Dropped Object Impact on a Submerged Flat Steel Plate

[Ussuri]

As part of the design of a subsea structure a critical load case to be assessed is the dropped object case. This is critical to ensure the integrity of the equipment contained within the structure.

Impact protection is often provided with roof panels fabricated from flat steel plate. The analysis of dropped object is based on a given impact energies, which in my area of the world are defined as 5kJ impact over a 100mm diameter, 20kJ impact over a 500mm diameter and 50kJ impact over a 700mm diameter (these are defined in NORSOK and ISO 13628). It is well know these are not related to any real life objects, and the impact energy of a dropped subsea tree could be in the thousands of kJ. The industry standard approach to demonstrate a safe design is to do the impact calculations on the assumption of an in-air impact.

However, in reality these plates are submerged, so the presence of the water will dictate the behavior (deflection) of the plate under impact. In order for an impacted plate to deflect the surrounding water must be moved, so the resistance of the plate to impact is not just a function of the plate shear and tensile capacity, but also the added mass (inertia) of the surrounding water.

I have been trying to find out if anyone has done research on this subject. There is plenty about impact on submerged pipelines (which are resting on the seabed) but nothing I can find about flat plates suspended in water. I have been through the normal online searches and paper searches but I have been unsuccessful.

Are any members aware of research on this topic, or something similar?

 

[SAIL3]

since water is considered incompressible(very low compressibility) and due to the instant affect of the impact (no time for water do be displaced) I could see the pl not deflecting to any degree except for local deformation and the energy being transferred into a shock wave thru the water...how one could quantify that ,well, I do not have a clue....

 

[rb1957]

agree ... the water will support the plate, and particularly at the bottom of the sea there will be a Vast pressure on (both sides of) the plate. Maybe run Ls-Dyna (or other impact modelling FEA) ?

another day in paradise, or is paradise one day closer ?

 

[Ussuri]

Thank you folks. My thoughts match SAIL3 and rb1957. The plate plus support from water has a capacity to resist an impact. Small impact from a scaffold bar, no problem, larger impact from a drill collar no problem, massive impact from a falling crane probably still gonna fail. Hence there is an in between good to no good point. Determining that point is the area I wondered if there had been any research on.

Blodgett is a very good reference, but its impact formulae are for impact in air. The closest thing to my case is Section 6 (page 2.8-3 in design of welded structures) where it acknowledges the effect of the own members inertia. It includes a term for the equivalent weight of the member We. This is similar to the Added Mass concept used in hydrodynamics. Blodgett suggests We is about 50% of the weight of the member. My puzzle would be what We to use for the Added Mass of the water. I think it will be orders of magnitude higher than the weight of the member, how to assess, no idea. Hence my hunt for research.

 

[GregLocock]

It might be worth researching underwater impact of shells on battleships. In WW2 the Japanese deployed so-called diving shells, the idea being to hit BBs UNDER the heavily armored belt area along the waterline. I don't know if any serious work was done on the effect of mass loading or structure/fluid coupling. My guess is probably not, a ton of metal, moving at ~1000 fps, accompanied by any HE in the warhead, is a significant impact with or without fluid effects. Another thing to look at is torpedo defense systems on capital ships in WW2. It was well known that an HE detonation under the keel of a ship would bend it a lot, if not break it in 2. Therefore people designed against that, so they must have had data or models to support those designs. Sorry, not a field I know much about.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

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[Erik Panos Kostson]

In any case if you calculate/design it for air that should be conservative since there is more damping in water thus in theory (SMSS) in water there should be a possibly lower vibrational amplitude due to a sudden impact (should be then OK in water); another parameter for more pulsed impacts (not sudden load impact where the dynamic amplification is 2 times the static one), is the ratio of the pulse duration to the eigen-mode (and frequency) in the impact direction of the plate, which is of course altered due to the water added mass. Of course validation and verification is always key, so do not rely on my assumptions here, test it out.

The hydrodynamic added mass (that arises from the movement of the plate as it moves the surrounding fluid) will not influence the displacements due to a sudden impact. This is easy to see when looking on a mass spring system that has a sudden applied impact force to it (similar to a falling object that will stick on it after impact, say in water, and that will exert a sudden and then constant force). The terms that decide the vibration amplitude, is the damping (xmax=F/k(1+exp(-zeta*pi)), because the dynamic amplification is (1+exp(-zeta*pi), which is 2 as expected when damping (zeta) is zero. Thus even if we add a hydrodynamic mass to the mass spring system, that will alter the frequency, but not the amplitude. Of course the hydrodynamic damping (due to various effects), will have a role, but that could be small (it should be possible to roughly estimate the hydrodynamic added damping increase in a submerged plate compared to air). Say that the damping is 0.5 % of critical in air and say higher, say just 20 % in water (damping could be anything here since it is hard to know), the dynamic amplification is still 1.6 so it (added fluid damping) does have some influence on the dynamic amplification of a mass spring system with damping that is very high (not when it is low), subject to a sudden force and then constant force. Now how much exactly the damping is for a specific case is probably hard to say (of course with experimental modal analysis one can calculate the modal damping, but I would not like to do that 30 m below the surface ).

Hence why we can use the impact in air, which as we say should be conservative since the damping of course is much lower in air.

The coupled equations for a fluid structure interaction problem like this one cannot be solved easily for such a system analytically. Hence one would need to use say FEA and Nastran in this case that has the capability of estimating the added mass/damping effects using a panel method (MFLUID), that can be used say for a submerged impact problem. Alternatively modified acoustic finite elements coupled to the structural elements (e.g., shells) can account for these effects (not sure about the damping though).
I hope this gives an idea of the options.

