MECHANICS OF GRANULAR MATERIALS
Unlike materials such as metals, polymers, cementitious concrete, rocks, etc., the strength and deformation characteristics of which are derived mainly from strong cohesive forces from chemical cementation, the constitutive behavior of uncemented granular materials, including strength, stiffness modulus behavior, dilatancy, localization of deformation, shear band formation, and instability behavior are to a large extent derived from interparticle friction resulting from normal forces acting on particles or particle groups. Particle bonding by short or long-term Coulombic forces and van der Waal-type forces may also play a role to a certain extent; however, the main sources of the constitutive relations and stability properties of cohesionless granular materials is interparticle friction, which, in turn, under low confining effective stress levels is highly dependent on gravitational body forces. Erosional processes and off-road locomotion are illustrative examples.
The force-displacement behavior of granular materials is fabric or structure dependent, highly nonlinear, dilatant and non-conservative. The gravity-induced stresses in laboratory specimens are nearly of the same order of magnitude as the externally applied tractions, thus limiting the size of the specimens. On the other hand, the same laboratory specimens must be sufficiently large to replicate the behavior of large geologic deposits in situ or the behavior of large masses of industrial or agricultural products during storage, handling and transportation. During critical, unstable states such as liquefaction of saturated loose sands under earthquakes and wave loading, landslides due to pore water pressure build-up, or the collapse of sensitive clays, gravity acts as a follower load, thus making the sequence of such phenomena impossible to observe and study as they occur either in the laboratory or in the field. In granular materials, gravity-driven particle convection induces material inhomogeneities and anisotropies during experiments, especially under very low confining pressures, which alter the initial fabric of the specimens and hence their constitutive relations. Accordingly, from an engineering point of view, uncertainties of unknown magnitude are introduced regarding the actual behavior of the large masses in the field the specific experiments are intended to emulate. Under moderate-to-high stress levels, the influence of gravity on the behavior of experiments may not be pronounced and, therefore, the test results in a terrestrial (1 g) environment may be sufficiently conclusive for engineering purposes. However, testing of granular materials under very low stress levels can only be performed in a microgravity environment. It should be emphasized again that the laboratory specimen that on one hand would resemble a magnified version of the elemental cube in a mechanics sense, should on the other hand, be representative of the real mass particle fabric. The gravity induced stresses within the specimen transform the experiment into a complex boundary value problem, where the constitutive properties and stability issues cannot be resolved by inverse identification techniques due to the highly nonlinear nature of the constitutive and stability behavior. For the same reasons, one cannot determine the constitutive relations of granular materials at very low effective stress levels by extrapolating results from centrifuge experiments performed at high stress levels. The same arguments could be made for the influence of gravitational body forces on a multitude of issues associated with granular materials under very low effective stress levels. Such issues include: determination of critical porosity or void ratio in granular materials and their relation to the maximum porosity of the same materials, both with and in the absence of shear-band formation; bifurcation instability and associated shear-band formation and strain softening at persistent and controlled effective stress states.
