Discrete Element Modelling of Critical State Soil Mechanics

土壤是由固体颗粒和空隙组成的复杂物质。当土壤被充分排水剪切时，在给定的应力水平下，松散的土壤收缩，而致密的土壤膨胀到相同的最终密度。对于一定的密度，如果土体在此密度下剪切，则无论初始应力条件是什么，都达到相同的最终有效应力条件。事实上，如果将剪切应力、平均有效应力（平均总应力减去孔隙压力）和空隙比（空隙体积/固体体积）绘制在三个相互正交的轴上，那么在这个空间中就存在一个唯一的临界状态线，土壤状态在剪切时将倾向于这条线。临界状态的概念已经存在了半个多世纪，是所有土力学和岩土工程的基础。临界状态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-这是在没有侧向应变的活塞中压缩的样品的孔隙比-对数应力空间线。最近，McDowell和de Bono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（空隙比）-log（应力）空间中是线性的，斜率是颗粒强度的尺寸效应的函数，随着颗粒破裂和变得统计更强，颗粒尺寸演变为分形分布。这是使用离散元素方法（DEM）完成的，该方法可以将土壤颗粒建模为一个球，一组球，或一组粘合球（“团块”），然后会破裂。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来计算加速度，它被积分两次得到位移，从而得到新的接触力。直到最近，用粘合球团块来表示粒子的问题是，模拟的粒子太多孔了。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，已经证明凝聚体需要至少有500个球才能代表真实粒子，这在计算时间方面太繁重了。McDowell和de Bono（2013）克服了这个问题，他们使用无孔固体颗粒来模拟土壤的压缩，当分布在它们周围的力达到临界值时，它们会破裂，然后每个破碎的颗粒被更小的碎片所取代。他们首次在不使用凝聚体的情况下，在三维空间中复制了一维正常压缩过程。预测的法向压缩线斜率是正确的，由此得到的粒度分布也是正确的。事实上，土壤的正常压缩现在可以通过用更小的碎片代替高应力下的球体来正确地建模，这意味着它应该有可能模拟整个临界状态土壤力学。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能够开发更准确的本构模型，其中包括土壤颗粒破碎。从长远来看，岩土工程行业将从这些改进的设计和分析模型中受益，最终将能够使用DEM来分析边界值问题。从长远来看，这将带来更好的设计、更高的安全性以及更好、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.