VM264

VM264
Terzaghi's One-Dimensional Consolidation Settlement Problem

Overview

Reference:

K. Terzaghi, Theoretical Soil Mechanics, Wiley New York, 1942.

Analysis Type(s):

Static analysis (ANTYPE = 0)

Element Type(s):

2D 8-Node Coupled Pore-Pressure Element (CPT213)

3D 8-Node Coupled Pore-Pressure Element (CPT215)

3D 20-Node Coupled Pore-Pressure Element (CPT216)

3D 10-Node Coupled Pore-Pressure Element (CPT217)

Input Listing:

vm264.dat

Test Case

The problem deals with consolidation of an infinite half-space idealized as a one-dimensional situation. The top surface is permeable and the bottom surface is impermeable. Pressure is applied at the top of a vertically stacked element pile. The distribution of pressure along the depth is computed and compared against reference solution.

Figure 455: Problem Sketch

Material Properties

Geometric Properties

Loading

E = 5.8E5 Pa

Nu = 0.0

Permeability k=8.62E-3 m/s

Height H=10m

Width W=1m

Pressure R =10 Pa

Analysis Assumptions and Modeling Notes

The problem is modeled and solved with two dimensional (CPT213) and three dimensional (CPT215), (CPT216), (CPT217) coupled pore pressure elements. The UZ degrees of freedom in the 3D model are constrained to make it behave like 2D elements. Displacements along X direction are constrained on all nodes and displacements along Y direction are constrained at the bottom surface. The top edge is made pore pressure free (pressure=0). Static analysis is performed with unsymmetric Newton-Raphson option with an end time of 0.02s and the distribution of pore pressure along the depth is computed.

Results Comparison

2D 8-Node Couple Pore-Pressure Element CPT213
Y/H (Depth)	P/R (Pre Pressure)
Y/H (Depth)	Target	Mechanical APDL	Ratio
0. 1	0.180	0.176	0.982
0.2	0.350	0.345	0.986
0.3	0.500	0.497	0.996
0.4	0.630	0.629	0.999
0.5	0.740	0.737	0.996
0.6	0.820	0.820	1.001
0.7	0.890	0.881	0.991
0.8	0.930	0.922	0.992
0.9	0.940	0.945	1.006
1.0	0.950	0.952	1.003

3D 8-Node Couple Pore-Pressure Element CPT215
Y/H (Depth)	P/R (Pre Pressure)
Y/H (Depth)	Target	Mechanical APDL	Ratio
0. 1	0.180	0.181	1.008
0.2	0.350	0.345	0.988
0.3	0.500	0.498	0.996
0.4	0.630	0.629	0.999
0.5	0.740	0.736	0.996
0.6	0.820	0.819	1.000
0.7	0.890	0.880	0.989
0.8	0.930	0.920	0.990
0.9	0.940	0.943	1.003
1.0	0.950	0.950	1.001

3D 8-Node Couple Pore-Pressure Element CPT216
Y/H (Depth)	P/R (Pre Pressure)
Y/H (Depth)	Target	Mechanical APDL	Ratio
0. 1	0.180	0.1768	0.982
0.2	0.350	0.3452	0.986
0.3	0.500	0.4978	0.996
0.4	0.630	0.6293	0.999
0.5	0.740	0.7371	0.996
0.6	0.820	0.8207	1.001
0.7	0.890	0.8816	0.991
0.8	0.930	0.9222	0.992
0.9	0.940	0.9453	1.006
1.0	0.950	0.9528	1.003

3D 10-Node Couple Pore-Pressure Element CPT217
Y/H (Depth)	P/R (Pre Pressure)
Y/H (Depth)	Target	Mechanical APDL	Ratio
0. 1	0.180	0.173	0.963
0.2	0.350	0.348	0.996
0.3	0.500	0.500	1.001
0.4	0.630	0.631	1.002
0.5	0.740	0.737	0.996
0.6	0.820	0.820	1.000
0.7	0.890	0.881	0.991
0.8	0.930	0.922	0.992
0.9	0.940	0.945	1.006
1.0	0.950	0.952	1.003

Figure 456: Pore pressure contour plot along the depth using CPT213 element