Persistent Discontinuities Research Articles

Graded impact of obstacle size on scanning by RNaseE.

In countless bacterial species, the lifetimes of most mRNAs are controlled by the regulatory endonuclease RNase E, which preferentially degrades RNAs bearing a 5' monophosphate and locates cleavage sites within them by scanning linearly from the 5' terminus along single-stranded regions. Consequently, its rate of cleavage at distal sites is governed by any obstacles that it may encounter along the way, such as bound proteins or ribosomes or base pairing that is coaxial with the path traversed by this enzyme. Here, we report that the protection afforded by such obstacles is dependent on the size and persistence of the structural discontinuities they create, whereas the molecular composition of obstacles to scanning is of comparatively little consequence. Over a broad range of sizes, incrementally larger discontinuities are incrementally more protective, with corresponding effects on mRNA stability. The graded impact of such obstacles suggests possible explanations for why their effect on scanning is not an all-or-none phenomenon dependent simply on whether the size of the resulting discontinuity exceeds the step length of RNase E.

Identification of the Potential Critical Slip Surface for Fractured Rock Slope Using the Floyd Algorithm

A rock slope can be characterized by tens of persistent discontinuities. A slope can be massive. The slip surface of the slope is usually easier to expand along with the discontinuities because the shear strength of the discontinuities is substantially lower than that of the rock blocks. Based on this idea, this paper takes a jointed rock slope in Hengqin Island, Zhuhai as an example, and establishes a three-dimensional (3D) model of the studied slope by digital close-range photogrammetry to rapidly interpret 222 fracture parameters. Meanwhile, a new Floyd algorithm for finding the shortest path is developed to realize the critical slip surface identification of the studied slope. Within the 3D fracture network model created using the Monte Carlo method, a sequence of cross-sections is placed. These cross-sections containing fractures are used to search for the shortest paths between the designated shear entrances and exits. For anyone combination of entry point and exit point, the shortest paths corresponding to different cross-sections are different and cluttered. For the sake of safety and convenience, these shortest paths are simplified as a circular arc that is regarded as a potential slip surface. The fracture frequency is used to determine the probability of sliding along a prospective critical slip surface. The potential slip surface through the entrance point (0, 80) and exit point (120, 0) is identified as the final critical slip surface of the slope due to the maximum fracture frequency.

Semi-stochastic generation of rock discontinuity networks based on traces exposed on cavern roof

The rapid development of digital mapping technologies such as terrestrial laser scanning, digital photogrammetry has allowed the exact acquisition of superficial information of discontinuities in rock exposures. Nevertheless, it remains challenging to quantify the spatial dimension and areal persistence of discontinuities due to the impossibility of direct observation of complete extent of discontinuities in three dimensions. The difficulties of characterizing individual discontinuities deterministically lead to the development of stochastic 3-D discontinuity networks. The stochastic modeling scheme are based on the statistical analysis of the measured discontinuity parameters; hence, the generated discontinuity networks represent discontinuity system in a statistical sense, and in most cases, the discontinuity traces formed by stochastic model are inconsistent with those observed at rock outcrops. To deal with this issue, this study presented a new method to simulate discontinuity network, which employs the real traces exposed on the cavern roof as the constraint condition of stochastic modeling and is described herein as semi-stochastic. The method takes discontinuities as circular discs and establishes geometrical relationship between the radius and the center of circular disc respectively for three classes of traces (i.e. trace has two ends, only one end, and neither end, visible in the sampling window). A case study with the proposed method shows that the traces yielded by the intersections of modeled discontinuity network with the cavern roof are in close agreement with actual situation. This semi-stochastic method further improves conventional stochastic modeling technique in terms of enabling a more realistic representation of rock discontinuities.

