With the LSF value established, failure probability can now be defined as follows:Ī great deal of research has been done on different methods to calculate this probability. On the other hand, positive LSF values indicate adequacy of the structural capacity that is, the structure is likely to remain safe under the given load. Therefore, the structure is likely to undergo some sort of failure. Negative values of LSF imply that the capacity is not adequate to bear the applied load. Therefore, a Limit State Function (LSF) can be defined as follows: Īssume a load (or the stress and strain caused by the load) is to be applied to a structure with a load-bearing capacity of if is greater than, the structure is safe, while being greater than renders the structure unsafe, incurring a level of damage which depends on the difference between and. Such a failure may not necessarily be in the form of structural collapse and can instead be defined as a certain level of failure under what is known as “performance level” in civil engineering regulations. Safety means that structures should not fail under typical loads. The main purpose of regulations and existing approaches in the analysis and design of structures, ranging from buildings to geotechnical structures, is to ensure the safety and proper performance when subject to probable loads. This revised approach was then presented in a step-by-step flowchart, for the purpose of easy programming and implementation. In this paper, a simple algorithm was proposed to estimate low failure probabilities using a small number of samples in conjunction with the Monte Carlo method. However, it does suffer from certain disadvantages, the biggest one being the requirement of a very large number of samples to handle small probabilities, leading to a high computational cost. Among the conventional methods used to assess structural reliability, the Monte Carlo sampling method has proved to be very convenient and efficient. As such, the past few decades have witnessed the development of numerous probabilistic approaches towards the analysis and design of structures. Structural load types, on the one hand, and structural capacity to withstand these loads, on the other hand, are of a probabilistic nature as they cannot be calculated and presented in a fully deterministic way.