Numerical Model with Finite Differences Approach for CRS Consolidation Test

Abderrahmane Henniche; Smain Belkacemi

doi:doi:10.11648/j.es.20180303.11

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Numerical Model with Finite Differences Approach for CRS Consolidation Test

Abderrahmane Henniche, Smain Belkacemi

Published in Engineering Science (Volume 3, Issue 3)

Received: 13 November 2018 Accepted: 5 December 2018 Published: 3 January 2019

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Abstract

The Constant Rate of Strain (CRS) consolidation test is extensively used in last time to estimate the settlement of clayey soils in many geotechnical laboratories. Different theoretical solutions and numerical models have been developed to estimate consolidation parameters from CRS consolidation test data, and investigate the strain rate effect on the CRS consolidation results. In this study, a new numerical model is developed to simulate CRS consolidation test for small and large strain conditions and for both linear and nonlinear soils. This numerical model is based on the solution of Terzaghi’s classical consolidation equation by finite differences approach, with taking into account the variation of sample height with test time. Results of this numerical model indicate that applied vertical load at the top boundary of sample and excess pore pressure at its base are dependent on the applied strain rate. Evaluation of the consolidation parameters from numerical results of this model with small and large theoretical solutions shows excellent agreement between all methods in small strain level, and when large strain conditions are reached only use of large strain theories can produce good convergence with model results. However, when great strain rates (approximately β ≥ 0.1) are applied, a significant error can be observed in consolidation parameters calculation by using both small and large solutions. Finally, simulation of some experimental CRS tests reported in literature with this numerical model provides comparable consolidation parameters to those evaluated from the experimental CRS tests data.

Published in	Engineering Science (Volume 3, Issue 3)
DOI	10.11648/j.es.20180303.11
Page(s)	26-35
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2019. Published by Science Publishing Group

Keywords

Consolidation, CRS Test, Compressibility, Strain Rate, Numerical Model, Consolidation Parameters

References

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[2]	R. E. Smith and H. E. Wahls, “Consolidation under constant rate of strain,” Journal of the Soil Mechanics and Foundations Division, ASCE95 (SM2), pp. 519–539, 1969.
[3]	A. E. Z. Wissa, J. T. Christian, E. H. Davis, S. Heiberg, “Consolidation at constant rate of strain,” Journal of the Soil Mechanics and Foundations Division, ASCE97(10), pp. 1393–1413. 1971.
[4]	Y. Umehara and K. Zen, “Constant rate of strain consolidation for very soft clayey soils,” Soil Found. 20(2), pp. 79–95. 1980.
[5]	K. Lee, “Consolidation With Constant Rate of Deformation,” Geotechnique, 31(2), 215–229. 1981.
[6]	D. Znidarcic, R. L. Schiffman, V. Pane, P. Croce, H. Y. Ko, H. W. Olsen, “The theory of one-dimensional consolidation of saturated clays: Part V. Constant rate of deformation test in grand analysis,” Geotechnique, 36(2), 227–237. 1986.
[7]	S. Leroueil, M. Kabbaj, F. Tavenas, R. Bouchard, “Stress-Strain-Strain Rate Relation for the Compressibility of Sensitive Natural Clays,” Geotechnique, 35(2), 159–180. 1985.
[8]	K. M. Sample and C. D. Shackelford, “Apparatus for Constant Rate-Of-Strain Consolidation of Slurry Mixed Soils,” Geotech. Test. J., 35(3), 409–419. 2012.
[9]	J. Rui, C. Jinchun, H. Takenori, “Interpretation of coefficient of consolidation from CRS test results,” Geomechanics and Engineering, 5(1), 57–70. 2013.
[10]	H. Pu, P. J. Fox, Y. Liu, “Model for Large Strain Consolidation Under Constant Rate of Strain,” International Journal for Numerical and Analytical Methods in Geomechanics, 37(11), 1574–1590. 2013.
[11]	Y. P. Vaid, P. K. Robertson, R. G. Campanella, “Strain rate behavior of Saint-Jean-Vianney clay,” Canadian Geotechnical Journal, 16(1), 34–42. 1979.
[12]	T. C. Sheahan, P. J. Watters, “Experimental Verification of CRS Consolidation Theory,” Journal of Geotechnical and Geoenvironmental Engineering, 123(5), 430–437. 1997.
[13]	T. Moriwaki, T. Satoh, “Method for determining the horizontal coefficient of permeability of clay,” Proceedings of the 44th Annual Presentation of Geotechnical Engineering, Yokohama, Japan, 219–220. 2009. (In Japanese).
[14]	A. L. Adams, “Laboratory Evaluation of the Constant Rate of Strain and Constant Head Techniques for Measurement of the Hydraulic Conductivity of Fine Grained Soils,” M. S. thesis, Massachusetts Institute of Technology, Cambridge, MA. 2011.
[15]	K. A. Kassim, S. A. R. Ahmad, B. H. K. Ahmad, S. Y. Chong, C. S. Lam, “Criteria of Acceptance for Constant Rate of Strain Consolidation Test for Tropical Cohesive Soil,” Geotechnical and Geological Engineering, 34(4), pp. 931–947. 2016.
[16]	H .Ahmadi, H. Rahimi, A. Soroush, A. Claes, “Experimental research on variation of pore water pressure in constant rate of strain consolidation test,“ Acta geotechnical slovenica 2, pp. 47–57. 2014.
[17]	C. T. Gorman, T. C. Hopkins, R. C. Deen, V. P. Drnevich, "Constant Rate of Strain and Controlled Gradient Consolidation Testing", Geotechnical Testing Journal, 1 (1), pp. 3–15. 1978.
[18]	B. M. Das, “Advanced Soil Mechanics,” 3thEdition. Taylor and Francis, London and NewYork, 300–310. 2008.
[19]	ASTM, “Standard test method for one-dimensional consolidation properties of saturated cohesive soils using controlled-strain loading,” D4186–06, West Conshohocken, PA. 2006.
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APA Style

