Consolidation of Sinking Infrastructures by Pore Pressure using XYY' Calculus

Abstract

The consolidation of sinking infrastructures on soft soils is characterized by unknown initial conditions () and ambiguous boundary conditions (type, shape, and size of drainage). Under these forensic conditions, classical Newton-Leibniz chronological frameworks and traditional consolidation methodologies fail, triggering the "Missing Time" problem. This paper introduces the application of the XYY' Calculus framework—originating from complex soil mechanics in the mid-1990s—to model infrastructural consolidation using exclusively localized pore pressure measurements, completely bypassing the need for physical settlement data. By transforming the process from the chronological time domain into a geometric state-space, pore water pressure is mapped directly against its instantaneous dissipation rate. This proves that late-stage consolidation converges into an invariant linear phase-space trajectory known as the Master Decay Asymptote. This linearity encapsulates the universal Central Operator (), allowing for the flawless extraction of the coefficient of consolidation () irrespective of initial loading times. The technique isolates pure hydrodynamic diffusion from secondary structural creep, rendering it a robust mechanism for 3D underground mapping. Optimal piezometer placement strategies permit the determination of vertical  at 30% to 40% consolidation, while radial consolidation parameters can be extracted at just 5% to 10% consolidation. This framework simplifies complex partial differential equations into linear algebraic relationships, providing ideal normalized feature sets for AI and Machine Learning applications in modern computational geomechanics. This is particularly useful for global infrastructure challenges like the Mexico City's subsidence, Kansai Airport, Jakarta City, the MOSE project Venice etc