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Method for predicting dynamic shear strength in soils – Part I: Proposal for a new criterion
Journal of Terramechanics xxx (xxxx) xxx
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Method for predicting dynamic shear strength in soils – Part I: Proposal for a new criterion Piotr Antoni Dudzin´ski Wrocław University of Science and Technology, Department of Off-Road Machine and Vehicle Engineering, Poland
a r t i c l e
i n f o
Article history: Received 30 July 2018 Revised 7 August 2019 Accepted 11 August 2019 Available online xxxx Keywords: Terramechanics Dynamic shear strength New criterion
a b s t r a c t The interaction between off-road machines and soil is usually a dynamic process of soil shearing. However, in practice, in order to interpret these processes, the empirical modified static Coulomb criterion, which does not take into account the soil strengthening, is commonly used. At Wrocław University of Technology a proposal for a method for predicting dynamic shear strength in soils was developed. This method takes into account primarily the soil shear velocity, the scale effect of the test device and its kinematics, which include the parameters of the process under investigation in terramechanics. The method will be presented in two parts of the following publication. The first part presents the results of the tests on soil shear strength carried out by the author of the article by means of soil ring shear test device. These results are discussed against the background of the results of soil research performed all around the world. On the basis of the tests conducted by the author, a new dynamic criterion of soil shear strength was formulated and the requirements for the innovative method for predicting dynamic shear strength in soils were established. This experimental method will be presented in the second part of the article. Ó 2019 ISTVS. Published by Elsevier Ltd. All rights reserved.
1. Introduction Producers of off-road machines and vehicles are continually searching for better solutions to meet the growing requirements for mobility. Design and optimization of that class of objects requires knowledge about the processes of interaction of the working tools and traction components with the soil. Interaction of working tools and traction components with soils in off-road machines and vehicles is connected with the deformation and shear strength of soils sf (see Fig. 1). In order to solve this complex problem, theoretical and experimental research is necessary. For theoretical research and problem solving, knowledge of the link between the state of stress and the state of strain in the considered body is essential. The mathematical models of these physical relations are constitutive performance of soil in terms of stress-strain relationships such as, for example, the Hooke’s law for metals. So far, there is lack of such universal constitutive law in soil mechanics. This lack results mainly from the random nature of the structure and physical characteristics of the soil. In addition, soil properties depend on temporary weather conditions, which is perhaps the biggest obstacle in ground theory development. Attempts at adapting various equations for other solids in soil
mechanics have not been satisfactory. Therefore, in practice, the so-called process analogues are used to identify soil strength. Such an analogue can be any device, for example a shear box, a soil ring shear test device, a plate shear test device, etc., which reacts to generated external loads, within the assumed tolerance limits, with the value of soil shear strength corresponding to the tested process in terramechanics. A systematic extensive research on the methods and devices for soil shear strength determination known world-wide, along with a comparative analysis of the results achieved with the particular ones, was conducted at Wrocław University of Science and Technology (Stefanow and Dudzin´ski, 2019). In classical soil mechanics, the Coulomb criterion given by Eq. (1) is usually used to describe the soil strength
sf ;C ¼ r tan u þ c
ð1Þ
where
sf ;C absolute value of shear strength on the failure r u c
surface total normal pressure on the failure surface (apparent) internal friction angle of the soil (apparent) soil cohesion
[kPa] [kPa] [°] [kPa]
E-mail address: [email protected] https://doi.org/10.1016/j.jterra.2019.08.005 0022-4898/Ó 2019 ISTVS. Published by Elsevier Ltd. All rights reserved.
Please cite this article as: P. A. Dudzin´ski, Method for predicting dynamic shear strength in soils – Part I: Proposal for a new criterion, Journal of Terramechanics, https://doi.org/10.1016/j.jterra.2019.08.005
´ ski / Journal of Terramechanics xxx (xxxx) xxx P.A. Dudzin
2
Fig. 1. Examples of interaction of traction components and working tools with soil: sf – soil shear strength, xt – turning velocity of wheel/track, xr – rotation speed of bucket in a bucket-wheel excavator.
It should be added that cohesion c is a measure of shear strength of the soil, independent of inter-particle friction u. Cohesive soil strength c can be attributed to inter-particle forces (i.e. the forces developed between the soil particles) which interact in resisting shear deformation and lead to specific arrangements of soil particles and stability. Disruption of soil particles occurs as the soil develops resistance to shear. According to (Dmitruk, 1971; Karafiath and Nowatzki, 1978; Koolen and Kuipers, 1983; Aysen, 2005), the later research in the scope of soils consolidation led to assuming the following formula of Coulomb – Hvorslev for saturated soils:
sf ;C ¼ ½r uðtÞ tan u0 þ c0
ð2Þ
where
sf ;C r uðtÞ
r0 ¼ r uðtÞ u0 c0 t
absolute value of shear strength total normal stress at a point in the skeleton pressure in the pore fluid (decreases with time t) effective normal stress at the point in the soil skeleton effective (true) internal friction angle of the soil effective (true) soil cohesion time
[kPa] [kPa] [kPa] [kPa] [°] [kPa] [sec]
For saturated soils it is common practice to use c0 and u0 instead of c and u, because drainage conditions in failure tests on saturated soil
have a great influence on soil water pressure u. It should be added that in unsaturated soil the apparent cohesion is greater than the true cohesion. This difference is caused by the clenching action of the suction in the soil water (Aysen, 2005). In a fully saturated soil, an externally applied load results in a stress increment at any point in soil mass. The stress inducted in the soil skeleton during the consolidation process is called the effective stress r0 = r – u(t). In this case, the stress is taken over jointly by the skeleton and the pore fluid (i.e. r – 0 and u(t) – 0). However, for the load duration t = 0+, the pore fluid carries the entire stress (u(t) – 0 and r = 0). At the completion of drainage, the entire load increment is carried by the soil skeleton (i.e. r – 0 and u(t) = 0). This case is the criterion for the final consolidation of soil. It should be mentioned that in addition to the empirical criterion of Coulomb in soil mechanics there is also a critical-state theory of soils formulated in the 1950s by Kenneth Roscoe from the Cambridge University. According to this theory in shear process of soil, a failure surface may develop before or after the critical state leading to a constant shear strength called