On the calculation of cumulative strain around full-flow penetrometers in steady-state conditions

© 2014 John Wiley & Sons, Ltd. An approximate solution for the effects of high strain rates, and gradual strength degradation, on the penetration resistance of penetrometers can be obtained by combining the strain-path method with the classical upper bound theorem. The stream path calculations require the integration of the material constitutive equation along the streamlines. Unless the geometry is simple so that the integration can be evaluated analytically, numerical procedures are required to backtrack streamlines. The strain at any location is calculated by finding the streamline that passes through the given point and integrating the strain rate along that streamline from its inlet boundary. Thus, the calculations can be complicated, and errors can be accumulated during the calculation procedure. This paper presents an efficient approach for evaluating cumulative strains around penetrometers without the need to backtrack individual streamlines. In this approach, the strain components are treated as field variables. The global solution is obtained using the streamline upwind Petrov-Galerkin method. The new method together with an Eulerian-based finite element formulation was used to study the cone penetration test and evaluate the effect of strain softening on the cone resistance.