动静态荷载下硐室结构应力场求解及防震设计研究

发布时间：2018-01-20 13:07

本文关键词： 层状地基应力场 Laplace变换 Fourier变换状态空间法动应力集中系数振动加速度　出处：《中国科学技术大学》2013年博士论文　论文类型：学位论文

【摘要】：硐室结构是最为常见而又十分重要的岩土工程结构,建造于地基或岩层之中,对硐室结构的精确工程力学计算有赖于对其相关地基或岩层问题的力学计算和自身的力学计算。研究地基或岩层力学问题的目的是了解硐室所处的外部力学环境,将外部力学环境和硐室结构本身的力学特征有机地结合起来,才能得到可靠的结果。然而迄今为止人们对硐室结构的受力研究中,同时考虑动静荷载的研究是比较薄弱的。尤其当硐室建造于层状地基或岩层中,需要深入了解硐室外部层状地基或岩层的力学问题,这方面的研究成果目前仅限于轴对称情况,工程应用有很大的局限性。本论文的第一部分(第二章至第五章)对层状地基的非轴对称应力场问题求解进行了新的探索性研究,给出了两种有效而便于推广应用的求解方法。论文的第二部分(第六章和第七章)对硐室在炸药爆炸产生的动荷载作用下的动应力集中问题和振动效应开展了研究,并且成功地将之应用到对矿山相邻巷道振动影响的分析之中。地基问题的应力场计算在岩土工程中占有十分重要地位。大量的工程实践表明很多地基呈层状分布,所以采用层状地基模型计算地基的应力场问题更为合理,这是由于该模型能够合理地模拟地基沿深度方向的不均匀性。而目前实际工程中地基应力场和位移的计算多是基于均质的半无限弹性体的Boussinesq解,其计算结果与实际工程有明显的差异。开展层状地基理论研究对岩土工程具有重要的理论和工程意义。本文是在直角坐标系下,首先将弹性力学中的基本方程在形式上转换为自动控制理论中的状态方程,然后针对不同问题利用不同的积分变换,在变换后的坐标域内得到真正的状态方程。最后利用状态空间理论和传递矩阵技术推导出半平面多层弹性地基、空间层状弹性地基应力及位移的求解方法。本文提出的方法尤其适用于非轴对称问题。对于半平面层状弹性地基问题,在直角坐标系下利用Fourier变换实现了将弹性力学中的基本方程转变为状态方程。利用控制理论中求解状态方程的方法得到了半平面多层弹性地基的应力和位移的解析法。作为特例,文中还利用本方法推导了弹性力学Flament解,能够得到与弹性力学完全一样的结果,说明了本文方法的正确性。本方法适用于条形层状地基的求解。在实际工程中地基的受力问题多为三维力学问题,目前绝大多数研究成果均是在柱坐标系下进行的,主要针对轴对称受力问题。通用的方法是利用Hankle变换将弹性力学中柱坐标系下的基本方程转换为状态方程,然后进行求解。个别文献在柱坐标系下借助于三角级数解研究了非轴对称问题,其本质仍然是轴对称受力问题方法,求解工程及公式推导十分繁杂,给推广应用带来不便。本文给出了两种在直角坐标系下求解任意荷载作用下空间层状地基的求解方法。一种方法是借助于Laplace变换及其微分性质,并将坐标原点选在荷载影响范围以外足够远的地方,在直角坐标系下实现了与柱坐标系下类似的求解方法。另一种方法是仿照有限单元法将无限大地基模型转化为足够大的有限地基模型,假定应力和位移可表示为分离变量的形式,借助于三角级数建立了用状态空间法的求解层状地基的方法。本文提供的层状地基三维问题的求解方法,对荷载的作用方式没有局限性,改变了以往只能在柱坐标系下求解层状地基轴对称问题的现状。使用范围更为广泛,便于推广应用。研究成果为进一步研究层状地基或岩层中硐室结构的动静应力场耦合提供了初步的理论基础。本文还对硐室的动力学特征进行了研究。岩层中的硐室在动荷载作用下,其破坏的主要原因是硐室周围的动态应力造成的。文中依据基本的波动方程引入两个势函数,将波动方程进行时空分离展开成分离变量形式,进而借助复变函数中的映射函数推导了平面P波在硐室周围的传播特性,该分析方法从理论上可得到任意不规则洞室的位移和动应力表达式,依此分析不同方向的爆炸源作用下硐室围岩的振动规律。文中还给出了一个直墙半圆拱的计算实例,得到了一些有一定使用价值的结论。分析表明不同工况对动应力集中系数影响较小,除了背爆侧局部范围之外,动应力集中系数会随着硐径的增大而减小；应力波的沿2700传播时,在迎爆侧,径向和切向振动加速度会随硐室的增大而增大,在背爆侧,与之相反；硐室直径对应力集中系数的影响程度要大于对振动加速度影响。作为对上述研究成果的一个应用实例,对河南栾川858地采矿山掘进巷道爆破振动进行了监测和数值分析,研究了爆破振动对相邻巷道的影响。得到了最大单段装药量与保护岩柱宽度的关系,并应用到实际工程之中,对优化工程设计、提高工程效率、保证工程安全有重要的指导意义。
[Abstract]:The chamber structure is the most common geotechnical engineering structure and very important, built on the ground or rocks, computational mechanics depends on the ground or rock the computation and its calculation of precise engineering mechanics chamber structure. Research on the ground or rock mechanics problems is to understand the mechanical environment of the room, mechanical characteristics of external mechanical environment and chamber structure itself together, in order to obtain reliable results. However, so far people to study the stress chamber structure, considering the study of static and dynamic load is relatively weak. Especially when the chamber was built in layered soil or rock need, mechanical problems in-depth understanding of external chamber or rock layered foundation, research in this area is currently limited to the axisymmetric case, the engineering application has great limitations. First this paper Part (chapter second to chapter fifth) of non axisymmetric layered ground stress field of problem solving are discussed and new research, gives two kinds of effective and convenient method for solving the application. The second part of the thesis (Chapter sixth and chapter seventh) of the chamber in the explosive explosion under dynamic load the dynamic stress concentration and vibration effect was studied, and successfully applied to the analysis of the impact on the mine roadway adjacent vibration.
The problem of ground stress field calculation plays an important role in geotechnical engineering. A large number of engineering practice shows that many foundation layer, so the layered soil model calculation of ground stress field is more reasonable, this is because the model can reasonably simulate the foundation inhomogeneity along the depth direction at present. The foundation in practical engineering calculation of stress field and displacement are semi infinite elastic homogeneous Boussinesq solution based on the calculation results and actual engineering have obvious differences. Research on layered foundation theory has important theoretical and engineering significance of geotechnical engineering.
This paper is in the Cartesian coordinate system, the basic equations of elasticity in the form of conversion for the automatic control equation of state theory, then according to different problems by using the integral transform of state equation in real coordinate domain transformation. Finally, after using the state space theory and transfer matrix technique derived semi planar multilayer elastic foundation, solving method and displacement space of layered elastic foundation. This method is especially suitable for non axisymmetric problems.
