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Designing civil structures such as bridges, dams or buildings is a complextask requiring many synergies from several experts. Each is responsible fordifferent parts of the process. This is often done in a sequential manner, e.g.the structural engineer makes a design under the assumption of certain materialproperties (e.g. the strength class of the concrete), and then the materialengineer optimizes the material with these restrictions. This paper proposes aholistic optimization procedure, which combines the concrete mixture design andstructural simulations in a joint, forward workflow that we ultimately seek toinvert. In this manner, new mixtures beyond standard ranges can be considered.Any design effort should account for the presence of uncertainties which can bealeatoric or epistemic as when data is used to calibrate physical models oridentify models that fill missing links in the workflow. Inverting the causalrelations established poses several challenges especially when these involvephysics-based models which most often than not do not providederivatives/sensitivities or when design constraints are present. To this end,we advocate Variational Optimization, with proposed extensions andappropriately chosen heuristics to overcome the aforementioned challenges. Theproposed methodology is illustrated using the design of a precast concrete beamwith the objective to minimize the global warming potential while satisfying anumber of constraints associated with its load-bearing capacity after 28daysaccording to the Eurocode, the demoulding time as computed by a complexnonlinear Finite Element model, and the maximum temperature during thehydration.

From concrete mixture to structural design -- a holistic optimization procedure in the presence of uncertainties