Toppling Failure Research Articles

Slope stability analysis of Nkran Pit at Asanko Gold Mine, Ghana

The West Wall of Nkran Pit Mine is vulnerable to slope instability, mostly due to mining activities. Detailed failure analysis of the discontinuity data of the selected slope was performed using the Dips (6.0) software. The study has shown the likelihood of planar failure, wedge failure, flexural toppling failure and direct toppling failure occurring per the slope angle design of 70°. When the slope angle was increased by 5° and 10°, there were percentage increases in planar, wedge, flexural toppling and direct toppling failure of (1.86 and 7.45)%, (1.23 and 2.81)%, (0.62 and 0.62)% and (0.60 and 1.70)% respectively. It has been recommended that flattening or reducing slope angle could be done as it reduces the weight of material which in turn improves the stability of the slope and also controlled blasting should be employed to minimise excessive damage to the walls.Keywords: Slope, Stability, Toppling, Mining

A modified stereographic projection approach and a free software tool for kinematic analysis of rock slope toppling failures

Toppling failure is one of the common instability modes of rock slopes. Up to date, the stereographic projection approach is still an indispensable tool for kinematic toppling failure analysis of rock slopes, since it is very convenient to perform kinematic analysis that is based on all discontinuity orientations, not just some representative values, and it visually shows the analysis results. This paper first discussed the limitations of the Goodman’s graphical approach for kinematic analysis of rock slope toppling failures, and then proposed a modified graphical approach and developed practical software in a spreadsheet of Microsoft Excel for practitioners. The discrepancy between the results obtained from Goodman’s approach and our modified approach was investigated with respect to different limit values of the intersection angle between the strikes of the slope and discontinuity (denoted as γTlim), cut slope dip angles, and discontinuity friction angles. The results showed that: (1) when γTlim = 30°, the designed slope according to the Goodman’s graphical approach might be conservative or unsafe, which is related to the cut slope angle and the friction angle of discontinuity; (2) when γTlim = 30° and cut slope dip angle ≤60°, with respect to discontinuity friction angle = 10°, 20°, 30° or 40°, the designed slope according to the Goodman’s graphical approach might be conservative; (3) when γTlim = 30° and cut slope dip angle ≥70°, with respect to discontinuity friction angle = 10°, 20°, 30° or 40°, the designed slope according to the Goodman’s graphical approach is possibly unsafe; (4) when γTlim = 30° and cut slope dip angle ≤60°, with the discontinuity friction angle increasing from 10° to 40°, the discrepancy of the critical regions determined by the two approaches increases with respect to the same values of cut slope dip angle; (5) when γTlim = 30° and cut slope dip angle ≥70°, with the discontinuity friction angle increasing from 10° to 40°, the discrepancy of the critical regions determined by the two approaches first increases and then decreases with respect to the same values of cut slope dip angle; and (6) therefore, when performing kinematic analysis of rock slope toppling failures, the modified graphical approach proposed in this paper is recommended.

Quantitative assessment for the rockfall hazard in a post-earthquake high rock slope using terrestrial laser scanning

Geometric information and discontinuity characterization of rock masses are the key aspects of the analysis of the evolution and failure mechanisms of rockfalls. With the advantageous use of terrestrial laser scanning (TLS), the accurate three-dimensional (3D) spatial information of rock slopes can be obtained without contact. By conducting a fuzzy K-means algorithm in this study, the automatic identification of discontinuity sets is achieved, and dominant occurrences of rock mass discontinuities in each local region can be acquired in great detail. This automatic identification method permits the user to visually identify the discontinuity sets and acquire their spacial distribution features, e.g. occurrences, spacings, trace lengths and their geometric compounding relationships. At the same time, based on the shortest distance (SD) algorithm and the surface-to-plane volume calculation algorithm, the distributions, shapes, volumes and scars of the rockfalls can be accurately detected over the monitored time interval. These methods are able to provide adequate investigations and quantitative assessment for the rockfall failure mechanisms and evolutions of the Hongshiyan post failure rock slope after the 2014 Ludian earthquake. The topography of the landslide surface, mechanical properties, scales and the structural features of the discontinuities have a significant effect on the failure mechanisms, distributions and volumes of rockfalls. The main failure mechanisms of the rockfall investigated in this rock slope can be divided into plane failure, wedge failure and toppling failure. The plane and wedge failures mainly occurred in the landslide surface while the toppling failures are mainly observed along the edge of the post failure slope, which is obviously responded by preferred discontinuities. The reverse-dip stratified structure characteristics and the excavation disturbances during the recovering and slope treatment stage induce numerous progressive and continuous failures of rockfalls. The results are beneficial for the design and optimization of rockfall treatments.

