An insight into time rate of consolidation
Lovisa, Julie (2012) An insight into time rate of consolidation. PhD thesis, James Cook University.
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Abstract
Terzaghi's elegant theory of one-dimensional consolidation is dependent upon a number of assumptions which can, at times, severely limit the predictive capabilities of the resulting analytical model. Although other more complex models exist, Terzaghi's one-dimensional model remains popular amongst practicing engineers due to its inherent simplicity and notoriety. The purposes of this study have been to explore key aspects of Terzaghi's consolidation theory, and extend the analytical solution to incorporate a variety of loading scenarios that may give rise to non-uniform distributions of excess pore water pressure. To do this, Terzaghi's consolidation equation was solved within the program MATLAB using a collocation approach to solve for series coefficients, instead of the more traditional orthogonality approach. A novel truncation technique was also employed in cases where discontinuities were present in the initial condition, which would have otherwise elicited Gibbs phenomena, an undesirable trait of series solutions.
By varying the initial condition in the MATLAB program, the consolidation behaviour of a soil subjected to a variety of different initial excess pore water pressure (uᵢ) distributions was analysed in terms of excess pore water pressure decay and percentage consolidation settlement. These simulations were conducted for both singly and doubly drained soil layers. In many singly drained cases, the excess pore water pressure within the soil layer decayed in a peculiar fashion, where a 'redistribution' of pore pressure occurred during the early stages of consolidation.
When viewing consolidation behaviour in terms of percentage consolidation (U), it was easily shown that any reference to drainage path length (H(d)ᵣ) should be avoided. In fact, continuing to use the traditional expression for time factor (T) in terms of H(d)ᵣ can actually complicate analyses. Instead, T should be expressed in terms of layer thickness (H) only. By adopting this alternative time factor expression, a relationship between the consolidation behaviour due to uniform and non-uniform uᵢ-distributions was developed. This relationship utilised the knowledge that after some short time during consolidation, any skewness attributed to the non-uniform uᵢ-distribution will disappear, and the decay of excess pore water pressure with depth will revert to a sinusoidal or half-sinusoidal shape, for doubly or singly drained cases, respectively. Correction factors were then developed so that the widely available U -T values can be easily adjusted to account for any non-uniform uᵢ-distribution.
Currently, some form of Terzaghi's consolidation theory is also used to analyse laboratory time-settlement data so that important consolidation properties such as the coefficient of consolidation (cᵥ) can be back-calculated. The efficacy of some of the more popular curvefitting techniques when applied to different soil types was assessed using a new cᵥ - calculation procedure which steers away from traditional curve-fitting procedures and instead takes advantage of the matrix manipulation capabilities of MATLAB. It was found that this proposed method and Taylor's square-root of time method yielded the most accurate values of cᵥ. Previously restricted to data obtained from a uniform uᵢ-distribution, the Taylor and Casagrande curve-fitting techniques were also generalised to account for a variety of non-uniform uᵢ-distributions. Two of these modified procedures (a singly/doubly drained layer subjected to a sinusoidal uᵢ-distribution) were also experimentally verified.
It was also shown that the traditional restrictions associated with consolidation oedometers are not as inflexible as previously assumed. Currently, standard practice requires the height to diameter ratio of a consolidating sample to remain less than 0.4 to avoid any effect of wall friction. However, results suggest that data obtained from a 'tall' oedometer with a height as much as twice its diameter can still be analysed using conventional curve-fitting techniques.
Finally, the effects of time-dependent loading were investigated using two approaches; a constant-rate loading approach, and a discretised loading approach, which more closely models the stepped nature of fill application in the field. It was found that for T increments less than 0.0143, the discretised loading approach effectively became a constant-rate loading problem, an inference that was also experimentally verified.
| Item ID: | 40012 |
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| Item Type: | Thesis (PhD) |
| Keywords: | consolidation; geotechnical engineering; pore pressure; soils; Terzaghi; Terzaghi’s consolidation theory; time rate |
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| Additional Information: | Publications arising from this thesis are available from the Related URLs field. The publications are: Lovisa, Julie, Read, Wayne, and Sivakugan, Nagaratnam (2010) Consolidation behaviour of soils subjected to asymmetric initial excess pore pressure distributions. International Journal of Geomechanics, 10 (5). pp. 181-189. Lovisa, Julie, Read, Wayne, and Sivakugan, Nagaratnam (2012) Consolidation behavior of soils subjected to asymmetric initial excess pore pressure distributions with one-way drainage. International Journal of Geomechanics, 12 (3). pp. 318-322. Lovisa, Julie, Read, Wayne, and Sivakugan, Nagaratnam (2011) A critical reappraisal of the average degree of consolidation. Geotechnical and Geological Engineering, 29 (5). pp. 873-879. Hanna, Daniel, Sivakugan, Nagaratnam, and Lovisa, Julie (2013) Simple approach to consolidation due to constant rate loading in clays. International Journal of Geomechanics, 13 (2). pp. 193-196. Lovisa, Julie, Read, Wayne, and Sivakugan, Nagaratnam (2013) Time factor in consolidation: critical review. International Journal of Geomechanics, 13 (1). pp. 83-86. Lovisa, Julie, and Sivakugan, Siva (2013) An in-depth comparison of cv values determined using common curve-fitting techniques. Geotechnical Testing Journal, 36 (1). pp. 1-10. Lovisa, Julie, and Sivakugan, Nagaratnam (2015) Tall oedometer testing: method to account for wall friction. International Journal of Geomechanics, 15 (2). pp. 1-9. Sivakugan, Nagaratnam, Lovisa, Julie, Ameratunga, Jay, and Das, Braja M. (2014) Consolidation settlement due to ramp loading. International Journal of Geotechnical Engineering, 8 (2). pp. 191-196. |
| Date Deposited: | 12 Aug 2015 22:20 |
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