# Distinct forms of application of the limit state method

As mentioned above, the limit state method has been applied in several distinct ways, which can be grouped under two major categories, designated by several authors as the European concept and the American concept (Ovesen and Orr, 1991; Becker, 1996a). Figure 3.6 illustrates, in a simplified manner, the difference between the two concepts, which is essentially based on the form of calculation of the resistance, R.

As shown in Figure 3.6a, in the so-called European concept, after selecting the characteristic values of the ground resistance properties, these are reduced by partial safety factors in order to obtain the corresponding design values, which are then introduced into the calculation models and lead to the design value of the resistance, Rd. The designation of this approach as European is justified because of its adoption by the Danish Geotechnical Code in 1965, following the pioneering work of Brinch Hansen (1953, 1956).

Figure 3.6 Comparison of limit state design approaches for ultimate limit states: a) European concept; b) North American concept (Ovesen and Orr, 1991).

In order to preserve this level, it does not make sense to modify one of these factors without adjusting the others.

As shown in Figure 3.6b, in the American concept, the characteristic values of the ground strength properties are directly used in the calculation models that supply the characteristic or nominal value of the resistance, R,„ which is then reduced by a resistance factor, Ф, in order to obtain the value of the factored resistance, <2>R„. The American concept is known as Load and Resistance Factor Design (LRFD).

There is considerable debate concerning the advantages and disadvantages of either methodology (Becker, 1996a; Simpson and Driscoll, 1998).

The European concept seems more elaborate, because it applies the partial safety factors to the material strength properties, which are the variables most affected by uncertainty. In so doing, it manages to calibrate the value of the partial safety factors according to the nature of the strength parameters (for instance, decreasing the undrained shear strength more than the angle of shearing resistance). The most pertinent limitation that is generally pointed out involves the fact that the failure mechanism considered in the calculation models depends on the values of the soil strength properties. Therefore, by reducing these properties, the mechanism can change and hence so can the computed resistance.

In the American concept, on the other hand, the resistance factor is meant to cover not only the uncertainties relative to the strength properties, but also those affecting the geometrical data and, additionally, the limitations of the methods or models used in the evaluation of the resistance.1

Another aspect to be considered in this context is that, in many cases, the resistance in geotechnical design is evaluated not by means of theoretical calculations (introducing the ground strength parameters), but with load tests (as in the case of pile foundations and ground anchors), or by empirical or semi-empirical correlations with in situ test results (for the design of shallow foundations from PMT results, for example). In these situations, the application of a resistance factor, in accordance with the American concept, does not raise difficulties, as would happen with the application of the European concept.

As will be seen later, the current version of Eurocode 7 (EN 1997-1: 2004) establishes three design approaches that follow not only the European concept but also the American concept (see Section 3.6). The latter is at the foundation of the American and Canadian design codes and will later be presented in more detail (see Section 3.7).