Innovative safety framework and direct load–settlement method to optimize vertical subgrade modulus in sustainable mat foundations

This work presents a rigorously formulated methodology for directly estimating the vertical subgrade modulus ( Ks ) in slab foundations, overcoming key deficiencies of conventional indirect and semi-direct approaches. The model integrates elastic half-space theory with multilayer settlement analysis and oedometer-based consolidation mechanics, explicitly incorporating depth of influence and load compensation effects—parameters typically excluded from standard practice. The proposed formulation yields a Ks value of 5.30 MN/m 3 , closely matching the harmonic mean of established upper (17.82 MN/m 3 ) and lower (2.91 MN/m 3 ) bounds, thereby producing a modulus consistent with elastic energy principles and mechanistically grounded, suitable for advanced soil–structure interaction modeling. A new, application-specific safety coefficient for Ks is introduced, offering a calibrated metric for reliability-based foundation design under spatially variable subsurface conditions. The study implements a life-cycle sustainability assessment across three reinforced concrete slab foundation alternatives, utilizing a hybrid neutrosophic analytic hierarchy process (NAHP-G) in conjunction with the ELECTRE IS multi-criteria decision method. This framework enables integrated evaluation across structural, environmental, and socio-economic dimensions. Results indicate a 2.5-fold enhancement in the social safety index and a 50 % relative improvement in sustainability performance compared with baseline methodologies. The outcomes delineate a unified analytical and decision-making framework for subgrade characterization and foundation optimization, advancing the state of practice in geotechnical design and sustainability integration. • A direct method links raft loads to settlements for Ks estimation with high fidelity. • A novel Ks safety factor accounts for uncertainty and improves serviceability design. • The method increases safety margins 2.5× and reduces embodied impacts by 50 %. • Ks estimation for sustainable design embedded in NAHP-G and ELECTRE IS framework. • Redefines Ks as a design variable, not a soil constant, resolving decades of misuse.