Traditionally, the soundness of rock foundation design is achieved through the use of safety factors. However, as parameters uncertainties are not being considered, these methods lack to quantify the risk. An alternative method consists in computing a reliability index that depends not only on the mean values of the parameters but also on their associated uncertainties. In the present work, reliability analysis of rock foundation is performed using various known methods FOSM, FORM, SORM and Crude Monte Carlo simulation (CMCS). The analysis is performed using normal and lognormal parameter distributions and has allowed appreciating parameters uncertainties effects. This study has led to select for each design method a dominating set of parameters for a reliability analysis.


The design of foundation starts with a description of the project. In this first phase of the project, the specific requirements of capacity or limit states, and safety, based on the customer objectives are identified. These specific conditions are necessary for the engineer to design the foundation under the constraints of both safety and economy Limit states are defined as conditions under which a structure or its component members no longer perform their intended functions. For foundation under axial compression, there are two main limit states that the engineer needs to consider [1]:

  • Serviceability limit states (SLS): represent those conditions which affect the function or service requirements of the structure under expected working loads. They include conditions that may restrict the intended use of the structure, such as the excessive total or differential settlement.

  • Ultimate limit states (ULS): pertain to foundation safety, and in a sense define a dangerous state; they involve catastrophic collapse of foundation such as: sliding, overturning, ultimate bearing capacity, etc. To ensure required conformity and quality, the engineers refer to codes of practice. The role of codes is to assist the engineers in making suitable decisions to ensure safe and economic foundation design.

Codes usually provide general guidance for site investigation requirements, for appropriate choice of geotechnical properties, for loads estimates, and to specify loads combinations. However, it is quite obvious that adverse performance remains possible under particular conditions. In geotechnical engineering design, decisions are made under various large uncertainties. These uncertainties are associated to imperfect information concerning [2]:

  • subsoil profile;

  • few field or laboratory tests used to evaluate in-situ engineering soil properties;

  • magnitude and distribution of loads;

  • the mathematical model used in the engineering analysis.

Confronted with potentially contradictory criteria of unfavorable behavior and economic constraints, the engineer establishes a reasonable level of safety through empirical results and his personal experience.

Safety factor and reliability index

Traditionally, foundation analysis and design are based on deterministic approaches; commonly, a set of design parameters are adopted to evaluate the loads and resistances.

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