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Introduction. At present, numerical methods enjoy widespread use in construction practice. They enable performing and analyzing complex non-linear, multi-factor models without excessive analytical procedures. However, as a rule, the most complex tasks, performed in a three-dimensional setting with account taken of physical, geometric and other nonlinearities, are performed in deterministic formulations without the analysis of the stochastic nature of physical processes. This seems particularly strange, given that numerical methods are well-suited for modeling stochastic processes. Numerical probabilistic and statistical approaches (PSA) can be applied to simulate and take into consideration various spatiotemporal aspects of the probabilistic nature of loads and forces, structural system resistances, materials and geological terrains. Even the most advanced numerical models of deterministic physical systems are merely a specific case of probabilistic and statistical modeling: they enable obtaining only one value (point) on the whole field of possible implementations, being unable to demonstrate an objective and exhaustive variety of probable outcomes. This article presents a case study of numerical probabilistic and statistical analyses of loads and forces. Methods of research. Materials from different sources, such as reference books, regulatory documents, laboratory test results, as well as available experimental data, were used as input parameters. The principal calculation and analysis of the integral function of loads was performed using the Monte Carlo numerical method of probabilistic and statistical modeling and various theoretical (statistical) and empirical distributions, followed by the quantitative assessment of design loads at various confidence probability values. Results. This study provides an example of the probabilistic and statistical calculation (determination) of the integral function of loads and forces with account taken of different origins of loads and varied input parameter distribution patterns, including empirical distributions. It has proven great importance of accurate description of initial distributions of a random value for the determination of reliable design load values. Conclusions. Probabilistic and statistical approaches have the ability to objectively assess the performance of structural systems based on the quantitative assessment of the probabilistic nature of load factors. These approaches have huge potential for increasing the reliability of buildings and structures and the cost effectiveness of construction projects.

В современной практике инженерных расчетов все более востребованным и повсеместным становится применение численных методик. В статье дается подробный обзор наиболее перспективной и все более востребованной модели грунтов модели упрочняющегося грунта (Hardening soil model (HSM)). Также приводится краткий обзор грунтовых моделей, которые до сих пор широко используются в отечественной практике инженерных расчетов с применением численных методов, модели, которые являлись предшествующими по отношению к модели HSM, на которых собственно, она основана. Изучение математических моделей грунтов в численных расчетах является залогом корректного применения компьютерных программ, залогом от бездумного нажимания клавиш компьютера, а значит залогом повышения надежности и безопасности строительства зданий и сооружений, а также повышения экономической эффективности проектов строительства. These days structural as well as geotechnical tasks usually being solved with the help of numerical analytical technics. The practice of using analytical methods based on linearelastic behavior assumptions become less and less popular or even outdated. Huge growth of computer numerical power gives opportunity for development and application of advanced and complicated nonlinear mathematical soil models. Understanding basics of soil mechanics and the constitutive mathematical models describing soils behavior are crucial for correct usage of fi niteelements software and computer analysis of geotechnical everyday tasks. One of the most popular soil model used these days in engineering practice is the hardening soil model (HSM) proposed by T. Shanz in 1999. The article gives a thorough review of the development of HS model which is based on linear MohrCoulomb model and hyperbolic DuncanChang model.

Introduction. Calculation and analysis of pile resistance to loads remains to be a relevant problem in geoengineering. The design of pile foundations is currently performed using diverse analytical, empirical and numerical methods. However, the reliability of these methods remains to be a topic of interest among researchers and designers. This research paper analyses methods used for calculating the lateral-load capacity of piles in comparison with field-test data. Materials and methods. The paper dwells upon the development of reliable analytical expressions based on mathematical models of the pile–soil interaction. Main existing mathematical models of the soil environment, including the Mohr – Coulomb elastic ideal plastic model and the hardening soil model (HSM) were analysed. A particular attention was paid to a variety of factors affecting the pile–soil interaction, such as natural factors, pile types, pile sinking depth and technology, configurations of loads, as well as time-changed processes. A comparison of methods for calculating the lateral-load capacity of piles was conducted. To that end, calculations using the Mohr – Coulomb model and the local elastic strain theory (still required by building codes) were performed. High-level solid elements were used to develop and compute a finite-element pile-in-soil model in a spatial setting. Another model on the basis of parametric pile elements was designed using the MIDAS software. Results. It is established that the use of numerical calculation methods for evaluating the capacity and movements of pile foundations provides results comparable to those of field tests. These methods demonstrate a higher reliability compared to standardized analytical techniques. Conclusions. The reliability of numerical calculations of pile resistance to lateral impact is shown to be sufficiently high, thus being feasible for use in geoengineering. The use of these methods should be based on advanced non-linear soil models, such as HS, CamClay, etc.