MECHANICS OF GRANULAR MATERIALS
Science information is obtained from four modes of analysis: digital (load, pressure, deformation, and volume change of specimens during compression), optical (in-flight video and post-flight profile measurements), CT, and internal examination. SAMS data also indicate whether external accelerations disturbed the experiments. Digital data collected from several types of transducers during compression is used to model behavior of granular material under load in the low-confining pressure region. Two types of soil behavior have been examined in the two types of experiments performed during MGM-II. The first consisted of testing 63.6 ± 1.4% relative density specimens under large strain, to obtain general static material properties: these tests are indicated as F2 and are identical to F1 (MGM-I, STS-79) experiments, with the exception of the relative density value. The second type of test examined 66.4 ± 0.4% relative density specimens under small-strain cyclic loading, to obtain cyclic behavior (for liquefaction applications, etc.): these tests are indicated as F3, and are identical to F2 experiments, with exception of the loading history. Three tests, at confining pressures of 0.007, 0.075, and 0.189 psi were performed on each type of experiment (F2 and F3), for a total of six tests. Optical analysis is important in two areas: supporting digital data gathered during compression and surface analysis. Video data were collected from three CCD cameras (spaced at 120 degrees) providing continuous coverage of the specimen deformation during testing. The video will provide shape and diameter information during compression. This will be used to study deformation patterns and membrane strain. Computed Tomography (CT) scans were performed in a terrestrial lab after the compressed specimens were returned to the PI. Scans were obtained at 1 millimeter spacing over the long axis of the specimen. While the resolution is not high enough to see individual grains, density information is available. This information reveals the internal features of the specimen and aids in planning for internal examination, which will be performed after the scanned specimens have been stabilized by impregnating epoxy into the pores of the material. Internal examination will involve cutting the specimens into thick and thin sections. When viewed under a microscope, these sections will allow viewing and measurement of void ratio, particle alignment, and other internal features at a high resolution, as individual particles will be visible. SAMS data were collected during the mission. The MGM team is examining the data recorded during experimentation, when specimens were in unstable states and may have been disturbed by small accelerations. This information will help locate possible external disturbances to the specimens. Digital, optical, CT, and internal examination data form the basis of understanding granular material behavior in microgravity. SAMS data reveals external influences on the experiments. All data will be correlated to form a comprehensive picture of the MGM flight experiments.
Preliminary findings in the digital data are related to load, pressure, displacement, and volume. Flight data showing principal stress ratio versus axial strain, and volumetric strain versus axial strain are shown below*. Principal stress ratio, the ratio of the axial stress to radial stress, normalizes the axial load over confining pressure, which allows direct comparison between tests of different confining pressures. The F2 specimens exhibited very high friction angles, within the range of 70 to 48 degrees, which decreased with confining pressure increase. Dilatancy angles were also very high, within the range from 27 to 31 degrees. Higher pressure terrestrial tests on the same material generally show lower friction and dilatancy angles. Plotting Friction Angle vs Confining Pressure* illustrates this variation with confining pressure, and show values of friction angle and dilatancy for terrestrial, F1, and F2 tests at relative densities of 65% and 85%. Data points with confining pressures above 1.30 kPa are derived from terrestrial test results, and data points with confining pressures below 1.30 kPa are derived from microgravity experiments. Both terrestrial and microgravity experiments were performed at 1.30 kPa. An interesting characteristic of the load cell data of the F2 experiments is the oscillation of load which appears to be periodic. All three experiments exhibit oscillations in the principal stress ratio-axial strain (load-displacement) line trace, though to varying extents. The oscillation is very prominent in Experiment 1, very small and nearly indistinguishable in Experiment 2, and small but distinct in Experiment 3. This oscillation in load is also seen in ground testing, to a small extent. The underlying cause of this phenomenon is still under investigation: speculations include a buckling of arches and columns of grains or a type of stick-slip behavior along shear planes within the specimen. Volumetric change is of great interest as well, as F2 specimens show a large amount of dilation, much greater than seen in ground testing. Specimens show an extremely small amount of volume decrease at start of test, and move almost immediately into volumetric expansion. The rate of expansion prior to reaching peak loads is dramatically higher than post-peak expansion. In addition, at the conclusion of the tests, the volume had not leveled out, indicating that a critical state was not achieved. However, it is apparent that critical state must exist at some density less than the lowest density achieved, 4% relative density, which occurred on the specimen tested at 1.30 kPa. Principal stress ratio from F3 experiments has revealed two interesting characteristics. First, stress ratios allow determination of peak internal friction angles, which may be compared to F2 data (Table 4) The friction angles from F3 tests show the same trend as F2 tests, but are higher for tests at the 0.05 and 1.30 kPa pressures. Secondly, the stress ratio during first cycles of F3 experiments increases at a greater rate than subsequent cycles. Volumetric data from F3 experiments is also important. There is a large volume increase in the first cycle, but on subsequent cycles, the net volume change is very little. The initial increase in volume indicates that critical void ratio is below the relative density of Å65%. This is also indicated by the large volume increase in F2 specimens. As a result, it is apparent that medium-dense cohesionless soil under low confining pressures will not liquefy. This evidence supports the observation that in-situ liquefaction does not occur at the soil surface, where confining pressures are generally low. Nominal Confining Pressure Peak Internal Friction Angle kPa F2 Tests F3 Tests 0.05 70¡ 75¡ 0.52 55¡ 55¡ 1.30 47¡ 56¡ Table 4. Comparison of peak internal friction angle between F2 and F3 experiments.