Effect of the number of coplanar rock bridges on the shear strength and stability of slopes with the same discontinuity persistence

Analyzing the shear resistance of a potential sliding surface based on discontinuity persistence usually does not consider the number of coplanar rock bridges. To examine the effect of the dispersion/number of rock bridges on the shear strength and rock slope stability, direct shear tests and large-scale rockslide simulations were conducted employing the 2D particle flow code (PFC2D). The shear strength of rock bridges under different configurations and the same discontinuity persistence was analyzed based on both the shear behavior controlled by the stress response and crack propagation. The results at both the laboratory and slope scales indicate that the shear resistance decreases with increasing dispersion/number of rock bridges due to multiple rock bridges breaking separately, the mechanism of which is that the rock bridge system more easily experiences initial failure with increasing dispersion/number of rock bridges. On this basis, a function of the strength reduction coefficient with the number of rock bridges was established considering the laboratory-scale numerical simulation results. A feasible stability analysis method, i.e., the improved limit equilibrium method based on the strength reduction coefficient, was proposed to consider the effect of the dispersion/number of rock bridges on the slope stability, which is a useful innovation to ensure that the stability analysis method of potential rockslides, including coplanar rock bridges, is more realistic and accurate.

Geo-environmental monitoring and 3D finite elements stability analysis for site investigation of underground monuments. Horemheb tomb (KV57), Luxor, Egypt

The Valley of the Kings (KV) is a UNESCO world heritage site with more than thirty opened tombs. Since the first tombs were constructed, at least 24 historical flash flood events has been identified, each of which has been contributed to the destruction and deterioration of the tombs. Recently, most of these tombs have been damaged and inundated after 1994 flood. In order to understand the Geo-environmental impact mainly the past flash floods due to the intensive rainfall storm on the valley of kings and the long-term rock mass behavior under geostatic stresses in selected Horemheb tomb (KV57) and its impact on past failures and current stability, Remote sensing, GIS, LIDAR, 3D finite element stability analysis and rock mass quality assessments had been carried out using advanced methods and codes. Our work provides environmental satellite space views via landviewer Erath Observation System (EOS) Platform with passive and active sensors which include the Normalized Difference Vegetation Index (NDVI), Soil-Adjusted Vegetation Index (SAVI), Atmospherically resistant vegetation index (ARVI), Green Chlorophyll Index (GCI), Normalized Burn Ratio (NBR), Normalized Difference Snow Index (NDSI), Light Detection And Ranging (LIDAR) images, Terrain (DEM) Digital Elevation Models, 3D geological maps. In other hand experimental and numerical geotechnical evaluations and modeling of the rock mass of these underground structures and their surroundings have been executed. We estimated the rock mass quality of the different members within the Thebes limestone and Esna shale formations using the mechanical testing and Rock Mass Rating (RMR), rock quality system (Q-system) and Geological Strength Index (GSI) systems. Our recent analyses show that the KV57 rock- cut tomb at Luxor has been cut into poor to very poor quality marl shale masses due to the impact of flash foods. Rock failures of ceilings and pillars were frequently facilitated by local, unfavorably oriented persistent discontinuities, such as tension cracks and faults. Other failures were related to the disintegration of the marl limestone and Esna shale Formations into individual nodules upon weathering. Our data suggest that, in ancient Egypt monumental tomb construction, low-strength rock masses rarely resulted in modifications of the planned tomb design in order to minimise the risk of rock falls and to prevent collapses. The current flood protection measures are not enough. For this two following measures are proposed 1—to rise the current wall by 50 cm. 2—to fill the depression by reshaping bathymetry.

Fragmented Rockfall Volume Distribution from Photogrammetry-Based Structural Mapping and Discrete Fracture Networks

The design of rockfall protection structures requires information about the falling block volumes. Computational tools for rockfall trajectory simulation are now capable of modeling block fragmentation, requiring the fragmented volume-relative frequency distribution of rockfalls as input. This can be challenging at locations with scarce or nonexistent rockfall records and where block surveys are not feasible. The work in this paper shows that simple discrete fracture network realizations from structural mapping based on photogrammetric techniques can be used to reliably estimate rock fall block volumes. These estimates can be used for dimensioning rockfall protection structures in cases where data is scarce or not available. The methodology is tested at two sites in the Canadian Cordillera where limestone outcrops have been the source of recurrent rockfalls. The results suggest that fragmentation will largely tend to occur through weak planes and expansion of non-persistent discontinuities, while other block breakage mechanisms exert less influence in the fragmented volume-relative frequency distribution of rockfalls. Therefore, block volume distribution can be estimated using a simple discrete fracture network (DFN) with fully persistent discontinuities. Limitations of the methods are also discussed, as well as potential future research to address such limitations.

