  Designing civil structures such as bridges, dams or buildings is a complex
task requiring many synergies from several experts. Each is responsible for
different 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 material
properties (e.g. the strength class of the concrete), and then the material
engineer optimizes the material with these restrictions. This paper proposes a
holistic optimization procedure, which combines the concrete mixture design and
structural simulations in a joint, forward workflow that we ultimately seek to
invert. In this manner, new mixtures beyond standard ranges can be considered.
Any design effort should account for the presence of uncertainties which can be
aleatoric or epistemic as when data is used to calibrate physical models or
identify models that fill missing links in the workflow. Inverting the causal
relations established poses several challenges especially when these involve
physics-based models which most often than not do not provide
derivatives/sensitivities or when design constraints are present. To this end,
we advocate Variational Optimization, with proposed extensions and
appropriately chosen heuristics to overcome the aforementioned challenges. The
proposed methodology is illustrated using the design of a precast concrete beam
with the objective to minimize the global warming potential while satisfying a
number of constraints associated with its load-bearing capacity after 28days
according to the Eurocode, the demoulding time as computed by a complex
nonlinear Finite Element model, and the maximum temperature during the
hydration.
