Estimates of the mechanical properties of lunar surface using tracks and secondary impact craters produced by blocks and boulders

Abstract

Estimates of bearing capacities of lunar surfaces using tracks and secondary impact craters produced by blocks and boulders shown in photographs taken by Lunar Orbiters II and III are the same order of magnitude as those reported by the Surveyor project, but they are generally less. Static analyses of 48 lunar blocks and boulders and their tracks yield friction angles between 10° and 30° and averaging about 17°. These values were computed using: (1) Terzaghi's bearing capacity equations for circular footings, (2) Meyerhof's dimensionless numbers for general shear on level surfaces, (3) a cohesion of 10 3 dynes per cm 2 , (4) a density of 1.35 gm per cm 3 for the near surface materials, (5) a density of 2.7 gm per cm 3 for the block or boulder, (6) spheroidal (triaxial) boulders unless definite shapes can be established, (7) footing radii equal to the half-width of the block or boulder, the half-width of the track, and(or) the half-width of the shadow near the base of the block or boulder. For 115 secondary impact craters and their corresponding blocks, dynamic strengths are estimated using: (1) the product of one-half the mass per unit area of the block and the normal component of velocity squared divided by the crater depth, and (2) the ratio of the kinetic energy of the block and the volume of the secondary crater. Velocities of the blocks are calculated using a ballistics equation and assuming an ejection angle of 45°. Block densities are taken as 2.7 gm per cm 3 . Dynamic strengths of the near surface materials using the first procedure average 25.2 x 10 5 dynes per cm 2 (37 psi); and, for the second procedure, they average 19.2 x 10 5 dynes per cm 2 (28 psi). Comparison between dynamic strengths and expected static strengths, computed for each block using the assumptions above, show that most of the dynamic strengths correspond to the static strengths when the friction angle is 30° and larger. Data on experimental low velocity impacts with natural targets are compared with the lunar data on secondary impacts. Nara's modified Poncelet equation for sand yields an average angle of internal friction near 34° using the appropriate block and soil constants mentioned above. Comparison of coefficients computed using the equations for sand of Clark and McCarty, Mortensen, and Moore for the lunar data with the corresponding constants for terrestrial data indicate the lunar coefficients are generally low. These low values can be brought into better agreement with terrestrial data on sand by increasing the assumed ejection angles to 60° or 70° and considering the effect of the low acceleration of gravity at the lunar surface.