Developments in a non-destructive method of determining rock strength: A reply

In a previous publication (Allison, 1989), a non-destructive method for indirectly determining rock strength by measuring Dynamic Young's Modulus was described. Data were presented to assess the Grindosonic apparatus in relation to standard laboratory techniques. A further Short Communication (Allison, 1990) evaluated the non-destructive test as a field technique, in part achieved by comparing the Grindosonic results with data collected using the Schmidt hammer. The Schmidt hammer is a widely used field technique in geomorphology for determining rock strength (see for example Day and Goudie, 1977; Day, 1981). Allison (1989, 1990) also suggested that the elastic properties of materials are becoming increasingly important in geomorphological studies. The opportunity to provide additional information and comments here is appreciated.     

Comments on Allison's (1990) developments in a non-destructive method of determining rock strength

In Developments in a non-destructive method of determining rock strength, Allison (1990) compares data collected using an ultrasonic apparatus with data obtained from Schmidt hammer tests. He concludes that the Schmidt hammer data shows a wide degree of scatter and that its accuracy as field technique is questionable. No discussion is made of how the Schmidt hammer was used or of the total number of readings taken and the range of values. The graphs presented comparing data derived from some samples using ultrasonic equipment do not appear markedly at variance from the Schmidt hammer-derived data but true comparison is not possible because the graphs use different measurement criteria. No information is given on comparative time and financial costs, which must be significantly different for the two techniques.     

Developments in a non-destructive method of determining rock strength

Material strength is an important variable for any study of the relationships between rock mass geomechanical characteristics and landform development. Standard field and laboratory tests for measuring strength present a variety of problems to the geomorphologist. Recent studies (Allison, 1988) have described a laboratory based non-destructive method for indirectly determining material strength, by measuring Dynamic Young's Modulus. Data presented here suggest that the same apparatus can be used as a field technique. Tests have been conducted on the Devonian limestone of the Napier Range, Western Australia. Laboratory results obtained using the non-destructive ultrasonic apparatus have a high correlation with triaxial Hoek Cell tests. Results from on-site tests have much greater accuracy than data collected using the Schmidt hammer, which is currently the most widely used geomorphological field technique for determining rock strength.     

A non-destructive method of determining rock strength

Rock material strength is an important component of many geomorphological studies. Current methods for determining this parameter result in sample destruction, preventing further analysis. A new non-destructive technique is described for indirectly determining material strength, by measuring Dynamic Young's Modulus. Tests have been conducted on Jurassic Portland Limestone and Upper Cretaceous Chalk to assess the apparatus. Young's Modulus is becoming an increasingly important rock material property.     

The effects of fire on rock weathering: some further considerations of laboratory experimental simulation

Fire in the natural environment is a widespread agent of geomorphological and biological change. Temperatures can exceed 1000°C. There is often a rapid rise from ambient conditions through a steep thermal gradient, promoting rock disintegration. Laboratory simulation studies have established that temperature changes which are representative of natural fires affect rock material properties, which can then be related to weathering susceptibility. This study extends previous work by more closely replicating the natural environment, (a) through the simulation of rainfall and (b) by encasing samples to reflect the exposure of a single rock face to a passing fire event. Rock samples collected on Cyprus were prepared and tested following previously reported procedures. Change in modulus of elasticity was monitored using a non-destructive ultrasonic method. The data corroborate previous work but with somewhat different degrees of change. The new results are more likely to be representative of natural conditions and real-world change. The rate of rock disintegration and effects such as case-hardening appear to be a function of rock thermal characteristics, material properties and environmental constraints such as diurnal temperature range. Copyright © 1999 John Wiley & Sons, Ltd.     

The micro-erosion meter: Use and limitations

Detection of anomalies in measurements of low rates of limestone surface lowering with a traversing micro-erosion meter (MEM) led to temperature-controlled laboratory and field investigations of some sources of error in the method. Regressions for the correction of temperature change in the instrument and in the stud-rock interface were obtained. Probe erosion tests permitted a correction to be devised and also provided information whereby a measure of operational irregularity was adopted. Corrections and error terms were applied to field measurements from two southern New South Wales karsts and a collection of Australian limestone slabs exposed at one site. Examination of these results and of published MEM rates from other parts of the world validated the MEM method. Marine platforms are lowered at such gross rates that these error sources may be neglected there. However limestone lowering in terrestrial environments cannot be assumed to proceed at rates which permit this and recommendations are made about procedures to ensure that investigations are prosecuted within the limitations of the method.     

