Implicit scheme for integrating constitutive model of unsaturated soils with coupling hydraulic and mechanical behavior

doi:10.1007/s10483-014-1859-6

Abstract

Abstract: A constitutive model of unsaturated soils with coupling capillary hysteresis and skeleton deformation is developed and implemented in a fully coupled transient hydro-mechanical finite-element model (computer code U-DYSAC2). The obtained results are compared with experimental results, showing that the proposed constitutive model can simulate the main mechanical and hydraulic behavior of unsaturated soils in a unified framework. The non-linearity of the soil-water characteristic relation is treated in a similar way of elastoplasticity. Two constitutive relations are integrated by an implicit return-mapping scheme similar to that developed for saturated soils. A consistent tangential modulus is derived to preserve the asymptotic rate of the quadratic convergence of Newton's iteration. Combined with the integration of the constitutive model, a complete finite-element formulation of coupling hydro-mechanical problems for unsaturated soils is presented. A number of practical problems with different given initial and boundary conditions are analyzed to illustrate the performance and capabilities of the finite-element model.

Key words: unsaturated soil, capillary hysteresis, elastoplastic coupling constitutive model, stress integration, finite-element method

2010 MSC Number:

TU44
O359+.2

Tian-tian MA;Chang-fu WEI;Pan CHEN;Hou-zhen WEI. Implicit scheme for integrating constitutive model of unsaturated soils with coupling hydraulic and mechanical behavior. Applied Mathematics and Mechanics (English Edition), 2014, 35(9): 1129-1154.