For half plane layered elastic foundation, the basic equations in elasticity into state equation by using the Fourier transform in the Cartesian coordinate system. The control method is used to solve the equation of state theory has been half plane elastic layered soil stress and displacement analysis method. As an example, this paper also make use of the using the method of Flament solution in elastic mechanics, elastic mechanics can be completely the same with the results illustrate the correctness of the proposed method. This method is suitable for solving linear layered foundation.
In the actual project stress problem of foundation is a three-dimensional problem, most research results are in the cylindrical coordinates, the main problem for axisymmetric stress. The general method is to use Hankle to transform the basic equations of elasticity in cylindrical coordinate system into a state equation, then to solve. Trigonometric series solution of non axisymmetric problems by means of individual literature in cylindrical coordinates, its essence is still the problem of stress and axial symmetry, and the formula derivation of engineering is very complicated, for the promotion and application of inconvenience.
This paper gives a method to solve two kinds of solved in the Cartesian coordinate system under arbitrary loading space of layered foundation. A method is based on the Laplace transform and its differential properties, and the origin of coordinates in outside load influence range far enough, in the Cartesian coordinate system is solved similar method in cylindrical coordinate system the other method is modeled on the finite element method the infinite foundation model into finite foundation model is large enough, assuming that the stress and displacement can be expressed as the form of separation of variables, with the help of trigonometric series is established by the method of layered foundation to solve the state space method.
Method for solving three-dimensional layered foundation problem are provided in this paper, the mode of action of load without limitation, changing the status that must be solved in cylindrical coordinates of layered foundation axisymmetric problems. A wider range, convenient popularization and application. Research results provide a theoretical basis for further research of the preliminary field coupling of layered foundation or rock chamber structure dynamic stress.
The dynamic characteristics of the chamber were studied. The rock cavern under dynamic loading, the main reason for the destruction of the dynamic chamber surrounding stress caused. Based on the basic wave equation by introducing two scalar potential functions of wave equation can be expanded into a temporal separation of variable separation. Then with the help of complex mapping function is derived in function of plane P wave propagation characteristics in the chamber around, this analysis method can be arbitrary irregular cavern displacement and dynamic stress in theory, the vibration law of chamber surrounding rock explosion source and effect analysis of different direction. The paper also presents a a straight wall top arch calculation example, and obtained some valuable conclusions. The results show that different conditions on the dynamic stress concentration coefficient has little effect, except the back blast side local scope, the dynamic stress concentration factor with When the stress wave propagates along 2700, the radial and tangential acceleration increases with the increase of the chamber. When the stress wave propagates along the chamber, it increases with the increase of the chamber. On the back side, the influence of the chamber diameter on the force concentration factor is greater than that on the acceleration.
As an application of the above research results, the Henan Luanchuan 858 mine laneway blasting vibration monitoring was conducted and numerical analysis on the influence of blasting vibration on adjacent tunnel. The relation between the maximum single charge and protection pillar width, and should be used in practical engineering, optimization of the project design, improve the efficiency of the project, which has important guiding significance to the safety of the project.

【学位授予单位】：中国科学技术大学
【学位级别】：博士
【学位授予年份】：2013
【分类号】：TU43

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