Abderrahmane Henniche, Smain Belkacemi. (2019). Numerical Model with Finite Differences Approach for CRS Consolidation Test. Engineering Science, 3(3), 26-35. https://doi.org/10.11648/j.es.20180303.11

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ACS Style

Abderrahmane Henniche; Smain Belkacemi. Numerical Model with Finite Differences Approach for CRS Consolidation Test. Eng. Sci. 2019, 3(3), 26-35. doi: 10.11648/j.es.20180303.11

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AMA Style

Abderrahmane Henniche, Smain Belkacemi. Numerical Model with Finite Differences Approach for CRS Consolidation Test. Eng Sci. 2019;3(3):26-35. doi: 10.11648/j.es.20180303.11

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@article{10.11648/j.es.20180303.11,
  author = {Abderrahmane Henniche and Smain Belkacemi},
  title = {Numerical Model with Finite Differences Approach for CRS Consolidation Test},
  journal = {Engineering Science},
  volume = {3},
  number = {3},
  pages = {26-35},
  doi = {10.11648/j.es.20180303.11},
  url = {https://doi.org/10.11648/j.es.20180303.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.es.20180303.11},
  abstract = {The Constant Rate of Strain (CRS) consolidation test is extensively used in last time to estimate the settlement of clayey soils in many geotechnical laboratories. Different theoretical solutions and numerical models have been developed to estimate consolidation parameters from CRS consolidation test data, and investigate the strain rate effect on the CRS consolidation results. In this study, a new numerical model is developed to simulate CRS consolidation test for small and large strain conditions and for both linear and nonlinear soils. This numerical model is based on the solution of Terzaghi’s classical consolidation equation by finite differences approach, with taking into account the variation of sample height with test time. Results of this numerical model indicate that applied vertical load at the top boundary of sample and excess pore pressure at its base are dependent on the applied strain rate. Evaluation of the consolidation parameters from numerical results of this model with small and large theoretical solutions shows excellent agreement between all methods in small strain level, and when large strain conditions are reached only use of large strain theories can produce good convergence with model results. However, when great strain rates (approximately β ≥ 0.1) are applied, a significant error can be observed in consolidation parameters calculation by using both small and large solutions. Finally, simulation of some experimental CRS tests reported in literature with this numerical model provides comparable consolidation parameters to those evaluated from the experimental CRS tests data.},
 year = {2019}
}

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TY  - JOUR
T1  - Numerical Model with Finite Differences Approach for CRS Consolidation Test
AU  - Abderrahmane Henniche
AU  - Smain Belkacemi
Y1  - 2019/01/03
PY  - 2019
N1  - https://doi.org/10.11648/j.es.20180303.11
DO  - 10.11648/j.es.20180303.11
T2  - Engineering Science
JF  - Engineering Science
JO  - Engineering Science
SP  - 26
EP  - 35
PB  - Science Publishing Group
SN  - 2578-9279
UR  - https://doi.org/10.11648/j.es.20180303.11
AB  - The Constant Rate of Strain (CRS) consolidation test is extensively used in last time to estimate the settlement of clayey soils in many geotechnical laboratories. Different theoretical solutions and numerical models have been developed to estimate consolidation parameters from CRS consolidation test data, and investigate the strain rate effect on the CRS consolidation results. In this study, a new numerical model is developed to simulate CRS consolidation test for small and large strain conditions and for both linear and nonlinear soils. This numerical model is based on the solution of Terzaghi’s classical consolidation equation by finite differences approach, with taking into account the variation of sample height with test time. Results of this numerical model indicate that applied vertical load at the top boundary of sample and excess pore pressure at its base are dependent on the applied strain rate. Evaluation of the consolidation parameters from numerical results of this model with small and large theoretical solutions shows excellent agreement between all methods in small strain level, and when large strain conditions are reached only use of large strain theories can produce good convergence with model results. However, when great strain rates (approximately β ≥ 0.1) are applied, a significant error can be observed in consolidation parameters calculation by using both small and large solutions. Finally, simulation of some experimental CRS tests reported in literature with this numerical model provides comparable consolidation parameters to those evaluated from the experimental CRS tests data.
VL  - 3
IS  - 3
ER  -

