COMSOL 6.4 - Wetting and Drying Paths for Partially Saturated Soil with the Extended Barcelona Basic Model

Wetting and Drying Paths for Partially Saturated Soil with the Extended Barcelona Basic Model

Soil wetting and drying experiments under cyclic loading are performed to understand the behavior of partially saturated soils. Mechanical and hydraulic loads, or a combination of both, affect the behavior of partially saturated soils, making their study much more complex than that of fully saturated soils. The Barcelona Basic Model is one of the most popular models used to understand the complex behavior of partially saturated soils.

In this example, the Extended Barcelona Basic model (BBMx) is examined for the cases presented in Ref. 1 and Ref. 2. With a certain choice of material parameters, the BBMx model can predict the soil behavior that qualitatively matches the results presented in the references. The model can also predict the collapse of the soil sample during wetting processes, which is an important case for unsaturated sands and clays.

Model Definition

In this example, a 10 cm cubic soil sample is subjected to isotropic compression and suction. The soil specimen is modeled using the extended Barcelona Basic Model.

Material Properties

The material properties are based on Ref. 1, and are given in Table 1.

Table 1: Material properties for the soil model.
Property	Variable	Value
Shear modulus	G	10 MPa
Density	ρ	2400 kg/m3
Swelling index	κ	0.02
Swelling index for changes in suction	κs	0.008
Compression index at saturation	λ	0.2
Compression index for changes in suction	λs	0.08
Angle of internal friction		25.4°
Weight parameter	w	0.75
Soil stiffness parameter	m	0.5 MPa
Plastic potential smoothing parameter	bs	100
Tension to suction ratio	ks	0.6
Initial yield value for suction	sy	0.3 MPa
Void ratio at reference pressure and saturation	eref0	0.9
Reference pressure	pref	0.1 MPa
Initial consolidation pressure	pc0	0.2 MPa

Constraints and Loads

•

Roller conditions are applied on three perpendicular surfaces.

•

For modeling isotropic compression, a normal displacement is applied on the three remaining mutually perpendicular surfaces using an interpolation function.

•

The initial and current suction in the soil sample is parameterized using an interpolation function.

Results and Discussion

The results from the wetting (decreasing suction) experiment are given in Figure 1.

Figure 1: Wetting paths: Specific volume as a function of mean stress in an isotropic compression test.

For the wetting path ABDF, from A to B a volumetric elastic expansion happens because of the decrease in suction (0.2 MPa to 0) with constant mean stress. With zero suction, the soil reaches a fully saturated condition and the BBMx model becomes equivalent to a conventional critical state model. The predicted behavior along the path BDF (zero suction and increasing mean stress) is similar to the results predicted by the Modified Cam-Clay model. For the wetting path ACDF, the wetting path CD (reduction in suction) takes place after isotropic compression given by the path AC. At this point, the soil sample has undergone plastic deformations, which causes small net volumetric compression. The elastic volumetric expansion due to a decrease in suction is smaller than the plastic volumetric compression, which causes a net volumetric compression and the collapse of the soil. After collapse, the soil follows the unique path DF for saturated soils. For the wetting path ACEF, after isotropic compression ACE, the wetting path EF takes place at a larger confining mean stress, which causes a larger collapse.

The results from the drying (increasing suction) experiment are given in Figure 2.

Figure 2: Drying paths: Specific volume as a function of mean stress in an isotropic compression test.

For the drying path BFE, from B to F the predicted behavior (zero suction and increasing mean stress) is similar to that predicted by the Modified Cam-Clay model. For the drying path FE (suction increases from 0 to 0.2 MPa) a slight volumetric compression takes place. For the drying path BAE, an initial increase in suction with a constant mean stress (path BA) in the elastic region gives a total volumetric compression. For the drying path BGHE, an initial increase in suction with a constant mean stress (path BG) in the elastic region gives a total volumetric compression. Path GH consists of isotropic compression with constant suction, followed by a drying path HE where the increase in suction while keeping the mean applied stress constant gives a slight volumetric compression (not visible in Figure 2, zoom the graph in the model).

The BBMx model is based on (although not identical to) the one presented in Ref. 2, and differs from the original BBM model in Ref. 1. The results presented here matches qualitatively well with the results presented in Ref. 1 and Ref. 2. The BBMx model is also able to predict soil behavior at cyclic loading including the collapse of the soil during wetting. The behavior of partially saturated soils is sensitive to the material parameters in the BBMx model. The weight parameter, w, and the soil stiffness parameter, m, are important material parameters, which govern the soil behavior in the plastic region. Also, note that the void ratio in the material model is not an initial void ratio but a void ratio at saturation (s = 0) and reference pressure (p = pref).

The mechanical (mean stress) and hydraulic (suction) load paths are shown in Figure 3.

Figure 3: Load paths.

Notes About the COMSOL Implementation

For better convergence and a faster computation during isotropic compression, use a instead of a . A parametric displacement in the normal direction is applied on three mutually perpendicular surfaces; this displacement is driven by the interpolation function Pressure through a node.

In order to change the initial suction, current suction and the mean stress according to the load paths shown in Figure 3, different study steps are concatenated under the same study, where the initial values for the study step is taken from the previous step. The interpolation functions InitSuction, Suction, and Pressure are used with the parameter para to vary the initial suction, the current suction, and the mean stress. Table 2 indicates the range of the load parameter para for the corresponding load paths. For example, for the wetting path ACDF, para changes from 3 to 4 for the path AC; from 4 to 5 for the path CD, and from 5 to 6 for the path DF in separate stationary study steps.

