) are coupled in probability-based designs of reinforced rock slopes, including a Hong Kong slope with exfoliation joints. Load–resistance duality is demonstrated and resolved automatically in a foundation on rock with a discontinuity plane. Other examples include the lengthy Hoek and Bray deterministic vectorial procedure for comprehensive pentahedral blocks with external load and bolt force, which is made efficient and more succinct before extending it to probability-based design via MCS-enhanced FORM. The FORM–MCS–FORM design procedure is proposed for cases with multiple failure modes. For cases with a dominant single failure mode, the time-saving importance sampling (IS) and the fast second-order reliability method (SORM) can be used in lieu of MCS. Two cases of 3D reinforced blocks (pentahedral and tetrahedral, respectively) with the possibility of multiple sliding modes are investigated. In the case of the reinforced pentahedral block, direct MCS shows that there is only one dominant failure mode, for which the efficient method of importance sampling at the FORM design point provides fast verification of the revised design. In the case of the reinforced tetrahedral block, there are multiple failure modes contributing to the total failure probability, for which the proposed MCS-enhanced FORM procedure is demonstrated to be essential. Comparisons are made between Excel MCS and MATLAB MCS.

Borehole TV Imaging Technology for Horizontal Directional Drilling Based on an Optimization Algorithm for Structural Planes

The horizontal directional drilling technology combined with the borehole TV imaging technology can be used to obtain most of the geological information in conventional adit exploration. This combination has little impact on the environment and is free from topographic constraints, thus contributing to green exploration. However, conventional algorithms for structural planes fail to accurately extract information on the attitudes of incomplete structural planes in boreholes of any azimuth. Moreover, existing borehole TV devices are mostly cable-based and, thus, difficult to put in place in horizontal drilling. They are prone to get stuck in the collapse section of boreholes, thus damaging the devices. Given these challenges, this study develops an optimization algorithm for structural planes: (1) first, information on multiple points in the 2D unfolded view is fitted using a sinusoidal function curve, three arbitrary points are constructed using the fitted curve, and the normal vector of the plane determined by the three points is calculated; (2) the normal vector in the geodetic coordinate system is obtained after two rotations of the spatial coordinate system based on the theory of transformation of Cartesian coordinate system; (3) finally, the dip angle and dip direction of a structural plane are calculated using the normal vector in the geodetic coordinate system. By making the best use of the information on multiple points in the 2D unfolded view, the optimization algorithm can overcome the defect that is difficult for conventional two-point methods to locate the highest and lowest points of discontinuous structural planes. Therefore, the optimization algorithm applies to calculating the attitudes of structural planes in boreholes of any azimuth. Based on this optimization algorithm, this study successfully develops a cable-free, storage-based TV device for boreholes of any azimuth. This device was employed for laboratory experiments on 20 complete structural planes and 32 incomplete structural planes. As indicated by the experiment results, the optimization algorithm proposed in this study is applicable to many types of structural planes, with a dip direction error of less than 10° and a dip angle error of less than 5°, thus meeting the production requirements.

SITE SELECTION FOR ENGINEERING STRUCTURES AND EARTHQUAKE

An earthquake is a natural event and it is quite easy and beneficial to convert it to wealth rather than disaster. A strong earthquake exerts its catastrophe on the buildings/structures found in the soil grounds. There is not even a single case study that creates catastrophe where structures/buildings are erected on/in the rocky ground whose extensive planar discontinuities are free of expansive clay minerals. Every strong earthquake has proven this reality. The last earthquake with a magnitude of 7.7 hit Pazarcik/Kahramanmaras/Turkey on the 6th of February. The epicenter is at the fertile soil plain of the township Çigdemtepe (Crocushill)/Pazarcik which has been erected on the weak rock of clayey limestone. Despite that, casualty (the number of dead and injured) is zero in the township of Crocushill) whereas a very severe disaster has occurred in (a) Battalgazi and (b) Harran soil plains which are orderly 160 and 200 km away from the epicenter. The reasons behind this fact are “the seismic energy attenuates in strong rock over a thousand times more than that in thick (t>20 m) soil mantle” and “wave velocity in rock is practically 30 times higher than that in saturated soil”. It should also be noted that there is no liquefaction in the rock. If the locations of engineering structures are chosen other than irrigable agricultural areas, fertile soils and possible landslide areas, no problems will be encountered. It is not important where and when the earthquake will occur, but where it will collapse. These hazardous areas also overlap with agricultural areas.

Breccia for Diversion Tunnel Construction at Bener DAM in Purworejo, Central Java, Indonesia: Fragments, Matrix, RMR

This study aimed to explain the detailed engineering geology investigation which has breccia geological units on Diversion Tunnel at Bener Dam, Purworejo Regency, Central Java Province. The investigation includes geological conditions both breccia fragment and matrix, to Rock Mass Rating (RMR) values each unit. The data were taken from face mapping tunnel with interval 10 meters at inlet 1-390 and 841-865 meters. The findings showed that geological engineering units consisted of Monomict Breccia. The geological units can be divided into geological engineering; Monomict Breccia Matrix (RMR 72-92), Polymict Breccia Matrix (RMR 82), Andesite Fragmen (RMR 52-62), and Tuff Fragmen (RMR 79-84). The discovery of Andesite and Tuff Fragments needs to be handled differently than Monomict Breccia or Polymict Breccia. Andesite Fragment unit with discontinuity of sheeting joint requires rock bolt reinforcement to be installed perpendicular to the discontinuity plane. While the dominant unit is the Tuff Fragment which has a UCS value of 5-7 MPa, it is not recommended to use the blasting excavation method even though it has an RMR value of 79-84.

