Step-path Failure Research Articles

Step-path failure mechanism and stability analysis of water-bearing rock slopes based on particle flow simulation

Step-path failure is a typical damage mode of rock slope featuring intermittent joints. In order to investigate the effect of water-fracture interaction on the stepped failure, laboratory experiments of rock materials and numerical simulation of slopes with intermittent joints were conducted. At the laboratory scale, the influence of water-fracture interaction on the mechanical characteristics and acoustic emission response of step-path failure in rocks was examined, and the particle flow model parameters were calibrated for uniaxial testing. At the field scale, the step-path failure process of the rock slope near Longmenqiao reservoir was numerically analyzed using the particle flow method to assess the effects of water and joint distribution on failure. Laboratory findings suggest that compared with dry red sandstone, the average uniaxial compressive strength and average elastic modulus of saturated red sandstone decrease by 35.82% and 23.33%, respectively. The increase in fissure angle in sandstone results in enhanced strength and stiffness, alongside a transition from shear to tension failure mode, with a delayed occurrence of large-scale acoustic emission events. In particular, within the 30°–60° range, the uniaxial compressive strength and elastic modulus of saturated sandstone increase by 66.78% and 29.64%, respectively. The analysis of crack propagation and stress field during slope deformation shows that step-path failure is a progressive process from bottom to top, and revealed the control mechanism of joint and bridge angle on slope stability. The research results enhance the understanding of the step-path failure mechanism and provide important theoretical support for the stability evaluation and landslide monitoring of rock slopes with intermittent joints.

Peridynamic modeling of step-path failure in rock slopes

This work is devoted to investigating the step-path failure of rock slopes using peridynamic theory. To this end, an extended bond-based peridynamic model that can explicitly distinguish between tensile and shear cracks from mixed-mode fracture phenomena, previously proposed by the authors, is first introduced. Then, the fracture processes of gypsum specimens with various triple-flaw distributions under uniaxial compression are simulated at a laboratory scale. Tensile, shear, and mixed tensile-shear failure modes are reproduced, and the feasibility of the numerical tool is verified via comparison with experimental observations. Finally, the progressive failure of rock slopes at the field scale is analyzed, in which crack initiation, propagation, coalescence, and eventual structural damage are well captured. The types of crack propagation and coalescence predicted in this study contribute to understanding step-path failure mechanisms in experimental research and nature.

Mechanical response of sandstone exposed to monotonic and multilevel fatigue loading: Insights from deformation, energy and acoustic emission characteristics

Rock masses containing intermittent discontinues under dynamic loading have rarely been investigated, although step-path failure frequently occurs in field engineering. This work aims to explore the action mechanism of dynamic cyclic loading and discontinuities on step-path failure. Four treatments including the control (Intact sandstone), pre-flawed samples with assemblage of two 30° dip fissures (type-I), assemblage of 10° and 65° dip fissures (type-II) and assemblage of two 65° dip fissures (type-III) were replicated. Laboratory experiments consisted of conventional uniaxial compression tests (UCT) and multilevel constant-amplitude fatigue tests (MLFT). Real-time acoustic emission (AE) monitoring was conducted along with scanning electron microscopy (SEM) observation on the fractured surfaces. Results indicated that the mechanical properties, energy evolution, AE characteristics and microscopic features of sandstones were significantly influenced by pre-existing fissures. The weakened rates of peak strength ranged from 2.80% to 85.63%, and regardless of loading methods, always followed the sequence of type-I > type-II > type-III. We contribute the weakening effect to the reduction in the effective bearing area and the increase in the dip angle of the rock bridge. With the same pre-fissure morphology, the sandstone under MLFT has enhanced its deformation resistance compared to under UCT. In addition, the maximum AE count/energy during the whole cyclic stage were always significantly lower than those during the monotonic rising process. SEM images revealed that long-term fatigue loading lead to numerous micro pores and transgranular cracks. Ultimately, a simple constitutive model was proposed based on the statistical damage mechanics and geometric damage theory.

