Impact of having flexible electrical hose buried into the reinforced concrete slab

Given:

• a reinforced concrete two-way slab at about 160 mm (the edges are cantilevered between the concrete walls)

• the electricians buried the flexible electrical hose into the slab (red lines in the image below) and then covered the tubes with mortar (the channel are about 30 mm depth)

• the mortar is a light one (probably supporting about 4 MPa or even less) and it covers the hoses superficially (1 to 3 mm over the top of the tubes)

• no rebars were cut

• the structure is not based on beams (the slab is sustained by precast concrete walls)

How does this affect the structure resistance of the reinforced concrete slab?

Based on your experience / simulations, could you provide an empirical percent regarding the new load capacity based on the initial load capacity?

Edit:

I believe that the load on the slab looks similar to this (where the vertical should look similar to the horizontal, including the red spots):

where red & yellow are for a top bending and blue is for a bottom bending.

P.S.: My purpose is to have the following stack over the slab for the permanent load (240 kg / m2):

• thin leveling screed => 40 kg / m2
• heating floor system based on water and insulated panels => 20 kg / m2
• sand-cement screed ~5 cm over the pipes (=> ~6.5 cm) => 145 kg / m2
• adhesive + ceramic tiles => 35 kg / m2

• Welcome to Engineering! You just made an edit saying "the edges are cantilevered between the concrete walls". What does that mean? Are the four edges connected to either walls or beams (the usual definition of a two-way slab)? Or are some of the edges unsupported? Or did you just mean that other than the walls around the edges, there are no beams going across the slab to support it? – Wasabi Jul 20 '19 at 19:24
• I mean that the floor is connected in all four edges to the walls, but it's not just put on the top of some walls. It has walls under and over it. – Elrond_EGLDer Jul 20 '19 at 20:38

You haven't specified any material parameters, so for calculation purposes, I am going to assume a reinforcement yield strength of 500MPa and a cylinder compression strength for both concrete and mortar of 25MPa. As I am basically just guessing these values, you will have to adjust the conclusion accordingly, if I haven't been so lucky as to guess correctly.

In bending failure, when the reinforcement yields and all concrete in tension cracks, the compression zone in concrete will have a height of approximately $$\frac{\frac{\frac{\pi}{4}\left(4mm\right)^2}{100mm}\cdot500MPa}{0.8\cdot25MPa}=3mm$$. (The factor of 0.8 is a correction factor for the shape of the stress-strain curve of concrete.) For a more correct value, this should be corrected for the safety factors, which will increase the compression zone a bit, but it will not matter much for the conclusion. Assuming we have a cover of at least, say, 10mm mortar on top of the hoses, there will be plenty of mortar above the hoses to transfer the compression, and the hoses themselves will not matter, as that part of the concrete would be fully cracked anyway and would not transfer any forces.

In shear failure, such a lightly reinforced slab will be even less sensitive to a few "missing" areas of concrete, as the hoses only weaken the slab locally. The actual calculation is rather more complex, but with a 4mm mesh the slab is unlikely to fail in shear before it fails in bending, so I am going to leave it as an "exercise for the reader".

So most likely, it will not have any significant effect on the structural capacity.

One potential issue is if the mortar, they used, is not equal strength to the regular concrete. This should not need to be a problems as mortars for these sort of usage scenarios are often made using ready-made mixes with a pretty high compression strength, but obviously I have no way of knowing if they chose the proper product here. And the mortar would obviously have to be appropriate for the environment in question.

• Unfortunately the schema is not so accurate. The number of hoses varies between 1 and 3 per groove and the hose diameter is just a little less than the depth of the groove. So the mortar usually covers the top of the hose only by 1-3 mm. Regarding the compression resistance, the mortar seems to be significantly weaker. The producer don't specify a compression resistance for that type, but other producers specify about 4 N / mm2 while on other kind of mortars they specify about 25 N / mm2. – Elrond_EGLDer Jul 15 '19 at 17:55
• If that is the case, there is most likely a significant reduction of the structural capacity. If the hoses are only barely covered, you would have to calculate the capacity using the height below the hose of 130mm. As the bending capacity is roughly proportional to the square of the thickness, it will be reduced to roughly (130mm/160mm)² = 66%. (It would be more accurate to use the height from the center of the rebars, which would only make the ratio worse.) And one of the grooves crosses through the center of the slab where the bending capacity is most important. – ingenørd Jul 15 '19 at 18:09
• This book: books.google.dk/books?id=w0bSBQAAQBAJ (Reinforced concrete design to Eurocodes) has something on this in section 4.4. That book is just one random example as there are obviously many others. – ingenørd Jul 16 '19 at 5:48
• The height of the compression zone is not an indicator of the strength. As your examples show, you can reduce it by both strengthening and weakening the structure. It is at most an indicator of whether the concrete is lightly or heavily reinforced. – ingenørd Jul 16 '19 at 15:37
• It's worth mentioning this is a two-way slab, so it's supported on all sides. This significantly improves the slab's load redistribution, so if a small segment is lower-strength due to the lower effective height, it will likely manage to redistribute the load to the surrounding thicker slab. This effect is basically impossible to calculate without FE modeling, though, so the conservative position adopted here is understandable. – Wasabi Jul 19 '19 at 2:13

While I agree with basically everything in @ingenørd's answer, I thought it best to add this answer, which is more optimistic overall, but also has some potentially really bad news.

