Experimental regularities of slopes stability loss, supported by different types of retaining structures
An unfavorable combination of various factors leads to the occurrence of landslides, as catastrophic manifestations of processes in rock massifs. As a result, there is a threat to human life, damage and destruction of residential and industrial buildings.
| Рубрика | Производство и технологии |
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| Язык | английский |
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Experimental regularities of slopes stability loss, supported by different types of retaining structures
Shapoval V., Dnipro University of Technology, Konoval V., Cherkasy State Technological University, Ponomarenko I., Cherkasy State Technological University, Skobenko O. Dnipro University of Technology, Barsukova S., Dnipro University of Technology, Zhylinska S., Dnipro University of Technology
An unfavorable combination of various factors (natural, man-made, human, etc.) leads to the occurrence of landslides, as catastrophic manifestations of processes in rock massifs. As a result, there is a threat to human life, damage and destruction of residential and industrial buildings and objects and infrastructure networks, significant material losses [1, 2, 3, 4].
It is also known that among emergency situations of geological origin, 60% are landslides [1]. retaining structures human life
Landslides occur all over the world, including in Ukraine. Thus, since 1992, the trend of increasing the frequency of landslides has occurred in almost all regions of Ukraine, especially in the Dnipropetrovsk, Kharkiv, Kyiv, Poltava and Cherkasy regions, the Carpathian region and Crimea [1, 4].
The manifestation of landslides in many regions of Ukraine and the world has a destructive and sometimes catastrophic character. This creates a constant threat of man-made and natural emergency situations, as well as a danger to people's health and life.
One of the ways to prevent landslides is the arrangement of retaining structures that absorb the shear pressure and thus either stabilize or completely prevent the occurrence of landslides [4].
However, the use of retaining structures requires large material costs, and the process of their arrangement requires significant labor and material costs, especially if the retaining structures are a solid structure [4, 5, 6].
Discrete retaining structures in the form of buttresses arranged with a certain pitch made of rectangular elements and drilled piles are much cheaper than solid ones, but the behavior of such structures under load (especially in the area of their contact with the sliding soil massif) has not been sufficiently studied. In addition, modern methods of their calculation and design give very different results [4, 6, 7, 8, 9, 10].
Therefore, we decided to present our accumulated experience of modeling and calculating the parameters of landslide processes, as well as the design of anti-landslide retaining structures in a series of monographs and articles.
This monograph includes and analyzes the results of tests of models of slopes and various types of retaining structures, performed by us using centrifugal modeling [7, 8, 9, 10, 11, 12, 13, 14, 15].
Devices and equipment. Methodology of conducting experiments using the centrifugal method modeling
For carrying out experiments was used centrifugal car, the photo of which is shown in Fig. 1, and the diagram is in Fig. 2.
The main parts of a centrifugal machine are:
- machine bed (item 1 in Fig. 1 and item 1 in Fig. 2);
- anchors necessary for fastening the machine bed (item 2 in Fig. 2);
- reinforced concrete floor, in which anchors are fixed (item 3 in Fig. 2);
- the vertical axis of rotation of the rocker arm (item 3 in Fig. 1 and item 4 in Fig. 2);
- a cassette with a slope model (item 4 in Fig. 1, as well as items 5 and 6 in Fig. 2);
- counterweight (item 6 in Fig. 1, as well as items 7 and 8 in Fig. 2);
- horizontal gearbox (item 7 in Fig. 1, as well as item 9 in Fig. 2);
- shafting (item 10 in Fig. 2);
- coupling (item 11 in Fig. 2);
- vertical gearbox (item 12 in Fig. 2);
- electric motor (item 13 in Fig. 2);
- rocker arm (item 2 in Fig. 1 and item 14 in Fig. 2).
Fig. 1. Centrifugal machine (photo)
1 - machine bed; 2 - rocker arm; 3 - vertical axis of rotation; 4 - cassette with a slope model; 5 - slope model;6 - counterweight; 7 - gearbox
Fig. 2. Centrifugal machine (diagram)
1 - machine bed; 2 - anchors; 3 - reinforced concrete floor; 4 - rocker arm rotation axis; 5, 6 - the position of the cassette with the slope model in the process of preparation and conducting the experiment; 7, 8 - the position of the counterweight in the process of preparing and conducting the experiment; 9 and 12 - horizontal and vertical gearboxes; 10 - shafting; 11 - coupling; 13 - electric motor; 14 - rocker arm
Centrifugal modeling processes can be conditionally divided into several stages:
1. Preparatory (that is, the stage of creating a model). At this stage, the following should be done operations:
1.1 Determination of the necessary scale of modeling and, as a result, the frequency of rotation of the centrifuge.
1.2 Preparation of necessary tools and materials needed for carrying out the experiment, in particular cassettes in which models of soil slopes are placed (Fig. 3).