Specialization in the vicarious learning of novel arbitrary sequences in humans but not orangutans.

Sequence learning underlies many uniquely human behaviours, from complex tool use to language and ritual. To understand whether this fundamental cognitive feature is uniquely derived in humans requires a comparative approach. We propose that the vicarious (but not individual) learning of novel arbitrary sequences represents a human cognitive specialization. To test this hypothesis, we compared the abilities of human children aged 3-5 years and orangutans to learn different types of arbitrary sequences (item-based and spatial-based). Sequences could be learned individually (by trial and error) or vicariously from a human (social) demonstrator or a computer (ghost control). We found that both children and orangutans recalled both types of sequence following trial-and-error learning; older children also learned both types of sequence following social and ghost demonstrations. Orangutans' success individually learning arbitrary sequences shows that their failure to do so in some vicarious learning conditions is not owing to general representational problems. These results provide new insights into some of the most persistent discontinuities observed between humans and other great apes in terms of complex tool use, language and ritual, all of which involve the cultural learning of novel arbitrary sequences. This article is part of the theme issue 'Ritual renaissance: new insights into the most human of behaviours'.

Determination of statistical discontinuity persistence for a rock mass characterized by non-persistent fractures

The discontinuity persistence is an important parameter that affects the strength of rock masses and stability in rock engineering. However, determining the 3D discontinuity persistence in practical field projects remains difficult. This study proposes an approach to determine the 3D discontinuity persistence (percentage of total discontinuity area to the area of the potential failure surface) on the basis of Dijkstra's shortest-path algorithm and Bayesian bootstrap method. First, Dijkstra's shortest-path algorithm is used to determine the linear discontinuity persistence (percentage of total discontinuity trace length to the length of 2D potential failure surface), which is essential to determining 3D discontinuity persistence. Second, geological analysis is performed to deduce 3D discontinuity persistence as a function related to two linear discontinuity persistence in two vertical directions. Lastly, Bayesian bootstrap method is used to analyze the linear and 3D discontinuity persistence. This approach can substantially simplify the process of determining discontinuity persistence and comprehensively considers the uncertainty of the fracture network. The mean, standard deviation, and p-value (i.e., value at the 95% confidence limit) are used as the statistical parameters of the linear and 3D discontinuity persistence.

Relevance of rock slope deformations in local seismic response and microzonation: Insights from the Accumoli case-study (central Apennines, Italy)

Based on a National Government Decree, detailed seismic microzonation studies were carried out after the seismic sequence of Central Italy (2016–2017) in support of post-earthquake reconstruction. During these activities mass rock creep deformations of slopes were observed in the municipality of Accumoli (Latium Region), involving two urbanized areas on the left bank of the Tronto River. The geological and geomorphological surveys as well as the geomechanical characterization of rock masses revealed a deformation process of flexural toppling which involves the sub-vertical thick sandstone layers down to 50 m of depth. Geophysical investigations, consisting of downhole tests, active surface-wave testing and seismic ambient noise measurements, were carried out in the areas involved in the deformational processes. The results highlighted that the rock mass involved in the flexural toppling exhibits peaks of the horizontal-to-vertical spectral ratios (HVSR) in a frequency band ranging from 1.5 up to 2.5 Hz. In one of the two areas, H/V calculated on weak-motions recorded during the seismic sequence within the deforming rock mass, showed a clear peak in the H/V frequency range 1.5–2.0 Hz, the same range pointed out by the ambient vibration analysis. Due to local morphological, lithological and bedding conditions, such an evidence cannot be related to a simple 1D resonance due to the seismic impedance contrasts originated from the local stratigraphy. Nevertheless, it seems more reliable that the HVSR peaks can be related to the 3D volume of intensely jointed rock mass, in agreement with the field evidence of flexural toppling, as these peaks result confined within the deforming mass. In addition, the lack of a clear polarization of the particle motion in the seismic ambient noise dataset suggests that the observed effect should not be linked to the interaction of seismic surface waves with persistent discontinuities in an anisotropic rock mass. According to the National guidelines for seismic microzonation studies, these rock masses have not been identified as unstable, i.e. involved in conventional landslide processes, but have been identified as seismic amplification prone microzones with associated amplification factors of at least 1.5 in the period range 0.1–0.5 s. The identification of such microzones within areas involved in gravity-induced slope deformations is a significant prerequisite for planning strategies of post-earthquake reconstruction.

