Reliability-based design - Risk and Reliability in Geotechnical Engineering - page 355

The design point is obtained as the most probable failure combinations of parametric
values, and the reliability index β, being the distance (in units of directional standard
deviations) from the safe mean-value point to the nearest failure boundary (the LSS,
Figure 9.1 ) , conveys information on the probability of failure. In LRFD or Eurocode
design, there is no explicit information on the probability of failure.
vi. It is clear from the above discussions that in an RBD, one does not use or specify the
partial factors. The design point values x * (and implied characteristic values and par-
tial factors) are determined automatically and reflect sensitivities, standard deviations,
correlation structure, and probability distributions in a way that prescribed partial
factors and “conservative” characteristic values cannot.
vii. In Figure 9.3 , by comparing the values under the nx column, it is evident that bearing
capacity is more sensitive to Q h than to Q v , for the case in hand with its statistical inputs.
viii. The x * value for c is slightly higher than the original mean value of c , due to the nega-
tive correlation between c and ϕ. In this case, the response is far more sensitive to ϕ
than to c . Negatively correlated c and ϕ means low values of ϕ tend to occur with high
values of c, and vice versa. Under such circumstances, an RBD will automatically
reflect sensitivities in obtaining design point values of c and ϕ that can be both lower
than their respective mean values, or one above average and the other below average
as in this case. For the case in hand, to have both design values of c and ϕ below their
mean values using partial factors are unrealistic.
The above discussions suggest that RBD can be a complementary alternative to EC7
design or LRFD design when the statistical information (mean values, standard deviations,
correlations, and probability distributions) of the key parameters affecting the design are
known and one or more of the following circumstances apply:
• When partial factors have yet to be proposed by EC7 to cover uncertainties of the less
common parameters, for example, in situ stress coefficient K in underground excava-
tions in rocks, dip direction and dip angles of rock discontinuity planes, and smear
effect of vertical drains installed in soft clay.
• When output has different sensitivity to an input parameter depending on the engi-
neering problems (e.g., shear strength parameters in bearing capacity, retaining walls,
and slope stability).
• When input parameters are by their physical nature either positively or negatively cor-
related. One may note that EC7 does not provide for the use of different characteristic
values and partial factors when some parameters are correlated. The same design is
obtained in EC7 with or without modeling of correlations among parameters.
• When spatially autocorrelated soil properties need to be modeled. This will be illus-
trated in Section 9.5 on a Norwegian slope with spatially autocorrelated soil unit
weight and undrained shear strength.
• When there is a target reliability index or probability of failure for the design in hand.
In this regard, one may note that a design by EC7 or LRFD provides no explicit infor-
mation on the probability of failure.
• When uncertainty in unit weight γ of soil needs to be modeled. This will be illustrated
in the RBD of the anchored sheet pile wall in Section 9.8.
The following sections revisit—with more elaborations and discussions—some of the geo-
technical examples of RBD and analysis from papers that the writer authored or coauthored,
focusing on subtleties and insights. The cases involve both ultimate limit states (rock slope,
a slope failure in San Francisco Bay mud, a Norwegian slope, a two-layered clay slope, an