One-dimensional shock loading, attenuation, and recompression data from gas-gun experiments on mechanical mixtures of alumina powder and epoxy were used to develop model parameters for stress-wave propagation. Specimens with 0.42, 0.34, and 0.20 volume fractions of alumina were investigated. Calculations simulating the experiments were performed using an extension of a Maxwell rate-dependent model which requires definitions of the instantaneous, equilibrium, and relaxation functions as input. Experimental observations indicated the shock-loading behavior is identifiable with the equilibrium response, and the release wave behavior is closely related to the instantaneous response. To model these effects, for negative strain rates, indicative of expansion, a relaxation time of 0.25 μs was used; this value gave agreement between the calculated and measured release wave behavior. For positive strain rates, indicative of compression, the relaxation time was permitted to decrease to 0.03 μs, which caused the shock-loading response to be dominated by the equilibrium function. Hugoniot data determined from the stress-wave profiles were compared to effective modulus calculations. This comparison suggests a strength effect which can be interpreted as an interaction between the components. Analysis using a self-consistent scheme for spherical particles shows good correlation between calculated and measured ultrasonic and Hugoniot intercept wave velocities.

Hugoniot data for porous copper of two initial densities, 6.052 and 7.406 g/cm3, are presented for compressive stresses ranging from 2 kbar to 1 Mbar. These densities respectively correspond to 67.8% and 82.9% of the density of solid copper. High explosives were used to generate the shock waves in the highstress region, and an air gun was used in the low-stress region. The profiles of the propagated distrubances in each porous copper at low stresses are characterized by three distinct waves. The first of these waves is a low-level wave (<0.5 kbar) traveling at about sonic velocity. The second wave, having an amplitude of ∼1.1 kbar in the 6.052 g/cm3 copper and ∼1.3 kbar in the 7.406 g/cm3 copper, travels at about one-half of the sonic velocity. The velocity and amplitude of the third wave increase with increasing input stress. The experimental Hugoniot data are compared with curves calculated from Hugoniot data for solid copper using the Mie-Grüneisen equation of state with the assumption that compaction of the porous copper is complete. At low stresses, the data approach the calculated curves asymptotically with increasing stress and indicate that compaction is essentially complete for stresses greater than about 21 kbar. At higher stress the experimental data agree very well with the calculated curves.

Principal Hugoniot, second-shock Hugoniot, and adiabatic release data obtained by gas gun experimental techniques are presented for porous copper prepared by hydrostatically pressing copper powder to a density of about 6.4 g/cm 3 • The bulk of the data presented pertain to a powder with initial particle diameters of 30 p., however, sufficient data are also presented for other particle diameters of 10, 50, and 100 p. to show that particle size variations over this range have no distinct effect on shock loading properties. Transmitted wave profiles for each of these materials are characterized by a single precursor wave (amplitude ",,1.4 kbar, velocity "'1.9 mm/p.sec) followed by a main shock wave. Principal Hugoniot data for stress levels above the precursor amplitude and over the entire stress range examined (up to ",35 kbar) are well represented by the rel~tion a2= 1 + (ai-I) eXPL -a(P2-PI)], where a2 is the distention ratio (density of solid copper/density of porous copper) at the stress level P2, PI is the precursor amplitude, al is the value of a at PI, and a is an adjustable parameter (found to be 0.254 kbac 1 ). Second-shock Hugoniot data (i.e., for a Hugoniot centered at a prestressed state P2, (2) are also well represented by the above equation provided al and PI are changed to correspond to the prestressed state. Release data indicate that the shock loaded porous copper unloads along a path that is essentially the same as the loading path. These data, however, extend only over the upper one-fourth of the stress range between the shock loaded state and the foot of the release adiabat and a straight-line continuation of the measured adiabat indicates that the compression process is not reversible.

Data are presented from a study conducted to examine the shock-loading behavior of a sintered porous tungsten with a density of 12.64 g/cm3 (corresponding to 65.3% of the density of solid tungsten). The experiments were performed by using a gas gun and high explosives. Hugoniot data obtained in the stress range between about 12 kbar and 1 Mbar indicate that compression of the porous material to a fully compacted state is essentially complete at 50 kbar. Above this level, a predicted Hugoniot, calculated from the Hugoniot of solid tungsten by using the Mie-Grüneisen equation of state, agrees well with experimental data. Below 50 kbar the Hugoniot of the porous tungsten deviates from the predicted Hugoniot increasingly with decreasing stress. Propagated wave profiles at lower stresses are characterized by two precursor waves, the faster being a low-level wave (∼0.2 kbar) traveling at about sonic velocity in the porous tungsten (∼3.04 mm/μsec). The slower precursor has an amplitude of 2.73 kbar and travels at 2.02 mm/μsec. The behavior of this porous tungsten is analogous to the behavior of sintered porous copper previously studied.

A finite-element computational procedure for simulating the reservoir compaction and subsidence processes at Ekofisk is described. Data inputrequirements are considered, and results are presented for selected reservoir management options. Field measurements of subsidence, subsidence rates, and subsidence-bowl profiles are shown to be in good agreement with calculated results.