Fig. 3. Cassette in which there is a slope
1.3 Preparation of the soil for conducting the experiment (in particular, sieving the soil on a sieve in order to achieve the design granulometric composition, moistening or drying it in order to achieve the design humidity and etc.).
1.4 Production of models of buttresses.
1.5 Wrapping the side walls of the metal form with a thin polyethylene film and lubricating their inner surface with machine oil. The goal is to reduce the friction between the soil from which the mold is made and the walls forms.
1.6 Layer-by-layer compaction of the soil in a metal form by tamping to the design density.
1.7 Sampling of compacted soil and preliminary determination of its properties.
1.8 Arrangement of the design profile of the slope according to the outline of the determined creation, according to which the modeling of the slope is performed (Fig. 4).
Fig. 4. Arrangement of the design profile of the slope model. 1- slope model; 2 - cassette wall
1.9 Application of the mesh on the side of the soil model (Fig. 5) and reverse installation of the side metal wall of the cassette with the soil model.
Fig. 5. Marking of the design profile of the slope model.
1- slope model; 2 - grid; 3 - ruler
1.10 Installation of finished models of buttresses (Fig. 6).
Fig. 6. Installation of finished models of buttresses.
1- cassette; 2 - model slope; 3 - buttresses
1.11 Weighing a cassette with a slope model.
1.12 Weighing the counterweight necessary for balancing on the cassettes with the model during rotation centrifuges.
At this stage, you should also select a counterweight that fully compensates for the weight of the cassette with the model when the centrifuge rotates.
1.13 Preliminary calculation of the scale of modeling and, on this basis, the frequency of rotation of the centrifuge rocker arm.
1.14 Mount a cassette with a plumb line model and a counterweight on the centrifuge rocker arm.
2. Actually, experiments on a centrifugal machine. They include in himself:
2.1 Adjusting the engine rotation parameters according to the design scale modeling.
2.2 Launching engine and rotation centrifuges according to from design time experiment.
2.3 Stopping engine.
2.4 If there is no destruction of the model, then it is
necessary to adjust the scale factor (and, as a result, the frequency of rotation of the centrifuge) and repeat the experiment.
2.5 Unloading the centrifuge and its preparation for a new one experiment.
3. Analysis of the results of the experiment in order to determine what is necessary for transfer model ones data in nature On this stage experiment perform the following actions:
3.1 Fixation and measurement of linear movements of nodes of the deformed grid on the wall models.
3.2 Photofixation of deformed parts of the model, soil damage - cracks, subsidence and deformations, what arose in as a result rotation on centrifuge (these data are necessary for compiling a qualitative picture of the experiment and determining its compliance with modern ideas about the stability of slopes).
3.3 Sampling of soil to determine its properties after the experiment. These data are given in the table 1.
Table 1.