Identification of strength equilibrium rock slopes: Further statistical considerations

Strength equilibrium slopes are rock slopes whose gradient θ and rock mass strength (RMS) are in adjustment. The identification of such slopes depends on the accurate specification of the strength equilibrium envelope. Previous attempts to delimit the envelope are reviewed and modifications are proposed that permit its more rigorous statistical definition. Because θ can be measured much more reliably than RMS, the structural relation between these variables is estimated by regressing RMS on θ, and the strength equilibrium envelope is defined by the 95 per cent confidence limits. The analysis is performed on a data set of 268 rock slopes, representing all the data on RMS and θ hitherto employed in published studies of strength equilibrium slopes.     

Use of the Acoustic Energy Meter (AEM) for rapid geomorphological field assessment of rock hardness: comparison with Schmidt hammer R‐value

Rapid, field‐based assessments of rock hardness are required in a broad range of geomorphological investigations where rock intact strength is important. Several different methods are now available for taking such measurements, in particular the Schmidt hammer, which has seen increasing use in geomorphology in recent decades. This is despite caution from within the engineering literature regarding choice of Schmidt hammer type, normalization of rebound (R‐) values, surface micro‐roughness, weathering degree and moisture content, and data reduction/analysis procedures. We present a pilot study of the use of an Acoustic Energy Meter (AEM), originally produced, tested and developed within the field of underground mining engineering as a rapid measure of rock surface hardness, and compare it with results from a mechanical N‐Type Schmidt hammer. We assess its capabilities across six lithological study sites in southeast Queensland, Australia, in the Greater Brisbane area. Each rock exposure has been recently exposed in the 20th/21st century. Using a ‘paired’ sampling approach, the AEM G‐value shows an inverse relationship with Schmidt hammer R‐value. While both devices show variability with lithology, the AEM G‐values show less scatter than the Schmidt hammer. We conclude that each device can contribute to useful rock hardness testing in geomorphological research, but the AEM requires further field testing in a range of environments, and in particular on older and naturally‐exposed rock surfaces. Future evaluations can extend this pilot study by focusing on sampling procedures, energy sources, and data reduction protocols, within the framework of a comparison study with other rock hardness testing apparatus. Copyright © 2016 John Wiley & Sons, Ltd.     

A new technique for non‐destructive field measurement of rock‐surface strength: an application of the Equotip hardness tester to weathering studies

Tafone‐like depressions have developed on the Aoshima sandstone blocks used for a masonry bridge pier in the coastal spray zone. A thin layer of partial granular disintegration was found on the surface in depressions. To evaluate quantitatively the strength of the thin weathered layer, the hardness was measured at the surface of the sandstone blocks using both an Equotip hardness tester and an L‐type Schmidt hammer. Comparison of the two testing results indicates that the Equotip hardness value is more sensitive in evaluating the strength of a thin layer of weathered surface rock than the Schmidt hardness value. By applying two methods, i.e. both the repeated impact method and the single impact method, the Equotip tester can evaluate the strengths of fresh internal and weathered surficial portions of rocks having a thin weathering layer. Comparison of the two strengths enables evaluation of strength reduction due to weathering. Copyright © 2007 John Wiley & Sons, Ltd.     

The influence of rock resistance on coastal morphology around Lord Howe Island,southwest Pacific

An Erratum has been published for this article in Earth Surface Processes and Landforms 27(7) 2004, 931. Lord Howe Island, in the northern Tasman Sea, is a remnant of a much larger Late Miocene basaltic shield volcano. Much of the island's coastline is exposed to waves that have unlimited fetch, but a marked contrast is provided by a fringing coral reef and lagoon that very effectively attenuate wave energy along a portion of the western coastline. The geology of the island is varied, with hard and resistant basalt lavas, breccias and tuffs of intermediate resistance, and highly erodible eolianites. This variability provides an excellent opportunity to examine the in?uence of rock resistance on the development of the spectacular rock coast landforms that occur around the island. The hardness of rocks and the extent of weathering around the coastline were assessed using a Schmidt hammer, and statistical analysis was undertaken to remove outlying values. On all but one occasion, higher mean rebound values were returned from fresh surfaces than weathered surfaces, but only half of these differences were statistically signi?cant. Shore platforms with two distinct levels are juxtaposed along two stretches of coastline and Schmidt hammer results lend support to hypotheses that the raised surfaces may be inherited features. Relative rock resistance was assessed through a combination of Schmidt hammer data and measurements of joint density, and constrained on the basis of morphological data. This approach formed a basis for examining threshold conditions for sea‐cliff erosion at Lord Howe Island in the context of the distribution of resistant plunging cliffs and erosional shore platforms. Copyright © 2004 John Wiley & Sons, Ltd.     

