【作者】 罗滔；

【导师】 傅少君；

【作者基本信息】 武汉大学 ， 岩土工程， 2016， 博士

【摘要】 颗粒破碎特性的影响因素有颗粒的强度、大小、圆度、粗糙度、风化程度、相对密度、颗粒级配以及组构等内因和围压大小、应力水平、加载路径、加载速率、含水量、制样方法等外因。揭示颗粒料破碎特性的途径主要有室内试验、数值模拟、原位测试及其间相结合的方法,随着计算机技术的发展和数学、力学理论的进步和日趋完善,近年来,数值模拟方法成为研究堆石体颗粒料力学特性热点课题,并取得了长足的进步,由于该课题的复杂性、不确定性等,但目前尚未形成系统准确的数值模拟体系,仍面临诸多关键科学技术问题亟待解决。鉴于此,论文将围绕堆石体颗粒料复杂形状、破碎的模拟问题开展数值分析方法研究,以期从颗粒层面为研究颗粒料的宏观力学特性探索一条数值模拟途径,该课题研究成果将对建造堆石体工程的分析、设计、施工、维护等都具有十分重要的理论意义和实用价值。论文的主要内容如下:(1)在考虑堆石料复杂颗粒形状的基础上,以凸多边形作为基本单元,建立了二维离散单元的实用算法,并研制了用于模拟堆石料的二维离散单元法程序PDEM,采用本程序对室内试验进行了数值模拟,且与PFC模拟进行了比较,得到了与室内试验一致的应力变形规律;(a)推导了半解析方法计算任意多边形的转动惯量的公式,为牛顿运动定律求解任意多边形单元的转动问题提供了方便;(b)采用线性搜索算法实现了求解多边形间交点坐标,求解任意两个多边形之间的交点最多只要2(n+m)次,且易于编程实现。提出了由近似接触判断到真实接触判断的适用于多边形的接触判断算法;(c)采用基于势能原理的法向接触模型,推导了求解多边形-多边形法向接触力,结合切向摩擦定律构成了一个完整的多边形-多边形接触模型,为多边形颗粒之间的相互作用提供了理论依据;(d)基于以上原理和思路,研制了多边形离散元计算程序PDEM,并对姜景山等的粗粒料二维模型试验进行了数值模拟,且与PFC采用clump技术的模拟进行了比较。通过与PFC模拟结果和试验结果的对比分析了论文方法、程序的可靠性。(2)针对具有尖角的堆石料在外荷载作用下容易发生颗粒破碎的现象,建立了一种将多边形离散元(PDEM)和比例边界有限元(SBFEM)两种方法结合起来的新的模拟颗粒破碎的数值方法(SBFDEM),可以同时发挥这两种方法的优势,从颗粒尺度揭示颗粒破碎机理及其对宏观力学效应的影响。(a)将具有尖角的颗粒用多边形单元表示,用多边形离散单元方法分析颗粒运动及其相互作用规律,采用多边形比例边界有限单元法对单个颗粒进行应力应变分析。每个颗粒既是离散元方法中一个独立的离散单元,又是比例边界有限元分析时的一个多边形单元;(b)应用Hoek-Brown准则判断任意单元中某个点的破坏,假定破坏点达到一定比例时,此单元即破碎;破坏路径假设为直线,对破坏点的分布采用加权最小二乘法进行直线拟合得到破坏路径;根据破坏路径将单元一分为二,新产生的单元直接进入下一步的离散元和比例边界有限元的计算;(c)将相关理论形成了一套系统的用于分析颗粒破碎的方法,并基于MATLAB研制了相应的程序SBFDEM。(3)应用SBFDEM程序对堆石料试样进行了不同围压下的双轴压缩试验数值模拟。分析了颗粒破碎对堆石料在双轴压缩条件下的力链演化、试样变形以及宏观应力应变关系等物理力学行为的影响;分析了不同初始颗粒粒径分布对堆石料在双轴压缩条件下的颗粒破碎行为的影响。论文研究工作丰富和发展了离散单元法、比例边界有限元法,研究成果为数值模拟堆石体颗粒料复杂形状、颗粒破碎等关键问题探索了一条高效、科学的途径。更多还原