Experimental and numerical study of step-path failure in jointed rocks

To study the failure process and mechanism of step-path failure in jointed rocks, experimental and numerical methods are conducted. In the damage evolution model, the previous damage field is introduced into the following finite element calculation. Based on this way, the initiation, propagation and coalescence of cracks can be simulated and presented. According to the results of numerical simulations and physical experiments, the brittle fractures caused by tensile stress may be the main reason of step-path failure, which interact with natural discontinuities to form macroscopic shear planes. Shear cracks also play an important role in the process of step-path failure, which can accelerate the process of step-path failure. Additionally, the proposed damage evolution model has a good agreement with the test results. According to the test and numerical results, the stability of jointed rocks by step-path failure is discussed, and the possible slides due to step-path failure are classified and analyzed, and the corresponding criterion and protective measures are also given. These results are expected to improve the understanding of step-path failure in rocks and can be used to analyze the stability of rock structures and rock masses, such as the slopes tunneling construction or, excavated underground openings.

A novel DIC-based methodology for crack identification in a jointed rock mass

Crack identification in brittle rocks is a challenging problem in rock mechanics. To represent the details of jointed rock masses, rock-like specimens containing inclined joint sets were generally prepared by three-dimensional (3D) printing using sand. Digital image correlation (DIC) was employed for full-field deformation measurement during loading. The results show that the sand 3D-printed specimen has distinct advantages in the preparation of jointed rock masses. DIC was extended to measure the displacement vector field around newly propagated cracks. Two types of cracks are recognized: tensile and shear cracks. Two different coalescence patterns are classified: step-path failure and planar failure. A covariance matrix-based multivariate measure, the rate of effective variance change (REVC), was proposed to quantify the dispersion of strain data. The variation in the strain dispersion measure was found to be closely related to the crack type. For the first occurrence of tensile and shear cracks, the rates of mutation (RMs) are within the ranges of 1.56–3.42 and 14.54–86.44, respectively, which can be considered a new crack identification criterion. A virtual extensometer method based on DIC was established to interpret the variation mechanism of the REVC associated with different crack types.

Tensile behavior of Brazilian disks containing non-persistent joint sets subjected to diametral loading: experimental and numerical investigations

Structural defects are part of the inherent characteristics of rock masses. They can be found in fishers, joints, and beddings and can be divided into persistent or non-persistent ones. The coalescence of non-persistent cracks may lead to the formation of persistent joints under the tensile stress field, leading to rock mass instability. The mechanical behavior of non-persistent jointed disks under tensile stress has important implications for rock structures. In this paper, experimental and Discrete Element Method (DEM) numerical simulation approaches were adopted to investigate the effect of joint continuity factor (the relationship between joint length and rock bridge length), bridge angle, joint spacing, and loading direction in relation to joint angle on the tensile strength and stiffness as well as failure pattern. Cement-mortar-based Brazilian disks containing open non-persistent joints were constructed and subjected to diametral loading and simulated using a two-dimensional Particle Flow Code (PFC2D). The investigations revealed that the tensile strength, stiffness, and failure pattern of Brazilian disks are highly affected by non-persistent pre-existing cracks. The increase of joint continuity factor and loading direction leads to the reduction of both tensile strength and stiffness. However, when spacing increases, tensile strength and stiffens have a minimum at the average spacing, but it was concluded that bridge angle does not affect both parameters. Finally, the results showed that the experimental and numerical approaches are in good agreement, and almost all the parameters affect the failure pattern, and some failure patterns such as step-path failure, splitting, or sliding may occur as a function of non-persistent joint sets.

