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Topic Title: Cable bedding Topic Summary: Effects on rating Created On: 20 September 2017 12:41 PM Status: Read Only 
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20 September 2017 12:41 PM


Hi,
How deep a bedding and blinding layer should be allowed before it's used instead of the native soil for the thermal resistivity? I not managed to find an answer in reference books so I've been conservative on this in the past (i.e. if sand has been used, of any depth, then for calcs assume welldrained sand @ 2.5Km/W). Obviously this depends on the backfill. I've compared results with some IECmethod tools and it seems to support my conservative approach but but I wonder if that's overkill in reality (since moisture retained in native clay would probably stop a few cm of sand drying out so quickly) and I can use smaller conductors / more bedding / less CBS. Which would be nice, but I'd like to have something to point at to back it up. J 



20 September 2017 01:28 PM


if you like to imagine the minimal bedding as a cylindrical sleeve of material around the cable, and the same heat sweats off through both the cable into the bedding, and then outwards from the bedding into the soil.
Now, the surface of the bedding material to soil boundary is larger, than that of the cable jacket to the bedding, in the ratio of the circumferences of the circles. (Imagine 'stripping' that coating as many concentric cylinders , and ironing each one out so you have a pile of rectangles of steadily increasing size..) Once the area ratio of the outer of the bedding to the outer of the cable, is greater than the ratio of the thermal conductivity of the soil to the thermal conductivity of the bedding, adding more bedding rapidly ceases to be beneficial. Once you are outside the region with the bulk of the temperature drop, the use of soil or bedding is less important, because the inner material, near the cable, has by far the greatest gradient of temperature with distance from the wire.  regards Mike 



20 September 2017 02:10 PM


Hi Mike,
Thanks for the reply but I was thinking of it the other way, as in, where native backfill is fine for STR but there's an argument for a less thermally attractive backfill (maybe too many sharps to sort and too sticky to riddle), how much is too much before it needs to be accounted for? J 



20 September 2017 11:26 PM


It the same concept in reverse..
misusing the formulae for insulated pipes borrowed pictures from here here we dont have the air term or the fluid term, as the cable temperature is fixed by the regs. If the cable diameter is say 4cm (2cm radius) and we once more assume our remarkable cylindrical backfill (or more likely some offsquare spade shape that we approximate by a circle of the same mean radius..) then firstly if the bedding is identical thermally to the soil, then as the thermal resistance of each skin at radius r is thickness / 2*pi*r and the temperature drop is proportional to this we are integrating out from temperature T0 at the cable radius, to a point where integral from R0 to " infinity "of 1/r dr is ln(Ro)ln(infinity) initially you may think this does not work as ln (infinity) is not finite. However logarithm is a very slow function. ln 2cmln4cm= 0.6 ln 2cmln5cm = 1.1 ln 2cmln6cm= 1.38 ln 2cmln7cm = 1.6 ln 2cmln8cm= 1.79 ln 2cmln9cm = 1.94 ln 2cmln10cm= 2.08 ln 2cmln15cm = 2.5 ln by 20cm = 2.9 by 50cm 3.9 100cm 4.6 So the temperature drop in the first 1.5cm around the pipe  a total diameter of 5cm is half that of the temp drop out to 10cm, which in turn is more or less equal to the drop in the next 100cm. And by then we dont really care much, as turning 100cm into 10m is half as much temperature drop again, but really by then we would have broken to surface and really are in 'ambient' Now lets say the local ground and the bedding have thermal conductivities in the ratio 2:1, and the bedding is more insulating. Well we double the temp rise in the region of bedding.  regards Mike 



21 September 2017 02:35 PM


Wow thank you.
More coffee required to attack those formulae but the takehome appears to be that for any practical amount of bedding, it's the bedding that will determine the STR (for easy maths) or at the very least needs to be accounted for in a multilayered apporach that you've kindly described. 



21 September 2017 10:40 PM


Sorry, not trying to make it too complex, but your conclusion is right, so for most sensible cases of cable size and trench width, once the bedding is more than a cable diameter or two thick, the temperature rise is substantially the value it would have been if it was solid bedding.
 regards Mike 



23 September 2017 08:50 AM


The theory above is correct  it's basically an internally heated cylinder
The big variable is moisture content  dry sand is significantly more insulating than wet Basically  where any quartz based backfill is used it will be effective in allowing higher cable ratings if it retains moisture where it is at least 3 x cable OD as a surrounding layer If however you have enough cables and enough current then the heating effect dries out the sand and the thermal resistance increases  not good if you are running the cables hard So  depending on where you are in the world it's the assessment of ground water that dominates  and that could be very low moisture in both hot arid areas or very cold permafrost areas There are empirical thodologies for this  but you need a degree of caution and to understand the load profile and attitude to risk Regards OMS  Let the wind blow you, across a big floor. 


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