A reliability assessment of grandstand elements

Abstract

On the 17th of October 2021, a concrete grandstand element collapsed at the Goffert stadium in the Netherlands after a crowd jumped on it for 8 seconds. An investigation by an engineering consultancy firm concluded that the design loads in the building code are too low, raising questions about the safety of grandstand elements. Currently, no method to assess the reliability of grandstand elements exists.

This thesis presents a state-of-the-art method to determine the reliability of concrete grandstand elements. The reliability is assessed by performing a non-linear dynamical analysis. The element is modelled as a non-linear single-degree-of-freedom system. Excitation signals are synthetically generated by consulting the literature and by analyzing a data set of jumping crowds. A bi-linear force- displacement relationship based on technical drawings of the collapsed grandstand element is adopted and extended by a model uncertainty parameter which accounts for both the non-linearity of the analysis and the uncertainty related to the dynamical basis of the analysis. The reliability is determined through a Monte Carlo simulation: almost 100,000 simulations can be performed per assessment.

Out of the 100,000 simulations, 0 failed. This result is not in line with what happened; one failed out of only a few elements. This gives rise to two different investigations. On the one hand, the failure of the Goffert stadium grandstand elements has to be explained. On the other hand, the lifetime reliability of a grandstand element has to be determined.

The first assessment indicated that if the element’s resistance conforms to the technical drawings, there is no cause for concern regarding its reliability. Measurements on 23 other grandstand elements in the same stadium showed a high variation in the concrete cover. The collapsed element was, therefore, also likely subjected to a high variation in the concrete cover. To understand the influence of an increased concrete cover on the reliability, two additional analyses were performed, where the post-yielding resistance of the structure was slightly reduced. This resulted in an increase in the probability of failure, which indicates that this parameter plays a crucial role in determining the reliability of grandstand elements. These points combined make it more plausible that the element failed because the concrete cover was larger than intended rather than the design loads being too low, as concluded by the engineering firm.

When investigating the lifetime reliability of grandstand elements in general, no collapse is expected after 8 seconds but rather after 30 seconds or even longer durations. Therefore, two additional analyses were performed where signals of longer durations (120 seconds and 300 seconds) excited the system. In these analyses, it is assumed that the resistance of the grandstand element conforms to the technical drawings. Signs of a converged reliability were perceived as 120- and 300-second excitation signals led to a probability of failure of the same order of magnitude, indicating that a steady-state solution is obtained after 120 seconds of jumping. In that case, the lifetime reliability of a grandstand element would be equal to the 120-second reliability. The corresponding reliability passes the lifetime reliability requirements for existing structures in consequence class 2 (for a reference period of 15 years).

While the results presented are estimations, and a larger sample size is needed for a converged probability of failure, the proposed method provides a valuable framework for assessing the reliability of grandstand elements. This method can easily be extended to any grandstand element by changing the model parameters, and the true reliability of grandstand elements can be assessed by performing more (1-10 million) simulations.