Improved Schmidt Method - Simple Simulation of Mass Concrete Curing

[willowman]

Hi all,

I am trying to prepare an excel spreadsheet following the logic defined in 'Improved Schmidt Method for Predicting Temperature Development in Mass Concrete' by Christopher P. Bobko, Vahid Zanjani Zadeh, and Rudolf Seracino (attached).

I am obtaining unexpected results, I wondered if anyone had experience with this method or could spot my obvious error....it is driving me mad!

I am studying an element with width 1.6m. I have site thermocouple data from the curing of this element at 1 hour intervals. Therefore, to allow good comparison of the two data sets I would like the time interval in my Schmidt method to be 1 hour.

I have solved the below for a Δt = 1 hour using h = 0.00387096m^2/hour. My result is x = 0.005m (5mm). I don't really understand the significance of this result...I guess the smaller the value of x, the more computational power required..? The node spacing doesn't seem to impact the results in any other way.

So, at each time step n, (Δt = 1 hour) and for each node, i, (spaced at 0.005m), the method requires me to average the temperature of the two adjacent nodes (call them j and k) from the previous time step (call this n-1) and then add to this the heat generated during the current time step n. The heat generated during the time step n is represented by Qh. In order to account for the ever accelerating rate of heat production in maturing concrete, it is necessary to define an 'equivalent age' for each time step and for each node. This equivalent age value t(e) is a variable within the function for Qh.

. I have determined the values of the variables alpha, beta, mu etc....I have the chemical constituents of the concrete well constrained.

By inspection of the formula for t(e), if the concrete cures above the reference temperature (taken as 293.15K) within a given time step, then t(e) increases in value. Because t(e) is larger, the value for Q(h) in that time-step is increased. This makes sense....hotter concrete will hydrate faster than cooler concrete...which in turn means that heat is generated faster. In order for this to be represented in Q(h) we have to use an equivalent rage rather than the actual age..

What isn't clear is whether the value for t(e) which I input into the function for Q(h) should be the sum of all the t(e) values for the previous time-steps? Or whether it should be the t(e) value calculated within the current time step? If I do sum the equivalent age values (t(e)), the summed value for t(e) increases very quickly and this results in unrealistic values for Qh (something like 200 Kelvin increase in temperature in one step??)..


Not such an easy topic to try and explain in words....hopefully there is someone out there who can assist. I can share my excel sheet calculations if a responder would like to take a look.

Thanks in advance,

willowman

 

[willowman]

Has anybody come across this topic before? I am tearing my hair out....

 

[dik]

It's the first time I've encountered it, but I'm not big into concrete.

See attached starting on page 41...

https://usbr.gov/tsc/techreferences/hydraulics_lab/pubs/EM/EM34.pdf

and

https://ijret.org/volumes/2018v07/i13/IJRET20180713001.pdf

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[SwinnyGG]

it should be the t(e) value calculated within the current time step

.

 

[willowman]

Thanks to dik and SwinnyGG for the reply.

I checked out the pages in

https://usbr.gov/tsc/techreferences/hydraulics_lab...

and that definitely clears up the Δt and Δx relationship. Although, the Δx value does not impact the calculations of heat generation at all....but as I understand, the relationship between Δt and Δx has to be true for the Schmidt method to be valid...is that correct?

I am still having problems obtaining reasonable temperature generation values. There is one thing which continues to jump out at me.

Within 'Improved Schmidt Method for Predicting Temperature Development in Mass Concrete', the following paragraph explains how to convert the heat generation per unit volume into a temperature rise.

Next, the temperature rise generated during the time interval is calculated using the heat generation rate Q(te) provided by Eq. (4) multiplied by the time interval Δt and divided by the heat capacity of the concrete, C. This temperature rise is added to the average temperature of the neighboring nodes from the prior time step, giving the new temperature.

Doing a basic dimensional analysis I have:

Q = heat generation per unit volume = J/m^3·h
Δt = time interval = hr
C = heat capacity of the concrete = J/g·K

Completing the operation as stated in the paper, I get (J/m^3·h) * (hr) * (g·K/J) = g.K/m3

g.K/m3 is a strange unit...and it seems like I cannot use this value as my temperature rise. There must be another operation to obtain temperature rise in Kelvin (K)....which I can add on to the temperature from the previous time-step to work out the new temperature.

Thanks again

 

[CarlB]

You need to use the volumetric heat capacity rather than the specific heat capacity for units to work out.
So just multiply the specific heat capacity by the density of concrete.

https://en.wikipedia.org/wiki/Volumetric_heat_capacity

 

[willowman]

Thanks CarlB...it makes sense to use the volumetric heat capacity, and indeed the units do now make sense. I end up with a value for heat generation in Kelvin.

Unfortunately I am no closer to a useful simulation. The volumetric heat capacity is some 1778790 J/m^3K....clearly I have to divide the rate of heat generation by this value to obtain the heat generation in Kelvins. I am obtaining very small values for heat generation at the start of the simulation(when the concrete temperature is well below the reference temperature)...in the order of magnitude of 10^-3 K.

Because the heat generation is so small, even after 10 hours of curing...the concrete temperature has not risen by even 1 degree Kelvin. I know this is false because I have site data that indicates around 20 degrees temperature gain over 10 hours.

Would anyone be interested to take a look at my spreadsheet? I am convinced that it is a unit problem...

Thanks in advance...

 

[CarlB]

I might take a look at your spreadsheet, if you attach it.

 

[willowman]

Hi CarlB, thanks for the reply.

See attached my excel sheet. Cement properties on sheet 1, node spacing calculation on sheet 2, temperature history on sheet 3 which uses the formulas variables stored in sheet 4.

Let me know when you have had chance to take a look.

Thanks,