摘要
土体大变形通常表现为边坡、基坑、路堤等的失稳破坏,往往会造成构(建)筑物的严重破坏和人员的重大伤亡。土体大变形的分析对于工程设计和防灾减灾具有重要的意义,但目前还没有得到较好的解决,其中一个关键原因是数值计算并没有完全反映土体大变形的力学特征。
针对土体大变形的变形运动特性,本论文采用光滑质点流体动力学方法(Smoothed Particle Hydrodynamics,简称SPH方法)分析了土体大变形中的典型问题,主要进行了以下几个方面的工作:
(1)对目前土体大变形分析的研究成果进行了较为系统的总结和分析,并指出了现有土体大变形数值模拟常用方法存在的问题和不足。在此基础上,针对本文所使用的SPH方法,评析了其在土体大变形分析中的研究基础。
(2)详细分析了SPH方法的基本原理,说明SPH方法是一种应用质点表示物质的方法(不需要预先定义质点间的联系,只需对计算对象进行质点的初始分布),同时指出其核心问题是函数的光滑近似逼近和质点近似逼近。这样,具备了无网格、质点形式和拉格朗日性质的SPH方法避免了网格变形问题,适宜处理大变形问题。同时,并基于SPH核心理论,阐述了流体动力学控制方程和弹塑性力学的SPH格式建立过程。
(3)相对于网格化方法,分析了SPH方法中处理压力求解的办法,介绍了各种质点搜索方法和光滑核函数对计算范围和精度的影响,并从中选取了Verletneighbor list方法作为本文的质点搜索技术,同时选择了一种三次样条函数作为光滑核函数,并在此基础上,基于FORTRAN语言自主研制了适合于土体大变形分析的SPH数值计算程序;
(4)针对本文所研制的SPH方法数值模拟模型进行了严格的验证,实现了溃坝水体自由运动的计算,和完全弹性体单剪试验的数值模拟计算,并通过相关的试验数据和理论解析解,完成了对本文所编制SPH程序的验证工作,同时体现出SPH方法在解决大变形问题上无网格、质点形式、拉格朗日性质以及自适应性等优点。
(5)针对土体大变形的流体动力学特性和弹塑性力学特性,分别使用宾汉姆流体模型和修正剑桥模型改进了相应的SPH模型,完成了土体大变形流动模型试验和土样大变形非排水单剪试验的数值模拟分析。通过与试验实测资料和理论解析解的对比,结果表明了SPH方法在不同理论下进行土体大变形研究的有效性。
本文基于SPH方法,针对土体大变形问题,通过建立相应的SPH方法数值模型进行了数值计算分析,并获得了较好的效果。分析中,以弹塑性力学为主的同时引入流体动力学手段,达到了促进土体变形研究方法多元化的目的,获得了对土体大变形研究的进一步认识,这为进一步指导实际工作和促进土体变形研究方法多元化奠定了一定的基础。最后针对本文研究内容及当前国内外研究现状,提出了亟待解决的问题和进一步的研究工作。
It is very important to know the behavior of soil subjected to large deformation for design of structures and prediction of geodisasters. In practical engineering, the soil usually exhibits large deformation coupled with different mechanisms: fluid dynamics and elasto-plastic dynamics. This makes it hard to exactly predict all deformation characteristics in one method, particularly for the extreme deformation. To solve the difficulty, it is necessary to capture the large deformation performance of the soil in the sense of coupled mechanics, instead of single method.
The main study of this thesis is to apply Smoothed Particle Hydrodynamics(SPH) method in solving soil large deformation problems. As a meshfree, Lagrange, particle method, SPH has its own particular characteristics with some special advantages over the traditional grid-based numerical methods, especially in the application of large deformation analysis. The research work is completed as follows:
(1)The state-of-art of the soil subjected to large deformation is summarized in this paper. Combined with dynamical characteristics and engineering demand of large deformation analysis in practical engineering, the problems and shortcomings of existed numerical methods are pointed out.
(2) As SPH method is a newly emerged method for the applications in the fields relative to Geotechnical Engineering, the basic concept is introduced in detail. It has been shown out that SPH has two key steps, Fuction Approximation and Particle Approximation. In SPH method, the problem domain is represented by a set of arbitrarily distributed particles. So the SPH method is able to deal with large deformation. And the SPH formulations of fuild mechanics and elasto-plastic mechanics are presented.
(3) Some numerical aspects such as artificial viscosity, particle searching method and smoothing kernel function are described in the aim at improving SPH calculation precision. Based on the discussion, Verlet neighbor list is selected as the particle searching method and one kind of cubic spline interpolation function as the smoothing function. Then the SPH programs for soil large deformation are developed in FORTRAN language.
(4) In order to verify the SPH programs, the dam break and simple shear test on completely elastic body are imployed in the numerical simulation. The calculation results show good agreement with the relative test data and theoretical solution; still the results can get the moving information of every particle.
(5) In the aim at solving the problem in soil large deformation with two different methods, the Bingham Fluid constitutive model combined with the Mohr-Coulomb failure criterion and modified Cam-clay model are introduced in SPH program respectely. The ground flow model test and soil undrained simple shear test are simulated in the programs, and the numerical result and test data are compared in detail, they show good agreement with each other.
In this thesis, the elasto-plastic mechanics and fluid dynamics are introduced in the analysis.Based on SPH method, the fuild and elasto-plastic programs are developed for soil large deformation. The SPH programs are verified and validated through large calculation comparison with test data and theoretical solution. In the finality, based on the conclusions of the whole work, the problems requiring further studies are discussed.
引文
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