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Grain size distributions of investigated wide-graded material samples 

Grain size distributions of investigated wide-graded material samples 

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Scour protection around hydraulic structures in fluvial, estuarine, and coastal waters is an essential component of a meaningful and durable design. The continuous optimization of scour protection systems and design approaches leads to faster and more cost-effective construction processes. Although scour protection now often consists of a two-layer...

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Context 1
... applied material was a wide-graded quarry-stone mixture made of granodiorite with a grain size distribution in the range of 0.063-200 mm. Material samples were obtained by the manufacturer on the basis of wheel-loader-filled big bags with volumes of approximately 1 m 3 each. Fig. 2 presents the grain size distributions of the three individual samples, which were obtained from site analysis of the individual big bags. The analysis of the three samples showed significantly varying grain size distributions, which stressed the necessity for experimental repetition to guarantee reasonable reproduction and to account ...
Context 2
... therefore, only for these load cases could the largest grain size be defined. Table 5 summarizes the mass of bed load collected by the sediment trap, illustrating the significant differences of erosion between the three experiments. The amount of collected bed load correlates with the amount of finer fractions in the three material samples (cf. Fig. 2). Therefore, differences in bed surface structure (see Fig. 4) as well as in the initial material distribution should be considered in the analysis of the results. In the following, the experimental results, which were obtained on the basis of the earlier outlined methodology, are presented and ...
Context 3
... u 1 and u 2 as the velocities at the bed-nearest positions z 1 and z 2 . As a consequence of the inhomogeneous bed and the progressing erosion of the bed, the distances z 1 and z 2 as well as the corresponding velocities u 1 and u 2 vary heavily between the measurement points ( Fig. 4) and with increasing loading. Exemplarily, Table 4 shows values for these parameters for Experiment B. Subsequently, the shear velocity and local bed-shear stresses were calculated using [Eq. (1)]. Fig. 7 shows the distribution of mean bed-shear stresses t 0 , which are the averaged shear stresses over all positions for a speci fi c load case and the standard deviations for all experiments in reference to mean fl ow velocity. While the bed-shear stresses for the individual experiments are quite similar for a certain fl ow velocity, the shear stress variations caused by the inhomogeneous bed and the resulting turbulence are obvious and underline the need for several different measurement positions to get an suf fi cient overview of existing bed-shear stresses. The assessment of the erosion stability of the investigated material was based on the determination of fractional critical shear stress as a condition for the incipient motion. Because of the relative small amount of available load cases with suf fi cient transport rates, a meaningful relation between the obtained bed-shear stress and the transport rate of available sediment fractions could not be de fi ned. Instead, the comparison of the calculated bed-shear stresses with representative grain sizes from the sediment trap is applied as critical condition for incipient motion. Here, the largest grain fraction collected by the sediment trap and determined by sieve analysis was considered as critical grain size in accordance with the largest-grain method. In each experiment and load case coarser fractions were still available in the bed as a consequence of the wide-graded material properties with grain sizes up to 200 mm. However, the grain size distribution could be determined only for the last four load cases in each experiment; therefore, only for these load cases could the largest grain size be de fi ned. Table 5 summarizes the mass of bed load collected by the sediment trap, illustrating the signi fi cant differences of erosion between the three experiments. The amount of collected bed load correlates with the amount of fi ner fractions in the three material samples (cf. Fig. 2). Therefore, differences in bed surface structure (see Fig. 4) as well as in the initial material distribution should be considered in the analysis of the results. In the following, the experimental results, which were obtained on the basis of the earlier outlined methodology, are presented and discussed. During the experiments a signi cant coarsening of the bed surface at higher fl ow velocities has been observed by visual inspections. Particularly, the selective erosion of large quantities of the fi ner fractions rather quickly led to a coarsening of the bed at the beginning of each load case. Unfortunately, the amount of suspended material was not measured during the experiment and therefore no quantities can be given. The investigated material contained fi ner fractions, which would have been expected to be transported as suspended sediment. Surprisingly, only a modest turbidity of the water could be observed visually, despite the erosion of fi ner fractions at the beginning of each load case and the fact that the circulation fl ume is a closed system. Especially in the fi rst three load cases, the ner fractions clumped together and formed a dense surface structure. Because of occurring hiding processes, not all of the fi ner fraction was eroded, so that even in the highest load case, these fractions were available on the bed surface. In summary, the turbidity of the water and the amount of suspended load appeared to be unexpect- edly small. Nevertheless, an unknown amount of material was eroded as suspended load and this has to be considered in the assessment of the sediment trap results. But given the fact that only a small amount of fi ner fractions was transported as suspended load, the estimation of critical shear stresses by the largest-grain method should not be affected. With the removal of the test bed after the end of each experiment the formation of a very compact and tight grain structure was revealed, in which all fractions of the initial material were present. By the end of each load case