Help with my calculations, please. How deep should the foundation be ?

[ToughButterCup]

I need to prepare our carpark: one edge of it has a low wall which supports part of the parking area. The stone (local stone) wall forms the border to a footpath. 

 

I would like to calculate the minimum depth of the foundation.

 

I need  to take the wall down, dig out the back of the wall to make space for the foundation [ and the shingle drainage and french drain] , then put a block wall up, and face that block wall with the stone I took down. 

 

The wall height varies between 450mm and 700mm. The ground is medium clay, and it's fairly damp most of the year. (I think its glacial till ) Wet Clay repose is (say) 20 degrees or so. 

 

This is the first site I googled that gives me a formula to calculate the minimum depth of the foundation

 

The formula is given as 

where p = the soil bearing capacity

w = density of the soil

and the angle of repose is that funny phi (or is it summat else ?) looking thing

 

That means

p = 250 kN per square meter 

w = 1760 kg per cubic meter

Angle of repose is 20 ish

 

 

1 - sine 20 is 1 - .342   =  0.658

1 + sine 20                    = 1.342

 

Minimum depth is ( 250 / 1760 )  *  ( 0.658 / 1.342)  

 

= 0 .1420 *  0.490

 

= 0.6958

Here's where I'm stumped ---- is that 0.6958 mm or is it 69.58mm or is it something else ? 

 

Thats the trouble with google: a little knowledge = danger. hence this post

 

I 'feel' the foundation needs to be 100mm of C25. But it would be good to know why I'm wrong - or, more rarely, right.

 

 

 

 

 

[Bonner]

Can’t comment on the validity of this formula however the result should be 0.06958 and the unit is metre, therefore 69.58mm so you were right!

[ToughButterCup]

Cheers @Bonner..... 

[markc]

I don’t have anything to do with groundwork’s or geotechnical but Just looking at this and my first thought is that the calculation would be for the minimum depth below the lowest point to prevent a slide or shear down the slope.

that aside, min foundation depth is generally to get below a level that will be affected by movement from shrink, heave or frost etc.

[SteamyTea]

By the looks of it you started in mm, rather than converting to m.

So the answer will be in mm.

 

And it is Phi.

[Russell griffiths]

Show us a picture buttercup. 

 

[ToughButterCup]

.... of the intended design.....

 

 

and the reality of what's there now .... erm, needs a bit of strimming maybe   🫣

 

 

 

[LnP]

9 hours ago, ToughButterCup said:

I need to prepare our carpark: one edge of it has a low wall which supports part of the parking area. The stone (local stone) wall forms the border to a footpath. 

 

I would like to calculate the minimum depth of the foundation.

 

I need  to take the wall down, dig out the back of the wall to make space for the foundation [ and the shingle drainage and french drain] , then put a block wall up, and face that block wall with the stone I took down. 

 

The wall height varies between 450mm and 700mm. The ground is medium clay, and it's fairly damp most of the year. (I think its glacial till ) Wet Clay repose is (say) 20 degrees or so. 

 

This is the first site I googled that gives me a formula to calculate the minimum depth of the foundation

 

The formula is given as 

where p = the soil bearing capacity

w = density of the soil

and the angle of repose is that funny phi (or is it summat else ?) looking thing

 

That means

p = 250 kN per square meter 

w = 1760 kg per cubic meter

Angle of repose is 20 ish

 

 

1 - sine 20 is 1 - .342   =  0.658

1 + sine 20                    = 1.342

 

Minimum depth is ( 250 / 1760 )  *  ( 0.658 / 1.342)  

 

= 0 .1420 *  0.490

 

= 0.6958

Here's where I'm stumped ---- is that 0.6958 mm or is it 69.58mm or is it something else ? 

 

Thats the trouble with google: a little knowledge = danger. hence this post

 

I 'feel' the foundation needs to be 100mm of C25. But it would be good to know why I'm wrong - or, more rarely, right.

 

 

 

 

 

I don't know anything about foundations, but I was curious ...  as I recall, one way to answer this question is to do dimensional analysis on the equation. Working through the dimensions on the RHS should give a dimension of L (depth of the foundation), but it doesn't so I'm wondering if there's something wrong with the equation .. here is the dimensional analysis:

 

p has dimensions force per unit area, and force=mass*acceleration, so p has dimensions M LT^-2L^-2

w is density which has dimensions ML^-3

The expression in the bracket is dimensionless.

