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Published: 10 December 2022
Last updated: 28 January 2023

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1

Poon, C. Tensile fracture of notched composite laminates. Ottawa, Ont: National Research Council Canada, 1991.

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2

Carli, Charles G. Tensile and compressive MOE of flakeboards. [Madison, Wis.?: U.S. Forest Service, 1988.

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3

Kruenate, Jittiporn. Investigation of the tensile strength of crosslinked thermoplastic materials. Manchester: UMIST, 1996.

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4

Showalter, K. L. Effect of length on tensile strength in structural lumber. [Madison, WI]: U.S. Dept. of Agriculture, Forest Service, Forest Products Laboratory, 1987.

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5

Bansal, Narottam P. Effects of HF treatments on tensile strength of hi-nicalon fibers. [Cleveland, Ohio]: National Aeronautics and Space Administration, Lewis Research Center, 1998.

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6

Bansal, Narottam P. Effects of HF treatments on tensile strength of hi-nicalon fibers. [Cleveland, Ohio]: National Aeronautics and Space Administration, Lewis Research Center, 1998.

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7

Misir, Hemlata. Tensile strength of Otoform K2 silicon impression material: A comparative study. Northampton: University College Northampton, 1999.

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8

Moore, Thomas J. Tensile strength of simulated and welded butt joints in W-Cu-composite sheet. Cleveland, Ohio: Lewis Research Center, 1994.

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9

Lee, J. A. High-strength aluminum casting alloy for high-temperature applications: (MSFC Center director's discretionary fund final project no. 97-10). [Marshall Space Flight Center, Ala.]: National Aeronautics and Space Administration, Marshall Space Flight Center, 1998.

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10

Harrington, M. The torque test: A proposed new test to establish the tensile strength of concrete. [London]: Queen Mary and Westfield College, 1998.

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11

Donaghe, Robert T. Strength and deformation properties of earth-rock mixtures. Vicksburg, Miss: Dept. of the Army, Waterways Experiment Station, Corps of Engineers, 1985.

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12

Strength and weathering of rock as boundary layer problems. London: Imperial College Press, 2001.

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13

Geier, J. E. Water-jet-assisted drag bit cutting in medium-strength rock. Pgh. [i.e. Pittsburgh] Pa: U.S. Dept. of Interior, Bureau of Mines, 1987.

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14

Tandanand, Sathit. Time-dependent behavior of coal measure rocks: Adsorption rate and strength degradation. Avondale, Md: U.S. Dept. of the Interior, Bureau of Mines, 1987.

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15

Wang, Qi, Bei Jiang, and Shucai Li. High Strength Support for Soft Surrounding Rock in Deep Underground Engineering. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-3844-5.

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16

Nefedov, V. I. O geometricheskoĭ nekorrektnosti fizicheskikh zakonov i adekvatnykh aksiomakh estestvoznanii︠a︡. Kazanʹ: "Novoe znanie", 2000.

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17

Grima, Mario Alvarez. Neuro-fuzzy modeling in engineering geology: Applications to mechanical rock excavation, rock strength estimation, and geological mapping. Rotterdam: A.A. Balkema, 2000.

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18

McWilliams, P. C. Estimation of shear strength using fractals as a measure of rock fracture roughness. Washington, D.C: U.S. Dept. of the Interior, Bureau of Mines, 1993.

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19

McWilliams, P. C. Estimation of shear strength using fractals as a measure of rock fracture roughness. Washington, D.C: U.S. Dept. of the Interior, Bureau of Mines, 1993.

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20

Zydroń, Tymoteusz. Wpływ systemów korzeniowych wybranych gatunków drzew na przyrost wytrzymałości gruntu na ścinanie. Publishing House of the University of Agriculture in Krakow, 2019. http://dx.doi.org/10.15576/978-83-66602-46-5.

