VM260

VM260
Two-Dimensional Consolidation Settlement Problem

Overview

Reference:

Schiffman, A. et al. "An Analysis of Consolidation Theories." Journal of Solid Mechanics and Foundation Division. (1969): 285-312.

Analysis Type:

Static (ANTYPE,0)

Element Type(s):

2D 4-Node Coupled Pore-Pressure Mechanical Solid Element (CPT212)

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

Input Listing:

vm260.dat

Test Case

An infinite rectangular half space plate is modeled with dimensions 12a by 9a. Pressure loading is applied on the center of the top surface (on one sixth of the total width). The top surface is made permeable and bottom surface is impermeable. Evolution of pore pressure computed with respect to depth and time are compared with reference values.

Nomenclature Used in This Problem

P = Pore pressure

Tv =

Tv = Time Factor

C_Vc = Consolidation coefficient

t = Time

Figure 447: Problem Sketch

Figure 448: Two-Dimensional Consolidation Pore-Pressure Problem -- Representative Finite Element Model

Material Properties

Geometric Properties

E = 1000 Pa

μ = 0.0

k = 0.267x10^-4m⁴/N/s

t = 374530s

a = 1 m

w = 1 m

R = 100 Pa

Analysis Assumptions and Modeling Notes

The plate is meshed using (CPT212) and (CPT213) elements with plane strain conditions. Permeability and Biot coefficients are defined to the material model using TBDATA command. Bottom surface is fixed in all directions and displacements along X directions are constrained on the right and left edges. Non-linear static analysis is then performed to compute the evolution of pore pressure with respect to time and depth.

Results Comparison for the Evolution of P with Depth

P/R (`CPT212`)	za	Target	Mechanical APDL	Ratio
	0	0.0000	0.0000	1.000
	0.5	0.6350	0.6053	1.049
	1	0.5700	0.5962	0.956
	1.5	0.4400	0.4555	0.966
	2	0.3500	0.3615	0.968
	2.5	0.2950	0.3029	0.974
	3	0.2600	0.2648	0.982
	3.5	0.2360	0.2390	0.988
	4	0.2200	0.2211	0.995
	4.5	0.2080	0.2087	0.997
	5	0.2000	0.2000	1.000

P/R (`CPT213`)	za	Target	Mechanical APDL	Ratio
	0	0.0000	0.0000	1.000
	0.5	0.6350	0.5983	1.061
	1	0.5700	0.6031	0.945
	1.5	0.4400	0.4578	0.961
	2	0.3500	0.3625	0.965
	2.5	0.2950	0.3037	0.971
	3	0.2600	0.2653	0.980
	3.5	0.2360	0.2394	0.986
	4	0.2200	0.2214	0.994
	4.5	0.2080	0.2089	0.996
	5	0.2000	0.2001	0.999

Figure 449: Evolution of Excess Pore Water Pressure with Respect to Depth

Results Comparison for the Evolution of P with Time

P/R (CPT212)	Tv (za)	Target	Mechanical APDL	Ratio
	0.01	0.7700	0.7466	1.031
	0.02	0.8000	0.7812	1.024
	0.03	0.7900	0.7928	0.996
	0.05	0.7300	0.7257	1.006
	0.09	0.6150	0.6072	1.013
	0.1	0.5900	0.6053	0.975
	0.2	0.4200	0.4267	0.984
	0.3	0.3300	0.3294	1.002
	0.4	0.2700	0.2687	1.005
	0.5	0.2300	0.2271	1.013
	0.6	0.2000	0.1969	1.016
	0.7	0.1750	0.1739	1.006
	0.8	0.1600	0.1558	1.027
	0.9	0.1450	0.1412	1.027
	1.0	0.1350	0.1291	1.046

P/R (CPT213)	Tv (za)	Target	Mechanical APDL	Ratio
	0.01	0.7700	0.7509	1.025
	0.02	0.8000	0.8298	0.964
	0.03	0.7900	0.8171	0.967
	0.05	0.7300	0.7497	0.974
	0.09	0.6150	0.6242	0.985
	0.1	0.5900	0.5983	0.986
	0.2	0.4200	0.4215	0.996
	0.3	0.3300	0.3258	1.013
	0.4	0.2700	0.2660	1.015
	0.5	0.2300	0.2251	1.022
	0.6	0.2000	0.1953	1.024
	0.7	0.1750	0.1725	1.014
	0.8	0.1600	0.1546	1.035
	0.9	0.1450	0.1402	1.034
	1.0	0.1350	0.1282	1.053

Figure 450: Evolution of Excess Pore Water Pressure with Respect to Time