## 2 Data-Driven Modeling  
After analyzing the collected database, the CBR was predicted using three artificial intelligence methods, including artificial neural network (ANN), genetic programming (GP), and support vector machine (SVM). The hypothesis of the performed study, is that artificial intelligence (AI) methods can be utilized to predict the California bearing ratio (CBR), which is a crucial parameter in geotechnical engineering, that measures the load-bearing capacity of soil, of soil stabilized with album sludge, a byproduct of water treatment plants.  
The California bearing ratio (CBR) is a penetration test performed on a compacted sample of soil or aggregate, to evaluate its strength and bearing capacity. It is a standardized test method used to determine the relative strength of a soil sample by measuring the pressure required to penetrate the sample with a plunger of standard area at a standardized rate. The CBR value is expressed as a percentage of the pressure required to penetrate a standard material, typically crushed rock or limestone, at the same penetration depth and under the same conditions. A higher CBR value indicates greater strength and load-bearing capacity of the soil or aggregate sample. The CBR test is widely used in civil engineering and construction to determine the design parameters of roads, airfields, and other infrastructure projects.  
The use of AI algorithms for material characterization and design, has been met with skepticism, due to concerns about the reliability of their complex models. The lack of transparency and knowledge extraction processes in AI-based models, is a major challenge. Mathematical modeling techniques can be categorized as white-box, black-box, and grey-box, depending on their level of transparency (Figure 1). While white-box models are based on first principles and provide an explanation of the underlying physical relationships of a system, black-box models do not provide any feasible structure of the model. Grey-box models, on the other hand, identify the patterns between the data, and provide a mathematical structure of the model. ANN is a popular black-box modeling technique widely used in engineering, but its weights and bias representation does not provide details about the derived relationships. GP is a newer grey-box modeling technique, that uses an evolutionary process to develop explicit prediction functions, making it more transparent than other ML methods, especially black-box methods such as ANN and SVM. The mathematical structures derived by GP can be used to gain important information about the system's performance.  
In civil engineering, SVM has been applied for predicting soil properties [65], classifying building materials [66], and detecting structural damage [67]. For instance, SVM has been used for predicting the shear strength of soil, by using the geotechnical parameters as input variables [68]. SVM has also been employed for detecting structural damage, by using the vibration signals from a structure as input variables [69].  
In civil engineering, GP has been used for optimization problems, such as the optimal design of structures and construction scheduling [70; 71]. For example, GP has been applied for optimizing the design of steel frames in high-rise buildings, by evolving the design variables such as beam size, column size, and connection details [72].