# Predictive Modeling and Experimental Analysis of Cyclic Shear Behavior in Sand-Fly Ash Mixtures
## 5 Data Analysis  
Data-driven approaches in geotechnical engineering use advanced data analysis and machine learning to improve predictions of soil behavior, optimize design processes, and enhance real-time monitoring of infrastructure. By analyzing large datasets and integrating sensor data, these methods allow for proactive decision-making, accurate risk assessments, and optimized construction practices. Additionally, data-driven insights support traditional modeling techniques, making analyses more efficient and reliable. Data-driven models are applied in geotechnical modeling, including tunneling [50], predicting shear strength parameters [51], estimating the liquefaction potential of soils [52], determining the bearing capacity of piles, foundations and soils [53; 54; 55], performing geotechnical characterization of soils and composite materials [2; 31; 56; 57; 58; 59; 60] solving slope stability problems [61; 62; 63], estimating deformations of deep excavations [64], in optimization of embankment designs [65], estimating the swelling potential of soils [66], investigating the seismic properties and amplification factors of soils [7; 67], and classifying soils [68]. As for the processing method, Time Series NARX (**N**onlinear **A**uto **R**egressive with **e**X**ternal inputs) Feedback Neural Network scans handled sequential data by learning the dependencies between the time steps (loading steps in this study), with LSTMs and GRUs being particularly effective for long-term dependencies. Data preprocessing, such as normalization and windowing, and feature engineering, such as creating lagged variables, are essential steps in preparing loading series data. Once trained, these models can be used to predict the future behavior of material under loading. In this study, loading steps were simulated as loading steps to derive behavior along the cyclic loading. Figure 8 illustrates the schematic representation of the discretized loops of data points from cyclic direct shear tests on sand-fly ash mixtures. Each point on these loops corresponds to a specific data point of horizontal stress and strain, capturing the cyclic loading behavior. These individual data points serve as inputs for the NARX prediction model, enabling it to interpret and predict the stress-strain relationship in sand-fly ash mixtures under cyclic shear loads. This discretization allows the NARX model to learn from each phase of the loading and unloading cycles, enhancing its accuracy in capturing cyclic response patterns. The flowchart in Figure 9 outlines the methodology adopted for developing a NARX neural network model based on experimental cyclic direct shear test data of clean sand and sand-fly ash mixtures. The process begins with 'compiling parameters' derived  
Figure 7: Variations in shear stress with horizontal strain for; (**a**) Clean sand and mixtures of (**b**) 2.5 (%) FA, (**c**) 5 (%) FA, (**d**) 10 (%) FA, (**e**) 15 (%) FA and (**f**) 20 (%) FA. from experimental results, including horizontal stress and strain data from cyclic direct shear tests of different sand-fly ash mixtures. Following this, the dataset is established using the compiled parameters, forming the foundation for the model. The next step involves constructing the model's architecture and then training the NARX model with the experimental dataset. Once trained, the NARX analysis is conducted, where the model's performance is evaluated against the desired outcomes. If the results are unsatisfactory, the process loops back to repeat the simulation with adjustments to improve model accuracy. Once satisfactory results are achieved, the analysis is concluded, and the performance plots are generated to visualize and interpret the model's predictive capability regarding the cyclic behavior of sand-fly ash mixtures under shear loading. This model was developed to predict the cyclic behavior of fly ash-sand mixtures under shear loading, specifically focusing on the relationship between fly ash content and shear stress during cyclic shear tests.