Advances in Civil Engineering

Volume 2018, Article ID 9406839, 9 pages

https://doi.org/10.1155/2018/9406839

## Failure Depth of a Floor of a Fully Mechanized Working Face When Passing a Collapse Column

^{1}School of Energy and Safety Engineering, Anhui University of Science and Technology, Huainan, Anhui 232001, China^{2}MOE Key Laboratory of Coal Mine Safety and High Efficiency Mining, Anhui University of Science and Technology, Huainan, Anhui 232001, China^{3}School of Architecture and Civil Engineering, West Anhui University, Lu’an, Anhui 237012, China

Correspondence should be addressed to Wensong Xu; moc.qq@120978953

Received 3 May 2018; Accepted 5 August 2018; Published 16 September 2018

Academic Editor: Luzhen Wang

Copyright © 2018 Jinlong Cai et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The stress change law of a collapse column and the failure depth of a coal seam floor before and after mining when the fully mechanized coal mining face passes through the collapse column are investigated. Here, we present the constructed program in FISH language, render the damage variable in FLAC3D to establish the numerical model, and complete the numerical calculation. The 10–115 working faces that pass the collapse column at a coal mine in Tuanbai are identified as the research object. The floor failure is numerically simulated to assess the damage. The following results were obtained: the failure depth of the full floor is stabilized at 14.6 m; the maximum failure depth of the floor near the collapse column is 18.2 m; and the stress concentration coefficient is 1.27 times greater than that of normal mining. The calculated depth failure of the floor of the working face without structural defects is 14.6–14.7 m based on the Hoek–Brown criterion. With the collapse column, the failure depth of the floor is 16.8–17.8 m. According to the water injection test, the maximum failure depth of the floor is 18 m. The three derived values agree well with one another.

#### 1. Introduction

In northern China, collapse columns are widely distributed in the Permian–Carboniferous coalfields. When the compaction and cementation of the fillings in the collapse columns are poor, the columns may be activated and transformed into Ordovician limestone water inrush channels under the action of mining and other external factors, which can lead to water disasters. Collapse columns can directly affect the safe and efficient operations of coal mines [1–4]. Prior to the full mechanization of a mining face that passes a collapse column, the influence of this collapse column on mining stress and the influence of mining stress on the collapse column and floor failure of the working face both need to be established. Many scholars have studied the stress distributions of collapse columns and their surrounding rocks and the related failure depth of floors. Gao et al. [5] summarized the law of floor water inrush and proposed the preferred plane theory of water inrush. Xu et al. [6] analyzed the mechanism and criterion of the collapse column’s activation and water conduction under weak runoff conditions to improve the accuracy of water inrush forecasts. Wang et al. [7–10] explained the burst of water inrush from the floor based on cusp catastrophe theory by using mathematical mechanics. Finite difference, finite element, and other numerical simulation methods have been applied in recent years to investigate water inrush in coal seams. Wang and Yin [11] numerically simulated the stress-strain characteristics of the surrounding rocks of a mining field under the influence of collapse columns by using FLAC3D with the finite difference method. Wang and Song [12] studied the randomness and connectivity of coal floor element failures with the renormalization group method. Liu and Xiong [13] and Hao et al. [14] conducted numerical simulation and found that the passing collapse column in a fully mechanized working face mainly undergoes three stages, and the greatest impact can be observed at the side of the goaf area, which are normally formed by lagging water inrush rather than the abovementioned working face. Wang and Park [15] explained the failure and water inrush mechanisms of a coal floor in a goaf area by conducting simulation analysis in FLAC3D. Many domestic and foreign scholars have studied the fracture evolution and the weakening of materials and rocks by applying damage and fracture mechanical methods. Subsequently, the corresponding constitutive relations and strength criteria that can be applied to the collapse column model are established. Zhu and Sun [16] applied self-consistent theory to deduce the equivalent flexibility tensor of rocks and the instantaneous modulus described by Krajcinovic and Fonseka [17], who previously proposed the idea of change in flexibility of damaged bodies due to macromechanical damage effects. Xu et al. [18] and Liu et al. [19] derived the constitutive relations of fractured rock masses from the reciprocal theorem and established the damage evolution equation and the probability model with a strength criterion by employing fracture mechanics. Both authors also verified the applicability of the water inrush law of collapse columns through theoretical analysis and numerical simulation. However, no interrelations were established between the two studies.

