Self Levelling - Formula to calculate volume of a sloping wedge?

OLDFLYBYNIGHT

Hello,

We have an old rectangular building with a floor that slopes from one corner to the furthest corner.

The foundations and ground have now been stabilised.

We are considering using a self levelling compound or 'runny' concrete.

We want to know the volume of material needed to finish with a flat floor.

Please advise if anyone knows the formula to calculate the cubic volume of this sloping wedge?

Data:
Corner1 is 16 metres to corner 2, 2 to 3 is 4m, 3 to 4 is 16m, and 4 to 1 is 4m.
Corner 1 is the datum = 0
Corner 2 is -132mm (lower than corner1)
Corner 3 is -186mm (lower than corner1)
Corner 4 is -18mm   (lower than corner1)

How much levelling material whould I need to pour to make my floor flat in cubic metres?

Thank you in advance for your contributions, and advice.

FreeBear

132mm & 186mm is a lot of depth to fill, way more than SLC will cope with. I would suggest filling the deeper end with a concrete mix and try to get the depth of your SLC down to under 20mm across the full area of the floor. Even better if you can get the average depth down to around 10mm - This will reduce the amount of cracks appearing (adding screed fibres to the mix will also help).

casper_gutman

Average depth = (0 + 13.2 + 18.6 + 1.8) / 4 = 8.4 cm
Plan area = 1600 * 400 = 640 000 cm²

Approximate volume = plan area * average depth = 5 376 000 cm³ = 5.376 m³

A room 16m long is BIG, and a depth of over seven inches is more than you'd usually see on a domestic job, so you need a lot of screed - even assuming there's a self-levelling material you can use which can be used up to that thickness.

If there are any doors etc. near corners 2 and 3, you'll have an issue with the level difference. The finished result may also look rather odd, as assuming the ceiling height is uniform to start with you'll end up with the ceiling 186mm lower in corner 3.

That said, based on the prices shown at https://www.easymixconcrete.com/screed/screed-prices/ you'd pay between £720 and £810 plus delivery for 6 m³ of screed (obviously labour costs on top of this), so the quantity needed doesn't seem too crazy.

getmore4less

is it a flat surface?

If not you need more data points.

OLDFLYBYNIGHT

Hello getmore4less, yes, it is I think for the calculation reasonably flat from an earlier concrete pour, a few wrinkles, but substantially flat. And, I think one has to consider it as an irreguar sloping flat surfaced wedge else you'd get flumaxed.  The flatest surface would have to be the top of the proposed 'poured' material, and I guess you have to think that every side of the 6 sided crooked wedge is flat too (top, bottom, side 3to4, and 2to3 being rectangles, but sides 1to4 and 1to2 being triangles).  I know the sort of shape, and the measurements, but I'm now thinking that the angles should come into it too, maybe.

caper-gutman, I was guessing a few cubic metres, but at the prices I've looked at for latex and fibred compounds that they say can be layered to get up to the 7 inches is up around £4,000 and using your 5.4 cu metres would be in the very expensive £6000 area.  So maybe 5 cubic metres of 'runny' cement, well pushed about may leave a decent 5 - 10mm to pour some compound on as FreeBear suggested.

It's only when I sit back and consider your formula, casper-gutman, that I think it's a lot more accurate than 'approximate', thank you,  but am I guilty of wishful thinking ...

Thank you for your thoughts and calculations, really appreciated.