Fractal techniques and the surface roughness of talus slopes

Linear plots of log N against log G, where N is the number of steps of length G to span a transit, are conventionally used as evidence that geomorphic surfaces are self-similar fractals (i.e. the surfaces have a constant fractal dimension). In this study 42 transits on talus slope surfaces in Niagara and Letchworth Gorges, western New York, are investigated to ascertain whether they are self-similar. Log N-log G plots, which r² values in excess of 0·99 suggest are linear, are found upon more rigorous testing to be curvilinear. It is concluded that the talus slope surfaces are not self-similar, and that log N-log G plots are relatively insensitive to departures from self-similarity. The curvilinearity of the log N-log G plots is explained with the aid of a randomized square-wave model of the talus slope surfaces. This model is used to extend the range of measurement beyond that which was possible in the empirical analysis. The negative of the gradient of the log N -log G relation at a point is the fractal dimension D. Measurements made upon the randomized square-wave model indicate that the relation between D and scale of measurement has an asymmetrical wave shape with a peak (i.e. maximum D) where the scale of measurement is equal to the characteristic scale of roughness. In other words the value of D for a surface is not absolute but depends on the scale of measurement relative to the scale of roughness. Linear regression analysis reveals that at the scale of measurement employed in this study, D is positively correlated with particle size. This is because the values of D fall on the right-hand tail of the wave-shaped relation between D and scale of measurement. Transects (normal to the direction of slope) are found to have higher values of D than profiles (parallel to the direction of slope), and this is explained in terms of particle orientation, shape, and juxtaposition. Because D varies continuously with scale of measurement, there are considerable difficulties in using it to characterize and compare the surface roughness of talus slopes. Generalizing from talus slopes to other ground surfaces, it is evident that to the extent that any natural ground surface has a characteristic scale of roughness, it will depart from self-similarity, and D should be used with caution in quantifying the roughness of the surface. Geomorphologists are therefore urged to be more rigorous in their testing of self-similarity before employing D to characterize surface roughness.     

The measurement and modelling of rill erosion at angle of repose slopes in mine spoil

The process of rill erosion causes significant amounts of sediment to be moved in both undisturbed and disturbed environments and can be a significant issue for agriculture as well as mining lands. Rills also often develop very quickly (from a single rainfall event to a season) and can develop into gullies if sufficient runoff is available to continue their development. This study examines the ability of a terrestrial laser scanner to quantify rills that have developed on fresh and homogeneous mine spoil on an angle of repose slope. It also examines the ability of the SIBERIA erosion model to simulate the rill's spatial and temporal behaviour. While there has been considerable work done examining rill erosion on rehabilitated mine sites and agricultural fields, little work has been done to examine rill development at angle of repose sites. Results show that while the overall hillslope morphology was captured by the laser scanner, with the morphology of the rills being broadly captured, the characteristics of the rills were not well defined. The digital elevation model created by the laser scanner failed to capture the rill thalwegs and tops of the banks, therefore delineating a series of ill defined longitudinal downslope depressions. These results demonstrate that an even greater density of points is needed to capture sufficient rill morphology. Nevertheless, SIBERIA simulations of the hillslope demonstrated that the model was able to capture rill behaviour in both space and time when correct model parameters were used. This result provides confidence in the SIBERIA model and its parameterization. The results demonstrate the sensitivity of the model to changes in parameters and the importance of the calibration process. Copyright © 2007 John Wiley & Sons, Ltd.     

