Stress on Rock
Stress on Rock
(OP)
Hi,
I have a configuration in which a peice of rock is under hydrostatic pressure (see attached figure) and i'm trying to figure out what the stress on this rock will be.
The boundary conditions on the Steel end plates are such that the right and left plates are restricted to move in the -ve X and +ve X directions respectively.
According to my calculations:
From FBD, -(6000 X 41.3) + (6500 X 31.6) = -42,400 lbf
Stress = 42400/41.3 = 1027 psi Compressive in axial direction
But I am not sure about my approach here. I did not account for the force due to 5,850 psi in the rock because it cancels out but I am not sure if it should cancel out or taken into account as an additional compressive load on the rock?
Thanks,
Mike
I have a configuration in which a peice of rock is under hydrostatic pressure (see attached figure) and i'm trying to figure out what the stress on this rock will be.
The boundary conditions on the Steel end plates are such that the right and left plates are restricted to move in the -ve X and +ve X directions respectively.
According to my calculations:
From FBD, -(6000 X 41.3) + (6500 X 31.6) = -42,400 lbf
Stress = 42400/41.3 = 1027 psi Compressive in axial direction
But I am not sure about my approach here. I did not account for the force due to 5,850 psi in the rock because it cancels out but I am not sure if it should cancel out or taken into account as an additional compressive load on the rock?
Thanks,
Mike






RE: Stress on Rock
RE: Stress on Rock
RE: Stress on Rock
RE: Stress on Rock
negative X --> -ve X
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RE: Stress on Rock
This has been tested in this exact same configuration with the rock being intact. So assume the rock is strong enough. The two Steel end plates are circular with cross sectional areas as shown in figure. The cross setional area of the rock is 41.3 in^2 and it is 30" long.
The rock is fully confined and the pressure is applied using a pressure vessel.
RE: Stress on Rock
RE: Stress on Rock
As I understand it, you have an open 3 1/2" diameter hole to rock under significant pressure and you want to know what local stresses in the rock are near the hole?
If you had a 3 1/2" diameter sample of rock, the rock with expand through the hole by delta L which could be calculated using poissons ratio. However, in this example, the rock restrains itself. at the hole there will be shears and arching action. Very difficult problem.
RE: Stress on Rock
Normally, you don't know what all the boundary stresses are, that's what you're trying to find.
RE: Stress on Rock
There is no 3-1/5" dia hole. It is one solid Steel component. The blue components on both ends are solid Steel parts.
JStephen,
I'm multiplying the pressure applied on those cross-sectional areas to get forces on the rock.
RE: Stress on Rock
tau max = (1/2(n1 - n2)^2 + tau12^2)^.5
ny = nz = 6500 psi
nx = 6000 psi
tau12 = 0
n max = 6,600 psi
tau max = 350 psi
RE: Stress on Rock
1. You have the whole outfit at the hydrostatic pressure, left side fixed, and then you apply mechanically 6000 additional pressure on the right surface.
The only differential pressure is that mechanically applied. Then the overall hydrostatic compression will be compounded with the additional axial compression from the right.
2. You have the right side excluded from hydrostatic pressure and apply there 6000 psi, whereas everything else is subject to hydrostatic force and the left side free to move axially but tight to rigid bearing on the left.
Then since the force from the right (247.8 kips) exceeds the hydrostatic force to the right (205.4 kips), the outfit will get compressed axially for a stess condition very similar to number 1 case, since the hydrostatic pressure applies to the whole rock test item and still has to support the axial compression.
3. As 2, but left surface welded to the rigid bearing. A very similar condition, again: hydrostatic loading plus the effect of axial loading.
If we dismiss the effects of volume change, the three previous cases amount to sigmax=sigmay<sigmaz, all sigmas compression and principal stresses.
As long you consider different boundary conditions and interfaces, plus you allow for more detail, different answers will follow.
RE: Stress on Rock