Constructing multivariate distributions for soil parameters - Risk and Reliability in Geotechnical Engineering - page 46

(a)

1 1

Baseline
a X = 2

Baseline
b X = -1

0.8
0.6
0.4

0.8
0.6
0.4

0.2
-5

0.2
-5

0
y

5 0

y

5

1 1

Baseline
a Y = 2

Baseline
b Y = 1

0.8
0.6
0.4

0.8
0.6
0.4

0.2
0

0.2
-5

-5 0

y
SU distribution (baseline is with a X = 1, b X = 0, a Y = 1, b Y = 0).

5 0

y

5

(b)

4 4

Baseline
a X = 2

Baseline
b X = 1

3 3

2 2

1 1

0 0 0 0

0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1

y y

4 4

Baseline
a Y = 2

Baseline
b Y = 1

3 3

2 2

1 1

0 0

0 0.5 1 1.5 2 0 0.5 1 1.5 2

y y

SB distribution (baseline is with a X = 1, b X = 0, a Y = 1, b Y = 0).

(c)

2 2

Baseline
b X * = 1

Baseline
a X = 2

1.5 1.5

1 1

0.5 0.5

0 0

0 0

1 2 3 4 5 1 2 3 4 5

y y

2

Baseline
b Y = 1 1.5

1

0.5

0 0

1 2 3 4 5

y

SL distribution (baseline is with a X = 1, b X * = 0, b Y = 0)

Figure 1.20 Some distributions in the Johnson system: (a) SU family; (b) SB family; and (c) SL family.