TrendMD

References

[1] Fredlund, D. G. and Rahardjo, H. Soil Mechanics for Unsaturated Soils, John Wiley & Sons Inc., New York (1993)
[2] Poulovassilis, A. Hysteresis of pore water: an application of the concept of independent domains. Soil Science, 93, 405-412 (1962)
[3] Topp, G. C. and Miller, E. E. Hysteresis moisture characteristics and hydraulic conductivities for glass bead media. Soil Science Society of America Journal, 30, 156-162 (1966)
[4] Cadoret, T., Mavko, G., and Zinszner, B. Fluid distribution effect on sonic attenuation in partially saturated limestones. Geophysics, 63, 154-160 (1998)
[5] Wei, C. F. and Dewoolkar, M. M. Formulation of capillary hysteresis with internal state variables. Water Resources Research, 42, W07405 (2006)
[6] Muraleetharan, K. K., Liu, C. Y., Wei, C. F., Kibbey, T. C. G., and Chen, L. X. An elastoplatic framework for coupling hydraulic and mechanical behavior of unsaturated soils. International Journal of Plasticity, 25, 473-490 (2008)
[7] Li, X. S. Thermodynamics-based constitutive framework for unsaturated soils 1: theory. Géotechnique, 57, 411-422 (2007)
[8] Ma, T. T., Wei, C. F., Chen, P., Tian, H. H., and Sun, D. A. A unified elastoplastic constitutive model of unsaturated soils with considering the effect of capillary hysteresis. Journal of Applied Mathematics, 2013, 537185 (2013)
[9] Alonso, E. E., Gens, A., and Josa, A. A constitutive model for partially saturated soils. Géotechnique, 40, 405-430 (1990)
[10] Bolzon, G., Schrefler, B. A., and Zienkiewicz, O. C. Elastoplastic soil constitutive laws generalized to partially saturated states. Géotechnique, 46, 279-289 (1996)
[11] Wheeler, S. J., Sharma, R. S., and Buisson, M. S. R. Coupling of hydraulic hysteresis and stressstrain behaviour in unsaturated soils. Géotechnique, 53, 41-54 (2003)
[12] Sun, D. A., Sheng, D., and Sloan, S. W. Elastoplastic modelling of hydraulic and stress-strain behaviour of unsaturated soils. Mechanics of Materials, 39, 212-221 (2007)
[13] Vaunat, J., Cante, J. C., Ledesma, A., and Gens, A. A stress point algorithm for an elastoplastic model in unsaturated soils. International Journal of Plasticity, 16, 121-141 (2000)
[14] Runesson, K. Implicit integration of elastoplastic relations with reference to soils. International Journal for Numerical and Analytical Methods in Geomechanics, 11, 315-321 (1987)
[15] Macari, E. J., Hoyos, L. R., and Arduino, P. Constitutive modeling of unsaturated soil behavior under axisymmetric stress states using a stress/suction-controlled cubical test cell. International Journal of Plasticity, 19, 1481-1515 (2003)
[16] Zhang, H.W., Heeres, O. M., de Borst, R., and Schrefler, B. A. Implicit integration of a generalized plasticity constitutive model for partially saturated soil. Engineering Computations, 18, 314-336 (2001)
[17] Simo, J. C. and Taylor, R. L. A return mapping algorithm for plane stress elastoplasticity. International Journal for Numerical Methods in Engineering, 22, 649-670 (1986)
[18] Sheng, D. C., Sloan, S. W., Gens, A., and Smith, D. W. Finite element formulation and algorithms for unsaturated soils, part I: theory. International Journal for Numerical and Analytical Methods in Geomechanics, 27, 745-765 (2003)
[19] Zienkiewicz, O. C., Chan, A. H. C., Pastor, M., Paul, D. K., and Shiomi, T. Static and dynamic behaviour of soils: a rational approach to quantitative solutions, I: fully saturated problems. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 429, 285-309 (1990)
[20] Zienkiewicz, O. C., Xie, Y. M., Schrefler, B. A., Ledesma, A., and Bicanic, N. Static and dynamic behaviour of soils: a rational approach to quantitative solutions, II: semi-saturated problems. Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences, 429, 311-321 (1990)
[21] Laloui, L., Klubertanz, G., and Vulliet, L. Solid-liquid-air coupling in multiphase porous media. International Journal for Numerical and Analytical Methods in Geomechanics, 27, 183-206 (2003)
[22] Li, X. K., Zienkiewicz, O. C., and Xie, Y.M. A numerical model for immiscible two-phase fluid flow in a porous medium and its time domain solution. International Journal for Numerical Methods in Engineering, 30, 1195-1212 (1990)
[23] Schrefler, B. A. and Zhan, X. A fully coupled model for water flow and airflow in deformable porous media. Water Resources Research, 29, 155-167 (1993)
[24] Olivella, S., Carrera, J., Gens, A., and Alonso, E. Nonisothermal multiphase flow of brine and gas through saline media. Transport in Porous Media, 15, 271-293 (1994)
[25] Thomas, H. R. and He, Y. A coupled heat-moisture transfer theory for deformable unsaturated soil and its algorithmic implementation. International Journal for Numerical Methods in Engineering, 40, 3421-3441 (1997)
[26] Nowamooz, H., Mrad, M., Abdallah, A., and Masrouri, F. Experimental and numerical studies of the hydromechanical behaviour of a natural unsaturated swelling soil. Canadian Geotechnical Journal, 46, 393-410 (2009)
[27] Simoni, L., Salomoni, V., and Schrefler, B. A. Elastoplastic subsidence models with and without capillary effects. Computer Methods in Applied Mechanics and Engineering, 171, 491-502 (1999)
[28] Wei, C. F. Static and Dynamic Behavior of Multiphase Porous Media: Governing Equations and Finite Element Implementation, Ph.D. dissertation, University of Oklahoma, Oklahoma (2001)
[29] Houlsby, G. T. The work input to an unsaturated granular material. Géotechnique, 47, 193-196 (1997)
[30] Roscoe, K. H. and Burland, J. B. On the generalized stress-strain behavior of “wet” clay. Engineering Plasticity, 535-609 (1968)
[31] Tamagnini, R. An extended Cam-clay model for unsaturated soils with hydraulic hysteresis. Géotechnique, 54, 223-228 (2004)
[32] Feng, M. and Fredlund, D. G. Hysteresis influence associated with thermal conductivity sensor measurements. Proceeding from Theory to the Practice of Unsaturated Soil Mechanics, Regina, 651-657 (1999)
[33] Borja, R. I. and Lee, S. R. Cam-clay plasticity, part 1: implicit integration of elasto-plastic constitutive relations. Computer Methods in Applied Mechanics and Engineering, 78, 49-72 (1990)
[34] Simo, J. C. and Taylor, R. L. Consistent tangent operators for rate-independent elastoplasticity. Computer Methods in Applied Mechanics and Engineering, 48, 101-118 (1985)
[35] Aravas, N. On the numerical integration of a class of pressure-dependent plasticity models. International Journal for Numerical Methods in Engineering, 24, 1395-1416 (1987)
[36] Wei, C. F. and Muraleetharan, K. K. A continuum theory of porous media saturated by multiple immiscible fluids: 1, linear poroelasticity. International Journal of Engineering Science, 40, 1807- 1833 (2002)
[37] Wei, C. F. and Muraleetharan, K. K. A continuum theory of porous media saturated by multiple immiscible fluids: 2, Lagrangian description and variational structure. International Journal of Engineering Science, 40, 1835-1854 (2002)
[38] Hassanizadeh, S. M. and Gray, W. G. General conservation equations for multi-phase systems: 1, averaging procedure. Advances in Water Resources, 2, 131-144 (1979)
[39] Hassanizadeh, S. M. and Gray, W. G. General conservation equations for multi-phase systems: 2, mass, momenta, energy, and entropy equations. Advances in Water Resources, 2, 191-203 (1979)
[40] Mualem, Y. A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resources Research, 12, 513-522 (1976)
[41] Hilber, H. M., Hughes, T. J. R., and Taylor, R. L. Improved numerical dissipation for time integration algorithms in structural dynamics. Earthquake Engineering and Structural Dynamics, 5, 283-292 (1977)
[42] Liakopoulos, A. C. Transient Flow Through Unsaturated Porous Media, Ph.D. thesis, University of California, Berkeley (1965)
[43] Sheng, D. C., Smith, D. W., Sloan, S. W., and Gens, A. Finite element formulation and algorithms for unsaturated soils, part II: verification and application. International Journal for Numerical and Analytical Methods in Geomechanics, 27, 767-790 (2003)
[44] Hoa, N. T., Gaudu, R., and Thirriot, C. Influence of the hysteresis effect on transient flows in saturated-unsaturated porous media. Water Resources Research, 13, 992-996 (1977)