Persistent Discontinuities Research Articles

Empirical Assessment of the Mean Block Volume of Rock Masses Intersected by Four Joint Sets

The estimation of a representative value for the rock block volume (Vb) is of huge interest in rock engineering in regards to rock mass characterization purposes. However, while mathematical relationships to precisely estimate this parameter from the spacing of joints can be found in literature for rock masses intersected by three dominant joint sets, corresponding relationships do not actually exist when more than three sets occur. In these cases, a consistent assessment of Vb can only be achieved by directly measuring the dimensions of several representative natural rock blocks in the field or by means of more sophisticated 3D numerical modeling approaches. However, Palmstrom’s empirical relationship based on the volumetric joint count Jv and on a block shape factor β is commonly used in the practice, although strictly valid only for rock masses intersected by three joint sets. Starting from these considerations, the present paper is primarily intended to investigate the reliability of a set of empirical relationships linking the block volume with the indexes most commonly used to characterize the degree of jointing in a rock mass (i.e. the Jv and the mean value of the joint set spacings) specifically applicable to rock masses intersected by four sets of persistent discontinuities. Based on the analysis of artificial 3D block assemblies generated using the software AutoCAD, the most accurate best-fit regression has been found between the mean block volume (\(V_{{{\text{b}}_{\text{m}} }}\)) of tested rock mass samples and the geometric mean value of the spacings of the joint sets delimiting blocks; thus, indicating this mean value as a promising parameter for the preliminary characterization of the block size. Tests on field outcrops have demonstrated that the proposed empirical methodology has the potential of predicting the mean block volume of multiple-set jointed rock masses with an acceptable accuracy for common uses in most practical rock engineering applications.

A discrete fracture network approach for the design of rock foundation anchorage

A major consideration in the design of high-capacity tiedown anchors for dams, bridges and tower foundations includes the tensile resistance of the rock mass to pullout typically as a result of overturning moments or hydrostatic uplift. Rock mass pullout capacity for installed anchors is developed from the tensile strength and fracture propagation properties of intact rock, the orientation and physical properties of the discontinuities and anchor confinement at depth. The typically assumed but conservative design approach is to assume that only the dead weight of a uniformly shaped inverted ‘rock pull out cone’ provides resistance to anchor pullout with an assumed initiation point and breakout angle. It is appreciated that the ‘dead weight’ cone assumption may be valid if the discontinuities are continuous and the geometry allows for a discrete block to form in the area of anchorage. However, if these persistent joints are not ubiquitously developed this failure mechanism may not represent the conditions across a foundation and can lead to a very conservative anchor designs. A less conservative approach is to consider the deadweight and the tensile strength across the surface area of the assumed pullout cones. Strength estimates are often estimated by a designer using correlations based on the Hoek–Brown failure criteria or the Barton Q-system. However, fundamental assumption of these empirical methods is that the discontinuities are sufficiently closely spaced such that the rock mass can be considered homogenous and isotropic – and this often not the case (Hoek, Carter and Diederichs 2013). In reality, at the scale of many rock anchor pullout problems, the strength and deformation properties of the rock mass are anisotropic, controlled by a few persistent discontinuities and small ‘rock bridges’ that exist between naturally occurring joints. To accommodate scale effects and the variability of jointing, this paper introduces a reliability-based design (RBD) approach for anchors that uses discrete fracture networks (DFNs) combined with numerical models. With this approach, limitations of the current practice for anchor design are addressed and opportunities are identified to optimise rock anchor designs provided that sufficient information is available to produce a representative DFN. Typically, this requires geological mapping to characterise the rock mass and verify the conditions at discrete anchor locations and in situ anchor testing can be carried out during construction.

Sequential city growth: Theory and evidence from the US

City growth patterns are attracting more attention in urban geography studies. This paper examines how cities develop and grow in the upper tail of size distribution in a large-scale economy based on a theoretical model under new economic geography framework and the empirical evidence from the US. The results show that cities grow in a sequential pattern. Cities with the best economic conditions are the first to grow fastest until they reach a critical size, then their growth rates slow down and the smaller cities farther down in the urban hierarchy become the fastest-growing ones in sequence. This paper also reveals three related features of urban system. First, the city size distribution evolves from low-level balanced to primate and finally high-level balanced pattern in an inverted U-shaped path. Second, there exist persistent discontinuities, or gaps, between city size classes. Third, city size in the upper tail exhibits conditional convergence characteristics. This paper could not only contribute to enhancing the understanding of urbanization process and city size distribution dynamics, but also be widely used in making effective policies and scientific urban planning.

