Zheng 2013-Numerical Modeling of Wetting-Induced Settlement of Embankments

Numerical Modeling of Wetting-Induced Settlement of Embankments

Yewei Zheng1, S.M. ASCE, Kianoosh Hatami2, M. ASCE, P.Eng. and Gerald A. Miller3, M. ASCE, P.E.

1Graduate Research Assistant, School of Civil Engineering and Environmental Science, University of

Oklahoma, 202 West Boyd Street, Room 334, Norman, OK 73019; [email protected] 2(Corresponding Author) Associate Professor, School of Civil Engineering and Environmental Science,

University of Oklahoma, 202 West Boyd Street, Room 334, Norman, OK 73019; [email protected] 3Professor, School of Civil Engineering and Environmental Science, University of Oklahoma, 202 West

Boyd Street, Room 334, Norman, OK 73019; [email protected] ABSTRACT: Compacted fills of embankments are typically in an unsaturated state. Water infiltration can weaken the embankments, resulting in excessive deformations and/or embankment slope failure. In this study, the Barcelona Basic Model (BBM) was implemented in the computer program FLAC (2D) to simulate the behavior of unsaturated soils. The BBM implementation in FLAC was verified using analytical results available in the literature. The verified BBM model in FLAC was then used to simulate the wetting-induced response of an example unsaturated embankment due to complete saturation as a worst-case scenario for the embankment design. It is shown that the magnitudes of wetting-induced deformations in the embankment could result in measurable amount of differential settlement in the embankment and even embankment slope failure. INTRODUCTION Wetting-induced collapse settlement of embankments is a pervasive problem around the world that leads to costly damages to infrastructure facilities including roadways and bridges (e.g. the bridge approach slabs and parapet walls, distresses in the pavement and embankment slope failure). Consequences of embankment collapse settlement problems cost the taxpayers hundreds of millions of dollars annually in repair and reconstruction of failed slopes and facilities.

333Geo-Congress 2013 © ASCE 2013

Geo-Congress 2013

Dow

nloa

ded

from

asc

elib

rary

.org

by

Que

en's

Uni

vers

ity L

ibra

ries

on

05/0

4/13

. Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

Lawton et al. (1992) determined that nearly all types of compacted soils can be susceptible to collapse under proper conditions. The compacted fills of embankments are typically in an unsaturated state. The wetting process of the embankment fill due to water infiltration can occur as a result of rising of water table, rainfall and/or flooding, resulting in wetting-induced deformations of embankments. In this paper, the Barcelona Basic Model (BBM) is used as a constitutive model to simulate the collapse behavior of unsaturated soils. The BBM is implemented in the finite difference computer program FLAC (Itasca 2005) and is verified against published analytical results. The wetting-induced response of an example unsaturated embankment is then simulated using the verified BBM model in FLAC and the results are discussed. IMPLEMENTATION OF BARCELONA BASIC MODEL (BBM) IN FLAC The Barcelona Basic Model (BBM) proposed by Alonso et al. (1990) is a constitutive model for unsaturated soils. It is an extension of the Modified Cam-Clay (MCC) model to include the influence of soil suction on its stiffness and strength.

The BBM includes two independent stress variables: the net normal stress (σ-ua) and suction (ua-uw), where σ is the total stress, ua is the pore-air pressure, and uw is the pore-water pressure. The implementation of BBM in FLAC is subject to certain assumptions: the pore-air pressure is assumed to remain constant and equal to zero, which is true for most practical engineering problems. Therefore, the net normal stress is expressed as the total stress, and the soil suction is a variable that influences the soil stiffness and strength.

In the BBM, both the net normal stress and suction can induce strain in the soil. The incremental strains induced by the net normal stress are divided into two components: elastic strain (dε e) and plastic strain (dε p). On the other hand, incremental strains due to loss of suction (dε s) are volumetric elastic strains which are induced as a result of wetting. Hence, the total strain increment (dε) in the soil can be written as:

e p sd d d dε ε ε ε= + + (1)

Details of each strain component are described in the following sections.

