# An Analytical Study of the Cone Penetration Test

The quasi-static penetration of a cone penetrometer into clay can be formulated as a steady state problem by considering a steady flow of soil past a stationary cone. The soil velocities are estimated from the flow field of an inviscid fluid, and the incompressibility condition is achieved by adopting a stream function formulation.

Emphasis is placed on obtaining an accurate velocity estimate and this is accomplished by a solution of the Navier-Stokes equations.

The strain rates are evaluated from the flow field using a finite difference scheme. The clay is modelled as a homogeneous incompressible elastic-perfectly plastic material and the soil stresses are computed by integrating along streamlines form some initial stress state in the upstream region.

These stresses do not in general obey the equilibrium equations, although one of the two equations can be satisfied by an appropriate choice of the man stress. Several attempts have been made to use the remaining equilibrium equation to obtain an improved velocity estimate and three plausible iterative methods are detailed in this thesis.

In a second study, a series of finite element calculations on the cone penetration problem is performed. In modelling the penetration process, the cone is introduced in a pre-formed hole and some initial stresses assumed in the soil, incremental displacements are then applied to the cone until a failure condition is reached. Although the equilibrium condition is satisfied very closely in the finite element calculations, it is extremely difficult to achieve a steady state solution.

In a third series of computations, the stresses evaluated by the strain path method are used as the starting condition for the finite element analysis. This is believed to give the most realistic solution of the cone penetration problem because both the steady state and equilibrium conditions are approximately satisfied. Numerically derived cone factors are presented and these are found to depend on the rigidity index of the soil and the in situ stresses. The pore pressure distribution in the soil around the penetrometer is estimated using Henkel’s empirical equation.

The dissipation analysis is based on Terzaghi’s uncoupled consolidation theory. The governing equation is formulated in the Alternating-Direction-Implicit finite difference scheme. This formulation is unconditionally stable and variable time steps are used to optimise the solution procedure. The dissipation curves are found to be significantly affected by the rigidity index of the soil and a dimensionless time factor is proposed to account for this effect.

Source: Oxford University

Author: C.I.Teh

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