the residual. However, this state is achievable only with very large strains. In overconsolidated soils, failure surface may develop immediately after the peak point and the critical state may not be obtained and the state of the fragment of soil moves towards the residual. Normally consolidated soil may not have a peak strength and the critical state may be obtained at relatively low strains (Aysen, 2005). In practice the two parameters c and u are called shear strength parameters of soil. These parameters are not constant for a given soil. Values of cohesion c and angle of internal friction u correspond only to the conditions in which they were determined experimentally. The values of cohesion and angle of internal friction depend very essentially on: the type of the device involved in the tests, especially its geometry, kinematics and shearing speed, the properties of a given soil in the course of determining its strength, such as density, moisture, consistency state, etc., the location of the test, i.e. in the laboratory or in situ, with disturbed or intact soil, etc., and on the history of stress state. The wide spectrum of known and applied equipment for testing the soil shear strength in the laboratory and in situ may be divided into the indirect (for example triaxial) and direct ones (for example a shear box, a ring shear test device, etc). The devices differ significantly in their structure, geometrical dimensions, kinematics of the shear process (the translational, rotational) and soil shear velocity. The results obtained for the same ground by different test devices may differ as much as several hundred percent (Bailey and Weber, 1965; Dunlap et al., 1966; Krick, 1971; Borst, 1973; Stafford and Tanner, 1982; Kogure et al., 1988; Shoop, 1992, 1993; Karmakar et al., 2007; Sutoh et al., 2017). Examples of comparative results are shown in Fig. 2 (Beretitsch, 1992). Geometrical dimensions of the test device have a significant influence on shear strength in soils. For example, (Cerato and Lutenegger, 2004) conducted shear tests on sand involving shear boxes with dimensions of 6 6 cm to 30 30 cm. The results showed that the angle of internal friction in sand, regardless of the sand compaction, decreased with the increase in shear box dimensions. In addition, the shear strength of sand increases with the height of the shear box. On the other hand, Dadakh in (Dadakh et al., 2010) studied cohesive clayed sand by means of shear boxes with dimensions of 6 6 cm, 10 10 cm and 30 30 cm. These studies have shown that with the increase in the size of the shear box the cohesion increases and the angle of internal friction
Please cite this article as: P. A. Dudzin´ski, Method for predicting dynamic shear strength in soils – Part I: Proposal for a new criterion, Journal of Terramechanics, https://doi.org/10.1016/j.jterra.2019.08.005
´ ski / Journal of Terramechanics xxx (xxxx) xxx P.A. Dudzin
Fig. 2. Results of a testing device type impact on the value of soil cohesion c:
3
so far. The above works mainly focused on determining the impact of shearing velocity on increase in strength of different soil types. The tests have shown that increase in shear velocity leads to significant increase in shearing strength of cohesive soils, whereas for sands the influence of shear velocity on shearing strength is rather small. Thus, the phenomenon described above is usually called the strengthening of cohesive soils. Exemplary ranges of soil shearing velocity in off-road machines are shown in Fig. 4 (Dudzin´ski, 1991; Beretitsch, 1992). Summing up, the review of the state-of-the-art presented in the introduction above indicates that no method for predicting dynamic shear strength in soils can be found in the world-wide literature. In this article (Part1) the author presents a concept of a new criterion of dynamic shearing strength of soils.
2. Tests of dynamic shear strength in soils decreases. Moreover, it was found that the highlighted scale effect decreases with increase in the size of the shear test device. In the research discussed in (Hanson et al., 1967; Ohu et al., 1986; Lucius, 1971; Panwar, 1968; Beretitsch, 1992) it was found that increase in soil density results in approximately linear increase in soil strength. The research carried out by (Wells and Treesuwan, 1978; Panwar, 1968; Ayers, 1987) also showed an approximate linear increase in cohesion and in the angle of internal friction of the soil with increasing soil density. However, in highly cohesive soils, the gradient of this growth decreases significantly with the increase in soil moisture. Numerous researchers, including: (Kuipers and Kroesbergern, 1966; Komandi, 1992; Beretitsch, 1992; Rajarama and Erbach, 1999; Manuwa, 2012; Matsushi and Matsukura, 2006; Mouazen et al., 2002; Shoop, 1992, 1993; Keen et al., 2013; Wieder and Shoop, 2018; Tong et al., 1994) showed that the main factor influencing the strength properties of the soil is the water content. The relationship between cohesion and humidity manifests its absolute maximum at the intermediate water content. This maximum depends on the type and condition of the soil. On the other hand, the angle of internal friction decreases continuously with increasing humidity. The results obtained by (Beretitsch, 1992) illustrating those phenomena are given in Fig. 3. The essential impact of the shear velocity on the soil strengthening has been found in many tests world-wide (Schimming et al., 1965; Hanson et al., 1967; Dmitruk, 1971; Lucius, 1971; Flenniken et al., 1977; Baladi and Rohani, 1979; Baladi, 1987; Dudzin´ski, 1987, 1991). A similar phenomenon was also observed in metals and rocks, but no sufficient explanation has been found
The tests of rapid static and dynamic shear strength on soil were performed on ring shear test device at Universität Fridericana in Karslruhe, Germany, Figs. 5 and 6. The electrohydraulic drive of the soil ring shear tester enabled a step-less rotation control within the range of angular velocity of 0.04–7.2 rad/s, as well as a step-less control of the normal stresses on the surface of the tested soil sample within the range from 0 to 300 kPa. During the tests the following quantities were measured: the reaction torque M(h), angular position of shear ring h, normal pressure exerted on soils r, the change in soil sample volume and duration time of the process. The reaction torque M(h) is related to the shear stress s in the shear surface and the geometry of the shear ring:
MðhÞ ¼ 2p
Z
ro
sðr; hÞr2 dr ½Nm
ð3Þ
ri
Assuming the linear distribution of shear stress on shear surface, the mean shear stress s was calculated from the equation:
sðhÞ ¼
3MðhÞ 2pðr 3o r 3i Þ
½kPa
ð4Þ
Moreover, comparative tests (only static ones) of shear strength of soils were also carried out on standard apparatus for direct shearing (shear box). The shear box was the WF 2500 type from Wykeham Farance Engineering Limited, in which the dimensions of the sheared surface amounted to 10 cm 10 cm, and the translation velocity was within the range of 0.813 108 [m/s] to 0.2032 104 [m/s]. The test was performed on cohesion soil typical of southwestern Germany, Fig. 7, and on sand. The sandy loam selected was of natural density qn = 1.82 t/m3, natural moisture Wn = 14.3%, and the dry sand was of natural density qn = 1,6 t/m3. Fig. 8 shows the results of grain-size distribution analysis for sandy loam highlighted in Fig. 7.