Research on the Influence of Interconnectivity Structure Parameters to Stability of Stratified Rock Slope

Based on the slope engineering of the expansion project from Laiwu to Linyi section of Beijing-Shanghai Expressway, this paper uses numerical simulation method and strength reduction theory to analyze the change law of stability and failure mode of rock slope under the change of structural plane inclination, cohesion and internal friction angle. The results show that: with the increase of structural plane inclination, the change law of the failure mode of the bedding layered slope is pull-bedding slip→shearing-slip→toppling failure; The change rule of the failure mode of the inverse-dip layered slope is from shearing-slip to toppling-slip; the stability of bedding layered slope and inverse-dip layered slope with steep structural plane inclination are increased with the growth of the structural plane cohesion, while the safety factors of the inverse-dip layered slope with a small structural plane inclination have no significant changes. The stability of bedding layered slope increases with the growth of the structural plane friction angle, while the inverse-dip layered slopes have obvious differences trend between steep and gentle structural plane inclination. The research can provide reference for similar projects.

Stability analysis of slopes with a potential of slide-head-toppling failure

Toppling is a mode of slope instability that may occur in a wide range of layered or blocky rock masses. If this instability is caused by some natural or man-made external factors, it is termed a secondary toppling failure. One of the important modes of toppling instability is the slide-head-toppling failure. When a layer of soil or weak rock is overlaid by a blocky or layered rock mass, the combination of a toppling failure in the rock at the top and a circular sliding in the soil or weak rock in the bottom leads to this hybrid failure. The mechanism of this hybrid failure is extremely complicated and it may occur in some special geological conditions in civil engineering and mining projects. In this paper, the mechanisms of toppling failures, in general, and the mechanism of slide-head-toppling failure, in particular, are presented and described. Then, the outcomes of seven physical models, which were constructed with base friction materials and conducted under static loading conditions by a tilting table apparatus, are summarized to investigate this hybrid failure mechanism. Subsequently, a new step by step theoretical approach is proposed for assessment of this failure mode and a typical example is analyzed to better demonstrate the results. Finally, the results of the physical modeling are compared with the outcomes of the proposed theoretical method and an existing analytical approach. This comparison shows that there are acceptable agreements between the physical and analytical results. Hence, both proposed and existing analytical approaches can be used for the analysis of the slide-head-toppling slope failure.

Slope Stability Analysis of a Rock Cut in a Residential Area, Madinah, Saudi Arabia: A Case Study

The stability of a granitic rock cut located within a densely populated residential area in Madinah, Saudi Arabia, was investigated to avoid rock failure consequences. Based on the field inspection, this cut is characterized by a very irregular face leading to the occurrence of rock sliding and rockfall events in the area. Moreover, this cut lacks any type of stabilization or protection measurements. Kinematic analysis was used to analyze rock sliding events while RocFall software was used to analyze the mechanism of rockfall incidents. The results indicated to the high probability of wedge failures to take place (≈ 67%) as well as the toppling failures but with lower probability (< 10%). Furthermore, it was found that some large loose rock blocks on the cut surface could be easily triggered and fallen down reaching all onto the road and causing loss of life and damages to properties. As a result, this research recommended immediate scaling for loose rocks as well as constructing effective catch ditch in addition to anchoring large intact rocks.

