Efficient method for probabilistic finite element analysis with application to reinforced concrete slabs

• M-DRM implementation for stochastic FEA of large scale and/or complex structures.
• Numerical accuracy and computational efficiency of the M-DRM.
• Capability of the M-DRM for deriving the probability distribution of the response.
• Use of the Python programing language for applying stochastic FEA in ABAQUS.
• Check of punching shear code provisions under material uncertainty.

In this paper, probabilistic finite element analysis (FEA) is applied using the Monte Carlo simulation (MCS) and the multiplicative dimensional reduction method (M-DRM). M-DRM is proposed for stochastic FEA of large scale and/or complex problems, as it provides the probability distribution of the structural response, apart the statistical moments, and requires fairly small computational time. MCS and M-DRM results are compared, indicating that both are in a good agreement. In addition, sensitivity analysis is also performed using the M-DRM, which does not require any extra analytical effort. The probabilistic FEA is applied with the use of the ABAQUS software, where the development of the FEA model and the updating of each input random variable for the required simulations, are both implemented with the use of the Python programing language. Two previously tested reinforced concrete flat slabs, with and without shear reinforcement, are examined. The concrete damaged plasticity model is used for the modeling of the concrete, which is offered in ABAQUS. The results of the deterministic FEA simulation show reasonable response compared to the behavior of the test specimens in terms of ultimate load, deflection and cracking propagation. For the probabilistic analysis, only the material uncertainty is taken into account, in order to examine the accuracy and efficiency of the proposed M-DRM framework and the contribution of the material uncertainty to the output response. Finally, design codes (ACI 318-11 and EC2 2004) for punching shear and the critical shear crack theory (CSCT 2008, 2009) are examined, considering the same input uncertainties. Useful outcomes are presented indicating the predictive capability of the proposed probabilistic FEA for future studies.