Eco-design of airborne sound insulation in Recycled Lightweight Concrete walls for Brazilian social housing: A reliability-based approach

In Brazil, normal strength concrete (NSC) and steel bars are commonly used to construct residential buildings with concrete walls. However, recent discussions have highlighted the environmental impact of these traditional methods, particularly in terms of carbon footprint and the use of virgin materials. In response, alternative materials such as lightweight recycled coarse aggregates are promising. While Eco-design often focuses on structural and material aspects, acoustic efficiency is often neglected. This paper focuses on the airborne sound insulation of a single-story house in a Brazilian housing program constructed using a concrete wall system made of NSC. An accurate experimental validation was carried out in this house, recording a measured and simulated Weighted Standardized Level Difference ($D_{nT,w}$) of 50 dB for a partition wall between two living rooms, outperforming the national standard requirement of 40 dB. With the simulation data validated, an innovative assessment using reliability methods was proposed to analyze the sensitivity of the problem in terms of the main variables, using three alternative wall materials: NSC, Lightweight Concrete (LC) and Recycled Lightweight Concrete (RLC). A sensitivity analysis using Sobol's indices identified wall thickness, density, and Young's modulus as the most critical input parameters to the model. Monte Carlo Simulation (MCS) was used to calculate the failure probability of each assumed thickness, and Reliability-Based Design Optimization (RBDO) was used to determine the optimum thickness to meet the standard requirement. Through RBDO, we determined optimal wall thicknesses for the concrete mixes studied, aiming at a sound reduction index ($R_w$) of 43 dB, following the Brazilian standard ABNT NBR 15575-4 and ISO 12354-1. The optimal thicknesses were 7.3 cm for NSC, 11.15 cm for LC, and 10.27 cm for RLC. Innovative acoustic-carbon efficiency indices are proposed to evaluate the studied materials: the Carbon-Acoustic Efficiency Index (CAEi) and the Recyclability-Acoustic-Carbon Efficiency Index (RACEi), which are used for a comprehensive assessment of both sustainability and acoustic performance between materials. Using these indices, the study shows that RLC can definitively replace NSC for airborne sound insulation, offering additional environmental benefits such as recyclability.