Covariance matrix adaptation evolution strategy for topology optimization of foundations under static and dynamic loadings

Abstract This paper studies the topology optimization for jet-grout distribution as a structural material beneath a foundation under static and dynamic loadings. The material distribution is optimized in a manner to minimize the vertical displacement, beneath the center of the foundation, under static loading and vertical velocity under dynamic loading. For this purpose, the efficient gradient-free optimization algorithm called Covariance Matrix Adaption Evolution Strategy (CMA-ES) is used and coupled with finite element method. The important parameters that affect the optimal jet-grout layouts such as loading frequency, soil type, and foundation rigidity are explored. The results show that the jet-grout mainly tends to concentrate near the edges of the foundation. It is also observed that variations in the dynamic loading frequency, foundation rigidity, soil stiffness, and soil-foundation interaction change the layout of the structural material and mitigation capacities (MC). Furthermore, it is found that topology optimization is more operational in increasing MC value in the soft soil and type of soil-foundation interaction does not affect the ultimate MC value. The results show that as loading frequency increases, jet-grout moves to the left and bifurcates at the bottom. Moreover, flexible foundations have lower MC values in both static and dynamic loading cases.