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Surface Stress

In February 2009, the US Army’s Cold Regions Research and Engineering Laboratory published a study by Tyler Olmstead and Erika Fischer titled “Estimating Vertical Stress on Soil Subjected to Vehicular Loading”. This study investigated soil Surface Stress when loaded by various vehicles. The US Army was concerned with the surface stress generated by vehicles in minefields. The US Air Force also wanted to understand the difficulties being encountered by its C-130s and C-17s taking off and landing on unpaved and semi-prepared airfields. In the past, Europeans had conducted similar soil dynamic studies of heavy tractor tire loading to improve crop yields.

Throughout the past century, various methods of modeling and sensing soil surface stress distributions have been explored. Notably, Boussinesq in 1885 created the following general solution of the elastic distribution of surface stress under a point-load applied to a semi-infinite mass.

equation 1
Fig 1: Boussinesq Equation in Elliptic Cylinder Coordinates

This equation can be simplified assuming a uniformly loaded area and isotropic soil. In addition in 1934, O K Froehlich introduced a concentration factor that alters a soil’s surface stress distribution based on soil strength. This leads to a surface stress equation that is solved without the need for numerical methods as shown in Figure 2.

equation 2
Fig 2: Froehlich Modification to Boussinesq Equation

This study compared predicted surface stress results from the Froehlich-modified equation with experimental data taken with a Tactilus® sensor pad. Tactilus® is a matrix-based tactile surface sensor. It recorded and interpreted time-dependent, pressure distribution and magnitude between vehicle tires and the soil surface using a powerful Windows®-based tool kit.

The architectural philosophy of Tactilus® is modular, allowing for portability, easy scalability, and simultaneous data collection from up to six discrete sensor pads. Tactilus® employs sophisticated mathematical algorithms that intelligently separate signal from noise, and advanced electronic shielding techniques maximize the sensor’s immunity to noise, temperature, and humidity. Each Tactilus® sensor is carefully assembled to exacting tolerances and is individually calibrated and serialized

The predictions from the Froehlich equations compared favorably with the experimental data from the Tactilus® sensor pad. Sensor Product specs the accuracy of Tactilus® at ± 10%. The percent error on the average data for two days of sand testing was 4.63% and 7.68%. Figure 3 shows some screen shots of the Tactilus® results.

surface stress
Fig 3: Tire Tracks and Tactilus® Screen Shots