Dynamic failure analysis and support optimization for web pillars under static and dynamic loading using catastrophe theory

Abstract

Web pillars enduring complex coupled loads are critical for stability in high-wall mining. This study develops a dynamic failure criterion for web pillars under non-uniform loading using catastrophe theory. Through the analysis of the web pillar-overburden system’s dynamic stress and deformation, a total potential energy function and dynamic failure criterion were established for web pillars. An optimizing method for web pillar parameters was developed in highwall mining. The dynamic criterion established was used to evaluate the dynamic failure and stability of web pillars under static and dynamic loading. Key findings reveal that vertical displacements exhibit exponential-trigonometric variation under static loads and multi-variable power-law behavior under dynamic blasting. Instability risks arise when the roof’s tensile strength-to-stress ratio drops below 1. Using catastrophe theory, the bifurcation set D<0 signals sudden instability. The criterion defines failure as when the unstable web pillar section length l1 exceeds the roof’s critical collapse distance l2. Case studies and simulations determine an optimal web pillar width of 4.6 m. This research enhances safety and resource recovery, providing a theoretical framework for advancing highwall mining technology.

1. Introduction

Highwall mining is an important method for recovering overlying coal resources under the final boundary slope of open-pit mines [1]. When recovering residual coal resources using highwall mining technology, a highwall machine is employed for drifting mining on the outcropping coal seam of the final boundary slope, forming multiple independent mining roadways. Web pillars are left between the roadways to ensure the safety of the mining process [2–4], as shown in Fig. 1. However, the non-uniform static loads of overlying rock strata and frequent blasting vibrations exert extremely adverse effects on the web pillars. If the design of web pillar parameters is unreasonable, they will fail to effectively bear external loads, leading to disasters such as mining opening collapse or even landslides, resulting in severe resource waste and economic losses [5–8]. Therefore, studying the failure mechanism of web pillars under the coupling effect of non-uniform static loads from overlying rock strata and blasting dynamic loads, and proposing a reasonable method for designing web pillar parameters, is of great significance for the safe and efficient continuation of highwall mining in open-pit mines [9].

Numerous scholars have conducted extensive research on the stability and parameter design of web pillars in highwall mining. Early studies mainly focused on the mechanical behavior of web pillars under static loads. After coal seam excavation and unloading, the vertical stress of web pillars is significantly higher than the initial in-situ stress of the original stratum. Based on the constitutive relationship of columns under compression, scholars divided them into elastic and plastic zones and analyzed the stress-strain distribution law through numerical simulation to determine the width of the elastic-plastic zone [10–12]. Wang et al. [13] established an analytical model for the width of the elastic-plastic zone of web pillars under stress superposition based on the Drucker-Prager criterion, improving the zoning theory under static loads. Porathur et al. [1] introduced correction coefficients on the basis of traditional empirical formulas.