# Application Study of the High-Strain Direct Dynamic Testing Method  
[PERSON]  
1 School of Transportation and Logistics Engineering, Wuhan University of Technology, Wuhan 430063, China, [EMAIL_ADDRESS]  
[PERSON]  
1 School of Transportation and Logistics Engineering, Wuhan University of Technology, Wuhan 430063, China, [EMAIL_ADDRESS]  
[PERSON]  
2 Department of Civil Engineering, Faculty of Engineering, Al Al-Bayt University, Mafraq 25113, Jordan 2*  
considered to be the standard method for assessing the bearing capacity of piles because of its straightforwardness and accuracy. However, this method is time-consuming, expensive, and often limited by geographical constraints. In contrast, the high-strain dynamic test has numerous advantages, such as lightweight equipment, a shorter testing time, lower costs, and a wider range of applicable situations. Consequently, this method has been rapidly adopted since its inception. The core principle of the high-strain dynamic testing method is to analyze the stress wave-by-wave theory within the pile during the driving process. In 1931, [5] first proposed that a one-dimensional wave equation can be applied to the practical application of stress wave theory. In 1960, [6] proposed a model representing the pile driving system using a series of mass blocks, springs, and dampers to simulate the hammer, pile, and soil. This model was solved using numerical difference methods. To better characterize the soil's resistance to the pile, he introduced two new parameters as follows: the soil's elastic limit and the damping coefficient. The analysis model, solution method, and parameters introduced by [PERSON] established the theoretical foundation for modern high-strain dynamic testing methods. The practical application of the high-strain dynamic method in engineering primarily stems from the work of [7; 8; 9; 10; 11; 12; 13; 14; 15] at Case Western Reserve University. Their invention, the Pile Driving Analyzer (PDA), transformed academic research into a process that the engineering community embraced. They also developed an analytical method called CAPWAP (Case Pile Wave Analysis Program) with the advent of digital computation. CAPWAP fits the calculated force curve to the measured force curve by making reasonable assumptions about the pile-soil model's parameters, ultimately determining the load-bearing capacity using the set of parameters that achieve the best fit. However, different sets of parameters can potentially yield the same fit, resulting in multiple possible solutions, which introduces ambiguity into the method. In 1980, the first international seminar on \"The Application of Stress-Wave Theory to Piles\" was held, promoting research on the high-strain method in multiple countries. Over the subsequent decades, researchers proposed a series of improved models [15; 16; 17; 18; 19], and extensive studies were conducted on the pile-soil interaction mechanism under impact loads [20; 21; 22; 23; 24]. In addition, the use of machine learning to describe the geomaterial heterogeneity is included in the numerical modeling methods [25]. With technological advancements, artificial intelligence has been integrated into pile-bearing capacity prediction models. For instance, [PERSON] et al. [26] applied genetic programming (GP) to enhance efficiency in predicting ultimate pile capacity, while [PERSON] et al. [27] combined machine learning (ML) with advanced optimization algorithms to improve prediction accuracy, developing three predictive models. These efforts yielded significant findings, making the high-strain method increasingly routine in pile foundation testing. The improved models offered clearer physical insights and better descriptions of the complex mechanical responses of the soil during pile driving. However, with the increase in parameters, these models became more complex and often difficult to implement in practical engineering applications.