Structural engineering involves the design and assessment of systems to ensure they perform safely under a variety of conditions. In a fully probabilistic design approach, the system design is selected such that it meets a target reliability requirement, while modeling uncertainties are explicitly taken into account and represented in terms of probability distributions. However, a fully probabilistic design is challenging and is used only in special cases.
Semi-probabilistic design
For routine design approaches, simplicity and standardization are important. Therefore, a classical design in structural engineering is based on a semi-probabilistic approach to achieve a reliable design in the face of uncertainties. As in a fully probabilistic design approach, in a semi-probabilistic approach, the relevant uncertain model parameters that influence the performance of the system's response are identified. However, contrary to a fully probabilistic design approach, these uncertain model parameters are not represented by probability distributions. Instead, the uncertainties are represented implicitly through characteristic values and partial safety factors, and a deterministic model is utilized to decide whether the investigated design can be accepted.
A semi-probabilistic design aims at ensuring that the value of a so-called design capacity $R_d$ (e.g., the resistance of the system of interest) is at least as large as the value of a so-called design demand $S_d$ (e.g., the load of the system of interest); i.e., $R_d\ge S_d$.
For the trivial case with only a single uncertain model parameter $R$ on the resistance side, we can write $R_d = R_k/\gamma_R$, where $R_k$ is the characteristic value of the $R$ and $\gamma_R$ is the partial safety factor associated with $R$. For parameters that act as resistances, the characteristic value is often selected as the $5\%$ quantile of $R$.
Similarly, if only a single uncertain model parameter $S$ acts on the load side, we can write $S_d = S_k\cdot\gamma_S$, where $S_k$ is the characteristic value of the $S$ and $\gamma_S$ is the partial safety factor associated with $S$. For example, the characteristic value of the annual maximum of a load value is often associated with the $98\%$ quantile of $S$.
Calibration of partial safety factors
The partial safety factors used in a structural design are typically provided by technical standards. Historically, the safety factors provided in technical standards were selected based on historically accumulated experience. Many of the safety factors provided in the current technical standards are still influenced by the historically accumulated experience. However, an increasing number of safety factors are calibrated based on fully probabilistic considerations.
For a reliability-based calibration of safety factors, an imaginary portfolio of structures is defined (that comprises all types of structures that will potentially be designed with the respective safety factors). Based on that portfolio, the safety factors are selected such that this portfolio meets — on average — the aspired target reliability.
Limitations of partial safety factors
A semi-probabilistic design based on partial safety factors is simple, flexible and ensures a uniform level of reliability across different structures and materials. However, it is a strongly simplified approximation of a fully probabilistic design and cannot exactly achieve the aspired target reliability for each structure — only for a large portfolio of structures. In some cases, partial safety factors may lead to an overdesign, increasing costs unnecessarily. Specific uncertainties associated with a certain type of structure may lead to a consistent bias in the average reliability achieved for that type of structure.
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