Toe Depth Research Articles

Wave, Tide and Topographical Controls on Headland Sand Bypassing

AbstractEmbayed beaches separated by irregular rocky headlands represent 50% of global shorelines. Quantification of inputs and outflows via headland bypassing is necessary for evaluating long‐term coastal change. Bypassing rates are predictable for idealized headland morphologies; however, it remains to test the predictability for realistic morphologies, and to quantify the influence of variable morphology, sediment availability, tides and waves‐tide interactions. Here we show that headland bypassing rates can be predicted for wave‐dominated conditions, and depend upon headland cross‐shore length normalised by surf zone width, headland toe depth and spatial sediment coverage. Numerically modeled bypassing rates are quantified for 29 headlands under variable wave, tide and sediment conditions along 75 km of macrotidal, embayed coast. Bypassing is predominantly wave‐driven and nearly ubiquitous under energetic waves. Tidal elevations modulate bypassing rates, with greatest impact at lower wave energies. Tidal currents mainly influence bypassing through wave‐current interactions, which can dominate bypassing in median wave conditions. Limited sand availability off the headland apex can reduce bypassing by an order of magnitude. Bypassing rates are minimal when cross‐shore length >5 surf zone widths. Headland toe depth is an important secondary control, moderating wave impacts off the headland apex. Parameterisations were tested against modeled bypassing rates, and new terms are proposed to include headland toe depth and sand coverage. Wave‐forced bypassing rates are predicted with mean absolute error of a factor 4.6. This work demonstrates wave‐dominated headland bypassing is amenable to parameterization and highlights the extent to which headland bypassing occurs with implications for embayed coasts worldwide.

On the toe stability of rubble mound structures

Toe design is an important task for coastal engineers as it ensures the stability of the main armor layer and prevents scour in front of the armor slope. Several laboratory experiments have been conducted to investigate the toe stability using different testing approaches, i.e. damage due to a single test condition and cumulative damage due to a number of conditions. In addition, the methods of measuring and reporting damage to the toe are not the same as some researchers have counted only stones that were washed away from the toe; while others counted all the stones that have been displaced. Several formulas with different levels of success have been developed based on these studies. However, the scatter in the results is large and effects of some parameters are disregarded. The aims of this study are (a) to briefly review the abovementioned differences and exiting formulas, and (b) to develop a and physically sound formula for common design conditions, which considers the effect of all governing parameters. To achieve this, first a comprehensive data base from existing reliable studies was collected. Then nondimensional parameters which capture effects of governing parameters such as wave height, wave period, water depth, toe depth, toe width and foreshore slopes were deployed to develop a stability formula using physical reasoning and regression analysis. The new formula outperforms existing formulae for toe stability. The coefficient of variation of the formula was also determined to be used for probabilistic design applications. Finally, some design hints are provided for practitioners.

Influence of toe berm geometry on stability of reshaping berm breakwaters

Reshaping berm breakwaters have been mainly designed and built for water depth less than 20 m. In such conditions, a toe structure may be needed to reduce bottom settlements and increase geotechnical stability in the loose subsoil condition. Also, a toe berm can be deployed to reduce the berm recession and increase the stability of the Reshaping berm breakwater, especially in deep water. Although many studies have been conducted to study the effects of toe berms on stability of conventional breakwaters, investigations on the influence of a toe berm on stability of reshaping berm breakwaters are rare. This paper presents results of an experimental work that has been carried out to investigate the influence of a toe berm on the hydraulic stability of reshaping berm breakwaters. In a 2D physical test setup in a wave flume, a total of 207 tests were conducted to systematically examine the effects of toe berm configuration on the reshaping of berm breakwaters with three types of armor stones. The experimental program covers the influence of different geometrical parameters of the toe berm on the berm recession under various sea state conditions. Comparing results of berm recession of the cases having a toe structure with the cases without a toe berm shows that the amount of berm recession with toe berm is considerably less than the analogous amount for without toe structure. It is observed that an increasing toe berm width and thickness both have considerable influence on recession reduction. However, the toe depth has a relatively larger influence on recession than the toe width, and the influence is larger for higher stability numbers. It is concluded that a toe berm in front of reshaping berm breakwater not only does have influence on recession due to the depth influence and the changing wave conditions, but also the toe depth has a direct influence on the reshaped profile by preventing the displaced rocks to fall down to deeper parts. Using the test results, a new formula is developed for estimation of berm recession by taking into account the influence of the toe berm configuration. Given an acceptable stability number (Ho) as a design criterion for reshaping berm breakwaters, the present method predicts that the recession can be reduced up to 35% by the application of a toe berm. Thus, the main berm width can be shortened, resulting in reduction of the required armor stones volume. So, by using a smaller stone size for the toe berm, the stability of the structure is secured and also the total cost of the breakwater can be reduced.

