Dynamics and Dimensional Similitude of Vehicle Impacts upon Soil-fixed Boulders in Cohesionless Soil

Open Access
Keske, Mark Palmer
Graduate Program:
Mechanical Engineering
Master of Science
Document Type:
Master Thesis
Date of Defense:
July 06, 2012
Committee Members:
  • Sean Brennan, Thesis Advisor
  • laterally loaded
  • soil
  • low order
  • vehicle impact
  • boulder
  • soil-fixed
  • cohesionless
  • similitude
  • scaling
  • small scale
This thesis describes development and application of a 2-D low-order model, scaling laws, and dimensionless equations of motion (DEOM) for a vehicle impact upon a soil-fixed boulder in cohesionless soil. The vehicle is represented as a lumped-parameter Maxwell model, the boulder is treated as a rigid body with non-negligible mass, and the soil is represented as a system of lumped-parameter Kelvin models. The low-order model has three degrees-of-freedom (DOFs), which are the linear translation of the vehicle and boulder and the angle of rotation of the boulder. The low-order model is used to simulate a vehicle impact on a soil-fixed boulder using numerical integration techniques. The simulation is then compared and validated against past full scale crash tests. All full scale crashes were performed according to ASTM F2656-07 at an M30 rating using a 6,800 kg (15,000 lb.) medium-duty sized truck. The results of the full scale simulation agree to within ± 3° of the measured boulder angle of rotation from full scale tests. Dimensional analysis is performed on the low-order model to develop the DEOM and scaling laws. The DEOM and scaling laws are then used to simulate small scale vehicle impacts and are first validated against full-scale simulations and full-scale crashes. Next, small scale crash tests are then designed, preformed, and validated against full scale crash tests using the scaling laws. The small scale crash tests are performed using a small equivalent vehicle mass of 8 kg. The small-scale simulations are in full similitude with the full-scale simulations, which implies 100% matching between scaled simulations. The experimentally-measured angles of rotation of the boulder for the small scale tests were found agree to within ± 3° of the full-scale past crash tests. The results from the low-order model simulations are then used to create pass/fail boundaries for various sized boulders. The pass/fail boundaries are chosen such that failures include boulder rotation beyond 20°; predicted boulder fracture; and excessive boulder masses. The pass/fail boundaries are then used to design a boulder of potential minimum mass that will rotate no more than 20°. At this time, simulations and small scale testing has been performed which show and an agreement of ± 3° of boulder rotation between the simulations and the small scale testing. The full scale test has not taken place at this time.