## 5 Conclusions  
The nonlinear kinematic hardening (NKH) model was used in this study to simulate the nonlinear strain-dependent dynamic properties of soils and rocks. Seven model parameters were estimated either by trial-and-error or by using a semi-automated procedure with \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Layer** & **Depth** & **V\({}_{\text{s}}\)** & **v** & **\(\rho\)** & **G** & **E** \\
**No** & **(m)** & **(m/s)** & & **(t/m\({}^{3}\))** & **(GPa)** & **(GPa)** \\ \hline
1 & 3 & 549.0 & 0.418 & 2.081 & 0.63 & 1.78 \\
2 & 9 & 554.6 & 0.416 & 2.081 & 0.64 & 1.81 \\
3 & 15 & 1010.6 & 0.361 & 2.145 & 2.19 & 5.96 \\
4 & 21 & 1152 & 0.35 & 2.161 & 2.87 & 7.74 \\
5 & 27 & 1173.3 & 0.35 & 2.161 & 2.97 & 8.03 \\
6 & 33 & 1781.9 & 0.356 & 2.321 & 7.37 & 19.99 \\
7 & 39 & 1798.5 & 0.337 & 2.321 & 7.51 & 20.08 \\
8 & 45 & 1815.2 & 0.338 & 2.321 & 7.65 & 20.46 \\
9 & 51 & 1832.1 & 0.338 & 2.321 & 7.79 & 20.85 \\
10 & 57 & 1848.8 & 0.339 & 2.321 & 7.93 & 21.25 \\
11 & 63 & 2804.2 & 0.33 & 2.481 & 19.51 & 51.90 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Fundamental property profiles for Wolsung NPP. Figure 11: G/Gmax and damping curves with the NKH model for two rocks in NPP profile: **(a)** layer 3 and **(b)** layer 5.  
the modeling of torsional shear test in either ABAQUS or MATLAB. The main conclusions are as follows:  
* The simplified nonlinear kinematic hardening (SNKH) model could simulate the strain-dependent nonlinear properties of soil with a simple procedure of calibrating model parameters using the yield strength of the material. However, limitations of the model were illustrated, such as the threshold shear strain, shear modulus, and damping at low strain level;
* Parameters for the nonlinear kinematic hardening (NKH) model were estimated by using the proposed method of estimation based on the G/Gmax curve with initial values defined from the SNKH back-stress curve. The NKH model with seven parameters improved on the limitations of the SNKH model, and its simulated nonlinear shear modulus degradation and damping curves of soil were much better than the frequently used SNKH model;
* The trial-and-error procedure was proposed to estimate NKH model parameters, with one drawback of considerable time consumed, which has resulted in the very limited implementation of the NKH model in geotechnical engineering;
* A semi-automated procedure was proposed to estimate the NKH model parameters based on the basic properties of soil and the nonlinear dynamic curves. By implementation with the help of MATLAB, the parameters of the NKH model could easily be estimated in a very short time, and considering either the shear modulus degradation or the damping of material. The procedure was also applied for rock material, with good results being obtained;
* In this study, the NKH model could accurately simulate the shear modulus degradation, but the damping was not well simulated, especially at the high shear strain level, which would be not appropriate for analyses of a strong earthquake. Moreover, a more automated procedure should be further developed in combination with ABAQUS for estimating NKH model parameters which would be more applicable for researchers and engineers. Additionally, a built-in model combined with yielding criteria for geotechnical material needs to be developed further for ABAQUS that has been available in other commercial programs. Conceptualization, J.-M.K., C.L. and V.-L.N. ; methodology, V.-L.N. and E.-h.L. ; software, V.-L.N. and E.-h.L. ; validation, V.-L.N. and C.L. ; formal analysis, V.-L.N. ; investigation, V.-L.N. and E.-h.L. ; resources, J.-M.K. ; data curation, V.-L.N. and E.-h.L. ; writing--original draft preparation, V.-L.N. ; writing--review and editing, V.-L.N. and C.L. ; supervision, C.L. and J.-M.K. ; project administration, J.-M.K. ; funding acquisition, J.-M.K. All authors have read and agreed to the published version of the manuscript. This research was supported by the Ministry of Trade, Industry & Energy (MOTIE) of Korea (No.20193110100020).