High‐efficiency gravel longshore sediment transport and headland bypassing over an extreme wave event

AbstractGravel beaches are common throughout the high latitudes, but few studies have examined gravel transport rates, in particular at high energy levels, and no studies have quantified gravel transport around headlands. Here, we present the first complete sediment budget, including supra‐, inter‐ and sub‐tidal regions of the beach, across multiple headland‐separated gravel embayments, combined with hydrodynamic observations, over an extreme storm sequence, representing at least a 1‐in‐50‐year event. Unprecedented erosion was observed (~400 m3 m−1, −6 m vertical), with alongshore flux of 2 × 105 m3, equivalent to annual rates. Total system volume change was determined to the depth of closure and then used to calculate alongshore flux rates. Alongshore wave power was obtained from a wave transformation model. For an open section of coastline, we derive a transport coefficient (CERC formula) of KHs = 0.255 ± 0.05, exceeding estimates in lower‐energy conditions by a factor of 5 or more. We apply this coefficient to rocky segments of the shoreline, determining rates of headland bypass from 0 to 31% of potential flux, controlled by headland extent and toe depth. Our results support the hypothesis that gravel is transported more efficiently at higher energy levels and that a variable rate or threshold approach may be required. Complete coverage and varying morphology make this dataset uniquely suited to improving model predictions of gravel shoreline change. © 2019 John Wiley & Sons, Ltd. © 2019 John Wiley & Sons, Ltd.

Using experimental biomechanics to reconstruct the evolution of hominin locomotor postures

Debates over the evolution of hominin bipedalism, a defining human characteristic, often revolve around whether early bipeds walked more like humans, with energetically economical extended hind limbs, or more like apes with flexed hind limbs. Here, we detail experimental data from humans and chimpanzees that links anatomy with lower limb posture and the energy costs of walking. Using these anatomical links, we examine the fossil record to determine when adaptations evolved that allowed for extended limb bipedalism.To complement anatomical studies of hominin fossils, we apply evolutionary biomechanics to the 3.6 million year old hominin footprints at Laetoli, Tanzania, which represent the earliest direct evidence of hominin bipedalism. We compare footprints from the original Lateoli Site G (n=8) and the newly described Site S (n=8) with experimentally generated footprints from modern humans (n=8 subjects) made using both extended and flexed limb, or Bent‐Knee, Bent‐Hip (BKBH) biomechanics. In our modern human sample, footprints generated during BKBH walking leave deeper toe relative to heel impressions compared with footprints generated during normal, extended limb walking (linear mixed effects model: p<0.001). The difference in proportional toe depth (calculated as log10[maximum fore‐foot depth/maximum heel depth]) is linked to the mechanical consequences of BKBH walking. During walking, the center of pressure (COP; the point of ground force application) moves from the heel at touchdown to the forefoot during toe‐off, and the forces applied to the ground determine, to some degree, the depth of the impression under the COP. As the COP travels past the mid‐foot the human heel rises due to the presence of a stiff longitudinal arch, and forces following heel rise deform the substrate under the toes. From experimentally generated force‐plate records, we demonstrate that the COP passes the mid‐foot earlier in the step in BKBH walking, leading to larger forces under the toes and relatively deeper impressions.Using linear mixed effects models, we show that prints from Site G and the newly described prints from Site S at Laetoli are most consistent with weight transfer patterns from extended limb biomechanics. Proportional toe depths do not differ significantly between the Laetoli sites (G vs. S: p=0.998), and do not differ between Laetoli and modern humans walking with an extended limb gait (p=0.195). However, the print morphology at Laetoli does differ significantly from those made by humans walking with a flexed limb (p<0.001) due to the uniquely deep toe depressions that occur in humans walking with this more ape‐like gait.Thus, using experimental data from living humans, we interpret morphology from both the Laetoli footprints and from early hominin skeletons to propose extended limb bipedal posture evolved by 3.6 Ma. These results represent the earliest direct evidence of kinematically human‐like bipedalism currently known. Thus, our results, suggest that selection acted to increase the energy economy of bipedalism early in human evolution and that efficient extended limb bipedalism evolved long before the appearance of the genus Homo.Support or Funding InformationFunded by the L.S.B. Leakey Foundation and the University of ArizonaThis abstract is from the Experimental Biology 2018 Meeting. There is no full text article associated with this abstract published in The FASEB Journal.

