# Large-Scale 3D Multi-Story Enterprise Layout Design in a New Type of Industrial Park in China
## 3 Problem Description
### Association Safety Risks
\begin{cases}1&if\ D_{ij}=0\\ \frac{\beta_{1}}{(\beta D_{ij})^{2}}&if\ D_{ij}>0\\ \frac{\beta_{2}}{(\beta D_{ij})^{2}}&if\ D_{ij}<0\end{cases}  \tag{3}\]  
where \(D_{ij}\) is the floor difference between enterprise \(j\) and enterprise \(i\), \(b\) is the floor-to-floor height, and \(\beta_{1}\) and \(\beta_{2}\) are the correction parameters. (ii) Explosion risk enterprises  
The physical effects corresponding to an explosion are the overpressure of the explosion shock waves, propellant fragments, and thermal radiation. One of the most representative types of damage is shockwave damage, which spreads widely and quickly and may cause chain damage. Shockwave injuries and destructive effects can be assessed using the overpressure criterion. When the shock wave overpressure reaches a specific value, it causes inevitable damage. In the shockwave propagation method, the energy propagates outward from the center of the explosion source. Its propagation characteristic is that the  
Figure 2: Schematic of the point source model. further away from the center it is, the smaller the effect of the overpressure state. The shockwave peak overpressure is generally considered a function of the distance. Many experimental studies have been conducted, and various empirical formulas have been summarized [55,56]. [PERSON] [57] compared and analyzed the prediction results of multiple empirical formulas and summarized the following formulas:  
\[Z=\frac{R}{W^{1/3}} \tag{4}\]  
\[P_{so}=\left\{ \begin{array}{ll}\frac{0.084}{Z}+\frac{0.27}{Z}+\frac{0.7}{Z^{ 3}}&if\ Z\leq 1\\ \frac{0.084}{Z}+\frac{0.255}{Z^{2}}+\frac{0.65}{Z^{3}}&if\ 1<Z\leq 15\end{array} \right. \tag{5}\]  
where \(Z\) is the proportional distance, \(R\) is the distance between the target point and burst center, \(W\) is the equivalent TNT dosage, and \(P_{so}\) is the shock wave peak overpressure. The explosion risk diffusion coefficient function is defined as follows:  
\[\gamma^{e}\big{(}D_{ij}\big{)}= \begin{cases}1&if\ D_{ij}=0\\ \frac{\alpha_{1}}{bD_{ij}}+\frac{\alpha_{2}}{\big{(}bD_{ij}\big{)}^{2}}+\frac {\alpha_{3}}{\big{(}bD_{ij}\big{)}^{3}}&if\ D_{ij}>0\\ \frac{\alpha_{4}}{bD_{ij}}+\frac{\alpha_{5}}{\big{(}bD_{ij}\big{)}^{2}}+\frac {\alpha_{6}}{\big{(}bD_{ij}\big{)}^{3}}&if\ D_{ij}<0\end{cases}  \tag{6}\]  
where \(\alpha_{1}\), \(\alpha_{2}\), \(\alpha_{3}\), \(\alpha_{4}\), \(\alpha_{5}\), and \(\alpha_{6}\) are correction parameters. When considering other environmental impact factors, such as wind direction, wall thickness, and safety barriers, the risk diffusion coefficient can be adjusted using correction parameters based on actual engineering experience. Furthermore, it can be combined with expert evaluations to increase the model's flexibility. (iii) Other types of risk enterprises  
In addition to fires and explosions, enterprises can also have other accidents. The model only considers the impact on the same floor for accidents that are less likely to occur or have a smaller scope of impact. The diffusion coefficient function is defined as follows:  
\[\gamma^{o}\big{(}D_{ij}\big{)}= \begin{cases}1&if\ D_{ij}=0\\ 0&\text{otherwise}\end{cases}  \tag{7}\]  
(4) Step 4: Determination of actual association safety risks  
Based on the above steps, the actual association risk of enterprises is determined by:  
\[R_{ij}^{a}= \begin{cases}R_{ij}*\gamma^{f}\big{(}D_{ij}\big{)}&if\ i\in F\\ R_{ij}*\gamma^{e}\big{(}D_{ij}\big{)}&if\ i\in E\\ R_{ij}*\gamma^{o}\big{(}D_{ij}\big{)}&if\ i\in O\end{cases}  \tag{8}\]  
where \(R_{ij}^{a}\) is the actual association risk with enterprises \(i\) and \(j\), \(R_{ij}\) is the association safety risk where enterprises \(i\) and \(j\) are adjacent, and \(F\), \(E\), and \(O\) represent fire types, explosion types, and other types of enterprises, respectively.