Key Takeaways & Executive Findings
- •• An improved 3D model accurately calculates backfill vertical stress at varying mine depths and positions along stope length, with error rates below 4% versus numerical simulation. • Maximum vertical stress σzz,max is positively correlated with rock-backfill closure; it increases with mine depth and backfill elastic modulus, but decreases with stope width, stope inclination, backfill friction angle, and rock mass elastic modulus. • σzz,max peaks at a stope length of 150 m and remains insensitive to rock-backfill interface parameters. • Reducing σzz,max improves backfill stability, providing direct guidance for backfill strength design and safe deep-mining pillar recovery.
Abstract
During upward horizontal stratified backfill mining, stable backfill is essential for cap and sill pillar recovery. Currently, the primary method for calculating the required strength of backfill is the generalized three-dimensional (3D) vertical stress model, which ignores the effect of mine depth, failing to obtain the vertical stress at different positions along stope length. Therefore, this paper develops and validates an improved 3D model solution through numerical simulation in Rhino-FLAC3D, and examines the stress state and stability of backfill under different conditions. The results show that the improved model can accurately calculate the vertical stress at different mine depths and positions along stope length. The error rates between the results of the improved model and numerical simulation are below 4%, indicating high reliability and applicability. The maximum vertical stress (σzz, max) in backfill is positively correlated with the degree of rock-backfill closure, which is enhanced by mine depth and elastic modulus of backfill, while weakened by stope width and inclination, backfill friction angle, and elastic modulus of rock mass. The σzz, max reaches its peak when the stope length is 150 m, while σzz, max is insensitive to changes in rock-backfill interface parameters. In all cases, the backfill stability can be improved by reducing σzz, max. The results provide theoretical guidance for the backfill strength design and the safe and efficient recovery of ore pillars in deep mining.
1. Introduction
The application of backfill in the upward horizontal layered mining method offers significant safety, economic, and environmental benefits [1]. Specifically, it can improve the stability of surrounding rock [2], minimize ore depletion, and enhance ore recovery [3]. However, if the backfill lacks sufficient strength to maintain stability, it may fail during the recovery of the cap and sill pillars, threatening the safety of workers and equipment and increasing ore depletion [4, 5]. Thus, it is necessary to determine the stress state of backfill for ensuring safe and efficient pillar recovery [6].
The stress state of backfill in mine stopes is crucial for evaluating its stability [7]. When assessing the three-dimensional (3D) stress state of the backfill in a mine stope, it is typically simplified to plane strain conditions [8] by two-dimensional (2D) theoretical modeling [9−12]. Most studies on the 3D stress state of the backfill assume that it is situated in a vertical stope [13−15], with limited consideration given to inclined stopes [7]. Furthermore, the current generalized 3D model for the vertical stress state of backfill fails to explain its variations with mine depth and the position along stope length. Additionally, as the backfill tends to settle after deposition, frictional stresses develop along the rock interface [7]. This will lead to the transfer of loads from backfill to rock mass and the formation of rock-backfill closure [4]. The extent of the closure is influenced by various factors [4, 16], such as mine depth, stope geometric parameters, backfill mechanics, and rock mechanics parameters.
Numerical modeling is an effective method for analyzing the stability and stress state of backfill [4, 8]. This can assess the stability of side-exposed backfill [17], simulate rock-backfill closure through surrounding rock deformation [18], and evaluate the impact of rock-backfill closure on the uniaxial compressive strength (UCS) of the backfill [4]. The maximum stress that the backfill can withstand before failure is typically determined by uniaxial compression test [19−21]. For safe stope operations, the backfill requires a UCS of not less than 300 kPa [22]. The UCS denotes the maximum vertical stress at which the backfill fails in uniaxial compression test [23, 24], underscoring the critical role of vertical stress in evaluating the stability of backfill.
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LIU Chun-kang, WANG Hong-jiang, WU Ai-xiang, LI Hao (2025). Improved model-based study of backfill stress distribution considering rock-backfill closure, mine depth, and position along stope length. Journal of Central South University. https://doi.org/10.1007/s11771-025-6007-2
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Frequently Asked Questions
What does the improved 3D model predict?
The improved three-dimensional model predicts the vertical stress distribution in backfill at different mine depths and positions along the stope length, unlike the generalized 3D model which ignores depth effects. It has been validated against Rhino-FLAC3D numerical simulations with error rates below 4%.
How does mine depth affect backfill vertical stress?
Mine depth enhances the degree of rock-backfill closure, which in turn increases the maximum vertical stress (σzz,max) in the backfill. Thus, deeper mining conditions generally lead to higher backfill stress and require careful strength design.
What is rock-backfill closure and why is it important?
Rock-backfill closure refers to the deformation and load transfer that occurs when backfill settles and interacts with the surrounding rock mass. It is crucial because it directly influences the vertical stress distribution and stability of the backfill, affecting pillar recovery safety.
At what stope length does the maximum vertical stress peak?
The maximum vertical stress (σzz,max) reaches its peak when the stope length is 150 m. Beyond or below this value, σzz,max tends to be lower, though it remains insensitive to changes in rock-backfill interface parameters.
How can backfill stability be improved?
Backfill stability can be improved by reducing the maximum vertical stress (σzz,max). This can be achieved by controlling factors such as stope width, stope inclination, backfill friction angle, and the elastic modulus of rock mass, or by adjusting backfill elastic modulus and mine depth as part of the design.
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