In-depth field survey of a rockslide detachment surface to recognise the occurrence of gravity-induced cracking

This work describes field evidence of gravity-induced cracking that has been identified on the failure scar of a small rockslide (volume = 6–7 m3) that occurred in March 2004 in the Rosandra Valley near the town of Trieste (north-eastern Italy). This shallow rock slope failure involved a limestone slope that was re-profiled through blasting about 135 years ago for the construction of an old railway, which has now been reconverted into a cycle path. Field observations ascertained that the slope failure was characterised by a cascading rupture process in which adjacent blocks collapsed in rapid sequence as a result of the progressive breakage of a number of rock bridges (domino-like collapse), thus highlighting a progressive failure mechanism. The rock bridges were localised in eccentric positions on lateral and rear release planes and failed in tension as a result of combined tensile and bending loading conditions (tensile strength of intact rock = 5 ± 2 MPa). The rockslide was triggered by cyclic loading related to freeze-thaw (ice jacking) that occurred over some consecutive days of daily snowmelt and nocturnal frost. The recognition of newly formed fractures also proves the current progressive development of 3D rupture surfaces of some unstable blocks susceptible to failure. This study provides innovative content to detect gravity-induced cracking in the field, which is an important precursory sign relating to the progressive failure of rock slopes. Gravity-induced cracks can be distinguished from pre-existing discontinuities for their more irregular profile (zigzag pattern), rougher surface, lower persistence and potentially different orientation. This study also provides some new insights into the step-path failure process of steep rock slopes. The mechanical process of initiation, growing and coalescence of gravity-induced fractures is strongly time- and stress-dependent. In the absence of external changing factors that profoundly modify the acting stress state (for instance, engineering countermeasures), progressive failure is a dynamic and irreversible process. For excavated slopes, the creation of a new rock face may abruptly provide the kinematic freedom of potentially unstable blocks, thus determining a very quick stress redistribution. If the mechanical system is not able to redistribute the stress on resisting stiff parts without overcoming the intact rock strength, gravity-induced cracking initiates and propagates until reaching slope collapse within times that are much shorter (from hours to 100–200 years) compared to natural rock slopes subjected to long-lasting geological processes (from 1000 to 2000 up to 10,000–20,000 years).

Experimental Investigation on Uniaxial Compression Mechanical Behavior and Damage Evolution of Pre-Damaged Granite after Cyclic Loading

Failure behavior of pillars in deep mines is affected by various cyclic loads that cause initial pre-damage. Pillars will be further damaged and developed in the long-term compressive stress until they are destroyed. To reveal the strength characteristics and crack damage fracture laws after rock pre-damage, uniaxial compression tests were carried out on granite specimens damaged by cyclic loading using the digital speckle correlation method. The experimental results indicate that the mechanical properties of pre-damaged specimens show large damage differences for different cycles. The damage variable of the pre-damaged specimens increases with the increase of cycle number and confining pressure. The damage of specimens is primarily due to the strength weakening effect caused by cycle numbers, and the confining pressure restriction effect is not obvious. The evolution laws of uniaxial compression damage propagation in the pre-damaged specimens show differences and obvious localization phenomenon. Pre-damaged specimens experienced three failure modes in the uniaxial compression test, namely tensile shear failure (Mode I), quasi-coplanar shear failure (Mode II), and stepped path failure (Mode III), and under different pre-damage stress environments with high confining pressures, the failure modes are dominated by Mode II and Mode III, respectively.

Numerical Study of Anisotropic Weakening Mechanism and Degree of Non-Persistent Open Joint Set on Rock Strength with Particle Flow Code