Slope stability in slightly fissured claystones and marls

The paper deals with the behavior of some characteristic soft rocks found in the Iberian Peninsula. In geological terms, they belong to Tertiary basins, the Keuper period and the Jurassic-Cretacic transition. The discussion is organized around the following aspects: (a) the intact material and its brittle behavior; (b) the weathering action of atmospheric events; (c) the persistent discontinuities and scale effects; and (d) the modification of strength after failure. In all cases, instability phenomena are addressed in connection with several case histories. Regarding material brittleness and the initial stress state, two cases of first time failures are discussed. Practical implications concerning the selection of operative strength will be given. Field observations of the relevance of weathering and, also, on the rate of weathering, are given for a Weald claystone. Field observations emphasize the importance of sharp transitions between weathered and intact (or slightly weathered) levels. A recent long-term laboratory investigation on the nature of degradation will be summarized. Macroscopic variables such as stiffness and tensile strength have been found to be uniquely predicted by a degradation law in terms of the accumulated plastic deformations. Persistent discontinuities and, in particular, sedimentation planes play a dominant role to explain slope failures not related to the shallow failures, usually associated with weathered profiles. The strength of discontinuities in a Weald formation was investigated by means of tests performed at two scales. Finally, the evolution in time of residual strength induced by chemical actions, associated with groundwater flow, is highlighted in connection with actual field data of unstable slopes.

Size Distribution for Potentially Unstable Rock Masses and In Situ Rock Blocks Using LIDAR-Generated Digital Elevation Models

In this paper, two analytical procedures which are independent from the existence of empirical data are presented for the calculation of (1) the size distribution of potentially unstable rock masses that expresses the potential rockfall size distribution, including big volumes corresponding to potential rare events with low susceptibility of failure and (2) the in situ block distribution on the slope face. Two approaches are, respectively, used. The first one involves the detection of kinematically unstable surfaces on a digital elevation model (DEM) and on orthophotos and the calculation of the volumes resting on them. For the second one the in situ block volumes formed by the intersection of the existing discontinuity sets are calculated using a high-resolution DEM. The procedures are presented through an application example at the country of Andorra and in particular at the chute of Forat Negre. The results from the first procedure indicate that it is kinematically possible to have mobilized volumes of some thousands of cubic meters; however, these are considered rare events with low susceptibility of failure. The size distribution of potentially unstable rock masses for big volume events was well fitted by a power law with an exponent of −0.5. The in situ block distribution on the slope face from the second procedure, assuming three types of intersection between the joints of the existing discontinuity sets and two extreme cases of discontinuity persistence, was also found to follow a power law, but with an exponent of −1.3. The comparison with the observed in the field block volume distribution on the slope face indicates that in reality discontinuities have a very high persistence and that considering only their visible trace length overestimates volumes, which is conservative.

Characterization of bi-planar and ploughing failure mechanisms in footwall slopes using numerical modelling

Footwall slopes refer to unbenched rock slopes in which the slope face is parallel to a set of persistent discontinuities (e.g. bedding planes, foliation, faults). These are commonly encountered in weak, thinly bedded, orthogonally jointed, sedimentary rock sequences. Common failure mechanisms include bi-planar failures where shallow dipping crosscutting structures daylight near the slope toe, enabling sliding to occur along steep dipping bedding planes. In the absence of crosscutting structures, failure occurs through deformation and rock mass yielding involving the formation of inter block shear and toe breakout surfaces. Because of the complexity of the toe breakout mechanism, evaluation methods are not well understood. An improved understanding of the failure mechanism, the role of adverse discontinuities, and characterization of the discontinuity, intact rock and rock mass strength properties are key for a successful footwall stability analysis. This paper investigates the development of the inter block shear and toe breakout surfaces with three approaches: i) continuum-based frictional plasticity theory; ii) discontinuum-based distinct-element modelling with Voronoi tessellation using the commercial software UDEC; and iii) hybrid continuum/discontinuum finite-/discrete-element brittle fracture modelling using the commercial software ELFEN. Numerical simulations using ELFEN and UDEC demonstrated a good agreement with frictional plasticity theory. Ploughing failure of footwall slopes is also evaluated, specifically the influence of cross-cutting discontinuity dip angle relative to the slope face. The effects of different geometrical parameters (e.g., slope angle and depth/height ratio) on bi-planar and ploughing failure are assessed using a sensitivity analysis approach. A “Damage Intensity” parameter is introduced and used to quantify damage in the numerical simulations using ELFEN.

