Hostname: page-component-76fb5796d-qxdb6 Total loading time: 0 Render date: 2024-04-26T03:48:36.914Z Has data issue: false hasContentIssue false
  • English
  • Français

A Constitutive Model of Sandstone Considering the Post Peak Behavior

Published online by Cambridge University Press:  18 September 2017

F. S. Jeng ,
M. C. Weng ,
F. H. Yeh ,
Y. H. Yang  and
T. H. Huang
F. S. Jeng
Affiliation:
Department of Civil EngineeringNational Taiwan UniversityTaipei, Taiwan
M. C. Weng*
Affiliation:
Department of Civil and Environmental EngineeringNational University of KaohsiungKaohsiung, Taiwan Department of Civil EngineeringNational Chiao Tung UniversityHsinchu, Taiwan
F. H. Yeh
Affiliation:
Department of Civil EngineeringNational Taiwan UniversityTaipei, Taiwan
Y. H. Yang
Affiliation:
Department of Civil EngineeringNational Taiwan UniversityTaipei, Taiwan
T. H. Huang
Affiliation:
Department of Civil EngineeringNational Taiwan UniversityTaipei, Taiwan
*
*Corresponding author (mcweng@nuk.edu.tw; mcweng@nctu.edu.tw)
Get access

Abstract

In rock engineering, evaluating the post-peak strength and deformation of rock is necessary. To explore the elasto-plastic behavior of sandstone in the post-peak stage, a series of strain-controlled triaxial tests were conducted under different confining pressures. According to the post-peak characteristics, a constitutive model based on nonlinear elasticity and generalized plasticity is proposed. This proposed model is characterized by the following features: (1) Nonlinear elasticity is observed under hydrostatic and shear loading; (2) the associated flow rule is followed; (3) substantial plastic deformation occurs during shear loading; and (4) post-peak softening behavior is accurately predicted. This model requires twelve material parameters, three for elasticity and nine for plasticity. The proposed model was validated by comparing the triaxial test results of Mushan sandstone at different hydrostatic pressures under dry and saturated conditions. In addition, the model is versatile; it can simulate the deformational behavior of two other sandstones. In summary, the proposed model can reasonably predict the complete stress–strain curve of sandstone.

