COMSOL 6.4 - Isotropic Compression Test for Structured Clays

Isotropic Compression Test for Structured Clays

Isotropic compression tests are common in soil testing to characterize the properties of the soil. It is also a common test for verification of new material models as a wide range of experimental data is available. In this example, the Modified Structured Cam-Clay (MSCC) soil model is examined, in particular the relation between the void ratio and the logarithm of the hydrostatic pressure or mean stress for four structured clays is studied.

This is a benchmark example given in the Ref. 1, where authors present experimental data as well as their simulation data. The four clays analyzed are: naturally structured Osaka clay, naturally structured Marl clay, artificially structured Ariake clay, and artificially structured Bangkok clay. Also, different cement contents by weight are considered for the two artificially structured clays.

Model Definition

In this example, a clay sample is placed inside a cylinder 10 cm in diameter and 10 cm in height, see Figure 1. Due to the symmetry, the model is solved in 2D axial symmetry.

Boundary loads are applied on the exterior boundaries to produce isotropic compression conditions.

Figure 1: Dimensions, boundary conditions, and boundary load for the isotropic compression test.

Modified Structured Cam-Clay Material Properties

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The four clays analyzed here are naturally structured Osaka clay, naturally structured Marl clay, artificially structured Ariake clay, and artificially structured Bangkok clay. Also, different cement contents by weight (Aw) are considered for the two artificially structured clays.

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The common material parameters are density ρ = 2000 kg/m3, reference pressure pref = 1 kPa, and critical effective deviatoric plastic strain εdcp = 0.1.

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Material properties like the shear modulus G, slope of critical state line M, compression index for destructured clay λd, swelling index for structured clay κs, void ratio at reference pressure for destructured clay erefd, additional void ratio at initial yielding Δei, plastic potential shape parameter ζ, destructuring index for volumetric deformation dv, destructuring index for shear deformation ds, initial consolidation pressure pc0, and initial structure strength pbi for the four different clays are shown in Table 1, Table 2, and Table 3.

Table 1: Material properties of Osaka and Marl Clays.
Material property	Osaka clay	Marl clay
G	3000 kPa	45000 kPa
M	1.15	1.30
λd	0.147	0.025
κs	0.027	0.009
erefd	1.92	0.67
Δei	0.62	0.085
ζ	2	1.5
dv	0.6	0.7
ds	1	1
pc0	100 kPa	4150 kPa
pbi	30 kPa	300 kPa

Table 2: Material properties of Ariake Clay with different cement content.
Material property	Aw = 6%	Aw = 9%	Aw = 18%
G	6000 kPa	8000 kPa	40000 kPa
M	1.60	1.45	1.35
λd	0.44	0.44	0.44
κs	0.06	0.024	0.001
erefd	4.37	4.37	4.37
Δei	1.50	2.25	2.65
ζ	1.8	0.5	0.1
dv	0.15	0.01	0.001
ds	10	10	30
pc0	50 kPa	200 kPa	1800 kPa
pbi	50 kPa	100 kPa	650 kPa

Table 3: Material properties of Bangkok Clay with different cement content.
Material property	Aw = 5%	Aw = 10%	Aw = 15%
G	14000 kPa	16000 kPa	30000 kPa
M	1.13	1.13	1.13
λd	0.26	0.26	0.26
κs	0.02	0.01	0.005
erefd	2.86	2.86	2.86
Δei	0.55	0.60	0.75
ζ	1.5	0.2	0.1
dv	0.02	0.01	0.01
ds	10	30	30
pc0	150 kPa	430 kPa	600 kPa
pbi	60 kPa	400 kPa	500 kPa

Constraints and Loads

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The left boundary is the axis of symmetry, a roller condition is applied at the lower boundary, and a boundary load is applied on the right and upper boundaries.

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The magnitude of the boundary load is different for different clays in order to cover an appropriate range of loading.

In order to reproduce the numerical and experimental results of Ref. 1, the load is controlled in a parameter continuation sweep.

Results and Discussion

Figure 2 reproduces the characteristic curves showing the Normal Compression Line (NCL) and the Swelling Line (or Initial Loading Line) of Osaka clay. The results match very closely with the numerical results given in Ref. 1. Unlike the case for the Modified Cam-Clay model, the NCL obtained with the MSCC model is not a straight line. The clay behavior is elastic on the initial loading line; on the NCL, the clay deforms elastoplastically. The dashed line is an Intrinsic Compression Line (ICL) for destructured clay, which has a slope defined by the compression index, λd. At p = pref on the normal compression line, the void ratio is e = erefd.

Figure 2: Void ratio as a function of the logarithm of the pressure in an isotropic compression test for Osaka clay.

The void ratio versus the logarithm of the pressure characteristics for Marl clay is shown in Figure 3. The results match very closely with numerical results given in Ref. 1. The initial loading line of Marl clay crosses the ICL approximately at p = 20 kPa and e = 0.587 in the reference, and at p = 20.5 kPa and e = 0.594 in the COMSOL Multiphysics solution.

Figure 3: Void ratio as a function of the logarithm of the pressure in an isotropic compression test for Marl clay.

The void ratio versus the logarithm of the pressure characteristics for Ariake clay with different cement contents are shown in Figure 4, replicating a similar behavior as observed in Ref. 1. As the cement content increases, the difference between the ICL of destructured clay and the NCL of structured clay increases drastically, indicating the need for a sophisticated material model like MSCC for structured clays. A similar observation can be noted for Bangkok clay, see Figure 5.

