Thoughts on subgrade modulus determination needed

[PE_JRM]

I own a small cabin North of Atlanta, GA that is built on a 4" unreinforced slab. Structurally the slab details aren't good but it has survived almost 60 years with no cracking. There is no gravel below the slab and the slab doesn't have thickened edges to spread the edge load. The slab is obviously a DIY and certain areas are worse (spalling) than others. I've measured the thickness in a bunch of places and its 4" everywhere I've checked.

I am renovating the cabin and will increase the floor loads substaintially by moving walls, etc. I want to get a better estimate of the subgrade modulus, K. My objective is to determine that the slab is OK with the higher loads. I need a K value to use any of the slab design resources I have available. To get started I've been using k=63 pci which Terzaghi recommended in a paper I found for a stiff clay if you have no other data. Georgia red clay in the piedmont is known for being pretty sturdy stuff so I feel 63 pci is probably very conservative. I am in an area zoned agricultural so I'm not subject to the county building code. However the county code PRESCRIBES 1500 psf as an allowable bearing strength if that provides any frame of reference. The Georgia Department of Transportation (GDOT) Pavement Design Manual reccommends a value of k=130 pci (appendix B) for the county where the cabin is located.

I'm an retired structural engineer (PE) and have very limited background in soils/foundations. I'm basing my assessment of the soil on my experience trying to manually dig post holes in it and the crude data I've collected. The soil is extremely stiff ... A post hole digging bar is required to go to any depth below the surface. Anyhow, lacking that Terzaghi paper I would probably use k=100 pci or a little higher. What I'm asking is how would you assign a value based on rules of thumb, experience or simple tests that I can do? I'm OK with a quick and dirty solution. The project is not big enough to justify a geotech report and the consequences of being off aren't that great.

The required slab thickness isn't too sensitive with respect to the subgrade modulus but it does make a difference. I'm using Army TM 5-809-1/AFM 88-3, Chap. 15 for my slab checks. The technical manual is a pretty conservative approach but its the free resource I have that doesn't require expensive software. If the slab cracks its probably not a huge deal but I would prefer that it doesn't because it won't neccessarily behave well after cracking since it has zero reinforcement, including temperature steel and there is no compacted gravel base.

 

[human909]

Based on your description, with a 4" slab with a "sturdy" clay underneath you should be totally fine. Shifting the loads around doesn't sound like it would be a huge worry. If there clay was problematically reactive then the effects would likely already be evident. Below is a reasonable guide on bearing strength.

Very Soft - Exudes between fingers when squeezed. - <20 kN/m2
Soft - Moulded by light finger pressure. - 20-40 kN/m2
Firm - Moulded by strong finger pressure. - 40-75 kN/m2
Stiff - Cannot be moulded - indented by thumb. 75-150 kN/m2
Very Stiff - Indented by thumb nail (‘hard’>300 kN/m2) - >150 kN/m2

https://files.engineering.com/getfi...dd7b27e16c&file=GF-Soil-Description-Chart.pdf

You can convert to subgrade modulus by the various rule of thumb formulas available. Or from other sources such as this.


Of course all of this is always a game of cross your fingers and hope. But if the slab is good after 60 years and the soil is good then you have a damn good starting point. Not to mention it is a cabin, not a 3 storey building.

 

[PE_JRM]

Thanks human909. Your reasonable guide is helpful. The concerning issue is a little more than shifting loads around, though.

I'm completely changing the load paths. Right now the foundation is a slab on grade and the floor loads go straight to the ground (the nice thing about a slab). The slab is right at grade so it gets very damp around the edges when it rains hard. I want to elevate the floor a few feet with pony walls. The distributed floor load will become line loads around the edges of the slab. I'm not allowed to change the grade (explained below). The slab will become the floor of a crawl space.

I was calculating the loads (DL+LL only) last night and they vary from 300 to 400 plf. I'm using a spreadsheet I found called GRDSLAB which is based on the Army technical manual I mentioned in my original post. It is an ASD approach rather than ultimate loads.

Regarding code, I'm currently not required to meet it (zoned agricultural) but in the course of the renovation there is a good chance the property will get rezoned. The property (land) is leased from the Federal government and there is an ongoing program for it to be sold to the leasees. The Feds are adamant about not touching the grade or doing any digging. My approach has been to meet code in anything new that I do. That means designing for loads the original (marginal) structure was never intended to carry.

