Cálculo de las conductividades hidráulicas

Creep and shrinkage are two common time-dependent phenomena in concrete. Creep may be described as the increase in deformation with time due to permanent actions, and shrinkage as a decrease of volume over time as concrete ages. In terms of crack behaviour, long-term

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shrinkage strain decreases the mean concrete tensile strain (or tension stiffening), thus increasing the nett mean strain and crack widths, as shown by Kaklauskas et al (2015) where tensile stresses in concrete induced by shrinkage were found to significantly reduce cracking resistance, thus increasing cracking and crack width.

Crack models were mostly developed considering short-term shrinkage and creep, and

generally do not take long-term effects into account. However, in the design of structures such as LRS, these long-term effects need to be considered. With this in mind, MC 2010,

representing a more recent code development, includes long-term shrinkage in the

determination of mean strain which the previous MC 1990 did not. In addition, the MC 2010 formulation when applied to long-term loading, specifies the use of the effective concrete modulus, thus taking compressive creep into account, as does the EN 1992 formulation. Thus, the effective modular ratio is used in determining stresses and strains. However, EN 1992 does not take long-term shrinkage into account. This also applies to the BS 8007 and the Frosch crack models. Both Gilbert and Nejadi (2004) and Castel and Gilbert (2014) on investigating the influence of time-dependent effects on cracking in reinforced concrete beams in separate tests, established that long-term crack widths were found to increase with time due to creep and shrinkage. Shrinkage was found to be the greater influence. Castel and Gilbert (2014)

determined in their experimental research that MC 2010 gave a reasonable estimate of crack width for both long-term and short-term loading using the measured free shrinkage, εsh.

However, the EN 1992 formulation underpredicted crack widths for the long-term loading case. The free shrinkage strains measured are shown in Figure 2.9.

Figure 2.9: Free shrinkage strain over time (Castel & Gilbert, 2014)

Referring to Figure 2.9, free shrinkage strains initially increase rapidly but this rate of increase slows over the long-term.

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The development of both creep and shrinkage phenomena depends strongly on the ambient humidity and environmental conditions, the dimensions of the element and the composition of the concrete. Creep is also influenced by the maturity of the concrete when the load is first applied, as well as the duration and magnitude of the loading. Creep relieves some of the shrinkage strain and reduces the concrete modulus, and in turn the modular ratio, as is well known. The age-adjusted effective concrete modulus must therefore be used for long-term loading. SANS 10100-1 and EN 1992 use the same equation to calculate the effective concrete modulus, namely: = +  c,28 c,eff E E 1 (2.18)

where Ec,28 is the concrete modulus at 28 days and  is the creep coefficient. The creep

coefficient depends on the age of the concrete, humidity and exposure conditions. The effective modular ratio is then used in the determination on tension stiffening strain and crack spacing. Research by Alexander et al (1989), (1992a) on concrete durability and the elastic modulus of concrete aggregates, showed that the elastic modulus of concrete was influenced by the type of aggregate. This needs to be considered in concrete mix design and the control of cracking.

An appropriate choice of shrinkage strain model applicable to the design of LRS was

investigated as there are many models available for estimating shrinkage strain. One difficulty in measuring shrinkage and creep, and in deriving appropriate models, is the inter-

dependence between the two mechanisms whereas most models treat the mechanisms separately. Theiner (2014) compared several shrinkage models to experimental work, including those of ACI, EN 1992 and MC 2010. It was found that the ACI model tended to overestimate shrinkage, whilst the MC 2010 model slightly underestimated shrinkage, with EN 1992 producing values closest to the shrinkage measured. Research on creep and shrinkage, including long-term behaviour, has also been performed by South African researchers in developing models and comparisons to other models such as those of SANS 10100, ACI and EN 1992, amongst others, using data from experiments performed using local South African materials. Mucambe (2010) investigated creep and shrinkage models applied to South African concretes. Together with work done on shrinkage models by Gaylard (2011) and Gaylard et al (2013), an extensive database of experimental creep and shrinkage data has been created. The SANS 10100 model was found to predict long-term (30-year) shrinkage values satisfactorily. The EN 1992 model was found to fit the South African data

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reasonably well, but further research was recommended. It should be noted that the creep coefficient was devised considering compressive creep.

The conclusion that can be drawn regarding the long-term effects of creep and shrinkage, is that they need to be included in crack models. A point to note is that shrinkage strains would be expected to be lower in LRS than for general structures, as all aspects of the construction and concrete mix design is such that shrinkage must be controlled. In addition, for LRS in use and thus full, the interior faces (as the more critical in terms of cracking and leakage) of the structure elements would be consistently exposed to water with a resulting reduction in long- term shrinkage. This should be taken into account when choosing the value of shrinkage strain in evaluating long-term crack widths.