Reliability-based multi-objective optimisation for the design of vegetation planting strategy on landfill cover systems

Existing design criteria lack specific recommendations for vegetation planting strategies of final landfill cover systems. Factors such as inherent uncertainties in cover material and plant properties are generally ignored in design. Moreover, the current design mainly focuses on ensuring effectiveness while ignoring the total cost and carbon impact. In this study, a reliability-based multi-objective optimisation framework is developed for designing vegetated final cover systems. This framework balances the probability of failure (p_f, the probability that percolation exceeds a recommended limit), total cost, carbon sequestration and emissions of final cover systems. A numerical model integrated with a stress-dependent soil water retention curve and the hydraulic influence of vegetation is validated through soil column tests. The optimal planting strategy, including the selection of root architecture, depth, and plant spacing, is then determined. It is found that a triangular root is more effective in reducing p_f (by up to 3 orders of magnitude) than a uniform root, regardless of plant spacing and root depth. Increasing plant spacing from 0.5 m to 1.5 m in increments of 0.25 m raises p_f by at least 2 orders of magnitude for both root architectures. Conversely, increasing root depth from 0.3 m to 1.0 m in increments of 0.2 m (associated with greater biomass) reduces p_f by at least 77 % with the two root architectures considered. The optimal design, among 32 planting scheme combinations investigated, is a triangular root architecture with a 0.5 m planting spacing and a 0.3 m root depth. This combination can achieve high performance while minimising total cost and net carbon emission (carbon emission minus carbon sequestration).