Cracks on reinforced concrete dams

[ajose]

Hi there,

Let's focus on reinforced concrete dams. Just the intake of an Hidropower dam (a big cantiliver reinforced concrete).
Let's do no think about temperature, shrinkage and other things.
Just focus on stress due external loads (bending mainly)

Usually in reinforced concrete structures when cracks are checked by ACI art. 10.6.4 up to 1995 by:

z=fs(dc*A)^(1/3)
Where
fs service stress on rebar.
dc cover of the rebar.
A area of concrete with the same centroide of the rebar.
z a factor upon the type of element and the crack width

then past 1995 was changed to


s=540/fs - 2.5*cc

Where;
fs service stress on rebar.
cc cover of the rebar.
for width cracks 0.016in

Normal practice lead us to the "Z" formulae and the width is upon the study zone (some are more criticals than others)

My question:

Does somebody has some correlation between both formula and the real crack width?
I'm interested on normal concrete structure or masive concrete structure.

 

[dik]

I would have thought that most reinforced concrete dams were curved and intended to resist by compression and not flexure. Is this correct?

 

[ajose]

Hi dik,

Not really, Concrete arc dams only can be built where are narrow gorges. There is needed strong abutements where to achors the ends.
The statement most reinforced concrete dams were curved like arc, do not apply to a big number of dams.
For example Wanapam, Guri, Keenlyside.
The needs of Hidroelectric power plant could lead to a combination of materials for the construction.
Use of concrete where isgoing to be the powerhouse, and transition dams. Use of earth dams or rock dams with concrete face (waterproof) to finish the closure of the reservoir.
Well this could be long.

But the need of cost control lead to small but stable sections. Have to take care of the intake for turbines (where the water gets in) and the draft tube (where the water goes out). For this reason to parts of the structure the main stresses are bending.

Not talking about the place where the turbine is becuase is avery complex the behavior

 

[flamby]

ajose,
Can you give an idea of the base-width, height and foundation of the structure? It sounds more like a retaining wall to me and I think the guidelines for water retaining structures may be adopted as far as crack width is concerned. Is it a dam or intake? If intake, is it monolithic with the turbine cavity concrete or seperate?The requirements of stability against sliding, overturning and shear stresses generally lead the dam to be so massive that reinforcement is entirely omitted in most of the cases. Moreover the ICOLD guidelines limit the tension in concrete to around 0.5 MPa. I am curious to know how do you propose to avoid sliding if it is so thin.

 

[ajose]

To give an idea the cross section is more or less the following:

20
+--------+
| |
| | 30 <----- why to fill this block
| | with concrete
| |
60 | +--------+
| |
| | 30
| |
| |
+------------------+ x30 (m)
78
>----------> Flow


We just can not work on massive, becuase the cost rise to much and there is not benefit. Shure have to fullfit requirements for stability, pressures, sliding, etc.

Do not forget we are taltking about hidropower plant, we need to have an intake, it is less expensive use the dam like such structure because both have to be built.

We use the formulae that you call for checking, I'm still interestet on correlation with real cracks on this kind of structures or just normal structures.

 

[dik]

ajose:
thanks... was thinking of something a little larger for hydro power.

With the ASCII Art drawing, the face against the water is smooth and can readily accept a PVC expansion joint. The step in the face forces the centroid of the section to the water side to resist overturning better with a savings in material. I'm not sure where the cracking would occur since the visable face is in compression, unless shrinkage is an issue for the length. I wouldn't think that shrinkage would be an issue with the height. Reinforcing on the tension side would be to minimize strains (crack widths).

What is the climate?

 

[ajose]

For the size is not enough to be clasified like a big dam but:
The units in the sketch (meter)
I forgot to tell:
That is a unit, the total work in the example has 12 units (360m) and have to add the spillway (five units 150m), the intermedia dam (30m) the transition dam (two units 60m) and the rock fill and earth fill dam (8000m) for a total lenght of 8600m lenght.
The biggest concrete placement one one shoot is about 200m3. The total concrete is about 1.850.000m3

The surface upstream is not smooth because need to place equipment for the closure, but hard to sketch on ASCII

The average temperature is about 30C.

We use rebar on tension face to conctrol cracks for temperature, shrinkage and bending.

I'm trying to look for the accuracy of the formulae for bending cracks to make some savings, that why i asked for a correlation betwen real cracks and theoretical ones.

 

[flamby]

ajose,
Then it is already a massive structure, if not a Large Dam. I thought you were mentioning flexural cracks in your previous post.

Generally, we do not provide any reinforcement on U/S face for shrinkage cracks. Thermal cracking is most often discounted for the reason that U/S face is submerged in water to most of the height. Don't you have a drainage gallery in the dam body? If yes, you can allow some cracks in the dam and drain the percolaing water through intercepter galleries. This is a very popular practice. But I do not know of any instance where U/S face of a Gravity Dam was reinforced.