3. Results
Fig. 3. Dependence of cohesion c, cd and internal friction angle u, ud of soil on moisture for rapid static and dynamic tests.
The experimental studies have clearly confirmed that increase in shearing velocity causes an increase in the soil shear strength, i.e., its strengthening, (see Fig. 9). The characteristic feature for this phenomenon is the fact that the component of the ground shear strength assigned to cohesion s(c) shows essentially higher increases in strength than that assigned to the internal friction s (u). This explains the clear strengthening phenomenon in cohesive soils.
Please cite this article as: P. A. Dudzin´ski, Method for predicting dynamic shear strength in soils – Part I: Proposal for a new criterion, Journal of Terramechanics, https://doi.org/10.1016/j.jterra.2019.08.005
´ ski / Journal of Terramechanics xxx (xxxx) xxx P.A. Dudzin
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Fig. 4. Ranges of soil shearing velocity in classical mechanics and terramechanics.
Fig. 7. Experimental data of natural moisture Wn and natural density qn for typical soils of southwestern Germany.
Fig. 5. Soil ring shear test device.
Moreover, it follows explicitly from the performed tests that soil shear strength depends not only on the stress state but it is also significantly affected by the time elapsed from the moment of imposing an outside load until the moment of appearance of the soil failure (damage). The shorter the time the external load acts, the higher the strength resulting from soil strengthening.
New concepts are recommended to develop a new criterion for dynamic shearing strength of soils (see Fig. 10). Considering the above analyses of the experimental study, the results for the selected (sandy loam) soil have been presented synthetically in the graph in Fig. 11. From the study results presented in Fig. 11, it is clear that the soil shearing velocity appearing with the operation of off-road machines and vehicles causes very significant soil strengthening. It should be added that soils like the sandy loam do not crumble but plasticizes when wet, which may lead to shear strength weak-
Fig. 6. Functional diagram and basic data of soil ring shear tester: M(h) – measured soil shear reaction torque [Nm], N – normal force [N], A – shearing area [m2], r – mean normal pressure on the failure surface [kPa], s – shear stress, ro, ri – outer and inner radius of the shear ring [m], h – rotated angle of shear ring [rad].
Please cite this article as: P. A. Dudzin´ski, Method for predicting dynamic shear strength in soils – Part I: Proposal for a new criterion, Journal of Terramechanics, https://doi.org/10.1016/j.jterra.2019.08.005
´ ski / Journal of Terramechanics xxx (xxxx) xxx P.A. Dudzin
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Fig. 8. Grain-size distribution for the selected soil (sandy loam).
Fig. 9. Coulomb failure envelopes for rapid static and dynamic shear speed: c – static cohesion, cd – added dynamic cohesion.
Fig. 10. The dependence of soil strength sf on the time of load applied: sf,m – shear strength, for which the loading time is close to zero (instantaneous shear strength), sf,s – standard shear strength, which is derived by means of standard shearing devices as for example the shear box, etc., sr – shear strength, for which the loading time is close to infinity (residual state).
ening and that other types of soils may not necessarily exhibit shear strengthening. Therefore, further research will be carried out in order to thoroughly explain the problem of dynamic soil shear.
Fig. 11. Experimental results in soil ring shear tester on the impact of shearing speed on soil shear strength.
It can be seen that working tools on off-road machines, as well as wheels and tracks of the off-road vehicles create the limiting state in soil in the time approaching zero. Thus, a reliable strength parameter could be the value of the instantaneous shear strength sf,m. This proves that determining the soil shear strength by means of standard devices of classic soil mechanics might result in the values representing soil strength that is several times smaller in relation to the actual values that should be used in considerations performed in the field of terramechanics. This mainly results from the fact that the shear strength defined by the Coulomb’s criterion does not take into account the rheological properties of the soil and therefore, the results so obtained are far from those found in practice. Rheological properties of soils are mainly related to its properties such as viscosity and viscoelasticity, which in turn depend on the time of exposure to loads or temperature. In the face of the above, there is an urgent need for developing a new dynamic criterion. In order to meet this demand, the author of the following article proposed a new criterion for dynamic shearing strength of soils given with the Eq. (5). The criterion was developed on the basis of the results of experimental and theoretical research performed by the author. Namely, the equation was derived on the basis of the
Please cite this article as: P. A. Dudzin´ski, Method for predicting dynamic shear strength in soils – Part I: Proposal for a new criterion, Journal of Terramechanics, https://doi.org/10.1016/j.jterra.2019.08.005
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test results obtained for sandy loam with moisture of 14.3% and density of 1.82 t/m3 presented, for example, in Fig. 11.