The strength of a rock cut by non-persistent open joint set is controlled by complex interactions of the joint network and intact rock bridges. An extensive series of uniaxial numerical tests of the particle models are carried out under different joint fabrics and rock compression-tension strength ratios. The test results show joint dip angle is the main factor controlling the overall anisotropic strength characteristics. With joint dip angle increasing, the main failure modes successively appear as splitting failure, block rotation failure, step-path failure, planar failure, and splitting failure. Accordingly, the strength generally shows a trend of decreasing first and then increasing, and the joint dip angle corresponding to the minimum strength is biased towards 0°, usually at 15°–30°. The damage of rock bridges is mainly controlled by tensile failure, except in planar failure mode. Joint spacing has an impact on the local anisotropic strength characteristics. The joint spacing and persistence ratio jointly control the degree of penetration difficulty of the rock bridges. The compression-tension strength ratio of intact rock uniformly affects the absolute magnitude of the jointed rock strength and does not affect its anisotropic characteristics. Based on the weakening mechanism, an empirical strength formula is established to realize the practical equivalent characterization of the anisotropic weakening degrees of the non-persistent open joint set on the rock strength.

Mechanical behaviors of the brittle rock-like specimens with multi-non-persistent joints under uniaxial compression

The stability of rock engineering applications is significantly influenced by the mechanical behavior of jointed rock masses. However, the deformability, strength and failure characteristics of non-persistent jointed rock specimens have not been examined comprehensively. In this paper, laboratory tests and discrete element method simulations are used to investigate the influence of angle (α), spacing (S), joint length (L), and rock bridge length (B) on uniaxial compressive strength (UCS), Young’s modulus and failure processes of brittle rock-like specimens with multi-non-persistent joints. The orthogonal experimental method is used to quantify the influence of four geometric factors on the UCS and Young’s modulus through comparing different range values. The results show that the joint inclination angle has the most significant influences on UCS and Young’s modulus. The failure patterns can be classified into six categories: (1) stepped path failure caused by wing cracks; (2) stepped path failure caused by wing cracks and shear cracks; (3) vertical failure caused by wing cracks; (4) stepped path failure caused by anti-wing cracks; (5) transfixion failure along the diagonal caused by shear cracks; (6) intact failure. The evolution of micro-cracks divides the numerical stress-strain curve into four stages: stage I, linear elastic stage; stage II, stable development stage of micro-cracks; stage III, increment stage of micro-cracks before peak strength; stage IV, increment stage of micro-cracks after peak strength. Comparison between the experimental and numerical results confirms the capacity of the DEM model to simulate the non-persistent jointed rock specimens. These experimental and numerical results enhance our understanding of the influence of joints on the mechanical behavior of rock masses.

Characteristics of failure area and failure mechanism of a bedding rockslide in Libo County, Guizhou, China

Owing to the continuous rainfall, a bedding rockslide occurred at a construction site on the San-Li highway (Sandu County to Libo County) at 18:05 (UTC+8) on September 23, 2017, in Libo County, Guizhou Province, China. This bedding rockslide caused three deaths, six injuries, and an accumulation zone of approximately 1.8 × 105 m3 of medium weathered limestone that blocked the main line of the M ramp. To explore the triggering factors of this rockslide, the engineering geological condition, hydrogeological condition, slope excavation scheme, and statistics of rainfall data were investigated based on field investigations and geophysical drilling. The blasting failure of the upper unstable and dangerous rock masses after the bedding rockslide was analyzed. Three instability behaviors characteristics are distinguished: (1) the bedding characteristics of the rock formation and weak interlayer, (2) the steep slope (the largest dip angle being 46°), and (3) the appearance of the free face induced by the slope excavation. The results indicate that the above conditions are objective factors, and continuous rainfall triggers the bedding rockslide. The landslide follows the step-path failure mode.

Cracking process of a granite specimen that contains multiple pre‐existing holes under uniaxial compression

