**4. Conclusion**

100 Stochastic Modeling and Control

**Figure 16.** Safety index against Hammer efficiency using Hiley, Janbu and Gates formulae

**Figure 17.** Safety index against Hammer- energy rating using Hiley, Janbu and Gates formulae

Reliability-based design methods could be used to address many different aspects of foundation design and construction. However, most of these efforts to date have focused on geotechnical and structural strength requirements, such as the bearing capacity of shallow foundations, the side friction and toe-bearing capacity of deep foundations, and the stresses in deep foundations. All of these are based on the difference between load and capacity, so we can use a more specific definition of reliability as being the probability of the load being less than the capacity for the entire design life of the foundation. Various methods are available to develop reliability-based design of foundations, most notably Stochastic methods, the First-Order Second-Moment Method, and the Load and Resistance Factor Design method.

Deterministic method is not a very cost-effective way to produce reliable structures; therefore, reliability-based design should be adopted to quantify reliability, and thus used to develop balance designs that are both more reliable and less expensive.

From all the preceding sections it is apparent how a stochastic modelling can contribute to the improvement of a structural design, as it can take into account the uncertainties that are present in all human projects.