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A series of displacement-controlled triaxial compression experiments were performed in the SPACEHAB module of the Orbiter, during STS-89 mission to Mir. The experiments were conducted on six right cylindrical specimens 75 mm in diameter and 150 mm long at confining pressures ranging from 0.189 psi to 0.007 psi (1.30 kPa to 0.05 kPa). The displacement-controlled test configuration was chosen in order to maintain overall specimen-apparatus stability as well as local material stability in the event continuous or discontinuous bifurcation instability were to take place associated with respectively diffuse bulging or localization of deformation in narrow shear bands, which might lead to overall strain-softening and brittleness phenomena. In these tests the displacements are controlled through stiff and highly polished tungsten carbide end-platens, while a constant confining pressure is transmitted through a flexible, relatively thin, latex rubber membrane surrounding the cylindrical surface between the ends. In the first three experiments (denoted ÒF2Ó) five axial compression, loading and unloading cycles were completed at regular intervals up to an overall compressive strain of 25%. In the last three experiments (denoted ÒF3Ó), ten 0.5 mm loading and unloading cycles were followed by seven 5 mm loading and unloading cycles. Detailed recordings of data especially related to volume change were obtained during the loading, unloading and reloading cycles to study how complex and often counter-intuitive dilatancy phenomena originate. Specifically, the volume change (dilatancy) loops achieved in such loading cycles tend to magnify at low stress levels, which make it possible to observe them and possibly arrive at unambiguous conclusions regarding the kinematic-static mechanisms controlling deformation and strength behavior, especially at the low effective stress states associated with fluidization and liquefaction phenomena. In this manner, the specimens comprise a mixed, but well defined boundary value problem. The specimens consist of subrounded quartz sand, which were tested in the dry condition. During testing axial load, axial displacement, confining pressure, bulk volumetric changes, 360 degree video coverage, ambient pressure, temperature and acceleration levels were recorded. Optical techniques monitored overall behavior of the specimens, specifically to track any onset of formation of shear bands. A regular grid was printed on the membrane surface, which facilitated tracking of motion throughout the specimens' surfaces. After the experiments were completed, the specimens were subjected to non-destructive computed tomography and epoxy-impregnated. Later they will be cut into thin sections for further internal examination of pore space distribution, internal fabric features and zones of instability.
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The MGM experiment was initiated by Dr. Nicholas C. Costes in 1976. The PI, Stein Sture joined Dr. Costes' effort in 1977. It was reviewed and adopted by NASA's Physics and Chemistry Experiments in Space (PACE) working group in 1977. The MGM project has in the intervening years been subjected to 7 science peer reviews, including a high level review effort conducted by Dr. Robert Schrieffer (Nobel Prize, 1974). Eighteen different academicians and four industry researchers have participated at the various peer reviews. In addition, the project has been subjected to numerous internal NASA (MSFC, ARC, NASA Headquarters) and NAS/NRC program reviews. While the project started at MSFC, it was for two years (1980-1982) managed by ARC, but returned to MSFC. The project was selected for space flight in 1991, when detailed apparatus concept design efforts began. While all early science efforts took place at MSFC and the University of Colorado at Boulder, apparatus design and manufacturing was carried out at Sandia National Laboratories. The Laboratory for Atmospheric and Space Physics (LASP) of the University of Colorado at Boulder became an important partner in the project in 1993, aiding in the first set of MGM experiments on STS-79, where three tests were successfully carried out. LASP has assumed responsibility for missions following STS-79.
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Specimen Preparation (Pre-flight)
The steps taken to minimize differences between test specimens are described below. Test specimens are prepared at the Laboratory for Atmospheric and Space Physics (LASP) at University of Colorado at Boulder, using F-75 Ottawa sand placed by dry pluviation. Each specimen is weighed and diameter measurements are taken, and relative density is calculated. Once calculations confirm that specimen preparation is satisfactory, a test cell is assembled and pressurized to 15 psig. The cell is then observed until delivery, with minor maintenance performed. Periodic repressurization is performed to account for any relaxation of cell materials, and cell and specimen integrity is monitored. Relaxation is minimal, and largely takes place within the first day after initial pressurization, and thus is successfully dealt with by repressurization.
Five test cells were prepared for MGM-I, and eight test specimens were built in preparation for MGM-II, with four designated for the F2 series tests, and four designated for the F3 series tests. Flight cells were chosen by taking the most uniform specimens with closest relative density and most favorable long-term behavior. The remaining specimens were set aside for use as flight spares, if required. As the spare test cells were not used for flight, they were dedicated as control specimens.
Below lists preparation and usage information for the prepared specimens.