Runoff generative process and runoff yield from arid talus mantled slopes

Previous works dealing with the influence of a stone cover on runoff yield showed that runoff, attributed to the sealing effect of the topsoil by raindrops impact, was negatively related to the per cent of stone cover and stone size. These works were conducted on gentle slopes (3–11·5 degree) with a per cent of stone cover generally lower than 50 per cent, and composed of gravels. The present study deals with the runoff yield of steep talus slopes (26–36 degree) whose per cent of stone cover is very high (90–100 per cent), composed of cobbles and boulders. Three stimulated rainstorms were performed at various rainfall. intensities and durations on each one of six plots representative of the North eastern sector of Sinai. Although the contiguous stony cover prevented surface sealing by raindrops impact, runoff developed quite quickly on most slopes, and reached at peak discharge, after approximately ten minutes, up to 56 per cent of the rainfall. Differences between plots, in time lag, peak discharge and other hydrological variables, could be attributed mainly to the properties of the upper stony layer, with stone size as the most influential factor. Contrary to previous works, a positive relationship, was obtained between stone size to runoff yield. The result is explained by the process of water concentration. Each cobble and boulder behaves, on a smaller scale, like a bare rocky surface and yields per unit area water amounts beyond the infiltration rate of the limited uncovered areas. For a given stony cover the effect of water concentration is quicker with the big blocks than with gravels. A series of graphs trying to relate theoretically the relative importance of sealing and water concentration processes in runoff generation, at various conditions of stone cover and stone size, is proposed. The graphs enable to reconcile the results of the present study with those of previous works.     

Investigations regarding Alpine talus slopes using ground‐penetrating radar (GPR) in the Bavarian Alps,Germany

The applicability of ground‐penetrating radar (GPR) for the investigation of loose debris was tested at two sites (Viererkar and Zugspitzplatt). A pulseEKKO 100 GPR system equipped with 25 MHz antennae was utilized. The aim of the investigation was to record the base of the debris layer, and thereby acquire an estimation of the backweathering rates of the adjacent rockwalls. The study areas are situated in the Northern Alps near the German–Austrian border. The sites are characterized by steep limestone rockwalls and extensive talus accumulations. A total of six profiles was surveyed. The method is suitable and effective for a quick survey in this dry, high‐ohmic substrate. The GPR system was able to deliver information about the subsurface stratigraphy to c. 70 m depth. The boundary line to the bedrock was discovered – depending upon the profile surveyed ?5 to 25 m below the surface. The base of the debris material sometimes shows no distinct reflection. Buried features (V‐shaped furrows, zones overdeepened by ice action, geological structures) could be detected. Arched structures well below the talus–bedrock interface can be interpreted as drainage systems in the karstic bedrock. A thick scree layer of Late Glacial age was separated from a thinner layer on the talus surface, which was related to the Holocene. The backweathering rates were fixed by a calculation of talus volume to c. 100 mm/10³ a during the Holocene (Viererkar) and 150–300 mm/10³ a (Zugspitzplatt). The detrital formation in north‐exposed sites is twice as intense as in south‐exposed sites. These results match the rates of recent rockfall in the same area of investigation. The calculated backweathering for the late glacial period is 150–730 mm/10³ a. The magnitude of the calculated rockwall retreat lies well within the range of previous measurements. The discrepancy between some weathering rates highlights the fact that recent and past relief formation must be differentiated. Otherwise recent removal rates may be overestimated. Copyright © 2001 John Wiley & Sons, Ltd.     

Oceanic ridges and transform faults: Their intersection angles and resistance to plate motion

The persistent near-orthogonal pattern formed by oceanic ridges and transform faults defies explanation in terms of rigid plates because it probably depends on the energy associated with deformation. For passive spreading, it is likely that the ridges and transforms adjust to a configuration offering minimum resistance to plate separation. This leads to a simple geometric model which yields conditions for the occurrence of transform faults and an aid to interpretation of structural patterns in the sea floor. Under reasonable assumptions, it is much more difficult for diverging plates to spread a kilometer of ridge than to slip a kilometer of transform fault, and the patterns observed at spreading centers might extend to lithospheric depths. Under these conditions, the resisting force at spreading centers could play a significant role in the dynamics of plate-tectonic systems.     

