How much energy is needed to blow up stone (and other materials)?

[Ax_xiom]

TL;DR Summary

I am interested in trying to find how much energy needed to blow up stone and is looking for a bit of help

So I am trying to find the amount of energy needed to break apart stone into different sized chunks (when either punching it or blowing it up) and I'm using this method to estimate it:

1. Assume the object got broken up into cubes of the desired diameter
2. Find the surface area of all the cubes
3. Multiply this area by a "roughness factor" to account for smaller pieces, the fact that fragments won't be perfectly smooth etc
4. Multiply the new area by the specific fracture energy to get the energy needed

So my first question is if this is a valid method of estimating the energy needed? If not what would be a better method

Assuming that this model is correct I made a spreadsheet with all the specific fracture energies of materials I could find and got the "Destruction values" from them. Some of these values seem a bit low (this spreadsheet says that 100 kilotons of TNT would be enough to completely fragment mt fuji into chunks of 40cm or less) so I decided to use the Kuznetsov equation to change the roughness factor, basically "tuning" the model

So what I did is I got 2 situations from the Kuznetsov equation and attempted to change the roughness factor value as much as possible to make it align. From this I got a value of 1230, which is really high as that means it takes half a kiloton of tnt to turn 1 cubic meter of silver to dust. Even using the fact that only 6% of the energy of blasting goes into breaking rock and using a reduced value of 75 we still get a value that is higher than the value needed to vapourise the cubic meter of silver As calculated here

Edit: to elaborate on the tuning thing I did, what I did was that I calculated the tons of tnt used in 2 situations which should be usual in blasting operations (Powder factor of 0.7kg/m^3 for granite, and 2 charge values which result in average particle sizes of 10 and 20 cm) Then I put the 2 scenarios back into my method and tuned the roughness factor to get it as close as possible and landed on a value of 1230 which is way too high

So am I doing something wrong? I'm happy to answer any questions about my method

 

[anuttarasammyak]

Your idea seems better applied to liquids. Surface tension energy of two droplets is larger than that of merged single droplet. Naturally they merge. I am not sure this idea is easily applicable to solids.

 

[jbriggs444]

Your idea seems better applied to liquids. Surface tension energy of two droplets is larger than that of merged single droplet. Naturally they merge. I am not sure this idea is easily applicable to solids.

It seems plausible. I've long thought that the rubble size from a fallen building should depend strongly on the original height of the building.

 

[Ax_xiom]

Your idea seems better applied to liquids. Surface tension energy of two droplets is larger than that of merged single droplet. Naturally they merge. I am not sure this idea is easily applicable to solids.

Why? Specific fracture energy isn't a property of liquids?

If this idea doesn't work what would the best alternative be?

It seems plausible. I've long thought that the rubble size from a fallen building should depend strongly on the original height of the building.

This is for explosions and stuff so the height where it was dropped from wouldn't be a factor (because it was blown up rather than dropped

I've made a few edits to the original post but still remain perplexed on why it's not working

 

[anuttarasammyak]

Why? Specific fracture energy isn't a property of liquids?

Here is an example of computing whole bonding energy of solid
https://www.feynmanlectures.caltech.edu/II_08.html

8–3The electrostatic energy of an ionic crystal​

I observe that this calculation makes no difference for a macro large block and macro pieces made of the same number of molecules. Thogh negligible order than this bonding energy, total surface area where bonding partner is less thus minus bonding enegy is less than inside bulk could matter as you expect. In case of liquid water this surface energy is conventionally treated as surface tension energy which can be calculated.

 

[Ax_xiom]

Here is an example of computing whole bonding energy of solid
https://www.feynmanlectures.caltech.edu/II_08.html

I notice that the equation for the energy of a charged sphere is quite similar to the equation of graviational binding energy of a planet

So are you saying that be best method for to calculate this is to look at the charges at the surface of the particles and calculate the energy needed to break them apart?

Also why wouldn't/doesn't my method work?

Also if that isn't the best way to go what would the best way be? I want something that can calculate it for a range of materials and a range of values (so the Kuz Ram model won't work)

 

[anuttarasammyak]

So are you saying that be best method for to calculate this is to look at the charges at the surface of the particles and calculate the energy needed to break them apart?

Also why wouldn't/doesn't my method work?

