Probabilistic forensic assessment of a collapsed concrete grandstand element under a jumping crowd load

H.J.J. Weijs ¹, R.D.J.M. Steenbergen ^{1, 2}, M.A.N. Hendriks ³

¹ TNO Mobility and Built Environment, Reliable Structures, the Netherlands
² Ghent University, Faculty of Engineering and Architecture, Belgium
³ Delft University of Technology, Faculty of Engineering Structures, the Netherlands

On the 17^th of October 2021, a concrete grandstand element collapsed at the Goffert football stadium in the Netherlands under a jumping crowd load. In this paper the cause for the collapse is investigated from a probabilistic point of view. Various investigations raised some belief that the actual loads were larger than the design loads for the grandstand elements, also questioning the general reliability of these elements. There are also indications towards construction errors. This paper presents a full probabilistic method to determine the failure probability of the collapsed element in the Goffert stadium, subjected to dynamical crowd loads. Suitable distribution types and parameters of stochastic variables related to forces generated by jumping are derived. Randomly generated excitation signals are created that are used to excite the structure, which is modelled as a non-linear single-degree-of-freedom system with a bi-linear force-displacement relationship. A Monte Carlo simulation shows that 0 of about 10⁵ simulations lead to failure of the structure under the crowd loading present during the collapse, if we would model it according to the design drawings. This result makes it unrealistic that the actual loads were higher than the design loads or that the design is unsafe since then we would expect a relatively large failure probability. In situ inspection of the concrete cover on other elements in the stadium show that large variation exists in this parameter, suggesting that the collapsed element could have had a large cover, which reduced its capacity. A sensitivity analysis concludes that the post-yielding stiffness highly influences the failure probability of the grandstand element. These two points combined make it more plausible that the element failed because the actual resistance of the structure was weaker than intended by the design drawings.

Key words: Structural reliability, forensic engineering, jumping loads, concrete grandstand elements, non-linear dynamical analysis

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	Probabilistic forensic assessment of a collapsed concrete grandstand element under a jumping crowd load H.J.J. Weijs ¹, R.D.J.M. Steenbergen ^{1, 2}, M.A.N. Hendriks ³ ¹ TNO Mobility and Built Environment, Reliable Structures, the Netherlands ² Ghent University, Faculty of Engineering and Architecture, Belgium ³ Delft University of Technology, Faculty of Engineering Structures, the Netherlands On the 17^th of October 2021, a concrete grandstand element collapsed at the Goffert football stadium in the Netherlands under a jumping crowd load. In this paper the cause for the collapse is investigated from a probabilistic point of view. Various investigations raised some belief that the actual loads were larger than the design loads for the grandstand elements, also questioning the general reliability of these elements. There are also indications towards construction errors. This paper presents a full probabilistic method to determine the failure probability of the collapsed element in the Goffert stadium, subjected to dynamical crowd loads. Suitable distribution types and parameters of stochastic variables related to forces generated by jumping are derived. Randomly generated excitation signals are created that are used to excite the structure, which is modelled as a non-linear single-degree-of-freedom system with a bi-linear force-displacement relationship. A Monte Carlo simulation shows that 0 of about 10⁵ simulations lead to failure of the structure under the crowd loading present during the collapse, if we would model it according to the design drawings. This result makes it unrealistic that the actual loads were higher than the design loads or that the design is unsafe since then we would expect a relatively large failure probability. In situ inspection of the concrete cover on other elements in the stadium show that large variation exists in this parameter, suggesting that the collapsed element could have had a large cover, which reduced its capacity. A sensitivity analysis concludes that the post-yielding stiffness highly influences the failure probability of the grandstand element. These two points combined make it more plausible that the element failed because the actual resistance of the structure was weaker than intended by the design drawings. Key words: Structural reliability, forensic engineering, jumping loads, concrete grandstand elements, non-linear dynamical analysis