Probabilistic Method
1. Probability parameters 2. Reliability function
3. Probabilistic approach to determine service life
1. Probability Parameters
Frequency
• Probability density function (pdf)→ f(x)
• Cumulative distribution function (cdf)→ F(x)
An example of a probability density function are:
Distribution characteristic
2. Reliability Function
Example: R (μR = 45; σR= 5); S (μS= 35; σS= 7)
Example: VR
FRP(shear resistance with FRP strengthening)
3. Probabilistic Approach to Determine
Service life
Requirements for probabilistic approach:
1. Degradation model and its probability → R (t)
2. Load effect model and its probability → S(t)
3. Probability of failure Pf (t) = P(R(t)<S(t))
4. Fractile Pf(t)
Example 1: Pag 39-48.pdf
R (t) = depth of concrete cover S(t) = depth of Cl- penetration
S =
t
Statistical Parameters
Example 2: Mini Project.pdf
1. How many years is the lifetime of the reinforced concrete beam subjected to chloride ingress?
2. What is the effect of a membrane on the lifetime of the beam? How many years the
extention of lifetime provided by application of a
membrane?
R1(t) S1(t)
Initiation period Propagation period
S2 (t) R2 (t)
Related to chloride penetration Related to bending capacity Pf1 = P(R1(t)-S1(t) ≤0) Pf2 = P(R2(t)-S2(t) ≤0)
Limit state equals to a combination of two probability of failures as follows:
Pf =P[P(R1(t)-S1(t) ≤0)ΩPf = P(R2(t)-S2(t) ≤0)]
Used Pf1 and Pf2 = 5%
Initiation Period
2
0 1
2
0
(
4
−
−
−
= −
c c
c erf c
D T d
s
cr s
c
Rumus dasar penetrasi ion Cl-
Dengan data chloride profile, rumus dasar tersebut dipakai untuk mendapatkan nilai difusi D dengan cara fitting pada grafik profile
Waktu inisiasi korosi dapat dihitung dengan rumus dibawah dengan mengasumsikan kandungan Cl- kritis yang dapat memulai terjadinya korosi sebesar 0.05%-0.1% dari berat beton kering
2 ) (
0 ) , (
Dt erf x
c c
c c
s
t x
s
