The nonlinearity of the strain energy at an interval period of applying seismic load on the geostructures makes it difficult for a seismic designer to makes appropriate engineering judgments timely. The nonlinear stress and strain analysis of an embankment is needed to evaluate by using a combination of suitable methods. In this study, a large-scale geostructure was seismically simulated and analyzed using the nonlinear finite element method (NFEM), and linear regression method which is a soft computing technique (SC) was applied for evaluating the results of NFEM, and it supports engineering judgment because the design of the geostructures is usually considered to be an inaccurate process owing to high nonlinearity of the large-scale geostructures seismic response and such nonlinearity may induce the complexity for decision making in geostructures seismic design. The occurrence of nonlinear stress and nonlinear strain probability distribution can be observed and density of stress and strain are predicted by using the histogram. The results of both the simulation from the NFEM and the linear regression method confirm the nonlinearity of strain energy and stress behavior have a close value of R^{2} and root-mean-square error (RMSE). The linear regression and histogram simulation shows the accuracy of NFEM results. The outcome of this study guides to improve engineering judgment quality for seismic analysis of an embankment through validating results of NFEM by employing appropriate soft computing techniques.

Applying nonlinear strain energy on geostructures cases the unexpected excitation owing to internal and external loads interaction, under this situation nonlinear stress and nonlinear strain are developing. The concept of strain energy and the effect of the mechanical properties of the materials on nonlinear displacement development were studied in the geotechnical earthquake engineering field by using the nonlinear finite element method (NFEM) [

The nonlinear stress and strain were investigated using numerical simulation and experimental work [

There is necessary to study the application of advanced mathematical modeling for NFEM results validate in seismic geotechnical infrastructure design improvement. Apply the linear regression model and the histogram model on NFEM results were developed from the ABAQUS has not been found in the literature. In this study, to evaluate the accuracy of NFEM results and characterization of the nonlinearity stress and strain, a large-scale geostructure was seismically simulated and analyzed using the nonlinear finite element method, and linear regression method and histogram which are soft computing techniques (SC) were applied for evaluating the results of NFEM and support engineering judgment.

An elasto-plastic clay cohesive soil type [^{2}) are applied to simulating large-scale geostructure. The nonlinear strain energy is applied to the embankment-subsoil model in both positive and negative directions. The accuracy of the nonlinear strain and stress was evaluated using soft computing techniques.

The mechanical properties of the construction material are effective factor in the seismic design of each infrastructure, and the construction material plays one of the main functions in provide strength and stiffness of the geostructure. The mechanical properties of the soil are indicated in ^{3} respectively mentioned in

The nonlinear acceleration is applied to the geostructure, and it develops nonlinear strain and stress. The acceleration characteristics are shown in ^{th} seconds till the 9^{th} second was zoomed. At the 6.62 seconds +5.9242 m/s^{2} and at 6.295 seconds the −9.10367 m/s^{2} are maximum acceleration m/s^{2} in the positive and negative direction, respectively. The occurrence of two consequent acceleration peaks at a close time causes a high level of nonlinearity on the embankment-subsoil model.

Young’s Modulus, E (MPa) | Poisson’s ratio, ν | Unit weight, γ (kN/m^{3}) |
---|---|---|

24 | 0.2 | 18.5 |

Cohesion, C (kPa) | Friction angle, ϕ (deg) | Dilatancy angle, ψ (deg) |
---|---|---|

17 | 40 | 2 |

The developing nonlinear strain and stress relate to modeling geometry and the nonlinear acceleration were applied to the geostructure. The geometry of a large-scale geostructure model is shown in

The external eigenfrequency and seismic acceleration initiate are applying to the model beneath the subsoil. Owing to using the same construction material in modeling embankment and subsoil, it is assumed embankment and subsoil interaction was occurred due to geometry and there is not any influence of construction material in the embankment-subsoil interaction, has been considered. After applying the external eigenfrequency and seismic acceleration to the model, the results of the NFEM were reported in 80 stages, and the maximum and minimum value of the stress and strain have been selected from each stage for modeling by using linear regression and histogram. In the linear regression analysis, 80 maximum stress and 80 maximum strain have been selected for analysis of the R^{2} and RMSE, and to evaluate the accuracy of NFEM results, the R^{2} and RMSE were considered. The 80 minimum stress and strain, and 80 maximum stress and strain have been selected to depict histogram graphs. The histogram is depicted for assessing the probability distribution of stress and strain.

To study nonlinear stress and strain distribution on the large-scale geostructure, only maximum and minimum levels of 80 stages at numerical analysis were selected. The acceleration was applied to the large-scale geostructure model for simulation nonlinear strain and stress using the nonlinear finite element method (NFEM), and linear regression method which is a soft computing technique (SC). The flowchart for the entire study process is shown in

To establish a nonlinear stress-strain classification and prediction geostructure seismic monitoring, the histogram was developed with different intervals and the frequency. The histogram supports stress-strain characterization. In using NFEM, with using the 80 stages of the numerical simulation, the histogram was developed, it made because the whole stages of the numerical simulation reveal the embankment-subsoil model seismic response. To discover the intensity of reiterating stress-strain at the specified presented interval, the Central Limit Theorem was used.

