# Ground-Borne Vibration Model in the near Field of Tunnel Blasting
## 1 Introduction  
In tunnel construction, the use of explosives for rock mass excavation offers several technical and economic advantages when compared with other excavation methods. However, given the several safety issues and, particularly, environmental impacts associated with blasts, for example, when dealing with an urban environment, ground-borne vibrations play a significant role in the application of blasts for rock excavation, as they can lead to lower severity consequences, such as the discomfort of nearby populations or malfunctions in sensitive equipment, and high-severity consequences such as structural building damage [1, 2]. Given this, ground-borne vibrations have been a target for higher environmental restrictions, with the publication of new standards all over the world. These restrictions may be critical for the productivity and feasibility of geotechnical projects, and prediction models have become increasingly important. To control ground vibration production due to a blast, there is the need to impose certain maximum allowable vibration amplitudes that affect infrastructures. In 1962, the U. S. Bureau of Mines published a review for estimating damage to structures due to vibrations produced by blasts [3]. In this review, field data and associated structural damage observations were subjected to a thorough statistical analysis to determine if one of the variables, ground displacement, velocity, or acceleration, is more reliable than the others for damage estimates of structures. It was concluded that particle velocity was the most closely related to the degree of structural damage. Therefore, peak particle velocity(hereafter abbreviated as \(V\)) has been used as the controlling parameter in many countries and regions [4; 5], such as China's safety code for blasting [6]. Then, to correctly answer these damage criteria, the next step was to determine the means of predicting ground vibration levels for a given blast operation. The U. S. Bureau of Mines published the first results of statistical studies [7] based on ground vibration monitoring data from quarries and construction sites, which resulted in a well-known ground vibration prediction model that relates particle velocity as a function of the distance and explosive charge weight per delay. Since then, many studies have presented different relations between these three parameters. The studies of [PERSON] et al. [8] and [PERSON] et al. [9] made a summary of the several mathematical models presented over the decades by different authors that related ground vibration amplitudes to the so-called scaled distance. In fact, these kinds of formulas are actually derived from regression statistics and have good guiding significance for vibration control in the far field of blasting. However, the tests and studies on the near-field vibration of tunnel blasting indicate that they are not suitable for the calculation and control of the near-field vibration of blasting and cannot guide the drilling and blasting construction of an adjacent tunnel [10; 11]. Because the rock response near explosives is a highly nonlinear problem [12], and these formulas are mostly expressed as linear relations, the effects of millisecond blasting delay time, charge length, and explosive detonation velocity on blasting vibration velocity are not considered [13]. Therefore, it is obviously inappropriate to use these formulas to solve all the prediction problems of blasting vibration velocity. In China's blasting engineering, when evaluating the vibration impact of blasting on different types of ground buildings, equipment in the central control room of power stations, tunnels and roadways, high rock slopes, and newly poured mass concrete, the Sadovsky formula is usually used to calculate the peak particle vibration velocity of the foundation where the protection object is located. In addition, with the support of a large number of test data, the reference values of \(K\) and \(a\) under different lithology conditions in the blasting area are put forward [6].