MODELING OF LIQUEFACTION USING COUPLED FINITE ELEMENT ANALYSIS

Abstract

Soils are made of an assemblage of particles having different shapes and sizes in form of a skeleton whose voids are made up of water and air. The interaction of pore pressure with soil skeleton during earthquake results in the 'weakening' of soil-fluid composite which reduces the effective stress in soil mass, causing liquefaction. Liquefaction takes place often in saturated loose sands under earthquake and impact loadings. The pioneering experimental work associated with liquefaction phenomenon and cyclic mobility was proposed by Seed and Lee (1966), Seed and Idriss (1971), Castro and Poulos (1977), Seed 1979, Seed et al. (1985). The physical phenomenon is well defined whereas; the analytical modeling of soil liquefaction and computer simulation remains a challenge. Therefore, soil behaviour has been analysed by considering the effects of transient flow of the pore-fluid through voids. Hence, it requires a two-phase continuum formulation for saturated porous media. Based on a detailed review of literature, the present study has been directed towards the establishment of an adequate mathematical framework to describe the liquefaction phenomenon. In the proposed study, a fully coupled formulation is developed to predict the liquefaction phenomenon of a finite and semi-infinite saturated sandy layer assuming plane strain condition. The saturated soil mass is considered as a saturated porous media using Biot’s theory with u–p formulation. The variational principle is applied to the field equations of fluid flow in a fully saturated porous elastic continuum, and the finite element method is used to numerically solve the resulting continuity equation and equilibrium equation. The soil behaviour is defined using Pastor–Zienkiewicz Mark III model which describe the inelastic behaviours under dynamic loadings. This formulation is used to evaluate the responses of respective pore fluid and soil mass. A transmitting boundary is introduced to differentiate between near field and far field. Kelvin elements have been incorporated at transmitting boundary to absorb the wave energy and prevent back propagation of wave into the domain. In the far field, infinite elements are incorporated in the solution algorithms to simulate the infinite extent of the domain in 2-D plane strain finite element analyses. Newmark-Beta method is used for integration in time domain. In-situ stresses are computed from static analysis prior to dynamic analysis. Cyclic and Seismic analysis are performed considering finite and infinite domain. A parametric study is conducted to highlight the significance of ii permeability, shear modulus and frequency on the response of liquefaction phenomenon. A significant reduction in displacement and EPP is observed with increase in shear modulus. Displacements are affected marginally with change in permeability whereas EPP is affected significantly. With decrease in permeability, considerable increase in EPP is observed. Effect of cyclic frequency is drastic for the range of frequencies considered in the analysis. It is noticed that the liquefaction occurs throughout all the depth of sand layer at frequency 1 Hz and 2 Hz of the cyclic loading, whereas no liquefaction is observed at 0.5 Hz. Similar trends of displacements and EPP are observed for variation in shear modulus and permeability for El-Centro earthquake input motion. For the case of Bhuj earthquake ground motion, only soil domains with shear modulus more than 50000 kPa are sustainable. For smaller values of shear modulus, soil domain is liquefying at early stage of earthquake ground motion. PLAXIS 3D software based on UBC3D-PLM model has been used to analyze 3-D modeling of liquefaction and mitigation. The present study was directed to examine the effectiveness of remedial measures for liquefaction. The models with and without remedial countermeasures were analyzed. A comparative study was performed to highlight the effect of countermeasure on liquefaction. The stone column resulted in the smaller strains and cyclic mobility of the soil stratum. Maximum lateral strains and highest EPP in soil domain were observed in the no-remediation case with surcharge. Smaller values of displacements are predicted in comparison with the benchmark Model 1, but the variation is marginal. In lack of surcharge at surface, stone-columns are apparently ineffective in controlling settlements. As compared to Model 1, a reduction of around 40% in EPP is visible in Model 2. Predicted values for Model 4 are less than those evaluated for the benchmark Model 3 and the variation is noteworthy. Due to presence of a surcharge, stone columns are very effective in settlement reduction. The values obtained in Model 4 are about 50% less than those in Model 3, signifying the competency of the Model 4 in controlling the displacement produced during seismic shaking showing stiffer composite-material behavior. A significant reduction value of maximum EPP is visible in Model 4 as compared to maximum EPP in Model 3. Study presented effectiveness of mitigation measures in controlling liquefaction.