Numerical investigation into the blasting-induced damage characteristics of rocks considering the role of in-situ stresses and discontinuity persistence

This paper presents a 3D coupled Smoothed Particle Hydrodynamics (SPH) and Finite Element Method (FEM) model, which was developed to investigate the extent of damage zone and fracture patterns in rock due to blasting. The RHT material model was used to simulate the blasting-induced damage in rock. The effects of discontinuity persistence and high in-situ stresses on the evolution of blasting-induced damage were investigated. Results of this study indicate that discontinuity persistence and spatial distribution of rock bridges have a significant influence on the evolution of blasting-induced damage. Furthermore, high in-situ stresses also have a significant influence on the propagation of blasting-induced fractures, as well as the patterns of fracture networks. It is also shown that the blasting-induced cracks are often induced along the direction of the applied high initial stresses. Moreover, additional cracks are normally generated at the edges of the rock bridges probably due to the relatively high stress concentration.

Numerical and theoretical study of bi-planar failure in footwall slopes

Bi-planar failure is the commonest type of failure in steep and high footwall slopes. This paper presents an investigation of the bi-planar failure mechanism and a stability analysis model for footwall slopes based on the study of eleven diabase mines in Hunyuan County, Shanxi Province, China. First, a detailed investigation of the site and tests were carried out to obtain a geological model and calculation parameters for the slope. Then, the failure process in footwall slopes was investigated by a trigon approach performed using the Universal Distinct Element Code (UDEC) software package. A mechanism was then obtained for bi-planar compression–shear failure by combining the results obtained for the stress, displacement, and crack development. Subsequently, based on the limit equilibrium and frictional plasticity theories, a new columnar mechanical model was proposed for bi-planar footwall slope failure. The results demonstrate that the UDEC trigon approach was well suited to simulating bi-planar failure in steep and high footwall slopes. Employing this approach, a sliding failure surface that initiates, develops, and propagates in the discontinuity and intact rock could be correctly captured and the evolution of the damage in the toe of the slope could be quantitatively investigated. The results also indicate that shear failure first occurs at persistent discontinuities and then compression–shear failure occurs in the intact rocks. In addition, the failure surface of the rock emanates from the toe of the slope, is oriented upwards at an angle to the persistent discontinuity thus forming the through sliding surface (this angle can be determined using frictional plasticity theory). The critical heights and safety factors of footwall slopes could be readily obtained by employing this new columnar mechanical model giving results that are consistent with the results of numerical simulations. Furthermore, the results of a parameter-sensitivity analysis show that the dip angle of the toe breakout surface increases as the slope angle increases. However, the angle between the toe breakout and internal shear surfaces remains unchanged as the slope angle increases. Moreover, the critical height of the footwall slope decreases linearly as the slope angle increases. The method proposed provides theoretical guidance for the stability analysis of steep and high footwall slopes. The results produced should also help engineers to gain a better understanding of the mechanisms of bi-planar failure in such rock slopes.

