Cracking Due to Edge Restraint and Early Thermal Effects in Concrete

Crack width is calculated by multiplying the crack inducing strain by the crack spacing (i.e. the movement over a length equal to the crack spacing). Crack inducing strain ε_cr is calculated based on whether the element is subjected to edge restraint (which can be early or long term thermal effects), end restraint, and flexure/direct tension. In this article, we are going to shown how to calculate the crack width of a structural element subjected to edge restraint and early thermal cracking.

Edge restraint occurs where the young concrete section (say a wall) is cast on a hardened concrete base. This means that restriction is only in one direction, and there is interaction between the old and new concrete in terms of distribution of cracks. Edge restraint is different from end restraint because the crack width is a function of restrained strain rather than the tensile capacity of the concrete.

At the early age of freshly poured concrete (within 3 days), the crack inducing strain due to edge restraint in concrete element is given in equation (3.6) of CIRIA C660 which is shown below.

ε_cr = K[α_cT₁ + ε_ca] R₁ – 0.5 ε_ctu

where;
K = allowance for creep
= 0.65 when R is calculated using CIRIA C660
= 1.0 when R is calculated using BS EN 1992-3.

α_c = coefficient of thermal expansion
T₁ = difference between the peak temperature of concrete during hydration and ambient temperature °C (See Table 1).
ε_ca = autogenous shrinkage strain – value for early age (3 days, see Table 2)
R₁ = restraint factor from Figure L₁ of BS EN 1992-3 for the short-term situation
ε_ctu = tensile strain capacity of the concrete (see Table 3)

Table 1: Typical values of difference between the peak temperature of concrete during hydration and ambient temperature (Narayanan and Goodchild, 2012)

Table 2: Typical Values of Autogenous Shrinkage Strain

Table 3: Values of Tensile Strain Capacity of Concrete (CIRIA C660)

Calculation Example

Calculate the early thermal crack width of concrete wall cast in Nigeria with the following data;

Thickness of wall = 400 mm
Reinforcement provided = H12@150mm c/c on both faces
Concrete cover = 50 mm
Type of restriant = Edge restraint
Concrete grade = C30/37
Type of coarse aggregate = Granite

Solution

Crack width w_k = s_r,max ε_cr

The maximum crack spacing s_r,max = 3.4c + 0.425 (k₁ k₂ϕ/ρ_p,eff)

To see the definition of these terms, see the post below;

Crack width and crack spacing calculation in concrete

c = 50 mm to outer face
k₁ = 0.8
k₂ = 1.0
ϕ = 12 mm
ρ_p,eff  = 754/{1000 × min[400/2; 2.5 × (50 + 12/2)]}
ρ_p,eff  = 754/(1000 × 140) = 0.00538

s_r,max = 3.4 × 50 + 0.425 (0.8 × 1.0 × 12 / 0.00538) = 170 + 758.36 = 928.36 mm

Early age crack-inducing strain, ε_cr = K[α_cT₁ + ε_ca] R – 0.5 ε_ctu

Using CIRIA C660 the following parameters can be determined;

K = 0.65
α_c = 10 × 10^–6 (granite coarse aggregate, see coefficient of thermal expansion of concrete)
T₁ = Using 35 °C (for a 400 mm thick wall cast in Nigeria, assuming Class N cement, 18 mm marine plywood, concrete grade C30/37 and cement content not less than 360 kg/m³, see Table 1)
ε_ca (autogenous shrinkage strain for grade 30/37 concrete at 3 days) = 15 × 10^–6 (see Table 2)
R = Restraint factor R_j =  1/(1 + E_nA_n/E_oA_o)

Where;

E_n and E_o are the elastic modulus of new and old concrete respectively
Assume E_n/E_o = 0.80 (CIRIA C660)
A_n and A_o are the areas of new and old concrete respectively (use A_n/A_o = h_n/2h_o assuming that the wall is cast remote from the edge of slab) = 0.4/2(0.4) = 0.5

R = 1/[1 + (0.8 × 0.5)] = 0.714

ε_ctu = 76 × 10^–6 (for early age thermal cracking, see Table 3)

ε_cr = K[α_cT₁ + ε_ca] R – 0.5 ε_ctu = 0.65 [(10 × 10^–6 × 35) + 15 × 10^–6] 0.714 – 0.5(76 × 10^–6) = 1.3139 × 10^–4

Therefore the early age crack width = w_k = s_r,max ε_cr = 928.36 x 1.3139 × 10^–4 = 0.121 mm

Since this crack width is less than 0.2mm, the early crack width can be considered acceptable for water retaining structures.