Penetration of falling object into sediment (after water)

[Calcifur]

Hi All,

Long time absentee from the forums hoping for some direction in my new research.

I've been tasked to look into the stages of motion of objects (dropped from various heights), hitting a body of water (of various depths) and eventually hitting the seabed (of various sediment types). I am currently struggling mostly on where to start with the last part. The most important factor I am required to calculate is the final penetration depth of the item into sediment after falling through a body of water first.

I am able to calculated terminal velocity in air and I am aware of Stoke law for calculating terminal velocity of a particle in water. However, the shape of my objects may be more complex than a sphere (cubic, cylindrical etc) and furthermore, the depths may be so shallow that the object may not yet have reached terminal velocity in water before impacting the soil.
Just to add even more complexity, the soil types may also vary (sand, clay etc.)

I'm at a loss of where to even start with this research. Would anyone happen to have any experience with this?

Many thanks in advance!

 

[A.T.]

The falling through air and water part is the easiest part here. The impact on water and sinking into sediment is very difficult to predict. The sediment can behave as a non-Newtonian fluid.

 

[anorlunda]

Shape is totally dominant here. Think of a needle shape compared to a thin flat disc with the same momentum. IMO, you can't even start without specifying the shape.

Edit: even if the shape is spherical, there would be a huge difference between a solid sphere and a hollow one.

 

[Dr. Courtney]

Done a few penetration type projects. Taking an empirical approach where you effectively end up interpolating between a variety of experimental results is often more accurate than attempting accurate predictions from first principles.

 

[Calcifur]

The falling through air and water part is the easiest part here. The impact on water and sinking into sediment is very difficult to predict. The sediment can behave as a non-Newtonian fluid.

Thanks for your input here A.T. It does not surprise me about the sediment behavior. I imagine with Clay, the behavior would be different though in comparison to non-cohesive soils such as sand and gravel ?

Shape is totally dominant here. Think of a needle shape compared to a thin flat disc with the same momentum. IMO, you can't even start without specifying the shape.

Edit: even if the shape is spherical, there would be a huge difference between a solid sphere and a hollow one.

Anorlunda, thanks for your points. I totally agree. Like I said , this research is pretty broad so shape is variable. I'd really like to be pointed in the right direction of similar research so that I can see the formulas (if any) for myself. My preliminary shapes however will be spheres, cuboids and ellipsoids.

Done a few penetration type projects. Taking an empirical approach where you effectively end up interpolating between a variety of experimental results is often more accurate than attempting accurate predictions from first principles.

Dr. Courtney, thanks for your comment! Given your previous work, are you aware of any decent academic papers/ authors out there that cover this field? I'm really struggling! I keep getting directed to old military reports on ballistics which I'm planning on reading at some point but wanted to check the more academic avenues first.
I'm assuming that the reason you say empirical approach is best is due to the mechanics simply being too complicate to predict?

 

[Dr. Courtney]

Dr. Courtney, thanks for your comment! Given your previous work, are you aware of any decent academic papers/ authors out there that cover this field? I'm really struggling! I keep getting directed to old military reports on ballistics which I'm planning on reading at some point but wanted to check the more academic avenues first.
I'm assuming that the reason you say empirical approach is best is due to the mechanics simply being too complicate to predict?

There is some stuff on spheres being dropped into sand through the air. Search for crater depth rather than penetration, and it should come up.

But going through water and hitting a water-soaked substrate really complicates things. It's a big tough problem. Even finite element based approaches are going to have problems due to the complexity of the problem statement and unknown material properties.

Is it too complicated to predict?

With pencil and paper? Yes.

With a big computer, lots of funding, and all the software tools and material properties you need? No.

 

[Calcifur]

There is some stuff on spheres being dropped into sand through the air. Search for crater depth rather than penetration, and it should come up.

But going through water and hitting a water-soaked substrate really complicates things. It's a big tough problem. Even finite element based approaches are going to have problems due to the complexity of the problem statement and unknown material properties.

Is it too complicated to predict?

With pencil and paper? Yes.

With a big computer, lots of funding, and all the software tools and material properties you need? No.

Dr. Courtney, once again, thanks for your response. I appreciate you directing me towards the "crater depth" research. I'm sure it will undoubtedly prove to be useful to me.

If, as you say, modelling the problem, is too complex and costly (I doubt my company would provide me with the funding for the necessary materials) I think I will take the "empirically based prediction approach" and look at the current data out there perhaps with an aim of running my own test experiments in the future.

Thanks again for your input, it has been very helpful.

 

[anorlunda]

You might also look into ballistics. There must have been criminal forensic cases where similar questions arose.

 

[Calcifur]

You might also look into ballistics. There must have been criminal forensic cases where similar questions arose.

Thanks anorlunda. Yes, as I told Dr. Courtney above, I actually keep getting directed to military papers on ballistics regularly, so this may well be my most useful source of research (despite not all of my object being bomb or bullet shaped) .