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The aim of the paper was to determine the influence of root systems of chosen tree species found in the Polish Flysch Carpathians on the increase of soil shear strength (root cohesion) in terms of slope stability. The paper's goal was achieved through comprehensive tests on root systems of eight relatively common in the Polish Flysch Carpathians tree species. The tests that were carried out included field work, laboratory work and analytical calculations. As part of the field work, the root area ratio (A IA) of the roots was determined using the method of profiling the walls of the trench at a distance of about 1.0 m from the tree trunk. The width of the. trenches was about 1.0 m, and their depth depended on the ground conditions and ranged from 0.6 to 1.0 m below the ground level. After preparing the walls of the trench, the profile was divided into vertical layers with a height of 0.1 m, within which root diameters were measured. Roots with diameters from 1 to 10 mm were taken into consideration in root area ratio calculations in accordance with the generally accepted methodology for this type of tests. These measurements were made in Biegnik (silver fir), Ropica Polska (silver birch, black locust) and Szymbark (silver birch, European beech, European hornbeam, silver fir, sycamore maple, Scots pine, European spruce) located near Gorlice (The Low Beskids) in areas with unplanned forest management. In case of each tested tree species the samples of roots were taken, transported to the laboratory and then saturated with water for at least one day. Before testing the samples were obtained from the water and stretched in a. tensile testing machine in order to determine their tensile strength and flexibility. In general, over 2200 root samples were tested. The results of tests on root area ratio of root systems and their tensile strength were used to determine the value of increase in shear strength of the soils, called root cohesion. To this purpose a classic Wu-Waldron calculation model was used as well as two types of bundle models, the so called static model (Fiber Bundle Model — FIRM, FBM2, FBM3) and the deformation model (Root Bundle Model— RBM1, RBM2, mRBM1) that differ in terms of the assumptions concerning the way the tensile force is distributed to the roots as well as the range of parameters taken into account during calculations. The stability analysis of 8 landslides in forest areas of Cicikowicleie and Wignickie Foothills was a form of verification of relevance of the obtained calculation results. The results of tests on root area ratio in the profile showed that, as expected, the number of roots in the soil profile and their ApIA values are very variable. It was shown that the values of the root area ratio of the tested tree species with a diameter 1-10 ram are a maximum of 0.8% close to the surface of the ground and they decrease along with the depth reaching the values at least one order of magnitude lower than close to the surface at the depth 0.5-1.0 m below the ground level. Average values of the root area ratio within the soil profile were from 0.05 to 0.13% adequately for Scots pine and European beech. The measured values of the root area ratio are relatively low in relation to the values of this parameter given in literature, which is probably connected with great cohesiveness of the soils and the fact that there were a lot of rock fragments in the soil, where the tests were carried out. Calculation results of the Gale-Grigal function indicate that a distribution of roots in the soil profile is similar for the tested species, apart from the silver fir from Bie§nik and European hornbeam. Considering the number of roots, their distribution in the soil profile and the root area ratio it appears that — considering slope stability — the root systems of European beech and black locust are the most optimal, which coincides with tests results given in literature. The results of tensile strength tests showed that the roots of the tested tree species have different tensile strength. The roots of European beech and European hornbeam had high tensile strength, whereas the roots of conifers and silver birch in deciduous trees — low. The analysis of test results also showed that the roots of the studied tree species are characterized by high variability of mechanical properties. The values Of shear strength increase are mainly related to the number and size (diameter) of the roots in the soil profile as well as their tensile strength and pullout resistance, although they can also result from the used calculation method (calculation model). The tests showed that the distribution of roots in the soil and their tensile strength are characterized by large variability, which allows the conclusion that using typical geotechnical calculations, which take into consideration the role of root systems is exposed to a high risk of overestimating their influence on the soil reinforcement. hence, while determining or assuming the increase in shear strength of soil reinforced with roots (root cohesion) for design calculations, a conservative (careful) approach that includes the most unfavourable values of this parameter should be used. Tests showed that the values of shear strength increase of the soil reinforced with roots calculated using Wu-Waldron model in extreme cases are three times higher than the values calculated using bundle models. In general, the most conservative calculation results of the shear strength increase were obtained using deformation bundle models: RBM2 (RBMw) or mRBM1. RBM2 model considers the variability of strength characteristics of soils described by Weibull survival function and in most cases gives the lowest values of the shear strength increase, which usually constitute 50% of the values of shear strength increase determined using classic Wu-Waldron model. Whereas the second model (mRBM1.) considers averaged values of roots strength parameters as well as the possibility that two main mechanism of destruction of a root bundle - rupture and pulling out - can occur at the same. time. The values of shear strength increase calculated using this model were the lowest in case of beech and hornbeam roots, which had high tensile strength. It indicates that in the surface part of the profile (down to 0.2 m below the ground level), primarily in case of deciduous trees, the main mechanism of failure of the root bundle will be pulling out. However, this model requires the knowledge of a much greater number of geometrical parameters of roots and geotechnical parameters of soil, and additionally it is very sensitive to input data. Therefore, it seems practical to use the RBM2 model to assess the influence of roots on the soil shear strength increase, and in order to obtain safe results of calculations in the surface part of the profile, the Weibull shape coefficient equal to 1.0 can be assumed. On the other hand, the Wu-Waldron model can be used for the initial assessment of the shear strength increase of soil reinforced with roots in the situation, where the deformation properties of the root system and its interaction with the soil are not considered, although the values of the shear strength increase calculated using this model should be corrected and reduced by half. Test results indicate that in terms of slope stability the root systems of beech and hornbeam have the most favourable properties - their maximum effect of soil reinforcement in the profile to the depth of 0.5 m does not usually exceed 30 kPa, and to the depth of 1 m - 20 kPa. The root systems of conifers have the least impact on the slope reinforcement, usually increasing the soil shear strength by less than 5 kPa. These values coincide to a large extent with the range of shear strength increase obtained from the direct shear test as well as results of stability analysis given in literature and carried out as part of this work. The analysis of the literature indicates that the methods of measuring tree's root systems as well as their interpretation are very different, which often limits the possibilities of comparing test results. This indicates the need to systematize this type of tests and for this purpose a root distribution model (RDM) can be used, which can be integrated with any deformation bundle model (RBM). A combination of these two calculation models allows the range of soil reinforcement around trees to be determined and this information might be used in practice, while planning bioengineering procedures in areas exposed to surface mass movements. The functionality of this solution can be increased by considering the dynamics of plant develop¬ment in the calculations. This, however, requires conducting this type of research in order to obtain more data.
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21

