Formulation of the Conditions for the Existence of a Mathematical Model for Emergency Prevention in Areas Contaminated by Residues of Rocket and Artillery Strikes
Abstract
Purpose. To formation the conditions for the existence of a mathematical model for emergency prevention in areas contaminated by residues of rocket and artillery strikes through the selection of geometric dimensions for the site of comprehensive soil assessment.
Method. The study employs an approach combining mathematical modeling, stratified soil sampling, and the construction of a risk index assessment, taking into account the spatial structure of contamination and pollutant interactions.
Findings. The study proposes the conditions for the existence of a mathematical model based on the selection of optimal geometric dimensions of the comprehensive soil assessment area (100×100 m horizontally and stratified layers up to 2 m deep). Formulas for hazard indices have been established, accounting for different types of pollutant interactions.
Theoretical implications. The results expand existing approaches to soil contamination risk assessment by integrating multilevel analysis of spatial distribution and pollutant interaction typology.
Practical implications. The results support the planning of monitoring activities, identification of priority areas for hazard assessment, and implementation of soil reclamation measures.
Originality/Value. A novel approach is proposed for the mathematical description of threat propagation in the affected zone, considering both pollutant concentration profiles and their interactions.
Research limitations/Future research. Limitations relate to the accuracy of initial data concerning the type, quantity, and composition of pollutants. Future research is aimed at the development of a mathematical model for emergency prevention in areas contaminated by residues of rocket and artillery strikes.
Downloads
References
Rashkevych, N. V. (2023). The relevance of determining soil hazard for the restoration of affected areas. In Proceedings of the International Scientific and Practical Conference “Problems of Emergency Situations” (pp. 118–119). Kharkiv: National University of Civil Protection of Ukraine.
Rashkevych, N. V. (2025). Identification of the main sources of soil and water pollution during military conflicts. In Proceedings of the International Scientific and Practical Conference “Problems of Emergency Situations” (pp. 119–120). Cherkasy: National University of Civil Protection of Ukraine.
Rashkevych, N. V. (2022). Factors influencing the distribution of heavy metals in the soil environment. In Proceedings of the International Scientific and Practical Conference “Problems of Emergency Situations” (pp. 217–218). Kharkiv: National University of Civil Protection of Ukraine.
Rashkevych, N. V., Shevchenko, R. I., & Rebrov, O. V. (2024). Justification of soil sampling optimization procedures to prevent technogenic emergencies. In Proceedings of the International Scientific and Practical Conference “Problems of Emergency Situations” (pp. 93–94). Kharkiv: National University of Civil Protection of Ukraine.
Bondarenko, A. Yu., Rashkevych, N. V., & Shevchenko, R. I. (2024, May 16). Methods for studying soil conditions in the context of solving civil protection tasks of territorial communities. In Proceedings of the All-Ukrainian Scientific and Practical Conference of Cadets, Students, and Postgraduates “Science of Civil Protection as a Way of Formation of Young Scientists” (pp. 12–14). Cherkasy: Chornobyl Heroes Cherkasy Institute of Fire Safety.
Rashkevych, O. S., Rashkevych, N. V., Shevchenko, R. I., & Khmyrova, A. O. (2024, August 1–3). Stages of forming a mathematical model for emergency prevention in the combat zone. In Proceedings of the XI International Scientific and Practical Conference “Innovative Development of Science, Technology and Education” (pp. 145–149). Vancouver, Canada.
Kardanpour, Z., Jacobsen, O. S., & Esbensen, K. H. (2015). Local versus field scale soil heterogeneity characterization – A challenge for representative sampling in pollution studies. Soil, 2(1), 619–645.
Wang, Y., Qi, Q., Bao, Z., Wu, L., Geng, Q., & Wang, J. (2023). A novel sampling design considering the local heterogeneity of soil for farm field-level mapping with multiple soil properties. Precision Agriculture, 24(4), 1–22.
Gao, B., Lu, A., Pan, Y., Huo, L., Gao, Y., Li, X., ... Chen, Z. (2017). Additional sampling layout optimization method for environmental quality grade classifications of farmland soil. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 10(12), 5350–5358.
Ju, L., Guo, S., Ruan, X., & Wang, Y. (2023). Improving the mapping accuracy of soil heavy metals through an adaptive multi-fidelity interpolation method. Environmental Pollution, 330, 121827.