So the RHS has dimensions (M LT^-2L^-2)/(ML^-3).

If you cancel that through, you end up with dimensions for the RHS of L²T^-2, but it should have dimensions just L for the depth. So we need to get LT^-2 out of the RHS. LT^-2 are the dimensions of acceleration, so the dimensions would come out right if p was in kg/m² rather than N/m².

So I would say that if you put in a number for p in kg/m², your answer will be in m.

 

Willing to have my maths homework corrected if I got this wrong 🙂

[saveasteading]

11 hours ago, ToughButterCup said:

is that 0.6958 mm or is it 69.58mm or is it something else

 

If anyone remembers slide rules: digits were shown as an answer, but we had to know ourselves where the decimal point went.

In a complex sum, it required a bit of working out. 

But with this sort of calculation, it is common sense. What sort of number do I expect to see? 7mm or 70mm or 700mm or 7m?

The answer here is fairly obvious and it usually is.   Assuming the calcs are right and the fundamental principle is valid.*

 

For example, I offer each school client a practical maths class. the first challenge is how much concrete do i need to order for he floor slab. H x L x th.

decimal places  are always the biggest challenge. So I help by asking how many concrete lorries feels right? for example is  it 3 or 30 or 300? some kids immediately feel what is right, but others don't. It's the way our brains are wired i guess.

 

 

Now, from a quick look at your link...

*Rankine's formula doesn't, as I recall, apply to foundation depths.  But he did a lot of stuff so..@Gus Potterhelp please.

There is no such thing as The Institute for Civil Engineers, not in UK and Commonwealth anyway, It is the Institution of Civil Engineers, and these are not they.

 

Who knows who wrote this googled page?

 

So to your wall. I wouldn't calculate this, as its not exactly a motorway where disaster could result.  700mm seems very deep to me. 450? /500? just do what feels right.

 

If it fails it will be by falling over, not settling.

[LnP]

This website gives a different version of the equation, which does check out OK by dimensional analysis, so perhaps your equation is wrong.

Caveat again, I know nothing about foundations!

[ToughButterCup]

A depth of 1 m of C25 concrete  -- wow! Thats a lot, @LnP

 

Debbie suggests we use RAAC.  Ever the bright spark...... I suppose I could get my Paddle Mixer out and whisk it up into a bit of a froth. Its the autoclave I'm struggling with

 

I'm with you @saveasteading - it'll fall over rather than sink.....

Does that imply that the foundation design should anticipate that force - maybe tilt it a bit to the right (away from the path in the image above). The deepest the wall gets is 700mm or so - not much.

 

Just waiting for @Russell griffiths to say that I'm overthinking it (again)

 

 

[markc]

Some confusion here regarding depth and thickness.

depth is how deep into the ground the excavation is .. to resist movement.

 

thickness of a found depends on the loads it will carry, bearing capacity of the ground under it and the founds resistance/breaking to bending when the loads are applied

Edited September 14, 2023 by markc

[ProDave]

Am I missing something here.

 

It is not just a foundation for a wall.  That is easy.  Just dig until you hit hard undisturbed ground, no calculation will tell you what you will find when you dig.

 

Bit this is not any old wall, it is a retaining wall, if I am reading it right to keep your driveway from sliding down into the piggery?  If so I have not seen discussion of the height of what it has to retain and the forces trying to overturn the retaining wall.

[joe90]

Perhaps I am getting lazy in my old age but do you need to park close to that wall?, my immediate thought was to slope the ground at 45’ (do you still have your digger?) use the stone as a rockery on the slope 🤷‍♂️

[SteamyTea]

Just to clarify something.

° is for degrees.

' is minutes, a 60^th of a degree.

 

I degree. °, is 60 minutes,'.

And, just to be a pendant, 3600 seconds, which has the sign, ".

[joe90]

10 minutes ago, SteamyTea said:

Just to clarify something.

° is for degrees.

' is minutes, a 60^th of a degree.

 

I degree. °, is 60 minutes,'.