Indeed, the areas which were cut out for the cables will have diminished capacity. I personally don't even think the strength of the mortar used to cover the hole is that relevant, since the lack of rebar to "bind" that mortar to the rest of the structure means the mortar almost certainly wouldn't act monolithically with the rest of the slab.

That being said, the reduced lever arm would likely reduce the beam's strength by around 70%1 (read that footnote: this is the definition of a lazy, back-of-the-envelope calculation). Pretty significant, but likely covered by the safety factor.

Since one should never go "oh, well, that's what the safety factor's for!", we can also remember the effect of load redistribution. These areas have a lower capacity, but they're also far less rigid (around 60% as rigid)2, so they'll need to resist a far lower load than the rest of the slab as well (though this equally means the rest of the slab will need to resist a larger-than-expected load, but that'd be distributed throughout the nearby slab).

Now, the areas that concern me the most by far are the cut-outs along the walls (the areas of the bottom and right edges with the cutouts).

Since this slab is supported by walls, there may be a non-trivial amount of negative bending moment near the supports. Since these cut-outs are transversal to the slab's direction of action (the slab near the bottom wall is mostly working in an up-down direction, this means the entire dimensioning cross-section of the slab has this reduced height.3

Making matters worse, 3 cm is pretty deep into a residential/office-building slab. If the cutout actually just cut right through the negative steel reinforcement, that could very well be catastrophic, since that'd mean the rebar was removed exactly where it's needed the most. And even if they didn't cut through the rebar, they almost certainly reduced its concrete cover, which could lead to long-term harm due to faster oxidation unless effective impermeabilization was performed.4

1 Result obtained in the most back-of-the-envelope way possible: adopting ingenørd's result of 3 mm of compression area and rounding it up to 4 mm, assuming we can discard the entirety of the cut-out (which seems likely), adopting a concrete cover of 20 mm, and $$\phi10$$ rebar, we get an original lever arm of $$160-20-5-1.5 = 133.5\text{ mm}$$, versus a reduced lever arm of $$160-20-5-30-2 = 103\text{ mm}$$, or 77% of the original. And then rounded down because I felt like it.

2 Again, just using the fact that moment of inertia is proportional to the cube of the height, so these areas would be $$\dfrac{130^3}{160^3} = 54\%$$ as stiff. Though the stiffness is likely affected by the fact we're dealing with a two-way slab. Though that fact also improves load redistribution, I believe.

3 Slabs are usually calculated on a "per-meter" basis. In the rest of the slab, this means that a "one meter slab" has a small 9 cm-wide cutout at the top, which doesn't sound too bad. In that bottom-right area, however, the entire "one meter slab" is shorter.

4 Though, honestly, if they didn't cut through the rebar, I'd take that as a very reassuring piece of news. 3 cm would be an absurdly high concrete cover for non-infrastructure projects. So not only would it mean they probably won't cause the building to collapse, but that the designing engineers took all this into consideration (whether by agreement with the electricians or just previous experience) and placed their negative rebar accordingly. In which case it's also reasonable to assume they calculated the entire slab appropriately, taking the reduced cross-section into consideration as well.

• Thanks for answer! It's quite useful. I understand that you and @ingenørd considered a thinner slab in every point. What I don't understand is why the load is proportional with the cube in your case and with the square in ingenørd example. You pointed something interesting at number 3: that some missing centimeters from the slab is better than having that lack of material on the whole surface. But why do you see a problem at the bottom-right area. To my mind the corners are the most safe for this kind of cutting. I'll add an image in the initial post. – Elrond_EGLDer Jul 21 '19 at 8:33
• @ROMANIA_engineer: Your model is for bending in one direction (around the vertical axis, it seems). Assuming the boundary constraints are symmetrical around the slab, the bottom face would also have negative moment, only around the horizontal axis. And due to that transversal cutout, the entire bottom face (well, where there's the cutouts) needs to resist that negative moment with a lower effective height. – Wasabi Jul 21 '19 at 14:28
• You are right. This is the best image I found on the Internet. I should have the red parts also on the vertical direction. I'll try to edit, but I chose it just to emphasize the idea that the corners look very safe for cutting because there is almost no tension or compression. To my mind the questions are: 1. Will the center area resist to compression? 2. Will the area near the center of the walls resist to tension? But this are only my thoughts, please correct if I am wrong ... – Elrond_EGLDer Jul 21 '19 at 16:19
• @ROMANIA_engineer: Ah, I see that I expressed myself poorly. My concern isn't with the bottom-right corner (even though that's what I wrote...). It's with the wide swaths of the bottom and right edges which have those cutouts, especially given that the middle of each of those edges has cutouts, and that region suffers negative bending. – Wasabi Jul 21 '19 at 17:00