Influence of anthropogenic land‐use change on hillslope erosion in the Waipaoa River Basin, New Zealand

AbstractEuropean settlement of the Poverty Bay Region resulted in deforestation and conversion of > 90% of the landscape to pastureland. The resulting loss of vegetation triggered a rapid increase in hillslope erosion as widespread landslide complexes and gully systems developed on weak lithologic units in the Waipaoa Basin. To quantify the rate and volume of historic hillslope degradation, we used a 1956–2010 sequence of aerial photographs for a ~16 km2 catchment to map temporal changes in the spatial extent of active landslides. Then we created a ‘turf index’ based on the extent and style of pastoral ground disruption, which correlates with downslope velocity. Based on the movement of trees and other features, we assigned average velocities to the turf classes as follows: (1) minimal disrupted ground: 0.6 m/yr, (2) a mix of disrupted ground and intact blocks: 3.4 m/yr, and (3) no intact blocks or vegetation: > 6 m/yr. We then calculated the average annual sediment flux using these turf‐derived velocities, the width of the landslide‐channel intersection, and an average toe depth of 4.4 ± 1.3 m (mean ± standard deviation [SD]) from 37 field measurements. The resulting catchment averaged erosion rates are (mean ± SD): 29.9 ± 12.9 mm/yr (1956), 28.8 ± 13.7 mm/yr (1969), 13.4 ± 4.9 mm/yr (1979), 17.0 ± 6.2 mm/yr (1988), and 9.9 ± 3.6 mm/yr (2010). Compared with long‐term (post‐18 ka) erosion rates (1.6 mm/yr) and the long‐term uplift rate (~1 mm/yr) for this site, the 50‐year anthropogenically‐driven rate is an order of magnitude larger (~20 mm/yr). Previously, we measured an increase in erosion over the past 3.4 kyr (2.2 mm/yr), and here, we demonstrate this increase could be primarily due to human land‐use change – showing that a century of rapid erosion superimposed on the background geologic rate can profoundly skew the interpretation of erosion rates. Copyright © 2016 John Wiley & Sons, Ltd.

Analysis of Climate Change Effects on Seawall Reliability

Crown heights of seawalls should be designed to suppress overtopping discharge to a permissible level. The permissible level is determined from viewpoints of the structure types of coastal seawalls and hinterland use. It is usually difficult to design the crown heights of seawalls, especially in the present time where climate change due to global warming is expected. This study analyzes climate change effects such as sea level rise (SLR) and increase of waves and surges on the failure probability of seawalls under various conditions of crown height, toe depth and slope by using a Level III reliability analysis. It was found that the difference of SLR trends (fast, medium or low) has less impact on overtopping rates than the differences in wave height change for a seawall at a target location.

Mapping coastal morphodynamics with geospatial techniques, Cape Henry, Virginia, USA

The advent and proliferation of digital terrain technologies have spawned concomitant advances in coastal geomorphology. Airborne topographic Light Detection and Ranging (LiDAR) has stimulated a renaissance in coastal mapping, and field-based mapping techniques have benefitted from improvements in real-time kinematic (RTK) Global Positioning System (GPS). Varied methodologies for mapping suggest a need to match geospatial products to geomorphic forms and processes, a task that should consider product and process ontologies from each perspective. Towards such synthesis, coastal morphodynamics on a cuspate foreland are reconstructed using spatial analysis. Sequential beach ridge and swale topography are mapped using photogrammetric spot heights and airborne LiDAR data and integrated with digital bathymetry and large-scale vector shoreline data. Isobaths from bathymetric charts were digitized to determine slope and toe depth of the modern shoreface and a reconstructed three-dimensional antecedent shoreface. Triangulated irregular networks were created for the subaerial cape and subaqueous shoreface models of the cape beach ridges and sets for volumetric analyses. Results provide estimates of relative age and progradation rate and corroborate other paleogeologic sea-level rise data from the region. Swale height elevations and other measurements quantifiable in these data provide several parameters suitable for studying coastal geomorphic evolution. Mapped paleoshorelines and volumes suggest the Virginia Beach coastal compartment is related to embryonic spit development from a late Holocene shoreline located some 5 km east of the current beach.

