## 1 Introduction  
Construction activities such as pile driving frequently generate high-intensity ground vibrations that adversely affect surrounding environments. Numerous standards and specifications [1; 2; 3; 4] define the allowable vibration limits of nearby objects, such as buried services, structures, people, and ultra-precision equipment. These limits are usually represented as peak particle velocity in the time domain or root mean square velocity in the frequency domain. Direct comparisons of vibration intensities with the allowable vibration limits are typically used to assess the impact of construction-related vibrations on nearby objects. Therefore, the prediction of ground vibration intensities due to common construction activities is a key part of such a vibration impact assessment procedure. Various prediction models of ground vibration intensities have been developed in the literature. They can be categorized into three types, namely, empirical, theoretical, and engineering models [5]. Empirical models based on historical on-site measurements are often expressed in empirical formulas that describe how vibration intensity attenuates with distance from the vibration source [3; 6; 7; 8]. Theoretical models are usually based on numerical and analytical modeling using various computer programs, in which complete dynamic responses of soil and/or structures during the process of common construction activities were simulated [9; 10; 11; 12]. Engineering models often integrate the empirical, theoretical, and engineering knowledge to consider the dynamic characteristics of construction sites. For example, the past studies [13; 14] focused on the derivation of the propagation function for vibration sources by performing seismic tests on a targeted construction site. Among these three categories, although theoretical and engineering models present higher reliability than empirical models, the former two also require more execution time and more sophisticated technical knowledge. Given that empirical models are comparatively simple to apply and require a small amount of input data, they are widely used to predict vibration intensities in real construction projects. Empirical models are typically developed based on past field measurements, in which vibration intensities at different distances from vibration sources were measured by installing vibrometers at selected locations. According to the regression analyses of field measurement data, [PERSON] [7] suggested a simplified model:  
PPV \[=kD^{-n}\] (1a)PPV \[=K\left(\frac{D}{\sqrt{E}}\right)^{-n}\] (1b)  
where PPV (mm/s) refers to the peak value of the resultant particle velocity, \(D\) (m) is the distance from the vibration source, \(k\) is the value of vibration amplitude at \(D\) = 1 m, \(E\) (J) is vibration source energy, \(D/E^{0.5}\) represents the scaled distance, \(K\) is the value of vibration amplitude at \(D/E^{0.5}\) = 1 (m/N)\({}^{0.5}\), and \(n\) ranging from 1.0 to 2.0 refers to the attenuation rate exponent that accounts for both geometric and material damping. Site-specific vibration attenuation models can be developed by adopting Equation (1a). For example, [PERSON] and [PERSON] [15] measured vibration intensity on ground surface points due to vibratory sheet pile driving with rated kinetic energy \(E\) = 1000-3000 J on different construction sites. Through the regression of data points, both mean values (\(n\) = 1.5, \(k\) = 32) and upper bound values (\(n\) = 1.5, \(k\) = 80) for Equation (1a) were suggested for the attenuation of ground vibration intensity along the distance. [PERSON] et al. [16] measured ground vibrations generated by vibratory sheet pile driving and rotary mini-pile driving. By using Equation (1a), they proposed the upper bounds of ground vibration intensity for vibratory sheet pile driving (\(n\) = 1.1, \(k\) = 43) and rotary mini-pile driving (\(n\) = 1.3, \(k\) = 12). Based on their statistical analyses of recorded data, [PERSON] et al.