Bayesian analysis for learning and updating geotechnical parameters and models with measurements - Risk and Reliability in Geotechnical Engineering - page 250

Prior joint PDF

4

3.5

3

2.5

μ K

2

1.5

1

0.5

20 25 30 35 40 45 50 55

μ φ (°)

Posterior joint PDF

4

3.5

3

2.5

μ K

2

1.5

1

0.5

20 25 30 35 40 45 50 55

μ φ (°)

Figure 5.12 Contour plots of the prior and posterior joint PDF of μ φ and μ K given CPT measurement
outcomes.

random variables γ, μ K , and μ φ that characterize the soil material. The likelihood function of
this information can be expressed as follows:

L (, γµ µ , ) ((, = I h γ µµ , ) ≤ 0 ),

(5.55)

K ϕ K ϕ

where I is the indicator function and h (γ, μ K , μ φ ) is an LSF describing the information and
is given by

h (, γµ µ , ) = kVQ

2

− (, γ µµ , .

(5.56)

K ϕ m u K ϕ