An example of a reconstruction is shown in figure 5.2.
Figure 5.2: An example of a reconstructed surface of a measurement in water. Every blue dot represents a data point calculated for the reconstruction. The left and right cone are the sediment and reference cone, respectively. The edge of the bendable plate is seen at y ≈ 300.
This shows the two cones: the left one being the sediment cone and the right one being the reference cone. On the right side in the figure, at y ≈ 300, the edge of the bendable plate is also visible. The flat surface is not at zero, due to it being on the bottom plate, which is 9 mm thick, and the bendable plate, which is 1 mm thick.
The angle of repose underwater versus dry conditioned results
The figure shows inconsistencies in the flat surface. This is due to the actual surface not being flat, but slightly bent due to floating of the plate or held upwards by a sediment particle below it. This is a disadvantage of the bendable plate.
5.3 Calculating the angle
When the data is separated for a band, the data is being analyzed as described in section 4.4. An example of such an analysis is shown in figure 5.3.
Figure 5.3: An example of an analysis of a band of data from a measurement with water. The blue dots represent data points calculated. The blue line on the bottom represents the lowest value found for the height and is then plotted for the whole line for clarification. The black line is the fit of the data points.
The light blue and red line are the lines for displaying the calculated angle, plotted through the point where the maximum value for the fit derivative is located.
When looking at the analyses from all the bands, it was noticed that the data on the left side of the cone, with respect to its top, was less dense than the data on the right side of the cone, as seen in figure 5.3. The side of the cone which is closer to the projector will be referred to as the front, which is the right side in the figure, and the other side as the back. The less dense data led to the fit being less consistent on the back. It can be seen that the angles located on the backside vary much more than the angles located on the front side. For this reason, only the angles calculated on the front side will be used in the further calculations.
After analyzing all the bands, the result was plotted. Figure 5.4 shows an example of a final result, where all the calculated angles are displayed by the red and black lines, including the angles located on the back of the cone.
The angle of repose underwater versus dry conditioned results
Figure 5.4: An example of the final results from one measurement. The blue dots represent the calculated data points. The black lines represent the angles downwards. The red lines represent the angles upwards.
In total eleven measurement were done, five measurements underwater and six dry measurement. Two of the dry measurements were excluded in the calculations of the average angle of the cone. This is due to the sediment cone not being properly formed. In the reconstruction, it can be seen that the cone is skewed, probably due to the cylinder not being straight while depositing the sediment. After that, every band was checked for consistency and having enough data for the fit to be correct. The bands which did not meet that requirement were excluded from the average angle of the cone. This lead to less then 17 angle values per measurement.
The average is taken from all of the angles measured for each medium, after applying the mentioned exclusions. The average angle calculated for the measurements without water was based on 59 measured angles and is calculated to be θ = 39.9 ± 1.9 degrees, with the error being presented by the corrected sample standard deviation for this average. The average angle calculated for the measurements underwater was based on 60 angles measured and is calculated to be θ = 42.3 ± 1.5 degrees, with the error being presented by the corrected sample standard deviation for this average.
The angle of repose underwater versus dry conditioned conclusion
6 Conclusion
The angle of repose for the measurement in air was found of θ = 39.9 ± 1.9 degrees and the angle of repose for the measurements in water was found of θ = 42.3 ± 1.5 degrees. As the range of these values intersect, the results should be interpreted with caution. According to the theory described in section 3, there should not be a difference in the angle of repose for different media, as the angle of repose is not dependent on the medium that it is located in.
If looking at the method of deposition, the sediment is set into motion when being released from the cylinder. The motion is generated by particles settling due to gravity as shown in figure 6.1.
Figure 6.1: Schematic overview of a particle being released from the cylinder in water. The net force of gravity is being displayed, as described in (3.5). The grey bars represent the cylinder. The yellow dots represent the sediment. The blue background is the water. The light grey bar represents the tank.
As the particles are set into motion due to gravity, there is a difference between underwater and dry conditions. The net gravitational force acting on the particles in water is substantially smaller than the net gravitational force acting on the particles in air. As the density of the particles is close to the density of water, buoyancy is close in size to the gravitational force. Buoyancy is acting in opposed direction to gravity and therefore the net force acting on the particles is small. The difference in the net force between underwater and dry conditions leads to a difference in the velocity of the particles. As the particles are in motion, drag is acting on the particles in opposed direction to their motion, similar to buoyancy. This drag is substantially large for the particles in water, as the density of the particles is close to the density of water. This leads to the maximum velocity of the particles in water being reduced and therefore lowering the average velocity of the particles in water. The difference in their velocity was relatively large as the velocity of the particles in air could be up to 15 times as fast as in water 5.1. With a lower velocity, the particles come at rest more easily through friction, which leads to the particles settling at an steeper slope of the surface. Therefore, the particles in water settle at a larger angle in comparison to particles in air.
Another phenomenon to take into consideration is that the particles come at rest through kinetic friction as they are in motion. Kinetic friction is smaller than static friction due to the lower coefficient of friction. This means that the particles could be at an even steeper incline when held at rest through the static friction. Therefore, this could be one of the causes that the measured angles are lower than the angle of repose.
To conclude, the difference found between the range of angles measured of the cone underwater and in air is 2.4 degrees and might be due to the deposition method causing motion to the particles. As the particles are really light and have a density comparable to water, the buoyancy acting on the particles in water has a large influence on their behaviour. The buoyancy makes the net gravitational force
The angle of repose underwater versus dry conditioned conclusion
acting on the particles smaller. As the particles are in motion, kinetic friction is the force leading to the particles come at rest. Kinetic friction is smaller than static friction and therefore the particles come at rest at a smaller angle. The angles that were calculated do not represent the actual angle of repose of the sediment, due to their motion. The calculated angles are lower, but close to the actual value.
As the particles in water have a smaller velocity, the value of the angle measured in water is the most representative for the angle of repose.
6.1 Recommendations for future research
Two other ways to measure the angle of repose are, for example, with a mould or with an plate with an adjustable incline [6]. The mould should be able to be filled with sediment and then be lifted to release the sediment. As the angle of repose is not known in many cases, multiple moulds are needed or one which is adjustable. The mould should be shaped to a form where the sediment will form an inclined surface, for example the shape of an funnel upside down. This inclined surface should start as steep as possible and be flattened every time the sediment collapses after releasing. In this method the mould is lifted and thus causes motion in the medium where it is located in, which means two options should be considered: either the sediment should be heavy enough to not be influenced by the motion or the mould should be lifted slowly to make sure the motion is not large enough to influence the sediment.
The method with the plane with an adjustable incline has the sediment on top of the plate, placed there as flat as possible. The incline should be increased until the sediment starts rolling down the surface.
In this method motion is present as well. Therefore the same options should be considered, but in this case the plate should be moving slow enough.
Another improvement could be implemented through the patterns. The patterns can be adjusted to have more space in between the dots, this means that higher changes in the height gradient of the surface could be measured. This means more patterns are needed to find the same amount of data points and will take more time to do one measurement. This could be further extended to making even more patterns, to make even more data points. This will lead to more precise measurements, especially for the calculations of the angle. As in this experiment only 20000 data points were made, while in fact 1 million could be used, since there are 1280 × 780 pixels, a lot more data points could be made.
The angle of repose underwater versus dry conditioned REFERENCES
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