Reliability-based design - Risk and Reliability in Geotechnical Engineering - page 354

General concepts of ultimate limit state design in Eurocode 7:

(if “=”, then “design point”)

Diminished resistance ( c k / γ c , tan ϕ k /γ ϕ ) ≥ Amplified loadings

Characteristic values Based on characteristic values and

partial factors for loading
parameters. Partial factors

“Conservative”, for example, 10 percentile for strength parameters, 90
percentile for loading parameters

The three sets of partial factors (on resistance, actions, and material properties) are
not necessarily all applied at the same time.
In EC7, there are three possible design approaches:

Design Approach 1 (DA1): (a) factoring actions only; (b) factoring materials only.
Design Approach 2 (DA2): factoring actions and resistances (but not materials).
Design Approach 3 (DA3): factoring structural actions only (geotechnical actions
from the soil are unfactored) and materials.

Figure 9.4 Characteristic values, partial factors, design point, and design approaches (DA) in Eurocode 7.

ii. The mean value, standard deviation, and design point value of a parameter can be
related to the characteristic value and partial factor of the same parameter in the EC7
design approach. For example, for the given mean and standard deviations of the angle
of friction ϕ, the characteristic value ϕ k (assuming at 10 percentile of the lognormal
distribution) is 21.9°. The partial factor of ϕ (denoted by the symbol γ ϕ ) implied in the
design point (the x * values) is γ ϕ = ϕ k /ϕ* = 21.9°/20.76° = 1.055. (Note that in EC7, the
partial factor γ ϕ is applied to tanϕ k , and not to ϕ k . Had the mean and standard deviation
been given for tanϕ rather than ϕ, the characteristic value tanϕ k and its corresponding
partial factor can be back calculated from the FORM results by the same principle.)
iii. On the other hand, for the load parameter Q h , with mean 300 and standard deviation
45, the characteristic value Q hk (assuming at 90 percentile of the lognormal distribu-
tion) is 359. The partial factor of Q h (denoted by the symbol γ Qh ) implied in the design
point (the x * values) is γ Qh = Q h */ Q hk = 412.6/359 = 1.15.

iv. For lower mean value and standard deviation of Q h , or for problems in different realms
(e.g., slope stability or earth-retaining walls), the back-calculated partial factors could
be different. To apply the same rigid partial factors across different realms or different
levels of parametric uncertainty may not imply the same target failure probability. In
an RBD, the same target reliability index (with its implied probability of failure) can
be used across different realms and different levels of parametric uncertainty and cor-
relations, including asymmetric probability distribution if appropriate. Also, if higher
reliability is required where the consequence of failure is severe, a safer design can be
obtained by raising the target reliability index. Such flexibility and automatic reflec-
tions of parametric sensitivities and correlations are not found in a Eurocode design
based on code-recommended partial factors.

v. Note that the back-calculated partial factors are corollary by-products of an RBD,
which requires statistical inputs (mean values, standard deviations, parametric cor-
relations, and probability distributions) but not partial factors or characteristic values.