Foundation Bearing Capacity Quantification for Shallow Spherical Cavities

The patent transitions from traditional two-dimensional plane analysis to a three-dimensional spatial axisymmetric calculation model. By introducing the spherical coordinate system and considering spatial variables (radial distance, polar angle, azimuthal angle), the model comprehensively accounts for three-dimensional stress distribution around shallow-hidden spherical cavities, thereby improving assessment accuracy while maintaining computational tractability through axisymmetric assumptions.

The patent segments the stress analysis into distinct components: self-weight stress of overlying rock-soil layer, virgin rock stress, and external vertical load. Each stress component is calculated separately using appropriate theoretical formulas, and then superimposed to obtain the total stress state. This segmentation allows systematic consideration of multiple factors without overwhelming computational complexity.

The patent employs a spatial axisymmetric calculation model that incorporates three-dimensional spatial characteristics through the spherical coordinate system. The axisymmetric assumption reduces the full three-dimensional problem to a two-dimensional radial-polar problem, maintaining accuracy while reducing computational complexity. The model integrates self-weight stress, virgin rock stress, and external load effects in a unified theoretical framework.

The patent utilizes the Laplace displacement method with spherical coordinates as key parameter changes. By transforming the stress analysis into the spherical coordinate system (r, θ, φ) and applying the Laplace equation for displacement potential, the model simplifies the governing differential equations while accurately representing the three-dimensional stress field around spherical cavities.

The patent introduces the Laplace displacement method as an intermediary theoretical tool that connects measurable geometric parameters (cavity radius, depth, overburden thickness) with the complex three-dimensional stress field. This intermediary approach allows indirect determination of stress distribution and bearing capacity through solutions to the Laplace equation, avoiding the need for direct measurement of internal stress states.

The patent replaces direct mechanical measurement of complex three-dimensional stresses with theoretical calculations based on elasticity theory and the Mohr-Coulomb strength criterion. By substituting physical stress measurements with computational mechanics approaches, the model achieves reliable bearing capacity assessment using only readily obtainable geometric and material parameters.