Rock mass quality and preliminary analysis of the stability of ancient rock-cut Theban tombs at Sheikh ‘Abd el-Qurna, Egypt

The ancient Theban tombs at the hillside cemetery of Sheikh ‘Abd el-Qurna (SAQ), west of Luxor, Egypt, were excavated mainly in the Thebes Limestone Formation and show varying degrees of damage of rock pillars and ceilings. In order to understand the rock mass behaviour in selected tombs and its impact on past failures and current stability, we carried out geological mapping and rock mass quality assessments. Our work provides a geological map and geotechnical evaluation of the rock mass of these SAQ tombs and their surroundings. We mapped and described rock fractures in situ and with remote sensing data, and estimated the rock mass quality of the different members within the Thebes Limestone Formation using the Rock Mass Rating (RMR) and Geological Strength Index (GSI) systems. In addition, we conducted a rock pillar analysis. Analyses and mapping were supported by new high-resolution terrain models computed from ground-based and aerial photogrammetry and from terrestrial laser scanning. Our analyses show that the tombs at SAQ have been cut into poor to very good quality rock masses. Rock failures of ceilings and pillars were frequently facilitated by local, unfavourably oriented persistent discontinuities, such as tension cracks and faults. Other failures were related to the disintegration of nodular limestone into individual nodules upon weathering. Our data suggest that, in 18th Dynasty monumental tomb construction, low-strength rock masses rarely resulted in modifications of the planned tomb design in order to minimise the risk of rock falls and collapses.

Automatic Mapping of Discontinuity Persistence on Rock Masses Using 3D Point Clouds

Finding new ways to quantify discontinuity persistence values in rock masses in an automatic or semi-automatic manner is a considerable challenge, as an alternative to the use of traditional methods based on measuring patches or traces with tapes. Remote sensing techniques potentially provide new ways of analysing visible data from the rock mass. This work presents a methodology for the automatic mapping of discontinuity persistence on rock masses, using 3D point clouds. The method proposed herein starts by clustering points that belong to patches of a given discontinuity. Coplanar clusters are then merged into a single group of points. Persistence is measured in the directions of the dip and strike for each coplanar set of points, resulting in the extraction of the length of the maximum chord and the area of the convex hull. The proposed approach is implemented in a graphic interface with open source software. Three case studies are utilized to illustrate the methodology: (1) small-scale laboratory setup consisting of a regular distribution of cubes with similar dimensions, (2) more complex geometry consisting of a real rock mass surface in an excavated cavern and (3) slope with persistent sub-vertical discontinuities. Results presented good agreement with field measurements, validating the methodology. Complexities and difficulties related to the method (e.g., natural discontinuity waviness) are reported and discussed. An assessment on the applicability of the method to the 3D point cloud is also presented. Utilization of remote sensing data for a more objective characterization of the persistence of planar discontinuities affecting rock masses is highlighted herein.

Use of an integrated finite/discrete element method-discrete fracture network approach to characterize surface subsidence associated with sub-level caving

The LKAB Kiruna sub-level cave mine, located in Kiruna, Sweden, is one of the most well studied sub-level cave mines. Due to proximity of the city to the hanging wall, the mine has developed a comprehensive surface deformation monitoring program which is perhaps unparalleled in the mining industry. This surface monitoring scheme provides an excellent data source with which to constrain numerical modelling. In this study, a finite/discrete element modelling approach coupled with a discrete fracture network (FDEM-DFN) is utilized to analyse the Kiruna hanging wall surface subsidence with an emphasis on investigating the influence of discontinuity persistence and spacing. The FDEM-DFN data interpretation uses a variety of novel approaches including time-displacement hanging wall deformation characterization, numerical inverse velocity analysis and virtual hanging wall inclinometer simulation to improve our understanding of the extent and mechanism of hanging wall failure with mine advance. The simulated displacements correspond closely to the actual field data, illustrating the ability of the proposed approach to reproduce sub-level cave behaviour. Three distinct time-displacement phases namely: regressive, progressive and steady state are observed in the FDEM-DFN models. The paper also reviews the potential application of the inverse velocity method and virtual inclinometers in characterizing sub-surface brittle failure associated with sub-level caving.