Tunnel behaviour and support associated with the weak rock masses of flysch

Flysch formations are generally characterised by evident heterogeneity in the presence of low strength and tectonically disturbed structures. The complexity of these geological materials demands a more specialized geoengineering characterisation. In this regard, the paper tries to discuss the standardization of the engineering geological characteristics, the assessment of the behaviour in underground excavations, and the instructions–guidelines for the primary support measures for flysch layer qualitatively. In order to investigate the properties of flysch rock mass, 12 tunnels of Egnatia Highway, constructed in Northern Greece, were examined considering the data obtained from the design and construction records. Flysch formations are classified thereafter in 11 rock mass types (I–XI), according to the siltstone–sandstone proportion and their tectonic disturbance. A special geological strength index (GSI) chart for heterogeneous rock masses is used and a range of geotechnical parameters for every flysch type is presented. Standardization tunnel behaviour for every rock mass type of flysch is also presented, based on its site-specific geotechnical characteristics such as structure, intact rock strength, persistence and complexity of discontinuities. Flysch, depending on its types, can be stable even under noticeable overburden depth, and exhibit wedge sliding and wider chimney type failures or cause serious deformation even under thin cover. Squeezing can be observed under high overburden depth. The magnitude of squeezing and tunnel support requirements are also discussed for various flysch rock mass types under different overburdens. Detailed principles and guidelines for selecting immediate support measures are proposed based on the principal tunnel behaviour mode and the experiences obtained from these 12 tunnels. Finally, the cost for tunnel support from these experiences is also presented.

APPLICATION OF LASER SCANNING SURVEYING TO ROCK SLOPES RISK ASSESSMENT ANALYSIS

Abstract. The methods for understanding rock instability mechanisms and for evaluating potential destructive scenarios are of great importance in risk assessment analysis dedicated to the establishment of appropriate prevention and mitigation actions. When the portion of the unstable rock mass is very large, effective actions to counteract the risks are complex and expensive. In these conditions, an optimal risk management cannot ignore procedures able to faster and accurately acquire i) geometrical data for modeling the geometry of the rock walls and implementing reliable forecasting models and ii) monitoring data able to describe the magnitude and the direction of deformation processes. These data contributes to the prediction of the behavior of a landslide if the measurements are acquired frequently and reliable numerical models can be implemented. Innovative geomatic techniques, based on GPS, Terrestrial Laser Scanning Surveying (TLS), automated total station and satellite and ground SAR Interferometry, have been recently applied to define the geometry and monitoring the displacements of unstable slopes. Among these, TLS is mainly adopted to generate detailed 3D models useful to reconstruct rock wall geometry by contributing to the estimation of geo-mechanical parameters, that is orientation, persistence and apparent spacing of rock discontinuities. Two examples of applications of TLS technique to the analysis of a large front in a quarry and of a rock shoulder of a dam are presented.

Discontinuities in the evolution of the city system in Texas from 1850 to 2010

We report the results of a historical investigation and quantification of discontinuous evolution, and a gap statistic analysis of discontinuities, on city size distributions of the city system in Texas, USA, over a 160-year period from 1850 to 2010. The growth of the city system exhibits four stages that are evident from our quantitative analysis of the convergence of population in large cities and qualitative analysis of historical socioeconomic and technological developments. The decadal city size distributions in the aggregate evolve with a persistent pattern while individual cities over time shift positions in the urban hierarchy as the result of adapting or passing growth opportunities in infrastructure innovations, economic change, and industrial transformations. These decadal city size distributions exhibit persistent discontinuities that mainly occur in the upper and lower tails. The observed patterns and discontinuities are indicative of the stability and resilience of a complex adaptive system of cities.

Modeling progressive failures in rock slopes with non‐persistent joints using the numerical manifold method

SUMMARYRock slope failure is a complex process that usually involves both opening/sliding along pre‐existing discontinuities as well as fracturing of intact rock bridges. Discontinuity persistence is an important factor governing rock slope instabilities. However, traditional slope failure analysis assumes persistent discontinuities, and rock slope fails along a predefined persistent continuous potential failure surface because of the limitations of the analysis tools. This paper proposes the numerical manifold method (NMM) incorporated with a Mohr–Coulomb criterion‐based fracturing algorithm to simulate the progressive failure of rock slopes with non‐persistent joints. Detailed fracturing algorithm is first presented. Then, the NMM enabling fracturing is calibrated through simulating an edge‐cracked plate and the Brazilian test. Lastly, the developed code is applied to investigate the failure process of rock slopes involving non‐persistent joints. Numerical results indicate that the proposed method can capture the opening/sliding along existing discontinuities, the fracturing in intact rock bridges and the final kinematic release. Progressive slope failure is well exhibited. Copyright © 2013 John Wiley & Sons, Ltd.

