Weakly cemented granular materials: study at multiple length scales
Cemented granular systems are encountered at various scales in nature and artificially. We present an experimental study carried out on the structure and mechanical behaviour of weakly cemented granular materials. We study the cemented granular materials at two scales -- micro (particle-bond-particle) scale and macro (ensemble) scale. At the micro-scale studies, a set of x-ray computed tomography experiments are performed. We characterize the structure of initial configuration of weakly cemented granular materials. We discuss, in detail, quantification of fabric and structure such as coordination number, fabric tensor, directional distribution of contact normal and particles, and grain size distribution. An alternative approach to arrive at the fabric tensor is also discussed. To obtain these characteristics, the scanned volume from XCT is segmented into particles and contacts (bonds - for a contact bound structure). For the segmentation, watershed along with h-minima or h-maxima transform are used. The algorithm is presented in detail for a two dimensional example image. From the segmentation results, it is observed that the particles of cemented granular materials orient themselves away from the direction of the gravity or body force whereas the contact normals have a tendency to orient along the direction of gravity. Further, we perform a set of uni-axial compression tests inside the X-ray computed tomograph. It is observed that the initial structure of cemented granular material does not changes significantly before the peak load is reached. The average coordination number increases at lower strains due to contraction of the specimen however at larger strains, continuous reduction in coordination number is observed. The evolution of average porosity field has similar trend to the volumetric strain. Further, the particle and contact align themselves along the direction of load at lower strains whereas at higher strains, they orient themselves away from the loading direction. At macro-scale, we perform a set of triaxial and hollow cylinder shear tests to understand the effect of confining pressure, intermediate principal stress ratio, and density on weakly cemented sands. These results are analyzed in the framework of plasticity theory. We present the extraction of gross yield points of bonds, plastic work contours or yield curves, plastic strain increments, and failure. Further, we calibrate and validate the Lade's single hardening elastic-plastic model. The details of model parameter calibration and integration algorithms for prediction of behaviour are provided. The Lade's model uses stress transformation for accommodation of cementation in the model. Stress transformation implies the translation of elastic-plastic surface along the hydrostatic axis in the stress-space by bond strength of cemented sands. With this stress transformation, the stress-strain response is predicted satisfactorily however, the volumetric predictions only show contraction. In contrast, the experimental volumetric behaviour is initially contractive followed by a dilative response (in the range of confining pressure tested). To validate the applicability of stress transformation, we perform a set of experiments with cemented sands and sands (equivalent sand) subjected to elevated confining pressure (increased by the bond strength). The response suggest that the stress transformation is satisfactory at small strain however due to bond breakage, a deviation in the cemented sands and equivalent sand is observed. This behaviour suggest that the inclusion of bond degradation with stress transformation should work successfully. To verify this, we include the bond degradation in the stress-dilatancy relation for prediction of stress-dilatancy behaviour of cemented sands. With inclusion of bond degradation, the Rowe's and Zhang-Salgado's stress dilatancy relation successfully predict the stress-dilatancy behaviour of cemented sands. We provide microstructural insights from our tomography experiments to the macro level response observed under various stress conditios. Further, a set of scaling studies are also performed on unconfined compressive strength with varying particle sizes (particle size effect), specimen sizes (specimen size effect), and controlled study (scaling specimen and particle sizes proportionally to keep number of particles fixed). With increase in the specimen size, the peak compressive strength of weakly cemented granular material increases. The peak compressive strength decreases with increase in the size of particle. In controlled study, the strength is insensitive to proportional scaling of specimen and particles. The scaling in these contact bound granular materials is significantly different from brittle and quasi-brittle solids such as rocks and concrete. To understand the emergence of the scaling, we use microstructural characteristics obtained from XCT. In particular, we obtain the geometric clusters which are akin to force chains i.e. geometric clusters are able to predict the force distribution in a granular material from its structure. Using the percolation probability of these geometric cluster and normalized cluster size, similar trends as strength are obtained. The primary source of these scaling is results of entanglement of force chains which is presented here by entanglement of geometric cluster.
- Civil Engineering (CiE)