Tensile strength of an interlocking composite connection. Gaithersburg, MD: U.S. Dept. of Commerce, Technology Administration, National Institute of Standards and Technology, 2000.

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22

National Institute of Standards and Technology (U.S.), ed. Tensile strength of an interlocking composite connection. Gaithersburg, MD: U.S. Dept. of Commerce, Technology Administration, National Institute of Standards and Technology, 2000.

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23

Through-the-thickness tensile strength of textile composites. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1994.

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24

Through-the-thickness tensile strength of textile composites. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1994.

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25

G, Ifju Peter, and Langley Research Center, eds. Through-the-thickness tensile strength of textile composites. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1994.

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26

G, Ifju Peter, and Langley Research Center, eds. Through-the-thickness tensile strength of textile composites. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1994.

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27

Method for Measuring Dynamic Tensile Strength of Optical Fiber. Global Engineering Documentation, 1991.

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28

Vliet, M. R. A. Van. Size Effect in Tensile Fracture of Concrete & Rock. Delft Univ Pr, 2000.

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29

W, Green David, and Forest Products Laboratory (U.S.), eds. Moisture content and tensile strength of Douglas fir dimension lumber. Madison, WI: U.S. Dept. of Agriculture, Forest Service, Forest Products Laboratory, 1990.

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30

The Elasticity, Extensibility, and Tensile Strength of Iron and Steel. Adamant Media Corporation, 2001.

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31

Moisture content and tensile strength of Douglas fir dimension lumber. Madison, WI: U.S. Dept. of Agriculture, Forest Service, Forest Products Laboratory, 1990.

