The equivalent linear method on the FEA NX is applied to free field analysis and 2D equivalent linear analysis. The equivalent linear method approximates the ground material nonlinearity as an equivalent linear material property for linear iterative analysis. It is generally valid for strain sizes of .

For the equivalent linear method, the initial element shear modulus G and initial damping ratio h need to be set for each layer. Generally, the values when the strain is minimum are used, and the frequency domain analysis is conducted to calculate the maximum shear strain of each layer or element. The effective shear strain is calculated as 0.65 or using the earthquake magnitude by multiplying to that value and the shear modulus G and damping ratio h are calculated using the dynamic material function curve, created from the effective shear strain of each layer or element. This analytical process is repeated until the G and values h converge, generally determined by the relative error of 5% or less, then the analysis is complete and the calculated results are output.

Free field analysis finds the ground response to an input earthquake at the in-situ ground stage before structure construction. Free field analysis is often used to for the determination of design response spectrum using ground surface vibration estimation, liquefaction assessment using dynamic stress-strain computation and the determination of earthquake load that causes instability of ground or structures.

2D equivalent linear analysis not only provides analysis for the ground, but also for soil-structure interaction. To minimize the earthquake damage, the seismic design for underground structures is performed, and the stability examination needs to be done to the structure that considered seismic safety. If the structure is built on a soft ground layer such as clay or silt layers, the vibrations in the bedrock due to earthquakes can be greatly amplified at the surface and hence, the effects on the structure by the soil-structure interaction due to earthquake vibrations need to be assessed in detail. Because underground structure are different from ground structures in that the structural response to earthquakes is mostly controlled by the ground displacement, the dynamic material properties of the ground and modeling method determines the analysis results. The figure below displays the general information on modeling the actual analysis domain using the finite element method (FEM) for soil-structure interaction analysis.

<Schematic diagram of analysis domain and FEM modeling>

<Table. FEM model size to minimize analysis result interference cause by the boundary>

The main difference between soil-structure interaction problems and normal structural dynamic problems is the radiation damping effect due to the infinite property of the ground. Normal damping properties come from material friction etc. that dampens the structural movement, but radiation damping radiates the wave energy into the infinite ground space to dampen the structural energy. Hence, seismic analysis conducted using the equivalent linear method to consider the material nonlinearity and use the frequency domain analysis, that makes the modeling of radiation damping easier.

The analysis method depending on the shear modulus  G and shear strain γ  relationship is shown in the figure below.