DEVELOPMENT OF SOFTWARE BASED ON THE PROPOSED MODEL
4.3 Evaluation of the proposed model’s parameters
Figure 4.5 – Probability of Failure and Reliability Index vs. time.
Table 4.1 – Value of variables for simulation for reference case 1.
Variable Distribution
Type Parameter 1 - Average Parameter 2 - Standard deviation
xC (mm) N (normal) 35, 45, 55, 65, 75, 85 10 DCOEF (e-12.m2/s) N (normal) 1, 3, 6, 9, 12, 15 2.5 CS (% /weight concrete) N (normal) 0.4, 0.6, 0.8, 1.0, 1.2 0.3 CCR (%/weight concrete) N (normal) 0.06, 0.08, 0.10, 0.15, 0.2 0.02 α N (normal) 0.3, 0.4, 0.5, 0.6, 0.7, 0.8 0.06
t0 (days) D (deterministic) 28 ---
T (ºC) N (normal) 1, 7, 14, 21, 28 2
In the second reference case, an average value for the model parameters is chosen from the range presented in Table 4.1, and the standard deviation is varied. This is obtained by varying the coefficient of variation (CoV) over a valid range, from 5 % to 30 %. Table 4.2 shows the parameter information needed for the simulation.
Table 4.2 – Value of variables for simulation for reference case 2.
Variable Distribution
Type Parameter 1 - Average Parameter 2 - Standard deviation (CoV - %)
xC (mm) N (normal) 55 55 (5,10,20,30)
DC (e-12.m2/s) N (normal) 9 9 (5,10,20,30)
CS (% /weight concrete) N (normal) 0.8 0.8 (5,10,20,30)
CCR (% /weight concrete) N (normal) 0.1 0.1 (5,10,20,30)
α (-) N (normal) 0.5 0.5 (5,10,20,30)
t0 (days) D (deterministic) 28 ---
T (ºC) N (normal) 15 15 (5,10,20,30)
In the third reference case, the effect of low quality (LQ) and high quality (HQ) of concrete is analysed at an age of 50 years, varying the concrete reinforcement cover from 5 to 125 mm.
Table 4.3 shows the values used in the simulation. A CoV of 10 and 30% was used for each of the concrete qualities. In this way, the effect of different quality concretes on the performance is analysed, each with a large and small scatter of the parameter in question.
Table 4.3 - Value of variables for simulation for reference case 3.
High Quality Low Quality
Variable Dist. Type
Parameter 1 Parameter 2 Parameter 1 Parameter 2
DCOEF (1e-12.m2/s) N (normal) 3.5 0.7 10.0 2.5
CS (% /wt.concrete) N (normal) 1.0 0.3 1.0 0.3
CCR (% /wt.concrete) N (normal) 0.08 0.008 0.07 0.007
α (-) N (normal) 0.4 0.04 0.4 0.04
t0 (days) D (determ.) 28 --- 28 ---
T (ºC) N (normal) 21 2 21 2
xC (mm) variable from 5 - 125 mm depth t (years) 50 years
4.3.2 Concrete cover
The average concrete cover parameter was varied from 35 mm to 85 mm with a 10 mm standard deviation. The minimum value chosen is smaller than the minimum requirement for concrete cover in standards for marine environments. The 10 mm standard deviation is based on the value given for the deviation of xC in ENV 13670-1, for Portugal. From figure 4.6, the effect of concrete cover on service life is clearly noticeable. Small increases in concrete cover vary significantly the performance of the concrete through out the service life. This effect is even greater at earlier ages, for example 10 years, where the difference in probability of failure between a concrete cover of 35 mm and 55 mm is almost 50 %.
Figure 4.6 – Effect of various concrete covers (Xc) with time.
Figure 4.7 – Influence of concrete cover scatter on the probability of failure.
The influence of the scatter on the concrete cover measurements on the probability of failure can be observed in figure 4.7. With a CoV of up to 30 %, the final result, i.e the probability of failure is affected by approximately 10 %. The greater the CoV, the lower the probability of failure is, for ages greater than 12 years. Before this age, the trend is the opposite.
4.3.3 Diffusion coefficient
The average diffusion coefficient parameter was varied from 1.0 x 10-12 m2/s to 15.0 x 10-12 m2/s with a 10 % CoV. These two extreme values represent extremely high and low concrete qualities according to Nilsson (1998). Figure 4.8 shows the importance of the diffusion coefficient as a parameter for service life design. The differences between 1.0e-12 m2/s and 15.0e-12 m2/s are significant. An increase of one order of magnitude in the diffusion coefficient results in an improvement of the performance by at least 90 % at 50 years. This effect is still large at earlier ages, for example 10 years, where the difference in probability of failure is almost 55 %.
From figure 4.9, the influence of the scatter of the diffusion coefficient on the performance can be observed. A CoV up to 30% influences the final result, i.e the probability of failure, by approximately 5 %. A pattern seems to appear, the higher the scatter the lower the probability of failure.
