ANALYSIS OF UNDRAINED CONE PENETRATION AS A STEADY FLOW PROBLEM. - Houlsby, G; Wheeler, A; Norbury, J (A. A. Balkema, 1985)
A formulation is described for the analysis of the penetration of a cone, of similar geometry to that used in the CPT test, into an undrained clay. The penetration problem is modelled as a steady state flow of soil past a static cone, and for this problem the governing differential equations for the six variables (two velocities and four stresses) have both elliptical and hyperbolic properties. The streamlines are the characteristics of the hyperbolic equations. This approach is contrasted with the more conventional small strain incremental approach to elastic-plastic problems, with the important difference being the inclusion of the equations of steady flow. A solution scheme which takes advantage of the mixed nature of the equations is presented. The scheme can readily be adapted to more complicated constitutive laws for the soil.