Meli, M., Auclerc, A., Palmqvist, A., Forbes, V. E., & Grimm, V. (2013). Population-level consequences of spatially heterogeneous exposure to heavy metals in soil: An individual-based model of springtails. Ecological Modelling, 250, 338–351.
Houlong, J., Daibin, W., Chen, X., Shuduan, L., Hongfeng, W., Chao, Y., ... Lina, G. (2016). Comparison of kriging interpolation precision between grid sampling scheme and simple random sampling scheme for precision agriculture. Eurasian Journal of Soil Science, 5(1), 62–73.
Yu, D., Zha, Y., Shi, L., Bolotov, A., & Tso, C. H. M. (2021). Spatiotemporal sampling strategy for characterization of hydraulic properties in heterogeneous soils. Stochastic Environmental Research and Risk Assessment, 35, 737–757.
Wang, Y., Song, Y., & Li, T. (2019). Vertical distribution of heavy metals in soil profile and implications for groundwater pollution. Environmental Pollution, 254, 113083. https://doi.org/10.1016/j.envpol.2019.113083
Zhang, X., Wang, H., & Li, J. (2020). Optimal sampling depth and grid resolution for heavy metal monitoring in agricultural soils. Science of The Total Environment, 709, 136111. https://doi.org/10.1016/j.scitotenv.2019.136111
Wadoux, A. M. C., Brus, D. J., & Heuvelink, G. B. M. (2019). Sampling design optimization for soil mapping with random forest. Geoderma, 355, 113913. https://doi.org/10.1016/j.geoderma.2019.113913
De Caires, S. A., Martin, C. S., Atwell, M. A., Kaya, F., Wuddivira, G. A., & Wuddivira, M. N. (2025). Advancing soil mapping and management using geostatistics and integrated machine learning and remote sensing techniques: A synoptic review. Discover Soil, 2, 53.
Ministry of Health of Ukraine. (2020, July 14). Order No. 1595 “On approval of hygienic regulations for permissible content of chemical substances in soil”. Retrieved from https://zakon.rada.gov.ua/laws/show/z0722-20#Text
State Standard of Ukraine (DSTU ISO 10381-1:2004). (2004). Soil quality. Sampling. Part 1: Guidance on the development of sampling programs (ISO 10381-1:2002, IDT). Retrieved from https://online.budstandart.com/ua/catalog/doc-page?id_doc=58984
State Standard of Ukraine (DSTU ISO 10381-2:2004). (2004). Soil quality. Sampling. Part 2: Guidance on sampling techniques (ISO 10381-2:2002, IDT). Retrieved from https://online.budstandart.com/ua/catalog/doc-page?id_doc=58855
State Standard of Ukraine (DSTU ISO 10381-4). (n.d.). Guidelines for the investigation of natural, near-natural and cultivated sites. Retrieved from https://online.budstandart.com/ua/catalog/doc-page?id_doc=52991
State Standard of Ukraine (DSTU ISO 10381-5:2009). (2009). Soil quality. Sampling. Part 5: Guidance on the procedure for investigation of urban and industrial sites with regard to soil contamination (ISO 10381-5:2005, IDT). Retrieved from https://online.budstandart.com/ua/catalog/doc-page.html?id_doc=77011
Abstract views: 192 PDF Downloads: 89
Copyright (c) 2025 Nina Rashkevich, Olga Shevchenko, Ivan Rushchak, Volodymyr Kradozhon, Viacheslav Krasnov

This work is licensed under a Creative Commons Attribution 4.0 International License.
The authors agree with the following conditions:
1. Authors retain copyright and grant the journal right of first publication (Download agreement) with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
2. Authors have the right to complete individual additional agreements for the non-exclusive spreading of the journal’s published version of the work (for example, to post work in the electronic repository of the institution or to publish it as part of a monograph), with the reference to the first publication of the work in this journal.
3. Journal’s politics allows and encourages the placement on the Internet (for example, in the repositories of institutions, personal websites, SSRN, ResearchGate, MPRA, SSOAR, etc.) manuscript of the work by the authors, before and during the process of viewing it by this journal, because it can lead to a productive research discussion and positively affect the efficiency and dynamics of citing the published work (see The Effect of Open Access).










