Overview of the LIQCA Liquefaction Analysis Program

1. Introduction

The LIQCA liquefaction analysis program is characterized by its effective stress liquefaction analysis method, which uses a coupled finite element method that accounts for permeability and is based on a formulation based on Biot’s two-phase mixture theory, with u (soil displacement) – p (pore water pressure) as unknowns. It has been proposed as an analytical method capable of early evaluation of the effectiveness of gravel drains against liquefaction. ^{2, 3)} In particular, 1) the accuracy of finite element analysis has been verified, 2) the nonlinear kinematic hardening law has been introduced into the constitutive equation for sand, 3) analytical stability has been confirmed, and 4) application to unsaturated soil has been widely used for liquefaction analysis. Currently, the program has been expanded and refined to include clayey soil analysis, finite deformation analysis, advanced constitutive equations, unsaturated soil handling, ⁴⁾⁹⁾ and joint element handling. ⁵⁾

2. LIQCA: A Liquefaction Analysis Program for Dynamic Analysis of Saturated and Unsaturated Soils

Analysis of solid-liquid two-phase systems employs a variety of formulations, depending on the unknowns and approximation methods. Complete formulations include the u-U-p formulation, which uses the solid phase displacement u, the liquid phase displacement U, and the pore water pressure p as unknowns, and the u-w-p formulation, which uses the relative displacement of the liquid phase relative to the solid phase w. LIQCA uses the u-p formulation, which uses the solid phase displacement u and pore water pressure p as unknowns. The u-p formulation does not explicitly treat the liquid phase displacement, assuming that the relative acceleration of the liquid phase relative to the solid phase is small compared to the solid phase acceleration. This reduces the number of degrees of freedom to be solved, which is advantageous in terms of computational cost.³⁾

The LIQCA liquefaction analysis programs available include the 2D LIQCA2D, the 3D LIQCA3D, and the finite deformation analysis method LIQCAFD2D, which assume small deformation gradients.　LIQCA2D uses the finite element method and finite difference method to spatially discretize the governing equations. The finite element method is used for spatial discretization of the balance equation, and the finite volume method is used for spatial discretization of the pore water pressure term in the continuity equation. Meanwhile, Newmark’s β method, an implicit method, is used for time discretization. The accuracy of the analysis methods is verified by comparison with analytical solutions for the transient response of saturated poroelastic media.

The formulation (u-p formulation) uses the displacement u of the solid phase (soil skeleton) and the pore water pressure p as unknowns, and makes the following assumptions⁴⁾:

 1) strain is a small deformation gradient, 2) the spatial gradient of the porosity and the hydraulic conductivity of the liquid phase (pore water) is sufficiently small, 3) the relative acceleration of the liquid phase to the solid phase and the gas phase to the liquid phase is small compared to the acceleration of the solid phase, 4) for unsaturated soil, the air pressure is assumed to be small and zero, and the skeleton stress and suction are used in the constitutive equation, 5) the interaction between the gas and liquid phases is not taken into account, 6) soil particles are incompressible, and 7) Rayleigh damping is used.

To reproduce the deformation of ground during an earthquake due to liquefaction, a model capable of reproducing strain during cyclic loading is required. LIQCA uses the cyclic elasto-plastic model proposed by Oka et al.⁶⁾ and the extended constitutive equation proposed by Oka and Kimoto⁷⁾ as the constitutive equation for sand. Its features include: 1) small strain theory, 2) elasto-plastic theory, 3) non-associated flow law, 4) overconsolidated boundary surface concept, 5) nonlinear kinematic hardening law, and 6) strain dependence of stiffness. For clayey soils, the cyclic elasto-viscoplastic constitutive equation proposed by Kimoto et al.⁸⁾ can also be used for non-liquefiable layers for simplicity. LIQCA2D incorporates the modified Takeda model for reinforced concrete structural members.

