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Нелинейный (степенной) закон трения для талых и мёрзлых грунтов

Геворкян С.Г.

Нелинейный (степенной) закон трения для талых и мёрзлых грунтов

Геворкян Сергей Георгиевич, кандидат физико-математических наук, старший научный сотрудник, ОАО «Фундаментпроект» (Москва)

E-mail: Sergev99@yandex.ru

В настоящей статье на основании анализа и обобщения результатов экспериментальных и теоретических исследований А.Е.?Шайдеггера, С.С.?Григоряна и Н.Н.?Маслова, а также наших собственных экспериментов, предложено эмпирическое соотношение, которое, в отличие от традиционного закона трения Кулона, описывает нелинейное изменение сопротивления грунтов сдвигу с ростом действующей на грунт нагрузки. Практическое значение предложенного нелинейного закона трения заключается в возможности решения с его помощью задач прогноза дальности выброса и скорости перемещения обвальных масс по склону в зоне аккумуляции. Актуальность такой задачи обусловлена нуждами гидротехнического и линейного строительства, горного дела, формирования крупных территориально-производственных комплексов, инженерной защиты промышленных и гражданских объектов, а также охраны природной среды.

Ключевые слова: крупномасштабные горные обвалы и оползни; сопротивление грунтов сдвигу; закон трения Кулона; нелинейный закон трения; мёрзлые грунты.

Gevorkyan S.G. Nonlinear (Described by the Power Function) Friction Law for Thawed and Frozen Grounds

Sergey G. Gevorkyan, Sc.D. (Physics and Mathematics), Senior Researcher, OJSC "Fundamentproect", Moscow, Russia

E-mail: sergev99@yandex.ru

In the present article on the basis of analysis and generalization of results of experimental and theoretical studies of A.E Scheidegger, S.S. Grigoryan and N.N. Maslov, and our own experiments we propose an empirical relation. Unlike traditional Coulomb friction law, this relations describes the nonlinear variation of shear strength of soils with the growth of acting on the ground of the load. Practical importance of the proposed nonlinear law of friction is the possibilities to solve with its help the problems of the forecast range release and speed of moving of landslide masses on a slope in the area of accumulation. The urgency of this task is caused by the needs of hydraulic and linear construction, mining, formation of large territorial-production complexes, engineering protection of industrial and civil objects, as well as environment protection.

The proposed nonlinear friction law describes the effect of reducing the shear strength of the frozen and thawed soils at loads above certain thresholds. When values of existing loads are below the threshold, this law limited to a traditional Coulomb law of friction. The question of the applicability of the new law of friction to the dispersed both frozen and melted soils we consider in this work.

For our researches of the frozen soils shear strength we used the method of the single-plane shearing. In our research we used the device VSV-25, which is designed for determination of shear strength of clay and sand soils with the sample section area of 40 cm² with vertical load in the range of up to 25 kg/cm². The tests were performed in accordance with the consolidated drained scheme. In accordance with the test procedure, samples of a ground were pre-compacted. Sample pre-compaction was done at such standard pressures at which shear strength was determined. The pressure was applied to soil samples in steps.

After pre-compaction, the samples were quickly unloaded, and the working rings with samples were placed into the freezing chamber where they were frozen at the temperature below the experimentally pre-set temperature of overcooling of this soil. After freezing, the samples were transferred to the test chamber where they were left for 24 hours at the same negative temperature at which the tests were to be performed. The test was carried out with constant speed and deemed completed when in 2 minutes after the beginning of the test the total shear deformation reached 5 mm.

We have proved the nonlinear friction law is applied for all solids, so this law has a universal character. This is the novelty of our findings.

Keywords: large-scale rock falls and landslides; resistance of soils shift; the Coulomb law of friction; nonlinear friction law; frozen soil.