[Editor May 22, 2007] The author has made changes to this article. It was updated May 8, 2007 on his website, NCS Consultants, LLC. My apologies for not publishing these changes sooner. [/Editor]

GeoPrac.net is very pleased to present this article on Load Resistance Factor Design (LRFD) for Bridge Substructure Design by Naresh C. Samtani, PE, PhD. This will hopefully be the first in a series of technical notes by Naresh on this topic. Through his firm, NCS Consultants, LLC, he is heavily involved in assisting the Arizona Department of Transportation in the implementation of the latest AASHTO code and with developing additional guidelines related to the specific soil conditions encountered in Arizona. He is also the lead instructor for the Ryan R. Berg and Associates, Inc. team of instructors for the LRFD Course for design of substructures offered through the FHWA's National Highway Institute (NHI). Don't miss this great geotechnical article.

LRFD for Bridge Substructure Design - A Note on Limit States and Interaction between Structural and Geotechnical Specialists

By
Naresh C. Samtani, PE, PhD
President, NCS Consultants, LLC (www.ncsconsultants.com)

The Load and Resistance Factor Design (LRFD) approach is currently being implemented across the United States, particularly in the realm of federally funded transportation facilities.  The American Association of State Highway and Transportation Officials (AASHTO) recently released the 4^th Edition of the Bridge Design Specifications based on the LRFD approach (AASHTO, 2007).  Starting October 1, 2007, the AASHTO-LRFD approach will have to be fully implemented by states seeking federal funding for new transportation projects.   It is important that the structural and geotechnical specialists involved in the design of such transportation facilities properly understand the basics of the LRFD approach as included in AASHTO’s specifications. 

In the context of bridge design, the substructure portion is considered to include all the elements below the level of the bridge deck.  The piers and abutments transfer the loads from the bridge deck to the foundations.  The way these loads are combined in the AASHTO-LRFD (AASHTO, 2007) approach and compared to resistances is significantly different from that in the Allowable Stress Design (ASD) approach in the 17^th Edition of AASHTO’s standard specifications for highway bridges (AASHTO, 2002).  This note briefly presents the concept of limit states in the AASHTO-LRFD framework, identifies the common limit states, discusses the basic concept of load combinations and finally provides some thoughts on the interaction between structural and geotechnical specialists in the design of highway bridge substructures.

1.0 Concept of Limit States in the AASHTO-LRFD Framework

The AASHTO-LRFD approach uses reliability (probability) theory to quantify the uncertainty in loads, Q, and resistances, R.    In the AASHTO-LRFD framework, once the load factors, g, are established by using reliability theory, the factored loads are combined as discussed in Section 3.0 to create a maximum load effect.  A specific resistance factor, f, is then developed corresponding to the load combination(s) based on measured resistances and their computed variances from nominal resistances predicted by numerical models for resistance, e.g., the b-method for side friction of drilled shafts in sands.  Similar to the loads, the uncertainties in the resistances are quantified based on reliability (probability) theory.  The load and resistance factors include a consideration of the differences between measured and nominal values of the loads and resistances, respectively.

By using factored loads, γQ, and factored resistances, φR, the designer can establish a limit state, γ.     A limit state is a condition beyond which the bridge or component ceases to satisfy the provisions for which it was designed.  The limit state may be defined by linear (addition or subtraction) and/or non-linear (product or ratios) combinations of factored loads and factored resistances.  The linear version, γ = φR-γQ ≥ 0, is the most commonly used formulation of a limit state in the AASHTO-LRFD framework.  From practical considerations, an acceptable risk level is determined for each limit state, i.e., the probability that φR-γQ < 0, because otherwise the design for the case of φR-γQ ≥ 0 (i.e., no failure) will be very expensive.  Thus, in the AASHTO-LRFD approach, safety considerations are incorporated through load and resistance factors derived on the basis of an acceptable level of risk or acceptable probability of failure.  This process is in contrast to the traditional ASD approach (AASHTO, 2002) where safety is achieved with a single factor of safety applied to the resistance to obtain an allowable stress (or load). 

It is important to realize that when the load and resistance factors are developed in the limit state concept as described above, they are completely tied to each other and form a pair.  In other words, neither the load nor the resistance factor can be changed unilaterally in the AASHTO-LRFD framework.  This does not mean that these factors cannot be changed based on local practices or past successful practices.  Rather it means that if one factor is changed, the owner/designer should perform the appropriate reliability-based calibration computations to determine the other factor.

