Robust Design Optimization of Concrete Circular Underground Pipes Considering Seismic Effects

Abstract

Robust design optimization (RDO) of an existing underground reinforced concrete pipe subjected to seismic load is presented. The pipe considered is from a straight section of a water transmission pipeline system located in Kolkata City, India. Ovaling deformation due to earthquake is considered in the RDO. The seismic effect has been estimated by a “simplified” model based on beams on elastic foundation subjected to sinusoidal seismic waves, and validated with a more detailed nonlinear time-history analysis of the finite element model of pipe. Generally, underground structures are designed considering all parameters to be deterministic. However, along with the random seismic load, there are other parameters that are random and chaotic. To consider those, the RDO has been executed in the following two separate modules: (1) under probabilistic uncertainty; and (2) with uncertain-but-bounded (UBB) type parameters (as many system parameters cannot be ascertained accurately with their prevailing statistics). The deterministic design optimization problem is cast as a cost minimization problem subjected to moment, shear, axial thrust, and crack control constraints. The uncertainty is incorporated by Monte Carlo simulation (MCS). The probabilistic RDO case is formulated by the weighted sum method and the penalty function approach, whereas the UBB-based RDO is posed through hyperellipsoidal convex programming. The results of RDO with probabilistic parameters, UBB parameters, and the ASCE and British code-based deterministic approaches are compared. The results show that the RDO yields design solutions that require marginally higher costs than the conventional ASCE or British code-based design, even when considering the seismic effect. With the RDO approach, optimal design solutions become insensitive to uncertainty effects. It has been observed that, by accepting a marginal increment in costs, a designer can achieve a reliable, sustainable, and economical solution through the present RDO approach.