1.14.3 Finite-strain consolidation of a two-dimensional solid

Product: ABAQUS/Standard  

This example involves the large-scale consolidation of a two-dimensional solid. Nonlinearities caused by the large geometry changes are considered, as well as the effects of the change in the void ratio on the permeability of the material. The material is assumed to be linear elastic. The example exhibits many features in common with the one-dimensional Terzaghi consolidation problem discussed in The Terzaghi consolidation problem, Section 1.14.1, notably the reduced settlement magnitudes predicted by finite-strain analysis in comparison with the results provided by small-strain theory.

Problem description

Loading and time stepping

The analysis is performed using two *SOILS, CONSOLIDATION steps. In the preliminary step the full load is applied over two equal fixed time increments. The load remains constant in the subsequent step during which the soil undergoes consolidation.

In the analysis accounting for finite-strain effects, the preliminary step requires six iterations for convergence of the first increment and seven iterations for convergence at full load. These relatively large numbers of iterations are due to the large geometry changes experienced by the soil. As shown in Figure 1.14.3–2, at full load the midpoint vertical deflection in this case is about 0.49 times the width of the strip that is loaded. The geometrically linear analysis predicts the midpoint vertical deflection to be approximately 0.52 times the width of the strip that is loaded.

Practical consolidation analyses require solutions across several orders of magnitude of time (see Figure 1.14.3–2, for example), and the automatic time stepping scheme is designed to generate cost-effective solutions for such cases. The algorithm is based on the user supplying a tolerance on the pore pressure change permitted in any increment, UTOL. ABAQUS uses this value in the following manner: if the maximum change in pore pressure at any node is greater than UTOL, the increment is repeated with a proportionally reduced time step. If the maximum change in pore pressure at any node is consistently less than UTOL, the time step is increased. In this case UTOL is set to 0.103 MPa (15 lb/in2). This represents about 3% of the maximum pore pressure in the model following application of the load. With this value the first time increment is 7.2 seconds, and the final time increment is 1853 seconds. This is quite typical of diffusion processes: at early times the time rates of pore pressure are significant, and at later times these time rates are very low.

Results and discussion

Input files

References

Figures

Figure 1.14.3–1 Two-dimensional elastic consolidation problem description.

Figure 1.14.3–2 Midpoint settlement time history.

Figure 1.14.3–3 Pore pressure time history.