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Abstract

A compliant beam subjected to large deformation is governed by a multifaceted nonlinear differential equation. In the context of theoretical mechanics, solution for such equations plays an important role. Since it is hard to find closed-form solutions for this nonlinear problem and attempt at direct solution results in linearising the model. This paper investigates the aforementioned problem via the multi-step differential transformation method (MsDTM), which is well-known approximate analytical solutions. The nonlinear governing equation is established based on a large radius of curvature that gives rise to curvature-moment nonlinearity. Based on established boundary conditions, solutions are sort to address the free vibration and static response of the deforming flexible beam. The geometrically linear and nonlinear theory approaches are related. The efficacy of the MsDTM is verified by a couple of physically related parameters for this investigation. The findings demonstrate that this approach is highly efficient and easy to determine the solution of such problems. In new engineering subjects, it is forecast that MsDTM will find wide use.

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Authors and Affiliations

Theddeus Tochukwu Akano
1
Patrick Shola Olayiwola
1

  1. University of Lagos, Lagos, Nigeria.
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Abstract

Large deformation in roadways is an inevitable problem faced by many coal mines, and bolt installation is widely adopted to keep roadway stability. To provide a theoretical basis for bolt supporting scheme design in order to eliminate hazards associated with roadway failure, the interaction principle between bolts and the bolted strata should be studied thoroughly. This research attempts to investigate the above principle through theoretical analysis through a group of selected statistics from fifteen different coal mines. At the same time, the thick board support method was proposed and applied for controlling the ribs deformation in a particular coal mine. It is concluded that the interaction of the rock-bolt entity is subjected to the fluctuation balance law. When deformation increases, the bolted structure experiences periodic equilibrium variation. Both the supporting force needed to stabilise the surrounding rocks and the supporting capability of bolted strata show a trend of decrease in this process. The interaction principle of surrounding rocks and bolts is in essence the mechanical phenomenon caused by their mutual load transformation, and the load-carrying capacity varies with the bolted structure’s deformation, which is subjected to the following law: elastic roadway>plastic roadway> fractured roadway>broken roadway. The designed bolted thickness of the ribs should be more than 1/5 of roadway height to make full use of the self-stability of surrounding rocks. Finite Difference Method simulation and on-site monitoring data showed that the roof subsidence and ribs convergence of 2201 roadway in Shuguang coal mine was reduced by 83.7% and 88.6% respectively after utilising the proposed support method, indicating that the thick-board method was effective. Results of this research can lay a foundation for support design in large deformation roadways.
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Authors and Affiliations

Xun Yuan
1
ORCID: ORCID
Shuangsuo Yang
2
ORCID: ORCID

  1. Sichuan University – The Hong Kong Polytechnic University, Institute for Disaster Managementand Reconstruction, 610207 Chengdu, China
  2. Taiyuan University of Technology, College of Mining Engineering, 030024 Taiyuan, China
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Abstract

Influenced by the dynamic pressure of the front abutment pressure and the lateral abutment pressure, large deformation of surrounding rock occurs advancing working face in the entry heading adjacent to the active longwall mining face. Based on the cause analysis of entry large deformation, a new technology was put forward to solve the problem, and the designing method of drilling hole parameters for directional hydraulic fracturing was formed. Holes are drilled in the entry or in the high drainage entry to a certain rock layer over the adjacent working face, hydraulic cutting or slotting at the bottom of a borehole were also applied in advance to guide the hydraulic fractures extend in expected direction, through which the hard roof above the coal pillar can be cut off directionally. As a result, the stress concentration around the entry was transferred, and the entry was located in a destressing area. The field test at Majialiang coal mine indicates that the propagation length of cracks in single borehole is more than 15 m. After hydraulic fracturing, the large deformation range of the entry is reduced by 45 m, the average floor heave is reduced by 70%, and the average convergence of the entry’s two sides is reduced by 65%. Directional hydraulic fracturing has a better performance to control the large deformation of the dynamic pressure of the entry heading adjacent to the advancing coal face. Besides, it can improve the performance of the safety production.

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Authors and Affiliations

Bingxiang Huang
Xinglong Zhao
Jian Ma
ORCID: ORCID
Tianyuan Sun

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