AbstractThe pre‐existence of openings, which play an important role in the mechanical properties and cracking behaviours of rock, is prevalent in rock mass. The interaction among pre‐existing openings (or holes) complicates the instability problems when rock contains multiple holes. Studying the strength failure behaviour of rock that contains multiple pre‐existing holes contributes to the fundamental knowledge of the excavation and stability of underground rock engineering. In this study, first, a series of uniaxial compression tests were performed on granite specimens that contain multiple small holes to investigate the effect of the geometry of pre‐existing holes on the strength and fracture behaviours of rock. The crack initiation, propagation and coalescence process, and acoustic emission (AE) characteristics were investigated using photographic and AE monitoring. Three failure modes were identified, ie, splitting failure, stepped path failure, and planar failure modes. Second, a set of micromechanical parameters in the PFC3D model were calibrated by comparison with the experimental results of an intact granite specimen. The numerically simulated peak strength, peak strain, and failure mode of preholed specimens were consistent with the experimental results. In accordance with the numerical results, the failure modes of the preholed specimens were dependent on the bridge angle and number of holes. Last, the internal fracture characteristics of numerical specimens were revealed by analyzing the horizontal and vertical cross sections at different positions.

Numerical investigation of the mechanical properties of coal masses with T-junctions cleat networks under uniaxial compression

Evaluating the mechanical properties of coal masses is essential to the further understanding of coal bumps, pillar design, roadway support design and movement of overlying strata, etc. It is generally understood that the cleat network of a coal mass plays a major role in determining its mechanical behavior. Based on an extensive review of the characteristics of coal cleats, a novel method was proposed to generate a realistic model of T-junctions cleat network. Using the synthetic rock mass (SRM) approach, five sets of cubic cleat networks, with uniform sizes of 1 × 1 × 1 m3, were initially generated. Afterwards, smaller cubic cleat networks, with edge lengths of 5 cm, 10 cm, and 15 cm, were randomly cut from the large cubic cleat networks and then embedded into bonded-particle models (BPMs) to form SRM coal specimens of varying sizes. The SRM coal specimens were tested under unaxial compression conditions and the results of the tests were compared with the experimentally determined mechanical properties. The scale effect of uniaxial compression strength (UCS), relationships between failure modes and stress-strain behaviors, and the principal causes of fluctuations in the stress-strain curves were intensively investigated. The results demonstrated that the existence and intensity of scale effect mainly depends on sampling methods and cleat network geometry. SRM coal specimens whose failure modes were intact matrix failure and planar failure, and block failure and step-path failure exhibit typical strain softening behavior and fluctuating ductile behavior, respectively, in their stress-strain curves. Moreover, the fluctuations in the stress-strain curves are attributed to the changes in cleat aperture throughout the uniaxial compression tests.

Crack Propagation and Coalescence of Step-Path Failure in Rocks

To provide insight into the understanding of step-path failure in rocks, gypsum specimens containing various configurations of preexisting flaws are used to investigate the crack behaviors of step-path failure in rock slopes under compression in terms of the inclination angle and number of flaws. The results show that step-path failure is usually caused by wing cracks (or tensile cracks) when the preexisting flaws are isolated or when two preexisting flaws are adjacent. Additionally, with an increase in the number of flaws, step-path failure is more likely to be caused by mixed wing-secondary crack formation (or tensile–shear crack formation), indicating that the mechanism of step-path failure is associated with the characteristics of the flaw (including the number of flaws, flaw inclination angle, flaw spacing, etc.). In the process of step-path cracking and failure, wing cracks can initiate at or near the middle of a preexisting flaw when the preexisting flaw has a small inclination angle (e.g., 0° or 15°), and secondary cracks usually propagate in three directions: (1) in the horizontal direction of the specimen; (2) coplanar or quasi-coplanar to the preexisting flaw; (3) in the direction perpendicular to that of wing crack propagation. Additionally, the closer the inclination angle is to 90°, the harder the secondary crack initiates. In addition, four types of coalescence cracks are identified from the specimens containing two preexisting flaws. The peak load of the specimen is influenced by the inclination angle; the closer the inclination angle is to 90°, the greater the peak load of the specimen. Furthermore, the equation describing the wing crack path of an isolated flaw, two types of spalling formations and the characteristics of the wing and secondary crack surfaces are determined and discussed.