 

[ajose]

flame,

You are mixing two subjects.
Shure we have galleries, but the focus of the galleries is take out the underground water pressure, by this way we take care of the stabillity and sliding so monitoring the foundation. We do not use the galleries for the drainage the body of the dam.

I can not said it is not massive concrete but have a different behavior that the one that you are thinking about.

While designing we went to Keenlyside (Canada) to check the behavior of the concept i was talking about (bending). By now i do dot remember U/S dam. In Macagua III (Venezuela) this behavior was checked too.

In the powerhouse zone, more specifically the intake by equipments and hidraulics requirements have to be walls of 4m thickness to allow the water get in. This zone is normally in the base of the dam, so the complete is supported by them. And in the go out of the water (draft tube) the same is happen. So in these zones you have to talk about bending-compresion (don not talk about the place where the turbine is).

We have structures that behaves in the way that you are talking, but i'm concerned about the other structures

By the way, thermal crackin is very important. For example Hoover dam to thermal control was issued with a lot of piping through it, only to cooling down with water (just like a machine). Later on they injected the pipe with concrete. The minimal rebar is for thermal effect.
And for shrinkage have enough importance to place contraction joints every 30 to 60m.

 

[flamby]

ajose,
You have enough of a base width to avoid any kind of tension due to bending. I just threw in your dam to Robot software to have a quick and dirty check and you will be surprised that I saw no tension whatsoever on upstream face. I do not understand that how you are getting a &quot;different behaviour&quot;. The bending stresses are nullified by the self-weight of the concrete.

 

[etompos]

If I'm not mistaken the ACI commentary states that the equations for rebar spacing are intented to limit average crack widths to 0.016-in. Cracks of this size have not been found to cause corrosion problems. To estimate other crack sizes review the references on the crack control provisions and obtain the reference most likely a (journal article). The easiest way to get the article for free, request it via inter-library loan through your local library--this has worked great for me in the past if you don't need the information in a hurry.

 

[letrab]

Hi ajose,

The commentary to the code states that laboratory tests have shown reasonable correlation in one way slabs reinforced with deformed wire fabric. Since you are referring to a cantilevered intake, which is a one way spanning structure, the correlation with the flexural cracks would likely be reasonable. However I doubt the lab tests referred to such massive structures .
In my experience the stucture should be designed for strength and serviceability purposes. With massisve structures the rebar required to control cracking are normally more than that required to resist the actual loads.
You may find it useful to check your structure in accordance with the British code. I have found the correlation between the formulae and reality pretty consistent as long as you ensure the temperature used in the calculations are realistic.
Just a comment, if you are going to restrict the pours to 200m3 how long would it take to complete 1850000m3.

 

[ajose]

Hi letrab,

The information about correlation is what i was looking for, do you have some refrence about it?

You are right about serviciability and stress, but the feseability studies, push to the max economy without compromise the structure, so we are pushed to a reasonable limit.

We do not limit to 200m3 the placement of concrete, we just make thermal studies of the placement and have some correlation with minimun rebars. Do not forget that there is a limit to themperature placement or the volume of concrete (for crack control due thermal effect) it is just a point of view.

Well we are on the way to a new design but the one under construction take mor or less 5 years to complete concrete works, and for 12 units we have 3 in operations and the others erecting.

 

[letrab]

Hi Jose,
Apologies for the inordinate delay, I did not notice your query until today.

The reference quoted is:
&quot;Crack control in One-way Slabs Reinforced with Deformed Wire Fabric&quot; ACI Journal, Proceedings V.66 No. 5 May 1966,pp366-376

 

[rowe]

The way I read the current commentary from ACI 10.6.4 is:

the bar spacing formula was changed because of controversial data that suggested that the danger of corrosion of rebar is not directly related to crack width.

There were no comments stating that the crack width formula (z factor) was not accurate, just that the crack width didn't make as much difference to structural integrity of the rebar. So now the code is trying to limit cracks based upon &quot;a width that is generally acceptable in practice...&quot;

Therefore, I would suggest that if you need to know the crack width, use the z-factor formula (or rather the crack width formula by Gergely-Lutz upon which the z-factor was derived)

the crack width formula w=C(Bh)(fs)(dc*A)^(1/3) where:
w=width of crack (inches)
Bh=h2/h1; h2=dist. from extreme tension fiber to neutral axis and h1=dist. from centroid of tension rebar to neutral axis
fs=ksi
dc=inches
A=sq.in.
C=experimental constant=.000076 sq.in./kip

P.S. Z=w/C(Bh); Bh was assumed to average about 1.2

 

[unclesyd]

There should be some information coming out of China. I understand that the Three Groges Dam has a cracking problem that is not shrikage related.

 

[ajose]

unclesyd,

You are right about that, but for now the information it is not available at internet or at least i did not find it.

Thank to all for the information i will try to get the reference


ajose