Effects of Geo-Engineering Characteristics of the Soft Tuffs and Environmental Conditions on the Rock-Hewn Historical Structures at Zelve Open Air Museum, Cappadocia, Turkey

The Cappadocia region, with its very distinct culture, is one of the attractive tourist sites of Turkey due to its spectacular and unique landforms and historical heritage. In this region, the structures carved into thick and soft tuffs have survived and kept their integrity for about 12–13 centuries. The Zelve Open Air Museum, consisting of three valleys, is one of the oldest antique semi-underground settlements in the region and is designated as a World Heritage Site in Turkey. Although it was closed to human habitation due to collapses, which occurred within some of the rock-hewn structures and resulted in three casualties in 1950s, it is open to tourists. Particularly in the first valley, there are a lot of rock-hewn openings of different sizes and several churches with some geo-engineering problems. This study aims to assess the geo-engineering characteristics of the soft tuffs surrounding the rock-hewn historical structures and environmental conditions in the first valley of the Zelve Open Air Museum and their possible effects on the geo-engineering problems observed in this museum. The results mainly suggest that the strength of rock is reduced drastically under saturated conditions, and the processes of freezing-thawing and wetting-drying accelerate further degradation of rock under saturated conditions. Over a period of about five years, the amount of erosion, which mainly resulted from the two strong agents of rainfall and wind, ranged between 1.07 and 6.21 mm. Assuming that the erosion is homogeneous, determined annual average erosion ranges between 0.21 and 1.24 mm/yr. These observations suggest that erosion is an important phenomenon in this site and increases particularly in the winter and spring seasons. The failure modes, such as falling, sliding, bending, spalling, and slabbing, observed in the valley are considered to be mainly associated with deterioration and erosion of tuffs near vertical and laterally persistent discontinuities generally oriented perpendicular and parallel to the valley, and property changes due to cyclic freezing-thawing and wetting-drying processes. Spalling and slabbing occurring in cliffs and semi-underground openings are the indicators of yielding of rock. These phenomena result in the formation of slabs with different thicknesses, and consequently cause a change in geometry of the openings in the valley to trigger failures.

Stability of Rock Pillars with Singular and Persistent Discontinuities

Problem statement: The strength of rock pillars in the presence of single, persistent, natural discontinuities can seriously be compromised and lead the pillar to collapse because of instability along the discontinuity itself. Approach: A specific analysis method for this kind of problem has been set up in this study to evaluate the stability of pillars and to determine the dimension that this kind of pillar should have in order to guarantee the minimum requested safety factor. Results and Conclusion: The objective is to determine the limit shear stress and the actual acting shear stress at 25 points distributed along the discontinuity in order to then be able to obtain the safety factor concerning collapse of the pillar along the discontinuity surface.

Hydrogeological site characterization of marly-silici-calcareous rocks through surveys of discontinuities and pumping tests

One of the challenges in the characterization of fractured aquifers is to define whether the approximation to a porous medium is valid or not. In this context, the present study concerns the hydrogeological characterization of a small area constituted by densely fractured marly-silici-calcareous rocks. The hydrogeological investigations included fracture network surveys and pumping tests. The survey of the outcrops showed a rock mass characterized by a high number of persistent discontinuities with a wide spatial distribution, high frequency and a wide range of values of the aperture in the different systems. These characteristics imply the possibility of considering the rock mass as an equivalent porous medium at the outcrop scale. Pumping tests highlighted a consistent reaction of the various monitoring points and a similar trend of the drawdown-time curve, resulting in considering the aquifer as continuous medium at the scale of the volume influenced by pumping. The drawdown maps seems to be related to a weak anisotropy of the aquifer in the horizontal plane with the major axis of the ellipse aligned along the direction NE-SW, consistent with the directions of the principal components of the hydraulic conductivity resulting from the hydraulic model of the rock mass. Although the aquifer can be considered an equivalent anisotropic porous medium at the scale of the study, the comparison between the results of pumping tests and of the rock mass survey indicates that this approach would be not sufficient to characterize groundwater movement.