Field estimate of paleoseismic slip on a normal fault using the Schmidt hammer and terrestrial LiDAR: Methods and application to the Hebgen fault (Montana,USA)

The weathering characteristics of bedrock fault scarps provide relative age constraints that can be used to determine fault displacements. Here, we report Schmidt hammer rebound values (R‐values) for a limestone fault scarp that was last exposed in the 1959 Mw 7.3 Hebgen Lake, Montana earthquake. Results show that some R‐value indices, related to the difference between minimum and maximum R‐values in repeated impacts at a point, increase upward along the scarp, which we propose is due to progressive exposure of the scarp in earthquakes. An objective method is developed for fitting slip histories to the Schmidt hammer data and produces the best model fit (using the Bayesian Information Criterion) of three earthquakes with single event displacements of ≥ 1.20 m, 3.75 m, and c. 4.80 m. The same fitting method is also applied to new terrestrial LiDAR data of the scarp, though the LiDAR results may be more influenced by macro‐scale structure of the outcrop than by differential weathering. We suggest the use of this fitting procedure to define single event displacements on other bedrock fault scarps using other dating techniques. Our preliminary findings demonstrate that the Schmidt hammer, combined with other methods, may provide useful constraints on single event displacements on exposed bedrock fault scarps. Copyright © 2018 John Wiley & Sons, Ltd.     

Dynamics of deformation and water flow in heterogeneous porous media and its impact on soil properties

The interaction of geomechanics and flow within a soil body induces deformation and pore pressure change. Deformation may change hydrogeological and elastic properties, which alters the mechanical behaviour and results in non‐linearity. To investigate this interaction effect in a heterogeneous porous medium, a stochastic poroelastic model is proposed. Monte Carlo simulations are performed to determine the mean and uncertainty of the parameter changes, displacement, and change in pore water pressure. Hydraulic conductivity is treated as the only random variable in the coupled geomechanics‐flow system due to its large variation compared to other mechanical and hydrogeological properties in natural environments. The three considered non‐linear models for the interaction between parameters and deformation are those that consider (1) porosity and hydraulic conductivity; (2) porosity and Young's modulus; and (3) a combined effect that includes porosity, hydraulic conductivity, and Young's modulus. Boundary effects on the coupled system are also explored. The relationships between changes of porosity, hydraulic conductivity, and Young's modulus are analytically shown to be non‐linear. Among the considered parameters, the deformation effect induces the largest reduction in hydraulic conductivity. The deformation‐induced change in hydraulic conductivity shows the most significant effect on the mean and variance of the change in pore water pressure and displacement, while changes in Young's modulus have the least effect. When the deformation effect is considered, the superposition relationship does not exist in the mean displacement and mean change in pore water pressure for the three scenarios considered; it exists for the case without deformation effects. Deformation also causes a reduction in the effective hydraulic conductivity for the whole domain. The scenario that considers both loading and discharge boundaries has larger changes in hydrogeological and geo‐mechanical parameters than those in scenarios that consider loading and discharge boundaries separately. The results indicate that the interaction between deformation and changes in parameters has a profound effect on the poroelastic system. The effect of deformation should thus be considered in modelling and practice. Copyright © 2009 John Wiley & Sons, Ltd.     

Prestack amplitude versus angle inversion for Young's modulus and Poisson's ratio based on the exact Zoeppritz equations

