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Three-dimensional elastic–viscoplastic consolidation behavior of transversely isotropic saturated soils

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Abstract

This paper investigates three-dimensional elastic–viscoplastic consolidation behaviors of transversely isotropic saturated soils. The Drucker–Prager yield criterion for isotropic materials is extended for modeling transversely isotropic medium. By coupling Perzyna’s viscoplastic theory with a transversely isotropic soil model, the incremental one-dimensional (1D) Nishihara’s constitutive model is established and then extended to formulate a three-dimensional (3D) material model. The method to obtaining the material parameters for the proposed model is also provided. The return mapping algorithm and algorithmic tangent matrix are presented to numerically implement the proposed theory into the finite element package—ABAQUS. We have validated the proposed theory by comparing numerical results with the uniaxial compression testing data of Shanghai soft clay and the field observations of soft soil embankments in the Dongting Lake area in China. Then, several numerical examples are conducted to study the influences of elastic–viscoplastic and transversely isotropic parameters on the time-dependent behavior of saturated soils.

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Acknowledgements

This study was supported by the National Natural Science Foundation of China (Grant No. 41672275). We would like to express our sincere appreciation to Professor Xiaoyu Song in University of Florida for his careful and constructive comments on this paper.

Funding

National Natural Science Foundation of China, 41672275, Zhi Yong Ai.

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Authors and Affiliations

  1. Department of Geotechnical Engineering, Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, College of Civil Engineering, Tongji University, 1239 Siping Road, Shanghai, 200092, People’s Republic of China

    Zhi Yong Ai, Yong Zhi Zhao, Ye Cheng Dai & Zhen Zhao

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  1. Zhi Yong Ai
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Correspondence to Zhi Yong Ai.

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Appendix

Appendix

The kernel of the subroutine in ABAQUS is presented as follows:

"DO I = 1,NTENS.

DO J = 1,NTENS.

VERATE(I) = VERATE(I) + VMA(I,J)*STRESS(J)*(1.0 + E1/E0)/eta1.

ENDDO.

VERATE(I) = VERATE(I)-E1*STRAN(I)/eta1.

ENDDO.

DSTRIAL = 0.0

DO I = 1,NTENS.

DO J = 1,NTENS.

DSTRIAL(I) = DSTRIAL(I) + VEJM(I,J)*(DSTRAN(J)-Bn*VERATE(J)).

ENDDO.

STRIAL(I) = DSTRIAL(I) + STRESS(I).

ENDDO.

I1 = STRIAL(1) + STRIAL(2) + STRIAL(3)

J2 = 0.5*((STRIAL(2)-STRIAL(3))**2.0 + (STRIAL(3)-STRIAL(1))**2.0 + lambda*(STRIAL(1)-STRIAL(2))**2.0 + 12.0*lambda_tao*(STRIAL(5)**2.0 + STRIAL(6)**2.0) + (4.0*lambda + 2.0)*STRIAL(4)**2.0)/(2.0 + lambda)

q_tri = SQRT(3.0*J2).

p_tri = I1/3.0

F = q_tri + p_tri*A_phi.

c = c0 + H*EVPSTRAN.

F0 = K*c

Dgamma = 0.0

IF (F.LE.F0) THEN.

STRESS = STRIAL.

DDSDDE = VEJM.

VESTRAN = VESTRAN + DSTRAN.

ELSE.

EVPSTRAN_G = EVPSTRAN.

EVPSTRAN_E = EVPSTRAN.

c_G = c0.

c_E = c0.

d = -SQRT(3.0)*VG-VK*A_phi*A_psi-K*K*H.

DO I = 1,100.

Dgamma = Dgamma-(F-F0)/d.

EVPSTRAN_G = EVPSTRAN_G + K*Dgamma.

c_G = c0 + H*EVPSTRAN_G.

F = q_tri-SQRT(3.0)*VG*Dgamma + (p_tri-VK*A_psi*Dgamma)*A_phi.

F0 = K*c_G

F (F-F0.LE.TOL) THEN.

I1_New = I1-3.0*VK*A_psi*Dgamma

DO J = 1,NDI.

STRESS(J) = (1.0-SQRT(3.0)*VG*Dgamma/q_tri)*(STRIAL(J)-I1/3.0) + I1_New/3.0

STRESS(J + NDI) = (1.0-SQRT(3.0)*VG*Dgamma/q_tri)*STRIAL(J + NDI).

ENDDO.

goto 10.

ENDIF.

if(I =  = 100)THEN.

call xit().

endif.

ENDDO.

10 continue.

IF ((SQRT(J2)-VG*Dgamma).LT.0.0) THEN.

DVPSTRAN = 0.0

d = K*K*H/(A_psi*A_phi) + VK.

DO I = 1,100.

R = c_E*K/A_psi-p_tri + VK*DVPSTRAN.

DVPSTRAN = DVPSTRAN-r/d.

EVPSTRAN_E = EVPSTRAN_E + DVPSTRAN*K/A_phi.

c_E = c0 + H*EVPSTRAN_E.

IF (ABS(r).LE.TOL) THEN.

EVPSTRAN = EVPSTRAN_E.

c = c_E.

FORALL(J = 1:NDI) STRESS(J) = p_tri-VK*DVPSTRAN.

FORALL(J = 1:NDI) STRESS(J + NDI) = 0.0

goto 20.

ENDIF.

if(I =  = 100)THEN.

call xit().

endif.

ENDDO.

ELSE.

EVPSTRAN = EVPSTRAN_G.

c = c_G.

ENDIF.

20 continue.

ENDIF.

STATEV(1) = EVPSTRAN.

RETURN.

END".

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Ai, Z.Y., Zhao, Y.Z., Dai, Y.C. et al. Three-dimensional elastic–viscoplastic consolidation behavior of transversely isotropic saturated soils. Acta Geotech. 17, 3959–3976 (2022). https://doi.org/10.1007/s11440-021-01423-2

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  • DOI: https://doi.org/10.1007/s11440-021-01423-2

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