I guess I am not sure what you are asking. If you wonder why basecalc has a higher loss than yours, there are two answers:
Basecalc is looking at the entire basement, not merely the slab. 40 percent of its predicted loss happens in the foundation walls above grade, even with all that ICF foam. Most of the rest happens in or near the walls below grade. So by focusing on the slab, you are trying to make the tail wag the dog.
Second, in tests of basecalc's methodology in real basements -- it has been around for 25 years -- the consistent criticism is that it overestimates heat loss. That said, academics accept its 3-D approach as the most realistic model. You can see its acceptance in requirements for frost protected shallow foundations.

Posted By toddm on 08 Apr 2010 09:53 AM
The other 4 MBTU goes nowhere, soil being a relatively poor conductor. Delta T shrinks by the day until the soil in contact with the slab is so close to 70 degrees that it barely matters if you used xps or not. Your formula assumes that lost heat zips into the ether; it doesn't work for what it is effectively a closed system. (more or less, depending on site specifics.)
This is not a lonely view held north of the border. Rescheck ignores underslab insulation as well, except in walkout situations. Even for slabs on grade, you reduce UA by sinking perimeter walls deeper and insulating them better.

Empirical evidence at my own home in MA would indicate otherwise. 

My basement slab is less than a foot from the water table most of the year (under the water table after periods of serious rain- 4 sump pumps keep it from flooding) and it measures in the low to mid 50s year round quite independently of room air temps.  it may not be lost in the ether, but that lost heat is truly gone with the flow.  I may get around to insulating it someday, but there are still higher priorities on the envelope-fix list.

Not all soils behave the same either.  Clays are much more conductive than gravels or sands etc., and it has to be dry to some depth to have a significant insulative value.

You mean anecdotal evidence, Dana, but allow me to disclaim one more time: If your footer excavation fills overnight, your neighbors set hip boots by the cellar door, or your excavator pounded away for three days with a backhoe ram to get to the frost line, xps is your friend. Among the people who know finer subterranean points: your county soil conservation district, your septic designer, your well digger and your soil engineer.

Now can we agree that more information and a proper understanding of physics is better than the opposite?

Posted By toddm on 08 Apr 2010 11:20 AM
You mean anecdotal evidence, Dana, but allow me to disclaim one more time: If your footer excavation fills overnight, your neighbors set hip boots by the cellar door, or your excavator pounded away for three days with a backhoe ram to get to the frost line, xps is your friend. Among the people who know finer subterranean points: your county soil conservation district, your septic designer, your well digger and your soil engineer.

Now can we agree that more information and a proper understanding of physics is better than the opposite?

Yes, we agree that all generalizations are bound to be wrong in the particulars, and that the design decision must be made on actual rather than theoretical or presumed site conditions.  (FWIW, I have a degree in physics, but haven't actively worked in science for coupla decades now.)

But it's still empirical, not anecdotal- I've logged the temperature variations of the slab & basement air over a period of years- do I need to publish the data somewhere to move from anecdotal to empirical in your book?   

I s'pose it's anecdotal to you since it's just an unverified report from "some guy on the internet", but empirical to me 'cuz I've actually measured it. I tend to trust stuff that's measured more more than mere models or anecdotal assertions, even if both the later often offer useful insights.

Your situation is anecdotal evidence on the xps question because, while the facts clearly apply to you, their larger significance can not be determined without a whole lot of additional research. So, unless you can also prove that your logs have relevance to Jerkylips in Wisconsin and BBICF in Saskatchewan, you are tracking an exception that does not disprove the rule. I believe I have noted those exceptions repeatedly.

I am sure that your logs are terrific. I do not consider you "some guy on the internet." I have benefited from your advice, and I am content to read that your slab will wait because you have larger envelope fish to fry. If there aren't subterranean hitches at their sites, shouldn't Jerkylips and BBICF also be lining up fish by size?

Add to my list of local sources the county cooperative extension and geothermal designers. Depending on local crops and practices, both have occasion to study soil heat characteristics -- ahem -- in depth.

In discussions with others about the Passivhaus tools' earth-conductivity and slab heat loss modeling, the consensus has been:

A: It models the problem very well.

and

B: It's cheaper to put in more insulation than it is to do all of the testing & investigation required to discover whether it's actually cost-effective or necessary.

I have no experience with BaseCalc on which to base an opinion, and I'll assume that it models the problem reasonably, but feel obligated to point out that exceptions are not rare when it comes to heat transfer issues in soil, the difference in the result can be significant, and that assuming too much can and will lead the designer astray. A single datapoint does not a trend make, but it's a datapoint far enough away from the rule for me to urge others to their homework, and not assume anything as fact that could actually verified with a bit of ... DIGGING... (in-depth even ! :-) )

Basecalc is easy to use and I recommend running it. It does show a significant (but not huge) change in heat flow when ground water is close to a slab. As I recall, it doesn't allow input of the ground water flow rate.

I definitely agree on a holistic approach to energy use and costs.

Dana and Todd,
I congradulate you two on having a civilized debate concerning a difference of opinion.
And you managed to do it in a way that does not try to drown each other in engineering mathspeak.
I am impressed. I would have been 'pounding the desk' by now.