Elastic parameters such as Young's modulus, Poisson's ratio, and density are very important characteristic parameters that are required to properly characterise shale gas reservoir rock brittleness, evaluate gas characteristics of reservoirs, and directly interpret lithology and oil‐bearing properties. Therefore, it is significant to obtain accurate information of these elastic parameters. Conventionally, they are indirectly calculated by the rock physics method or estimated by approximate formula inversion. The cumulative errors caused by the indirect calculation and low calculation accuracy of the approximate Zoeppritz equations make accurate estimation of Young's modulus, Poisson's ratio, and density difficult in the conventional method. In this paper, based on the assumption of isotropy, we perform several substitutions to convert the Zoeppritz equations from the classical form to a new form containing the chosen elastic constants of Young's modulus, Poisson's ratio, and density. The inversion objective function is then constructed by utilising Bayesian theory. Meanwhile, the Cauchy distribution is introduced as a priori information. We then combine the idea of generalised linear inversion with an iterative reweighed least squares algorithm in order to solve the problem. Finally, we obtain the iterative updating formula of the three elastic parameters and achieve the direct inversion of these elastic parameters based on the exact Zoeppritz equations. Both synthetic and field data examples show that the new method is not only able to obtain the two elastic parameters of Young's modulus and Poisson's ratio stably and reasonably from prestack seismic data but also able to provide an accurate estimation of density information, which demonstrates the feasibility and effectiveness of the proposed method. The proposed method offers an efficient seismic method to identify a “sweet spot” within a shale gas reservoir.     

Measuring the flow resistance of submerged grass

Through laboratory experiments conducted in a grass‐lined flume, the hydraulic resistance of grass is measured and quantified. For the grass examined, it is found that Manning's n value is greater than those recommended in well‐established texts such as Chow (1959. Open Channel Flow. McGraw‐Hill: Singapore), relatively lower than those predicted by n‐UR methods, but corresponds well with the value found from calibration studies of two‐ and three‐dimensional numerical models. The assumption of a uniform Manning's n value with flow depth, which is often made in numerical modelling, may be invalid depending on the relative submergence of the vegetation. Drag coefficients are evaluated for a method applicable to three‐dimensional numerical models. Further detailed experimental investigation and application of these approaches within a numerical modelling framework is now recommended. Copyright © 2002 John Wiley & Sons, Ltd.     

Modelling flow resistance in vegetated streams: review and development of new theory

Aquatic macrophytes are often the dominant factor influencing flow conditions within the channels they occupy. Existing knowledge of how stream plants affect the flow is outlined, and the different scales at which vegetation resistance operates are proposed. Resistance is shown to be a function of the size of the plants, their structural properties, location in the channel, and the local flow conditions. Current models to calculate this composite resistance effect are assessed in the light of theoretical considerations of the nature of vegetation resistance. New theory is also presented, which demonstrates the non‐linear relationship between channel resistance and the proportion of the channel occupied by vegetation. Copyright © 2004 John Wiley & Sons, Ltd.     

Spatial variation in soil resistance to flowing water erosion along a regional transect in the Loess Plateau

The factors influencing soil erosion may vary with scale. It remains unclear whether the spatial variation in soil erosion resistance is controlled by regional variables (e.g. precipitation, temperature, and vegetation zone) or by local specific variables (e.g. soil properties, root traits, land use, and farming operations) when the study area enlarges from a hillslope or catchment to the regional scale. This study was performed to quantify the spatial variations in soil erosion resistance to flowing water under three typical land uses along a regional transect on the Loess Plateau and to identify whether regional or local specific variables are responsible for these changes. The results indicated that the measured soil detachment capacities (D_c) of cropland exhibited an irregular trend along the regional transect. The D_c of grassland increased with mean annual precipitation, except for two sites (Yijun and Erdos). The measured D_c of woodland displayed an inverted ‘U’ shape. The changes in rill erodibility (K_r) of three land uses were similar to D_c, whereas no distinguishable trend was found for critical shear stress (τ_c). No significant correlation was detected between D_c, K_r and τ_c, and the regional variables. The spatial variation in soil erosion resistance could be explained reasonably by changes in soil properties, root traits, land use, and farming operations, rather than regional variables. The adjustment coefficient of K_r for grassland and woodland could be well simulated by soil cohesion and root mass density (R² = 0.70, P < 0.01), and the adjustment coefficient of critical shear stress could be estimated with aggregate stability (R² = 0.57, P < 0.01). The results are helpful for quantifying the spatial variation in soil detachment processes by overland flow and to develop process‐based erosion model at a regional scale. Copyright © 2015 John Wiley & Sons, Ltd.     