sf ;d ¼ sf ;s þ Dsf ;d ¼ sf ;s þ sf ;m sf ;s
(
1
Va Vs
k )
½kPa
ð5Þ
where
sf ;s Dsf ;d
sf ;m Va Vs k
rapid static shear strength (classic soil mechanics) dynamic soil shear strength (terramechanics) shear strength for which the loading time is close to zero actual dynamic shearing speed (terramechanics) rapid static shearing speed (classic soil mechanics) regression coefficient determined experimentally by means of the shearing tester, dependent on the type and state of ground
[kPa] [kPa] [kPa] [m/s] [m/s]
The criterion for applying Eq. (5) is current shear speed Va, existing in practice, which generates the strengthening of cohesive soils. The equation is universal. For example, for rapid static shearing speed Va equals Vs. In this context, component Dsf,d of dynamic soil strength equals zero. Shear strength is then calculated in line with Coulomb criterion. 4. Conclusions The systematic studies were performed on the impact of soil shearing velocity on its strength within the static/rapid static shearing velocity range of test devices applied in classic soil mechanics to dynamic shearing velocity appearing in terramechanics. The results of the experimental studies clearly confirmed that an increase in shearing velocity causes an increase in soil shearing strength, which is its strengthening. The component of soil shearing strength assigned to cohesion s (c) shows significantly greater growths in strength than the component assigned to internal friction s (u). A new criterion (Eq. (5)) for dynamical strength of soils was proposed. The criterion is easy for practical applications. The extensive validation of the new criterion for different types of soils, performed on the innovative shear tester, will be presented in the second part of the article. It follows from the author’s own research and literature studies that the shear test device as the analogue of the process should reproduce in the closest way the real interaction of working tools or tracks/tires with the ground. Because of this, such a shear test device should have the shearing kinematics and generate velocity corresponding to the real process and the geometry, thus eliminating the effect of scale and a bulldozing effect. Such an innovative, patented shear test device developed at Wrocław University of Science and Technology in Poland, will be presented in the second part of the article.
Acknowledgements This research was conducted at Fridericana University in Karlsruhe, Germany during Alexander von Humboldt fellowship.
This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. References Ayers, P.D., 1987. Moisture and density effects on soil shear strength parameters for coarse grained soils. Trans. ASAE 30, 1282–1287. Aysen, A., 2005. Soil Mechanics: Basic Concept and Engineering Applications. A.A. Balkema Publishers, a member of Taylor & Francis Group. Bailey, A.C., Weber, J.A., 1965. Comparison of methods of measuring soil shear strength using artificial soils. Trans. ASAE 8, 153–160. Baladi, G.Y., Rohani, B., 1979. A Terrain-Vehicle Interaction Model for Analysis of steering Performance of Track-Laying Vehicles. Technical Report GL-79-6, U.S. Army Engineer Waterways Experiment Sation, Ce, Vicksburg, MS. Baladi, G.Y., 1987. Terrain evaluation for off-road mobility. 9th International Conference of International Society for Terrain Vehicle Systems in Barcelona, Proceedings, vol. I, pp. 1–19. Beretitsch, S., 1992. Force distribution in system cutting tool – soil. Thesis, Institut für Maschinenwesen im Baubetrieb, Universität Fridericana in Karslruhe, Reihe F/Heft 41 (in German). Borst, J., 1973. Soil machine studies: the effects of shear ring and grouser size on soil shear measurements. Report SIT-DL-73-1677, U.S. Army Tank-Automotive Command. Cerato, A., Lutenegger, A., 2004. Disturbance effects of field vane tests in a varved clay. Proceedings of the 2th International Symposium on Geotechnical Site Characterization, Porto, Portugal, vol. 1, pp. 861–867. Dadakh, R., Ghafoori, M., Ajalloeian, R., Lashkaripour, G., 2010. Effect of scale direct shear test on the strength parameters of clayedy sand in Isfahan City, Iran. J. Appl. Sci. 10 (18), 2027–2033. Dmitruk, S., 1971. Evaluation of strength parameters when determining cutting resistances. Górnictwo Odkrywkowe, No. 1, pp. 49–52 (in Polish). Dudzin´ski, P.A., 1987. Contribution to the studies on the dynamic shearing strength of soils. 9th International Conference of International Society for Terrain Vehicle Systems in Barcelona, Proceedings, vol. I, pp. 53–62. Dudzin´ski, P.A., 1991. Comparison of Steering Systems in Wheeled Off-Road Machines. Thesis. Dresden University of Technology (in German). Dunlap, W.A., Vandenberg, G.E., Hendrick, J.G., 1966. Comparison of soil shear values obtained with devices of differential geometrical shapes. Trans. ASAE 9, 896–900. Flenniken, J.M., Hefner, R.E., Weber, J.A., 1977. Dynamic soil strength parameters from unconfined compression tests. Trans. ASAE 20. Hanson, T.L., Johnson, H.P., Young, D.F., 1967. Dynamic shearing resistance of soils. Trans. ASAE, 439–447. Karafiath, L.L., Nowatzki, E.A., 1978. Soil Mechanics for Off-Road Vehicle Engineering. Trans Tech Publications, Claustthal, Germany. Karmakar, S., Kushwaha, R.L., 2007. Development and laboratory evaluation of a rheometer for soil visco-plastic parameter. J. Terramech. 44, 197–204. Keen, A., Hall, N., Soni, P., Gholkar, M.D., Cooper, S., Ferdous, J., 2013. A review of the tractive performance of wheeled tractors and soil management in lowland intensive rice production. J. Terramech. 