Soil properties
|
The name of the characteristic |
The value of the characteristic |
|||||||||
|
Experiment number |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
|
|
Density of soil particles, kN/m3 |
27 |
27 |
27 |
27 |
27 |
27 |
27 |
27 |
27 |
|
|
Soil density, kN/m3 |
16.1 |
16.2 |
16.5 |
16.5 |
16.3 |
16.6 |
16.5 |
16.7 |
16.5 |
|
|
Natural humidity, units |
0.18 |
0.18 |
0.19 |
0.19 |
0.17 |
0.19 |
0.18 |
0.19 |
0.19 |
|
|
Density of dry soil, kN/m3 |
13.6 |
13.7 |
13.8 |
13.9 |
14.0 |
14.0 |
14.0 |
14.0 |
13.9 |
|
|
Porosity coefficient, units |
0.98 |
0.97 |
0.95 |
0.94 |
0.93 |
0.93 |
0.93 |
0.93 |
0.94 |
|
|
Moisture at the yield point, units |
0.22 |
0.21 |
0.21 |
0.21 |
0.2 |
0.21 |
0.21 |
0.21 |
0.2 |
|
|
Moisture at the limit of rolling, units |
0.14 |
0.14 |
0.14 |
0.13 |
0.13 |
0.14 |
0.14 |
0.13 |
0.13 |
|
|
Number of plasticity, units |
0.08 |
0.07 |
0.07 |
0.08 |
0.07 |
0.07 |
0.07 |
0.08 |
0.07 |
|
|
Liquidity rate, units |
0.51 |
0.60 |
0.74 |
0.69 |
0.50 |
0.67 |
0.56 |
0.80 |
0.79 |
|
|
Angle of internal friction, degrees |
14.2 |
14.4 |
14.5 |
14.7 |
14.8 |
14.9 |
15.0 |
15.0 |
15.0 |
|
|
Specific adhesion, kPa |
6.3 |
6.2 |
6.1 |
6.0 |
5.9 |
5.8 |
5.8 |
5.8 |
5.9 |
|
|
Modulus of total deformation, MPa |
6.2 |
5.6 |
5.0 |
5.5 |
6.4 |
6.4 |
6.0 |
6.2 |
6.8 |
Methodology and results of experiments
Below are the methods and results of the most characteristic and demonstrative experiments. Their difference from each other is as follows:
1. During the tests of model No. 1, a slope without a retaining structure was tested.
2. During the tests of model No. 2, a slope with a discrete retaining device was tested construction.
3. During the tests of model No. 3, a slope with a solid support was tested construction.
Next, we will dwell on the methodology and test results of models 1-3 more carefully.
When making model No. 1 a two-layer base was used.
Soil properties are listed in Table 1 (column 1). The general view of the model before the test is shown in Fig. 7.
Fig. 7. Model No. 1 before testing. There are no retaining structures
Vertical and horizontal lines are drawn with ink on the side surface of the model, by the curvature and breaks of which it is convenient to judge the deformation and destruction of the model after the test.
A photo of the slope model without a retaining structure after the test is shown in Fig. 8.
Fig. 8. Model No. 1 before testing. There are no retaining structures. Red in color marked the sliding surface
From Fig. 8 it follows what took place deformation soil in zone shear, (that is, above the sliding surface) and there are no deformations beyond it. The data obtained during the experiment, listed under natural conditions, are shown in Fig. 9 (actual dimensions of the slope) and Fig. 10 (shear pressure curve).
Fig. 9. Natural coordinates, calculated after testing model No.1.
Notes: 1. The blue color shows the daytime surface. 2. The sliding surface is marked in red color 3. The shear body is marked in gray color
Fig. 10. Shear pressure diagram under natural conditions, calculated on the basis of testing model No. 1. There are no retaining structures. Note: This Figure should be read together with Fig. 9.
First model tested in machine at 200 revolutions per minute corresponding to the scale factor n = 102. After the test, the model did not destroyed.
Next, the number of revolutions of the machine was increased to 220 revolutions per minute, which corresponds to a scale factor of n = 123.4. With such a number of revolutions slope lost stability. From Fig. 10, in particular, it follows what curve sliding pressure starts and ends at a value close to zero. This means that the slope is maintained at the expense of the internal ones
Model No.2 is a slope, the stability of which is provided by discrete retaining structures (more precisely, buttresses that provide frontal resistance to the sliding soil massif and resistance on the side surface).
In the production of model No. 2, a two-layer base was used. The properties of the soil used in the manufacture of model No.2 are given in Table 1 (column 2).
Below the soil layer is a cement-sand layer of material, brand M75, is necessary to prevent the soil from sliding on the metal bottom of the cassette and to fasten the buttresses (in Fig. 11 and 12, this layer has light color).
Fig. 11. Model No. 2 before testing. Retaining structures - two buttresses
Fig. 12. Model No. 2 after testing. Sliding surfaces are marked in red color
On the side surface of the model, vertical and horizontal lines were drawn with ink, by the curvature and breaks of which it is convenient to judge the deformations of the model after the test.
As a retaining structure, 2 concrete buttresses were used, the distance between which was 50 mm.
When testing the model in a centrifugal machine, the soil was lost stability and climbing on the supporting wall and in the gap between the buttresses (Fig. 12).
Initially, the number of revolutions of the machine was 200 revolutions per minute, which corresponds to a scale factor of n = 102.
Then the number of revolutions of the machine was increased to 240 revolutions per minute, what responds large scale multiplier n = 150. At such quantity the soil lost its spin stability (more precisely, displacements, breaks and cracks appeared in it).
