LRFD for Geotech – Note 2

LRFD for Substructures Concept of Failure and Reliability Index

By Naresh C. Samtani, PE, PhD
President, NCS Consultants, LLC
E-mail: or

Editor’s Note: Naresh is the employer of Randy Post, the owner and editor of

In a previous article (NCS, 2007), the concept of limit state in the framework of Load and Resistance Factor Design (LRFD) as adopted by American Association of State Highway and Transportation Officials (AASHTO) was discussed.  A limit state was defined as a condition beyond which the bridge or component ceases to satisfy the provisions for which it was designed.  Once a limit state is exceeded, a failure is considered to occur from the perspective of the criterion or criteria for which the design was performed. 

The word “failure” connotes an unacceptable difference between expected and observed performance (Leonards, 1982).  The simplest manifestation of a failure may be in the form of cracking of an engineered component or structure during its design life.  Other manifestations may include loss of intended serviceability, excessive maintenance costs, economic losses, collapse and/or loss of life.  Since the design for the case of absolutely no failure is theoretically impossible within the context of stochastic processes and design for a very small probability of failure will be very expensive, a certain acceptable probability of failure, Pf, needs to be defined.  Thus, from practical considerations, an acceptable risk level should be determined for each limit state, i.e., the probability that a failure can occur.  In the AASHTO-LRFD framework (AASHTO, 2007), this is achieved by defining a reliability index, β (also referred to as safety index)  The use of the term “reliability index,” has an important psychological advantage, i.e., it avoids the negative connotation of the word “failure.”  This article discusses the concept of failure and reliability index.  Readers interested in a primer on LRFD are referred to NCS (2006).