Performance based design

Table 2.10 - Proposed values for design working lives from ENV 1990.

Design life

category Indicative design

life (years) Examples

1 10 Temporary structures

2 10 to 25 Replaceable structural parts (e.g. gantry girders, bearings) 3 15 to 30 Agricultural and similar structures 4 50 Building structures and other common structures 5 100 Monumental building structures, bridges, and other

civil engineering structures

from the undesired or adverse states in situations, acceptable to the owner, which a structure may be subjected to during its lifetime.”

The limit state that have been defined in the structural codes are:

• Serviceability limit state (SLS), defined as the limit between the state where the performance of the structure is acceptable and the state where the structure is no longer serviceable. Normally associated with economical consequences. Example of SLS are the onset of corrosion, crack widths, spalling, vibrations, aesthetics, etc.

• Ultimate limit state (ULS), defined as the limit between the state where the structure is no longer serviceable and the state where the structure has collapsed, for example, due to excessive material degradation. Example of ULS are collapse, buckling, and loss of instability of the structure.

The EN 1990 defines a number of limit states as “beyond which the structure no longer fulfils the relevant design criteria”. These limit states define the “failure criteria” dealt with in the design. The “failure criteria” for ULS is linked to structural resistance, while the end of SLS might be characterized by a “Design Service Life” (number of years). The failure criteria for ULS are fairly well defined in the Eurocodes. The failure criteria for the SLS of a concrete structure should be quantified in EN 1992 (basis of design – material specific). Such SLS criteria are however only described in a qualitative way not suited as a direct basis for probabilistic calculations.

The fundamental requirement for a structure is that during the intended service life the probability to exceed specified limit states is sufficiently small (Beeby 1993). Many times ULS and SLS are coupled, e.g. if corrosion of reinforcement is initiated, where first an aesthetic problem occurs, with rust stains on the surface of the structure (SLS), then cracking and spalling due to the formation of corrosion products (SLS) and finally collapse of the structure due to reduction of the cross-section area of the reinforcement (ULS).

Definition of limit states of degradation for corrosion

A number of limit states have been proposed to define critical points in the deterioration of a structure (Cairns 2003). Those proposed include initiation of corrosion, initiation of longitudinal cracking, a limiting longitudinal crack width, loss of steel section to a defined level, and loss of structural integrity.

• Depassivation of reinforcement - The service life is limited to the initiation period, which means the time for the aggressive substance to reach the reinforcement and induce

depassivation. The initiation phase ends when the chloride concentration at the reinforcement reaches a critical threshold value or when the carbonation front reaches the reinforcement. Depassivation does not necessarily represent an undesirable state.

However, this event must have occurred for corrosion to begin.

• Cracking of concrete cover - It is evident that initiation of corrosion, although representing a crucial change of condition for durability, is of no immediate consequence for structural capacity, and constitutes a limit state of durability only. The second event is cracking of the concrete cover due to the expansive forces generated by the corrosion products. In this case the service life includes a certain propagation period of corrosion activity during which the cross section area of the reinforcement is progressively reduced. The crack width depends on the amount of corrosion, the cover/diameter ratio, the concrete quality (tensile strength) and the position of the bar. It is typically reported that reductions in reinforcement radius of between 0.01 mm and 0.04mm are required to initiate longitudinal cracking. This represents a reduction of less than 2% of cross sectional area for a small diameter reinforcement, and less for larger reinforcement. Clearly, cracking develops well before loss of bar section becomes structurally significant. Bond strength at initiation of cracking is generally also reported to be similar to or higher than that of the structure as new. Longitudinal cracking will thus precede significant loss of structural capacity, and is also a durability limit state only. According to the DuraCrete project (1998), a crack width of ≈ 0.3 mm is commonly considered to represent a serviceability limit stale for structural design. The limit is selected mainly on aesthetics grounds, as narrower cracks are considered to be not readily noticeable.

• Spalling of concrete cover - Corrosion continuing after cracking may lead to spalling of the concrete cover. Depending on the bar spacing, the concrete cover, and the tensile strength of the concrete, spalling may be either in the form of local triangular formed parts of concrete along each corroding bar, or the splitting forces from several corroding bars may interact and spall the cover over larger areas. The loss of reinforcement cross section and to some extent also the loss of concrete section will lead to a reduced load carrying capacity. Spalling of concrete is usually considered an unacceptable condition.

However, spalling does not necessarily lead to collapse of the structure and can, therefore, be considered as a serviceability limit state. On the other hand, spalling of concrete on a public structure such as a highway over bridge is clearly unacceptable. In such a case spalling must be considered as an ultimate limit state. Based on available knowledge spalling is supposed to occur when a crack width of approximately 1.0 mm has been reached. The propagation time is assumed to end at this stage. The limit state of spalling,

defined according to Rodriguez et al. (1996), is the time to growth of longitudinal crack width to 2.0 mm.

• Collapse - An ultimate limit state is reached when a structure or a part collapses. Collapse of the concrete structure will occur if the load carrying capacity of the element is reduced sufficiently due to ongoing corrosion, by further cross sectional loss of the concrete and steel, or loss of bond. A reasonable margin of safety must therefore he maintained against an ultimate limit state being reached. In the context of corrosion damaged concrete, an ultimate limit state could be reached at collapse of a structure or object, of a component, or, through spalling of cover concrete of a surface of a component. A section loss (typically of 10% of reinforcement cross section) has on occasion been considered to represent a limiting condition (Cairns 2003).