The structure and sedimentology of relict talus,Trotternish, northern Skye,Scotland

Sections up to 3·5 m deep cut through the upper rectilinear segment of relict, vegetated talus slopes at the foot of the Trotternish escarpment reveal stacked debris-flow deposits intercalated with occasional slopewash horizons and buried organic soils. Radiocarbon dating of buried soil horizons indicates that reworking of sediment by debris flows predates 5·9–5·6 Cal ka BP , and has been intermittently active throughout the late Holocene. Particle size analyses of 18 bulk samples from these units indicates that c. 27–30 per cent of the talus deposit is composed of fine (<2 mm) sediment. Sedimentological comparison with tills excludes a glacigenic origin for the talus debris, and the angularity of constituent clasts suggests that in situ weathering has been insignificant in generating fine material. We conclude that the fine sediment within the talus is derived primarily by granular weathering of the rockwall, with syndepositional accumulation of both fine and coarse debris, implying that c. 27–30 per cent of rockwall retreat since deglaciation reflects granular weathering rather than rockfall. The abundance of fines within the talus deposits is inferred to have been of critical importance in facilitating build-up of porewater pressures during rainstorms, leading to episodic failure and flow of debris on the upper parts of the slope. A wider implication of these findings is that the mechanical properties of talus slopes cannot be regarded as those of free-draining accumulations of coarse clasts, and that models that treat talus slopes as such have limited value in explaining their form and evolution. Our findings lend support to models that envisage the upper straight slope on talus accumulations as the product of mass-transport as well as rockfall, and indicate that episodic debris flow has been the primary agent of mass-transport at this site. © 1998 John Wiley & Sons, Ltd.     

各向异性介质中的入射角、反射角和透射角

对各向异性介质中波动现象的数学描述,远比对各向同性介质中的数学描述要复杂得多．这一复杂性主要来自各向异性介质中的许多物理特性,不同于各向同性介质中的物理特性．因此,计算各向异性界面处的反射角和透射角在数学意义上变得非常复杂,各向同性介质中的Snell定律已不再适用于各向异性介质,必须加以修改．本文发展了一种计算各向异性介质分界面处入射角、反射角和透射角的新算法,即修正后的各向异性介质中的Snell定律．      

Sedimentation processes and facies on a semi-vegetated talus,Lousteau, southwestern France

A two-year survey of clast displacements on a small rockfall talus at Lousteau, southwestern France, shows that creep reaches up to 19 cm/month near the talus apex, whereas the distal segment remains stable. Movements are not distributed homogeneously but concentrate in distinct areas because of the deflection of clasts by vegetation patches. Sections across the talus reveal stratified deposits, thought to result from the lateral shifting of the tongues of very mobile debris. Poorly sorted gravel layers alternate with coarser debris corresponding to former pavements developed where sedimentation is reduced due to the protective effect of vegetation. Similar deposits have been found in larger, semi-vegetated taluses from the forest belt of the French Alps. Interactions between vegetation development and sedimentation possibly controlled by the climatic changes during postglacial times, may be responsible for their stratification. Copyright © 1999 John Wiley & Sons, Ltd.     

Difference between static and dynamic angle of repose of uniform sediment grains

In the investigation of sediment transport, it is necessary to differentiate various definitions of angle of repose (AoR) available in the literature. The static AoR, composed of upper and lower angle of slope, forms just before and after slope instability, while the dynamic AoR can be observed when sediment grains are moving continuously down an inclined plane. In the present study, a series of laboratory experiments was conducted to measure static and dynamic angle of repose for uniform natural sedi-ments with median diameter of 0.28–4.38 mm. The results show that the different slope angles have different characteristics. The upper and dynamic AoR increase slightly with increasing grain diameter, while the lower AoR is not sensitive to changes in sediment size and may assume a constant value. The average of the upper and lower AoR is equivalent to the dynamic AoR, and the difference between them increases with increasing grain diameter. The present study suggests that the different angles of repose should be treated with caution when applying in investigations of bedload transport, dune migration and local scour development.     

