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Grain crushing in sand-structure problems
Grain crushing in sand-structure problems
Zeghal, M.; Edil, T.B.
NRCC-39818
A version of this document is published in / Une version de ce document se trouve dans: CANCAM 2003, Calgary, Alberta, June 1-6, 2003, pp. 312-313
GRAIN CRUSHING IN SAND-STRUCTURE PROBLEMS
Morched Zeghal
1and Tuncer B. Edil
21
Institute for Research in Construction, National Research Council Canada, Ottawa, Ontario, K1A 0R6
2Department of Civil & Environmental Engineering, University of Wisconsin-Madison, USA, 53706
Existence of grain crushing
The results of modified direct shear tests provided by Hoteit (1990) were analyzed to confirm the existence of crushing and to evaluate the extent of its effect. Hoteit conducted an extensive experimental program on both loose and dense Quiou sand from Bretagne, France, at two initial confining pressures, 100 and 350 kPa, at the Institut National Polytechnique de Grenoble. Quiou sand is a uniform (Cu =
9.4) and calcareous sand with a mean grain size of 0.40 mm and an effective grain size of 0.05 mm. Also, he performed tests for constant stress and for constant volume stress paths. Hoteit measured the grain size distribution prior to the test and monitored its change during the shear test. The data were analyzed using the breakage factor defined by Lee and Farhoomand (1967). They evaluated the amount of crushing by defining the ratioD15i/D15f whereD15i is the diameter corresponding to 15% finer before shearing andD15fis the diameter still corresponding to 15% finer but after shearing occurred. The analysis done using bothD10 and D50suggests that using the ratioD50i /D50fis more suitable to describe crushing. Figure 1 shows the variation of the breakage factor as a function of the plastic work (at the end of shear tests) usingD50. The data is more scattered in the case of D10. This is explained by the small quantity, which makes it very sensitive to change.
Figure 2, showing the percentage retained by each sieve, clearly supports that the bigger grains are crushing first (reflected in the curve corresponding to the beginning of shear) and crushing the most (curve at the end of shear). Figure 3 shows crushing occurs for loose and dense sand; for both high (350 kPa) and low (100 kPa) confining pressures; and for both stress paths (constant stress and constant volume). This suggests that the amount of crushing can be assumed to be independent of the stress path and initial confining pressure but, it is clearly a function of the plastic work. Of course, plastic work is not solely due to
grain crushing and there are other significant mechanisms that contribute to plastic work; however, it seems that empirical data show that the degree of grain crushing is remarkably well correlated to plastic work (Figure 3). More significantly, the relationship appears to be independent of the direct shear stress path taken, i.e., constant normal stress or constant volume providing a basis for a unified formulation.
Figure 1. Breakage factor for calcareous sand based on D50
versus plastic work at the end of test
Figure 2. Breakage analysis-calcareous sand
2000 3000 4000 5000 6000 7000 8000 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5 1.55
Plastic Work [kPa.mm]
Breakage Factor (D50i/D50f)
0 pan 400 200 50 30 16 0 5 10 15 20 25 30 35 Sieve Number Percentage Retained Original Beginning of Shear End of Shear
Figure 3. Breakage factor versus plastic work for calcareous sand (CS: constant stress test and CV: constant volume test)
Coefficient of mobilised friction as a function of plastic work
Figure 4 shows the normalised shear stress as a function of total plastic work (used as an index of grain crushing and other plastic mechanisms) for the experimental data provided by Sengara (1991). It shows that the curve for constant stress and constant volume for the same initial confining pressure coincide even though the constant volume curve continues as a constant function of plastic work beyond the termination of the constant stress curve. The same observations were noted when the analysis was extended for the calcareous sand.
Figure 4. Normalised shear stress versus plastic work for Silica sand (CS: constant stress test and CV: constant volume test).
Experimental evidence from two different sources supports the idea of a changing coefficient of mobilized friction during the interface shear. The idea of changing the coefficient of mobilized friction as a function of the plastic work appears to be reasonable and is backed by the experimental data. The curves showing the change of the coefficient of friction as a function of plastic work appear very similar to the widely used hyperbolic model used in soil mechanics i.e.
where, a and b are two parameters related to the initial slope and the asymptotic limit of the above curves. These parameters can be obtained as the intercept and the slope of a plot of the ratio of plastic work to normalised shear stress versus plastic work.
Conclusions
Analysis of direct shear test data for two different sands (calcareous and Silica) confirmed that grain crushing occurs independently of the direct shear path taken (constant normal stress or constant volume tests). It also revealed a close correlation between mobilized coefficient of friction and plastic work, which can be used as an index of the amount of grain crushing.
References
[1] N. Hoteit: "Contribution à l’Étude du Comportement d' Interface Sable-Inclusion et Application au Frottement Apparent", Doctorate thesis, Institut National Polytechnique de Grenoble, France (1990). [2] K. L. Lee., and I. Farhoomand: "Compressibility and
Crushing of Granular Soils in Anisotropic Triaxial Compression", Canadian Geotechnical Journal, Vol. 4, No. 1, pp 68-100 (1967).
[3] I. W. Sengara: "Finite Element and Experimental Study of Soil-Structure Interfaces", Ph.D. thesis, University of Wisconsin-Madison, Department of Civil and Environmental Engineering (1991).23 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 100 200 300 400 500 600
Plastic Work [kPa.mm]
Normalized Shear Stress
CV at 35 kPa CV at 69 kPa CV at 138 kPa CS at 35 kPa CS at 69 kPa CS at 138 kPa p p bW a W + = µ 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5 CV at 350 kPa (loose) CV at 350 kPa (dense) CV at 100 kPa (loose) CV at 100 kPa (dense) CS at 350 kPa (loose) CS at 350 kPa (dense) CS at 100 kPa (loose) CS at 100 kPa (dense)
Plastic Work [kPa.mm]
