## Calculating the Lateral Soil Load on Propped Retaining Wall

## Calculating the Lateral Soil Load on Propped Retaining Wall

(OP)

I have a query on the calculation of lateral earth load on a propped retaining wall where the soil height is above the prop. This arises because I suspect that some software I am reviewing gets the calculation wrong but as I'm only a humble computer scientist I thought I'd check that it is not my understanding of the engineering that is at fault.

Take as an example the situation as per enclosed diagram. A retaining wall retains 3m of soil (Soil height, S=3m) and is propped at 2m (Prop height, P = 2m), the wall is idealised as a propped cantilever pinned at 2m and fixed at base and both prop and base are fully braced. Using a simple Rankine model the overall earth pressure on the wall would be a triangular distribution with resultant of magnitude K x S squared x soil unit weight / 2 applied at a height of S / 3 (ie one third of soil height).

However when designing the portion of the wall below the prop - i.e. to determine bending moments, surely only the load on the section of the wall between base and prop is of concern, i.e. the prop carries the load of the upper soil (ignoring load sharing or any mechanisms that transfer load within the cantilever). The total force is the integral of soil loads between base and prop, i.e. the trapezoid as drawn, which gives a resultant which is the equivalent of a soil load of height P (magnitude K x P squared x soil unit weight / 2 applied at height P / 3), plus the load from a uniform surcharge corresponding to 1m of soil (ie magnitude K x 1 x soil unit weight applied at height P / 2). Never mind the magnitude of the resultant from combining these two forces the point of application will be a height somewhere between P / 2 and P / 3.

My point is that it would surely be wrong to use the resultant values calculated from the overall earth pressure on the wall, - the magnitude would be too great (but that's conservative) however the point of application is also too high, i.e. S / 3, and that's not conservative. To take it to an extreme if the prop height is less than a third of the soil height (P < S / 3) then using the overall figures would give a resultant applied at a height above the prop – i.e. which implies that there is no earth load on the wall section below the prop contributing to bending moment. Clearly false, I hope.

Is my analysis correct? If not then I'd very much like an explanation of why it is correct to use S / 3 as the height of the resultant to improve my understanding of the engineering!!

Any help much appreciated - you never know you might be using the software...

Take as an example the situation as per enclosed diagram. A retaining wall retains 3m of soil (Soil height, S=3m) and is propped at 2m (Prop height, P = 2m), the wall is idealised as a propped cantilever pinned at 2m and fixed at base and both prop and base are fully braced. Using a simple Rankine model the overall earth pressure on the wall would be a triangular distribution with resultant of magnitude K x S squared x soil unit weight / 2 applied at a height of S / 3 (ie one third of soil height).

However when designing the portion of the wall below the prop - i.e. to determine bending moments, surely only the load on the section of the wall between base and prop is of concern, i.e. the prop carries the load of the upper soil (ignoring load sharing or any mechanisms that transfer load within the cantilever). The total force is the integral of soil loads between base and prop, i.e. the trapezoid as drawn, which gives a resultant which is the equivalent of a soil load of height P (magnitude K x P squared x soil unit weight / 2 applied at height P / 3), plus the load from a uniform surcharge corresponding to 1m of soil (ie magnitude K x 1 x soil unit weight applied at height P / 2). Never mind the magnitude of the resultant from combining these two forces the point of application will be a height somewhere between P / 2 and P / 3.

My point is that it would surely be wrong to use the resultant values calculated from the overall earth pressure on the wall, - the magnitude would be too great (but that's conservative) however the point of application is also too high, i.e. S / 3, and that's not conservative. To take it to an extreme if the prop height is less than a third of the soil height (P < S / 3) then using the overall figures would give a resultant applied at a height above the prop – i.e. which implies that there is no earth load on the wall section below the prop contributing to bending moment. Clearly false, I hope.

Is my analysis correct? If not then I'd very much like an explanation of why it is correct to use S / 3 as the height of the resultant to improve my understanding of the engineering!!

Any help much appreciated - you never know you might be using the software...

## RE: Calculating the Lateral Soil Load on Propped Retaining Wall

pls see diagram attached.i think the wall should be designed this way. and loading on wall should be taken as triangular uniform loading and not the point load applied on h/3.

## RE: Calculating the Lateral Soil Load on Propped Retaining Wall

## RE: Calculating the Lateral Soil Load on Propped Retaining Wall

Not all propped or braced walls have triangular earth pressure distributions. Different soils may have different pressure distributions. I have never seen a propped, braced, or anchored wall designed with the assumption that the base of the wall is a fixed connection. The cantilevered portion of the wall (above the brace) reduces the bending moment below the brace. There are many references that discuss the design of non-gravity retaining walls. Look for design manuals on the FHWA geotechnical web site or on other state DOT web sites. Look for the Pile Buck Steel Sheet Piling Design Manual. Search these forums for other design references.

## RE: Calculating the Lateral Soil Load on Propped Retaining Wall

The assumptions you state make the wall statically indeterminant. This makes many of the load distribution assumptions that follow incorrect.

Why would you state this?

## RE: Calculating the Lateral Soil Load on Propped Retaining Wall

I have previously found a number of mathematical errors in these spreadsheets (eg one reported in previous post – which apparently went unnoticed for 9 years). From the diagrams and other aspects I suspect that this sheet was written with the assumption that the retained soil level was below the level of the prop (described at being at the top of the wall). However it is possible to enter a soil height that is higher than the prop height (see enclosed screen dump) I was concerned that in this case the calculations might not be valid.

My concerns arose because the spreadsheet has no representation for the wall above the prop (e.g. it is not shown on 'Wall Geometry') – it only calculates bending moments etc. for the wall between the base and prop and the calculated weight of the wall (e.g. when it calculates bearing pressure) is only that up to the height of the prop. My statement about ignoring loads above the prop and load transfer was an attempt to articulate the fact that if you had no knowledge of what was above the prop one could not assume anything about its properties.

My first thought to verify the calculations was to compare them with those calculated from an equivalent situation (my original query) – and here I was thrown by the representation used by the spreadsheet, as I compared it with the software's calculation for soil height equal to the prop height with a surcharge equivalent to the weight of the soil above. I now realise that if the soil height is higher than the prop height as far as calculating bending moments is concerned the software's calculations implicitly model the upper (cantilevered) part of the wall above the prop and my 'equivalent' is not equivalent since as stated in responses the rotation of upper cantilever reduces the bending moment on lower part of the wall. Though other elements of the software's calculations are incorrect if the soil height is above the prop, as far as bending moments are concerned the calculation is correct. I make no comment on whether the engineering assumptions behind this calculation are appropriate (triangular soil load etc.) - they were not my concern.

I sorry if anyone thinks that it is presumptuous of a computer scientist to check engineering calculations ('way over my head') but the issue (software failing to check whether entry values are outside the valid range assumed during design) is a software issue. My approach (comparing the results from two alternative paths through the software) is a standard one - if you get two different answers then query which is right. My error (which was an engineering one – in choice of 'equivalent') was caused by taking the representation given (the diagram of 'Wall Geometry') at face value and not thinking carefully enough about the engineering reality.

## RE: Calculating the Lateral Soil Load on Propped Retaining Wall