I showed an example of ionic crystal. Each rocks, concretes, and steel have different mechanism of binding which should be considered for precise estimations.

Usually broken pieces have kinetic energy and high temperature. It suggests that breaking process has high energy barrier which might exceed energy level difference of initial state and final state. If you find your method does not work well, such a factor might harm it.

If I were you, I would search real world civil and mining engineers wisdom of "how much dynamite we need and where we should set them to break such tons of granites or any other kind of rock" and know their logic in order to validate/improve the method.

 

[Ax_xiom]

If I were you, I would search real world civil and mining engineers wisdom of "how much dynamite we need and where we should set them to break such tons of granites or any other kind of rock"

So that would involve looking at stuff like the Kuz-Ram model? if so how would I generalise stuff like that to pulverising objects (because the Kuz-Ram model is a series of empirical equations that were built for fragmenting stone into cm sized pieces not dust) and generalising to blowing up materials that aren't stone (like steel, concrete and even more esoteric materials like gold and silver)

Also I kinda tried doing that before and got a value for turning silver to dust which was higher than vapourising it entirely and many more probably had energies higher than what was needed to melt them

 

[Frabjous]

TL;DR Summary: I am interested in trying to find how much energy needed to blow up stone and is looking for a bit of help

As calculated here

What is 10.49 gm/cc?
What is 2162 K?

 

[Ax_xiom]

What is 10.49 gm/cc?
What is 2162 K?

Density and boiling point of silver respectively. The numbers may be a bit off but the value I calculated to turn Silver to dust is 2 orders of magnitude needed to boil it so the numbers can't be right

Edit: I forgot about the specific latent heat of fusion and vapourisation of silver which makes my pulverisation value only 4 times that needed to vapourise silver, progress!

 

[Ax_xiom]

If anyone is wondering this is how I did the "calibration" of my model
I used sketchbook because I don't know how to use Latex

 

[berkeman]

Thread closed temporarily for Moderation...

 

[berkeman]

A side conversation about generating an electrical arc through the stone has been deleted. Thread is reopened; thanks for your patience.

 

[Ax_xiom]

A side conversation about generating an electrical arc through the stone has been deleted. Thread is reopened; thanks for your patience.

Sorry I was getting confused about how it was relevant to this

Do you know what's going on with this?

 

[berkeman]

Sorry I was getting confused about how it was relevant to this

Do you know what's going on with this?

My advice would be to ignore the (now deleted) posts. Electric arcs through stone are very specialized (think lightning strikes), and not a good technique for breaking rocks up into many small pieces like it sounds you want to do.

 

[Ax_xiom]

My advice would be to ignore the (now deleted) posts. Electric arcs through stone are very specialized (think lightning strikes), and not a good technique for breaking rocks up into many small pieces like it sounds you want to do.

Ok, they weren't relevant anyways as I wan't to know how much energy would be needed specifically to punch or blow up stone (and other materials) into small pieces

For more context this is for the use for calcs in powerscaling, so a prefectly exact answer isn't really needed and only needs to be within an order of magnitude

Edit: To add more detail to anyone who may want it.
So in powerscaling to calculate the energy used to destroy something we first get the volume of the object destroyed, find how destroyed the object is (like was it fragmented, pulverised, melted etc), find the relevant destruction value for it and then multiply the 2 together

The values for Fragmentation, Violent fragmentation and Pulverisation (which means breaking up into large chunks, small chunks and dust respectively (whatever large and small mean)) are based off of shear strength, tensile strength and compressive strength which is wrong as these values have pretty much nothing to do with blowing things up (and I don't think you can just convert from MPa to MJ/m^3 like that) so I'm attempting to create new ones

 

[Ax_xiom]

I may have figured out why the calibration using Kuz Ram might have been so high. One of the main critisms of the Kuz-Ram model is the fact that it doesn't take into account fine particles, which would be very relevant with my model because those would reduce the mean particle size by quite a bit and add a lot of crack surface area

Edit: Also what would reasonable values be for turning 1 cubic meter of stone into fragments/dust? I might try the calibration thing again

 

[anuttarasammyak]

I enjoyed reading https://en.m.wikipedia.org/wiki/Mill_(grinding) to know what they do in making powders.

 

[Ax_xiom]

I enjoyed reading https://en.m.wikipedia.org/wiki/Mill_(grinding) to know what they do in making powders.