The data obtained during the experiment, listed under natural conditions, are shown in Fig. 13 (actual dimensions of the slope) and Fig. 14 (shear pressure curve).
Fig. 13. Natural coordinates, calculated after testing model
No. 2. Notes: 1. The blue color shows the daytime surface. 2. The sliding surface is marked in red color. 3. The shear body is marked in gray color.
Fig. 14. Shear pressure diagram in natural conditions, calculated on the basis of testing of model No. 2. Note: This Figure should be read together with Fig. 13
From Fig. 14, in particular, it follows what curve sliding pressure begins at zero pressure and ends at a value close to 40 kN/m. It means what slope is kept by score internal forces and interaction with the retainer construction.
It was also established that the volume of soil elements adjacent to the buttresses decreased by approximately 2 times. This is due to its squeezing between buttresses.
Model No. 3 is a slope, the stability of which is ensured by a solid retaining structure (more precisely, a retaining wall). A two-layer base was used in the production of model No. 3. Properties soil, which was used at manufacturing models No. 3, listed in Table 1 (column 3).
Below the soil layer is a cement-sand layer of material, brand M75, is necessary to prevent the soil from sliding on the metal bottom of the cassette and to fasten the buttresses (in Fig. 15 and Fig. 16, this layer has light color).
Fig. 15. Model No. 3 before testing. The retaining structure is a solid retaining wall
Fig. 16. Model No. 3 after testing. The sliding surface is marked in red color
On the side surface of the model, vertical and horizontal lines are applied with ink line. On distortion and gaps these lines determined state and deformations of the model before and after experiment.
A continuous concrete wall without gaps was used as a retaining structure. Testing of such a structure is necessary to build a complete picture of the influence of the type of retaining structure on the stability of slopes.
Initially, the number of revolutions of the machine was 200 revolutions per minute, which corresponds to a scale factor of n = 102.
With such a number of revolutions per minute, the slope turned out to be stable. When the number of revolutions of the machine increased to 230 revolutions per minute, the slope destroyed. The scaling factor n = 135 corresponds to this number of revolutions. The data obtained during the experiment, listed under natural conditions, are shown in Fig. 17 (actual dimensions of the slope) and 18 (shear pressure curve).
Fig. 17. Natural coordinates, calculated after testing model No. 3. Notes: 1. The blue color shows the daytime surface. 2. The sliding surface is marked in red color 3. The shear body is marked in gray color.
Distance, ш
Fig. 18. Shear pressure diagram under natural conditions, calculated on the basis of tests of model No. 3. There are no retaining structures. Note: This Figure should be read together with Fig. 17.
From Fig. 18, in particular, it follows that curve sliding pressure begins at zero pressure and ends at a value close to 40 kN/m. It means that slope is kept by score internal forces and interaction with the retaining construction.
In general, the above results of experiments No. 1, 2 and 3 on a centrifugal machine made it possible to draw the following qualitative conclusions:
1. Curves sliding pressure slopes with retaining constructions and without them significantly are different between yourself: if retaining construction missing then in at the end of the shear, the curve has a value close to zero, and if a retaining structure is located at the end of the shear, then the shear pressure is significantly different from zero.
2. The shear pressure curves of continuous and discrete retaining structures have the following common feature: at the location of the retaining structure, the shear pressure is different from zero
3. The destruction of slopes in the presence of continuous and discrete retaining structures has a significant difference in that in the second case it has the place of soil compression between retaining elements structures.
Since the problem of compression and stability of the soil in the gaps between the elements of discrete retaining structures has not been sufficiently studied, it was conducted six special experiments, in whose varied the distance between the retaining elements constructions
A special structure was developed for conducting experiments, which consisted of from a plate 8 millimeters thick, in which with step by step in 10 millimeters holes with a diameter of 6 mm and a thread were made. Rods with a diameter of 10 mm were screwed into these holes, which the retaining elements were modeled structures.
Such construction supporting buildings allowed do step between elements of the retaining structure model 1, 2 and 3 centimeters.
A total of six experiments were performed (2 - at the distance between the retaining elements in axes 20 mm, 2 - at distance between retaining elements in the axes of 30 mm and 2 - when the distance between the retaining elements in the axes is 40 mm).