sediment transport could no longer be observed. With the formation of a stable and immobile bed surface as indicators, the development of a static armor layer at the end of each load case can be concluded (Jain 1990; Marion and Fraccarollo 1997; Parker and Sutherland 1990). Due to the successive increase of fl ow velocities, the existing static armor layer was degraded at the beginning of each load case to develop a new one until the end of the respective load case. However, with the available velocities no suf fi ciently critical fl ow condition for a complete failure and destruction of the armor layer was achieved. Therefore, additional experiments with higher fl ow velocities are needed in the future for the determination of application-relevant load limits and de fi nite assessment of the material performance. The analysis of the sand trap results showed that in all experiments only grain sizes smaller than the d 50 grain size of the initial bed were moved, which indicates relations of d i = d 50 < 1 for further analysis. The coarsening of the eroded bed load with increasing velocity is clearly observable for all experiments, indicating a continuously coarsening of the bed surface as well. Fig. 8 shows the development of the grain size distributions of the trapped bed load for Experiment B for the last four load cases. Based on the DEMs, plots of bed elevation differences between individual load cases were created, illustrating erosion and accumulation areas on the bed from sediment displacement processes. Figs. 9 – 11 show the displacement processes at the end of each experiment resulting from seven subsequently increased load stages after a total load exposure of 14 h. As expected, the erosion areas (dark gray) outweigh the accumulation areas (light gray). At the same time, erosion patterns occur more globally distributed, re ecting areas with large quantities of fi ner fractions (dash-lined circles in Figs. 9 – 11), whereas accumulation is locally concentrated behind larger stones or similarly pro- tected parts (full-lined circles in Figs. 9 – 11). Erosion as well as accumulation areas and depth intensify with successively increasing fl ow velocities, especially for the last four load cases. As shown in Table 6 the mean erosion, averaged over the scan area, adds up to 1.4 mm for Experiment A, 3.6 mm for Experiment B, and 3.3 mm for Experiment C. Because of its heterogeneous appearance, this erosion should not be mistaken as a general lowering of the bed. Furthermore, the amount and the areas of erosion do not correlate with the streamwise nonuniformity of the fl ow over the fl ume width shown in Fig. 3. In Experiments B and C a large proportion of the erosion takes place on the inner side of the circulation fl ume, where the smallest velocities have been measured. For example, in Experiment B, while 47% of the total erosion volume was measured in the outer third of the fl ume width ( y ...
Context 4
... hydraulic model tests have been performed to investigate the armor layer development of wide- graded quarry stone under unidirectional fl ow and to assess the stability of this material with respect to the fractional critical shear stress of nonuniform sediments. The hydraulic model tests were performed in the closed-circuit fl ume of the Franzius-Institute for Hydraulic, Estuarine and Coastal Engineering, Leibniz University Hannover, Germany. Detailed information and technical drawings of the fl ume can be found in Goseberg et al. (2013). In addition to their experimental setup, the arti fi cial ramp was removed so that a horizontal bottom could be used in the tests. Groins and a fl ow straightener were installed upstream of the sediment pit to reduce the in fl uence of the fl ume bend on the lateral velocity distribution. The model tests were performed in a scale of 1:1 to avoid scaling effects that could particularly bias the behavior of fi ner sediment fractions in the tested sediment mixture. The applied wide-graded material was installed in a deep pit with a width of 1.0 m, a length of 2.7 m, and a depth of 0.6 m resulting in a specimen surface of 2.7 m 2 . The material was built in at the level of the fl ume bed in a thickness of 200 mm (corresponds to the maximum grain diameter) without further compaction. In reference to the available maximum fl ow velocities in the fl ume and as a requirement for the largest- grain method, the movement of the largest grains, i.e., 200 mm, was not anticipated or observed during the experiments. The depth of the material layer should be enough to guarantee an unaffected erosion of ner fractions, particularly since the median diameter ( $ 50 mm) is far smaller than the depth of the material layer. To ensure a good interlocking with the subsurface, an additional material layer was placed under the material bed. This sublayer consisted of the same wide-graded material with a grain size distribution similar to the investigated material, but from a different sample. In contrast to the investigated material on top, the sublayer has not been removed during the experiments. Information of the experimental setup in the circulation fl ume is illustrated in Fig. 1. To determine the changes of the bed topography over time and to identify erosion and deposition areas on the rough bed after fl ow exposure, digital elevation models (DEMs) of the bed topography were measured with a laser distance sensor (OADR 2016480, Baumer, Friedberg, Germany; resolution 0.015 – 0.67 mm). A vertical accuracy of approximately 1.0 mm was achieved by calibration in preliminary tests and subsequent error correction. The eroded bed load fractions have been collected by an adjacent sediment trap, which was placed 6.0 m downstream of the sediment bed (Fig. 1). For constructional reasons the sediment trap was designed as an arti fi cial pit trap above the concrete fl ume bottom, consisting of a container with fl at slopes on both ends. The sediment trap had a total length of 0.8 m and spans the whole fl ume width. Suspended material was not measured by the sediment trap. Apart from obtaining the amount of eroded material, the grain size distribution of the eroded bed load was determined for each test run. To estimate bed-shear stresses in accordance with the fi ndings from a literature search, three-dimensional (3D) velocity measurements were performed by an acoustic Doppler velocimeter (ADV) (Vectrino þ , Nortek, Rud, Norway). A sampling rate of 200 