The line loads I'm estimating around the perimeter are right at the slab allowable according to GRDSLAB. When I started down the path of considering possibilities (preliminary design) I was satisfied with estimating the subgrade modulus. I'm trying to sharpen my pencil to better nail down the number. In the end it will still be an estimate (when isn't it?). But it will hopefully be a better more accurate estimate.

 

[fel3]

PE_JRM…

In addition to Army TM 5-809-12, you may also want to look at ACI 360R, "Guide to Design of Slabs-on-Ground", and the Portland Cement Assocation's, "Slab Thickness Design for Industrial Concrete Floors on Grade". Their methods are not identical, so comparing the three documents can be useful. All of my own slab-on-grade designs in the past 20+ years have been for low-speed industrial traffic and parking slabs to accommodate heavy trucks and construction equipment, not buildings. I mostly follow ACI 360R, but I also pay attention to the wisdom contained in the ARMY TM and the PCA document. For your use, I have attached ACI 360R and the PCA document below. I have also included a document that Dik of these forums posted several years ago that might also prove useful.

Fred

============
"Is it the only lesson of history that mankind is unteachable?"
--Winston S. Churchill

 

[PE_JRM]

fel3, thanks for the links. I am aware of both documents and I've already taken a look at them before I posted the question. I'll look at them again but as I recall neither document really fit my situation well. The problem with those documents is that my 4" slab and light loads(compared to typical industrial loads) are always off the bottom of the nomographs. I could be wrong but I think that standard practice is that 5" thick is the minimum for an unreinforced slab on grade.

 

[fel3]

PE_JRM…

You are correct that the charts in the PCA document only go down to 5". It's not my primary reference and I hadn't noticed that before. Also, all of my traffic slab designs have resulted in a section thickness of at least 6".

ACI 360R, on the other hand, is equation-based and should apply to 4" slabs as well. Also, ACI 360R has several charts that go down to 4" (e.g., Figures 6-6, A1.2, A2.3, A2.4, A3.1, and A3.2). I prefer equation-based design guides because they are more amenable to setting up in Mathcad or Excel. I have several Mathcad worksheets that still require inputting data from nomographs, but as I have time I am reverse-engineering the nomographs to develop equations that I can use in Mathcad.

I hope this helps.

============
"Is it the only lesson of history that mankind is unteachable?"
--Winston S. Churchill

 

[PE_JRM]

Thanks again fel3 for your willingness to help. All of the examples you mentioned in ACI 360R are for solving for post or tire loads ... essentially point loads or a grid of point loads. My load cases are line loads (300 to 400 plf) due to walls on the edge of the slab and a couple walls in the interior area. Of particular concern to me are the corners and where interior walls intersect the exterior walls. I don't see a way to use ACI 360 to check a line load or line load near an edge.

I believe the spreadsheet I mentioned, GRDSLAB, is basically the Army Tech Manual procedure since it gives me about the same answers as hand calcs. It covers most of what I need to check. Using it I can determine that a 4" 3000 psi slab on a k=100 pci subgrade is right at the allowable limit (ASD approach) for my wall line loads at the exterior walls and OK with some margin on the interior walls. I've made an educated guess on the concrete strength and the K value. I'm not comfortable starting the renovation until I can better nail down the concrete strength and K value.

Unfortunately the Army TM doesn't cover corner wall intersections or wall T-intersections. I'm still thinking about how to handle that.

I'll explain what I'm doing with the foundation a little more. I'm lifting the cabin about 2.5 feet and supporting it on a perimeter knee wall. The knee wall will be constructed of PT wood to minimize the new load and will be supported by the slab. The slab will become the floor of the crawl space and a conventionally framed new wood floor will be constructed above the crawl space. Interior load bearing walls will be supported in the same fashion as the perimeter wall. This plan results in a grid of line loads on the old slab.

 

[fel3]

ACI 360R, Chapter 5, Section 5.5 talks about line and strip loads, but provides no math, then refers to Chapter 7, Section 7.2 (Case 4 might apply to your situation). Chapter 7 also references the Appendices, which include examples using the PCA and Army TM methods, but I haven't looked at these in detail. I'm not sure that converting your line loads to an adjoining series of fake wheel loads, then applying superposition, would work because it might invalidate the empirical critical tension equations.

