Cracking of Plain Concrete 1

[yakpol]

I need to calculate crack width in unreinforced concrete section (tunnel lining) subjected to flexure and compression. It's pretty simple to find a tensile concrete strain under given loads, but how to determine the spacing between the cracks? If any design codes cover this subject?

Greatly appreciate your help

 

[Lion06]

I don't think you are allowed to have flexural cracking in plain concrete. If that happens then you reduce your S value and the crack propogates a little further up the section, then your S value is reduced further and the crack moves up even more.

 

[yakpol]

The section is under combined compression and flexure, so at moderate flexure the crack will not propagate too far.

 

[BarryEng]

Have a look at the British Water Retaining Code (BS 8007) with some info on crack sizes & spacing.
Most of this info came from Prof Barry Hughes in the UK (Uni of Birmingham). In his book (Limit State Theory for Reinforced Concrete Design) he has developed formulas (used in BS 8007) for crack size & spacing.

The Australian (water retaining) code uses a DTS (deemed to satisfy clause) & limit cracking by the use of a minimum of reinforcement (0.48% for N12, 0.64% for N16 etc), & a maximum stress (N12 - 150MPa, N16 - 140 MPa, etc). That stress is for direct tensile. Bending stress allowable (remember the code is working stress, not ultimate, because the limit of cracking is a serviceability limit state, not an ultimate limit state) has a factor of 1.25, & short term loading has another factor of 1.25 for stress.

The problem with unreinforced concrete, is that you can never be sure as to whether you will have a 5 mm crack every 10 m, or a 0.5 mm crack every 1 m (it depends on the degree, & distribution, of restraint). Once the concrete cracks, the crack will tend to become wider rather than develop another crack (depending on restraint). In your case, the compression will probably do the same thing as reinforcement (to a certain extent) & tend to distribute the cracking.

Best of luck & if you find the info, let us all in on it.

 

[flamby]

Tunnel linings are usually designed as thick cylinders under external pressure and the thickness is so chosen as to control the buckling. Stresses are seldom any problem. As far as cracking is concerned, the lining is allowed to crack. It will anyway crack when subjected to internal pressure, if it is a water tunnel, as plain concrete will not take up any tension.

Ciao.

 

[BarryEng]

I agree that you should not rely on tensile stresses in tunnel linings, tho tensile stresses are used for conc tank design (as in PCA circ conc tanks). I suppose that it depends on the level of rock bolting & the development of the circular compression zone (in the rock) around the tunnel & the pressure inside the tunnel.

When the BS 8007 code came out, I arranged to test concrete to determine the 3 day tensile strengths (basis of the UK code - 1.15MPa). The results were 0.38 sqrt(f'c) (an average of 2.3 MPa). The Oz code for concrete has a value of 0.40 sqrt (f'c) for the 28 day tensile, but this was achieved in only 3 days with our local cements. So be careful if you are going to rely on code values.

 

[yakpol]

Thank you everyone for valuable help!