As for boundary conditions, single-point constraints and simple multi-point constraints are used for soil displacement. Single-point constraints treat fixed or free boundaries. Multi-point constraints make the displacements of any two nodes equal (constant displacement boundary condition). For pore water, any element edge is set to drained (specified head) or undrained (discharge 0). To simulate the infinite nature of the analysis domain, viscous boundaries are used on the sides and bottom. The constant displacement condition avoids problems during consolidation that occur with lateral viscous boundaries.

For 2D problems, plane strain elements (4-node isoparametric elements) are used for the framework, and for 3D problems, solid elements (8-node isoparametric elements) are used. Structural beam elements and 2D joint elements are also used. The up-p method is used, and the weak form is formulated and solved using the finite element method with an updated Lagrangian form.⁹⁾ With the updated Lagrangian form, the configuration is updated at each step, and the configuration at the current time is used as the reference configuration. Eight-node isoparametric elements are used for the surface and four-node isoparametric elements for the water.

References

1) Oka, F., Uzuoka, R., Kimoto, S., Tateishi, A., Kato, R., and Adachi, Y., “Earthquake Response Analysis of Ground Using the Liquefaction Analysis Program LIQCA,” Journal of the Geotechnical Society of Japan, 63 (10), pp. 12-15, 2015-10.(in Japanese)

2) Oka, F., Yashima, A., Shibata, T., Kato, M., and Uzuoka, R.: “FEM-FDM Coupled Liquefaction Analysis of a Porous Soil Using an Elasto-Plastic Model,” Applied Scientific Research, Vol. 52, pp. 209-245, 1994.

3) Mitsuru Kato, Fusao Oka, Atsushi Yashima, Yukiyoshi Tanaka, Pore Water Pressure Suppression by Gravel Drains during Earthquakes and Verification by numerical method, Journal of the Japan Society Geotechnical Society, 42(4), 39-44, 1994.(in Japanese)

4) Ryosuke Kato, Fusao Oka, Sayuri Kimoto, Takeshi Kodaka, Susumu Sunami, Unsaturated Seepage-Deformation Coupled Analysis Method and Its Application to River Levees, Transactions of the Japan Society of Civil Engineers, Vol. 65, No. 1, pp. 226-240, 2009.(in Japanese)

 4)-2Kato,R.,F. Oka & S. Kimoto,A numerical simulation of seismic behavior of highway embankments considering seepage flow,Computer Methods and Recent Advances in Geomechanics, Oka, Murakami, Uzuoka & Kimoto (Eds.), Proc. 14thICIACMAG, Taylor & Francis Group, London, ISBN 978-1-138-00148-0,2014,pp.755-760.

5) LIQCA Liquefaction Geo Research Institute (Representative Director: Fusao Oka), LIQCA2D25/LIQCA3D25 (2025 Release Edition) Materials, Part I: Theory, Part II: Practice, Part III: Manual, 2025. (in Japanese). (2024 edition by PDF is in English)

6) F. Oka, Yashima, A., Tateishi, A., Taguchi, Y. and Yamashita, S.: A cyclic elasto-plastic constitutive model for sand considering a plastic-strain dependence of the shear modulus, Geotechnique, Vol. 49, No. 5, pp. 661-680, 1999.

7) Fusao Oka and Sayuri Kimoto, A cyclic elastoplastic constitutive model and effect of non-associativity on the response of liquefiable sandy soils, Acta Geotechnica, Vol.13,6,pp.1283-1297, 2018.

8) Kimoto, S., Shahbodagh Khan, B., Mirjalili, M., Oka, F.A Cyclic Elasto-Viscoplastic Constitutive Model for Clay Considering the Nonlinear Kinematic Hardening Rules and the Structural Degradation, Int. J. Geomechanics, ASCE, Vol.15(5),pp.A4014005-14,2015.

9) Oka, F. and Kimoto, S.: Computational Modeling of Multi-phase Geomaterials, Taylor & Francis, 2012.