Here, we simulate a real terrain to construct a program in FISH language, render the damage variables in FLAC3D, and complete the calculation, in which the damage and the stress and failure depth of the floor are considered, by numerically simulating the floor failure.

#### 2. Engineering Background

The minefield in Tuanbai is located at the central part of the Huoxi coalfield at the southern part of Huozhou mine. The minefield is widely covered by Quaternary loess. The exposed area of the bedrock is approximately 20% of the total area of the minefield, and it is mainly distributed in the ridge and gully areas in the midwestern area. The stratum is the lower Shihezi formation type of Lower Permian (P1x) and upper Shihezi formation type of Upper Permian (P2s). The floor elevation of #10 coal mine in the past 5 years is from +380 m to +460 m, and the average thickness is 6 m. The water level elevations of the K2 and O2 aquifers are 480 m and 520 m, respectively. Therefore, #10 coal is mined under pressure relative to the two aquifers. The fracture water of the Ordovician limestone karst is the main factor affecting #10 coal mine. In addition, the lower coal group is similar to the Ordovician limestone. The average interval between #10 coal mine and the Ordovician limestone is 36 m. The aquiclude is mainly the Taiyuan and Benxi formation types.

Collapse columns are well developed at the Tuanbai minefield with an average of 29.6 columns per square kilometer. They are rarely seen on the surface because of the Cenozoic strata coverage and the slip-and-collapse effect of rocks; in other words, they are mostly located underground and unexposed. The cross sections of the collapse columns are mainly elliptical, but some are circular or irregular. The cross-sectional areas differ in terms of dimensions. The long axis is 20–98 m (mostly 40–60 m), and the short axis is mostly 20–40 m. The largest cross-sectional area is approximately 15,000 m^{2}, and the smallest is 100 m^{2}. Most of the cross-sectional areas are approximately 1000 m^{2}. The presence of collapse columns suggests the demarcation of noncoal zones that can affect the layout of the mining area and its working face. Consequently, tunneling costs and the degree of difficulty of realizing a fully mechanized coal mine are greatly increased. Collapse columns may also indicate a water drench phenomenon, which implies water inrush, and thus can complicate the hydrogeological conditions of the mine.

#### 3. Realization of the Damage Theory in FLAC3D

A rock is a complex material composed of several mineral particles, pores, and cements. Under long-term geological conditions, rock materials inevitably acquire micropores and microcracks that are randomly distributed in different sizes and shapes. In damage mechanics, the macroscopic mechanical effects caused by the formation and development of internal defects of materials and the process and law to explain the material damages are mainly studied. The internal state variable called “damage variable” is also introduced to describe the mechanical effects of materials that contain microdefects and the mechanical behavior of the damaged materials. Furthermore, the morphology, distribution, and evolution law of all types of damages are explored, i.e., from the microscopic scale by using the averaging method to reflecting the findings in terms of their corresponding macroscopical mechanical behavior.

In general, the study of damage mechanics consists of four stages:(1)Selecting the appropriate damage variable.(2)Establishing the damage evolution equation.(3)Constructing the constitutive model by considering the material damage.(4)Solving the stress-strain and damage values of the different points of materials based on their initial conditions and boundary conditions and then evaluating the damage states of these points based on the damage values. If the damage reaches a critical value, then the point is considered damaged. Then, similar calculations are rendered based on the distribution of the new damage and boundary conditions, repeated, and finally terminated when the damage criterion of the component is reached.

Figure 1 simplifies the total stress-strain curve of rocks of the double-line type. The AB segment is the elastic stage without damage, while the BC segment is the strain-softening stage with isotropic damage. Thus,where and are the stress and strain of the peak point, respectively; and are the stress and strain of any point in the softening segment, respectively; is the final stable strain; and is the residual stress.