The data of these experiments are summarized in Table 2,
which indicates the distance between the elements of the retaining structure, the number of revolutions of the centrifuge at which the slope destroyed occurred, the scaling factor, the actual distance between the elements of the retaining structure, the actual thickness of the sliding soil layer, the shear pressure, and other necessary parameters to check the theoretical results of research. In particular, it follows from the table that there is a clear tendency to decrease the number of revolutions of the centrifugal machine and the scale factor, corresponding to the destruction of the slope, with an increase in the distance between the elements of the discrete retaining structures. This fact should be taken into account when conducting theoretical studies and developing a methodology for calculating and designing discrete retaining structures.
Table 2.
Results of tests of retaining structures
|
The name of the characteristic |
Unit of measure ment |
Experiment number |
|||||||||
|
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
|||
|
Experimental characteristics |
|||||||||||
|
The diameter of the element of the retaining structure of the model |
mm |
-- |
-- |
-- |
10 |
10 |
10 |
10 |
10 |
10 |
|
|
The distance between the elements of the retaining structure of the model |
mm |
50 |
20 |
20 |
30 |
30 |
40 |
40 |
|||
|
The thickness of the soil layer at the location of the retaining structure of the model |
mm |
-- |
19.5 |
20 |
18 |
20 |
19 |
21 |
21 |
20 |
|
|
The number of revolutions of the centrifugal machine at the time of model destruction |
rev/min |
220 |
240 |
230 |
230 |
232 |
230 |
234 |
228 |
230 |
|
|
Scale factor |
units |
123.4 |
150.0 |
135.0 |
135.0 |
137.0 |
135.0 |
140.0 |
132.0 |
135.0 |
|
|
Actual diameter of the retaining structure element |
m |
-- |
-- |
-- |
1.25 |
1.20 |
1.20 |
1.27 |
1.17 |
1.22 |
|
|
Natural distance between the elements of the retaining structure |
m |
-- |
7.50 |
-- |
2.37 |
2.74 |
4.05 |
4.20 |
5.28 |
5.40 |
|
|
Natural thickness of the soil layer at the location of the retaining structure |
m |
-- |
2.93 |
2.70 |
2.37 |
2.72 |
2.68 |
2.89 |
2.81 |
2.67 |
|
|
Soil specific gravity |
kN/m3, |
16.1 |
16.2 |
16.5 |
16.5 |
16.3 |
16.6 |
16.5 |
16.7 |
16.5 |
|
|
Angle of internal friction |
degrees |
14.2 |
14.4 |
14.5 |
14.7 |
14.8 |
14.9 |
15.0 |
15.0 |
15.0 |
|
|
Specific adhesion |
kPa |
6.3 |
6.2 |
6.1 |
6.0 |
5.9 |
5.8 |
5.8 |
5.8 |
5.9 |
|
|
Shear pressure |
kN/m |
0.0 |
42.0 |
40.0 |
34.0 |
48.4 |
42.2 |
42.9 |
42.8 |
39.7 |
General conclusions
1. The peculiarities of the process of centrifugal modeling of the stability of slopes are considered.
2. On this basis, the equipment and methodology for determining the stability of slopes reinforced by discrete retaining structures were developed.
3. Curves sliding pressure slopes with retaining constructions and without them significantly are different between yourself: if retaining construction missing then in at the end of the shear, the curve has a value close to zero, and if a retaining structure is located at the end of the shear, then the shear pressure is significantly different from zero
4. The shear pressure curves of continuous and discrete retaining structures have the following common feature: at the location of the retaining structure, the shear pressure is
5. The destruction of slopes in the presence of continuous and discrete retaining structures has a significant difference in that in the second case it has the place of soil compression between retaining elements structures.
6. It was established that in the case of reinforcement of slopes with discrete retaining structures, the stability and strength of the soil should be ensured not only on the sliding surface, but also in the zone of influence of the discrete retaining structures.
7. It is shown that the problem of compression and stability of the soil in the spaces between the elements of discrete retaining structures has not been sufficiently studied. Therefore, it is necessary to carry out special theoretical research in this direction.
References:
1. Shapoval V. H., Zhylinska S. R., Amer Abdelrakhman Mokhamed, Mosycheva I. I., Andrieiev V. S. Sovremennie tendentsyi proiavlenyia opolznei v mire. [Modern trends in the manifestation of landslides in the world]. International scientific and practical conference "Perspectives for the development of construction technologies", p. 35-43 [in Russian].
