# Prediction of Blast-Induced Ground Vibration Using an Adaptive Network-Based Fuzzy Inference System
## 2 Mechanism of Ground Vibration and the Vibration of Buildings
Among these standards, DIN 4150 is the most conservative and restrictive, and aims to reduce vibration effects and complaints [28]. Standard DIN 4150 also specifies safe vibration levels according to the type and condition of a building; thus, allowance is made for the type of building. The Norwegian Standard [29] limits the PPV to 80 mm/s for a structure made of reinforced concrete founded directly on hard rock. The limit values of vibrations, which take into account the magnitude, frequency, duration of the vibration, and the type of building are also provided in the British Standard BS 7385-2 [30]. The guideline values of the vibrations of various standards were summarized by [PERSON] et al. [31]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Type of Rock** & **Density (kg/m\({}^{3}\))** & \begin{tabular}{c} **Seismic** \\ **Velocity (m/s)** \\ \end{tabular} & \
\begin{tabular}{c} **Compressive** \\ **Strength (MPa)** \\ \end{tabular} &
\begin{tabular}{c} **Tensile** \\ **Strength (MPa)** \\ \end{tabular} \\ \hline Granite & 2700–2800 & 4500–6000 & 200–360 & 10–30 \\ Diabase & 2800–3100 & 4000–5000 & 290–400 & 19–30 \\ Limestone & 2400–2700 & 3000–4500 & 130–200 & 17–30 \\ Marble & 2800–3000 & 6000–7000 & 150–190 & 15–25 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Rock characteristics influencing blasting. Vibration standards are typically plotted graphically using logarithmic scales in both vertical and horizontal directions. The peak particle velocity (m/s) is presented on the vertical scale and the vibration frequency (Hz) is on the horizontal scale, as shown in Figure 1 [28]. Ground vibrations caused by blasting in tunnel construction can cause structural failures. Therefore, the effects of blast vibrations on buildings must be reduced or suppressed. The intensity of ground vibrations depends on controllable and non-controllable parameters. The main controllable parameters are the type and quantity of the explosive, sequence of initiation, powder factor, drilling, steaming, and hole depth while the main uncontrollable parameters are rock mass properties, geology, and joint formation. The vibration level at a certain point away from the charge is proportional to the weight of the explosive, while it is inversely proportional to the distance. Equations that are currently used for calculating and estimating the vibration level and the amount of charge per delay generally show high deviations between the measured and calculated peak particle velocity (PPV) values. The following conventional empirical equation provides the intensity of vibration in the form of PPV [19]:  
\[PPV=K\cdot\left(\frac{Q^{\alpha}}{d^{\beta}}\right) \tag{2}\]  
where \(PPV\) (mm/s) is the peak particle velocity, \(K\) (-) is the rock constant, \(Q\) (kg) is the charge per detonator delay number, \(d\) (m) is the distance between the blasting and measurement points, and \(\alpha\) (-) and \(\beta\) (-) are the damping coefficients. As the damping coefficients are difficult to determine, the equation does not provide sufficient results [19]. To determine the damping coefficient, the measured attenuation data should be well-matched with the predicted data [32]. For practical reasons, several authors have proposed simplified equations, which are listed in Table 2. The on-site constants (\(K\), \(B\)) can be obtained by using multiple regression analysis. The conventional blast vibration estimators are not able to estimate the \(PPV\) up to an acceptable limit because of the data scattering of blast vibrations. [PERSON] and [PERSON] [33] reported that the errors between predicted and actual PPV are due to the fact that cap scattering in the pyrotechnic based delay initiation system varies between \(\pm\) 10% and \(\pm\) 20%. Figure 1: Safe levels of blasting vibrations for houses.