Todd,
The number you get for basement heat loss makes some sense now. I thought you were breaking out the contribution of the slab alone not the slab + walls.
 When you actually start looking through the primary literature at experimental results measuring heat loss in basements, there are a ½ dozen actual tests that can be found easily. There is the foundation test facility in Minnesota, The Japanese Test house in Sendai Japan, a site in Cardiff Wales, and one at the university of Westminster in England.
There are several hundred papers on theoretical modeling of behavior of heat loss through soil based on soil type, water table depth,, but little actual data. Below I list the 2 studies that I can find that bear directly on the issue of slab insulation, as well as the executive summary of the results:

The first study below was done recently in Finland. They measured the heat loss of a slab on grade comparing one with in floor radiant heat to one with conventional radiators and measuring subslab temperatures both near the walls and center slab.
The conclusion was that the slab accounted for between 13 and 19% of the total energy loss of the house. In BTU terms the house lost up to 20.7 million BTU year through the slab. The slab had 20 cm of eps insulation underneath as well as insulation along the edge (R31) ! The losses near the edge were twice what they were in the center of the slab. . The data here is quite applicable to the common walk out basement. I suspect the center of slab numbers would be similar to a basement slab. So to recap, R30 under the slab, still accounts 19% of the heat loss IF you use in floor radiant 13% that if you use radiators or forced air.

“”INTERNATIONAL JOURNAL OF ENERGY RESEARCH Int. J. Energy Res. 2006; 30:929–938 Published online 27 April 2006 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/er.1190
Heat loss into ground from a slab-on-ground structure in a floor heating system Jukka Rantala1,n,y and Virpi Leivo2 1 Innosteel, Hame University of Applied Sciences, Laajama¨entie 1, 13430 Ha¨meenlinna, Finland 2 Laboratory of Structural Engineering, Tampere University of Technology, P.O. Box 600, 33101 Tampere, Finland
 

The second study was done by researchers at NREL, and at Colorado State University.
This study compared heat loss in slab on grade as well as full basement, with and without 5 cm of XPS. They also look at the effect of ground water level. This is mainly theoretical based on some of their earlier experimental measurement.
Graph 7 is a summary of the findings related to full basements
 If the water table is 3meters the insulated slab looses 2.9 MJ/m vs 12.9 MJ/m for the uninsulated slab .
If the water table is 10m the insulated slab looses 1.1 MJ/m vs 2.1 MJ/m for the uninsulated slab,
5m water table data falls in the middle.
Comparing walls to slab all in units of MJ/m:
3m water table Uninsulated wall vs slab= 7.6 vs 12.9, insulated wall vs insulated slab= 2.0 vs 1.19
10m water table Uninsulated wall vs slab= 6.5 vs 2.1, insulated wall vs insulated slab= 1.8 vs 1.1
So if you have a high water table, the slab is a huge heat loss and 2” of insulation can cut the heat loss by a factor of 4.5.  If you have very dry soil with low water table the slab is a lower heat loss and 2” of insulation can cut the heat loss by a factor of 1.9

1 GJ= 0.93MBTU for conversions 

 For a 10M square basement in Ft Collins Colorado with a high water table, daily average winter heat loss from the slab:No insulation =1.29gJ/day,232 gJ/winter insulated =0.29 gJ/day. 52 gJ/ winter if it is a dry area, No insulation =0.21GJ/day, 38 GJ/winter insulated =0.11 GJ/day. 19.8 GJ/winter.
 
Based on both these studies, I would strongly recommend adding subslab insulation in all well insulated houses in cold climates. If the area is WET or it is slab on grade, insulation makes an even  bigger contribution.

""Ground-Coupled Heat and Moisture Transfer from Buildings Part 2–Application J. Sol. Energy Eng. -- February 2002 -- Volume 124, Issue 1, 17 (5 pages) doi:10.1115/1.1435651 ""

I need to pick a hammer again, and there is nothing to be gained in dueling studies, so let me make two final points: What BaseCalc does, that your studies do not, is look at basement heat loss on an annual basis, including the summer when an uninsulated slab can make amends. (My simulation assumed year-round conditioning of 20C.)
Also, you should set aside the exponents for a moment of reflection. If your heating season energy use was 18 million btu, and Basecalc says you basement heat loss is 13 million btu (admittedly with the rest of the year to run) either you are doing something really great above grade or Basecalc is overstating your loss. And 13Mbtu translates at $12/MCF to $156. I hesitate to speak for Jerkylips, but I don't think he is after perfection.
I think we can agree on the basement priority list anyway: h*** yes for basement walls and thermal breaks to separate the slab from walls and footers. The middle of the slab? It can wait.
It CAN wait you know. Basecalc suggests that XPS is more effective overslab than underslab (at the expence of floating a floor over it.) Putatively, it is also drier. If you want to lose some sleep, read Dow's limited thermal warranty on Blue Board.

Expressing basement heat loss as a percent of whole house heat loss is highly non-applicable to other situations and shouldn't even be discussed. Talk of 232 gJ/winter through a basement slab is off by 10x (math errors are less likely with software). The best use of actual measurements is to validate simulation software - there are too many variables (slab on grade vs basement, depth, exposed basement, etc) to try and apply some particular data to another situation.

Most importantly, IMO, all the figures should be expressed as %IRR - while some might spend $2000 on insulation to save $50/year, I definitely wouldn't.