First results of infrared thermography applied to the evaluation of hydraulic conductivity in rock masses

An innovative methodological approach using infrared thermography (IRT) provides a potential contribution to the indirect assessment of hydraulic conductivity of jointed rock masses. This technique proved a suitable tool to evaluate the degree of fracturing of rock masses along with their discontinuity systems, which expedite water flow within the rock mass itself. First, based on the latest scientific outcomes on the application of IRT to the geomechanics of rock systems, rock mass surveys were carried out at different outcrops (dolostone, limestone and porphyroid) and hydraulic conductivity was empirically assessed through approaches well known in the international literature. Then, IRT campaigns were performed at each surveyed rock mass, with the purpose of evaluating the corresponding Cooling Rate Index, strictly linked to the cooling attitude of the rock. Such index was correlated with the assessed hydraulic conductivity and satisfactory regression equations were achieved. The interesting results show that hydraulic conductivity values are likely to be linked with the cooling behavior of rock masses, which, in turn, is affected by spacing, aperture and persistence of discontinuities.

Forensic Excavation of Rock Masses: A Technique to Investigate Discontinuity Persistence

True persistence of rock discontinuities (areas with insignificant tensile strength) is an important factor controlling the engineering behaviour of fractured rock masses, but is extremely difficult to quantify using current geological survey methodologies, even where there is good rock exposure. Trace length as measured in the field or using remote measurement devices is actually only broadly indicative of persistence for rock engineering practice and numerical modelling. Visible traces of discontinuities are treated as if they were open fractures within rock mass classifications, despite many such traces being non-persistent and actually retaining considerable strength. The common assumption of 100% persistence, based on trace length, is generally extremely conservative in terms of strength and stiffness, but not always so and may lead to a wrong prediction of failure mechanism or of excavatability. Assuming full persistence would give hopelessly incorrect predictions of hydraulic conductivity. A new technique termed forensic excavation of rock masses is introduced, as a procedure for directly investigating discontinuity persistence. This technique involves non-explosive excavation of rock masses by injecting an expansive chemical splitter along incipient discontinuities. On expansion, the splitter causes the incipient traces to open as true joints. Experiments are described in which near-planar rock discontinuities, through siltstone and sandstone, were opened up by injecting the splitter into holes drilled along the lines of visible traces of the discontinuities in the laboratory and in the field. Once exposed the surfaces were examined to investigate the pre-existing persistence characteristics of the incipient discontinuities. One conclusion from this study is that visible trace length of a discontinuity can be a poor indicator of true persistence (defined for a fracture area with negligible tensile strength). An observation from this series of experiments was that freshly failed surfaces through pre-existing rock bridges were relatively rough compared to sections of pre-existing weaker areas of geologically developed (though still incipient) discontinuities. Fractographic features such as hackle and rib marks were typical of the freshly broken rock bridges, whereas opened-up areas of incipient discontinuity were smoother. Schmidt hammer rebound values were generally higher for the rock bridge areas, probably reflecting their lower degree of chemical and physical weathering.

Forensic analysis of rockfall scars

We characterise and analyse the detachment (scar) surfaces of rockfalls to understand the mechanisms that underpin their failure. Rockfall scars are variously weathered and comprised of both discontinuity release surfaces and surfaces indicative of fracturing through zones of previously intact rock, known as rock bridges. The presence of rock bridges and pre-existing discontinuities is challenging to quantify due to the difficulty in determining discontinuity persistence below the surface of a rock slope. Rock bridges form an important control in holding blocks onto rockslopes, with their frequency, extent and location commonly modelled from the surface exposure of daylighting discontinuities. We explore an alternative approach to assessing their role, by characterising failure scars. We analyse a database of multiple rockfall scar surfaces detailing the areal extent, shape, and location of broken rock bridges and weathered surfaces. Terrestrial laser scanning and gigapixel imagery were combined to record the detailed texture and surface morphology. From this, scar surfaces were mapped via automated classification based on RGB pixel values.Our analysis of the resulting data from scars on the North Yorkshire coast (UK) indicates a wide variation in both weathering and rock bridge properties, controlled by lithology and associated rock mass structure. Importantly, the proportion of rock bridges in a rockfall failure surface does not increase with failure size. Rather larger failures display fracturing through multiple rock bridges, and in contrast smaller failures fracture occurs only through a single critical rock bridge. This holds implications for how failure mechanisms change with rockfall size and shape. Additionally, the location of rock bridges with respect to the geometry of an incipient rockfall is shown to determine failure mode. Weathering can occur both along discontinuity surfaces and previously broken rock bridges, indicating the sequential stages of progressively detaching rockfall. Our findings have wider implications for hazard assessment where rock slope stability is dependent on the nature of rock bridges, how this is accounted for in slope stability modelling, and the implications of rock bridges on long-term rock slope evolution.

