Stochastic Model for Time-Dependent Compression of Particulate Media
Publication: Journal of Engineering Mechanics
Volume 127, Issue 6
Abstract
The volumetric creep of loose granular materials, in absence of pore fluid pressure, is modeled as a stochastic process of diffusion-convection for excess porosity under sustained, applied loading. The analogy of the underlying concepts, with the theory of sedimentation in Brownian motion, and differences with the earlier contribution of Marsal (1965) are discussed. The analytical formulation and numerical solution are presented for a 1D compression with finite strain and moving boundary surface. The results represent the time evolution of the spatial distribution of the material porosity and the rate of settlement. The compression versus time relationship is normalized in dimensionless form to facilitate the determination of the governing equation coefficients from test data. Examples of determination and comparisons with the model response are presented. According to the model, final settlement is reached asymptotically with equilibrium porosity. At transient states, the spatial distribution of porosity is not necessarily uniform, even when both initial and final distribution are uniform.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Biarez, J., and Hicher, P. Y. ( 1989). “An introduction to the study of the relation between the mechanics of discontinuous granular media and the rheological behavior of continuous equivalent media—application to compaction.” Proc., Int. Conf. on Micromechanics of Granular Media, Clermont-Ferrand, France, Balkema, Rotterdam, The Netherlands, 1–13.
2.
Bourdeau, P. L. ( 1986). “Analyse probabiliste des tassements d'un massif de sol granulaire.” These de Doctorat es Sciences Techniques, No. 628, Swiss Federal Institute of Technology, Lausanne.
3.
Bourdeau, P. L. ( 1987). “Probabilistic analysis of settlement in loose particulate media.” Proc., 5th Int. Conf. on Application of Statistics and Probability to Soil and Struct. Engrg., ICASP5, Vancouver, N. C. Lind, ed., 2, 977–984.
4.
Bourdeau, P. L., and Harr, M. E. ( 1989). “Stochastic theory of settlement of loose cohesionless soils.” Geotechnique, 39(4), 641–654.
5.
Buisman, A. S. K. ( 1936). “Results of long duration settlement observations.” Proc., 1st Int. Conf. on Soil Mech. and Found. Engrg., Cambridge, Mass., 103–106.
6.
Cambou, B. ( 1993). “From global to local variables in granular materials.” Proc., 2nd Int. Conf. on Micromech. of Granular Media, Birmingham, United Kingdom, Balkema, Rotterdam, The Netherlands, 73–86.
7.
Chandrasekhar, S. ( 1943). “Stochastic problems in physics and astronomy.” Rev. Modern Physics, 15(1), 1–89.
8.
Chang, C. S., Chang, Y., and Kabir, M. G. (1992a). “Micromechanics modeling for stress-strain behavior of granular soils. I: Theory.”J. Geotech. Engrg., ASCE, 118(12), 1959–1974.
9.
Chang, C. S., Chang, Y., and Kabir, M. G. (1992b). “Micromechanics modeling for stress-strain behavior of granular soils. II: Evaluation.”J. Geotech. Engrg., ASCE, 118(12), 1975–1992.
10.
Feda, J. ( 1992). Creep of soils and related phenomena, Elsevier Science, Amsterdam.
11.
Feller, W. ( 1957). An introduction to probability theory and its applications, Vol. 1, Wiley, New York.
12.
Feller, W. ( 1971). An introduction to probability theory and its applications, Vol. 2, Wiley, New York.
13.
Gear, C. W. ( 1971). Numerical initial value problems in ordinary differential equations, Prentice-Hall, Englewood, N.J.
14.
Gibson, R. E., and Lo, K. Y. ( 1961). “A theory of consolidation of soils exhibiting secondary compression.” Publication No. 41, Norwegian Geotechnical Inst., Oslo.
15.
Gibson, R. E., England, G. L., and Hussey, J. L. ( 1967). “The theory of one-dimensional consolidation of saturated clays: I. Finite non-linear consolidation of thin homogeneous layers.” Géotechnique, 17, 261–273.
16.
Gibson, R. E., Schiffman, R. L., and Cargill, K. W. ( 1981). “The theory of one-dimensional consolidation of saturated clays: II. Finite non-linear consolidation of thick homogeneous Layers.” Can. Geotech. J., 18, 280–293.