The Effect of Joint Dip Angle on the Mechanical Behavior of Infilled Jointed Rock Masses under Uniaxial and Biaxial Compressions

Due to the complex formation process of a rock mass, a large number of fissures, joints, faults, other defects exist and the defects commonly contain infilled materials. The jointed rock masses are in a complex geological environment, in which the geometric distribution and the boundary condition can greatly affect the mechanical behavior of the infilled jointed rock mass. In this study, the infilled jointed rock mass specimens with different dip angles are prepared using similar materials, and the uniaxial and biaxial compression tests on the specimens are conducted. The effect of the joint dip angle on the mechanical behavior of the infilled jointed rock mass under uniaxial and biaxial compressions is investigated. The results show that the uniaxial compressive strength shows a W-shaped variation, and the biaxial compressive strength shows a V-shaped variation with an increase in the dip angle. Most of the cracks appear in pairs around the joint and occur symmetrically in a bilateral distribution, and the existence of the infilled joints induces a nonlinear mechanical behavior in the specimen. In addition, the specimens exhibit three failure modes under uniaxial compression: splitting failure, step-path failure and planar failure. The specimens present two failure modes under biaxial compression: splitting failure and planar failure.

Strength and failure characteristics of brittle jointed rock-like specimens under uniaxial compression: Digital speckle technology and a particle mechanics approach

The strength and failure characteristics of most natural rock mass are influenced by discontinues such as fissures, joints, and weak surfaces. In the present study, the strength and failure behavior of ubiquitous-joint rock-like specimens under uniaxial loading have been investigated by DIC (digital image correlation) and discrete element numerical method (PFC2D). The results are obtained. Firstly, the UCSJ of specimens with γ = 15° or 30° shows similar tendency while α goes from 0° to 75°. With γ = 45° or 60°, the UCSJ of specimens increases when α goes from 0° to 30° and decreases after α goes beyond 30°. With γ = 75°, the peak UCSJ value is reached when α = 0°. The UCSJ value shows an increasing trend when α goes from 60° to 75°. Secondly, the ubiquitous-joint specimens present different failure modes for various levels of α and γ(β-α). Based on the experimental results, the failure mode of ubiquitous-joint specimens can be classified into three categories: stepped path failure, failure through parallel plane, and failure through cross plane.

Failure characteristics of jointed rock-like material containing multi-joints under a compressive-shear test: Experimental and numerical analyses

Extensive efforts have been made to gain a better understanding of the failure behaviour of rocks and rock-like materials, but crack propagation and failure processes under compressive-shear loading have not yet been comprehensively investigated. To address this area of research, the peak shear strengths (τ) and failure processes of specimens with multiple joints are studied by lab testing and particle flow code (PFC2D). Four types of failure modes are observed: (a) shear failure through a plane (Mode-I), (b) intact shear failure (Mode-II), (c) oblique shear crack connection failure (Mode-III), and (d) stepped path failure (Mode-IV). The failure mode gradually transformed to Mode-III as α (joint inclination angle) increases from 0° to 90° in the specimens. In addition, with increasing joint distance (d) in the specimens, the failure mode changes to Mode-II. As the non-overlapping length between joints (c) in the specimens increases, the failure mode changes to Mode-IV. The joint geometry has a major influence on the shear strength of the jointed specimens. The peak shear strength of specimens with different joint inclination angles is obtained when α=45°. Additionally, the peak shear strength increases as the joint distance (d) and non-overlapping length (c) increase.

Failure behavior around a circular opening in a rock mass with non-persistent joints: A parallel-bond stress corrosion approach

The stability of underground excavations is influenced by discontinuities interspaced in surrounding rock masses as well as the stress condition. In this work, a numerical study was undertaken on the failure behavior around a circular opening in a rock mass having non-persistent open joints using PFC software package. A parallel-bond stress corrosion (PSC) approach was incorporated to drive the failure of rock mass around the circular opening, such that the whole progressive failure process after excavation was reproduced. Based on the determined micro parameters for intact material and joint segments, the failure process around the circular opening agrees very well with that obtained through laboratory experiment. A subsequent parametric study was then carried out to look into the influence of lateral pressure coefficient, joint dip angle and joint persistency on the failure pattern and crack evolution of the rock mass around the circular opening. Three failure patterns identified are step path failure, planar failure and rotation failure depending on the lateral pressure coefficient. Moreover, the increment of joint dip angle and joint persistency aggravates the rock mass failure around the opening. This study offers guideline on stability estimation of underground excavations.