However, for Bangkok clay there is one notable difference between the results presented in Ref. 1 and those obtained in COMSOL Multiphysics. The void ratio in the elastic region (including at initial consolidation pressure) increases in COMSOL Multiphysics when the cement content (Aw) is changed from 10% to 15%, as opposed to the results presented in Ref. 1. In Ref. 1, the void ratio at initial consolidation pressure (erefc0) decreases with an increase in the cement content. However, the results obtained in COMSOL Multiphysics can be verified analytically.

The void ratio at initial consolidation pressure (erefc0) is given by

(1)

Based on material properties given in Table 3, the void ratio at the initial consolidation pressure (erefc0) is 2.1072, 1.8834, and 1.9467 for Bangkok clay with a cement content (Aw) of 5%, 10%, and 15%, respectively. The COMSOL Multiphysics results matches these values at p = pc0 exactly, indicating their correctness.

Figure 4: Void ratio as a function of the logarithm of the pressure in an isotropic compression test for Ariake clay with different cement content.

Figure 5: Void ratio as a function of the logarithm of the pressure in an isotropic compression test for Bangkok clay with different cement content.

Notes About the COMSOL Implementation

Note that the log operator used in the definition of the void ratio is implemented in base “e” and not in base “10”.

Reference

1. J. Suebsuk, S. Horpibulsuk, and M.D. Liu, “Modified Structured Cam Clay: A Generalized Critical State Model for Destructured, Naturally Structured and Artificially Structured Clays,” Computer and Geotechnics, vol. 37, pp. 956–968, 2010.

Geomechanics_Module/Verification_Examples/isotropic_compression_mscc

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select > .

Click .

Click

In the tree, select > .

Click

The four different structured clays are analyzed in this model using a parametric switch option. Eight different nodes are created to model the eight different clay materials shown in Table 1, Table 2, and Table 3.

Load the material properties from different text files for each parameter case.

Global Definitions

Clay Material Properties

In the window, under click .

In the window for , type Clay Material Properties in the text field.

Locate the section. Click

Browse to the model’s Application Libraries folder and double-click the file isotropic_compression_mscc_osaka_parameters.txt.

In the toolbar, click

In the window for , type Natural Osaka Clay in the text field.

In the toolbar, click

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file isotropic_compression_mscc_marl_parameters.txt.

In the text field, type Natural Marl Clay.

In the toolbar, click

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file isotropic_compression_mscc_ariake_Aw6_parameters.txt.

In the text field, type Cemented Ariake Clay, Aw = 6%.

In the toolbar, click

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file isotropic_compression_mscc_ariake_Aw9_parameters.txt.

In the text field, type Cemented Ariake Clay, Aw = 9%.

In the toolbar, click

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file isotropic_compression_mscc_ariake_Aw18_parameters.txt.

In the text field, type Cemented Ariake Clay, Aw = 18%.

In the toolbar, click

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file isotropic_compression_mscc_bangkok_Aw5_parameters.txt.

In the text field, type Cemented Bangkok Clay, Aw = 5%.

In the toolbar, click

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file isotropic_compression_mscc_bangkok_Aw10_parameters.txt.

In the text field, type Cemented Bangkok Clay, Aw = 10%.

In the toolbar, click

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file isotropic_compression_mscc_bangkok_Aw15_parameters.txt.

In the text field, type Cemented Bangkok Clay, Aw = 15%.

Parameters 2

In the toolbar, click

and choose > .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
para	0	0	Parameter

Create an interpolation function to define the boundary load.

Boundary Load

In the toolbar, click

and choose > .

In the window for , type Boundary Load in the text field.

Locate the section. In the text field, type Pressure.

In the table, enter the following settings:


t	f(t)
0	0.01*p0
1	10*p0
2	50*p0

Geometry 1

Rectangle 1 (r1)

In the toolbar, click

In the window for , locate the section.

In the text field, type 5[cm].

In the text field, type 10[cm].

Click

Materials

Clay Material

In the window, under right-click and choose .

In the window for , type Clay Material in the text field.

Solid Mechanics (solid)

Elastoplastic Soil Material 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

Find the subsection. From the C(ν,G) list, choose .

From the Γ(θ) list, choose .

From the εfp,dev list, choose . In the associated text field, type 0.1.

From the e0 list, choose .

In the pref text field, type 1[kPa].

In the pc0 text field, type Pc0.

To get better convergence, the number of local iterations and tolerance of the plasticity algorithm needs to be adjusted.

Click the

button in the toolbar.

In the dialog, in the tree, select the checkbox for the node > .

Click .

In the window for , click to expand the section.

From the list, choose .

In the text field, type 50.

In the text field, type 1e-8.

Boundary Load 1

In the toolbar, click

and choose .

Select Boundaries 3 and 4 only.

In the window for , locate the section.

From the list, choose .

In the p text field, type Pressure(para).

Roller 1

In the toolbar, click

and choose .

Select Boundary 2 only.

Materials

Clay Material (mat1)

In the window, under > click .

In the window for , locate the section.

In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Shear modulus	G	GG	N/m²	Critical state model
Slope of critical state line	M	MM	rad	Critical state model
Density	rho	Rho	kg/m³	Basic
Swelling index for structured clay	kappaSwelling0	kappas	1	Modified structured Cam-clay
Compression index for destructured clay	lambdaCompd	lambdas	1	Modified structured Cam-clay
Void ratio at reference pressure for destructured clay	evoidrefd	ee	1	Modified structured Cam-clay
Destructuring index for volumetric deformation	dv	dvs	1	Modified structured Cam-clay
Destructuring index for shear deformation	ds	dss	1	Modified structured Cam-clay
Additional void ratio at preconsolidation pressure	Deltaec0	deltae	1	Modified structured Cam-clay
Initial structure strength	pb0	Pbi	Pa	Modified structured Cam-clay
Plastic potential shape parameter	zeta	zetas	1	Modified structured Cam-clay