Keywords

Constitutive modelGeneralized plasticityPost-peak behaviorSandstone
Type
Research Article
Information
Journal of Mechanics , Volume 35 , Issue 1 , February 2019 , pp. 13 - 25
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2019 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Jeng, F. S., Weng, W. C., Huang, T. H. and Lin, M. L., “Deformational Characteristics of Weak Sandstone and Impact to Tunnel Deformation,” Tunnelling and Underground Space Technology, 17, pp. 263–264 (2002).Google Scholar
2. Goodman, R. E., Introduction to Rock Mechanics, 2nd Edition, John Wiley & Sons, New York (1989).Google Scholar
3. Zhang, J., Wong, T. F. and Davis, D. M., “Micromechanics of Pressure-Induced Grain Crushing in Porous Rocks,” Journal of Geophysical Research, 95, pp. 341–352 (1990).Google Scholar
4. Zimmerman, R. W., Compressibility of Sandstones, Elsevier, Amsterdam (1991).Google Scholar
5. Bernabe, Y., Fryer, D. T. and Shively, R.M., “Experimental Observations of the Elastic and Inelastic Behaviour of Porous Sandstones,” Geophysical Journal International, 117, pp. 403–418 (1994).Google Scholar
6. Bésulle, P., Desrues, J. and Raynaud, S., “Experimental Characterization of the Localisation Phenomenon Inside a Vosges Sandstone in a Triaxial cell,” International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, 37, pp. 1223–1237 (2000).Google Scholar
7. Weng, M. C., Jeng, F. S., Huang, T. H. and Lin, M. L., “Characterizing the Deformation Behavior of Tertiary Sandstones,” International Journal of Rock Mechanics and Mining Sciences, 42, pp. 388–401 (2005).Google Scholar
8. Tsai, L. S., Hsieh, Y. M., Weng, M. C., Huang, T. H. and Jeng, F. S., “Time-Dependent Deformation Behaviors of Weak Sandstones,” International Journal of Rock Mechanics and Mining Sciences, 45, pp. 144–154 (2008).Google Scholar
9. Papamichos, E. et al., “Constitutive Testing of Red Wildmoor Sandstone,” Mechanics of Cohesive-Frictional Materials, 5, pp. 1–40 (2000).Google Scholar
10. Wang, D., Liu, C. W., Wang, D., Cao, L. and Du, X. L., “Failure Prediction and Post-Failure Behavior of Typical Rock under Triaxial Compression,” Journal of Southwest Jiaotung University; 47, pp. 90–96 (2012). (In Chinese)Google Scholar
11. Zienkiewicz, O. C. and Mroz, Z., “Generalized Plasticity Formulation and Applications to Geomechanics,” Proceedings of Mechanics of Engineering Materials, Desai, C. S., Gallagher, R. H. (eds), Wiley, New York, pp. 655–679 (1984).Google Scholar
12. Pastor, M. and Zienkiewicz, O. C., “A Generalized Plasticity, Hierarchical Model for Sand under Monotonic and Cyclic Loading,” Proceedings of 2nd International Symposium on Numerical Models in Geomechanic, Ghent, pp. 131–149 (1986).Google Scholar
13. Pastor, M., Zienkiewicz, O. C. and Chan, A. H. C., “Generalized Plasticity and the Modelling of Soil Behavior” International Journal for Numerical and Analytical Methods in Geomechanics, 14, pp. 151–190 (1990).Google Scholar
14. Pastor, M., Zienkiewicz, O. C., Guang-Duo, X. and Peraire, J., “Modelling of Sand Behaviour: Cyclic Loading, Anisotropy and Localization,” Modern Approaches to Plasticity, Kolymbas, D. (eds), Springer, Berlin (1992).Google Scholar
15. Bolzon, G., Schrefler, B. A. and Zienkiewicz, O. C., “Elasto–Plastic Constitutive Laws Generalised to Partially Saturated States,” Géotechnique, 46, pp. 279–289 (1996).Google Scholar
16. Ling, H. I. and Liu, H., “Pressure-Level Dependency and Densification Behavior of Sand through a Generalized Plasticity Model,” Journal of Engineering Mechanics, 129, pp. 851–860 (2003).Google Scholar
17. Manzanal, D., Fernández Merodo, J. A. and Pastor, M., “Generalized Plasticity State Parameter-Based Model for Saturated and Unsaturated Soils. Part 1: Saturated State,” International Journal for Numerical and Analytical Methods in Geomechanics, 35, pp. 1347–1362 (2011).Google Scholar
18. Manzanal, D., Pastor, M. and Fernández Merodo, J. A., “Generalized Plasticity State Parameter-Based Model for Saturated and Unsaturated Soils. Part II: Unsaturated soil modeling,” International Journal for Numerical and Analytical Methods in Geomechanics, 35, pp. 1899–1917 (2011).Google Scholar
19. Weng, M. C. and Ling, H. I., “Modeling the Behavior of Sandstone Based on Generalized Plasticity Concept,” International Journal for Numerical and Analytical Methods in Geomechanics, 37, pp. 2154–2169 (2013).Google Scholar
20. Weng, M. C., “A Generalized-Plasticity Based Model for Sandstone Considering Time-Dependent Behavior and Wetting Deterioration,” Rock Mechanics and Rock Engineering, 47, pp. 1197–1209 (2014).Google Scholar
21. Jeng, F. S., Weng, W. C., Lin, M. L. and Huang, T. H., “Influence of Petrographic Parameters on Geotechnical Properties of Tertiary Sandstones from Taiwan,” Engineering Geology, 73, pp. 71–91 (2004).Google Scholar
22. Weng, M. C. and Li, H. H., “Relationship between the Deformation Characteristics and Microscopic Properties of Sandstone Explored by the Bonded- Particle Model,” International Journal of Rock Mechanics and Mining Sciences, 56, pp. 33–43 (2012).Google Scholar
23. Rock Characterization Testing and Monitoring-ISRM Suggested Methods, Pergamon, New York (1981).Google Scholar
24. Weng, M. C., Tsai, L. S., Hsieh, Y. M. and Jeng, F. S., “An Associated Elastic-Viscoplastic Constitutive Model for Sandstone Involving Shear-Induced Volumetric Deformation,” International Journal of Rock Mechanics and Mining Sciences, 47, pp. 1263–1273 (2010).Google Scholar