50/1, 45–62. Koolen, A.J., Kuipers, H.A., 1983. Agricultural Soil Mechanics. Springer-Verlag Berlin Heidelberg, New York Tokyo. Komandi, G., 1992.On. the mechanical properties of soil as they affect traction. J. Terramech. 29 (4/5), 373–380. Kogure, K., Yamaguchi, H., Ohira, Y., 1988. Comparison of the strength and soils thrust characteristics among different soils tests. J. Terramech. 25 (3), 201–221. Krick, G., 1971. Interaction Between Wheel, Tyre and Soils. Thesis. Muenchen University of Technology (in German). Kuipers, H., Kroesbergern, B., 1966. The significance of moisture content, pore space, method for sample preparation and type shear annulus used on laboratory torsional shear testing of soils. J. Terramech. 3 (4), 17–28. Lucius, J., 1971. Study of the influence of speed of deformation on the strength of soil. Deutsche Agrartechnik 21 (11), 526–528 (in German). Manuwa, S.I., 2012. Evaluation of soil/material interface friction and adhesion of akure sandy clay loam soils in southwestern Nigeria. Adv. Nat. Sci. 5 (1), 41–46. Matsushi, Y., Matsukura, Y., 2006. Cohesion of unsaturated residual soils as a function of volumetric water content. Bull. Eng. Geol. Env. 65, 449–455. Mouazen, A.M., Ramon, H., De Baerdemaeker, J., 2002. Effects of bulk density and moisture content on selected mechanical properties of sandy loam soil. Biosyst. Eng. 83 (2), 217–224. Ohu, J.O., Raghavan, G.S.V., McKyes, E., Mehuys, G., 1986. Shearing strength predicted of compacted soils with varying added organic matter contents. Trans. ASAE 29. Panwar, J.S., 1968. Shear Strength and Energy of Soil Failure Related to Density and Moisture. M.S. Thesis. University of Illinois. Rajarama, G., Erbach, D.C., 1999. Effect of wetting and drying on soil physical properties. J. Terramech. 36, 39–49. Schimming, B.B., Hass, I.J., Saxe, H.C., 1965. A comparison of dynamic and static shear strengths of cohesionless, cohesive and combined soils. Air Force Weapons Laboratory, Technical Report No. AFWL TR-65-48. Shoop, S.A., 1992. Comparison of thawing soil strength measurements for predicting vehicle performance. US Army Corps of Engineers, CRREL Report 92-17.
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´ ski / Journal of Terramechanics xxx (xxxx) xxx P.A. Dudzin Shoop, S.A., 1993. Terrain characterization for trafficability. US Army Corps of Engineers, CRREL Report 93-6. Stafford, J.V., Tanner, D.W., 1982. Field measurement of soil shear strength and a new design of field shear meter. Proceedings of the 9th Conference of the International Soil Tillage Research Organization (ISTRO). Osijek, Yugoslavia, pp. 656–661. Stefanow, D., Dudzin´ski, P.A., 2019. Comparison of soil shear strength measurement methods – state of the art (in preparation).
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Sutoh, M., Wakabayashi, S., Hoshimo, T., 2017. Influence of atmosphere on lunar rover performance analysis based on soil parameter identification. J. Terramech. 74, 13–24. Tong, J., Ren, L., Chen, B., Qaisrani, A., 1994. Characteristics of adhesion between soil and solid surfaces. J. Terramech. 31 (2), 93–105. Wieder, W.L., Shoop, S.A., 2018. State of the knowledge of vegetation impact on soil strength and trafficability. J. Terramech. 78, 1–14. Wells, L.G., Treesuwan, O., 1978. The response of various soil strength indices to changing water content and bulk density. Trans. ASAE 21.
Please cite this article as: P. A. Dudzin´ski, Method for predicting dynamic shear strength in soils – Part I: Proposal for a new criterion, Journal of Terramechanics, https://doi.org/10.1016/j.jterra.2019.08.005
Contents lists available at ScienceDirect
Journal of Terramechanics journal homepage: www.elsevier.com/locate/jterra
Method for predicting dynamic shear strength in soils – Part I: Proposal for a new criterion Piotr Antoni Dudzin´ski Wrocław University of Science and Technology, Department of Off-Road Machine and Vehicle Engineering, Poland
a r t i c l e
i n f o
Article history: Received 30 July 2018 Revised 7 August 2019 Accepted 11 August 2019 Available online xxxx Keywords: Terramechanics Dynamic shear strength New criterion
a b s t r a c t The interaction between off-road machines and soil is usually a dynamic process of soil shearing. However, in practice, in order to interpret these processes, the empirical modified static Coulomb criterion, which does not take into account the soil strengthening, is commonly used. At Wrocław University of Technology a proposal for a method for predicting dynamic shear strength in soils was developed. This method takes into account primarily the soil shear velocity, the scale effect of the test device and its kinematics, which include the parameters of the process under investigation in terramechanics. The method will be presented in two parts of the following publication. The first part presents the results of the tests on soil shear strength carried out by the author of the article by means of soil ring shear test device. These results are discussed against the background of the results of soil research performed all around the world. On the basis of the tests conducted by the author, a new dynamic criterion of soil shear strength was formulated and the requirements for the innovative method for predicting dynamic shear strength in soils were established. This experimental method will be presented in the second part of the article. Ó 2019 ISTVS. Published by Elsevier Ltd. All rights reserved.
