# CASES

## INTRODUCTION

The purpose of this report is to study the force of waves when they impact a vertical obstacle.

This study is the result of a school project called MCIPA. In four sessions of four hours, I learnt how to use JADIM and I simulated four singletons.

My personal goal was to get an idea about the force of waves. This small study is an introduction to the impact of waves in structures like offshore oil-platforms, boats, breakwaters, sea walls and all structures that have to resist to waves.

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## GENERALITIES

. The BOX
To study singletons, the following rectangular box was chosen.
.. SIZE: 8m * 4m,
.. CELLS: 128*32 (squares),
.. LIMITS PROPERTIES: symmetry for the horizontal limits and wall for the vertical limits.
.. STRENGTH STUDY: strength is measured at x = 8m (wall = squarre of 2m*1m). The singleton initialy moves from the left to the rigth.

. INITIAL CONDITIONS and SINGLETON DEFINITION
The initial conditions chosen were singletons of different amplitudes. This type of initialization implies:
.. a initial plane level of the water (h0),
.. a initial amplitude of the singleton (am),
.. and a initial position of the center of the singleton (x0).

. REMARKS
For all the cases, Ho was set to 0.4 m and xo to 4 m. Consequently, the study is only on the amplitude of the singletons. Ho is voluntary small to avoid long duration calculus. Furthermore, Ho and Amo have to be chosen to keep the water in the box. The symmetrical limits imposed the flow not to pass through these limits, in these limits the flow can only be horizontal. This constituted a limitation of the study. This limitation could have been avoided via changing the size of the box but, in fact, Amo is also limited by the linear approximation and this aspect is the most problematic.

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## CASE 1

. INITIALISATION

In this case, the initial amplitude was 0.2 m. With the definition of the mesh, the wave amplitude is coded only with 3 cells. In the following picture, the lines represent the surface of a concentration of water equal to 0.2, 0.5 and 0.8. These lines allow a better definititon of the interface and they can be helpfull to evaluate the quality of the relsults.

. RESULTS

Scales: t = 0 : 2.5s, Fpx = 0 : 5000 N, Fxy = -0.04 : 0.05 N

To see the animation of the wave impact, click HERE

. CONCLUSION

This study constitutes a limitation for JADIM since very cells are used to represent the wave.

The evolution of the vertical strength is quite normal: it increases when the wave impacts and is going up along the wall and it decreases when the wave is going down along the wall.

The evolution of the horizontal strength is more difficult to analyze. The increase is expected but not the small decrease and the second peak. Furthermore the second peak is more important than the first one and is equal to the maximum of the case 2 singleton... Besides, the decrease seems to be not normal: a smaller value is expected. This can be explain via the movie. Indeed, in the movie, a small wave can be seen near the wall and the water level is not the normal level.

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## CASE 2

. INITIALISATION

In this case, the initial amplitude was 0.3 m. With the definition of the mesh, the wave amplitude is coded only with 4 cells. In the following picture, the lines represent the surface of a concentration of water equal to 0.2, 0.5 and 0.8. These lines allow a better definititon of the interface and they can be helpfull to evaluate the quality of the relsults.

. RESULTS

Scales: t = 0 : 2.5s, Fpx = 0 : 5000 N, Fxy = -0.04 : 0.08 N

To see the animation of the wave impact, click HERE

. CONCLUSION

In this study, the second peak also appears in the horizontal strength graphs. After this peak, the decrease is the one expected: the force is very well reduced just after the wave leaves the wall.

The evolution of the vertical strength is quite normal: it increases when the wave impacts and is going up along the wall and it decreases when the wave is going down along the wall.

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## CASE 3

. INITIALISATION

In this case, the initial amplitude was 0.4 m. With the definition of the mesh, the wave amplitude is coded only with 6 cells. In the following picture, the lines represent the surface of a concentration of water equal to 0.2, 0.5 and 0.8. These lines allow a better definititon of the interface and they can be helpfull to evaluate the quality of the relsults.

. RESULTS

Scales: t = 0 : 2.5s, Fpx = 0 : 7000 N, Fxy = -0.04 : 0.1 N

Sorry, there is no movie

. CONCLUSION

In this study, the second peak does not appear in the horizontal strength graphs. But the decrease is not linear and seems to be very complex. In fact, it is as if the peak has been transform into a plane level. The final level is the one expected: the force is very well reduced just after the wave leaves the wall.

The evolution of the vertical strength is quite normal: it increases when the wave impacts and is going up along the wall and it decreases when the wave is going down along the wall.

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## CASE 4

. INITIALISATION

In this case, the initial amplitude was 0.5 m. With the definition of the mesh, the wave amplitude is coded only with 8 cells. In the following picture, the lines represent the surface of a concentration of water equal to 0.2, 0.5 and 0.8. These lines allow a better definititon of the interface and they can be helpfull to evaluate the quality of the relsults.

. RESULTS

Scales: t = 0 : 2.5s, Fpx = 0 : 8000 N, Fxy = -0.04 : 0.12

To see the animation of the wave impact, click HERE

. CONCLUSION

This case shows a limit of JADIM. In this case, the singleton is to high and it is broken in 2 pieces at the beginning. Consequently, only a partial wave impacted the wall. We also show (in the animated movie) that the box is too small since the water is going out at the uppest limit and the downest one. Consequently, the calculus are not reliable.

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