2.0 Common Limit States in Bridge Substructure Design

In the AASHTO-LRFD framework, there are five distinct limit states: (a) strength (or ultimate) limit states, (b) serviceability limit states, (c) extreme event limit states, (d) fatigue limit states and (e) constructability limit states.  For most cases, the routine design of a bridge or a component is generally governed by either the strength or the service limit states.  These common limit states are briefly discussed below (Samtani and Nowatzki, 2006):

• Strength (or ultimate) limit states are limit states that pertain to structural safety.  These limit states may be reached through either geotechnical or structural failure.  Evaluation of strength limit states is based on inelastic behavior of the structure, which is accomplished by using increased or factored loads (i.e., γ > 1.0) and on modification of soil behavior, which is accomplished by using reduced or factored strengths (i.e., φ < 1.0).  From a geotechnical viewpoint, strength limit states are reached when they involve the partial or total collapse of the structure due to sliding, bearing capacity failure, etc.  For well-designed structures strength limit states have a low probability of occurrence.
• Serviceability limit states are the limiting conditions affecting the function of the structure under expected service conditions.   Serviceability limit states occur before collapse.  These include conditions that may restrict the intended use of the structure, e.g., excessive total or differential settlements, cracking, local damage, rough rideability, etc.  Evaluation of serviceability limit states is usually performed by using expected service loads (i.e., load factors = 1.0), nominal strengths (i.e., resistance factors = 1.0) and elastic analyses.  Compared to strength limit states, the serviceability limits states have a higher probability of occurrence but, if exceeded, involve less danger of loss of life.

3.0 Load Combinations in Limit States

Because there are many different types of loads, the manner in which the loads are combined to create a limit state has sometimes been unclear in the traditional use of ASD.  For instance, it is unlikely that the most extreme values of the live loads, wind load, stream load, and earthquake load will occur at the same time.  The AASHTO-LRFD provides a solution to this problem by specifying several load combinations with load factors based on probability of occurrence.  In essence, the AASHTO-LRFD approach implements Turkstra’s rule (Turkstra, 1970) which is based on the observation that when one load component reaches an extreme value, the other load components are often acting at their average values.  In other words, the probability of two or more load components acting at their extreme values simultaneously is so remote that it is negligible.  Turkstra’s rule states that for i load components, the designer should consider i possible combination of the loads to get the maximum value of the total load.  The essence of this rule is reflected in the AASHTO-LRFD approach by consideration of several load combinations within each limit state, e.g., Strength I, Service II, etc.  The intent of each load combination is to create a maximum load effect.  The key is that in the AASHTO-LRFD framework, each combination of the loads within a given limit state has an equal probability of occurrence. 

Since each combination of load has an equal probability of occurrence, all possible applicable load combinations in all limit states should be considered in design.  Note that not all possible load combinations may be applicable for a given bridge structure, e.g., Strength IV may not govern for low (< 3) dead load to live load ratios as in the case of short-span bridges.  For the new user who may not be familiar with such considerations, it may be prudent to check all possible load combinations and then develop a feel for the applicable load combinations for a given bridge structure.

4.0 Role of Structural and Geotechnical Specialists in LRFD Framework

Since the substructure elements include both structural and geotechnical aspects it is imperative that the structural and geotechnical specialists work together during the design of substructures.   For example, in the design of a deep foundation it is necessary to consider limit states with respect to various factors such as structural axial strength, soil strength, lateral load behavior, structural lateral strength, settlement, scour, ship impact response and earthquake response.  This degree of complexity necessitates an interaction between the structural and geotechnical specialists.  During this interaction, it is important for both structural and geotechnical specialists to develop an understanding of each other’s work and refrain from adding “comfort” factors to the nominal load and resistance values to account for their discomfort or mistrust in each other’s preference.  Such “comfort” factors can lead to modification of the load and the resistance factors to an extent that they may not be applicable as developed for various limit states in the AASHTO-LRFD framework.  Such modifications can lead to spurious designs, which may be either overly conservative or unsafe.  Overly conservative designs misuse tax payer’s money while unsafe designs can lead to failures that may result in loss of life and/or potential litigation.

Acknowledgement:  The author wishes to acknowledge Dr. Edward A. Nowatzki, PE, Principal Engineer of NCS Consultants, LLC, for his effort in reviewing this article and providing comments.

References

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