Stress Diffusion in Granular Materials: The Role of Anisotropy
Publication: Geo-Congress 2024
ABSTRACT
The potential connection of stress diffusivity to anisotropy is explored. The approach taken in this investigation is empirical. It is postulated that material (microstructural) anisotropy would affect stress distribution given by the diffusion theory in ways analogous to what is observed in elastic anisotropy solutions; that is, it modifies attenuation with depth and lateral distribution in similar ways. A case example of a horizontal layer, with two-dimensional geometry, subjected to a uniform strip load, is analyzed using both stress diffusion and anisotropic elasticity theories, and correlations between the resulting stress fields are observed over a range of stress diffusivity coefficients and anisotropy ratios. A strong empirical relationship is found to relate the two parameters; the diffusivity coefficient increases with increasing anisotropy ratio. Overall, the study confirms that anisotropy is a factor in stress diffusion and contributes to a better understanding of the meaning and assessment of the diffusivity coefficient.
Get full access to this article
View all available purchase options and get full access to this chapter.
REFERENCES
ABAQUS. (2020). User’s Manual, Vers. 6.20. Dassault Systèmes Simulia Corp, Johnston, RI.
Alpan, I. (1967). “The empirical evaluation of the coefficient K0 and K0R.” Soils and Foundations, 7(1), 31–40.
Bellotti, R., Jamiolkowski, M., Presti, D. L., and O’Neill, D. A. (1996). “Anisotropy of small strain stiffness in Ticino sand.” Géotechnique, 46(1), 115–131.
Bourdeau, P. L. (1986). Analyse probabiliste des tassements d’un massif de sol granulaire. Doctoral Thesis No 628, Swiss Ferderal Institute of Technology, Lausanne (in French).
Bourdeau, P. L., and Harr, M. E. (1989). “Stochastic theory of settlement of loose cohesionless soils.” Géotechnique, 39(4), 641–654.
Bourdeau, P. L. (2001). “Stochastic model for time-dependent compression of particulate media.” Journal of Engineering Mechanics, 127(6), 531–543.
Bourdeau, P. L. (2009). “Stochastic modeling of load-induced settlement in loose granular materials.” Journal of Aerospace Engineering, 22(1), 33–42.
Chikwendu, S. C., and Alimba, M. U. (1979). “Diffusion analogy for some stress computations.” Journal of the Geotechnical Engineering Division, 105(11), 1337–1342.
Chikwendu, S. C. (1981). “The dependence of probabilistic stresses on relative density in granular media.” International Journal of Engineering Science, 19(11), 1449–1454.
Dantu, P. (1957). “Contribution à l'étude mécanique et géométrique des milieux pulvérulents.” Proc. 4th ICSMFE, London, 1957.
Golden, J. M. (1984). “Stochastic models of granular materials.” Journal of Engineering Mechanics, 110(11), 1610–1626.
Hanna, A., and Al-Romhein, R. (2008). “At-rest earth pressure of overconsolidated cohesionless soil.” Journal of Geotechnical and Geoenvironmental Engineering, 134(3), 408–412.
Harr, M. E. (1977). Mechanics of Particulate Media: a Probabilistic Approach. McGraw-Hill Co. New York.
Kamrin, K., and Bazant, M. Z. (2007). “Stochastic flow rule for granular materials.” Physical Review E, 75(4), 041301.
Love, A. E. H. (1892). A Treatise on the Mathematical Theory of Elasticity. Two volumes. Cambridge University Press.
Mayne, P. W., and Kulhawy, F. H. (1982). “K0-OCR Relationships in Soil.” Journal of the Soil Mechanics and Foundations Division, 108(6), 851–872.
Meyerhof, G. G. (1976). “Bearing capacity and settlement of pile foundations.” Journal of the Geotechnical Engineering Division, 102(3), 197–228.
Oda, M. (1972). “Initial fabrics and their relation to mechanical properties of granular material.” Soil and Foundations, 12(1), 17–36.
Oda, M. (1974). “A mechanical and statistical model of granular material.” Soils and Foundations, 14(1), 13–27.
Papoulis, A. Probability, Random Variables, and Stochastic Processes. McGraw-Hill, New York, 1965.
Sergeev, I. T. (1969). “The application of probability-processes equations to the theory of stress distribution in non-cohesive soil foundation beds (discussion).” Soil Mechanics and Foundation Engineering, 6(2), 84–88.
Seyhan, U., and Tutumluer, E. (2002b). “Anisotropic Modular Ratios as Unbound Aggregate Performance Indicators.” Journal of Materials in Civil Engineering, American Society of Civil Engineers, 14(5), 409–416.
Tutumluer, E. (1995). Predicting Behavior of Flexible Pavements with Granular Bases. Georgia Institute of Technology.
Information & Authors
Information
Published In
History
Published online: Feb 22, 2024
ASCE Technical Topics:
- Anisotropy
- Continuum mechanics
- Deformation (mechanics)
- Diffusion
- Diffusion (porous media)
- Elastic analysis
- Engineering materials (by type)
- Engineering mechanics
- Geomechanics
- Geotechnical engineering
- Granular materials
- Materials engineering
- Soil mechanics
- Soil properties
- Solid mechanics
- Stress (by type)
- Stress analysis
- Stress distribution
- Structural analysis
- Structural engineering
- Structural mechanics
- Thermodynamics
- Transport phenomena
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.