Figure 4.8 – Effect of various diffusion coefficient with time.
Figure 4.9 – Influence of diffusion coefficient scatter on the probability of failure.
In figure 4.10, a comparison is made between the performance of a high and low quality concrete at the age of 50 years. The diffusion coefficients used were 3.5e-12 m2/s and 10.0e-12 m2/s, respectively. If the structure is assumed to have a 50 mm concrete cover, the low quality concrete cover would have a probability of failure of 100 % meaning that corrosion has started.
The high quality concrete cover would have a probability of failure of approximately 35 %.
According to the Norwegian Standard for requirements to reliability in design of structures (NS 3490 1999), the probability of failure for a serviceability limit state should not exceed 10 %, and according to Eurocode 1 (2002) the probability of failure for a serviceability limit state should not be more than approximately 7 %. If the 10 % limit is adopted, the low quality concrete would require a concrete cover of approximately 105 mm to reach this limit after 50 years. The high quality concrete would only require approximately 60 mm. This is a huge difference that
influences the design of a structure drastically.
Figure 4.10 – Comparison of the performance of high quality and low quality concrete (influence of the diffusion coefficients) at various concrete cover depths after 50 years.
The influences of the diffusion coefficient scatter (CoV of 10 % and 30 %) on the performance of the concrete result in the need to increase the concrete cover by approximately 5 mm in concrete cover, if the scatter is increased.
4.3.4 Critical chloride content
The average critical chloride thresholds were varied from 0.06 % to 0.2 % by weight of concrete with a 10 % CoV. These values correspond to the limits of values presented in literature, irrespective of the concrete type. It is clear that this parameter, although still important, does not influence the performance as much as the concrete cover or the diffusion coefficient (Figures 4.6 and 4.8 respectively). The probabilities of failure curves are further apart in Figures 4.6 and 4.8 than in Figure 4.11, indicating greater influence on the performance. This separation is maintained until 50 years. After 50 years, the influence in the probability of failure between the maximum value and the minimum value is 20%. However, at 10 years, the difference is large being approximately 45 %. This suggests that with time, the effect of the different critical chloride thresholds become less significant. This is due to the fact that with time, ever more parts of the structure begin to deteriorate and corrode.
The influence of the scatter of the critical chloride thresholds on the performance is observed to be negligible (see Figure 4.12). This suggests that this parameter can be considered to be deterministic. Its quantification is still vital, while the scatter seems to have no influence.
Figure 4.11 – The effect of different critical chloride thresholds with time.
Figure 4.12 – Influence of the critical chloride thresholds scatter on the probability of failure
In figure 4.13, a comparison is made between the performance of a high and low quality concrete at the age of 50 years. The critical chloride thresholds used were 0.08 % and 0.07 % respectively, by weight of concrete, with CoV of 10 %. If the structure is assumed to have a 50 mm concrete cover, the low quality concrete cover would have a probability of failure of over 95 %, where as, the high quality concrete cover would be approximately 30 %. According to the Norwegian Standard for requirements to reliability in design of structures (NS 3490, 1999), the probability of failure for a serviceability limit state should not exceed 10 %, and according to Eurocode 1 (2002) the probability of failure for a serviceability limit state should not be more than approximately 7 %. If the 10 % limit is adopted, the low quality concrete would require a concrete cover of approximately 100 mm to reach this limit after 50 years. The high quality concrete would only require approximately 60 mm. This is a significant difference that can
influence the design of a structure markedly.
Figure 4.13 - Comparison of the performance of high quality and low quality concrete (influence of the critical chloride thresholds) at various concrete cover depths after 50 years.
The influence of the critical chloride content scatter (CoV of 10 % and 30 %) in the performance of concrete results in the need to increase the concrete cover by approximately 2-3 mm. This indicates that the scatter of the critical chloride content has little bearing on the concrete cover in the proposed model (see Figure 4.13).
4.3.5 Surface chloride content
The average surface chloride content is varied between 0.4 % and 1.2 % by weight of concrete, with a 10 % CoV. These values correspond to a moderately low concentration of chloride ions, which can be associated with brackish waters, and a moderately high concentration of chloride ions.
It is clear from Figure 4.14 that this parameter, although still important, does not influence the performance as much as the concrete cover (figure 4.6) or the diffusion coefficient (figure 4.8).
After 50 years, the influence in the probability of failure between the maximum value and the minimum value is 18%, however, at 10 years, the difference is large, approximately 42 %. This is probable obvious because the lower the surface chloride content, longer time is needed for the chloride to penetrate the concrete cover in sufficient quantities to initiate corrosion. Therefore, at 50 years, the values are closer to one another than at 10 years.
Figure 4.14 - The effect of different surface chloride content on the probability of failure with time.