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Author Information

Abderrahmane Henniche

Department of Civil Engineering, University of Medea, Medea, Algeria
Smain Belkacemi

Department of Civil Engineering, Ecole Nationale Polytechnique, Algiers, Algeria

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APA Style

Abderrahmane Henniche, Smain Belkacemi. (2019). Numerical Model with Finite Differences Approach for CRS Consolidation Test. Engineering Science, 3(3), 26-35. https://doi.org/10.11648/j.es.20180303.11

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ACS Style

Abderrahmane Henniche; Smain Belkacemi. Numerical Model with Finite Differences Approach for CRS Consolidation Test. Eng. Sci. 2019, 3(3), 26-35. doi: 10.11648/j.es.20180303.11

Copy | Download

AMA Style

Abderrahmane Henniche, Smain Belkacemi. Numerical Model with Finite Differences Approach for CRS Consolidation Test. Eng Sci. 2019;3(3):26-35. doi: 10.11648/j.es.20180303.11

Copy | Download

@article{10.11648/j.es.20180303.11,
  author = {Abderrahmane Henniche and Smain Belkacemi},
  title = {Numerical Model with Finite Differences Approach for CRS Consolidation Test},
  journal = {Engineering Science},
  volume = {3},
  number = {3},
  pages = {26-35},
  doi = {10.11648/j.es.20180303.11},
  url = {https://doi.org/10.11648/j.es.20180303.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.es.20180303.11},
  abstract = {The Constant Rate of Strain (CRS) consolidation test is extensively used in last time to estimate the settlement of clayey soils in many geotechnical laboratories. Different theoretical solutions and numerical models have been developed to estimate consolidation parameters from CRS consolidation test data, and investigate the strain rate effect on the CRS consolidation results. In this study, a new numerical model is developed to simulate CRS consolidation test for small and large strain conditions and for both linear and nonlinear soils. This numerical model is based on the solution of Terzaghi’s classical consolidation equation by finite differences approach, with taking into account the variation of sample height with test time. Results of this numerical model indicate that applied vertical load at the top boundary of sample and excess pore pressure at its base are dependent on the applied strain rate. Evaluation of the consolidation parameters from numerical results of this model with small and large theoretical solutions shows excellent agreement between all methods in small strain level, and when large strain conditions are reached only use of large strain theories can produce good convergence with model results. However, when great strain rates (approximately β ≥ 0.1) are applied, a significant error can be observed in consolidation parameters calculation by using both small and large solutions. Finally, simulation of some experimental CRS tests reported in literature with this numerical model provides comparable consolidation parameters to those evaluated from the experimental CRS tests data.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Numerical Model with Finite Differences Approach for CRS Consolidation Test
AU  - Abderrahmane Henniche
AU  - Smain Belkacemi
Y1  - 2019/01/03
PY  - 2019
N1  - https://doi.org/10.11648/j.es.20180303.11
DO  - 10.11648/j.es.20180303.11
T2  - Engineering Science
JF  - Engineering Science
JO  - Engineering Science
SP  - 26
EP  - 35
PB  - Science Publishing Group
SN  - 2578-9279
UR  - https://doi.org/10.11648/j.es.20180303.11
AB  - The Constant Rate of Strain (CRS) consolidation test is extensively used in last time to estimate the settlement of clayey soils in many geotechnical laboratories. Different theoretical solutions and numerical models have been developed to estimate consolidation parameters from CRS consolidation test data, and investigate the strain rate effect on the CRS consolidation results. In this study, a new numerical model is developed to simulate CRS consolidation test for small and large strain conditions and for both linear and nonlinear soils. This numerical model is based on the solution of Terzaghi’s classical consolidation equation by finite differences approach, with taking into account the variation of sample height with test time. Results of this numerical model indicate that applied vertical load at the top boundary of sample and excess pore pressure at its base are dependent on the applied strain rate. Evaluation of the consolidation parameters from numerical results of this model with small and large theoretical solutions shows excellent agreement between all methods in small strain level, and when large strain conditions are reached only use of large strain theories can produce good convergence with model results. However, when great strain rates (approximately β ≥ 0.1) are applied, a significant error can be observed in consolidation parameters calculation by using both small and large solutions. Finally, simulation of some experimental CRS tests reported in literature with this numerical model provides comparable consolidation parameters to those evaluated from the experimental CRS tests data.
VL  - 3
IS  - 3
ER  -

Copy | Download