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Jul 23, 2019
09:37 PM

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Jul 23, 2019
09:37 PM

Integrating Strain Function Not Converging

Hey all,

I'm trying to implement Mathcad's integration function to calculate ground settlement using a code-based correlation. Basically, the code presents a graphical figure that I've digitized (see attached PNG) and recast as a function of soil profile and depth. The first issue arises when I attempt to integrate the function that relies on N160, which becomes asymptotic as depth goes to zero. Mathcad returns the error message "The calculation is not converging to a solution...." The second issue is when trying to integrate log(sigma_vf/sigma_vo), since the denominator goes to zero as depth goes to zero.

Any suggestions? I'd prefer to keep things in functional form and simply "CTRL + SHIFT + I" (integrate) to calculate the settlement as a function of depth.

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11 REPLIES 11

Jul 23, 2019
09:41 PM

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Jul 23, 2019
09:41 PM

The attached file is Mathcad Prime 3.0

Jul 24, 2019
10:16 PM

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Jul 24, 2019
10:16 PM

Hi,

The five lines do not line up in the original text file. You need to bring it into EXCEL to sort the columns of data so they line up then export as csv to read into Mathcad to keep the columns lined up. You can see how the data is currently read wrong by plotting the data.

Fix the data then we can talk about the rest of the file.

Cheers

Terry

Jul 24, 2019
10:27 PM

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Jul 25, 2019
04:37 AM

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Jul 25, 2019
04:37 AM

Thanks for this, Terry.

I reviewed my input data file (.txt) and realized a couple errors. I've updated the data file to work w/ my lookup array and to properly filter NaN's as the text file has five (5) x-y traces of varying number of indices for each trace. The updated Mathcad Prime 3.0 file and .txt file are attached w/ some screenshots highlighting my attempt to integrate the C(z) function - still trying to figure that one out.

Jul 25, 2019
07:25 AM

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Jul 25, 2019
07:25 AM

Not sure whats wrong, but here is a possible workaround (redefinition of C)

Jul 25, 2019
07:41 AM

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Jul 25, 2019
07:41 AM

Hi,

You need to redefine the calculation of "n(z)" based on the index of the columns in the data matrix.

Cheers

Terry

Jul 25, 2019
09:17 AM

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Jul 25, 2019
09:17 AM

@terryhendicott wrote:

Hi,

You need to redefine the calculation of "n(z)" based on the index of the columns in the data matrix.

This does not solve the integration problem, but the plots definitely look a bit more reasonable 😉

Jul 25, 2019
09:41 AM

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Jul 25, 2019
09:41 AM

Hi,

The import of the data is still not perfect. Part of the last line (columns 8,9) is missing. Part of the second line (columns 2,3) is composed of data from the third line (column 4,5)

correct import from a csv file is possible

Cheers

Terry

Jul 25, 2019
11:00 AM

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Jul 25, 2019
11:00 AM

Can't duplicate that effect using the last sheet the OP posted.

Using your csv-file instead of the originial txt-file seems to have no effect - the integral problem still exists.

EDIT: I jsut gave it a try and compared. The matrix data created by the OP's last txt-file and the one created by your csv-file are identical (up to 10^-7 precision). The only difference is that you omitted the last line and the last column (which are the result of the text "blank" in the txt-file).

Jul 25, 2019
01:04 PM

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Jul 25, 2019
01:04 PM

It doesn't seem to like something in the data file, it appears. I tried a b-spline and it wouldn't solve.

Pasting in a simple x&y set from Terry's file everything was fine.

OR=ORIGIN

Jul 25, 2019
05:33 PM

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Jul 25, 2019
05:33 PM

From your pic we don't see which data you used and which failed.

As I explained and showed above, the only difference between the OP's data and Terry's is the last row and the last column (NaN's) and of course the empty strings "" vs. NaN's if you read in via READCSV.

Furthermore you may notice that for the integral in question none of the data columns is directly the variable of integration as you seemed to have assumed. Just look at the file of the OP.