Ok, so I'll look into crushing and see how much energy is used to do that and I'll then use it to calibrate the model again (hopefully this doesn't come out to something stupid again)

This should be more accurate as the energy transfers should be less complicated and more of the energy should go into fragmentation

 

[Ax_xiom]

So I did the calibration thing again with the Bond Work index of different materials and I got a roughness factor of 256.2, which is way too high as it says that the energy needed to pulverise many materials (Steel, Stainless Steel, Silver, Aluminium, Tin, Copper, Bronze, Brass, Zinc, Tungsten, Gold, Calcium, Titanium and Chromium) is higher than the energy needed to melt many materials and for Silver the energy predicted by this model is higher than the energy needed to vapourise it.

So is there a fundamental problem with the way I'm calculating this? And if there isn't why every time I attempt to do some sort of calculation with this the values are way off?

 

[Ax_xiom]

So I realised that only 3% of the energy in crushing goes into breaking stone which then results in a roughness factor of around 7.5, does this sound reasonable? For context here are the new destruction values

 

[anuttarasammyak]

@Ax_xiom thank you for your effort to find and share interesting insight. I am sorry to say that I am not enlightend enough to comment on your results of calculation.

In order to get your idea, I would like to ask you a quesion : When final grain size is halved, so in volume 1/8, how would the blowing up energy change in your theory ?

[EDIT] My attempt for understanding your theory.

In making same size 8 pieces from volume $L^3$ block, total cut area is $3L^2$.

In making same size 8 pieces from volume $(L/2)^3$ block, total cut area is $3(L/2)^2$.
We do it for 8 pieces so total cut area is $6L^2$

In making same size 8 pieces from volume $(L/4)^3$ block, total cut area is $3(L/4)^2$.
We do it for $8^2$ pieces so total cut area is $12L^2$.

---

In making same size 8 pieces from volume $(L/2^n)^3$ block, total cut area is $3(L/2^n)^2$.
We do it for $8^n$ pieces so total cut area is $3L^2 8^n / 2^{2n}$

---


So the total cut area A for the effort to get grain is

$$A=3L^2(1+ \sum_{n=1}^N 2^n)=3L^2 (2^N-1)$$

where $L/2^N$ is the final size of grain. Your conjecture says that Energy we need for doing it is proportional to A. Am I following you correctly ?

 

[Ax_xiom]

So what I did here is to estimate the crack surface area as the total area of the cubes, which would include faces that are already exposed. But as the fragment size gets smaller compared to the object size it gets more and more accurate (and given I'm going to use this to calculate stuff like mountains exploding I think it's fair.

So my method is given a Cube with side length L, the volume of the side lengths would be L³, and given a Fragment size of R the volume of each fragment would be R³, so the number of fragments would be L³/R³.

The surface area of the fragments is 6R³, so the total fragment area would be
L³/R³ * 6R² or more simply

6L³/R

Then I multiply the area by the SFE to get the energy

E = 6*SFE*L³/R

And since we want energy per volume we can divide the expression by L³ to get

D = 6*SFE/R

But I realised that the crack area may be quite a lot larger than what the cubes may suggest, that's why I added the roughness factor

Edit, this model does break down when the fragment size is close to the original size of the object but at that point you could estimate the crack area directly

 

[anuttarasammyak]

E = 6*SFE*L3/R

Thanks. In my [edit], I counted area by cutting made pairs e.g. 3 not 6 and did not count initial block surface area of 6 L^2. They do not make big difference.
Does SFE stand for surface energy ? How “roughness factor” is incorporated in SFE or any other things?

 

[Ax_xiom]

Thanks. In my [edit], I counted area by cutting made pairs e.g. 3 not 6 and did not count initial block surface area of 6 L^2. They do not make big difference.
Does SFE stand for surface energy ? How “roughness factor” is incorporated in SFE or any other things?

SFE stands for Specific Fracture Energy

Roughness factor is less incoporated into SFE and more incorporated into the area, which would be much higher than the cube model predicts as cracks are perfectly straight, smaller fragments may form, dust may be created etc

 

[anuttarasammyak]

Roughness factor is less incoporated into SFE and more incorporated into the area, which would be much higher than the cube model predicts as cracks are perfectly straight, smaller fragments may form, dust may be created etc

Thanks. How is it expressed by formula in relation with E ? How do you evaluate it around 7.5 ?