A Masterful Symphony of Strength and Stability: An Exquisite Analysis System for the Load-Bearing Behavior of Stepped Block Arch Bridge Foundations

Across the central and western expanses of China, where soft rock formations dominate the geological landscape, arch bridges have long reigned supreme as the preferred structural choice. Their foundations, ingeniously engineered with a stepped-block configuration, boast exceptional overall rigidity—striking a masterful balance between structural integrity and economic efficiency by curbing infrastructure costs without compromising on deformation resistance. Drawing upon the foundational engineering of the Lantian Yangtze River Five Bridges, this study embarks on a profound investigation into the load-bearing behavior of stepped block foundations embedded within soft rock strata. It introduces a refined rigid-flexible judgment criterion and unveils an advanced, standard-anchored Optimization Specification C Method for stress-displacement analysis—a paradigm shift in computational precision. A novel analytical formula for the local shear failure angle is derived, shedding light on the underlying mechanics of shear collapse, while the verification framework for foundation deformation characteristics is meticulously enhanced. The culmination of this research is a comprehensive, high-fidelity bearing performance analysis system, exquisitely tailored for practical engineering application. Key findings reveal that both the rigid-flexible classification and the Optimization Specification C Method are eminently suited for assessing the bearing capacity of stepped arch foundations in soft rock environments, with design protocols firmly advocating for rigid foundation behavior under displacement-controlled criteria. The newly developed computational model transcends traditional limitations by delivering multidimensional output—capturing not merely singular values but the intricate spatial distribution of stress and displacement across the foundation zone. Remarkably, the Optimization Specification C Method achieves a 34% reduction in relative error compared to conventional standards, underscoring its superior accuracy, reliability, and real-world applicability. Critically, under conditions of global horizontal sliding of the arch structure, localized shear failure may initiate within the frontal rock mass adjacent to the stepped foundation. Furthermore, four distinct failure modes have been identified, each intrinsically linked to specific geometric configurations of the stepped block foundation—implying that optimal design must be guided by precise evaluation of the failure angle. By integrating bearing capacity assessments with stringent displacement control benchmarks, a holistic evaluation of foundation performance is achieved. While the current arch bridge foundation design successfully satisfies all load-bearing requirements, its deformation response reveals considerable untapped potential for refinement. Engineering case analyses further confirm that conventional single-dimensional performance checks, though inherently conservative and generally safe, fall short of capturing the full complexity of foundation behavior.