And, just to be a pendant, 3600 seconds, which has the sign, ".

Sorry steamy I only have an iPad which does not have those “things”, I am sure people know what I mean 🤷‍♂️

[kandgmitchell]

I'm with ProDave here. The foundation depth here needs to go deep enough to avoid frost action in the clay (if any trees are ignored - and this is only a garden wall). 0.5m -0.6m should be plenty for that. Of more importance is the overturning effect on the retaining wall caused by the loads on the upper side. What's the difference in height between levels?

[joe90]

6 minutes ago, kandgmitchell said:

What's the difference in height between levels?

 

22 hours ago, ToughButterCup said:

The wall height varies between 450mm and 700mm.

 

[kandgmitchell]

As soon as I pressed that reply button I thought - I've seen that ..................

[Conor]

As a general rule, if a wall is, or is in part, retaining, then the width of the footing should should be equal to the height of the retaining portion of the wall. In your case, about 600-700mm? In these cases the footing acts more like a beam, so depth is less important as the load is spread out over the soil, rather than down through it.

 

I'd dig down deep enough to firm ground, the full width of the path, and pour 25nm concrete to the depth that allow you to pave directly on top with about 30mm mortar. You'd want a wee bit of steel in there as well. Even just dowels for the first course.

 

Our retaining wall founds are only 250mm thick and about the same under the surface. But they are 1200-1700mm wide with a fair bit of steel. In fact, one is at FGL and forms the base of a "shed".

 

 

This wall is 100mm RC tied in to the slab, bricks and block used as shuttering.

[ToughButterCup]

22 minutes ago, kandgmitchell said:

.... What's the difference in height between levels?

 

450mm at one end and 700 ish at the other

 

1 hour ago, ProDave said:

.... Just dig until you hit hard undisturbed ground,....

 

Bit this is not any old wall, it is a retaining wall, if I am reading it right to keep your driveway from sliding down into the [ footpath in the image above ]?  If so I have not seen discussion of the height of what it has to retain and the forces trying to overturn the retaining wall.

 

I know from our piling trial pits (one was right next to this wall) that we have glacial till under about 700mm of MOT1  (put there during the build )

 

Height :  450 to 700mm ish and the forces are the weight of the MOT1 and gravel next to the wall and any cars parked close to the wall.... I assume that a car parked one car-width away from the wall will have no real effect on the wall.

 

At best, only two cars will be able to park right next to the wall: and by right next to the wall I mean one car-door width plus a bit next to the wall.

[SteamyTea]

39 minutes ago, joe90 said:

only have an iPad which does not have those “things

It does, press and hold the zero 'key', the ⁰ symbol will reveal itself.

[kandgmitchell]

Well, when there's a vertical load the rule of thumb difference in height allowable is 4 x thickness of wall - 750mm would suggest 187.5mm. However, this is a pure retianing wall with no vertical load, only a horizontal one, however unless a really heavy truck was to be parked alongside the wall I would have thought a total of 100mm block plus 150mm stone = 250mm would do.

 

If you wanted more certainty without involving a structural engineer then how about a strip of horizontal mesh in the foundation with vertical bars at intervals. Make the vertical rods L shaped and wire the "foot" to the mesh. When set, use 225mm hollow concrete blocks with the vertical rods threaded up the voids and backfill the voids with concrete. Face with stone. I can't see that being pushed over easily.

[S2D2]

10 minutes ago, ToughButterCup said:

I assume that a car parked one car-width away from the wall will have no real effect on the wall.

 

At best, only two cars will be able to park right next to the wall: and by right next to the wall I mean one car-door width plus a bit next to the wall.

Until you have visitors, who will inexplicably park on lawns/middle of roads/millimetres from the edge of your retaining wall...

[ToughButterCup]

1 hour ago, kandgmitchell said:

...

If you wanted more certainty without involving a structural engineer then how about a strip of horizontal mesh in the foundation with vertical bars at intervals. Make the vertical rods L shaped and wire the "foot" to the mesh. When set, use 225mm hollow concrete blocks with the vertical rods threaded up the voids and backfill the voids with concrete. Face with stone. I can't see that being pushed over easily.

 

Top idea. Thanks. Cheque's in the post.