1. Introduction Producers of off-road machines and vehicles are continually searching for better solutions to meet the growing requirements for mobility. Design and optimization of that class of objects requires knowledge about the processes of interaction of the working tools and traction components with the soil. Interaction of working tools and traction components with soils in off-road machines and vehicles is connected with the deformation and shear strength of soils sf (see Fig. 1). In order to solve this complex problem, theoretical and experimental research is necessary. For theoretical research and problem solving, knowledge of the link between the state of stress and the state of strain in the considered body is essential. The mathematical models of these physical relations are constitutive performance of soil in terms of stress-strain relationships such as, for example, the Hooke’s law for metals. So far, there is lack of such universal constitutive law in soil mechanics. This lack results mainly from the random nature of the structure and physical characteristics of the soil. In addition, soil properties depend on temporary weather conditions, which is perhaps the biggest obstacle in ground theory development. Attempts at adapting various equations for other solids in soil
mechanics have not been satisfactory. Therefore, in practice, the so-called process analogues are used to identify soil strength. Such an analogue can be any device, for example a shear box, a soil ring shear test device, a plate shear test device, etc., which reacts to generated external loads, within the assumed tolerance limits, with the value of soil shear strength corresponding to the tested process in terramechanics. A systematic extensive research on the methods and devices for soil shear strength determination known world-wide, along with a comparative analysis of the results achieved with the particular ones, was conducted at Wrocław University of Science and Technology (Stefanow and Dudzin´ski, 2019). In classical soil mechanics, the Coulomb criterion given by Eq. (1) is usually used to describe the soil strength
sf ;C ¼ r tan u þ c
ð1Þ
where
sf ;C absolute value of shear strength on the failure r u c
surface total normal pressure on the failure surface (apparent) internal friction angle of the soil (apparent) soil cohesion
[kPa] [kPa] [°] [kPa]
E-mail address: [email protected] https://doi.org/10.1016/j.jterra.2019.08.005 0022-4898/Ó 2019 ISTVS. Published by Elsevier Ltd. All rights reserved.
Please cite this article as: P. A. Dudzin´ski, Method for predicting dynamic shear strength in soils – Part I: Proposal for a new criterion, Journal of Terramechanics, https://doi.org/10.1016/j.jterra.2019.08.005
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Fig. 1. Examples of interaction of traction components and working tools with soil: sf – soil shear strength, xt – turning velocity of wheel/track, xr – rotation speed of bucket in a bucket-wheel excavator.
It should be added that cohesion c is a measure of shear strength of the soil, independent of inter-particle friction u. Cohesive soil strength c can be attributed to inter-particle forces (i.e. the forces developed between the soil particles) which interact in resisting shear deformation and lead to specific arrangements of soil particles and stability. Disruption of soil particles occurs as the soil develops resistance to shear. According to (Dmitruk, 1971; Karafiath and Nowatzki, 1978; Koolen and Kuipers, 1983; Aysen, 2005), the later research in the scope of soils consolidation led to assuming the following formula of Coulomb – Hvorslev for saturated soils:
sf ;C ¼ ½r uðtÞ tan u0 þ c0
ð2Þ
where
sf ;C r uðtÞ
r0 ¼ r uðtÞ u0 c0 t
absolute value of shear strength total normal stress at a point in the skeleton pressure in the pore fluid (decreases with time t) effective normal stress at the point in the soil skeleton effective (true) internal friction angle of the soil effective (true) soil cohesion time
[kPa] [kPa] [kPa] [kPa] [°] [kPa] [sec]
For saturated soils it is common practice to use c0 and u0 instead of c and u, because drainage conditions in failure tests on saturated soil
have a great influence on soil water pressure u. It should be added that in unsaturated soil the apparent cohesion is greater than the true cohesion. This difference is caused by the clenching action of the suction in the soil water (Aysen, 2005). In a fully saturated soil, an externally applied load results in a stress increment at any point in soil mass. The stress inducted in the soil skeleton during the consolidation process is called the effective stress r0 = r – u(t). In this case, the stress is taken over jointly by the skeleton and the pore fluid (i.e. r – 0 and u(t) – 0). However, for the load duration t = 0+, the pore fluid carries the entire stress (u(t) – 0 and r = 0). At the completion of drainage, the entire load increment is carried by the soil skeleton (i.e. r – 0 and u(t) = 0). This case is the criterion for the final consolidation of soil. It should be mentioned that in addition to the empirical criterion of Coulomb in soil mechanics there is also a critical-state theory of soils formulated in the 1950s by Kenneth Roscoe from the Cambridge University. According to this theory in shear process of soil, a failure surface may develop before or after the critical state leading to a constant shear strength called the residual. However, this state is achievable only with very large strains. In overconsolidated soils, failure surface may develop immediately after the peak point and the critical state may not be obtained and the state of the fragment of soil moves towards the residual. Normally consolidated soil may not have a peak strength and the critical state may be obtained at relatively low strains (Aysen, 2005). In practice the two parameters c and u are called shear strength parameters of soil. These parameters are not constant for a given soil. Values of cohesion c and angle of internal friction u correspond only to the conditions in which they were determined experimentally. The values of cohesion and angle of internal friction depend very essentially on: the type of the device involved in the tests, especially its geometry, kinematics and shearing speed, the properties of a given soil in the course of determining its strength, such as density, moisture, consistency state, etc., the location of the test, i.e. in the laboratory or in situ, with disturbed or intact soil, etc., and on the history of stress state. The wide spectrum of known and applied equipment for testing the soil shear strength in the laboratory and in situ may be divided into the indirect (for example triaxial) and direct ones (for example a shear box, a ring shear test device, etc). The devices differ significantly in their structure, geometrical dimensions, kinematics of the shear process (the translational, rotational) and soil shear velocity. The results obtained for the same ground by different test devices may differ as much as several hundred percent (Bailey and Weber, 1965; Dunlap et al., 1966; Krick, 1971; Borst, 1973; Stafford and Tanner, 1982; Kogure et al., 1988; Shoop, 1992, 1993; Karmakar et al., 2007; Sutoh et al., 2017). Examples of comparative results are shown in Fig. 2 (Beretitsch, 1992). Geometrical dimensions of the test device have a significant influence on shear strength in soils. For example, (Cerato and Lutenegger, 2004) conducted shear tests on sand involving shear boxes with dimensions of 6 6 cm to 30 30 cm. The results showed that the angle of internal friction in sand, regardless of the sand compaction, decreased with the increase in shear box dimensions. In addition, the shear strength of sand increases with the height of the shear box. On the other hand, Dadakh in (Dadakh et al., 2010) studied cohesive clayed sand by means of shear boxes with dimensions of 6 6 cm, 10 10 cm and 30 30 cm. These studies have shown that with the increase in the size of the shear box the cohesion increases and the angle of internal friction
Please cite this article as: P. A. Dudzin´ski, Method for predicting dynamic shear strength in soils – Part I: Proposal for a new criterion, Journal of Terramechanics, https://doi.org/10.1016/j.jterra.2019.08.005
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Fig. 2. Results of a testing device type impact on the value of soil cohesion c:
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so far. The above works mainly focused on determining the impact of shearing velocity on increase in strength of different soil types. The tests have shown that increase in shear velocity leads to significant increase in shearing strength of cohesive soils, whereas for sands the influence of shear velocity on shearing strength is rather small. Thus, the phenomenon described above is usually called the strengthening of cohesive soils. Exemplary ranges of soil shearing velocity in off-road machines are shown in Fig. 4 (Dudzin´ski, 1991; Beretitsch, 1992). Summing up, the review of the state-of-the-art presented in the introduction above indicates that no method for predicting dynamic shear strength in soils can be found in the world-wide literature. In this article (Part1) the author presents a concept of a new criterion of dynamic shearing strength of soils.
