Penetration of a stake as it goes deeper into the soil

In summary: I got another question, would friction be proportional purely to surface area of contact or the volume of displacement, I feel like a blade which has more surface to displacement might experience less friction then a thin blade which has less surface to displacement?Friction is proportional to the area of contact, and the amount of displacement.
  • #1
byarble
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I was quite curious when I noticed that a stake gets progressively harder to drive the deeper it goes into the soil. When I tried looking up ballistics formulas they seemed to disagree and state that there should be a force that should work to penetrate all depths. Does the force increase because a stake increases in friction since more of it comes into contact with the soil? Thus in something like steel where the forces of breaking it would far exceed those of friction, would it just be as the ballistic formula states? What are the forces involved in putting a stake in the ground?
 
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  • #2
Welcome, @byarble !

Friction is the main thing to overcome in that case, unless your stake hits solid rock.

Power actuated pins into steel beams are also hold in place by friction.
The normal force comes from the elasticity of the deformed metal into which the pin is forced.

0313-in-2.jpg


 
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  • #3
Soils also get compacted which increases their resistance. Also at the surface, there is room for material to flow which makes things easier.
 
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  • #4
byarble said:
I noticed that a stake gets progressively harder to drive the deeper it goes into the soil.
As an addition for all things already mentioned above, the top layers of soil are usually more loose than below.
 
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  • #5
byarble said:
When I tried looking up ballistics formulas they seemed to disagree and state that there should be a force that should work to penetrate all depths.
That depends on the analysis, and the meaning or context of "penetrate all depths".

Since the projectile has a fixed length, once it has fully entered the solid material, friction is constant along the path.
The limit to projectile penetration is loss of energy as it opens and moves along a path through the target material. At some point, the projectile will melt, fragment, or it will stop when momentum reaches zero.

A ground stake is subjected to friction, proportional to the depth of penetration, plus the point force, needed to open the ground. The increasing force needed to penetrate, is transferred along the stake, so the stake must have a sufficient section, to avoid buckling or bending during insertion.
 
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  • #6
Lnewqban said:
Welcome, @byarble !

Friction is the main thing to overcome in that case, unless your stake hits solid rock.

Power actuated pins into steel beams are also hold in place by friction.
The normal force comes from the elasticity of the deformed metal into which the pin is forced.

View attachment 323507


I think I get it now so I have 1 more question, in the case of projectiles, friction would increase with projectile length yes?
 
  • #7
byarble said:
I think I get it now so I have 1 more question, in the case of projectiles friction would increase with projectile length yes?
Yes, but that assumes the target is thicker than the length of the projectile.
For sheet targets, thinner than the length of the projectile, the frictional force will be proportional to the thickness of the sheet.
 
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  • #8
byarble said:
I think I get it now so I have 1 more question, in the case of projectiles, friction would increase with projectile length yes?
I believe it would not, as friction does not depend on area.
I may be wrong, because I don't know anything about how different types of projectiles perform.
 
  • #9
byarble said:
in the case of projectiles, friction would increase with projectile length yes?
The impact is a science of its own. Sometimes you get wider hole than the projectile (common for high speed impacts), sometimes the bullet can even stuck... Too many variables for a general question.

Ps.: for any stake-like (slow) event: yes.
 
  • #10
Lnewqban said:
I believe it would not, as friction does not depend on area.
That is true, for a constant force such as weight. But for a slow projectile, the crowd pressure on the projectile is a function of target elasticity, which will close the hole on the projectile or Hilti DX fastner, as it penetrates and passes. A longer projectile has a greater area subjected to the confining pressure from the target, so the force is greater, in proportion to contact length.
 
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  • #11
Baluncore said:
That depends on the analysis, and the meaning or context of "penetrate all depths".

Since the projectile has a fixed length, once it has fully entered the solid material, friction is constant along the path.
The limit to projectile penetration is loss of energy as it opens and moves along a path through the target material. At some point, the projectile will melt, fragment, or it will stop when momentum reaches zero.