ENGINEERING GEOLOGICAL MAPPING ON SLOPE DESIGN IN THE MOUNTAINOUS AREA OF SABAH WESTERN, MALAYSIA

The geology in the mountainous area of Sabah western provides a favourable setting for engineering geological instability. The area is underlain by the Trusmadi Formation (Palaeocene to Eocene age), the Crocker Formation (Late Eocene to Early Miocene age) and vary recent Quaternary alluvial materials which are still being deposited. The argillaceous nature and intense deformation suffered by the Trusmadi Formation and the highly jointed sandstone and mudstone beds of the arenaceous Crocker Formation makes them highly susceptible to weathering and instability. The weathered materials are unstable and may experience sliding due to by high pore pressure and intensively of geomorphological processes. In this study, a total of 20 selected critical slope failures were studied and classified into two main groups; rock slope (ten) and soil slope (ten). Soil slope failures normally involved large volumes of failed material as compared much rock slopes, where the failures are mostly small to medium. Kinematics rock slope analyses indicates that the variable potential of circular, planar, wedges, and toppling failures modes as well as the combination of more than one mode of aforementioned failure. Rock and soil slopes stability analysis indicates that the factor of safety value as unsafe (0.56 to 0.95). The geological influence had transformed the slopes in the Sabah mountainous area to be highly unstable and susceptible to landslide occurrences. Six (6) related main parameters to the landslide occurrence in the study area were attributed; 1) local and regional geology, 2) hydrological and geohydrological, 3) mineralogical and micro structures, 4) local discontinuities structures, 5) physical and engineering properties of soil and rock, and 6) geomorphological processes which can help in evaluating landslide problems. Therefore, development planning has to consider the slope hazard and risk management. This engineering geological mapping may play a vital role in disaster risk reduction programme in Sabah to ensure the public safety and to be extend with different environment.

A Systematic Approach of Rock Slope Stability Assessment: A Case Study at Gunung Kandu, Gopeng, Perak, Malaysia

The stability of the limestone cliff at Gunung Kandu, Gopeng, Perak, Malaysia was assessed based on the Slope Mass Rating (SMR) system on 53 cross sections of the Gunung Kandu hill slopes. The slopes of Gunung Kandu were identified as class I (very good) to IV (poor). The kinematic analysis showed that 12 out of 53 hill slopes of Gunung Kandu were identified as having potential wedge, planar and toppling failures. The assessment showed that the stability of the western flanks can be classified as stable to unstable with the probability of failure from 0.2 to 0.6. The stability of the eastern and southern flanks range from very stable to partially stable with the probability of failure from 0.0 to 0.4. While the stability of northern flanks are from very stable to stable with the probability of failure of 0.0 - 0.2. This systematic approach offers a practical method especially for large area of rock slope stability assessment and the results from probability of failure values will help engineers to design adequate mitigation measures.

A systematic approach for the analyses and design of jointed rock mass slopes against wedge and toppling failures: a case study of the stability of the abutments of the bridge across the Chenab River

ABSTRACT The stability of jointed rock mass slopes in highly seismic areas is governed by the orientation of the joints with respect to the slope and the joint characteristics and the seismic accelerations. The paper presents a systematic approach for the analysis and design of jointed rock mass slopes against wedge and toppling failures in highly seismic areas. There are nine load cases to be considered in the analyses of slopes. To address the concerns on the uncertainty and variability of the geological data, the process of “Design as you go” was suggested. The bridge across the Chenab river gorge with a main arch span of 467m which is under construction is located in a highly seismically active zone. The approach proposed in this paper was successfully implemented in the stabilization of the abutments of the Chenab bridge which enhanced the confidence in the adequacy of slope stabilization measures.

Evaluation of Rockfall-hazard Potential For Rockville, Utah, Following a 2013 Fatal Rockfall