Incidence, reflection and transmission angles in anisotropic media

IntroductionGenerallyspeaking,theinclusionofanisotropy(exceptdeclaration,anisotropyreferstohomogenousanisotropy)rendersthemathematicalformulationquitecomplicated.Snell'Slawisnotanexceptionandthecalculationofreflectionandtransmissionanglesisnotatrivialtask.ThegraphicalapproachestocalculatingreflectionandtransmissionanglesforanisotropicmediawerepresentedbyAuld(1973)andRokhlin,etal(1986).DaleyandHorn(1977,1979)andSlawinski(1996)deriveSnell'slawintheparticularcasesoftransverselyisotropicandelli…     

Rates of surface processes on slopes,slope retreat and denudation

Results taken from 270 publications on rates are summarized, and collated with those from 149 publications reviewed previously (Young, 1969, 1974). The data are classified by major climatic zone, normal or steep relief, and consolidated or unconsolidated rocks. Representative rates and their ranges are given for soil creep, solifluction, surface wash, solution (chemical denudation), rock weathering, slope retreat, cliff (free face) retreat, marine cliff retreat, and denudation, the last being compared with representative rates of uplift. Solifluction is of the order of 10 times faster than soil creep, but both cause only very slow ground loss. Solution is an important cause of ground loss for siliceous rocks, on which it may be half as rapid as on limestones. Total denudation, brought about mainly by surface wash, reaches a maximum in the semi-arid and probably also the tropical savanna zones. Acceleration of natural erosion rates by human activities ranges from 2–3 times with moderately intense land use to about 10 times with intensive land use (and considerably higher still where there is recognized accelerated soil erosion). Where there is active uplift, typical rates are of the order of 10 times faster than denudation, although in some high, steep mountain ranges these may approach equality.     

Stratigraphic evidence of episodic talus accumulation on the isle of skye,Scotland

Evidence of episodic development of alluvial talus is given. Three phases of accumulation are identified within the last 3000 years. Average rates of accumulation range from 0·2–1·7 mm yr^?1 during each period. Conventional models relating climate to slope activity are inappropriate due to the local conditions.     

Disturbance,geomorphic processes and recovery of wildfire slopes in North Tyrol

Wildfires in the sub‐alpine belt of the Austrian Limestone Alps sometimes cause severe vegetation and soil destruction with increased danger of secondary natural hazards such as avalanches and debris flows. Some of the affected areas remain degraded to rocky slopes even decades after the fire, raising the question as to whether the ecosystems will ever be able to recover. The mean fire interval, the duration of recovery and the role of geomorphic processes for vegetation regeneration are so far unknown. These questions were tackled in a broad research approach including investigation of historical archives to determine the frequency of historical wildfires, mapping vegetation regeneration on 20 slopes of different post‐fire ages, and soil erosion measurements on two slopes. To date, > 450 historical wildfires have been located in the study area. The mean fire interval per square kilometre is c. 750 years, but can be as low as 200–500 years on south‐facing slopes. Vegetation regeneration takes an extremely long time under unfavourable conditions; the typical window of disturbance is between 50 and 500 years, which is far longer than in any other wildfire study known to us. Soil erosion constantly increases in the years after the fires and the elevated intensity can be maintained for decades. A two‐part vegetation regeneration model is proposed depending upon the degree of soil loss. In the case of moderate soil erosion, spreading grassland communities can slow down shrub re‐colonization. In contrast, after severe soil destruction the slopes may remain degraded for a century or longer, before rather rapid regeneration occurs. The reasons are not fully understood but are probably governed by geomorphic process intensity. The interdependence of vegetation regeneration and geomorphic processes is a paradigm of ecology–geomorphology interaction, and is a unique example of a very long‐lasting disturbance response caused by wildfire in a non‐resilient ecosystem. Copyright © 2012 John Wiley & Sons, Ltd.     

多维地震激励下曲线梁桥简化模型及最不利输入方向研究

曲线梁桥只有在某一特定方向输入地震动时,结构某点或某截面的内力(或应力)才能达到最大值,需要沿多个可能方向输入计算才能确定地震动最不利输入方向。根据隔震曲线梁桥受力特点,将桥梁上部结构和桥墩简化均具有两个水平自由度和一个围绕质量中心轴扭转自由度的堆积质量模型,建立双质点六自由度简化分析模型,通过求解曲线梁桥的动力学方程研究结构的动力特性和地震动行为。算例表明,双质点模型计算结果与传统的有限元模型基本一致,且计算方法简单,可以考虑各种敏感因素的影响,借助编程更适合提出规律性的设计方法。进而在双质点模型基础上应用MATLAB编程探讨多维地震作用下曲线梁桥地震波最不利输入方向的问题,针对不同参数的隔震曲线梁桥,改变相关参数后只需运行一次就可以实现最不利输入角度的确定,可为有限元法最不利地震波输入方向的确定提供参考,并大大减少多个方向输入试算的工作量。     

