Insertion problems in geomechanics with the particle finite element

This work develops a numerical technique in which the Particle Finite Element method is applied to simulate solid intrusion problems in Geotechnical Engineering. The work describes the numerical developments that made the method functional and showcases its potential with various application problems.

New numerical developments include: integration schemes for large-strain, elasto-plastic constitutive models, novel integration methods for rigid body contact constraints and stabilized mixed formulations for single-phase and two-phase problems.

An explicit stress integration scheme is developed for elasto-plastic, large-strain constitutive models using a multiplicative split of the deformation gradient. This scheme uses adaptive substepping and a yield violation drift correction technique.

Rigid bodies with pre-specified shape and motion may be modeled. Contact constraints are introduced using a penalty method in which tangential behavior is treated with an elasto-plastic analogy. This elasto-plastic contact model is integrated by means of an implicit integration technique; an alternative scheme using the Implex algorithm is also described and assessed.

Low-order (linear) elements are employed to speed computation. These elements may suffer volumetric locking in quasi-incompressible conditions. For soils, such conditions appear under undrained loading or at critical state. To alleviate this problem, mixed formulations are developed and stabilization techniques are applied. Two different three-field mixed formulations for the coupled hydro-mechanical problem are presented, adding either the effective pressure or the Jacobian as nodal variables to the solid skeleton displacement and water pressure. Stabilization terms are used in the mass conservation equation of the biphasic medium and in the rest of scalar equations. Several mixed formulations are also implemented for the simplified single-phase problem, which approximates saturated soil behavior under undrained conditions.

The first application examples are three total stress problems: indentation of a rigid strip footing, T-Bar motion and a rough cone penetration test. All are frequently used benchmark problems; they allow to compare the performance of the developed numerical scheme with other techniques. It appears that the numerical strategy followed by PFEM, obtains similar results than those attained with alternative numerical methods with significant savings in computational efforts.

A total stress approach is also used in a parametric study of tube sampling in clay. The parameters explored include sampler geometry (round-tipped or beveled cutting shoes; outer diameter to wall thickness ratios); constitutive parameters, roughness factor and boundary conditions are studied. Outputs are analyzed in terms of classical sampling disturbance measures: the centerline strain path and the specific recovery ratio. The results show good agreement with experimental evidence and question the frequently accepted reference role of Strain Path method solutions.

The set of simulations in which a rough interface behavior is considered has been used to assess the theory proposed by Paikowsky and Whitman (1990) to predict the occurrence of a plug inside of an open-ended pile. The numerical results obtained here corroborate this theory: a plug inside of the tube is formed once the mobilized forces are equal to those that would mobilize a smooth closed-ended pile. Indeed, the failure mechanism that prevails during the penetration of a plugged tube is coincident with that of a closed-ended pile.

The last analysis of this work is the hydro-mechanical simulation of the cone penetration test in a Modified Cam Clay soil. A parametric analysis covers the effect of the permeability of the soil -from drained to undrained conditions- and the interface friction angle. The effect of these parameters on the cone resistance, sleeve friction and pore pressure at three potential measurement points is fully characterized. These numerical results are used to assess several techniques to estimate the permeability of soils from CPTu testing. Special attention is paid to on-the-fly techniques, in which permeability could be directly estimated from the CPTu data stream without the need for any stoppage.