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Damage Propagation vs Time

SLM Limit States/Evidence
 Entrance of aggressive agents/Cores or Drilling
 Initiation of corrosion/LPR or halfcell
 Rust staining/visual
 Cracking/visual
 Spalling/visual
 Structural failure/closure


Initiation phase
 Deterministic; measured values, well established models, single output value
 Probabilistic; distribution curves/mean and standard deviation, probability/reliability as output

SLM  chloride models
 Data from cores, labs, literature
 NaCl ponding test, seal all faces except top with epoxy, determine chloride profile after 90 days

Chloride Initiation Phase  Diffusion model
 C_{x,t} = chloride depth x, at time t_{ }
 C_{s} = surface chloride_{}
 D_{app} = chloride diffusion coefficient apparant
 T = time
 x = cover depth
 erf = error function
 requires concentration of chlorides at bar to initiate corrosion to predict service life. Chloride % by weight can be expected to decrease exponentially as depth increases
 Reaches max. value

Chloride diffusion coefficient, D_{app}
 D_{tm }chloride diffusion coefficient at time t_{m} and n is the material coefficient. e.g. t_{m }at age zero is 1
 n factor; OPC 0.264, PFA 0.699, GGBS 0.621

Chloride Diffusion Model; surface chloride C_{s}
 where Cs < 0.06 (or any other preset value)
 alpha is a constant depending upon exposure conditions
 C_{0} is the initial surface concentration
 t time in years
 e.g. mean values OP cement 0.36%, Blended cements 0.51%

Chloride Diffusion Model
Rate of chloride build up at surface in different marine environments

Using Chloride Diffusion Model to determine cover required

Chloride Propagation Phase  Diffusion model
 Diffusion Model can be used as basis for propagation but considerable uncertainty exists.
 Uncertainty increases as the propagation continues from cracking to spalling to structural failure.
 If using then predict corrosion rate first. Actual measurements or:
 CR = a.e^{bCx}micron/year
 CR – corrosion rate, a and b are constants and Cx is the chloride content

Calculating chloride corrosion rate for propagation phase for uncracked concrete
 CR = 0 (Cx <0.46% by weight of cement)
 CR = 0.55e^{1.564Cx} (0.46%<Cx <3.0% by weight of cement)
 CR = 60 (3.0%<Cx by weight of cement)

Chloride corrosion propagation. Crack penetration
 p_{cr} = (83.4 + 7.4c/d_{b}  22.6f_{ct})/1000
 c – cover
 d_{b} – bar diameter
 f_{ct} – tensile splitting strength of concrete

Chloride corrosion propagation. Crack propagation
 w_{cr} = 0.05 + Beta(p(t)  p_{cr}) >0
 Where
 Beta – 12.5 top cast, 10 bottom cast bars
 p(t)– mean corrosion penetration at time t

Chloride corrosion propagation. Residual cross section
A_{res} = pi(d_{b} – 2p(t))^{2}/4

SLM  carbonation modelling
 Depth of Carbonation =
 Q + k1.k2.k3.k4.k5.C.t^{x}
 Q = Instantaneous Carbonation
 C = Carbonation Coefficient for Concrete (Assumptions for C are made for differing grades of concrete)
 t = time
 k1 = factor  effect of CO2 concentration in the air
 k2 = factor  effect of Exposure
 k3 = factor  effect of orientation (N,S,E,W)
 k4 = factor  effect of Curing
 k5 = factor  effect of supplementary cementitious materials (e.g.  flyash, BFS)
 x = factor effect of asset type and method of construction^{}

SLM  carbonation initiation phase
 x_{c}(t) = Kt^{0.5}
 t – time
 x_{c}(t) – carbonation depth at time t
 K – constant
 K can be determined from site data given carbonation depth at time t.

Carbonation initiation impacted by:
The environment. Time of wetness & temperature

Carbonation initiation, rates for various concrete strengths

SLM Initiation Phase  Probabilistic models
 Distribution function for each variable
 Normal, t, chi squared, WeiBull, etc
 Surface chloride, chloride diffusion coefficient, cover depth (age factor, temperature)
 Monte Carlo simulation (or similar) to build up a distribution pattern for results
 Analyse probability that result gives desired service life

SLM Initiation Phase  probabilistic models examples
 RMIT research project
 Model uses analogy between heat transfer and diffusion
 Time dependant analysis
 Variation in models
 Model replicates at concrete pile with different rates of chloride build up
 FEA Mesh
 Comparison at point y (midpoint)
 Other models. Questionable accuracy:
 Freeze/Thaw
 Sulphate attack
 ASR

