Reliability Based Optimal Design of Steel Grain Silos under Random Discharge Pressures and Time Dependent Corrosion: A Life Cycle Cost Approach with Contamination Risk Considerations

Abstract

Steel silos that store grain are not just simple containers; they are critical nodes in the global food supply chain. Their failure – whether by buckling, seam rupture, or even gradual corrosion – can destroy hundreds of tonnes of food and sometimes introduce heavy metals into the stored product. This paper tries to tackle two main sources of uncertainty: the random nature of discharge pressures (which depend on the grain’s friction properties and the silo’s geometry) and the slow, time‑dependent wall thinning caused by organic acids from moist grain. A reliability‑based design optimisation (RBDO) framework is developed for a 10 m diameter, 20 m tall wheat silo. A detailed 3D finite element model (Abaqus) is built, and then a Gaussian process surrogate is trained on 500 FE runs to make the optimisation computationally feasible. Four failure modes are considered: local buckling, first yield, seam fatigue, and – unusually but importantly – grain contamination by leached heavy metals (lead, cadmium, chromium) from corroded steel. Corrosion is modelled as a power‑law process with parameters fitted from inspection records of 45 real silos. The RBDO minimises the total expected 50‑year life‑cycle cost (initial steel, maintenance, failure risk) while keeping the annual reliability index above β = 3.5. The optimal design uses a thicker lower wall (9.5 mm vs. 7 mm in a deterministic Eurocode design), variable stiffener spacing, and a mix of S355 and S235 steel. This design reduces the total expected cost by about 38% compared to a conventional deterministic design, mainly by slashing the failure risk in the silo’s later life. Sensitivity analysis shows that the wall friction angle is the most influential uncertain parameter. The paper also borrows insights from recent studies on heavy metals in medicinal plants and food products – work by Alinia‑Ahandani and colleagues in Iran – to argue that contamination monitoring should become part of structural design codes for food storage facilities.