# Penetration of falling object into sediment (after water)

• Calcifur
In summary, the conversation discusses the difficulty of predicting the final penetration depth of objects dropped from various heights into a body of water and then into different types of sediment. The participants mention the challenges of considering factors such as terminal velocity in air and water, shape of the objects, and the varying behaviors of different types of sediment. Some suggest taking an empirical approach by using existing experimental data, while others mention the possibility of using computer modeling and forensic investigation techniques to analyze the problem.
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?

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.

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.

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.

A.T. said:
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 ?

anorlunda said:
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.

Dr. Courtney said:
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?

Calcifur said:
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.

Dr. Courtney said:
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.

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

anorlunda said:
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) .

## What is the process of penetration of a falling object into sediment after water?

The process of penetration of a falling object into sediment after water involves several factors, such as the density and size of the object, the density and composition of the sediment, and the velocity and angle at which the object enters the sediment. When a falling object enters the sediment, it displaces the water and creates a cavity. The sediment then begins to flow around and over the object, gradually filling in the cavity and causing the object to sink deeper into the sediment.

## What factors affect the depth of penetration of a falling object into sediment?

The depth of penetration of a falling object into sediment depends on several factors, including the velocity and angle of entry, the density and size of the object, and the density and composition of the sediment. Objects with higher velocities and larger sizes tend to penetrate deeper into the sediment, while objects with lower velocities and smaller sizes may only penetrate a shallow depth. The density and composition of the sediment also play a role, as denser and more compact sediments offer more resistance to penetration compared to loose and less dense sediments.

## How does the angle of entry affect the penetration of a falling object into sediment?

The angle of entry of a falling object into sediment can greatly impact the depth of penetration. When an object enters at a steeper angle, it creates a smaller cavity and therefore has less sediment to displace and flow around it. This results in a shallower penetration depth compared to an object entering at a shallower angle, which creates a larger cavity and displaces more sediment, allowing for deeper penetration.

## What happens to the sediment as a falling object penetrates it?

As a falling object penetrates the sediment, it displaces the water and creates a cavity. The sediment then begins to flow around and over the object, filling in the cavity and causing the object to sink deeper. This process is known as fluidization, where the sediment behaves like a fluid due to the movement of the object. The sediment also exerts pressure on the object, which increases as the object penetrates deeper into the sediment.

## How is the penetration of a falling object into sediment studied?

The penetration of a falling object into sediment is studied through laboratory experiments and numerical simulations. In laboratory experiments, a controlled environment is created to mimic the conditions of the real world. Different variables, such as object size, angle of entry, and sediment composition, are manipulated to observe their effects on the penetration depth. Numerical simulations use mathematical models to predict and visualize the penetration process and can provide valuable insights into the behavior of different objects in different sediment conditions.

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