17.
Harr, M. E. ( 1977). Mechanics of particulate media. A probabilistic approach, McGraw-Hill, New York.
18.
Jenkins, J. T., Cundall, P. A., and Ishibashi, I. ( 1989). “Micromechanical modeling of granular materials with the assistance of experiments and numerical simulations.” Proc., Int. Conf. on Micromech. of Granular Media, Clermont-Ferrand, France, Balkema, Rotterdam, The Netherlands, 257–264.
19.
Kandaurov, I. I. ( 1959). Theory of discrete stress and compressive strain distributions in homogeneous and layered soil foundation (in Russian), Gosstroyizdat, Leningrad.
20.
Kandaurov, I. I. ( 1991). “Mechanics of granular media and its application in civil engineering.” Geotechnika 6, Balkema, Rotterdam, The Netherlands.
21.
Karlin, S. ( 1966). A first course in stochastic processes, Academic, New York.
22.
Lade, P. V., and Liu, C. T. (1998). “Experimental study of drained creep behavior of sand.”J. Engrg. Mech., ASCE, 124(8), 912–920.
23.
Litwiniszyn, J. ( 1964). “An application of the random walk argument to the mechanics of granular media.” Proc., IUTAM Symp. on Rheology and Soil Mech., Grenoble, France, J. Kravchenko and P. M. Sirieys, eds., 83–89.
24.
Marsal, R. J. ( 1965). “Stochastic processes in the grain skeleton of soils.” Proc., 6th Int. Conf. on Soil Mech. and Found. Engrg., Montreal, 2, 303–307.
25.
Marsal, R. J. ( 1973). “Mechanical properties of rockfill.” Embankment Dam Engineering, Casagrande Volume, Hirschfeld and Poulos, eds., Wiley, New York, 109–200.
26.
Mitchell, J. K. ( 1993). Fundamentals of soil behavior, 2nd Ed., Wiley, New York.
27.
Mullins, W. W. ( 1972). “Stochastic theory of particle flow under gravity.” J. Applied Phys., 43(2), 665–678.
28.
Papoulis, A. ( 1965). Probability, random variables, and stochastic processes, McGraw-Hill, New York.
29.
Schiffman, R. L., Pane, V., and Gibson, R. E. ( 1984). “The theory of one-dimensional consolidation of saturated clays: IV. An overview of nonlinear finite strain sedimentation and consolidation.” Proc., ASCE Symposium on Sedimentation-Consolidation Models, San Francisco, Calif., 1–29.
30.
Schmoluchowski, M. V. ( 1916). “Drei Vortrage uber Diffusion. Brownische Bewegung und Koagulation von Kolloidteichen,” Phys. Zeits., 17 (in German).
31.
Sergeev, I. J. ( 1969). “The application of probability-processes equations to the theory of stress distribution in non-cohesive soil foundation beds.” Soil Mech. and Found. Engrg., 2, 84–88.
32.
Sweet, A. L., and Bogdanov, J. L. (1965). “Stochastic model for predicting subsidence.”J. Engrg. Mech., ASCE, 91, 091(EM2), 21–45.
33.
Taylor, D. W. ( 1948). Fundamentals of soil mechanics, Wiley, New York.
34.
Taylor, D. W., and Merchant, W. ( 1940). “A theory of clay consolidation accounting for secondary compression.” J. Math. and Phys., 19, 167–185.
35.
Terzaghi, K. ( 1925). “Erdbaumechanik,” F. Deuticke, Vienna, Austria.
36.
Yamamuro, J., and Lade, P. V. ( 1993). “Effects of strain rate on instability of granular materials.” Geotech. Testing J., ASTM, 16(3), 304–313.
37.
Znidarcic, D., Croce, P., Pane, U., Ko, H. Y., Olsen, H. W., and Schiffman, R. L. ( 1984). “The theory of one-dimensional consolidation of saturated clays: III. Existing testing procedures and analysis.” Geotech. Testing J., ASTM, 7(3), 127–133.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 127 • Issue 6 • June 2001
Pages: 531 - 543
History
Received: Jun 7, 2000
Published online: Jun 1, 2001
Published in print: Jun 2001
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.