IntroductionThe emerging hydromechanical response of natural clays at an engineering scale (macro) is governed at the materials science scale (micro); that is, the microstructural effects arising from the particle assembly and interparticle interactions within the clay lead to a complex hydromechanical response observed at the engineering scale. Burland (1990) denoted the microstructural effects that are observed in a wide range of soils as the structure of soils: a combination of fabric and the (apparent) bonding between the particles (Leroueil and Vaughan 1990). In the following, the bonding is interpreted as the nonfrictional interparticle forces in the clay (Santamarina 2003), whereas the fabric describes the distribution of the directional data, e.g., orientation of clay particles, void space, and/or contacts (Ken-Ichi 1984). Methods from materials science, such as scanning and transmission electron microscopy (SEM/TEM), mercury intrusion porosimetry (MIP), and wide or small angle X-ray or neutron scattering (W/SAXS, SANS) (e.g., Glatter and Kratky 1982; Toer and Reimer 1998; Giesche 2006) have been introduced in geomechanics to further probe clays at microscale despite their inherent limitations for use in fine-grained materials (Yao and Liu 2012; Deirieh et al. 2018). The ultimate aim is to link the micro and macro response (e.g., Pusch 1970; Delage and Lefebvre 1984; Djéran-Maigre et al. 1998; Hicher et al. 2000; Ringdal et al. 2010; Delage 2010; Hattab and Fleureau 2011; Hattab et al. 2013; Suuronen et al. 2014; Wensrich et al. 2018; Birmpilis et al. 2019; Cotecchia et al. 2019; Delage and Tessier 2021; Abed and Sołowski 2020; Schuck et al. 2020; Dor et al. 2020; Zhao et al. 2020). Regardless of the experimental method, either a bulk response of the complete sample volume (MIP, W/SAXS, SANS), a two-dimensional (2D) map of the integrated response along the transmitted X-ray/electron beam (scanning W/SAXS and TEM), or a 2D surface profile (with a certain depth of view) is obtained (SEM). Therefore, none of the methods are truly three-dimensional (3D), which hampers the characterization of the complex spatially organized dense systems of polydisperse particles that are present in natural clays.X-ray computed tomography (XCT) overcomes the aforementioned limitations because it obtains 3D image data of the sample under test and is already used for characterization and process monitoring of fine-grained geomaterials, such as clay and clayrock (e.g., Viggiani et al. 2004; Hemes et al. 2015; Wang et al. 2017; Stavropoulou et al. 2020). In these studies, spatial heterogeneities from features that are substantially larger than the particle size of individual clay platelets were investigated, such as the characteristics of macro pores, crack formation, or continuum scale deformations devised from an evolving (natural) speckle pattern during a mechanical test. Submicron spatial resolution is required for the study of fine-grained soils, such as natural clays for which the largest dimension is on the order of O(μm) (Mitchell and Soga 2005). Recently, synchrotron-based imaging instruments, including at the beam lines ID16 and ID19 of the European Synchrotron (ESRF) (Martínez-Criado et al. 2016; Boller et al. 2017) used in this study, have started to attain the required submicron spatial resolutions. Furthermore, the favorable attributes of a synchrotron X-ray source allow the exploitation of phase contrast mechanisms (i.e., Cloetens et al. 1999; Paganin et al. 2002), which is essential for imaging natural clays that generally have poor absorption contrast (Birmpilis 2020).The importance of the fabric on the emerging mechanical response of geomaterials is undisputed. Experimental quantification of fabric started with 2D plane stress experiments on photoelastic discs (Oda and Konishi 1974) and have since progressed to the study of more complex assemblies of (natural) granular materials using laboratory- or synchrotron-based XCT (Imseeh et al. 2018; Rorato et al. 2020; Wiebicke et al. 2020; Zhao et al. 2021). For the latter, directional measurements of fabric are based on geometrical features extracted from the 2D and/or 3D image data. Alternatively, the output from discrete element modeling has been used in the absence of experimental data (e.g., Yimsiri and Soga 2010; Zhao and Guo 2013; Kuhn et al. 2015). In coarse grained materials, the orientation of contact normal vectors, void vectors, and branch vectors or simply the orientation of the primary axis of the particle (e.g., Bathurst and Rothenburg 1990; Fonseca et al. 2013; Kuhn et al. 2015) are all used as input for the fabric tensor in contemporary continuum models for coarse grained materials (Wang et al. 2020). In contrast, for clay samples, the particle orientations are most often extracted as a measure for fabric from microscopy data (e.g., Cotecchia et al. 2019; Zhao et al. 2020), W/SAXS (Birmpilis et al. 2019), or SANS (Wensrich et al. 2018). However, the continuum models starting from the fabric measured experimentally at the particle scale are still in their infancy.In this work, the 3D fabric, that is, the particle directions for different size fractions, is quantified experimentally from unprecedented high resolution nano- and microtomography data on undisturbed samples of a natural sensitive clay from Sweden.Measurement MethodsISP MethodThe integral suspension pressure (ISP) method (Durner et al. 2017) was utilized to obtain the distribution of the mass fractions of the natural clay tested. ISP is a column sedimentation method in which Stokes’ law is applied to determine particle sizes related to the measured temporal change of the suspension pressure that results from the reduction of the particle concentration during sedimentation at a specific depth. The sample was prepared for the determination of the particle size distribution by wet sieving and the sedimentation method according to SS-ISO 11277:2020. Amendments in the procedure were made based on the recommendations for the use of the PARIO soil particle analyzer (METER Group, Pullman, Washington) (Gee and Or 2002). In particular, all particles <2  mm were removed prior to the treatment of the sample by sieving. After the organic content was measured to be 4% [loss on ignition: SS-EN 15935:2012 (SIS 2012)], the sample was treated for organic matter destruction [SS-ISO 11277:2020 (SIS 2020)]. Soluble salts were removed through washing by centrifuge drainage for 15 min at a relative centrifugal force (RCF) of 400 g [SS-ISO 11277:2020 (SIS 2020)] until the measured electrical conductivity was 2.1  mSm−1 (far below the limit of 40  mSm−1). For chemical dispersion, sodium hexametaphospate was used following Gee and Or (2002), and physical dispersion was achieved by using an horizontal orbital shaking table at 125  min−1 overnight. The sedimentation measurement lasted 12 h, and the suspension was subsequently sieved using the wet sieving method to obtain the data for the larger fractions in the range of 63  μm

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