Advances in Civil Engineering

Volume 2018, Article ID 2606108, 13 pages

https://doi.org/10.1155/2018/2606108

## Subsidence Prediction of Overburden Strata and Surface Based on the Voussoir Beam Structure Theory

^{1}School of Mines, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China^{2}State Key Laboratory of Coal Resources and Safe Mining, Xuzhou, Jiangsu 221116, China

Correspondence should be addressed to Jialin Xu; nc.ude.tmuc@ljxtmuc

Received 14 February 2018; Accepted 21 March 2018; Published 31 May 2018

Academic Editor: Dengke Wang

Copyright © 2018 Changchun He and Jialin Xu. 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 hard and stiff strata (key strata) bear the overburden load in the form of a voussoir beam structure (VBS) after break. The VBS affects both the surface subsidence and the stope underground pressure. Therefore, the reasonable method to predict the surface subsidence is based on the whole subsidence formulae of the VBS. This study first establishes the subsidence formulae of the VBS analytically. The influence of the block length on the subsidence curve and the VBS level on the zero-subsidence range are then analyzed based on the subsidence formulae of the VBS. The results show the half-subsidence curve of the VBS is an S-shaped curve. The block length hardly affects the S-shaped subsidence curve determined by the width of the undercompacted zone. Furthermore, a greater undercompacted zone width corresponds to a greater offset distance of the inflection point. The higher the VBS level, the farther the zero-subsidence range, and the flatter the subsidence curve. The subsidence of the highest VBS can approximately represent the surface subsidence when the topsoil is thin enough.

#### 1. Introduction

Coal mining will lead to overburden fracturing [1, 2], groundwater pollution [3–6], and landslides [7]. Moreover, all of the environmental damage relates to the surface subsidence. Therefore, it is especially important to study the surface subsidence caused by coal mining. To date, several methods can be used to predict the surface subsidence, including profile function [8], modelling [9], and influence function [10–12] methods. Most of these approaches are in light of ground station-based statistics predicting the surface subsidence without considering the control action of the key strata (KS) on the surface subsidence. However, field observations and physical model simulations have shown that the KS dynamically controls the surface subsidence [13–15], which means that the KS and the controlled soft rocks obtain synchronous subsidence and subsidence speed. This suggests that in order to accurately predict the surface subsidence, it is necessary to first calculate the KS subsidence within the overburden.

The overlying strata are usually divided into a caved zone, a fractured zone, and a continuous deformation zone [16]. The KS in different zones will present different characteristics. The KS in a caved zone will collapse after mining while that in a fractured zone will bear the overlying load with the voussoir beam structure (VBS). Meanwhile, the KS in a continuous deformation zone deform like a complete rock beam. The KS controls the surface subsidence in the form of a VBS when the coal seam is not deeply buried. Therefore, the subsidence formulae of the VBS should be determined before predicting the surface subsidence. The deformation mechanisms and the stability of undermined sedimentary rock layers have been studied [17, 18], but the influence of the VBS on the overlying strata subsidence was not considered. An enhanced subsurface subsidence prediction model considering overburden stratifications had been derived in the literature [19]. This model equally divides the overburden strata into a finite number of layers and considers the percent of hard rocks in each layer. The subsidence of each layer is then predicted progressively upward based on the influence function method. The model provides a new method for the subsurface subsidence prediction, but it does not consider the control action of the KS and only divides the overburden strata into several equal parts. The proposal of the “voussoir beam theory” [20] based on field measurements brought a qualitative leap to the understanding of the stope underground pressure. The mechanical model of the VBS proved that the KS after break was essentially a semiarch structure, despite it looking like a rock beam. The condition was that the key block in the VBS must meet the condition of “S-R” (sliding-rotation) stability. The voussoir beam theory explained the structure form of the overburden strata after coal seam mining, the reason for the front abutment pressure greater than the rear abutment pressure, and the displacement constraints above “immediate roof supports” [21]. The voussoir beam theory could explain most of the stope underground pressure phenomena and guides the control of the stope underground pressure and the prevention of roof accidents. Hence, the Mining and Metallurgy roll of the encyclopedia of China has accepted the “voussoir beam” concept. However, the mechanical model of the VBS only analyzes the force balance and displacement of the breaking blocks and does not provide the whole subsidence formulae, which are the basis for the calculation of overburden strata subsidence and the surface subsidence.

The analytical formulae of the whole VBS subsidence are initially derived and used to analyze the influence of the VBS level on the zero-subsidence range and the block length on the subsidence curve. Field tests are then utilized to validate the analytical subsidence formulae. The VBS subsidence can approximately represent the surface subsidence when the topsoil is extremely thin, but it cannot represent the surface subsidence when the topsoil is thick because the topsoil has its own complex movement law. The effect of the topsoil, if it is thick enough, should not be ignored in predicting the surface subsidence based on the overburden strata subsidence. Moreover, the surface subsidence can be theoretically calculated according to the deformation characteristics of the topsoil and the relationship between the surface and the VBS. Herein, only the VBS subsidence is studied, which will be the basis for the overburden subsidence-based surface subsidence prediction.

#### 2. Subsidence Formula of the VBS above the Mined-Out Area

The overlying voussoir beam is divided into two parts (i.e., one above the mined-out area and another above the rib side separated by the blue line and represented with capital A and B, respectively, in Figure 1(a)). This is because the breaking blocks above the mined-out area interlock with each other, forming a stable mechanical structure and bearing the overburden load, while the voussoir beam above the rib side deforms in the form of an unbroken beam. Furthermore, different external forms of the voussoir beam have different mechanical models. One is the continuous mechanical model, and another is the discontinuous mechanical model.