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32

W, Green David, and Forest Products Laboratory (U.S.), eds. Moisture content and tensile strength of Douglas fir dimension lumber. Madison, WI: U.S. Dept. of Agriculture, Forest Service, Forest Products Laboratory, 1990.

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33

Karl-Heinz, Pfeffer, ed. Rock strength - weathering - slope evolution. Berlin: Gebrüder Borntraeger, 2007.

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34

Center, Langley Research, and United States. National Aeronautics and Space Administration., eds. Synthesis and characterization of modified phenylethynyl terminated polyimides. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1998.

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35

1954-, Salpekar Satish A., United States. Army Aviation Research and Technology Activity., and Langley Research Center, eds. Scale effects on the transverse tensile strength of graphite epoxy composites. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1992.

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36

R, Wheeler Donald, Dickerson Robert M, and United States. National Aeronautics and Space Administration., eds. Tensile strength and microstructural characterization of uncoated and coated HPZ ceramic fibers. [Washington, DC]: National Aeronautics and Space Administration, 1996.

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37

Strength scaling in fiber composites. [Washington, DC]: National Aeronautics and Space Administration, Scientific and Technical Information Division, 1990.

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38

A, DiCarlo James, and NASA Glenn Research Center, eds. Comparison of the tensile, creep, and rupture strength properties of stoichiometric SiC fibers. [Cleveland, Ohio]: National Aeronautics and Space Administration, Glenn Research Center, 1999.

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39

A, DiCarlo James, and United States. National Aeronautics and Space Administration., eds. Thermomechanical behavior of advanced SiC fiber multifilament tows. [Washington, DC]: National Aeronautics and Space Administration, 1997.

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40

C, Goldsby Jon, DiCarlo James A, and United States. National Aeronautics and Space Administration., eds. Tensile creep and stress-rupture behavior of polymer derived SiC fibers. [Washington, DC]: National Aeronautics and Space Administration, 1994.

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41

C, Goldsby Jon, DiCarlo James A, and United States. National Aeronautics and Space Administration., eds. Tensile creep and stress-rupture behavior of polymer derived SiC fibers. [Washington, DC]: National Aeronautics and Space Administration, 1994.

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42

A, DiCarlo James, and United States. National Aeronautics and Space Administration., eds. Time/temperature dependent tensile strength of SiC and Al₂O₃-based fibers. [Washington, D.C: National Aeronautics and Space Administration, 1997.

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43

A, DiCarlo James, and United States. National Aeronautics and Space Administration., eds. Time/temperature dependent tensile strength of SiC and Al₂O₃-based fibers. [Washington, D.C: National Aeronautics and Space Administration, 1997.

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44

A, DiCarlo James, and United States. National Aeronautics and Space Administration., eds. Time/temperature dependent tensile strength of SiC and Al₂O₃-based fibers. [Washington, D.C: National Aeronautics and Space Administration, 1997.

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45

George C. Marshall Space Flight Center., ed. High-strength aluminum casting alloy for high-temperature applications: (MSFC Center director's discretionary fund final project no. 97-10). [Marshall Space Flight Center, Ala.]: National Aeronautics and Space Administration, Marshall Space Flight Center, 1998.

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46

George C. Marshall Space Flight Center., ed. High-strength aluminum casting alloy for high-temperature applications: (MSFC Center director's discretionary fund final project no. 97-10). [Marshall Space Flight Center, Ala.]: National Aeronautics and Space Administration, Marshall Space Flight Center, 1998.

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47

George C. Marshall Space Flight Center., ed. High-strength aluminum casting alloy for high-temperature applications: (MSFC Center director's discretionary fund final project no. 97-10). [Marshall Space Flight Center, Ala.]: National Aeronautics and Space Administration, Marshall Space Flight Center, 1998.

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48

Justa, Steve. Rock, Iron, Steel: The Book of Strength. Ironmind Enterprises, 1998.

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49

Tensile properties of weldments in alloy GTD 222. [Washington, DC]: National Aeronautics and Space Administration, 1996.

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50

Tensile properties of weldments in alloy GTD 222. [Washington, DC]: National Aeronautics and Space Administration, 1996.

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