A ground stake is subjected to friction, proportional to the depth of penetration, plus the point force, needed to open the ground. The increasing force needed to penetrate, is transferred along the stake, so the stake must have a sufficient section, to avoid buckling or bending during insertion.
so I got another question, would friction be proportional purely to surface area of contact or the volume of displacement, I feel like a blade which has a lot of surface area would perform better in penetration than a cylinder with comparatively less surface area but more volume, wouldn't this also mean that there is a material property with the SI units of kg m^-2 s^-2
 
  • #12
byarble said:
... , I feel like a blade which has a lot of surface area would perform better in penetration than a cylinder with comparatively less surface area but more volume, ...
"Perform better" is meaningless, unless you specify an application and criteria for assessment.

The path must be deformed beyond yield by initial penetration, so sectional area is important. But at low speeds, the material will elastically spring back, against the entire surface area, making surface area also important.

At high speeds, the surface will not have time to pinch the sides and tail of a projectile, so the analysis must then be different.

Points without an edge penetrate, but do not cut. Flat blades cut roots, ligaments, pipes, cables and arteries.

If there is a fibrous structure in the material, that is turned along the path of the penetration, then the material may later pinch and so lock, preventing extraction. That happens with nails in wood, and bayonets in bone. It also makes wood screws harder to initially reverse.

There is no single SI unit that I know of with dimensions of; Length-2⋅Mass+1⋅Time-2
 
  • #13
byarble said:
I was quite curious when I noticed that a stake gets progressively harder to drive the deeper it goes into the soil. When I tried looking up ballistics formulas they seemed to disagree and state that there should be a force that should work to penetrate all depths. Does the force increase because a stake increases in friction since more of it comes into contact with the soil? Thus in something like steel where the forces of breaking it would far exceed those of friction, would it just be as the ballistic formula states? What are the forces involved in putting a stake in the ground?
Since you are interested in stakes driven into the ground, ballistics calculations do not apply. Unless, of course, that stake is fired into the ground at high velocity. The forces to push a stake into the ground can be calculated using the methods of soil mechanics. This image, from Introductory Soil Mechanics and Foundations 3rd Edition by Sowers and Sowers is for piles, which are very large stakes.
Pile.jpg

The rest of the chapter goes into the details of calculating the total load the pile can support. That load is the same as the force to drive it deeper. The procedure is to separately calculate the force from skin friction and end bearing, then add the two forces. Since the force due to skin friction is proportional to the side area in contact with the soil, the force to drive the stake deeper must increase as the stake is driven deeper.

I see that the 4th edition of that book is available from Amazon. It's a good buy if you want to get deeper into the subject.
 

FAQ: Penetration of a stake as it goes deeper into the soil

What factors affect the penetration of a stake into the soil?

The penetration of a stake into the soil is influenced by several factors, including the soil type (e.g., clay, sand, loam), soil moisture content, the diameter and shape of the stake, the force applied during penetration, and the presence of any obstacles like rocks or roots in the soil.

How does soil moisture content impact the penetration of a stake?

Soil moisture content significantly impacts stake penetration. Wet or moist soil generally allows for easier penetration due to reduced friction and increased soil pliability. Conversely, dry soil can be harder and more resistant, making it more difficult for the stake to penetrate.

What is the optimal shape and material for a stake to penetrate soil effectively?

The optimal shape for a stake to penetrate soil effectively is typically pointed or tapered at the end to reduce resistance. Materials like steel or hardwood, which are strong and durable, are often preferred as they can withstand the force applied during penetration and resist bending or breaking.

How does the force applied influence the depth of stake penetration?

The force applied directly influences the depth of stake penetration. Greater force generally results in deeper penetration, assuming the stake and soil can withstand the pressure. However, excessive force can damage the stake or compact the soil excessively, making further penetration more difficult.

Can the presence of rocks or roots in the soil affect stake penetration?

Yes, the presence of rocks or roots can significantly affect stake penetration. Rocks can create hard barriers that are difficult to penetrate, while roots can entangle the stake or deflect it from its intended path. Both obstacles can reduce the depth of penetration and may require additional effort to navigate or remove.

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