Geomechanical method for determining stability

Abstract

A geomechanical governance system and method called Unified Shrinkage Stoping (USS) is presented, designed for evaluating the stability of critical underground excavations in rock masses subjected to high horizontal compression regimes, prevalent in the Pacific Ring of Fire. The method integrates the empirical analysis of Mathews' Stability Chart N with two novel analytical corrections that address the limitations of the current state of the art. Technical Problem and Novelty (Inventive Leap): The geomechanical design of critical underground excavations is traditionally based on determining the Stability Number (N = Q times A times B times C), assuming a standard horizontal stress factor of k=2. The USS method addresses the following shortcomings: Tectonic Underestimation (k greater than or equal to 3): In plate convergence environments such as the Andean orogeny, the k factor consistently ranges between 2.5 and 3.5.The limitation of the standard curves ak=2 leads to an underestimation of the maximum induced stress and an overestimation of the Stability Number, generating errors in the Factor of Safety of up to 50%. The Ruiz Molina algorithm dynamically penalizes the A factor, reducing the N by at least 21 percent for k=3, shifting the evaluation from a stable zone to a transition zone. Dimensional Failure (2D): The stability analysis of long galleries, where the length is much greater than the width and height, is usually based on the simplification of Plane Stress (2D). This approach is inadequate for the stability of the roof or slab, since under these dimensions the rock behaves like a beam or plate under load. Key Claims: The procedure is claimed for the following essential features: Claim 1: Tectonic Correction.An improved procedure incorporating the evaluation of the Stress Factor (A) using design curves that allow the use of a Tectonic Activity Factor (k) with a numerical value of 3 or higher, preventing overestimation of the Stability Number in contexts of high horizontal compression. Claim 2: Extreme Geometry Analysis. A procedure that, for excavations with a high slenderness ratio, adds a complementary analytical methodology based on Beam or Plate Theory to estimate the safety factor against roof bending and the potential fall height of the roof for support design. Claim 3: Column Optimization. The procedure includes the vector calculation of load on inclined columns for optimization of the Extraction Ratio.Industrial Application: This procedure is applicable to the underground mining industry for the design of critical infrastructure such as haulage drifts, extraction tunnels, and stopes in deposits located in areas of high seismic activity. In addition to ensuring operational safety, it allows for a legal reduction in the financial guarantees required for mine closure plans by demonstrating the long-term physical stability of the mining unit.