Discrete Element Modelling of Critical State Soil Mechanics

土是由固体颗粒和孔隙组成的复杂材料。当土壤在充分排水的情况下被剪切时，对于给定的应力水平，松散的土壤收缩，而致密的土壤膨胀到相同的最终密度。对于一个给定的密度，如果土壤在这个恒定的密度剪切，然后达到相同的极限有效应力条件，无论初始应力条件是什么。事实上，如果剪应力、平均有效应力（平均总应力减去孔隙压力）和空隙率（空隙体积/固体体积）被绘制在三个相互正交的轴上，则在该空间中存在唯一的临界州线，当剪切时，土壤状态将趋向于该临界线。临界状态的概念已经存在了半个多世纪，并构成了所有土力学和岩土工程的基础，但临界州线的微观力学起源从未被探索过。传统上，CSL已被接受为平行于一维法向压缩线-这是在没有横向应变的活塞中压缩的样品的空隙比-对数应力空间中的线。最近，McDowell发表了一个模型（McDowell和de Bono，2013），该模型表明，一维法向压缩线在log（空隙率）-log（应力）空间中是线性的，斜率是颗粒破碎时颗粒强度的尺寸效应的函数，并且在统计学上变得更强，并且颗粒尺寸的分形分布逐渐形成。这是使用离散单元法（DEM）完成的，它可以将土壤颗粒模拟为一个球、一组聚集的球或一组结合的球（“团聚体”），然后可以破裂。颗粒之间的接触力与它们的相对位移有关。这些力通过牛顿第二定律用于计算加速度，加速度被积分两次以给出位移和新的接触力。直到最近，使用粘结球的聚集体来表示颗粒的问题是模型化的颗粒太多孔。这意味着当颗粒破裂时，内部空隙变成外部空隙。这使得很难正确地模拟土壤的压实。此外，已经表明，团聚体中需要至少有500个球才能代表真实的颗粒，这在计算时间方面过于繁重。McDowell和de Bono（2013年）通过使用无孔固体颗粒模拟土壤的压缩来克服这个问题，当分布在它们周围的力达到临界值时，这些颗粒就会破碎，然后每个破碎的颗粒都会被更小的碎片所取代。他们第一次在没有使用团聚体的情况下，在三维空间中复制了一维正常压缩的过程。预测的法向压缩线的斜率是正确的，得到的粒径分布也是正确的。现在可以通过用较小的碎片代替高应力下的球体来正确模拟土壤的法向压缩，这意味着可以模拟整个临界状态土力学。临界状态土力学的微观力学知识将使研究人员和执业工程师开发更准确的本构模型，包括土壤颗粒破碎。从长远来看，岩土工程行业将受益于这些改进的模型在设计和分析，并最终将能够使用DEM分析边界值问题。从长远来看，这将导致更好的设计，更好的安全性以及更好和更经济的基础设施。采矿和粉末技术行业也将受益于使用该模型来模拟矿物破碎和粉末压实等过程。

Soil is a complex material comprising solid particles and voids. When a soil is sheared with full drainage, for a given stress level, a loose soil contracts and a dense soil dilates to the same ultimate density. For a given density, if the soil is sheared at this constant density, then the same ultimate effective stress condition is reached, no matter what the initial stress conditions are. In fact, if shear stress, mean effective stress (mean total stress minus pore pressure) and the voids ratio (volume of voids/volume of solids) are plotted on three mutually orthogonal axes, then there is a unique CRITICAL STATE LINE in this space, which a soil state, when sheared, will tend towards. The concept of the Critical State has been around for over half a century and forms the basis for all soil mechanics and geotechnical engineering.The micro mechanical origin of the Critical State Line has never been explored. Tradtionally, the CSL has been accepted as being parallel to the one-dimensional normal compression line - this is the line in voids ratio - log stress space for a sample compressed in a piston with no lateral strain. Recently, McDowell has published a model (McDowell and de Bono, 2013) which shows that the one-dimensional normal compression line is linear in log(voids ratio)-log(stress) space and the slope is a function of the size effect on particle strength as particles break and become statistcally stronger, and a fractal distribution of particle sizes evolves. This was done using the Discrete Element Method (DEM), which can model a soil particle as a ball, a clumped group of balls, or a group of bonded balls (an "agglomerate") which can then fracture. The contact forces between the particles are related to their relative displacements. These forces are used via Newton's 2nd law to calculate accelerations, which are integrated twice to give displacements and hence new contact forces. Until recently, the problem with using agglomerates of bonded balls to represent particles was that the modelled particles were too porous. This meant that the internal voids become external voids when the particles break. This made it difficult to model the compaction of soil properly. In addition, it has been shown that agglomerates need to have at least 500 balls in them to be representative of real particles, and this is too onerous in terms of computational time. McDowell and de Bono (2013) overcame this problem by modelling the compression of soil using non-porous solid particles, which break when the forces distributed around them reach critical values and each broken particle is then replaced by smaller fragments. They replicated the process of one-dimensional normal compression, in three dimensions, for the first time, without using agglomerates. The slope of the predicted normal compression line was correct, as was the resulting particle size distribution which evolved. The fact that the normal compression of soil can now be modelled correctly by replacing spheres under high stress with smaller fragments, means that it should be possible to model the whole of Critical State Soil Mechanics. A knowledge of the micro mechanics of Critical State Soil Mechanics will enable researchers and practising engineers to develop more accurate constitutive models which incorporate soil particle crushing. The geotechnical industry will benefit in the long term from these improved models in design and analysis, and ultimately will be able to use DEM to analyse boundary value problems. This will, in the long term, lead to better design, improved safety and better and more economic infrastructure. The mining and powder technology industries will also benefit from using this model to simulate processes such as mineral crushing and powder compaction.