In northern forests, winter is the preferred time for logging operations, since, when wet soils freeze, their strength increases, which ensures a high load-bearing capacity of winter forest roads and reduces the cost of forestry work by increasing the load on forestry equipment, including when driving through frozen lowlands. The present article analyzes frozen loamy–sandy soil, which, at subzero temperatures, behaves like a brittle material with a sufficiently high, but limited, strength. Well-known models commonly use empirical parameters, correlations, and numerical methods to estimate the strength of such materials. An analytical model of the full load–displacement curve would reduce the number of necessary calculations and increase the ability to predict the bearing capacity of winter forest roads. However, there are few of these models. Such models were developed, as a rule, to study stress–strain in concrete and rocks, meaning that researchers have to recalculate the load into stress and displacement into deformation, which is not always simple. This work aimed at theoretically justifying a new analytical model for quantifying the bearing capacity of winter forest roads and assessing the adequacy of the model by comparing it with experimental data. To achieve this purpose, the concepts of fracture mechanics and methods of mathematical modeling were used. The model was verified using experimental data, and model examples for determining the peak load were provided. Prospects for development of the research topic were also considered, taking into account new developments in forest road monitoring for logging management.

In this paper, load-displacement and stress-strain diagrams are considered for the uniaxial compression of concrete and under three-point bending. It is known that the destruction of such materials occurs on the descending branch of the load-displacement diagram. The attention of the presented research is focused on the explanation of this phenomenon. Fracture mechanics approaches are used as a research tool. The method for determining effective stresses and modulus of elasticity of concrete based on the results of uniaxial compression tests has been substantiated. The ratios necessary for the calculation were obtained without any assumptions about the reinforcement of concrete and the mechanical properties of its components. However, the effect of these properties is considered indirectly, using the stress and strain peaks determined by standard concrete compression tests. It was found that the effective stresses increase both on the ascending branch and on the descending branch of the load-displacement diagram. This explains the destruction of concrete on the descending branch of the load-displacement diagram. The results of determining the stresses and modulus of elasticity under uniaxial compression are comparable with the results obtained in experiments known in the literature.

This paper discusses modeling the behavior and prediction of fracture of brittle materials. Numerous publications show that progress in this area is characterized by the emergence of a number of new models that meet the requirements of the mining industry, construction and other engineering practices. The authors focus only on one class of models, paying special attention to the compromise between simplicity of solution and versatility of the model. A new version of the model is proposed, taking into account the advantages of previous models. We present a differential energy criterion for brittle fracture substantiated, according to which, fracture occurs at a certain ratio of dissipated and stored (elastic) energy. Fracture is considered as the end of the deformation process with a virtual transformation of the initial material almost without cracks into a real material with cracks. The highest and lowest elastic moduli are analytically determined, respectively, on the ascending and descending branches of the stress–strain curve. A graphical version of the algorithm for determining the brittle fracture point on the post-peak branch of the stress–strain curve is proposed. The modeling results are consistent with the experimental data known from the literature.

This article deals with the problem of predicting the brittle fracture of rocks and similar materials, which can also include frozen sandy soils. Such materials, due to the diversity of their conditions of origin, are characterized by natural heterogeneity at the micro-, meso-, and macro-levels, which makes it difficult to develop sufficiently universal criteria for their strength. Despite a number of known models and criteria of strength and fracture, the search for such criteria remains an urgent problem. In this paper, using the energy approach to the mathematical modeling of mechanical systems, the fracture criterion is justified, which differs from the known criteria that do not require integration to calculate the strain energy $W_e$ and dissipation energy $W_d$. The well-known relation for the input energy $W=W_e+W_d$ is used. The object of the study was the ratio of $dW=d{W}_e+d{W}_d$. The main research question concerned what the ratio of $d{W}_e$ and $d{W}_d$ would be at the point of brittle failure. The search for an answer to the question led to the justification of a differential energy criterion for the failure of brittle materials on the descending branch of the full stress–strain curve. It was found that the point of predicted fracture is determined by the equality $\sigma =0.5 \epsilon E_{tangential}$ (if there is an inflection point on the ascending branch) or $\sigma =0.5 \epsilon E_{secant}$_secant. The main result of the work was ascertaining the differential strength and fracture criteria of brittle materials in the form of inequalities and equations, which were oriented for application in engineering calculations. Examples of application of the developed criteria are given; their consistency with the experimental data known from the literature confirmed.

Drying, as a process of changing the moisture content and temperature of capillary-porous materials, is a necessary step in many technologies. When predicting moisture changes, it is necessary to find a balance between the complexity of a model and the accuracy of the simulation results. The purpose of this work was the development of a mathematical model for drying a capillary-porous material with direct consideration of its initial moisture content and drying temperature. Methods of mathematical modeling were used in the work. Using the developed model, an analysis of the features of the drying process of materials with high and low initial moisture content has been carried out. The analytical relationship for determining the time at which the extremum of the drying rate is reached has been substantiated. A model has been developed to directly take into account the influence of the initial material moisture content and drying temperature. The simulation results are consistent with the experiments on drying ceramic blocks for construction which are described in the literature. The obtained results can be taken into account in studies of the effect of drying modes on the energy consumption of a drying process.