STABILITY ANALYSIS AND FAILURE MECHANISMS OF OPEN PIT ROCK SLOPE

Rock mass in nature tend to be unideal, for it is heterogeneous, anisotropic and has discontinuity. The discontinuity makes anisotropic strength and stress in the rock mass, and also controls the changing of the elastic properties of rock mass. This condition results to disruptions in the rock mass strength balance, and finally drives the slopes to collapse. This study aims to determine the slope failure mechanisms in the area of case study, as well as its variations based on the Rock Mass Rating (RMR), Geological Strength Index (GSI), Slope Mass Rating (SMR), kinematic analysis, numerical analysis and monitoring approach slope movement in a coal mine slope applications. The site investigations were implemented to obtain information about slope collapse. Prior to the collapse, the slope inclination was 38° with of 94 meters height, strike slope of N 245 E and direction of slope surface of 335°. After the collapse, the slope was became 25º; and after the collapse materials were cleared, it was 35º. The discontinuity mapping obtained 5 sets of discontinuities, and the data were developed to obtain the value of RMR. The result of piezometer measurements was that at occurrence of collapse, slope elevation was 44.40m. Displacement value from monitoring SSMR showed that when the slope was collapsing in two stages, the first stage value was 70.61cm (a more critical condition, the value was rounded down to 70cm to the implementation in modelling) and the second stage value was at 124.25cm. The value of RMR89 in this study was greater than the value of GSI and SMR. As for the average value, it was obtained 34.67 for RMR89 value and 29.67 for GSI value, these rocks then can be classified into Poor Rock class number IV. The result of kinematic analysis found that sliding planar failure at dips 36°, and wedge failure at dips 36°, 35° and 34°. Acquisition SMR value obtained at 25, 27, 28 and 29. The SMR values classified the rock mass quality into class number IV, the description of the rock mass was relatively poor, the slope stability was low or unstable and the collapse manifold was planar or wedge failure. The result from the analysis of the model with its criteria obtained was that un-collapse conditions at angle 29°. It is recommended to use 29° angle to repair the slopes, and also recommended for overall high wall slope angle. Type of collapse that occurred on the slope failure mechanisms in all of the analysis that has been done, it is known that the mechanisms involved are complex types (combine of wedge failure, planar failure, and step-path failure) or classified into large scale rock slope failure surface.

Experimental and Numerical Study of Failure Behavior and Energy Mechanics of Rock-Like Materials Containing Multiple Joints

This paper investigates the influence of joint geometry parameters on the characteristic stress, failure pattern, and energy mechanism of multiple jointed rock-like specimens under uniaxial compression. Both the laboratory and numerical results show that the higher value of UCS occurs when α is around 0° and γ changes from 15° to 30° or when α is around 30° and γ changes from 45° to 75°. However, the lowest value appears when α is around 45° and γ changes from 15° to 30°. The CDiS (critical dilatancy stress) and CIS (crack initiation stress) show a similar tendency to UCS. Moreover, the specimens present different failure modes for various levels of α, γ, and k, and the failure mode can be classified into four categories: stepped path failure; failure through parallel plane; failure through cross plane; material failure. In addition, with higher strength, the input energy and strain energy are higher than those with lower strength. Dissipation energy is affected by the failure modes of the specimens. At the same time, when k changes from 0.2 to 0.6, the boundary energy, strain energy, and dissipation energy show a decreasing trend.