|Test Cell ID#
|0||8/13/96||87.3%||0.007 psi F1 Test
|4||6/19/96||85.9% ||0.075 psi F1 Test
|7||6/17/96||86.4%||0.189 psi F1 Test
|2||6/19/96||84.3%||1-g test (SS32)
|0||11/10/97||64.8%||0.007 psi F2 Test
|1||10/30/97||62.2%||0.075 psi F2 Test |
|2||11/11/97||65.0%||0.189 psi F2 Test
|H||11/08/97||66.7%||0.007 psi F3 Test
|E||11/02/97||66.3%||0.075 psi F3 Test |
|G||11/03/97||66.0%||0.189 psi F3 Test
Flight Experiments (In-Flight)
Each of the three F2 flight experiments was performed using an axial, quasi-static, relatively large magnitude cyclic displacement loading mode. The loading sequence consisted of 5 displacements (compressions) of 5% axial strain each separated by unloading cycles, for a total axial strain of 25%. The displacement rate during loading was 35 mm/hr. The displacement rate during unloading was 17.5 mm/hr. Each of the three F3 flight experiments was performed using an axial, quasi-static, small magnitude cyclic displacement loading mode. The loading sequence was comprised of 10 small cycles and 7 larger cycles. Each of the ten small cycles consisted of a 0.5 mm compression followed by a 0.5 mm extension. Each of the seven larger cycles consisted of a 5 mm compression followed by a 5 mm extension. The displacement rate during the small cycles was 35 mm/hr. The displacement rate during the larger cycles was 75 mm/hr. The 3 F2 experiments were performed on 3 identical test cells, using the same experiment sequence each time. The confining pressure was set at 0.007 psid for Experiment 1, at 0.075 psid for Experiment 2, and at 0.189 psid for Experiment 3. The 3 F3 experiments were performed on 3 identical test cells, using the same experiment sequence each time. The confining pressure was set at 0.007 psid for Experiment 4, at 0.075 psid for Experiment 5, and at 0.189 psid for Experiment 6. Confining pressure was closely controlled throughout the experiments.
SAMS Data Collection (In-Flight)
The Space Acceleration Measurement System (SAMS) , sponsored in support of microgravity science experiments by the NASA Microgravity Science and Applications Division, recorded the acceleration environment during MGM experiments. The C-Head sensor was mounted near the TDLA. The cut-off frequency of this head was 25 Hz. The post-flight archived SAMS data are available through the Principal Investigator Microgravity Services Project at NASA Lewis Research Center. The SAMS data were downloaded from the NASA Lewis Research Center server for the time periods of active operation (power on) of the three MGM flight experiments. The data, consisting of acceleration ÒgÓ values in the X-, Y-, and Z-axes of the C-Head sensor, referred to STS coordinates as a function of mission time, were examined to determine deviations from +/- 1 milli-g (mg) requirements for each experiment data set.
Specimen Computed Tomography Scanning (Post-Flight)
The six flight specimens and the undeformed flight spare specimen underwent computed tomography scans at the Kennedy Space Center Computed Tomography System. The scanning generated two-dimensional images of slices perpendicular to a specimen's cylindrical axis which were combined electronically to generate volumetric data sets that allow analysis of internal features. The CT scanning method substantially enhanced the science by allowing observation of internal features and provided a guide for cutting specimens in preparation for internal examination. The process was performed on 4 specimens at a time, and took cross-axial scans at 1 mm intervals over the length of the specimen.
Specimen Stabilization (Post-Flight)
The 6 flight specimens and the undeformed flight spare specimen are being stabilized by epoxy impregnation to permit evaluation by classical thin-sectioning techniques. Introduction of epoxy into the specimens and subsequent curing and hardening stabilized the sand grains against disturbance. This allows safe handling of the specimens and dissection by saw-cutting and preparation of thick and thin sections that will be analyzed to assess specimen fabric and pore structure. The epoxy impregnation is performed with a 4 part epoxy mix that is low in viscosity and well suited for saw cutting, grinding and polishing in preparation of thin sections. To facilitate the internal analysis, two dyes are incorporated into the epoxy to enhance contrast in both reflected and transmitted illumination during microscopic examination. After thorough mixing the dyed epoxy is introduced into the bottom of the specimen by gravity feed. By adjusting the level of liquid epoxy in the feed vessel the flow rate upward into and through the specimen is controlled within predetermined limits that ensure no disturbance of particle structure. After the specimen is completely filled with epoxy the specimen was placed in a 70°C oven and cured for 16 hours. Currently, the three F3 specimens, the undeformed flight spare, and one F2 specimen (Experiment 3) have been stabilized. The remaining two specimens are scheduled to be stabilized in the near future.
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