# On Mathematical Analysis of Soil Structure using Consolidation Equations

## Main Article Content

## Abstract

This paper deals with an explicit finite difference solution for the one- and two-dimensional consolidation of a homogeneous clay layer. The finite difference method approximates the solution of a continuous problem by representing it in terms of a discrete set of elements such that there is an integer number of points in depth and an integer number of times at which we calculate the field variables; in this case, just the excess pore water pressure. The calculation of the average degree of consolidation is used as a medium for comparison between the numerical analysis and the empirical analysis. Here, we have solved two-dimensional consolidation equations numerically by using Alternating Direction Implicit (ADI) Method. Moreover, tridiagonal methods are used here alongside the ADI method. The main idea behind this technique is to avoid the complexities which usually occur while solving higher order partial differential equations. Finally, numerical examples are presented to show the relationship between the Pore Water Pressure (PWP) and Depth Time Grids (DTG). It was also discovered that the Average Degree of Consolidation (*U _{ave}*) directly varies with respect to the Time factor (

*T*) as the time step increases.

_{v}## Article Details

*Journal of Scientific Research and Development*,

*17*(1), 65-72. Retrieved from http://jsrd.unilag.edu.ng/article/view/44

## References

Bartholomeeusen, G. (2003). Compound shock waves and creep behaviour in sediment beds. University of Oxford, Oxford, UK, p. 210.

Bartholomeeusen, G., Sills, G., Znidarcic, D., Van Kesteren, W., Merckelbach, L. M., Pyke, R., Carrier, W. D., Lin, H., Penumadu, D. and Winterwerp, H. (2002). Numerical prediction of large strain consolidation. Géotechnique, 52(9): 639–648.

Been, K. (1980). Stress strain behaviour of a cohesive soil deposited under water. University of Oxford, Oxford, United Kingdom.

Been, K. and Sills, G. (1981). Self-weight consolidation of soft soils: an experimental and theoretical study. Géotechnique, 31(4): 519–535.

Bürger, R., Damasceno, J. J. R. and Karlsen, K. H. (2004). A mathematical model for batch and continuous thickening of flocculated suspensions in vessels with varying cross-section. Int. J. Miner. Process, 73(2): 183–208.

Carillo, N. (1942). Differential equation of a sliding surface in an ideal saturated plastic soil. J. Maths. Physics, 21(1): 1–5.

Coe, H. S. and Clevenger, G. H. (1916). Methods for determining the capacities of slime settling tanks. Trans. AIME, 55: 356–384.

Craig, R. F. (2007). Soil Mechanics. Van Nostrand Reinholdt (UK), Co. Ltd. Seventh Edition.

Das, B. M. S. and Herbich, J. B. (1991). Principles of Geotechnical Engineering. Coastal Engineering Handbook.

Das, B. M. (2008). Advanced Soil Mechanics, Washington, New York, London.

Davis, E. H. and Raymond, G. P. (1965). A non-linear theory of consolidation. Géotechnique, 15(2): 161–173.

Fitch, B. (1966). Current theory and thickener design. Ind. Eng. Chem., 58(10): 18–28.

Huerta, A. and Rodriguez, A. (1992). Numerical analysis of non-linear large-strain consolidation and filling. Comput. Struct., 44(1): 357–365.

Imai, G. (1981). Experimental studies on sedimentation mechanism and sediment formation of clay materials. Soils Found. 21(1): 7–20.

Imai, G., Hawlader, B. C. (1997). An elasto-viscoplastic analysis of self weight consolidation during continuous sedimentation, Computer Methods and Advances in Geomechanics: Proceedings of the International Conference on Computer Methods and Advances in 110 Geomechanics. A. A. Balkema, Arizona, USA, 1065.

Koppula, S. D. and Morgenstern, N. R. (1982). On the consolidation of sedimenting clays. Can. Geotech. J., 19(3): 260–268.

Kynch, G. J. (1952). A theory of sedimentation. Trans. Faraday Soc., 48: 166–176.

Liu, J. C. and Znidarčić, D. (1991). Modeling one-dimensional compression characteristics of soils. J. Geotech. Eng., 117(1): 162–169.

McRoberts, E. C. and Nixon, J. F. (1976). A theory of soil sedimentation. Can. Geotech. J., 13(3): 294–310.

Mikasa, M. and Takada, N. (1984). Self-weight consolidation of very soft clay by centrifuge, sedimentation consolidation models—predictions and validation, ASCE, 121–140.

Schiffman, R. L. (1982). The consolidation of soft marine sediments. Geo-Mar. Lett., 2(3): 199–203.

Schiffman, R. L. (2001). Theories of Consolidation. University of Colorado, USA.

Seneviratne, N. H., Fahey, M., Newson, T. A. and Fujiyasu, Y. (1996). Numerical modelling of consolidation and evaporation of slurried mine tailings. Int. J. Numer. Anal. Methods Geomech., 20(9): 647–671.

Sills, G. (1998). Development of structure in sedimenting soils. Trans. R. Soc., 356: 2515–2534.

Somogyi, F., Carrier III, W. D., Lawver, J. E. and Beckman, J. F. (1984). Waste phosphatoc clay disposal in mine cuts, in Sedimentation consolidation models: predictions and validation. (Eds. Yong, R. N. and Townsend, F. C.), ASCE, New York, 545–580.

Tan, S. A., Tan, T. S., Ting, L. C., Yong, K. Y., Karunaratne, G. P., Lee, S. L. (1988). Determination of consolidation properties for very soft clay. ASTM Geotechnical Testing Journal, 11(4): 233–240.

Terzaghi, K. (1943). Theoretical soil mechanics. John Wiley and Sons, Inc. New York,

Znidarčić, D., Schiffman, R. L., Pane, V., Croce, P., Ko, H. Y. and Olsen, H. W. (1986). The theory of one-dimensional consolidation of saturated clays Part V: Constant rate of deformation testing and analysis, Géotechnique, 36(2): 227–237.