To improve the seismic safety of the large-scale geostructures, a seismic design was performed, and suitable methods from the mathematical field were introduced to geotechnical engineering to enhancing decision making. The questions are, “do the results of the numerical simulation from NFEM is trustable for large-scale geostructures seismic design? And which methods are required to validate the results of the numerical simulation produced by the NFEM”?

The 13^{th} continuous range of nonlinear maximum principal stress (MPa) and the nonlinear maximum principal strain were showed in

The entire range of the stress and strain value are presented in

To focus on a large-scale geostructure seismic response and analysis, the linear regression model was applied to predict nonlinear maximum stress and nonlinear maximum strain for 80 stages of the nonlinear finite element method results. The maximum stress versus maximum acceleration and maximum strain versus maximum acceleration were depicted in ^{2} and RMSE for maximum stress and maximum strain indicate in ^{2} for maximum stress and maximum strain are 0.869 and 0.853, respectively. The value of RMSE for maximum stress and maximum strain are 0.102 and 0.005, respectively. The R^{2} and RMSE for maximum stress and maximum strain have confirmed the accuracy of the prediction made by the histogram model.

With considering nonlinear stress data and nonlinear strain data distribution which are presented in

-------- | Max stress | Max strain |
---|---|---|

R^{2} |
0.869 | 0.853 |

RMSE | 0.102 | 0.005 |

The nature of the seismic loads interaction influences the stress and strain distribution and causes the model excitation with different magnitude and shape. The resultants of the nonlinear stress distribution acting on the embankment-subsoil model and causes developing nonlinear deformation on the model in the period of excitation. When the nonlinear stress and strain distribution in loading and reloading stages are distributed at a high level of nonlinearity, higher model excitation is expected. Basis of the stress and strain evaluation by using histogram, the excitation, nonlinear deformation, and displacement of the model can be predicted.

In the histogram, the nonlinear strain has a more symmetric shape compared to the nonlinear stress, this phenomenon was occurred owing to embankment and subsoil have the same material. And more the nonlinear strain energy is expected in a model with multi-materials. The symmetric and bell-shaped histogram is presented normal distribution for stress and strain. With attention to the shape of the histogram, it makes more convenient for appropriate engineering judgment in a large-scale geostructure seismic design. This study supports the improvement of engineering judgment quality for seismic analysis of an embankment through validating results of NFEM by employing an appropriate soft computing technique. The close value of R^{2} and RMSE from the linear regression results show accuracy NFEM for the characterization of nonlinear stress and strain behavior. The R^{2} value from the linear regression model obtained for maximum stress and the maximum strain was confirmed the histogram prediction is applicable for simulation of the nonlinear finite element method results in the seismic design of a large-scale geostructure. The fitting line in a regression model which is presented in

With consider of the nonlinear stress-strain relationship and distribution which are presented in ^{2} and RMSE for maximum stress and maximum strain nonlinear relationship are indicated in ^{2} and RMSE have been obtained 0.99365 and 0.02245, respectively. These values are indicated the linear regression model was showed the accuracy of NFEM results. The stress-strain relationships for the embankment-subsoil model are shown from initial the stress-strain is not more nonlinear, while with increasing time of applying nonlinear load the nonlinearity of the stress-strain was increased.

R^{2} |
RMSE |
---|---|

0.99365 | 0.02245 |

The application of the linear regression model in the prediction of the seismic embankment was studied. The stress-strain relationship is changed, was showed by linear regression model. The histogram shows the regression model is adequate for validating NFEM results in the large-scale geostructure seismic design.

The elastic-plastic finite element analysis was performed to assess the local stress-strain reactions of the notch-root [

The nonlinear stress-strain relationship was investigated to assess seismic stability of embankment [

There are several problems are related to seismic and cycle fatigue that have excellently been solved and validate with different methods such as large-scale 3D simulations of seismic wave propagation [

The large-scale geostructure was seismically simulated and analyzed using the nonlinear finite element method (NFEM) and the soft computing technique (SC) was applied for evaluating the results of NFEM. The nonlinear stresses and nonlinear strains probability distribution occurrence and density are predicted by using the histogram.

The nature of the load interaction influences the stress and strain distribution. The large elastic strain and large stress range during loading are governing the main seismic excitation and failure of the large-scale geostructure. The determination of the nonlinear stress and strain distribution on the large-scale geostructure is supported decision-making in geostructures seismic design. The nonlinear stress and nonlinear strain probability distribution occurrence and density of the stress and strain are predicted through the histograms which are symmetric and bell-shaped, and these histograms are presented the normal distribution of the predicted stress and strain.

The linear regression model has plotted a linear curve pattern for maximum stress and strain. The R^{2} value from the linear regression model has confirmed the histogram prediction is applicable for simulation of the nonlinear finite element method results in the seismic design of a large-scale geostructure. The shape of the histogram and linear regression model are confirming the accurate prediction of the NFEM results for the large-scale geostructure seismic design. The R^{2} and RMSE for maximum stress and strain have confirmed the prediction made by the histogram model. The outcome of this study guides the improvement of a large-scale geostructure engineering design quality through evaluation of the stress-strain relationship of the simulated model by using appropriate soft computing techniques.

_{2}/PE-nanocomposites by inverse modeling based on FE-simulations of nanoindentation test