topic Re: Calculating Soil Wedge Area, Weight, and Centroid Behind a Retaining Wall and for Each Course in Mathcad

Calculating Soil Wedge Area, Weight, and Centroid Behind a Retaining Wall and for Each Course

Eng_ReyD_497 — Sun, 08 Feb 2026 07:41:20 GMT

This is an extension of a previous post where I worked on a complex task (for me!) to calculate the soil weight and area behind a wall.

referenced post and solution are located in

Algorithm-to-Calculate-Soil-Wedge-Area-Weight-and-Centroid

The post was brilliantly solved by @Werner_E . At that time, the wall had a simplified geometry with just one course. Now, I need to apply similar logic to multiple courses, which requires repeating the process for each course.

I would appreciate any assistance on how to adapt this logic to handle multiple courses, potentially up to 9 courses.

Re: Calculating Soil Wedge Area, Weight, and Centroid Behind a Retaining Wall and for Each Course

Werner_E — Mon, 09 Feb 2026 01:56:38 GMT

For a single block as in the previous thread the result were nine values (Area, Weight, CGx,CGy, xb, WS1, WS2, WS3, Pw) for each angle beta:

So each block would add another of these nine values.

If there would be, say three blocks as set up in your sheet, what should the desired output be?

Three tables like the one shown above?
A table with 28 columns?
28 single columns for each quantity as we had it highlighted in red in the previous sheet?

BTW, there was an error in my "calculate" function which only affected angle beta=90°.

The third element in the row vector should simply be deleted:

Also the last line in "Polygon" should be changed. This affected only angles smaller than 34°.

Re: Calculating Soil Wedge Area, Weight, and Centroid Behind a Retaining Wall and for Each Course

Werner_E — Mon, 09 Feb 2026 05:40:20 GMT

OK, here is the solution as demanded repeated for each course.

The results are provided in two ways, either as 2-dim. matrices or as nested vectors. So you have a choice.

I first created a solution using the same methods as in the previous sheet.

Then I added an alternate version which uses a linear interpolation function of the soil data, similar to my approach half a year ago.

You can delete the "Intersect" function and also the "start" function if you want to use this alternate approach.

So again you have two options to chose from 😉

For clarity I have removed all parts of the sheet (apart from your drawing at the top) which is not used in the calculations.

You may additionally remove all disabled regions which are highlighted in orange if you chose to use the alternate approach with the interpolated soil function.

See attached sheet

Re: Calculating Soil Wedge Area, Weight, and Centroid Behind a Retaining Wall and for Each Course

Eng_ReyD_497 — Tue, 10 Feb 2026 13:46:12 GMT

Thanks @Werner_E
I am going through the solution, I appreciate it. TO answer this one, my selection would be:

Three tables like the one shown above.

I think this is neater, Table1, Table2, Table3, etc, if naming would matter

Now I will review the other response

Re: Calculating Soil Wedge Area, Weight, and Centroid Behind a Retaining Wall and for Each Course

Eng_ReyD_497 — Tue, 10 Feb 2026 14:38:34 GMT

@Werner_E, thanks for jumping on this, great help as usual.

Further to my previous response, and with reference to the solution you provided, the first issue I noticed before proceeding further is the following:

The graph appears to show more blocks than are present in my model, I have only three blocks, but the plot shows five.

As you mentioned, part of the calculations were removed for clarity, so I assume this was not intended to be the complete solution.

That said, I expect the final output to be similar to the previous post, including a summary below the plot for each block, consistent with the example shown below.

…and also incorporating the surcharge effects for each block, as in the previous post for a single block, and calculating the governing (critical) values, as shown in the following two screenshots.

Hope this is clear. I very much appreciate your help on this! Thanks a lot

Re: Calculating Soil Wedge Area, Weight, and Centroid Behind a Retaining Wall and for Each Course

Werner_E — Tue, 10 Feb 2026 16:01:39 GMT

The graph appears to show more blocks than are present in my model, I have only three blocks, but the plot shows five.

Correct! I was playing around testing the plot to see if it really would accommodate for as many blocks as provided.

Therefore I wrote in the file

Delete the three assignments shown above and you should get the graphics for your original three blocks.

As you mentioned, part of the calculations were removed for clarity, so I assume this was not intended to be the complete solution.

I removed most of the parts in the sheet because they I considered the calcs not necessary for what you demanded - repeating the previous calculation for each block. And I modified my functions or wrote them from anew to be able to do so and then called them in a loop to get the desired outputs.

So actually the sheet was meant to be my final solution to your question so far. 😉

It should be fairly easy for you to find the maximum in each of the three Pw vector and do whatever calculations you need to do, isn't it.

After all the main part was to find the polygons, calculate their area and CG apply the surloads and calculate these values for each angle beta.

So if you need more than whats provided in the attached shee I would suggest that you give the missing calculations a try yourself and if you experience problems ask again and post your sheet.

Here is how to calculate the maximum Pw and the corresponding angles and xb distances. I am using the second provided data structure of the results (vector of vectors) but you could use the first one (multiple column matrix) as well if you simply replace the vector index for a column selector.

…and also incorporating the surcharge effects for each block, as in the previous post for a single block,

??? I guess the surcharge effect actually ARE considered, aren't they?