3D-printed rock models: Elastic properties and the effects of penny-shaped inclusions with fluid substitution

3D printing techniques (additive manufacturing) using different materials and structures provide opportunities to understand porous or fractured materials and fluid effects on their elastic properties. We used a 3D printer (Stratasys Dimension SST 768) to print one solid cube model and another with penny-shaped inclusions. The 3D printing process builds materials, layer by layer, producing a slight bedding plane, somewhat similar to a sedimentary process. We used ultrasonic transducers (500 kHz) to measure the P-and S-wave velocities. The input printing material was thermoplastic with a density of 1.04 g/cc, P-wave velocity of 2167 m/s, and S-wave velocity of 885 m/s. The solid cube had a porosity of approximately 6% and a density of 0.98 g/cc. Its P-wave velocity was 1914 m/s in the bedding direction and 1830 m/s normal to bedding. We observed S-wave splitting with fast and slow velocities of 879 and 835 m/s, respectively. Quality factors for P- and S-waves were estimated using the spectral-ratio method with Q(P) ranging from 15 to 17 and Q(S) from 24 to 27. By introducing penny-shaped inclusions along the bedding direction in a 3D printed cube, we created a more porous volume with density of 0.79 g/cc and porosity of 24%. The inclusions significantly decreased the P-wave velocity to 1706 and 1351 m/s parallel and normal to the bedding plane. The fast and slow S-wave velocities also decreased to 812 and 656 m/s. A fluid substitution experiment, performed with water, increased (20%-46%) P-wave velocities and decreased (9%-10%) S-wave velocities. Theoretical predictions using Schoenberg's linear-slip theory and Hudson's penny-shaped theory were calculated, and we found that both theories matched the measurements closely (within 5%). The 3D printed material has interesting and definable properties and is an exciting new material for understanding wave propagation, rock properties, and fluid effects.