2. Tests of dynamic shear strength in soils decreases. Moreover, it was found that the highlighted scale effect decreases with increase in the size of the shear test device. In the research discussed in (Hanson et al., 1967; Ohu et al., 1986; Lucius, 1971; Panwar, 1968; Beretitsch, 1992) it was found that increase in soil density results in approximately linear increase in soil strength. The research carried out by (Wells and Treesuwan, 1978; Panwar, 1968; Ayers, 1987) also showed an approximate linear increase in cohesion and in the angle of internal friction of the soil with increasing soil density. However, in highly cohesive soils, the gradient of this growth decreases significantly with the increase in soil moisture. Numerous researchers, including: (Kuipers and Kroesbergern, 1966; Komandi, 1992; Beretitsch, 1992; Rajarama and Erbach, 1999; Manuwa, 2012; Matsushi and Matsukura, 2006; Mouazen et al., 2002; Shoop, 1992, 1993; Keen et al., 2013; Wieder and Shoop, 2018; Tong et al., 1994) showed that the main factor influencing the strength properties of the soil is the water content. The relationship between cohesion and humidity manifests its absolute maximum at the intermediate water content. This maximum depends on the type and condition of the soil. On the other hand, the angle of internal friction decreases continuously with increasing humidity. The results obtained by (Beretitsch, 1992) illustrating those phenomena are given in Fig. 3. The essential impact of the shear velocity on the soil strengthening has been found in many tests world-wide (Schimming et al., 1965; Hanson et al., 1967; Dmitruk, 1971; Lucius, 1971; Flenniken et al., 1977; Baladi and Rohani, 1979; Baladi, 1987; Dudzin´ski, 1987, 1991). A similar phenomenon was also observed in metals and rocks, but no sufficient explanation has been found
The tests of rapid static and dynamic shear strength on soil were performed on ring shear test device at Universität Fridericana in Karslruhe, Germany, Figs. 5 and 6. The electrohydraulic drive of the soil ring shear tester enabled a step-less rotation control within the range of angular velocity of 0.04–7.2 rad/s, as well as a step-less control of the normal stresses on the surface of the tested soil sample within the range from 0 to 300 kPa. During the tests the following quantities were measured: the reaction torque M(h), angular position of shear ring h, normal pressure exerted on soils r, the change in soil sample volume and duration time of the process. The reaction torque M(h) is related to the shear stress s in the shear surface and the geometry of the shear ring:
MðhÞ ¼ 2p
Z
ro
sðr; hÞr2 dr ½Nm
ð3Þ
ri
Assuming the linear distribution of shear stress on shear surface, the mean shear stress s was calculated from the equation:
sðhÞ ¼
3MðhÞ 2pðr 3o r 3i Þ
½kPa
ð4Þ
Moreover, comparative tests (only static ones) of shear strength of soils were also carried out on standard apparatus for direct shearing (shear box). The shear box was the WF 2500 type from Wykeham Farance Engineering Limited, in which the dimensions of the sheared surface amounted to 10 cm 10 cm, and the translation velocity was within the range of 0.813 108 [m/s] to 0.2032 104 [m/s]. The test was performed on cohesion soil typical of southwestern Germany, Fig. 7, and on sand. The sandy loam selected was of natural density qn = 1.82 t/m3, natural moisture Wn = 14.3%, and the dry sand was of natural density qn = 1,6 t/m3. Fig. 8 shows the results of grain-size distribution analysis for sandy loam highlighted in Fig. 7.
3. Results
Fig. 3. Dependence of cohesion c, cd and internal friction angle u, ud of soil on moisture for rapid static and dynamic tests.
The experimental studies have clearly confirmed that increase in shearing velocity causes an increase in the soil shear strength, i.e., its strengthening, (see Fig. 9). The characteristic feature for this phenomenon is the fact that the component of the ground shear strength assigned to cohesion s(c) shows essentially higher increases in strength than that assigned to the internal friction s (u). This explains the clear strengthening phenomenon in cohesive soils.
Please cite this article as: P. A. Dudzin´ski, Method for predicting dynamic shear strength in soils – Part I: Proposal for a new criterion, Journal of Terramechanics, https://doi.org/10.1016/j.jterra.2019.08.005
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Fig. 4. Ranges of soil shearing velocity in classical mechanics and terramechanics.
Fig. 7. Experimental data of natural moisture Wn and natural density qn for typical soils of southwestern Germany.
