LRFD calibration of simple limit state functions in geotechnical soil-structure design - Risk and Reliability in Geotechnical Engineering - page 332

lrFD calibration of simple limit
state functions in geotechnical
soil-structure design

Richard J. Bathurst

8.1 IntroDuCtIon

The North American practice for design of soil structures in geotechnical applications is
based on a load and resistance factor design (LRFD) approach. Limit state design equations
for failure or serviceability modes can be expressed as follows (AASHTO 2012; CSA 2006):

≥ ∑

ϕ R γ Q (8.1)

n Qi i

where R n is the nominal resistance for a particular limit state, φ is the resistance factor,
Q ni is the nominal load contribution, and γ Qi is the (corresponding) load factor. The load
terms are due to permanent and live load contributions. For typical limit state design equa-
tions found in North American design codes, φ ≤ 1 and γ Qi ≥ 1. The expectation is that by
satisfying limit state design equations expressed as Equation 8.1 , design outcomes will have
a probability of failure that is acceptable (i.e., small). For the case of a single load term, the
limit state design equation can be expressed as

ϕ R ≥ γ Q

(8.2)

n Qn

The nominal values in the above equations are typically computed using closed-form
equations that are deterministic and/or prescribed values (e.g., yield strength of a steel ele-
ment). In LRFD design , the load terms are typically determined first and then the resistance
value (R n ) is adjusted so that the limit state design equation is satisfied. LRFD calibration
involves selecting values φ ≤ 1 and γ Qi ≥ 1 so that the probability of failure for multiple nomi-
nally identical structures does not exceed an accepted value.
This chapter describes the computational details of rigorous reliability theory-based cali-
bration to select load and resistance factors for simple limit state design equations (i.e.,
Equation 8.2 ). Computational details are presented to facilitate implementation within
Excel spreadsheets. An example of the general approach is demonstrated for the steel strip
reinforcement pullout failure limit state used in the internal stability design of mechanically
stabilized earth (MSE) walls.

8.2 PrelIMInarIeS

As a starting point, consider the following simple limit state equation (performance func-
tion) with one load term:

g = R m − Q m (8.3)

339