Abstract In December 2013, a rockfall in the town of Rockville, Utah, released an estimated 2,700 tons (2,450 tonnes) of rock from a 400-ft (122-m) high slope; the rock struck a house at the base of the slope, resulting in two fatalities. We performed detailed field and laboratory investigations to (1) identify the modes of failure and factors contributing to rockfalls along the east-west trending, south-facing slope where it passes through the town; (2) identify sections of the slope that pose the highest hazard for future property damage or injury; and (3) suggest potential remedial measures. Field investigations included mapping discontinuities, establishing stratigraphy, measuring slope geometry, and evaluating potential failure modes at four selected sites. Laboratory investigations included determining dry density, friction angle, and slake durability index of rock samples. Using the Dips software, we determined the principal joint sets and performed a kinematic analysis. The maximum rollout distances for rock blocks of various sizes were determined for each of the study sites using the RocFall software. Results of the kinematic analysis and field observations indicate that wedge, plane, and toppling failures are possible within the Shinarump Conglomerate Member of the Chinle Formation and the Upper Red Member of the Moenkopi Formation along the entire slope. Based on the results of the study, we developed a rockfall-hazard map that indicates that the western portion of the town faces the highest hazard from potential rockfalls. The most feasible future remedial measure is not to build close to the hazardous slopes. Other possible remedial measures include removing loose rock blocks, installing rock anchors, and using drapery mesh.

New stability calculation method for rock slopes subject to flexural toppling failure

Flexural toppling is one of the main failure modes of natural and manmade anti-dip layered rock slopes. Based on cantilever slab tensile theory, the failure mechanism of flexural toppling was analyzed. A toppling slope is divided into three parts: the stability, tensile and shear zones. By considering this failure mechanism, a new stability analysis method for slopes against flexural toppling failure is proposed using equilibrium theory. In addition, a sensitivity analysis is performed to investigate the locations of possible failure surfaces and zones as well as changes in the stability of anti-dip rock slopes under different conditions. The results show that the positions of the inter-column forces have almost no effect on the stability factor but affect the areas of the tensile zone and the shear zone. The angle of the most dangerous potential failure surface increases with increasing dip angle and slope height, whereas the stability factor is negatively correlated with the dip angle and slope height but is positively correlated with the layer thickness. The failure mode is essentially flexural toppling when the layer thickness is small, but the failure mode gradually transitions to shear-sliding with increasing layer thickness. Finally, a real case study is analyzed using this method, and the calculated results are consistent with the actual conditions.

Analytical technique for stability analyses of rock slopes subjected to block toppling failure

ABSTRACTIn the traditional analytical models for evaluating block toppling failure mechanisms of the slope, a single weak plane angle is assumed, running from upper rock columns and daylighting on the slope face. However, for some physical rock slopes, the weak plane bounding the potential toppling blocks may be dipping at two diverse angles within the rock masses and may not daylight on the predictable point on the face of the slope due to varying characteristics of the weak plane. The mathematical technique for estimating the counter-tilted angle of the weak plane has been proposed and incorporated into the modified analytical technique for evaluating slope stability subjected to block toppling failure. The physical slope with pre-existing weak plane dipping at two diverse angles within the rock slope subjected to block toppling was analysed using the modified analytical technique and results were validated using the discrete element method. The obtained simulated failure mode zones are consistent with those obtained by the modified analytical technique. The influence of the relative counter-tilted angles of the weak plane on slopes stability was studied and the results show that, progressive increase in the counter-tilted angles of the weak plane lead to gradual increase in slope instability.

Influence of counter-tilted failure surface angle on the stability of rock slopes subjected to block toppling failure mechanisms

In rock slopes where sedimentary rock masses dip into the face of the slope, failure may occur by block toppling. In traditional analytical models, the failure surface is assumed to be a single plane running from the upper columns to the toe of the slopes, which may be inconsistent with the physical situation, where the weak plane has undergone counter-tilting within the rock slope due to variations of lithology and weak plane characteristics. To better reflect the physical situations, the failure surfaces ought to be determined instead of basing it on assumptions and incorporated in the existing analytical methods for stability analyses. Therefore, a searching technique for determining the counter-tilted failure surface angle has been proposed and traditional analytical models for evaluating the stability of rock slopes subjected to block toppling failure mechanisms have been modified by incorporating the counter-tilted weak plane angle. The physical slope with counter-tilted failure surface was comprehensively analyzed using the modified analytical model and the results were validated using numerical simulation models. The simulated failure mode zones are consistent with the failure mode zones obtained by the modified analytical method. The influence of relative angles of the counter-tilted failure surface on the slope stability has been studied and the results show that progressive increase of the counter-tilted failure surface angles lead to a gradual increase in slope instability. The proposed analytical method could provide precise applications to evaluate the slope instability in rock slopes with counter-tilted failure surface.

