Scan line void fabric anisotropy tensors of granular media
Tóm tắt
Soil fabric anisotropy tensors are related to the statistical distribution of orientation of different microstructural vector-like entities, most common being the contact normal vectors between particles, which are extremely difficult to determine for real granular materials. On the other hand, void fabric based tensors can be determined by image based quantification methods of voids (graphical approaches), which are well defined and easy to apply to both physical and numerical experiments. A promising void fabric characterization approach is based on the scan line method. Existing scan line based definitions of void fabric anisotropy tensors are shown analytically to inherit a shortcoming, since numerous small void segments in a sample have an inordinate contribution towards unwarranted isotropy. Discrete Element Method (DEM) of analysis subsequently confirms this analytical proof. The fact that such scan line void fabric tensor definitions yield acceptable results when used in conjunction with physical image-based measurements, is shown to be attributed to the natural “cut off” of smaller void segments that occurs during such measurements. This is the motivation to propose using the existing definition of void fabric tensors, with exclusion of void segments less than a “cut off” value associated with an internal length of the granular assembly. In addition, an entirely new void fabric tensor was introduced using the squared length, instead of the length of a void segment, as the weighting factor for the definition of the scan line void fabric tensor. It was found by means of DEM analysis that both alternative definitions are void of the aforementioned shortcoming and compatible with existing image quantification methods of void fabric anisotropy.
Tài liệu tham khảo
Satake, M.: Fabric tensor in granular materials. In: Vermeer, P.A., Luger, H.J. (eds.) IUTAM Symposium on Deformation and Failure of Granular Materials, pp. 63–68. Delft, Amsterdam, Vermeer PA (1982)
Dafalias, Y.F., Papadimitriou, A.G., Li, X.S.: Sand plasticity model accounting for inherent fabric anisotropy. J. Eng. Mech. 130(11), 1319–1333 (2004)
Oda, M., Nakayama, H.: Yield function for soil with anisotropic fabric. J. Eng. Mech. 115(1), 89–104 (1989)
Li, X.S., Dafalias, Y.F.: Anisotropic critical state theory: role of fabric. J. Eng. Mech. 138(3), 263–275 (2012)
Gao, Z., Zhao, J., Li, X.S., Dafalias, Y.F.: A critical state sand plasticity model accounting for fabric evolution. Int. J. Numer. Anal. Methods Geomech. 38(4), 370–390 (2014)
Roscoe, K.H., Schofield, A., Wroth, C.P.: On the yielding of soils. Geotechnique 8(1), 22–53 (1958)
Schofield, A., Wroth, P.: Critical State Soil Mechanics. McGraw Hill, New York City (1968)
Jaquet, C., Andó, E., Viggiani, G., Talbot, H.: Estimation of separating planes between touching 3D objects using power watershed. In: Hendriks, C.L.L., Borgefors, G., Strand R. (eds.) Mathematical Morphology and Its Applications to Signal and Image Processing, pp. 452–463. Springer, Berlin (2013)
Ghedia, R., O’Sullivan, C.: Quantifying void fabric using a scan-line approach. Comput. Geotech. 41, 1–12 (2012)
Li, X., Li, X.S.: Micro-macro quantification of the internal structure of granular materials. J. Eng. Mech. 135(7), 641–656 (2009)
Fu, P., Dafalias, Y.F.: Relationship between void-and contact normal-based fabric tensors for 2D idealized granular materials. Int. J. Solids Struct. 63, 68–81 (2015)
Oda, M., Nemat-Nasser, S., Konishi, J.: Stress-induced anisotropy in granular masses. Soils Found. 25(3), 85–97 (1985)
Biscarini, F., Samori, P., Greco, O., Zamboni, R.: Scaling behavior of anisotropic organic thin films grown in high vacuum. Phys. Rev. Lett. 78(12), 2389 (1997)
Kahl, W.A., Hinkes, R., Feeser, V., Holzheid, A.: Microfabric and anisotropy of elastic waves in sandstone—an observation using high-resolution X-ray microtomography. J. Struct. Geol. 49, 35–49 (2013)
Pietruszczak, S., Krucinski, S.: Description of anisotropic response of clays using a tensorial measure of structural disorder. Mech. Mater. 8(2–3), 237–249 (1989)
Muhunthan, B., Chameau, J.-L.: Void fabric tensor and ultimate state surface of soils. J. Geotech. Geoenviron. Eng. 123(2), 173–181 (1997)
Cundall, P.A., Strack, O.D.: A discrete numerical model for granular assemblies. Geotechnique 29(1), 47–65 (1979)
Kuo, C.-Y., Frost, J.D., Chameau, J.-L.: Image analysis determination of stereology based fabric tensors. Geotechnique 48(4), 515–525 (1998)