Design For Life
Introduction
“Design For Life” is a mathematical model for assessing the life of marine structures. This model has been developed by Frank Papworth over the last 10years. This version (6.1) includes the analysis of a literature search up to March 2000. Whilst the model is a useful tool it can not cover all circumstances and should be used only by experts in concrete durability who understand the limitations of the algorithms used.
Data Entry
Data entry is set up to enable the user to enter details of the proposed concrete mix, the environment and the structures general arrangement whilst monitoring the life expectancy (figure 1).
The following outlines the data entry.
- Enter Temperature (k,oC)
- Enter mix details i.e.
- a) Cement content (kg/m3)
- b) C3A of cement (C3A, %)
- c) w/b ratio (wc)
- d) FA/Slag/MS dosage (MA, %)
- e) Inhibitor type and dosage (In, lt/m3)
- e) Chloride content of final mix (Bc, as wt % cement)
- 3. Enter geometry of reinforcing
- a) Cover to reinforcement (c, cm)
- b) Reinforcement diameter (d, cm)
- c) Length of anode and cathode (la and lc, cm)
- d) Select whether time to spalling or time to structural failure is a concern and if structural failure the loss of cross section that will lead to failure (this depends on design).
- 4. Select environment aggressiveness from table ie
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Exposure
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Surface Chloride (Co wt % cement)
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Potential Difference (V, mv)
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Wet time for splash (W, mins)
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Near Coastal (B1)
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1
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100
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0
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Atmospheric (B2)
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2
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200
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0
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Splash (C1)
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Soffit low
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8
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600
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200
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Other
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6
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200
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15
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Tidal (C2)
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2.5
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300
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120
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The height above HW that the splash zone extends too depends on the openness of the exposure i.e.
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Offshore
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Coastal
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Sheltered
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Soffits low
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0-4m
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0-2m
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0-1m
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Other
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0-20m
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0-10m
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0-3m
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Calculate Concrete Characteristics
From the inputs the model calculates all the concrete properties. These properties are based on international research using high quality materials and good quality workmanship. Where either is suspect than a suitable allowance should be made to the performance figures, preferably using actual data or if necessary conservative engineering judgment. The following sections outline the process the model follows.
Calculate Sorptivity
Calculate the sorptivity of the concrete from
S=wc 1.5 /(MA/F1)0.5
The sorptivity value is for a surface sorptivity and not a bulk sorptivity. The later will be significantly lower, particularly in fly ash and slag concrete. The value of F1 is selected based on the type of mineral admixture.
Calculate Chloride Diffusion Coefficient
Calculate 28day bulk saturated Chloride Diffusion coefficient for an OPC based on it’s w/c using Takewaka’s formula based on research on saturated samples.
Adjust Dc1 for the mineral admixture dosage (eg fly ash, slag or microsilica) based on relationships given and supported by the literature. This (Dc2) is the 90days diffusion coefficient for saturated concrete at 20oC.
Adjust Dc2 for temperature based on the Nernst Einstein equation with a q variable established by Amey. This (Dc3) is the modified coefficient based on an average temperature of the concrete. The concrete temperature might be significantly higher than the ambient temperature.
Calculates Dc3t for each year using the 90 day Dc3 value. For subsequent years Dc3 is reduced by (t/0.0027)n/f where t is time in years, f=factor of safety on reduction, and n = reduction factor from research.
Calculate Resistivity
Calculate the resistivity from
R=20000(1-wc0.5 )(1+(MA/F2)2 /20)
Where F2 is a factor depending on the type of mineral admixture. The resistivity is the expected 90day result.
Much lower results with time will be achieved in practice but these are ignored instead of utilising a safety factor on resistivity.
Calculate Activation Level
Calculate the activation level from AL1 from a formula related to w/c ratio and supported by Pettersson’s research. The activation level varies from 0.4 to 2.0 by wt of cement based on w/c.
Modify AL1 based on effect of C3A. This takes account of low C3A sulphate resisting cements to give AL2. This is based on Rasheeduzzafer measurements of free chloride at different C3A contents.
Modify AL2. based on the inhibitor type and dosage. The level is based on international research including data that shows minimal level of inhibitor required to be effective. Calculate allowable increase in chloride content at the bar AL3 = AL3-Bc Calculate chloride driving force C01=C0- Bc
Calculate Insitu Durability Performance
Knowing the concrete performance and the environment standard transport formula are used to calculate the chloride ingress and determine the time to activation. The corrosion rate is used to determine time to spalling and structural failure. Hence the T0+T1 time line is determined.
Calculate Sorptive Layer Thickness
The sorptive layer is based on a standard formula for penetration due to sorptivity ie s=W0.5 S/0.1 mm
Calculate Diffusion Layer Thickness
The diffusion layer is simply the cover less the sorptive layer
ie d’=d-(s/10) cm
Calculate Increase In Chloride At Bar Depth Each Year
This uses Fick’s second law ie C(xt)=C0(1-erf x) Where x=d’/(4Dc3t t)0.5 t is time in secs Erf x = (1-(1/1+a1x+a2x2 +a3x3 +a4x4 )4 a1=0.278393, a2=0.230389, a3=0.000972, a4=0.078108
The programme determine when C(xt) = AL3 and plots the chloride level at the bar with time and the chloride profile at time of activation. Adjust the current for temperature based on Pruckner’s research on corrosion rates and temperature.
Calculate current density by dividing the current by the anode area.
Determine corrosion rate from current density based on Faraday’s law.
Calculate time to spalling based on the corrosion rate, cover and bar diameter and the life to structural failure based on the allowable loss of bar section.
Summary
This corrosion model is very advanced in its concepts. This document is not a detailed guide but provides an indication of comprehensive tools available to BCRC in durability design.