# Results Analysis

The deferred Crack Mouth Opening Displacements (CMOD) are needed to calculate some creep parameters to analyse the long-term behaviour. As time reference, three specific lapses of time were selected: 14, 30 and 90 days. The parameters worked out to evaluate creep behaviour were the creep coefficients and the Crack Opening Rates (COR).

**4.3.1 Creep Coefficients**

The creep coefficient (ф) is defined as the ratio between the deferred deformation and instantaneous deformation. Deferred deformations were obtained for the selected time lapses to check the evolution of creep coefficients along time. Referring the creep coefficient to the creep stage, the instantaneous deformations occurred during the loading phase of creep tests. In this way, the instantaneous deformation was recorded just when the creep stress level I_{c} was reached (point D in Fig. 5). Therefore, the creep coefficient referred to creep stage at time j (U_{c}) can be calculated by means of Eq. (2):

where CMOD^{j}cd is the deferred crack opening at time j and CMOD_{ci} is the instantaneous crack opening occurred during the loading phase of creep tests (see Fig. 5).

Since the specimens were previously pre-cracked, there was a previous crack opening deformation before the creep test. Therefore, a new creep coefficient referred to the origin of deformations at time j (U_{o}) can be calculated by means of Eq. (3):

where CMOD_{c}^{o}i is the total deformation referred to the origin obtained by means of Eq. (4):

where CMOD_{pr} is the residual crack opening after the pre-cracking test (see Fig. 4) and CMOD_{ci} is the instantaneous deformations occurred during the loading phase of creep tests (see Fig. 5).

Both creep coefficients, referred to creep stage and referred to origin, where obtained for all specimens and compared. Figure 8 shows the creep coefficients results at 90 days for all creep stress levels I_{c}, referred to creep stage and to origin of deformations. Notice that some specimens with I_{c} > 80 % develop high creep

**Fig. 8 **Creep coefficients at 90 days referred to creep stage (u9^{0}) *-left-* and origin of deformations (uO^{0}) -right-

coefficients values. This fact was given due to sudden increases of CMOD deformations during creep test.

In case of SFRCs, the highest values of creep coefficients were given for those concretes reinforced with fibres with less slenderness (k = 45-50) and a high length (l = 50 mm). In those cases when low *I _{c}* < 70 % is given, creep coefficients referred to origin of deformations for all concretes remains always below ф = 1. The Model Code [12] stablish this limit (ф = 1) as the reference creep coefficient value for concretes. For higher stress levels, creep coefficients referred to origin of deformations are closer to 1 but most of them still remain below ф = 1. Those specimens that suffered sudden increases of deformations during creep stage are clearly over the limit of ф = 1.

On the other hand, for conventional RCs, both types of concretes (I and II) obtain low values for both creep coefficients even with a high I_{c}. In case of creep coefficients referred to origin of deformations, the values are below the MC recommendation. Due to the high residual strength of RC specimens, this behaviour may be influenced by creep deformations in compression zone of the specimens. It should be desirable to reach the way to distinguish between *tensile creep* in cracked zone and *compressive creep* in compression zone of the specimen in a flexural creep test.

**4.3.2 Crack Opening Rate (COR)**

The Crack Opening Rate or COR is a parameter that helps to evaluate the average velocity of deferred deformations between two time lapses. This COR parameter is obtained by means of Eq. (5):

**Fig. 9 ***COR ^{14 30} (left)*

**and**

*COR*

^{30 90}(right)**for all tested concretes**

where *j* and *k* are two different time lapses in days. This parameter is expressed in цш/day units. In this work, three lapses of time of creep test were analysed: from 0 to 14 days (2.74-59.72 цш/day), from 14 to 30 days (0.76-46.26 pm/day) and from 30 to 90 days (0.34-6.43 pm/day). Figure 9 shows the COR trends in two lapses of time: 14-30 and 30-90 days.

A global trend to reduce velocity with time can be observed. In case of FRCs type I, the minimum values were obtained for *I _{c} <* 80 % whereas for FRCs type II, minimum values were obtained for

*I*70 %. In both concretes, lower values of COR were detected in case of conventional rebar reinforcement and SFRCs with low

_{c}<*I*

_{c}.Although there is a trend to reduce velocity along time, the COR values are quite high in general, especially is cases of high stress level *I _{c}.* These high COR values are not suitable since it may turn into a local or global failure during life time of the FRC element.