Constructing multivariate distributions for soil parameters - Risk and Reliability in Geotechnical Engineering - page 60

(2014a). In addition, we generalize the concept of conditioning discussed in Section 1.4.5
from the normal case to the non-normal (Johnson distribution) case (Section 1.7.3).
Several valuable multivariate databases have been compiled by the authors so far (Ching
and Phoon 2012, 2013, 2014a; Ching et al. 2014b). These databases are labeled in accor-
dance to the template: (soil type)/(number of parameters of interest)/(number of data points).
The Clay/10/7490 database is the largest database compiled so far in terms of the number
of data points and the number of parameters of interest (equal to dimension of multivariate
probability distribution function).

1.7.1 Clay/10/7490 database
The Clay/10/7490 database compiles data from 251 studies. The number of data points
associated with each study varies from 1 to 419 with an average of 30 data points per study.
The clay properties cover a wide range of OCR (but mostly 1 ~ 10), a wide range of sensitiv-
ity ( S t ) (sites with S t = 1 ~ tens or hundreds are fairly typical), and a wide range of PI (but
mostly 8 ~ 100). Details are reported by Ching and Phoon (2014a).
Ten dimensionless clay parameters are compiled in this database. These parameters can
be divided into the following three broad categories:

1. Index properties:
• LL
• PI
• LI

2. Stresses and strengths:
• Normalized vertical effective stress

( )

σ v P ′ / (P a is one atmosphere pressure = 101.3

kPa)
• Normalized preconsolidation stress ( σ pa ′ /P )

• Normalized undrained shear strength (

s u ′σ [All s u values are converted into the
“mobilized” s u values, denoted by s u (mob), which is the in situ undrained shear
strength mobilized in embankment and slope failures (Mesri and Huvaj 2007)]
• Sensitivity (

)

Ss = / ss

re

)(

re

is the remolded undrained shear strength )

t u uu

3. CPTU parameters:
• Pore pressure ratio B q = ( u 2 − u 0 )/( q t − σ v ) ( u 2 is the pore pressure behind the cone;
u 0 is the hydrostatic pore pressure; q t is the corrected cone tip resistance; and σ v is
the total effective stress)
• Normalized cone tip resistance (

σ/
• Normalized effective cone tip resistance (

q

t −

) ′

v v

qu
t

−

2 /σ

)

′

v

It is clear that other dimensionless parameters of interest, such as the OCR, can be derived
from the above 10 dimensionless parameters. The basic statistics of these parameters (10
basic parameters together with OCR) are listed in Table 1.16 to provide a feel of the range
and distribution of the parameters. The number of data points ( n ) for each parameter is
shown in the second column. The statistics are the mean value, COV, minimum value (min),
and maximum value (max).
To keep notation concise, the physical random variables (or natural logarithm transform)
are denoted by

1. Y 1 = ln(LL)

Ž
‰
‰

2. Y 2 = ln(PI)

Index properties

3. Y 3 = LI