Table 2: Range of parameter para for All load paths.
Load paths	Range of para
ABDF	0–2
ACDF	3–6
ACEF	7–9
BFE	10–12
BAE	13–15
BGHE	16–19

References

1. E.E. Alonso, A. Gens, and A. Josa, “A constitutive model for partially saturated soils,” Géotechnique, vol. 40, no. 3, pp. 405–430, 1991.

2. D.M.Pedroso and M.M.Farias, “Extended Barcelona Basic Model for unsaturated soils under cyclic loadings,” Comput. Geotech., vol. 38, pp. 731–740, 2011.

Geomechanics_Module/Verification_Examples/wetting_and_drying_of_unsaturated_soil

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

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
para	0	0	Parameter

Create interpolation functions for the initial suction, the current suction, and the mean stress. Load the interpolation functions from a file.

Initial Suction Paths

In the toolbar, click

and choose > .

In the window for , locate the section.

In the text field, type InitSuction.

In the text field, type Initial Suction Paths.

Locate the section. Click

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

Locate the section. In the table, enter the following settings:


Argument	Unit
t	1

In the table, enter the following settings:


Function	Unit
InitSuction	MPa

Note that to avoid numerical problems, instead of zero suction, a value of 1 Pa is used.

Suction Paths

In the toolbar, click

and choose > .

In the window for , locate the section.

In the text field, type Suction.

In the text field, type Suction Paths.

Locate the section. Click

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

Locate the section. In the table, enter the following settings:


Argument	Unit
t	1

In the table, enter the following settings:


Function	Unit
Suction	MPa

Mean Stress Paths

In the toolbar, click

and choose > .

In the window for , locate the section.

In the text field, type Pressure.

In the text field, type Mean Stress Paths.

Locate the section. Click

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

Locate the section. In the table, enter the following settings:


Argument	Unit
t	1

In the table, enter the following settings:


Function	Unit
Pressure	MPa

Geometry 1

Block 1 (blk1)

In the toolbar, click

In the window for , locate the section.

In the text field, type 10[cm].

Click

Create a nonlocal integration coupling with a point selection for use in the interface that you will add shortly.

Definitions

Integration 1 (intop1)

In the toolbar, click

and choose .

Click the

button in the toolbar.

In the window for , locate the section.

From the list, choose .

Select Point 8 only.

This is the intersection point between the three perpendicular surfaces where the is applied.

Materials

Soil Material

In the window, under right-click and choose .

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

Solid Mechanics (solid)

Elastoplastic Soil Material 1

In the toolbar, click

and choose .

Select Domain 1 only.

In the window for , 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 e0 list, choose .

In the s0 text field, type InitSuction(para).

In the s text field, type Suction(para).

In the pref text field, type 0.1[MPa].

In the pc0 text field, type 0.2[MPa].

Enter the material data given in the model documentation.

Materials

Soil 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	10[MPa]	N/m²	Critical state model
Friction angle	internalphi	25.4[deg]	rad	Critical state model
Density	rho	2400[kg/m^3]	kg/m³	Basic
Swelling index at saturation	kappaSwelling0	0.02	1	Barcelona Basic
Swelling index for changes in suction	kappaSwellingsu	0.008	1	Barcelona Basic
Compression index at saturation	lambdaComp0	0.2	1	Barcelona Basic
Compression index for changes in suction	lambdaCompsu	0.08	1	Barcelona Basic
Weight parameter	wb	0.75	1	Barcelona Basic
Soil stiffness parameter	mb	0.5[MPa]	Pa	Barcelona Basic
Plastic potential smoothing parameter	bb	100	1	Barcelona Basic
Tension to suction ratio	kb	0.6	1	Barcelona Basic
Initial yield value for suction	sy0	0.3[MPa]	Pa	Barcelona Basic
Void ratio at reference pressure and saturation	evoidref0	0.9	1	Barcelona Basic

Solid Mechanics (solid)

Roller 1

In the toolbar, click

and choose .

Select Boundaries 1–3 only.

Prescribed Displacement 1

In the toolbar, click

and choose .

Select Boundaries 4–6 only.

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

In the u 0 n text field, type -disp.

Now add a for the normal displacement, so that the mean stress equals the prescribed one. For that, you need to show equation-based contributions.

Click the

button in the toolbar.

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

Click .

Global Equations 1 (ODE1)

In the toolbar, click

and choose .

Multiply the equation by a suitable penalty factor in order to strictly satisfy this criterion. For the current model, 1e5 is an appropriate penalty factor.

In the window for , locate the section.

In the table, enter the following settings:


Name	f(u,ut,utt,t) (1)	Initial value (u_0) (1)	Initial value (ut_0) (1/s)	Description
disp	(intop1(solid.pm)-Pressure(para))*1e5	0	0

Locate the section. Click

In the dialog, type disp in the text field.

In the tree, select > .

Click .

In the window for , locate the section.

Click

In the dialog, type pressure in the text field.

In the tree, select > .

Click .

Mesh 1

Mapped 1

In the toolbar, click

and choose .

Select Boundary 4 only.

Distribution 1

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the text field, type 1.

Swept 1

In the toolbar, click

Distribution 1

Right-click and choose .

In the window for , locate the section.

In the text field, type 1.

Click

Add a separate node for each wetting and drying path. In order to change the suction and the mean stress according to the load path, different stationary study steps are used under the same study. The initial values for the subsequent study step is taken from the previous study step.

The interpolation functions and are used with the para parameter to vary the suction and the mean stress. The appropriate parameter range for each study step is provided in Table 2.

Study: Wetting Path ABDF

In the window, click .