【Abstract】 The particle breakage is affected by internal factors such as particle strength,size,roundness,roughness,weathering degree,relative density,particle size distribution and fabric.It is also affected by external factors such as confining pressure,stress level,loading path,loading rate,moisture content et al.The particle breakage can be revealed by indoor test,numerical simulation,in situ test and the combination of these methods.With the development of computer,mathematics and mechanics in recent years,numerical simulation is becoming more and more popularly used for modelling the mechanical resposes of rock-fill materials.Due to the complexity and uncertenty of rock-fill materials,there is no efficient way for caputuring the characteristics of rock-fill materials.And also there are many key scientific and technological problems need to be solved.Numerical method counting for the complex shape of rock-fill particles is studied in this thesis.With an aim to develop a novel mthod to interprate the macro-scopic mechanical responses from particle-scopic.The outcomes of this study will be usefull in analysis,design,construction and maintenance for structures made by rock-fill materials,with great theoretical and practical value.This manuscript includes the following three main parts:(1)Every single particle is simulated by a polygon discrete element in order to capture the realistic shape for rock-fill materials.A polygon discrete element method is established and a program called PDEM is developed to model rock-fill material.A biaxial test of rock-fill sample is simulated by PDEM and PFC under different confining pressures.By comparing the results from PDEM with biaxial test and numerical results from PFC,the feasibility of the developed technique is demonstrated.This part includes the following aspects:(a)The moment of inertia of polygon with arbitrary number of sides is formulated by a semi-analytical method,which enables the calculation for the rotation of polygon to be convenient.(b)A linear search algorithm is adopted to obtain the coordinates for the intersection points,the total cost for searching the intersection points between two polygons is only 2(n + m)times,and easy to program.The contact detection for polygons is developed by a two-step process which includes approximation detection first and real contact detection after.(c)The normal contact force is calculated by a potential energy based polygon/polygon normal contact model,the tangential force is coupled by the sliding frictional model.This contact model solves both the normal contact forces and tangential contact forces for polygons results an theoretical foundation for the interaction of polygons.(d)A polygon discrete element program called PDEM is developed based on the theories mentioned above.A biaxial test of rock-fill sample which was conducted by Jiang et al.is simulated by PDEM and PFC under different confining pressures.By comparing the results from PDEM with biaxial test and numerical results from PFC,the feasibility of the developed technique is demonstrated.(2)In order to capture the particle breakage phenomenon in sharp-edged rock-fill materials,a novel numerical method called SBFDEM is developed by combine scaled boundary finite element method(SBFEM)and discrete element method(DEM).The developed technique makes the best use of the salient features of both the DEM and SBFEM.The particle breakage mechanism and its implication on macro-mechanical responses can by studied from particle scale simulation.This part includes the following aspects:(a)The sharp-edged particles are modelled by polygons,the motion and interaction of particles are solved by discrete element method,a full stress-strain analysis of each particle is obtained by using scaled boundary finite element method.Each particle is a discrete element in DEM and also a single polygon in SBFEM.The force calculation and transmission between these two modulus are demonstrated in this part in detail.(b)Hoek-Brown criterion is used to determine the ’plastic’ points,breakage is triggered if the ratio of ’plastic’ points reaches the critic value.The breakage path is assumed to be a straight line for simplicity and is determined by weighted least square approximation for all’plastic’ points.Once breakage happens,the broken particle is replaced by two smaller particles,and the new generated particles will join the next step DEM and SBFEM calculation without any change.(c)A novel SBFDEM is established based on the theories mentioned above,and a program called SBFDEM is developed by using MATLAB.(3)Two rock-fill samples are modelled under biaxial compression condition with different confining pressures considering particle breakage.The force chain evolution,deformation of samples and macro stress-strain relationship are studied.The implication of different initial particle size distribution on particle breakage under biaxial compression is also evaluated.This work enriches and develops both the discrete element method and scaled boundary finite element method.The novel Scaled Boundary Finite Discrete Element Method has advantages in modelling particle shape and particle breakage.更多还原