Stability Analyses of Jointed Rock Slopes with Counter-tilted Failure Surface Subjected to Block Toppling Failure Mechanisms

In rock slopes where sedimentary rock masses dip into the face of the slope, failure may occur by block toppling. In traditional analytical models, the failure surface is assumed to be single plane running from the upper columns to the toe of the slope which may be inconsistent with the physical situation where the weak plane has undergone counter-tilting within the rock slope due to variation of lithology and weak plane characteristics. To better reflect the physical situations, the failure surfaces ought to be determined instead of basing it on assumptions and incorporated in the existing analytical methods for stability analyses. Therefore, an analytical technique for determining counter-tilted failure surface angle has been proposed and traditional analytical model for evaluating the stability of rock slopes subjected to block toppling failure mechanisms has been modified by incorporating the counter-tilted weak plane angle. The physical slope with counter-tilted failure surface was comprehensively analysed using the modified analytical model, and results were validated using the numerical simulations models. The simulated failure mode zones are consistent with the failure mode zones obtained by the modified analytical method. The influence of relative angles of counter-tilted failure surface on the slopes’ stability has been studied, and the results show that progressive increase in the counter-tilted failure surface angles leads to gradual increase in slope instability. The proposed analytical method could provide precise applications to evaluate the slope instability in rock slopes with counter-tilted failure surface.

Study on the mechanisms of flexural toppling failure in anti-inclined rock slopes using numerical and limit equilibrium models

Flexural toppling failure (FTF) is one of the main types of toppling failures and frequently occurs in anti-inclined rock slopes. A new UDEC Trigon approach for simulating FTF of a model slope was presented in this paper. FTF of anti-inclined rock slopes characterized by tensile failure of rock columns was successfully captured with the new method. Subsequently, special effort was made to investigate the effects of joint cohesion and joint friction angle on flexural toppling movements' mechanisms. Furthermore, a limit equilibrium method, which can reflect the effects of the joint cohesion, was proposed to quantitatively evaluate the stability of anti-inclined rock slopes against FTF. The results demonstrate that the deformation process of FTF can be divided into three stages: elastic deformation due to cohesion, development of FTF after interlayer slip, and formation of the total failure surface. The inter-column normal forces will suddenly decrease when the failure surface begins to initiate inside the slope, which can be regarded as an instability indicator of anti-inclined rock slopes against FTF. Joint cohesion and joint friction angle were found to have significant effects on the stability of anti-inclined rock slopes, but make an insignificant impact on the shape, location, and formation process of the failure surface. The simulated results indicate that joint cohesion should be considered when using the limit equilibrium method to evaluate the stability of anti-inclined rock slopes against FTF. Inaccurate result will be predicted if the joint cohesion is neglected in the limit equilibrium method.

Susceptibility of lava domes to erosion and collapse by toppling on cooling joints

The shape of lava domes typically leads to the formation of radial patterns of cooling joints. These cooling joints define the orientation of the columnar blocks which plunge toward the center of the dome. In the lower parts of the dome the columns plunge into the dome at low angles and are relatively stable. Higher in the dome the columns plunge into the dome at steep angles. These steeply plunging columns are susceptible to toppling and, if the lower part of a dome is partially removed by erosion or collapse, the unstable part of the dome becomes exposed leading to toppling failure. Examples of this process are provided from coastal erosion of lava domes at Katsura Island, Shimane Peninsula, western Japan. An analogue model is presented to demonstrate the mechanism. It is proposed that the mechanism can contribute to collapse of lava domes during or after emplacement.