Hz and a measuring period of 30 s for each position were determined to be a fair balance between the amount of recorded data and repeatabil- ity. Because of the exceptionally rough surface structure (maximum grain diameter is 200 mm) the horizontal and vertical positions of the ADV device and the number of the velocity measurements had to vary between the experiments. To ensure comparable velocity measurements, the measurement positions were arbitrarily determined on the basis of similarity of surface formations in the given bed surface (e.g., near large single grains or in the vicinity of hiding structures). In combination with the collected bed load, the shear stress estimates provided the basis for the de fi nition of an initial- motion criterion and the possibility to assess the erosion stability of the material. To position the laser distance sensor and the ADV probe automatically and reproducibly, a three-way traverse system was installed over the sediment bed (Fig. 1). By using this system, the bed topography could be scanned in a gridlike pattern and the velocity measurements could be done at predetermined positions for the series of load cases within single test runs. The applied material was a wide-graded quarry-stone mixture made of granodiorite with a grain size distribution in the range of 0.063 – 200 mm. Material samples were obtained by the manufacturer on the basis of wheel-loader – fi lled big bags with volumes of approximately 1 m 3 each. Fig. 2 presents the grain size distributions of the three individual samples, which were obtained from site analysis of the individual big bags. The analysis of the three samples showed signi fi cantly varying grain size distributions, which stressed the necessity for experimental repetition to guarantee reasonable repro- duction and to account for the inherent uncertainties within the wide-graded material properties. Table 1 summarizes the grain size and gradation characteristics of the three material samples. To guarantee the reproducibility of the results, a series of three repeating experiments were accomplished. Each experiment consisted of seven load cases, with successively increasing mean fl ow velocities from 0.1 to 0.9 m/s (see Table 2). Mean fl ow velocities u were determined in preliminary tests without a sediment bed and represent the mean fl ow velocities averaged over a cross-sectional area at the inspection window. Exemplarily, Fig. 3 shows the distribution of streamwise fl ow velocities over the fl ume width for the highest load case ( u = 0.9 m/s). A slight nonuniformity of the fl ow between the outer (left) and inner (right) wall of the circulation fl ume is evident. Although the pattern of the streamwise nonuniformity is also present for slower velocities, the magnitude of differences between the inner and outer fl ume wall is smaller. Goseberg et al. (2013) found the in fl uence of the nonuniformity negligible and veri fi ed the general suitability of the circulation fl ume for the generation of long waves. The generated waves mimicking tsunami had effective periods of up to 120 s and the associated fl ow compris- ing the wave motion exhibited current characteristics. Their conclu- sion about the negligibility of the nonuniformity also applied to the described experiments. However, the formation of such nonuniformity should be prevented by the experimental setup. Using a new tilting fl ume, the nonuniformity will be accounted for in future studies. The duration for each load case T was at least 2 h, so that a cumulated exposure time of 14 h for each experiment was obtained. In each experiment a different material sample from the same wide- graded material was used (see Table 1). At the beginning of the experiments water was carefully fi lled in from both sides of the material bed to avoid unwanted washout effects of the fi ner fractions. No additional sediment was added to the fl ume upstream of the test bed during the experiments; however, minor amounts of suspended sediment were recirculated with the temporally stored fl ume water due to the closed system of the fl ume. Subsequent to each load case the water was carefully drained to allow an undisturbed measurement of the bed surface by the laser scanner and to extract the eroded material from the sediment trap. During the experiments the fl ow velocity over the sediment bed was measured at fi ve positions along the longitudinal axis of the fl ume. These positions were kept fi xed over all load cases within one experiment to ensure the comparability of the measured fl ow velocities. In addition, further positions for velocity measurements were chosen dependent on characteristic formations within the surface structure, in particular hiding and exposure areas. These additional positions changed between the individual experiments but remained the same during a single experiment. The positions of the measurement points are highlighted in the DEMs presented in Fig. 4. At each of the positions a velocity pro fi le was measured and resolved by eight points over half the water depth. The distances between the eight points were fi xed throughout all experiments with 1 cm for the fi ve points closest to the bed and 5 cm for the remaining three points. The distance of the point closest to the bed varied due to the very irregular surface structure of the sediment bed and due to the sediment displacement during the experiment. Since this distance between the closest measurement location and the specimen surface is very important for the determination of the correct bed- shear stress, it was determined by a built-in bottom check of the ADV probe for every position and load case. All velocity measurements were performed at the end of the individual load cases after a stabile bed was developed and sediment transport could no longer be observed. It should be noted that, as a result, a potential change of the fl ow fi eld due to erosion and increasing bed roughness during loading could not be considered. Table 3 summarizes the test parameters and conditions for the accomplished erosion tests for wide-graded quarry-stone mixtures. The scan area recorded by the laser distance sensor covered 60% of the total surface of the sediment bed as shown in Fig. 5. The reduction of the scan area was performed so that neither scour, due to bed roughness changes at the interface between test specimen and concrete channel bottom, nor wall effects had a negative ...