Evaluating Kinematic Controls on Planar Translational Slope Failure Mechanisms Using Three-Dimensional Distinct Element Modelling

This paper investigates the importance of kinematic release mechanisms on planar translational slope failure using three-dimensional distinct element codes. The importance of the dip and dip direction of the rear, basal and lateral release surfaces and their influence on failure mechanism, dilation, and the development of step-path failures is illustrated. The three-dimensional block shape and volume of the unstable rock masses simulated with the different discontinuity set geometries are characterized. Two assumed three-dimensional slope models are investigated in order to assess the importance of varying kinematic confinement/release mechanisms. These two assumed boundary conditions are shown to be critical in the development of asymmetrical rock mass deformation patterns. Scale effects due to the block size and discontinuity persistence are shown to control the calculated displacement and failure mechanisms. The numerical modelling results are also demonstrated to be sensitive to the assumed normal and shear stiffness of the discontinuities. The influence of the factors investigated on the failure of a single rock block versus a rock mass are compared and discussed.

Assessment of Parameter Uncertainty Associated with Dip Slope Stability Analyses as a Means to Improve Site Investigations

Uncertainty is inherent in geotechnical design. In regard to estimating the stability state of dip slopes, most of the uncertainty lies in the geologic model assumed and the geotechnical parameters used in the evaluation. Biplanar (or active-passive) sliding in dip slopes occurs along a slope-parallel sliding surface with toe breakout occurring at the base of the failure. Internal shearing is required to facilitate kinematic release. All three of these release surfaces work together for the slope to fail, but with different degrees of importance depending on the dip-slope inclination. Increased efficiency and value with respect to the site investigation resources can be gained by working toward minimizing the uncertainty of those parameters that have the greatest bearing on the outcome of the slope stability analysis. This can be done quickly and inexpensively by performing scoping calculations facilitated by the use of Spearman rank correlation coefficients. This paper demonstrates that for shallow-dipping dip slopes, stability is primarily dictated by the shear strength of the slope-parallel sliding surface, and therefore, efforts should be focused on constraining the shear strength of this surface. For steep dip slopes, the shear strength related to the toe breakout and internal shear release surfaces becomes dominant, and therefore, the rock-mass shear strength and that for any adversely dipping persistent discontinuities should be the focus of the geotechnical investigation. DOI: 10.1061/(ASCE)GT.1943-5606.0000515. © 2012 American Society of Civil Engineers. CE Database subject headings: Slope stability; Uncertainty principles; Rocks; Rock masses; Site investigation. Author keywords: Dip slope; Uncertainty; Rock engineering; Reliability; Rock-mass rating; Geological strength index.

C4 Rock slope stabilization

The assessment of rock slope stability is dependent on whether stability is controlled by: ### C4.1.1 Failure controlled by the intact rock strength For continuous rock masses, where discontinuities play no role in controlling stability, a given slope might be cut vertically for rock with high intact strength (Fig. C4.1) or treated as a soil if weak and cut to a shallow angle. Rock strength is a function of the mineralogy, the interaction (physical/chemical) between the grains and the processes which have affected the rock after its formation (e.g. Anon 1977). Fig. C4.1. Sandstone cut vertically where discontinuities play no role in stability. Hawkins (1998) compares various methods in place (e.g. Deere & Miller 1966, IAEG 1981, ISRM 1981, BSI 1999) for classifying rock by unconfined compressive strength (UCS) in terms of MPa. Field methods for estimating UCS are described, for example, in BSI EN (2003). ### C4.1.2 Failure controlled by discontinuities The most frequently occurring rock slope failures are due to either displacement along dominant persistent discontinuities or multiple closely-spaced discontinuities (as illustrated in Fig. C4.2). The strength of the intact rock is usually ignored when rock slope stability is discontinuity-controlled. Fig. C4.2. Discontinuity-controlled rock slope stability ( a ) persistent; ( b ) multiple, closely-spaced. ### C4.2.1 Discontinuity-controlled stability (assessment method 1) Usually, rock failures occur predominantly along a single discontinuity or a combination of two or three. The geometrical relationship between these discontinuities and the angle and orientation of the hillside or cut slope is usually the most important factor in determining rock slope stability. Discontinuity-controlled rock slope failure mechanisms are described and illustrated in Part A and include planar, wedge and toppling failures (Fig. C4.3 and Hoek & Bray 1981; Wyllie & Mah 2004). Along mountain roads, true wedge failures and topples are usually far less frequent than …