A field investigation of application of digital terrestrial photogrammetry to characterize geometric properties of discontinuities in open-pit slopes

In order to analyze the slope stability in open-pit mines, the structural parameters of rock mass such as persistence and spatial orientation of discontinuities are characterized through field surveys, which involve spending high costs and times as well as posing high risks of rock toppling and rock fall. In the present work, a new application of terrestrial digital photogrammetry is introduced for characterizing the rock mass structural parameters through preparing photogrammetry images from open-pit walls and building stereomodels. The data extracted from processing the stereo-model generations using photogrammetry images with different focal distances are highly consistent with the data collected through field surveys. However, it must be noted that the weather conditions, natural lighting angle, and applied observation scale may considerably affect the results obtained from stereomodel processing. Nevertheless, by taking into account the parameters such as time, cost, and full access to the required data, this new method can effectively be used in the estimation of rock mass structural parameters for analysis of steep slopes in open pits.

Improvements to field and remote sensing methods for mapping discontinuity persistence and intact rock bridges in rock slopes

Discontinuity persistence and intact rock bridges are critical factors that influence the stability of rock slopes. Persistence influences the extent of pre-existing potential failure surfaces, and intact rock bridges can add cohesion and tensile strength to an incipient failure surface, which must be destroyed before slope failure can occur. Despite continued research and improvements in mapping technology, computing power, and numerical modelling codes, there is no standard recommended methodology for field characterisation of intact rock bridges, or their incorporation into stability analysis. We use observations from remote sensing and field mapping investigations at three open pit mines and one natural rock slope to recommend improvements to field and remote sensing methods for mapping discontinuity persistence and intact rock bridges in rock slopes.We apply a fracture network engineering approach to discontinuity trace mapping, using new intensity factors to describe intact rock bridge trace intensity R21, and blast-induced fracture intensity B21. We emphasize the importance of multi-scale characterisation of discontinuity persistence and rock bridges in rock slopes, and we distinguish between different classes of intact rock bridges based on scale and geometry, with particular attention given to the distinction between laboratory sample scale intact rock bridges on incipient discontinuities, and larger rock mass bridges, which represent metre or larger scale intervals of fractured rock mass that may exist between very high persistence joints and faults.

Rank-size distributions of Chinese cities: Macro and micro patterns

A large number of studies have been conducted to find a better fit for city rank-size distributions in different countries. Many theoretical curves have been proposed, but no consensus has been reached. This study argues for the importance of examining city rank-size distribution across different city size scales. In addition to focusing on macro patterns, this study examines the micro patterns of city rank-size distributions in China. A moving window method is developed to detect rank-size distributions of cities in different sizes incrementally. The results show that micro patterns of the actual city rank-size distributions in China are much more complex than those suggested by the three theoretical distributions examined (Pareto, quadratic, and q-exponential distributions). City size distributions present persistent discontinuities. Large cities are more evenly distributed than small cities and than that predicted by Zipf’s law. In addition, the trend is becoming more pronounced over time. Medium-sized cities became evenly distributed first and then unevenly distributed thereafter. The rank-size distributions of small cities are relatively consistent. While the three theoretical distributions examined in this study all have the ability to detect the overall dynamics of city rank-size distributions, the actual macro distribution may be composed of a combination of the three theoretical distributions.