Chapter 2: Review of Restrained Cracking in Liquid Retaining Structure Design
2.3 Review of Design Codes
2.3.2 BS cracking model
The old British design code of practice for the design and construction of liquid retaining structures was BS 8007, which covered particularly tanks, reservoirs and other vessels that either contained or excluded an aqueous liquid (except for the case of aggressive liquids). Liquid retaining structures designed to BS 8007 were done so together with relevant parts of BS 8110-1 and BS 8110-2.
2.3.2.1 Permissible Crack Widths
A limit has been imposed on the maximum design crack width (based on the allowable permeability for the concrete) for liquid retaining structures depending on the exposure conditions that are to be endured by the structure. Under the BS 8007 code, it has been recommended that the maximum design surface crack width be limited to 0.2 mm for severe or very severe exposure conditions. However, where aesthetic appearance is a matter of concern, a limiting crack width of 0.1 mm was recommended.
2.3.2.2 Minimum Area of Steel
BS 8007 states that after the first crack has formed, the formation of cracks thereafter will be influenced by the provision of reinforcing in the concrete. The steel reinforcement controls the distribution of cracks by increasing the number of cracks that form whilst limiting their width to within the limiting crack width. This occurs where the reinforcement across the initial crack does not yield.
Where the tensile force experienced by the concrete is beyond the maximum tensile force capacity of the concrete (Acfct), cracking will occur. The steel reinforcement provided must be sufficient enough that the resistant tension force of the steel (Asfy) is at least equal to the maximum tensile force capacity of the concrete (Asfy ≥ Acfct ). For the steel reinforcements to effectively reduce the crack widths to within the limiting value, the minimum amount of steel reinforcement in the concrete needs to be as set out by BS 8007:
As = Ac X ρcrit, (2.5)
where,
ρcrit = fct
fy (the ratio between the direct tensile strength of the concrete taken at 3 days and the characteristic strength of the steel reinforcement).
As is the minimum area of steel
Ac is the area of concrete effective surface zones which follow the recommendations listed in figures A.1 and A.2 of Appendix A of BS 8007:1987.
In figure A.1, BS 8007 suggests that the effective tension zone (effective surface zones) for walls and suspended slabs with thickness ‘h’ less than or equal to 500 mm take up half the section depth. Where the wall and suspended slab thickness is greater than 500 mm, it is assumed that each reinforcement face will control 250 mm of the concrete’s depth. figure A.2, on the other hand, proposes that the effective tension zone of ground floor slabs with thickness
‘h’ under 300 mm will be h/2 on one reinforcement face with no reinforcement required for the bottom face of the section. Values for the ground slab thicknesses between 300 mm and 500 mm will produce an effective tension zone that is half the section thickness for the top reinforcement face and 100 mm was recommended for the bottom reinforcement face. Finally, where the ground slab thickness is found to exceed 500 mm, the surface zone was assumed to be 250 mm for the top reinforcement face with the bottom reinforcement face set at 100 mm.
2.3.2.3 Crack Spacing
A comprehensive discussion of the BS 8007 crack spacing formula is given by Bhatt, Thomas, McGinley and Choo (2006), a summary of which is presented below:
Slipping between the reinforcement and the concrete begins after the first crack forms. More cracks will then start occurring where the bond stress (fb) between steel and concrete is greater than the concrete tensile strength (fct) as such,
fbsƩu ≥ fctAc.
In this inequality‘s’ refers to the development length of bond stress and Ʃu is the total perimeter of bars at the section. Considering the ratio of the sum of the perimeter of reinforcement bars to area of reinforcement,
∑u/As=πφ/(πφ2/4),
it is understood that generally the same bar diameter is used at a cross section. The ratio of the sum of the steel reinforcement perimeter to steel area then becomes:
∑u/As=4/φ Ultimately the inequality may be rewritten in the form:
s ≥ fct
fb x Φ
4ρ
This describes the minimum crack spacing, with the maximum crack spacing being twice the minimum (Bhatt et al.,2006). Therefore, the maximum spacing to BS 8007 of the cracks formed in the concrete is to be determined by the following equation:
Smax = fct
fb x φ
2ρ , (2.6)
where:
The ratio fct
fb is the relationship between the tensile strength of the concrete and the average bond strength of the steel reinforcement with respect to the concrete.
φ is the bar diameter of the steel reinforcement
And ρ is the ratio of steel based on the effective concrete tension areas defined in figures A.1 and A.2 of appendix A of BS 8007: 1987 (reproduced here as Figure 2.9)
Figure 2.9 Effective Concrete Area (BS 8007:1987)
2.3.2.4 Crack Width Calculation
As per BS 8007 the estimated maximum crack width that can develop in the concrete due to thermal changes is equated to the product of the maximum crack spacing and the restrained strain:
wmax = Smax x ɛ (2.7)
where,
Smax is the maximum spacing of cracks as defined in equation 2.6 of section 2.3.2.3
ɛ is the restrained strain
Here, ɛ, the restrained strain of the concrete is assumed to follow the relationship:
ɛ = R αT,c (T1 + T2), (or otherwise ɛ = 0.5αT,c (T1 + T2) ) (2.8) where,
αT,c is the coefficient of thermal expansion of the mature concrete
R is the restraint factor that ranges from 0 to 0.5 (where creep is accounted for)
T1 is the drop in temperature from the hydration peak to the ambient temperature
T2 is the fall in temperature because of season variations
2.3.2.5 Restraint Conditions
The restraint that causes cracking may be either internal or external. Internal restraint is dominant where the concrete member is thick. Various external restraint conditions are given in figure A.3 of annex A in BS 8007, where the corresponding restraint factor R is given. As is evident in Figure 2.10, the restraint factor varies with its location within the member, the member’s proportions, as well as the type of restraint it is subjected to (be it edge or end restraint). This may be illustrated in Figure 2.10 taken from BS 8007:
Figure 2.10: Restraint Factors (Figure A.3 of BS 8007:1987)
Table 2.2 (initially table A.3 of BS 8007:1987) presents the differences in the restraint factors from the fixed edge (e.g. the base for a wall slab) of a restrained member to the opposite free edge (e.g. the top section of a wall slab) of that same restrained member.
Table 2.2: Restraint Factors at Centreline of Slab (Table A.3 of BS 8007:1987) Ratio L/H Design Centreline Horizontal Restraint Factors
Base of Panel Top of Panel
1 0.5 0
2 0.5 0
3 0.5 0.05
4 0.5 0.3
>8 0.5 0.5
H is the height or width to the free edge
L is the distance between full contraction joints
All values of the restraint factor, except where the restraint is zero at the top panel, may be less where L < 4.8 m
R = 0.5 is the restraint factor for a ground slab at mid-length cast onto smooth blinding concrete.
This restraint applies for the seasonal change in temperature T2, where the slab length is 30m or more. In accordance with BS 8007, the restraint factor R = 0.5 is assumed to vary uniformly from 0.5 to 0 at the ends of the slab.
Some restraint factors based on typical values of restraints that have been recorded for various pour configurations found in industry have been included in table 3.3 of BS 8110-2:1985, reproduced here as Table 2.3:
Table 2.3: Restraint Factors (Table 3.3 of BS 8110-2:1985)
Pour Configuration Restraint Factor
Thin wall cast on to massive concrete base 0.6 to 0.8 at base 0.1 to 0.2 at top Massive pour cast into blinding 0.1 to 0.2 Massive pour cast on to existing mass
concrete
0.3 to 0.4 at base 0.1 to 0.2 at top
Suspended slabs 0.2 to 0.4
Infill bays, i.e. rigid restraint 0.8 to 1