Assessment of periglacial slope stability for the 1988 Tschierva rock avalanche (Piz Morteratsch, Switzerland)

The Tschierva rock avalanche occurred on October 29, 1988 in the area of the Piz Morteratsch, Switzerland. Releasing a total volume of ~ 300,000 m 3, the avalanche ran out over 1 km destroying a hiking trail before stopping on the Tschierva Glacier. We analyze the setting of this periglacial slope failure, combining geomechanical and cryosphere investigations to identify the primary factors contributing to the rock avalanche. An approach to slope stability assessment is presented that copes with existing data limitations in an inaccessible alpine terrain. Results from the analyses of morphology, geology, glaciation history, permafrost, hydrology, and meteorological data allowed preliminary inferences to be made regarding the influence of these factors on slope stability. Conceptual kinematic and numerical slope stability modeling critically analyzed the role of kinematic degrees of freedom, glacier retreat, and water infiltration from above the detachment zone. Results highlight the strong influence of discontinuity orientation with respect to the slope face, the role of a fault zone with increased joint density, and long-term progressive development of persistent discontinuities induced by glacier retreat and groundwater loading cycles in leading to the rock avalanche. The role of permafrost could not be clearly assessed, however observations and analyses indicate that permafrost had no dominant influence on the slope failure. Extraordinary precipitation prior to the event is suggested to have played a role in triggering the rock avalanche, especially in combination with observed superficial ice that could have sealed the rock face generating high water pressures. Our results emphasize the importance of analyzing multiple contributing factors when assessing alpine rock slope failures, with careful consideration of data limitations prevailing in such areas.

Polyhedral modelling of underground excavations

Abstract The use of key-block theory for the analysis of blocky rock mass structures in mining and civil engineering is well established. Such methods have traditionally been used to analyse the stability of rock blocks at free surfaces only. These methods have also been limited to the analysis of relatively few discontinuities, usually assumed to be infinitely persistent. Development of more advanced algorithms has removed these limitations and allowed the development of a modeller capable of handling multiple curved, finite persistent discontinuities. We discuss this modeller and its capability of predicting the existence of polyhedra with unlimited facets and morphologies. This paper describes the use of this polyhedral modeller for the study of the stability of an underground excavation and offers significant advantages over the algorithm recently reported by Menendez-Diaz et al. (2009) [3] which is restricted to the analysis of pentahedral blocks formed by four discontinuity sets.

Close-range terrestrial digital photogrammetry and terrestrial laser scanning for discontinuity characterization on rock cuts

This paper reviews the application of close-range terrestrial digital photogrammetry and terrestrial laser scanning for discontinuity characterization on rock cuts. Terrestrial remote sensing techniques are being increasingly used as a complement to traditional scanline and window mapping methods. They provide more comprehensive information on rock cuts, allow surveying of inaccessible outcrops, and increase user safety. Selected case studies are used to estimate the accuracy of several 3D model registration approaches and the most time-, effort- and cost-effective methods are highlighted. It is shown that simple registration networks are able to provide adequate measurement of discontinuity orientation for engineering purposes. The case studies presented also illustrate the effects of sampling bias and limitations related to discontinuity characterization using remote sensing techniques. Vertical orientation bias and occlusion can be of particular concern when persistent discontinuities dip at the same angle as the camera/scanner line-of-sight. Major advantages of the techniques are presented illustrating how terrestrial remote sensing techniques provide rapid spatial measurements of discontinuity location, orientation and curvature and are well suited to the quantification of persistence magnitudes greater than 3 m.

On the role of discontinuities in mediating shore platform erosion

In this paper, we quantitatively demonstrate that dominant erosion processes on different shore platforms can be explained, in part, by geological properties. We selected sites with a considerable history of rock coast geomorphology study, to evaluate whether geological data can improve our understanding of spatial variations in erosion between sites. Schmidt Hammer tests and discontinuity data were collected on Blue Lias limestone shore platforms in Wales, UK, and sandstone platforms in Victoria, Australia. Significant differences in joint spacing, persistence of discontinuities and block size were found between the Australian and Welsh study sites. These data were related to evidence of meso-scale erosion to examine how geological contingency influences the nature and scale of erosion processes and thresholds. This study quantitatively demonstrates that discontinuities play a fundamental role in altering rock resistance. The findings of this research have important implications for the design of rock coast erosion studies concerned with measuring rates of change and determining the relative contributions of different processes to platform development.