Module 14 · Lesson 14.1

Cracking before the tank is filled

Why the critical load case happens in the first three days, and the ratio that decides whether cracking is controlled at all.

Why this matters

Everything so far has designed for a load. A water-retaining structure has a load case that involves no load at all: the concrete heats as it hydrates, cools, tries to contract, and cannot — because it is cast against something older that will not move with it. The crack that results forms within days, before the tank has held anything, and it is usually worse than anything the water will do afterwards.

By the end of this lesson you should be able to

Explain why serviceability governs completely here
Derive the critical steel ratio from what happens at the first crack
Say what changes either side of it
Calculate a restrained thermal strain

What you should already know

Crack width as spacing times strain (Module 6)
Minimum reinforcement (Module 4)
Shrinkage and thermal movement (Module 6)

A different failure

Ask what failure means for a water tank. It is not collapse — a tank wall designed for its hydrostatic pressure has an enormous margin against rupture. It is leakage, and a tank leaks through a crack far too fine to threaten its strength.

So the design is driven entirely by crack width, and the ultimate check is a formality afterwards. That is the same inversion as prestressed concrete, arrived at for a completely different reason.

And the crack that matters is usually not caused by the water.

From first principles

The critical steel ratio

We want to show: To find how much reinforcement is needed before cracking becomes distributed and fine, rather than concentrated in one wide crack.

Picture a bar of concrete with a single reinforcing bar down the middle, gripped at both ends and cooled so it wants to shrink but cannot. Tension builds in the concrete. At some point it reaches the concrete's tensile strength and a crack forms. At that instant the concrete either side of the crack lets go of the tension it was carrying — and every bit of that force lands on the steel crossing the crack. Now there are two possibilities, and they lead to completely different structures. If the steel yields under that sudden force, it stretches without limit. The crack opens wide, the rest of the bar relaxes, and nothing else ever cracks. One crack, very wide. If the steel does not yield, it takes the force elastically, transfers it back into the concrete a little further along through bond, and that concrete cracks too. Then again. Many cracks, each fine. So there is a threshold, and it is simply whether the steel can carry what the concrete lets go of.

Where the strain comes from

Concrete generates heat as the cement hydrates. A 400 mm wall in plywood formwork might rise 30°C above ambient in the first day, then cool over the next few. As it cools it wants to contract — and if it is cast onto a mature base slab, it cannot.

ε = R · α · T₁ · K

T₁ is the temperature rise and subsequent fall. It depends on the cement content, the section thickness and the formwork. It belongs to the concrete specification.
α is the coefficient of thermal expansion, about 12 × 10⁻⁶ per °C.
K is a creep relief factor, about 0.65. Young concrete relaxes a substantial part of the stress as it develops — which is genuinely helpful and is why the cracking is not worse than it is.
R is the restraint factor, and it is the only one a structural designer really controls.

A wall cast onto a mature base is restrained at about R = 0.5 at the joint, falling towards zero at the top. Casting in shorter bays, or leaving a gap and filling it a fortnight later, reduces R directly — which is why bay sizes and pour sequences appear on structural drawings for water-retaining work and nowhere else.

Worked example

Early thermal cracking in a tank wall

Given

Wall 400 mm thick, C30/37, cast onto a mature base slab
40 mm cover, H16 bars at 140 mm centres on each face
Temperature rise and fall T₁ = 30°C; restraint factor R = 0.5
Tensile strength at 3 days f_ct,eff = 1.8 N/mm²
Water 6 m deep against the wall

Find

Whether the cracking is controlled, and whether the width is acceptable.

Assumptions

Full restraint at the base joint
α = 12 × 10⁻⁶ per °C; creep relief K = 0.65
Crack-width limits are nationally determined and require verification

Predict first

A restrained wall has a steel ratio of 0.25%, below the critical 0.36%. A crack-width calculation gives 0.15 mm. What should you conclude?

Practice

A concrete has a tensile strength of 1.6 N/mm² at the age cracking is expected, with grade 500 steel. What is the critical steel ratio, as a percentage?

Practice

A wall is restrained at R = 0.5 with a temperature drop of 35°C. Taking α = 12 × 10⁻⁶ and K = 0.65, what is the restrained strain, in microstrain?

Practice

A 400 mm wall has 40 mm cover and H16 bars. What is the surface zone h_c,eff used for crack spacing, in mm?

Summary

A tank fails by leaking, so crack width governs and strength is a formality
The critical crack usually forms in the first days, before filling
ρ_crit = f_ct,eff/f_yk, and it uses the EARLY-AGE tensile strength
Below it: one wide crack, and the width formula is meaningless
ε = R α T₁ K, and R is what a designer actually controls
Minimum steel uses half the section; crack spacing uses the surface zone

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This is educational material. It uses simplified examples to teach principles, and must not be relied on for real design or safety-critical decisions. Module overview and checkpoint