非均匀弹性地基薄板变形的半解析解及在沿空掘巷中的应用

发布时间：2018-04-08 16:48

本文选题：非均匀弹性地基　切入点：薄板变形　出处：《中国矿业大学》2016年硕士论文

【摘要】：随着我国经济的发展,工程建设项目持续增多、规模不断扩大,非均匀弹性地基上板状结构物在在土木、地基和采矿工程领域有了越来越广泛的应用,因此非均匀弹性地基薄板的变形研究具有重要的工程实际意义。本文主要采用理论分析、数值计算和数值模拟等方法,针对非均匀弹性地基薄板的变形,提出了一种半解析解法,并将其应用到沿空掘巷回采工作面基本顶的变形计算中,分析了基本顶变形的周期演化规律,取得的研究成果总结如下：(1)基于任意形状区域的弹性地基分布假设,建立了非均匀弹性地基矩形薄板弯曲变形的力学模型,推导了非均匀弹性地基薄板弯曲变形的控制方程。针对各区域所受载荷、边界条件和弹性地基系数的差异及全域无统一挠度试函数的问题,提出了一种新的半解析解求解思路和方法,即将各区域挠度试函数设定为满足已知边界条件并含有待定参数的函数形式,应用常用解法求解出各区域的含待定参数表示的系数,再利用共有边界的连续性条件,确定出各待定参数的值,得到所有求解域的薄板挠度分布函数解,并通过算例验证了该方法的精确性和优越性。(2)基于沿空掘巷回采工作面基本顶破坏特征及受力分布,结合基本顶的周期破断和二次采动影响规律,建立了基本顶的非均匀弹性地基矩形薄板的力学模型,应用非均匀弹性地基矩形薄板变形半解析解法,通过MATLAB编程计算,分析了沿空掘巷回采工作面基本顶的变形演化规律。(3)结合工程实例,基于FLAC3D软件对沿空掘巷回采工作面基本顶变形进行了数值模拟,分析了基本顶下沉值随着工作面推进的演化规律,总结出回采期间沿空掘巷顶板、巷道变形最大的位置,并据此提出了巷道围岩控制技术。将数值模拟结果与理论计算结果对比,发现二者基本相符,验证了理论计算的可靠性和有效性,为沿空掘巷围岩变形和控制提供理论依据。
[Abstract]:With the development of our country's economy, the number and scale of construction project is increasing, and the plate structure on non-uniform elastic foundation has been widely used in civil engineering, foundation and mining engineering field.Therefore, it is of great practical significance to study the deformation of inhomogeneous elastic foundation thin plate.In this paper, a semi-analytical method is proposed for the deformation of thin plates of inhomogeneous elastic foundation by means of theoretical analysis, numerical calculation and numerical simulation, and it is applied to the calculation of the basic roof deformation of the mining face along the goaf roadway.The periodic evolution law of the basic top deformation is analyzed, and the research results are summarized as follows: (1) based on the assumption of elastic foundation distribution in arbitrary shape region, a mechanical model of bending deformation of rectangular thin plate on inhomogeneous elastic foundation is established.The governing equation of bending deformation of thin plate on inhomogeneous elastic foundation is derived.Aiming at the difference of load, boundary condition and elastic foundation coefficient in different regions and the problem that there is no uniform deflection test function in the whole region, a new method for solving semi-analytical solution is presented.The deflection test function of each region is set up as the function form which satisfies the known boundary conditions and contains undetermined parameters. The coefficients of each region with undetermined parameters are solved by using common solutions, and then the continuity conditions of common boundaries are used.The values of the parameters to be determined are determined, and the deflection distribution function solutions of thin plates in all the solving domains are obtained. The accuracy and superiority of the method are verified by an example. The results show that the method is based on the basic roof failure characteristics and the force distribution of the mining face along the goaf roadway.Combined with the law of periodic breaking and secondary mining of basic roof, the mechanical model of rectangular thin plate with inhomogeneous elastic foundation on basic roof is established. The semi-analytical method of deformation of rectangular thin plate on non-uniform elastic foundation is applied, and the calculation is carried out by MATLAB programming.This paper analyzes the evolution law of the basic roof deformation of the working face along the gob roadway. Combined with the engineering example, based on the FLAC3D software, the numerical simulation of the basic roof deformation of the mining face along the goaf roadway is carried out.This paper analyzes the evolution law of the basic roof subsidence value with the advance of the working face, sums up the position of the maximum deformation of the roadway during the mining period, and puts forward the control technology of the surrounding rock of the roadway.By comparing the numerical simulation results with the theoretical calculation results, it is found that the two results are basically consistent with each other, which verifies the reliability and validity of the theoretical calculation, and provides a theoretical basis for the deformation and control of the surrounding rock along the goaf roadway.
【学位授予单位】：中国矿业大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TD353

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