2. Maslov N.N. Mekhanika hruntov v praktike stroitelstva (opolzni i borba s nimi). [Soil mechanics in construction practice (landslides and their control)] (1977) Moskva: Stroyizdat, 320 [in Russian].
3. Iekkel Ye.B. Borba s opolzniami na avtomobylnikh dorohakh. [Landslide control on highways] (1960) Moskva: Izdatelstvo Avtotransporta i shosseinikh doroh, 183 [in Russian].
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5. Hinzburh L.N. Protivoopolznevie uderzhivaiushchie konstruktsii. [Landslide retaining structures] (1979) Moskva: Stroyizdat, 80 [in Russian].
6. Winter, H. Stabilization of clay slopes by piles/ H. Winter, W. Schwarz, G. Gudehus // Impruv. Ground. Proc. 8 Eur.:Conf. Soil Mech. and Found. Eng., Helsinki, 23-26 May, 1983.- Rotterdam, 1983. - V. 2. - pp. 545-550.
7. Ponomarenko I. O. Obgruntuvannia parametriv zakhysnoi systemy z dyskretnykh utrymuiuchykh konstruktsii pry vzaiemodii iz spovzaiuchym gruntovym masyvom dlia stabili- zatsii zsuviv. Dysertatsiia na zdobuttia vchenoho stupenia kandydata tekhnichnykh nauk. [Justification of the parameters of the protective system from discrete retaining structures in interaction with the sliding soil massif for the stabilization of landslides. Dissertation for the degree of Candidate of Technical Sciences] (2021) Cherkasy, 175 [in Ukrainian].
8. Ponomarenko I. O. Obgruntuvannia parametriv zakhysnoi systemy z dyskretnykh utrymuiuchykh konstruktsii pry vzaiemodii iz spovzaiuchym gruntovym masyvom dlia stabilizatsii zsuviv. Avtoreferat dysertatsii na zdobuttia vchenoho stupenia kandydata tekhnichnykh nauk. [Justification of the parameters of the protective system from discrete retaining structures in interaction with the sliding soil massif for the stabilization of landslides. Dissertation abstract for the degree of Candidate of Technical Sciences] (2021) Dnipro, 20 [in Ukrainian].
9. Recommendations on the choice of methods for calculating the slope stability coefficient and landslide pressure. Retrieved from https://gosthelp.ru/text/Rekomendacii Rekomendaciip 154.html
10. Recommendations for selection methods calculation coefficient stability slope and landslide pressure. Retrieved from https://files.stroyinf.ru/Data2/1/4294814/4294814196.pdf
11. R.V. Vysku, A.G. Solakian, L.S. Baldin. Tsentrobezhnyi metod ispytaniya modeley [Centrifugal method of testing models] (1935) Civil Engineering, 287 - 290 [in Russian].
12. Zaitsev A. A. Tekhnolohiya primenenyia ustanovok tsentrobezhnoho modelirovaniya dlia resheniya heotekhnicheskikh zadach (chast 1 istoricheskie svedeniya i rezultati issledovaniy). [Technology of using centrifugal modeling installations for solving geotechnical problems (part 1 historical information and research results)] (2020) https://doi.org/10.24108/preprints- 3111959 [in Russian].
13. Shahunyants G.M. Opredelenie raschetnyih parametrov mashinyi dlya tsentrobezhnogo modelirovaniya sooruzheniy iz grunta: Otchet o NIR «Kompleks-noe issledovanie rabotyi puti pod nagruzkoy». [Determination of design parameters of the machine for centrifugal modelling of structures made of soil: Report on Research and Development «Complex research of track operation under load»] (1962) Moskva:MIIT, 99 [in Russian].
14. Zaytsev A. A. Tehnologiya primeneniya ustanovok tsentrobezhnogo modelirovaniya dlya resheniya geotehnicheskih zadach (chast 3 metodika mode-lirovaniya na osnove opyita na tsentrobezhnoy ustanovke RUT). [Technology of application of centrifugal modelling units for solving geotechnical problems (part 03 modelling methodology based on the experience on the RUT centrifugal unit)] (2019) https://www.researchgate.net/ publication/338837979 [in Russian].
15. Yakovleva T.G. Opredelyayuschie protsessyi i opredelyayuschie parametryi pri tsentrobezhnom modelirovanii [Defining processes and defining parameters in centrifugal modelling] (1983) Moskva: Mezhvuzovskiy sbornik nauchnyih trudov «Trudi MIITa», 3 - 9 [in Russian].
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