Variability in erosion rates related to the state of landscape transience in the semi‐arid Chilean Andes

We quantify erosion rates in the higher sectors of the Huasco Valley, in the Main Cordillera of the semi‐arid Andes of Chile, using elevation differences between three successive geomorphic markers (pediments and paleo‐valleys) and the present day valley. Available Ar‐Ar ages of Neogene pediments are used to estimate mean erosion rates for the three periods (16 to 13 My, 13 to 8 My, and following 8 My). The landscape of the Huasco Valley is in a transient state, as indicated by well‐preserved pediment surfaces in interfluves, valleys deeply incised by fluvial and glacial erosion and scarped head‐valleys that represent the current knickzones. Higher erosion rates (45–75 m/My) are calculated for the more recent period (< 8 My) during which deep incision developed compared to previous periods (6–31 m/My). Quantitative data indicate that glaciers had a much higher erosional capability than fluvial activity in the higher sectors of the Main Cordillera. Comparison with erosion rates calculated in other drainage basins of the Chilean Andes suggests that the variability of erosion rates depends on the landscape's transient erosive state. The landscape's geomorphologic response to the uplift of the Main Cordillera results in the retreat of a knickzone, for which retreat velocity depends on precipitation rate pattern and glacial erosion intensity. Copyright © 2011 John Wiley & Sons, Ltd.     

The architecture, eruptive history, and evolution of the Table Rock Complex, Oregon: From a Surtseyan to an energetic maar eruption

The Table Rock Complex (TRC; Pliocene–Pleistocene), first documented and described by Heiken [Heiken, G.H., 1971. Tuff rings; examples from the Fort Rock-Christmas Lake valley basin, south-central Oregon. J. Geophy. Res. 76, 5615-5626.], is a large and well-exposed mafic phreatomagmatic complex in the Fort Rock–Christmas Lake Valley Basin, south-central Oregon. It spans an area of approximately 40 km², and consists of a large tuff cone in the south (TRC1), and a large tuff ring in the northeast (TRC2). At least seven additional, smaller explosion craters were formed along the flanks of the complex in the time between the two main eruptions. The first period of activity, TRC1, initiated with a Surtseyan-style eruption through a 60–70 m deep lake. The TRC1 deposits are dominated by multiple, 1-2 m thick, fining upward sequences of massive to diffusely-stratified lapilli tuff with intermittent zones of reverse grading, followed by a finely-laminated cap of fine-grained sediment. The massive deposits are interpreted as the result of eruption-fed, subaqueous turbidity current deposits; whereas, the finely laminated cap likely resulted from fallout of suspended fine-grained material through a water column. Other common features are erosive channel scour-and-fill deposits, massive tuff breccias, and abundant soft sediment deformation due to rapid sediment loading. Subaerial TRC1 deposits are exposed only proximal to the edifice, and consist of cross-stratified base-surge deposits. The eruption built a large tuff cone above the lake surface ending with an effusive stage, which produced a lava lake in the crater (365 m above the lake floor). A significant repose period occurred between the TRC1 and TRC2 eruptions, evidenced by up to 50 cm of diatomitic lake sediments at the contact between the two tuff sequences. The TRC2 eruption was the last and most energetic in the complex. General edifice morphology and a high percentage of accidental material suggest eruption through saturated TRC1 deposits and/or playa lake sediments. TRC2 deposits are dominated by three-dimensional dune features with wavelengths 200–500 m perpendicular to the flow, and 20–200 m parallel to the direction of flow depending on distance from source. Large U-shaped channels (10–32 m deep), run-up features over obstacles tens of meters high, and a large (13 m) chute-and-pool feature are also identified. The TRC2 deposits are interpreted as the products of multiple, erosive, highly-inflated pyroclastic surges resulting from collapse of an unusually high eruption column relative to previously documented mafic phreatomagmatic eruptions.     

Erodibility of soil and organic matter: independence of organic matter resistance to interrill erosion

The enrichment of organic matter in interrill sediment is well documented; however, the respective roles of soil organic matter (SOM) and interrill erosion processes for the enrichment are unclear. In this study, organic matter content of sediment generated on two silts with almost identical textures, but different organic matter contents and aggregations, was tested. Artificial rainfall was applied to the soils in wet, dry and crusted initial conditions to determine the effects of soil moisture and rainfall and drying history on organic matter enrichment in interrill sediment. While erosional response of the soils varied significantly, organic matter enrichment of sediment was not sensitive to initial soil conditions. However, enrichment was higher on the silt with a lower organic matter content and lower interrill erodibility. The results show that enrichment of organic matter in interrill sediment is not directly related to either SOM content or soil interrill erodibility, but is dominated by interrill erosion processes. As a consequence of the complex interaction between soil, organic matter and interrill erosion processes, erodibility of organic matter should be treated as a separate variable in erosion models. Further research on aggregate breakdown, in particular the content and fate of the organic matter in the soil fragments, is required. Copyright © 2007 John Wiley & Sons, Ltd.