Each test is listed with name, relative density (DR), confining pressure at peak stress ratio (s3), peak friction angle (fmax),friction angle at constant volume (fcv), and dilatancy angle (y).
|F1 0.05 kPa||87.3
|F1 0.52 kPa||85.9
|F1 1.30 kPa||86.4
|F2 0.05 kPa||64.8
|F2 0.52 kPa||62.2
|F2 1.30 kPa||65.0
|F3 0.05 kPa||66.7
|F3 0.52 kPa||66.3
|F3 1.30 kPa||66.0
Below are two figures indicating the dependence of the friction angle and dilatancy angle on confining pressure. The terrestrial data is tabulated in the terrestrial data section.
Video data (below)* reveal deformation characteristics of the flight F2 and F3 specimens, respectively. Specimens did expand radially, as expected. Bulging in the F2 specimens is also visible, but relatively uniform, revealing a very new phenomena of diffuse bifurcation instability resulting in overall bulging of the specimen. The small amount of bulging visible in F3 specimens indicates the low friction at the end platens at small strain.
Figures (below) show results from the CT scan on the F2 specimen tested at 1.30 kPa. The colorbar in the lower right corner of the figure shows an approximate density to color relation, where darker color is lower density, and lighter color higher density. Cross-sections normal to the axis of compression ("horizontal") show lower and higher density areas seeming to be separated into radial streams, tied together toward the center of the specimen, and normal to the outer surface. When examining cross-sections parallel with the axis of compression ("vertical"), extensive areas of generally uniform density are seen outside of shear zones. In both horizontal and vertical figures a shear cone and shear plane are visible. The F3 specimen is much more homogenous than the F2 specimen, though small shear cones and beginnings of conjugate shear bands are visible. The shear cone, visible in both the horizontal and vertical slices, is at a very low angle. In contrast, the shear cone visible in F2 specimens is steep. This indicates that at the beginning of an experiment, low end-friction is present, and probably increases as the specimen bulges. The conjugate shear bands also indicate that shear band development has begun by 3.3% axial strain in F2 tests, and that the numerous shear bands visible in F2 specimens develop throughout the entire test.
The CT data are being further examined. Initially, the calibration of the CT numbers to density was found using calibration standards (including aluminum and water.) This calibration can also be used to find the density within the specimens themselves. A comparison of bulk density found from the CT data is within approximately 0.05 g/cc of the data obtained from digital measurements. This is currently being examined in order to try and improve accuracy. Following satisfactory calibration, examination of the structure within the specimen will be examined, including shear band density, size, and population.
MICROGRAVITY CT SCANS
The data processing and analysis effort thus far has been very successful and shows exciting results. Due to excellent equipment performance and data collection, there is complete science data return, which will aid greatly in completing a full analysis. These experiments have both supported data from MGM-I and given researchers new unique data on the mechanics of granular materials. As with MGM-I, the microgravity tests indicate that the low confining pressures lend to high friction and dilatancy angles in cohesionless soil. Also, the overall volume change, in terms of expansion, and bifurcation instability, revealed in terms of relatively uniform bulging, are very new phenomena, which are currently being studied. Specimen shear and radial features are present in both MGM-I and MGM-II, and are being studied through CT information. While similarities are present and being studied between the two sets of data, differences are also important. In particular, the internal friction angles vary between MGM-I and MGM-II, as well as oscillatory behavior. The similarities and differences are being studied to understand how microgravity, low pressures, and density affect the behavior of a cohesionless material. MGM-II has also revealed new data. The volumetric expansion during F2 experiments led to extremely low density specimens, lower than achieved during MGM-I. As a result, a new upper-bound relative density at critical state has been distinguished. Also, direct comparison of CT data between F2 and F3 experiments has given researchers insight into the development pattern of shear band formations.
[Top of Page]
[MGM Home ]
[Science Team Page]
[Archive Scientific Publications]