Rockfall risk management using a pre-failure deformation database

Terrestrial laser scanning (TLS) monitoring has been used to estimate the location, volume, and kinematics of a variety of small magnitude rockfalls before failure (1–1000 m3 range), and in some cases, potential failure time has been assessed through the application of inverse velocity methods. However, our current understanding of rock slope pre-failure behavior for this magnitude range and prediction ability is based on observations of a small number of failure case histories. In this study, a pre-failure deformation database was constructed for rockfall volumes exceeding 0.1 m3, observed over a 1252-day study interval at the Goldpan rock slope, British Columbia, Canada, in order to better understand the pre-failure behavior of rock slopes and provide an empirical means of estimating temporal failure ranges. Repeated TLS datasets were acquired at an average scanning interval of 2–3 months. A total of 90 rockfall events were recorded at this site, during this time period, of which 64 (71%) exhibited measurable deformation prior to failure. Classification of rockfalls by volume suggests that a scale dependency may exist, as deformation was detected for a greater proportion of rockfalls > 5 m3 (92%) than for smaller rockfalls in the range of 0.1–0.5 m3 (61%). A lower rate of pre-failure deformation detection was also reported for planar sliding failures as compared with wedge or toppling failures, suggesting that deformation was less easily detected for these failure types. This study proposes and implements a framework for rockfall assessment and forecasting that does not require continuous monitoring of deformation.

Assessing rockfall susceptibility in steep and overhanging slopes using three-dimensional analysis of failure mechanisms

Rockfalls strongly influence the evolution of steep rocky landscapes and represent a significant hazard in mountainous areas. Defining the most probable future rockfall source areas is of primary importance for both geomorphological investigations and hazard assessment. Thus, a need exists to understand which areas of a steep cliff are more likely to be affected by a rockfall. An important analytical gap exists between regional rockfall susceptibility studies and block-specific geomechanical calculations. Here we present methods for quantifying rockfall susceptibility at the cliff scale, which is suitable for sub-regional hazard assessment (hundreds to thousands of square meters). Our methods use three-dimensional point clouds acquired by terrestrial laser scanning to quantify the fracture patterns and compute failure mechanisms for planar, wedge, and toppling failures on vertical and overhanging rock walls. As a part of this work, we developed a rockfall susceptibility index for each type of failure mechanism according to the interaction between the discontinuities and the local cliff orientation. The susceptibility for slope parallel exfoliation-type failures, which are generally hard to identify, is partly captured by planar and toppling susceptibility indexes. We tested the methods for detecting the most susceptible rockfall source areas on two famously steep landscapes, Yosemite Valley (California, USA) and the Drus in the Mont-Blanc massif (France). Our rockfall susceptibility models show good correspondence with active rockfall sources. The methods offer new tools for investigating rockfall hazard and improving our understanding of rockfall processes.

Probabilistic Analysis of Rock Slopes Against Block Toppling Failure

In the present paper, a probabilistic analysis procedure and related algorithm for the stability of rock slopes against block toppling failure have been developed using Monte Carlo simulation. For this purpose, first the deterministic model has been developed considering the presence of external loads and moments on the slope having non-orthogonal discontinuities. The discontinuity parameters (such as discontinuities orientations, friction angles) and seismic coefficient have been taken as normally distributed variables whereas spacing of discontinuities and pore water pressure have been considered as log normally distributed variables. The realizations of all the variable parameters, generated by central limit theorem, have been fed to the deterministic model for slope stability analysis. As a result, realizations of dependent variables [geometry, inter-block forces and factor of safety (FOS)] have been generated. Subsequently, the probability distribution function of FOS has been generated. Associated risk of slope failure in toppling for a particular value of FOS can be obtained. In addition, a comparative study has been performed to show the influence of external loads and moments on the stability of slope. External loads and moments have been found to have significant influence on the FOS and therefore probability of failure of rock slope.

An Analytical Solution for Block Toppling Failure of Rock Slopes during an Earthquake

Toppling failure is one of the most common failure types in the field. It always occurs in rock masses containing a group of dominant discontinuities dipping into the slope. Post-earthquake investigation has shown that many toppling rock slope failures have occurred during earthquakes. In this study, an analytical solution is presented on the basis of limit equilibrium analysis. The acceleration of seismic load as well as joint persistence within the block base, were considered in the analysis. The method was then applied into a shake table test of an anti-dip layered slope model. As predicted from the analytical method, blocks topple or slide from slope crest to toe progressively and the factor of safety decreases as the inputting acceleration increases. The results perfectly duplicate the deformation features and stability condition of the physical model under the shake table test. It is shown that the presented method is more universal than the original one and can be adopted to evaluate the stability of the slope with potential toppling failure under seismic loads.