Numerous countermeasures have been suggested since liquefaction can cause significant damage to structures. Previous experimental studies have demonstrated that the penetration of rigid bodies, such as timber, can effectively mitigate displacement caused by liquefaction. Moreover, the Discrete Element Method (DEM) is a convenient tool to monitor the microscopic and macroscopic characteristics of granular materials. This paper examines the impact of group pile distance on modifications to the surrounding soil properties, such as displacement and porosity, using DEM simulation with a periodically bounded domain. According to the tentative result, the axial force and overall particle displacement decrease as the distance between the shafts increases. Nevertheless, the displacement in the region adjacent to the shaft in a larger pile distance surpasses that in a shorter distance case. There is no distinctive trend in changes in voxel porosity with varying pile distances.

To investigate the seismic behavior of pile foundation in layered ground of dense and cemented sand, a series of centrifugal and numerical modeling were performed. The centrifugal modeling tests were performed with a laminar box whose upper half was the dense sand, and the lower half was the artificially cemented sand. The model piles penetrated through both layers and were fixed at the bottom of the container. When subjected to a seismic motion, the upper layer of the dense sand reached liquefaction and did not resist to the lateral displacement of the piles. In contrast,

the bottom layer of the cemented sand maintained the lateral resistance although the excess pore pressure ratio reached nearly 1.0. Furthermore, effective stress-based, numerical analyses were performed by using the code FLIP to examine its applicability for such condition. The behavior of dense sand was well reproduced by the conventional model for liquefiable material. Meanwhile, the cemented sand was well predicted when modeled without the effect of liquefaction. These results highlighted the distinct behavior of the cemented sand whose shear stiffness did not immediately diminish during an earthquake.

Seismic–induced liquefaction of saturated sandy soils may cause severe damage to civil infrastructures, pushing the scientific community toward a more in-depth understanding of the physical phenomenon and the development of effective strategies for its mitigation. Vertical gravel drains and stone columns are often used as a mitigation measure against liquefaction as, depending on site conditions, they can be easier to install and more cost-effective with respect to other design solutions. Standard design methods of the gravel drains are usually based on the seminal work by Seed and Booker (1977), which relies on several simplifying assumptions about: the direction of water flow (purely horizontal axisymmetric flow towards the drains), the physical and mechanical properties of the drain material (virtually infinite permeability), and the rate of excess pore pressure (described through empirical relationships based on undrained cyclic tests). The present paper illustrates a comparison between the seminal work proposed by Seed and Booker, which was subsequently improved by Onoue (1988), and the results of a fully-coupled, nonlinear dynamic 3D Finite Element analysis, where the cyclic behaviour of the saturated sand layer is described through an advanced constitutive model.

An effective stress analysis can evaluate the seismic behavior of liquefiable ground and it is ideal to consider this behavior in a design of the liquefaction countermeasure such as densification methods. Especially for planning the appropriate densification range, it is important to take groundwater movements into account because the development of the excess pore water pressure in the densified area can be predicted properly due to the reproduction of the seepage into a densified area from an adjacent undensified area. To consider groundwater movements in seismic response analysis, governing equations of a two-phase system (u-w formulation) were introduced into a general-purpose 3D-FEM program "TDAPⅢ". Additionally, an elasto-plastic constitutive law (Stress-Density model) was incorporated as a three-dimensional constitutive model to express the stress-strain relationship of liquefied sandy soil.

To investigate whether the effects of the densification on liquefiable ground and pile foundations are properly evaluated by implementing the new features, simulation analyses by "TDAPⅢ" were carried out on a series of centrifuge tests. The subjects of these tests were pile foundations surrounded by the ground where the densification is conducted.

As a result, the liquefaction suppression effects due to the densification were expressed in the simulations, and the influence of seepage on the behaviors of the pore water were explained by visualizing the flow direction of the groundwater. Furthermore, the trends of the bending moments and the horizontal subgrade reactions of the piles under the different densification range conditions were able to be evaluated in the simulations.