Figure 4.15 – Influence of the scatter of surface chloride content on the probability of failure
From figure 4.15, the influence of the scatter of the surface chloride content on the performance is relatively small, approximately 5 %.
In figure 4.16, a comparison is made between the performance of a high quality and a low quality concrete, at the age of 50 years. The surface chloride content used was 1.0 % by weight of concrete. If the structure is assumed to have a 50 mm concrete cover, the low quality concrete cover would have a probability of failure of 100 %, indicating that corrosion has started, whereas the high quality concrete cover would be less than 30 %.
Figure 4.16 - Comparison of the performance of high quality and low quality concrete (influence of the surface chloride content) at various concrete cover depths after 50 years.
If a 10 % probability of failure for a serviceability limit is adopted, the low quality concrete would require a concrete cover of approximately 102 mm to reach this limit after 50 years. The high quality concrete would only require approximately 57 mm. This is a significant difference that can influence the design of structures markedly.
The influence of the scatter of surface chloride content (CoV of 10 % and 30 %) on the performance of the concrete results in the need to increase the concrete cover by approximately 3-5 mm (Figure 4.16). Although small, this value is large enough to influence the design.
4.3.6 Age factor
The age factor α of the diffusion coefficient was varied between 0.3 and 0.8, with a 10 % CoV.
This corresponds to an intermediate range of values since the limiting values for the age factor are 0.0 and 1.0. Figure 4.17 indicates that the age factor influences the performance significantly even more than the concrete cover (figure 4.6) or the diffusion coefficient (figure 4.8). After 50 years, the influence in the probability of failure between the maximum value and the minimum value is 95%. At 10 years, the difference is still very large, approximately 90 %.
For this reason much care must be taken in choosing this parameter. From figure 4.18, the influence of the scatter of the age factors of diffusion coefficient on the performance is the largest observed, approximately 15 %. If determining the probability of failure for 50 years, the greater the scatter of the age factor measurements the lower the probability of failure will be.
Figure 4.17 – The effect of age factors of diffusion coefficient on the probability of failure with time.
Figure 4.18 - Influence of the scatter of the age factors of diffusion coefficient on the probability of failure.
In figure 4.19, a comparison is made between the performance of a high and low quality concrete at the age of 50 years. The age factor used was 0.4. If the structure is assumed to have a 50 mm concrete cover, the low quality concrete cover would have a probability of failure of 85-95 % where as the high quality concrete cover would be approximately 30-40 %. If the 10 % probability of failure for a serviceability limit is adopted, the low quality concrete would require a concrete cover of approximately 100 mm and over 140 mm for the 10% CoV and the 30%
CoV, respectively, to reach this limit after 50 years. The high quality concrete would only require approximately 55 mm or a 75 mm of concrete cover, for the 10% CoV and the 30%
CoV, respectively. Not only the difference is significant between the concrete qualities, but also the effect of the scatter of the age factor is high for the same concrete quality.
Figure 4.19 - Comparison of the performance of high quality and low quality concrete (influence of the diffusion coefficient age factors) at various concrete cover depths after 50 years.
The influences of the scatter of the age factor of diffusion coefficient (CoV of 10 % and 30 %) on the performance of concrete result in the need to increase the concrete cover by approximately 20-25 mm. Hence, the need to quantify adequately the age factor is crucial.
4.3.7 Temperature
The average temperature parameter was varied from 0 ºC to 28 ºC with a 10 % CoV. This is the normal range of average temperature for cold and hot climates. Figure 4.20 indicates that temperature, although still important, does not influence the performance as much as the concrete cover (figure 4.6) or the diffusion coefficient (figure 4.8). After 50 years, the influence in the probability of failure between the maximum value and the minimum value is 40 %. At 10 years, the difference is still higher, approximately 70 %. With time, the effect of temperature on the rate of the probability of failure decreases.
Figure 4.20 - The effect of different temperature with time.
Figure 4.21 shows that the influence of the scatter of the temperature on the performance is considerable, approximately 10 %. It further indicates that the higher the scatter of the parameter, the lower the probability of failure.
Figure 4.21 - Influence of the temperature scatter on the probability of failure
In figure 4.22, a comparison is made between the performance of a high and low quality concrete at the age of 50 years. The temperature used was 21 ºC. If the structure is assumed to have a 50 mm concrete cover, the low quality concrete cover would have a probability of failure of 95 % where as the high quality concrete cover would be approximately 35 %.
Figure 4.22 - Comparison of the performance of high quality and low quality concrete (influence of the temperature) at various concrete cover depths after 50 years.
If the 10 % probability of failure for a serviceability limit is adopted, the low quality concrete
would require a concrete cover of approximately 105 mm to reach this limit after 50 years. The high quality concrete would only require approximately 65 mm. This is a considerable difference that can influence the design of a structure markedly.
The influence of the temperature scatter (CoV of 10 % and 30 %) on the performance of the concrete results in the need to increase the concrete cover by approximately 5 mm.