Computational Modeling of Steel Plate Shear Wall (SPSW) Behavior

Steel Plate Shear Wall Behavior: Introduction

Steel plate shear walls (SPSW) and reinforced concrete shear walls (RCSW) are common structural members used for lateral resistance, particularly in earthquake zones. Both SPSW and RCSW can also provide significant protection against explosions. However, current design methods lack comprehensive equations or guidelines in handbooks for designing steel plate shear walls subjected to blast loads.

Additionally, there are no commercial applications available specifically for designing these structural elements under explosive conditions. Finite Element Analysis (FEA) is typically employed for simulating SPSW and RCSW, with each analysis taking anywhere from 30 minutes to several hours, depending on the system’s configuration. The time and cost of each analysis vary based on system setup and complexity.

To design an effective steel plate shear wall or RCSW that can withstand explosions, a parametric study with a minimum number of samples is crucial. The Taguchi method is an excellent tool for optimizing design with fewer samples. While increasing the number of samples can improve accuracy, the number of samples is directly tied to the number of design variables.

For optimization models, techniques like regression, machine learning, and hybrid or ensemble models are often used. Software such as SPSS, ABAQUS, and MATLAB support these advanced modeling techniques. This project will explore these three methods in depth, each presented in a dedicated workshop.

What is the steel plate shear wall, and what is its application?

Steel plate shear wall and RCSW are two structural members that are almost designed and used in the steel frame and reinforced concrete (RC) frame to increase the rigidity of the frame against seismic loads; however, they can be used against explosive loads because the surface absorbs the explosive energy. Therefore, SPSW and RCSW are used to counter seismic load and blast load.

Why a parametric study should be done for this target?

There is no standard, equation, reference book, or design book for the simulation of the steel plate subjected to explosion. Simulation of structural elements subjected to blast loads models is very complex and takes significant time for simulation. There are many design parameters that have an effect on the performance of Steel plate shear wall and RCSW subjected to blast loads; therefore, many samples should be simulated with various design parameters to specify the effect of the design parameters on the sample behavior.

How many samples should be simulated? | Optimizing Design Parameters for Steel Plate Shear Wall Behavior

The number of samples directly corresponds to the number of design parameters and the various levels at which these parameters can be adjusted. These levels are determined by design requirements, standards, construction realities, and any dimensional limitations. For instance, in a parametric study with four design variables, at least 91 samples are necessary to ensure reliable results.

Key design parameters include the dimensions of structural elements, steel and concrete strength, the ratio of steel reinforcement, thickness, distance from explosion to the structural element, and the weight of TNT. Methods such as the Taguchi approach can significantly reduce the number of samples needed while still achieving an acceptable and optimized design for a steel plate shear wall.

Simulation of the sample by finite element method (FEM) using ABAQUS

In this teaching program, ABAQUS is used for the simulation of both steel plate shear walls (SPSW) and reinforced concrete shear walls (RCSW) using Finite Element Method (FEM). Once the validated FEA model is developed, the samples, as defined in the previous section, are simulated and analyzed. The explosive load is modeled using the conventional weapons effect program (CONWEP), which calculates a range of blast effects from various high explosives and weapons. This includes blast loads, fragment penetration, wall breaching, projectile penetration, and cratering, along with ground shock.

Air blast calculations in CONWEP cover both free-field and reflected blast pressures from different explosion types. These include surface and buried explosions, as well as explosions in confined spaces like tunnels. For steel plate simulations, the Johnson-Cook model is applied, while the von Mises yield criterion is used to predict if materials like metals will yield or fracture under stress.

In total, 125 steel plate shear walls and 255 reinforced concrete shear walls are simulated using ABAQUS.

Simulation of the FEA results using the Artificial Intelligence method

These days, surrogate methods have been developed for presenting the alternative computational method with lower cost and time of calculation. Moreover, using these methods, the optimal design can be specified, and the behavior of the optimal design can be analyzed in a second instead of a complex and long analysis. The surrogate models, which are present in this package, include regression models, Gene Expression Programming, adaptive network-based fuzzy inference system (ANFIS), and hybrid and ensemble models. It is clear that the training dataset and testing datasets should be specified randomly. After training the models using the training datasets, the models should predict the behavior of steel plate shear wall and RCSW. All models can be compared based on the time and cost of calculation and accuracy. However, the accuracy of models is compared by the statistical parameters and error terms that include the coefficient of determination, root mean square error (RMSE), normalized square error (NMSE), fractional bias, maximum positive error, maximum negative error, distribution of errors, and mean absolute error.

Method 1: Using SPSS to generate the samples with various parameters

The samples and the variation in design parameters should be logical and based on the standards and reality. To optimize the number of samples for simulation, the Taguchi approach is used by SPSS.

Method 2: Using ABAQUS to validate a FEA model and simulation of all models

ABAQUS is used to validate an FEA model. In order to validate a FEA model, a sensitivity analysis should be conducted. After that, using the validated FEA model, the behavior of samples subjected to explosive loads is simulated.

Method 3: Using ABAQUS to validate a FEA model and simulation of all models

MATLAB is used to develop AI methods, including regression methods, GEP, ANFIS, and ensemble methods. The statistical parameters and error terms are calculated by one of these software.

Workshop 1: Design a parametric study and optimize the number of samples in a parametric study

In this workshop, first, the effective factors in designing the samples for a parametric study are presented. An appropriate parametric study should consider all effective variables; thus, specifying the effective variables for each parametric study is important. Although by increasing the number of samples, the accuracy of analysis will be increased, the time and cost of analysis will be increased; therefore, in the second part of this workshop, Taguchi as a method for designing a parametric study is explained to optimize the number of samples, although it keeps the accuracy of analysis for a big data.

Workshop 2:  FEA modeling of SPSW and RCSW subjected to explosive loads and validation of FEA model

In this Workshop, the simulation of SPSW and RCWS is explained step by step in ABAQUS software, and after that, four samples that refer to four experimental studies are simulated by ABAQUS. The validation of the FEA model is very important for each FEA model. Therefore, in the end, the validation of the FEA model using mesh sensitivity analysis and comparing the results of FEA with experimental results is presented.

Workshop 3:  Simulation of the behavior of SPSW and RCSW by surrogate models

Using regression models, GEP, Machine Learning (ML), Deep Learning (DL), hybrid, and ensemble models, the behavior of SPSW and RCSW is estimated. For using these approaches, the dataset, which is the collection of design parameters, loading conditions, and the response of SPSW and RCSW to the explosion, is separated randomly into two groups, including training and testing datasets. The training dataset is used to train the surrogate models, and after that, the models are used to predict the response of SPSW and RCSW based on design parameters and explosion conditions. The statistical parameters and error terms are used to compare the model in this Workshop.