Multi-Gradient Structural Regimes and Irreversibility in Built Environments

Current building assessment frameworks largely rely on isolated performance indicators such as operational energy, embodied carbon, or construction cost. While these metrics provide valuable insights, they frequently fail to capture the hierarchical interactions between structural, material, infrastructural, and ecological constraints that determine long-term adaptability. This study introduces a Hierarchical Multi-Gradient Model (HMG) designed to evaluate structural rigidity, scalability, and reversibility in distributed built systems. The central hypothesis is that rigidity emerges when primary gradients—territorial, material, or infrastructural—become discontinuous or structurally locked, thereby limiting future adaptive capacity regardless of subsequent local optimisation. The model integrates six hierarchical levels: territorial gradients (GT), material–carbon gradients (G1), infrastructural gradients (GI), envelope gradients (G2), scalability gradients (GS), and adaptive economic gradients (G3). Each level is quantified through normalised indicators, including embodied carbon (kgCO₂/m²), network accessibility metrics, hygrothermal continuity indices, ecological permeability indicators, and modular extension capacity. A comparative case study evaluates three structural systems under identical boundary conditions: reinforced concrete slab construction, timber frame construction, and recycled shipping container systems with ventilated envelopes and crawl space integration. Results indicate that, under the defined boundary conditions, systems with accessible infrastructural layers and distributed material gradients exhibit higher scalability and lower long-term rigidity despite similar short-term performance metrics. The proposed multiplicative hierarchical formulation allows identification of structural thresholds where adaptability declines non-linearly. The framework contributes a decision-support methodology that integrates carbon, durability, flow continuity, and scalability within a unified analytical structure. By reframing sustainability as a function of gradient continuity rather than isolated optimisation, the HMG model offers a quantifiable tool for assessing long-term systemic resilience in building design.