Earthquake-induced soil liquefaction can lead to significant structural damage, due to excessive foundation settlement and rotation. The numerical modelling of this phenomenon is challenging, demanding both an advanced constitutive model and a hydro-mechanically coupled calculation. The PM4sand constitutive model can be calibrated in a straight-forward manner, and has been shown to reasonably approximate complex soil response. The model is currently available in both the commercial numerical analysis codes FLAC 2D and PLAXIS 2D. While FLAC 2D offers the possibility of a fully-coupled dynamic analysis, PLAXIS 2D recently released a ‘‘quasi’’ coupled hydro-mechanical calculation. Aiming to assess their reliability and robustness, the two numerical analysis codes are comparatively assessed by simulating published plane strain centrifuge model tests (conducted at the University of Cambridge) of a SDOF structure resting on a liquefiable layer of loose Hostun sand. PM4sand has been calibrated against element tests on Hostun sand conducted at the laboratory of the Institute for Geotechnical Engineering (IGT) of ETH Zurich. The numerical models are assessed based on their ability to capture the excess pore-water pressures, the accelerations within the soil, and the rotation-displacement response recorded during the centrifuge model tests.

Pore water pressure dissipation is a method to mitigate excess pore water pressure by using highly permeable crushed stone columns or artificial materials. Pore water pressure dissipation was applied to the liquefiable layer below the embankment to prevent settlement caused by liquefaction. However, it has been pointed out that the effectiveness of pore water pressure dissipation decreases rapidly as acceleration increases, and it is considered to be less effective against large-scale earthquake motion. To address this issue, models were prepared with gravel drains, a type of pore water pressure dissipation method, installed in the liquefiable layer beneath the embankment slope. Another model without any countermeasures was also prepared. A shaking motion equivalent to a level 2 earthquake was applied to these models at 50 G. Although the maximum value of excess pore water pressure ratio in the improved ground reached 1 in the case with countermeasures, the settlement was reduced by about 30% compared to the case without countermeasures. Even if the excess pore water pressure ratio reaches 1, if the duration time is sufficiently short, it is considered to be effective in reducing settlement. Analysis for Liquefaction-Induced Deformation (ALID) was used to back-calculate the F_L factor of the improved ground, which can explain the settlement suppression effect of gravel drains. The results indicated that the improved ground with gravel drains corresponds to a condition in which the F_L factor is increased by about twice the original liquefiable layer.

Under strong earthquake, underground structures are vulnerable to severely damage due to liquefaction of saturated sand. In order to study the effect of grouting reinforcement on seismic response of the shield tunnel in liquefiable soil, the numerical models of grouting reinforcement and non-grouting reinforcement were established by using FLAC3D software respectively. The seismic responses characteristics of internal force and deformation of the tunnel structure and excess pore water pressure of sand under strong earthquake were studied, and the mechanism of grouting reinforcement weakening liquefaction of sand around the tunnel structure was revealed. Finally, the effect of grouting reinforcement on seismic performance of tunnel structures with different buried depths in liquefiable sand was systematically expounded. The results showed that: the excess pore water pressure in the sand around the shield tunnel could be reduced by grouting, resulting in liquefaction occurred only at the springing of the shield tunnel. After grouting, liquefaction is likely to occur in the middle of the two-lane tunnel, but the impact on the tunnel structure is small because the liquefaction area is small and does not spread. The maximum lateral convergence of the tunnel structure is reduced by 60%~80%, and the large deformation that occurs when the tunnel structure is extruded by the strata is effectively controlled; with the increase of buried depths, the liquefaction of the soil around the tunnel is reduced, and the uplift of the tunnel structure is reduced, and the lateral deformation and the internal force are increased. The research results can provide theoretical basis and scientific reference for the control of sand liquefaction under strong earthquake.