LLT-tandem inspection of thick-section welds using phased-arrays probes

The examination of welds for planar discontinuities whose plane lies perpendicular to the inspection surface is an inspection problem for which tandem ultrasonic testing has long been used as a solution. There exist standards that set out how to design a conventional tandem examination with 45° transverse-wave probes as well as how to design an LLT-tandem inspection in which angled longitudinal waves reflect from the far surface of a component so that they can undergo mode conversion on the face of a defect perpendicular to the surface and return to a receiving probe as transverse waves. For the End-of-Manufacture inspections of the high-integrity components of Hinkley Point C power station, the LLT-tandem technique has been applied to thick-section welds with internal cladding, by using phased-array probes to create a series of “crossing depth” configurations that cover the thickness of the weld. The considerations used for the design of the probes are explained. The resulting design covers the thickness with a 5 mm pitch with a single mechanical arrangement of two separate probes. The design enables coverage of welds with thickness exceeding 200 mm. Other multi-leg reflection modes are possible and the data analysts for these inspections were required to understand and recognise the other modes that could occur. The LLT-tandem inspections form part of multi-technique inspections for a number of high-integrity component welds that have been successfully subjected to Inspection Qualification prior to being used for the final examination of these welds.

Kelvin–Helmholtz instability at the interface of H ii region and molecular cloud under the influence of ambipolar diffusion: a discontinuous model of the interface

ABSTRACT For typical flow velocities in the interstellar medium (ISM), the Kelvin–Helmholtz instability (KHI) may result in the development of structures in molecular clouds near the interface between the clouds and H ii regions flowing past them (Berné et al. 2010). Ambipolar diffusion (AD) is one of the significant mechanisms considered frequently in the dynamics of molecular clouds. It may play a relevant role in the development of the KHI in the interface of the H ii region and the molecular clouds. Here, we examine the role of AD in the evolution of the KHI, using linear perturbation analysis. We model the interaction of two regions as a planar discontinuity separating two fluids in relative motion. Linear analysis, for a certain range of magnetosonic Mach number of flow ($\mathcal {M}_{sA1}\lt 1$), shows that AD has a destabilizing effect on the KHI and consequently decreases the e-fold time-scale of instability. The results indicate that AD is more effective on the KHI for large magnetosonic Mach numbers than for low magnetosonic Mach numbers. This may give rise to the development of larger numbers of KH structures in high-velocity flows. The results also indicate that AD is more effective for perturbation wavelengths $\lambda _{\rm KH} \ \lt \ 1\rm pc$ than for $\lambda _{\rm KH}\gt 1\rm pc$. This nominates a length-scale ($L=1 \rm \, pc$) above which AD is not important for the formation of KH structures. Conforming to the results, AD is proposed as a triggering factor in the development of the small-scale KH structures in the regions of high-velocity streams in ISM.

Effect of a singular planar heterogeneity on tensile failure

Many rocks contain planar heterogeneities, in the form of open fractures, veins and/or stylolites, but scarce data exist on how strength and fracture pattern formation is affected by the presence of a singular planar heterogeneity in an otherwise uniform matrix. The mechanics of stylolite-bearing and/or fractured limestone is of interest to several engineering applications, from quarries to subsurface gas or geothermal reservoirs. We have performed Brazilian Disc tests on pre-fractured Indiana limestone samples and Treuchtlinger Marmor discs which contain cohesive stylolites, investigating Brazilian test Strength and the resulting fracture pattern. All experiments were filmed, and where possible analyzed with particle image velocimetry. When viewed in 2D, the planar discontinuity was set at different rotation angles compared to the principal loading direction, where perpendicular to the loading direction is defined as 0⁰. The results show that all samples are weaker than their intact counterparts. For the pre-fractured Indiana limestone, there is 10–75% angle-dependent weakening. However, in the samples with a stylolite, strength is weakened by 35–75%, independent of direction. Several new cracks appeared when fracturing a stylolite-sample, where the orientation is heavily influenced by the stylolite orientation. The fracture pattern and associated stress drops are more complex for high angles. In these samples always more than one fracture formed, whereas in pre-fractured samples usually only one new fracture formed. This suggests a potential for more permeability increase when hydrofracturing a stylolite-rich interval. Comparison with Finite Element Models indicates that this difference in fracture pattern is caused by the strength contrast between the anastomosing stylolite zone and the matrix material, leading to stress concentrations effects. This causes (micro-) fracture nucleation to occur locally, promotes fracture coalescence and fracture growth at lower overall sample-load conditions compared to intact samples.

A Partitioned Rigid-Element and Interface-Element Method for Rock-Slope-Stability Analysis

The stability analysis of rock slopes has been a prominent topic in the field of rock mechanics, primarily due to the widespread occurrence of discontinuous structural planes in rock masses. Based on this complex characteristic of rock slopes, this paper proposes a novel numerical method, the Partitioned-Rigid-Element and Interface-Element (PRE-IE) method. In the PRE-IE method, the structure is modeled as several rigid bodies and discontinuous structural planes, which are, respectively, divided into partitioned rigid elements and interface elements. Taking the contact force of node pairs and the displacement of the rigid body centroid as mixed variables, according to the principle of minimum potential energy, the governing equations of PRE-IE can be established using the Lagrange multiplier method and then solved using the nonlinear contact iterative method and the incremental method. A classic case study demonstrates that using the failure of all contact node pairs as the criterion for slope failure is appropriate. This criterion is objective and avoids the potential impact of personal bias on safety factor calculations. Two numerical examples of differently shaped slopes are provided to verify the correctness and validity of the PRE-IE method. By comparing the safety factor calculated using the PRE-IE method with those obtained from other different methods, as well as comparing the computational time, it is shown that the PRE-IE method, in combination with the SRM, can accurately and efficiently analyze the stability problems of rock slopes.