Unfortunately, it appears that none of these resources really work for your situation as I now understand it. What you are doing is beyond my experience, but now you've got me hooked.

I looked in Roark's and didn't find anything close. It covers beams on elastic foundations and sort of covers disks on elastic foundations. An FEA program would probably work (I used an early version of IES VisualFoundation about a dozen years ago and I think it would have handled your situation).

I just found "Design of Slab-on-Ground Foundations" by the Wire Reinforcement Institute (https://wirereinforcementinstitute....9816/1918/8151/TF_700-R-07-Slab_on_Ground.pdf). It looks like it covers wall loadings. I can't promise that a document from the Wire Reinforcement Institute will have anything useful with regards to an unreinforced slab, but it might be worth a look.

I also did a Google search for [[design] [analysis] of unreinforced slab foundation for wall loads] and [[design] [analysis] of unreinforced residential slab foundation] and came up with a few interesting hits.
-- Here is what the City of Los Angeles, CA, has to say about situations like yours: https://www.ladbs.org/docs/default-...on-grads-as-foundations.pdf?sfvrsn=94f8f753_6
-- From pdhstar, SE-006 Design of Residential Foundation: https://pdhstar.com/wp-content/uploads/2018/10/SE-006-Design-of-Residential-Foundations-FINAL.pdf
-- From PDHonline, Course S198 Residential Foundation Design Options and Concepts: https://pdhonline.com/courses/s198/s198content.pdf

I hope something here will help. Good luck.

 

[PE_JRM]

fel3, thanks again for your suggestions. I have already found and looked at (and studied) most of the references you listed but there are a couple of new ones in there that I'll take a look at. The overarching problem with all of them is that they cover standard practice and good details. Unfortunately I don't have either of those. Here's what I'm thinking at the moment regarding how to deal with my situation:

a) Regarding the sub-base modulus K: I went to the site yesterday a dug up several samples for comparison. They were all about the same. When held in my hand the samples are stiff and crumbly so the moisture content is probably low and thus the K value is probably much higher than I've been using. Today I took a sample that I can weigh and dry out. Then I can calculate an approximate moisture content so I can at least use a reasonable K value from the charts I've found rather than using the lowest value for a clay.

b) Regarding the concrete strength: I am considering buying a concrete rebound hammer tester to hopefully nail down the f'c I'm dealing with. I just assumed 3000 psi based on a review of what was typical in this area during the mid 1960's. These testers aren't that expensive and hopefully it will give be a good idea of what I've got Honestly, I doubt the concrete is better than 3500 psi but who knows?

c) Regarding my end plan: Ultimately I would like to show the existing slab to be adequate without doing anything to it. Right now I'm showing it OK (barely) but I haven't checked the wall intersections and corners (not sure how I'll do this). I also haven't finalized some of the roof dead loads and they are likely to go up a little. The slab upgrade I'm considering is to use the Army Tech Manual approach and to thicken the slab ON TOP of (instead of beneath) the existing slab using the Army Technical manual reccomendations for the thickened dimensions. This would probably end up being a 4" x 12" thickened curb or "grade beam" on top of the existing slab beneath the knee walls. I would provide enough steel rebar "pins" so that the new 4" layer would act along with the existing 4" slab to behave like an 8" deep grade beam (replace the concrete shear capacity between the layers with rebar pins). I don't want to rely on bonding rather than pins because I have no confidence it will be done correctly. Its a lot of pins and a lot of effort to place those "grade beams" so it would be great if I could just show what I've got to be good.

d) Regarding your suggestion for FEM: I did an FEM model of a slab on grade about a month ago using winkler springs to get some idea of how the slab reacts to the loads. I used the free version of LISA 8.0 which isn't bad for a freebie. However, the free program limitations are somewhat limiting (haha). I only trust my limited model enough to confirm that the slab does about what I expected it to do....corners and wall intersections are hot spots. I wasn't able to correlate the shear and moment results with hand calcs from the Tech manual so I decided to leave well enough alone and stick with the Army Tech Manual.