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... One of the most common structural measures is using riprap or gabion baskets around the bridge pier foundation. A riprap is a layer of large stones placed around the pier to dissipate the energy of the flowing water and prevent soil erosion (Schendel et al 2016, Fazeres-Ferradosa et al 2021. Gabion baskets are wire mesh cages filled with stones around the pier to create a barrier against water flow. ...
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... As the related details and equations can be found in the literature, the methods are briefly explained as follows. These functions can be categorized into two approaches, as also outlined by Schendel et al. (2015). The first approach generally relates the grain diameter of the considered fraction in a sediment mixture (d j ) to the arithmetic mean grain diameter of the sediment mixture (d a ) or often the median grain diameter (d 50 ). ...
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... With the explosion of offshore wind farms, sea-crossing bridges, and deep-water ports, researches for erosion of buildings on marine environment become more and more significant for protecting offshore structures and improving the practicability and economy of structural design. [1] Many scholars had carried out researches on local scour of structures under unidirectional current [2] [3], wave [4] [5] and combined wave-current conditions [6] [7]et al., most of them dealing with the scour development at bridge piers. Actually, the area where the offshore structures are located is dominated by unsteady reciprocating tidal flow, in which flow velocity and direction changed periodically. ...
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Despite most of sea-crossing bridges and offshore wind farms being located in areas dominated by tides, researches about the effects of tidal current on the scour process around these buildings are still limited to this date. A three-dimensional sediment transport numerical model was established to investigate the local scour around a monopile under reciprocating tidal flow. The standard turbulence equation RNG (Renormalization-group) κ – ε was adopted to close the N-S equation and the finite difference method was applied to discretize the governing equation in the numerical model. Tidal currents were adapted by bidirectionally reversing sinusoidal currents. It showed in the results the scour pits grew periodically in the process of repeated scour and deposition with the change of the flow velocity and direction. Besides, it implied that tidal scour depth around the monopile deepened with the water depth, but the impact of water depth diminished gradually. The change of the maximum scour depth was less than 5% if water depth is more than 4 times pile diameter. It indicated that the scour depth around the pile will be almost no longer influenced by water depth if water depth is more than 4 times pile diameter. Therefore, the research results emphasize the significance of selecting suitable water depth conditions for the design process of offshore structures.
... Shvidchenko et al. (2001) proposed to use statistical parameters such as the relative grain size to include these effects. Further research was performed by Schendel et al. (2016) and Schendel et al. (2018) to investigate the stability of the wide-graded material under unidirectional and reversing currents. Both studies emphasized that the Shields approach is insufficient to assess the erosion stability and that the average grain diameter d 50 is insufficient to adequately represent the material characteristics. ...
... A lack of consistency in soil composition influences general erosion, particularly when infilling soil material is present. Designing tsunami-safe foundations requires reliable assessments of soil stability and effects occurring during tsunami inundation, which highlights the importance of an accurate analysis of soil properties [as discussed earlier, see also Schendel et al. (2016Schendel et al. ( , 2018 and Shvidchenko et al. (2001) for a description of the soil stability of wide-graded material in extreme flow conditions]. ...
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The September 28, 2018 earthquake and tsunami, which occurred north of Palu City, Indonesia, attracted widespread interest from the scientific community due to the unusually large tsunami that occurred after a strike-slip earthquake with a relatively small moment magnitude (M_W = 7.5). To understand the structural performance of buildings and infrastructure under hydrodynamic loads and their associated effects, the authors conducted field surveys in Palu City. Light wooden frame constructions and masonry infill walls were common in the area, some of which were severely damaged by the earthquake and tsunami. Reinforced concrete structures remained predominantly intact, although they suffered soil-related issues such as scour around rigid building members. Local structural failures caused by the loss of supporting soil were also observed during the field survey, resulting in an overall reduction in the stability of the inspected structures. Based on the observations made, knowledge gaps and research needs concerning coastal and structural scouring are discussed. These are tied into the latest community research activities and put in the context of a published ASCE standard chapter that discusses tsunami design.