# DEVELOPMENT OF A MATHEMATICAL MODEL FOR ANALYSING THE HAZARDOUS IMPACT ON THE STATE OF GROUNDWATER IN CITY AGGLOMERATIONS FROM MISSILE AND ARTILLERY ATTACKS

## Authors

• N. Rashkevych National University of Civil Defence of Ukraine
• R. Shevchenko National University of Civil Defence of Ukraine
• T. Vovchuk National University of Civil Defence of Ukraine

## Keywords:

mathematical model, groundwater, missile and artillery damage, critical infrastructure object, emergency prevention

## Abstract

The authors have developed a mathematical model for analysing the hazardous impact on the groundwater in urban agglomerations from missile and artillery attacks. The mathematical model consists of a system of four analytical dependencies. The first analytical dependence describes determining the area of groundwater intake from the groundwater level, considering the presence of artificial coatings, infiltration, evaporation, and transpiration, as well as the effect of evapotranspiration. The second dependence determines the area of influence of the missile and artillery danger from the type of weapon, the explosive charge, calibre (diameter), and territorial conditions, the key indicators of the content of which in the territory of the critical infrastructure object, which suffered damage, are further determined by expert calculation using natural samples of soils and groundwater. The third dependence determines the impact of harmful (polluting) substances on groundwater in the territory of the critical infrastructure object, which suffered damage, depending on the process of groundwater movement in the area of the emergency, taking into account the hydraulic pressure and water yield coefficient; the process of distribution of chemically dangerous substances in groundwater, taking into account the coefficient of hydrodynamic dispersion and the velocity of groundwater; convective diffusion of chemically hazardous substances, taking into account the kinetics of sorption. The fourth dependency allows us to choose an efficient concept for the organisation of groundwater monitoring on the territory of a critical infrastructure object that suffered damage based on the variation of formalised parameters for solving individual problems. The initial conditions of the mathematical model are related to the presence of chemically dangerous compounds in groundwater at the maximum permissible concentration level. The boundary conditions of the mathematical model relate to the non-overgrowth of consequences beyond the object level in terms of the number of victims.

## Author Biographies

### N. Rashkevych, National University of Civil Defence of Ukraine

PhD, Senior Lecturer at the Department of Fire Prevention in Settlements

### R. Shevchenko, National University of Civil Defence of Ukraine

Doctor of Technical Sciences, Full Professor, Head of the Department of Automatic Security Systems and Information Technologies

PhD Student

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2024-04-05

## How to Cite

Rashkevych, N., Shevchenko, R., & Vovchuk, T. (2024). DEVELOPMENT OF A MATHEMATICAL MODEL FOR ANALYSING THE HAZARDOUS IMPACT ON THE STATE OF GROUNDWATER IN CITY AGGLOMERATIONS FROM MISSILE AND ARTILLERY ATTACKS. Municipal Economy of Cities, 1(182), 229–240. https://doi.org/10.33042/2522-1809-2024-1-182-229-240

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