Representative Elementary Volumes of coarse-grained soils

标准的实验室试验，如三轴试验，通常用于校准旨在正确描述土壤行为的本构模型。为了获得真实的材料性能，这些试验被设计并假定为单元试验。试样被认为是一个具有代表性的基本体积（REV），即具有均匀性质和均匀行为的元素，代表土壤的行为，因此被解释为一个物质点。这对于三轴试验显然是不正确的，因为剪切带通常是肉眼可见的，或者在试件内部形成复杂的剪切带模式，导致从很早开始就出现高度不均匀的响应。必须解决实验室试验中观察到的现象与构成实验评估、本构模型校准和土壤行为描述基础的同质性假设之间的这些明显差异。事实上，样品不是一个单一的REV，而是由多个REV组成，每个REV代表样品内部的某个区域。这种REV的大小取决于内部长度尺度，例如颗粒大小或剪切带厚度，控制全局行为。REV的大小也被发现依赖于分析的变量，例如空隙率或接触织物。基于对标本加载过程中获得的x射线计算机断层扫描（ct）的分析，我们开发了一种考虑三个不同标准的REV大小确定方法。这种方法现在将用于表征对REV大小的不同影响，并确定整个加载过程中试样的非均匀状态。使用x射线CT进行这项研究，人们仅限于土壤的结构和运动学。最终，我们希望将REV行为与在试件边界测量的应力-应变关系所表征的全局观察行为联系起来。在微观尺度上，我们还需要考虑应力，这是x射线CT无法获得的。对于这样一个完整的描述，可以引入离散元法（DEM）。结合实验和数值得到的转速演变将为全面比较全局和局部行为提供基础。土壤非均质性的研究也允许将其纳入有限元模型，并加强本构模型的校准。考虑真实的初始状态可以改善模型的标定。本构模型甚至可以为选定的转速进行校准，例如，剪切带内的转速，这被认为是唯一达到真正临界状态的转速。这些调查的结果将构成一方面是传统的假设和评价，另一方面是微观尺度的观察和现象之间联系的基础。

Standard laboratory tests, such as the triaxial test, are commonly used to calibrate the constitutive models aiming to correctly describe the soil behaviour. In order to obtain true material behaviour, those tests are designed and assumed to be element tests. The specimen is considered to be a representative elementary volume (REV), i.e. an element with homogeneous properties and homogeneous behaviour, representing the soil behaviour and is therefore interpreted as a material point. This is obviously not true for the triaxial test where shear banding is usually visible to the naked eye or complex patterns of shear bands form inside the specimen leading to a highly heterogeneous response from very early on.These obvious discrepancies between the phenomena observed in laboratory tests and the assumption of homogeneity forming the basis for the experimental evaluations, the constitutive model calibration and the description of the soil behaviour have to be resolved. The specimen is, in fact, not a single REV but rather consists of multiple REVs, each representing a certain region inside the specimen. The size of such a REV depends on the internal length scales, e.g. the particle size or the shear band thickness, governing the global behaviour. The REV size was also found to depend on the analysed variable, e.g. the void ratio or the contact fabric.Based on the analysis of x-ray computed tomographies (CTs) acquired during the loading of a specimen, we have developed an approach for the determination of the REV size considering three different criteria. This approach will now be used to characterize the different influences on the REV size and to identify the heterogeneous state of the specimen throughout loading. Using x-ray CT for this study, one is limited to the fabric and kinematics of the soil. Ultimately, we want to connect the REV behaviour to the globally observed one characterised by a stress-strain-relationship measured at the boundary of the specimen.At the micro-scale, we also need to include the stresses, which cannot be obtained with x-ray CT. For such a complete description, the discrete element method (DEM) can be introduced. Combining the experimentally and the numerically obtained evolution of the REVs will offer the fundamentals for a comprehensive comparison between the global and the local behaviour. The study of the soil heterogeneity also allows for its incorporation in finite element models and an enhancement of the constitutive model calibration. The consideration of a realistic initial state has already been shown to improve the model calibration. Constitutive models could even be calibrated for chosen REVs, e.g. those inside the shear band, which have been assumed to be the only ones reaching a true critical state. The results of these investigations will form the basis for a link between conventional assumptions and evaluations on the one hand and micro-scale observations and phenomena on the other hand.