Derivation of unified wave overtopping formulas for seawalls with smooth, impermeable surfaces based on selected CLASH datasets

A set of unified formulas for prediction of the mean rate of wave overtopping at coastal structures with smooth, impermeable surfaces have been derived through the analysis of the selected CLASH datasets. The mean wave overtopping rate is expressed as the function of the significant wave height at the structural toe and the relative freeboard. The formulas are applicable for both vertical walls and inclined seawalls with smooth transition between them. The formulas are simple but cover the full range of water depth from the shoreline to deep water. The effects of the toe depth and the seabed slope on wave overtopping rate are duly incorporated in the formulas. Prediction performance of the new formulas is better than the EurOtop formulas for both vertical walls and inclined seawalls.

Proper shoe sizes for Thai elderly

Background Problems from improper shoe fitting are common, but there are limited foot data for the older Thai population. Objectives To study foot dimensions and determine proper shoe sizes for Thai elderly. Methods Healthy older people: 108 men, 105 women, aged 60–80 years, who were independent in walking, were recruited. Thirteen foot dimensions and current shoes used were measured. Side-to-side, gender difference, and correlations of main foot measurements were analyzed. Results About 50% women and 34% men wore too narrow shoes, and this was found to be associated with foot pain. At the same foot length (FL), men had larger foot width (FW) and toe depth. Foot width = 2.39 + (0.29 × FL), r = 0.50, p = 0.001 for women and = 2.48 + (0.31 × FL), r = 0.56, p = 0.002 for men. Arch length = 1.0 + (0.7 × FL), r = 0.93, p = 0.001 for both genders. Toe depth had constant values in all shoe sizes of each gender. Correlations of other foot parameters were reported. Conclusions These anthropometric data is essential for proper shoe fitting in order to provide foot ergonomics and prevent foot problems for older Thai people.

ＣＬＡＳＨデータベースに基づく統一的越波流量推定式の提案

A set of unified formulas for prediction of wave overtopping rate at coastal structures have been derived by analyzing the CLASH database. The new formulas are applicable for vertical seawalls, smooth impermeable slopes, and composite seawalls with frontal mounds built with Tetrapods. The formulas are simple but cover the full range of water depth from the shoreline to deep water. The effects of the toe depth and the seabed slope on wave overtopping rate are duly incorporated in the formulas. Prediction performance of the new formulas is better than the EurOtop formula for both vertical walls and inclined seawalls.

Wave Reflection and Overwash of Dunes

Seven tests consisting of 72 runs were conduced to measure wave reflection, overtopping, and overwash of dunes. The measured reflection coefficients and overtopping rates are compared with the empirical formulas developed for coastal structures. The equivalent uniform slope for reflection is assumed to be the beach slope at the still water shoreline. The equivalent uniform slope for overtopping is assumed to be the overall slope between the dune crest and the point where the water depth equals the significant wave height. The toe depth of the coastal structure is assumed to correspond to the water depth immediately seaward of the breaker zone on the beach. The formulas with these adjustments are then shown to predict the order of magnitude of the measured reflection coefficients and overtopping rates. Furthermore, the average volumetric sand concentration in the overwash flow was measured to be approximately 0.04 for these small-scale tests.

ENERGY DISSIPATION IN SKIMMING FLOW OVER STEPPED SPILLWAYS

ABSTRACT Stepped spillways are provided to reduce the size of stilling basins with the view of reducing the overall cost of spillway and energy dissipation device. The characteristics of flow over stepped spillway are still not well known. This paper presents an equation for estimation of energy loss on stepped spillway for skimming flow regime, which is required for economic design of stilling basin. The equation for energy loss is derived by regression analysis utilising the available experimental data from various authors. Expressions for prediction of toe depth and coefficient of friction for stepped spillway are also developed. These would be useful in design of stepped spillways.

Earthquakes in the Skagerrak recorded at small distances

During the winter 1977-1978 up to 3 seismographs were temporarily situated in the northern part of Jutland with the aim of recording near earthquakes. 3 seismic events, presumably earthquakes, have been recorded by 1, 2 or 3 of these seismographs. One of the earthquakes was large enough for a special investigation. The location of that earthquake is quite close to the coast of Jutland, while the two smaller earthquakes are located in the Norwegian Channel of the Skagerrak where a number of previous earth­quakes are known to have happened. The depth of the largest earthquake is 40 km. Toe depth estimate is more accurate than any previous estimate because of the near seismic stations, that recorded the ear­thquake.