Mathematical Model Prototype to Optimise Engineering Management of the Construction Site

Modern construction technologies strongly affect the environment. Therefore, design and building construction should also follow the sustainable development principle. In this case, design and construction work based on the sustainable development principle should aim at creating a safe and healthy living environment, the economical use of natural resources, and the stimulation of economic development to create the welfare for humans and favourable natural conditions. The article proposes a mathematical algorithm as a comprehensive solution for engineering management of the planning construction site, from the calculation of the earthworks to the automated creation of the engineering geological cross-sections. The paper integrates engineering management, mathematical modelling, and BIM technology. The application of the building information model is undoubtedly one of the most advanced technologies used in the engineering management field, whose advantages have been shown by researchers. In the preliminary stage of construction and production management, decisions should be made regarding material and human resources, schedules, and estimates. The main purpose of this article is the optimisation of the excavation. Other issues important to the organisation and management of the construction are the planning of safe work on the construction site, depending on the soil type. Geotechnical sections allow ascertaining the need for additional fortifications and the depth of the fortifications for safe work. The paper describes the principal mathematical model developed by the authors to design a construction site using BIM technologies. It presents the main formulas of a mathematical algorithm aimed at selecting the objects used on the building site and the need for them. It also gives the main principles of engineering management and methods for selecting the mechanisms used on the construction site. Understandably, a specialist’s visit to the construction site will not be avoided, and it is difficult to present the entire current situation only with a review report or photographs. Using a photogrammetric model, the expert has the opportunity not only to visually evaluate the current condition but also to perform measurements (length, width, and volume) directly in the photogrammetric model. Important and new information about the construction site indicates all relevant obstacles, i.e., plants, surrounding constructions, and other objects.