Fig. 5. Soil ring shear test device.
Moreover, it follows explicitly from the performed tests that soil shear strength depends not only on the stress state but it is also significantly affected by the time elapsed from the moment of imposing an outside load until the moment of appearance of the soil failure (damage). The shorter the time the external load acts, the higher the strength resulting from soil strengthening.
New concepts are recommended to develop a new criterion for dynamic shearing strength of soils (see Fig. 10). Considering the above analyses of the experimental study, the results for the selected (sandy loam) soil have been presented synthetically in the graph in Fig. 11. From the study results presented in Fig. 11, it is clear that the soil shearing velocity appearing with the operation of off-road machines and vehicles causes very significant soil strengthening. It should be added that soils like the sandy loam do not crumble but plasticizes when wet, which may lead to shear strength weak-
Fig. 6. Functional diagram and basic data of soil ring shear tester: M(h) – measured soil shear reaction torque [Nm], N – normal force [N], A – shearing area [m2], r – mean normal pressure on the failure surface [kPa], s – shear stress, ro, ri – outer and inner radius of the shear ring [m], h – rotated angle of shear ring [rad].
Please cite this article as: P. A. Dudzin´ski, Method for predicting dynamic shear strength in soils – Part I: Proposal for a new criterion, Journal of Terramechanics, https://doi.org/10.1016/j.jterra.2019.08.005
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Fig. 8. Grain-size distribution for the selected soil (sandy loam).
Fig. 9. Coulomb failure envelopes for rapid static and dynamic shear speed: c – static cohesion, cd – added dynamic cohesion.
Fig. 10. The dependence of soil strength sf on the time of load applied: sf,m – shear strength, for which the loading time is close to zero (instantaneous shear strength), sf,s – standard shear strength, which is derived by means of standard shearing devices as for example the shear box, etc., sr – shear strength, for which the loading time is close to infinity (residual state).
ening and that other types of soils may not necessarily exhibit shear strengthening. Therefore, further research will be carried out in order to thoroughly explain the problem of dynamic soil shear.
Fig. 11. Experimental results in soil ring shear tester on the impact of shearing speed on soil shear strength.
It can be seen that working tools on off-road machines, as well as wheels and tracks of the off-road vehicles create the limiting state in soil in the time approaching zero. Thus, a reliable strength parameter could be the value of the instantaneous shear strength sf,m. This proves that determining the soil shear strength by means of standard devices of classic soil mechanics might result in the values representing soil strength that is several times smaller in relation to the actual values that should be used in considerations performed in the field of terramechanics. This mainly results from the fact that the shear strength defined by the Coulomb’s criterion does not take into account the rheological properties of the soil and therefore, the results so obtained are far from those found in practice. Rheological properties of soils are mainly related to its properties such as viscosity and viscoelasticity, which in turn depend on the time of exposure to loads or temperature. In the face of the above, there is an urgent need for developing a new dynamic criterion. In order to meet this demand, the author of the following article proposed a new criterion for dynamic shearing strength of soils given with the Eq. (5). The criterion was developed on the basis of the results of experimental and theoretical research performed by the author. Namely, the equation was derived on the basis of the
Please cite this article as: P. A. Dudzin´ski, Method for predicting dynamic shear strength in soils – Part I: Proposal for a new criterion, Journal of Terramechanics, https://doi.org/10.1016/j.jterra.2019.08.005
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test results obtained for sandy loam with moisture of 14.3% and density of 1.82 t/m3 presented, for example, in Fig. 11.
sf ;d ¼ sf ;s þ Dsf ;d ¼ sf ;s þ sf ;m sf ;s
(
1
Va Vs
k )
½kPa
ð5Þ
where
sf ;s Dsf ;d
sf ;m Va Vs k
rapid static shear strength (classic soil mechanics) dynamic soil shear strength (terramechanics) shear strength for which the loading time is close to zero actual dynamic shearing speed (terramechanics) rapid static shearing speed (classic soil mechanics) regression coefficient determined experimentally by means of the shearing tester, dependent on the type and state of ground
[kPa] [kPa] [kPa] [m/s] [m/s]
The criterion for applying Eq. (5) is current shear speed Va, existing in practice, which generates the strengthening of cohesive soils. The equation is universal. For example, for rapid static shearing speed Va equals Vs. In this context, component Dsf,d of dynamic soil strength equals zero. Shear strength is then calculated in line with Coulomb criterion. 4. Conclusions The systematic studies were performed on the impact of soil shearing velocity on its strength within the static/rapid static shearing velocity range of test devices applied in classic soil mechanics to dynamic shearing velocity appearing in terramechanics. The results of the experimental studies clearly confirmed that an increase in shearing velocity causes an increase in soil shearing strength, which is its strengthening. The component of soil shearing strength assigned to cohesion s (c) shows significantly greater growths in strength than the component assigned to internal friction s (u). A new criterion (Eq. (5)) for dynamical strength of soils was proposed. The criterion is easy for practical applications. The extensive validation of the new criterion for different types of soils, performed on the innovative shear tester, will be presented in the second part of the article. It follows from the author’s own research and literature studies that the shear test device as the analogue of the process should reproduce in the closest way the real interaction of working tools or tracks/tires with the ground. Because of this, such a shear test device should have the shearing kinematics and generate velocity corresponding to the real process and the geometry, thus eliminating the effect of scale and a bulldozing effect. Such an innovative, patented shear test device developed at Wrocław University of Science and Technology in Poland, will be presented in the second part of the article.
Acknowledgements This research was conducted at Fridericana University in Karlsruhe, Germany during Alexander von Humboldt fellowship.
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Please cite this article as: P. A. Dudzin´ski, Method for predicting dynamic shear strength in soils – Part I: Proposal for a new criterion, Journal of Terramechanics, https://doi.org/10.1016/j.jterra.2019.08.005