Need to calculate if a large boulder can be moved by a river!! 1

[DanielRonn]

Hi. For environmental purposes, we need to calculate the minimal water/ice SPEED needed from the river to be able to move this large boulder laying on top of the rocky riverbed. The river is in Canada and fed by rainwater only. This is a non-profit project. Please advise on a formula to use.

It is a white water river during a few months a year, no vegetation only bare rocks, a very rough surface. Below data has been calculated with a photometric 3D scan of the boulder and 3D software. The boulder is pointy at the edge facing the waterflow:

Boulder weight:
17.47 metric tons.

Boulder footprint (area touching the riverbed):
6.4 square meters.

Boulder upstream surface in the direction of the water flow, exposed to the push of water and ice. This is the flat 2D surface. The real surface is larger but angled as its the pointy edge of the boulder that faces the riverflow:
2.9 square meters.

 

[r13]

A rough estimate of the flow velocity required to move the rock.

V = √[H/(ρ_wA)]
H = (W_rock - U)Tanø

A = Horizontal project area of the rock

 

[IRstuff]

Isn't this all moot? The water flow required to move such a boulder will cause widespread destruction and mayhem, and the positioning of this, or any other, will be irrelevant. The water flow that caused this is in no way normal flow, particularly given the high water mark on the boulder.

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert!

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[DanielRonn]

Hi. Thanks for all your answers. As LittleInch says, more details are needed. I have attached a Google maps image and some more photos here where the location of the boulder is. I appreciate all info and evaluations on wither the river could in fact move the boulder to its present location. Some questions..

- Why did the boulder not end up infront of the meander? As noted, the normal water level in this river is about 2 to 3 feet. It is fast during spring, but not very fast.

Retired13 posted a formula above. Could you please elaborate on all the variables? I'm not a math guy.

 

[DanielRonn]

Here is the Google Maps overview.

 

[DanielRonn]

What we now from geologists, is that the glacier could not have placed the boulder at its present location, as the overburden under it (the riverbed rocks) accumulated after the glacier was gone.

 

[LittleInch]

It is a bit odd isn't it as to why that single boulder seems to have survived and other haven't, but it seems to be off the main line and has become streamlined and hence any other boulders aren't impacting it directly in mega flood.

It might need a 1 in 500 yr flood to do this, but that isn't really a big boulder in real terms. It might have got "flung out" if the main flood path is different.

River channel width might have been a lot narrower leading to higher water velocities.

I've got no problems envisaging this being carried downstream in a serious flash flood.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[r13]

V - velocity (m/s)
H - buoyant force (N)
ρ_w - density of water (kg/m³)
A - horizontal project area of the rock (m²)
W_rock- weight of the rock (N)
U - net uplift (N), U = unit weight of water x depth of water volume of rock
Tanø - soil friction coefficient

Rock weight = 174.7 kN
Rock base area = 6.4 m²; assume rock height = 1.5 m
U = 10*6.4*1.5 = 96 kN
H = (174.7-96)*0.55 = 43.3 kN
Rock horizontal project area = 2.9 m²
Density of water = 1000 kg/m³
V = (43.3*1000/(1000*2.9))^0.5 = 3.9 m/s

 

[HTURKAK]

Dear DanielRonn ,



Will you please post other pictures (if any ) , along the river bed to see the steep hills and mountain valleys around ? ..This could happen after heavy storm flood , and the reason is rolling of the large boulders together with sand and gravel at river bed along the steep slope. You can see even more larger boulders at OMAN river beds.

 

[LittleInch]

And don't forget, you're looking at the boulder as it is now after a long time of being battered.

It may well have originally been more curved / round or rolled on what is now its side, not slid down the river bed.

If you rotated that boulder 90 degrees and rotated it on its axis 90 degrees so the front face was higher then it would start rolling at a much lower water speed and then just keep rolling along....

Now it might not have been as round as this one, but I think you get the drift...

https://www.youtube.com/watch?v=ou8v8zPAcOM

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[DanielRonn]

Here are some more photos...

 

[DanielRonn]

The other boulders in the photo above marked with red arrows, are about half the size of the large boulder.

 

[DanielRonn]

And the overview image again...

 

[DanielRonn]

Retired13.. thanks for a good formula!! Some questions...

V - velocity (m/s)
This is the velocity of the water as I understand it?

ρw - density of water (kg/m3)
I will find.

A - horizontal project area of the rock (m2)
Is this the total "flat" area facing the waterflow? Not counting for the pointy edge? Or is it the total area including the slanted sides on the pointy edge?

Wrock- weight of the rock (N)
Not in ton or kg? How do I get this in N?

U - net uplift (N), U = unit weight of water * height of rock.
What is unit weight of water?

Tanø - friction coefficient
Do you know this for a rough rock surface?

 

[r13]

Daniel,

I made correction on my definition of terms, and provided calculation. If my math is correct, the velocity shall be greater than 3.9 m/s in order to move the rock. See my previous post on above for other parameters/assumptions.

The friction coefficient is 0.55 as provided by you.

 

[DanielRonn]

retired13... THANKS!!!

Would it be possible for you to post the values you used? The coefficient 0.55 is for a flat dry rock surface on both the floor and the boulder. I have no other info on coefficients.

 

[r13]

I would guess the river bed consists of silt loam, for which ø = 25°, and the approximate friction coefficient will be Tan(0.7ø) = 0.32 (geotechnical guys should chime in here). The adjusted H = (174.7-96)*0.32 = 25.2 kN, then revised V = (25.2*1000/(1000*2.9))^0.5 = 2.94 m/s.


Derivation of equations:

 

[LittleInch]

No but then neither is this boulder a flat smooth surface sliding on another flat smooth surface.

So COF for even simple siding could be 0.8 or 0.9 and that's before it runs into another boulder.

So if that's 4m/sec, I reckon my 7-8 m/sec in real life isn't too far away.

That's a LOT of water, but flash floods can be intensely damaging and fast flowing.

A quick google for flash floods found this

https://www.sciencedirect.com/topics/social-sciences/flash-flood

"In 1976, Colorado’s Big Thompson Canyon experienced a flash flood with a channel velocity of 30 ft per second. At that speed, the floodwater moved 250 ton (227,000 kg) boulders (FEMA, 2006)"

So your measly little 17,000 kg boulder stands no chance.

And look at this and fig 94

http://assets.wwf.org.uk/downloads/flood_risk___part_c_ii_.pdf

Looks like "normal" flash floods are about 3m/sec, so that's why the boulder doesn't move very often, but an extreme event up to 9 or 10 is possible.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[r13]

Note the the calculated velocity occurs near the river bed, during flood, the velocity above will be much greater. Also, the width/shape of the flow channel will affect the velocity. So the calculated velocity only provides a rough idea.

 

[DanielRonn]

ok.. so the surface of the river will move much faster than 2.9? It would be great with a video of a river that moves in this speed at the bottom..

 

[LittleInch]

scroll / jump through to about 4mins 50.

https://www.youtube.com/watch?v=tWGK4CiWxeM

Then tell me the river couldn't shift your boulder??

I'm still struggling as to why you want / need to know.
Is someone trying to say a crowd of yetis dumped it there? Or big foot or whatever mythical huge hairy creature you have in northern canada ( and I don't mean the lumberjacks)

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.