 

[SAIL3]

on further thought....the area of pl the must have some relationship to the magnitude of the impact to effectively transfer the energy to the water....I can envision a minimum area of pl where it would become less effective and if taken to a minimum limit would not be able to transfer the impact load to the water without absorbing more of the energy itself thru defection or movement.....again more questions than answers....

 

[WARose]

My puzzle would be what We to use for the Added Mass of the water. I think it will be orders of magnitude higher than the weight of the member, how to assess, no idea. Hence my hunt for research.

To get precise: I don't know that the water would really add any mass to the plate.....it does change how it is loaded (i.e. the self-weight minus the buoyancy)....modeling that as a external load vs. self-weight would be up to the user.

 

[WARose]

I was messing with this last night and this morning. I found a solution (maybe) by putting drag into the impulse-momentum equations:

mv₁+F(Δt)=mv₂

Obviously here, mv₂ would equal zero (or very close to it, more on that in a minute). "F" would wind up being your average drag. (Since the force isn't a constant, ergo F_max would be twice that. And here I am neglecting the buoyancy since it isn't significant during this impact.)

In any case, you would have v₁ from the free fall calculations, you'd have "F"/drag from a simple fluids calculation....from all that you could get Δt.....and from that you could get the depth of penetration into the water since you know the speeds.

I ran it myself with the example of bullets fired into water and I got some similar results that you see in tests. (I.e. around 4-8 feet.) So although this is likely a crude approximation (considering the uncertainties of Reynold's number and so forth)....you can get a idea as to how far you'll penetrate before it becomes a slow sinking situation. After that, it should be pretty straight forward.

Speaking of that, a example I found in my old fluids text of a ball dropped from the surface (of the water) used Stokes's law (i.e. drag equation) to figure the drag in such a slow moving case.

As for the force on your plate.....whatever velocity you come up with at the point of impact.....it then becomes another impulse-momentum problem. One quick way to do it would be assuming a Δt and solving it similar to above. I would think the smallest Δt you could get would be about 0.01 s. (That's about the lowest number I've seen for water impacts for objects dropped in air. So you know a submerged impact would likely be more time and ergo less force.) Still another method could be Blodgett's stiffness method discussed above. (With the water "mass" accounted for via the way I mention in another post.)

 

[Erik Panos Kostson]

Just to add that except of the numerical tools mentioned, as Ussuri mentions it is possible to use CFD, coupled to FEA both ways (2 way fsi. , accounting for the fluid structure interaction). Here is a good and very relevant example

https://www.sharcnet.ca/Software/Ansys/16.2.3/en-us/help/wb2_sysc/SysCoupsysc_tutorial_plate.html.

Contacts are not applicable, but it would be sensible to apply a sudden constant force equal to the weight of the sinking part minus it's buoyancy on to the submerged plate.

It might also be possible to use explicit solvers with particle formulations(sph) for the fluid or other fluid or acoustic finite elements as long as one does not try to model the sinking part. So then this include's the fluid (mass,damping, flow, radiation waves) and apply the force on the submerged plate.

These are the tools which are advanced since the physics of this problem is complex involving both structural and fluid motion and their coupling

 

[Ussuri]

WARose. Thank you.

I am thinking about it this way . Once the object is in the water and gone through its velocity changes (as per projectile entering the water) it will then continue to fall at its terminal constant velocity such that the net force on the object is zero (object weight (W) = Buoyancy (Fb) + Drag (Fd)).

I possibly could use some approximation to calculate an impulse force. The crux of my problem, I think, is determining the deflection response of a submerged plate.

 

[WARose]

Once the object is in the water and gone through its velocity changes (as per projectile entering the water) it will then continue to fall at its terminal constant velocity such that the net force on the object is zero (object weight (W) = Buoyancy (Fb) + Drag (Fd)).

The problem I mention in my fluids book (above) does it like that (since there is no acceleration).

I possibly could use some approximation to calculate an impulse force. The crux of my problem, I think, is determining the deflection response of a submerged plate.

For such a short-term impact.....why not just use a impact factor (i.e. 2, since it is the max.)? You can figure the force of impact from the method I mention above and account for the dynamics of the submerged plate with the impact factor.

Or if you have software (like STAAD) you can model it there and use a short-term force function and see what you get.

 

[KootK]

My gut feel for it is that the open air solution is not just expedient but reasonably accurate as well. Thoughts:

1) open air solution is a fluid dynamics problem too, just at different viscosity.

2) Whether in open air or in water, I believe the crux of this to be the interplay between two things:

a) how fast the fluid gets out of the way of the falling object and;
b) how fast the fluid gets out of the way of the deflecting plate.

3) Owing to #2, I feel that the extremes of behavior will occur when there is a disparity in the fluid viscosities affecting 2a & 2b. An example might be a large steel plate held to rest at the water's surface. In this case, a free falling object probably would experience this much like impacting solid concrete, as proposed by OP above. That, because air gets out of the way of the falling object much more readily that water gets out of the way of the deflecting plate.

4) I feel that the key parameter here is the ratio between the 2a viscosity and the 2b viscosity. As such, whether you've got air for both viscosities or water for both viscosities, I feel that the resulting behaviors should be comparable. Another way to express this is as follows: In water, I'd expect the falling object's terminal velocity to be low enough that water could be expected to move out of the way of the deflecting plate fast enough that it would not produce an extreme of behavior like the #3 example.

This really is a complex problem. Put me down for a KootK confidence rating of 45%.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.