Flow and deformation failure of sandy slopes

The effects of earthquake induced pore pressure on seismic and post seismic stability conditions of cohesionless slopes are investigated with reference to the infinite slope scheme. In cohesionless slopes the shear strength reduction caused by pore pressure build-up may lead the slope to a deformation failure or to a flow failure if liquefaction conditions are approached. Two critical values of the seismic induced pore pressure ratio are introduced to evaluate the effect of shear strength reduction on the slope failure mechanism. The results are given in the form of stability charts and a procedure for the evaluation of the seismic stability condition is described. The procedure gives useful information about the failure mechanism that slopes may exhibit and the displacement analysis which should be carried out.     

Linking frequency of rainstorms,runoff generation and sediment transport across hyperarid talus-pediment slopes

Documenting hillslope response to hydroclimatic forcing is crucial to our understanding of landscape evolution. The evolution of talus-pediment sequences (talus flatirons) in arid areas was often linked to climatic cycles, although the physical processes that may account for such a link remain obscure. Our approach is to integrate field measurements, remote sensing of rainfall and modeling to link between storm frequency, runoff, erosion and sediment transport. We present a quantitative hydrometeorological analysis of rainstorms, their geomorphic impact and their potential role in the evolution of hyperarid talus-pediment slopes in the Negev desert, Israel. Rainstorm properties were defined based on intensity–duration–frequency curves and using a rainfall simulator, artificial rainstorms were executed in the field. Then, the obtained measured experimental results were up-scaled to the entire slope length using a fully distributed hydrological model. In addition, natural storms and their hydro-geomorphic impacts were monitored using X-band radar and time-lapse cameras. These integrated analyses constrain the rainfall threshold for local runoff generation at rain intensity of 14 to 22 mm h^-1 for a duration of five minutes and provide a high-resolution characterization of small-scale runoff-generating rain cells. The current frequency of such runoff-producing rainstorms is ~1–3 per year. However, extending this local value into the full extent of hillslope runoff indicates that it occurs only under rainstorms with ≥ 100-years return interval, or 1% annual exceedance probability. Sheetwash efficiency rises with downslope distance; beyond a threshold distance of ~100 m, runoff during rainstorms with such annual exceedance probability are capable of transporting surface clasts. The erosion efficiency of these discrete rare events highlights their potential importance in shaping the landscape of arid regions. Our results support the hypothesis that a shift in the properties and frequency of extreme events can trigger significant geomorphic transitions in areas that remained hyperarid during the entire Quaternary. © 2020 John Wiley & Sons, Ltd.     

Early Cretaceous sinistral shearing and associated folding in the South Kitakami Belt, northeast Japan

Abstract   Early Cretaceous structural development of the southern part of the South Kitakami Belt, northeast Japan, is discussed through precise structural mapping and the measurement of semiquantitative strain. The mapping and measurement revealed that wide north- to northeast-trending sinistral shear zones occupied by the 'slate' with higher strain than the surrounding rocks run from the axial part to the western limb of major synclines, with the wavelength of 5–10 km. The major synclines with a U-shaped rock distribution opening to the south are interpreted to be drag folds along the sinistral shear zones. These structures were modified by a second stage of Early Cretaceous sinistral shearing characterized by localized high-temperature mylonite zones along the rim of some of the 120 Ma granitoids that cut the major folds and baked the 'slate' in the older shear zones mentioned above. The rocks of the South Kitakami Belt, which had undergone two stages of shearing, were rapidly exhumed before the deposition of the Late Aptian–Albian Miyako Group. Finally, a restoration model is presented of the Early Cretaceous sinistral displacement and deformation in the study area.