Stress-Induced Elastic Strain The volumetric and deviatoric elastic strain increments due to net stress are respectively defined as:


Geo-Congress 2013

Dow

nloa

ded

from

asc

elib

rary

.org

by

Que

en's

Uni

vers

ity L

ibra

ries

on

05/0

4/13

. Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

1evd dp

Kε = (2)

1

3eqd dq

Gε = (3)

where K and G are the soil bulk modulus and shear modulus, respectively.

Stress-Induced Plastic Strain The yield surface in the p - q plane, f, is defined as:

2 20( )( ) 0sf q M p p p p= − + − = (4)

where

sp ks= (5)

*[ (0) ]/[ ( ) ]0 0( ) s

c c

p p

p pλ κ λ κ− −= (6)

( ) (0)[(1 )exp( ) ]s r s rλ λ β= − − + (7)

In equations 4 through 7, p and q are net mean stress and deviatoric stress, respectively, M is the slope of the critical state line, s is the matric suction, ps is the soil cohesion at suction s, po is the preconsolidation pressure at suction s, p*

o is the preconsolidation pressure for saturated condition, pc is a reference pressure, λ(0) is the slope of the normally consolidated line (NCL) for saturated condition, λ(s) is the slope of the NCL at suction s, κ is the slope of the swelling line, and r and β are parameters that control the soil stiffness as a result of change in suction.

In the BBM used in this study, an associate flow rule was used to calculate the plastic volumetric strain increment (dεv

p). Once the yielding occurs, the evolution of the preconsolidation pressure is controlled by a hardening law defined as:

*0

*0

1

(0)p

v

dp ed

pε

λ κ+=

− (8)


Geo-Congress 2013

Dow

nloa

ded

from

asc

elib

rary

.org

by

Que

en's

Uni

vers

ity L

ibra

ries

on

05/0

4/13

. Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

Suction-Induced Strain

In a wetting-induced deformation problem, the wetting path is in fact a suction unloading process. At any point during the analysis, the current suction value is assumed to be smaller than or equal to the maximum suction s0 ever experienced by the soil in the past. Hence, the soil remains in the elastic region in the p - s plane during the course of wetting. Rutqvist et al. (2011) determined the suction-induced strain by adding an equivalent mean stress increment to the net mean stress. This method was adopted in this study to determine suction-induced strains in the BBM.

The suction-induced volumetric strain is calculated as (Rutqvist et al. 2011):

1sv s

d dsK

ε = (9)

where Ks is the equivalent suction bulk modulus defined as:

(1 )( )s atm

s

e s pK

κ+ += (10)

in which patm is the atmospheric pressure and κs is a compressibility parameter related to the suction-induced elastic strain. The equivalent mean stress increment is:

s sv s

Kdp Kd ds

Kε= = (11)

The equations for suction-induced volumetric strain were implemented in FLAC through computational subroutines by adding the equivalent mean stress increment dp s to normal stresses σxx, σyy and σzz. VERIFICATION OF THE BBM IN FLAC The BBM implementation in FLAC was verified against the data from the published literature. In studying wetting-induced deformation problems, the wetting paths are the primary focus of the analysis. Alonso et al. (1990) reported three well-defined wetting paths AB (1), CD (2) and EF (3) in a BBM model prediction case study (Case 1) as shown in Figure 1. An ideal reference soil was subjected to isotropic compression in a triaxial stress space in Case 1. All three stress paths shown start from Point A which represents an initial net mean stress p = 0.15 MPa and suction s = 0.2 MPa. The wetting processes take place at three different confining pressures: 0.15, 0.35 and 0.6 MPa, resulting in wetting-induced volumetric deformation in the soil.


Geo-Congress 2013

Dow

nloa

ded

from

asc

elib

rary

.org

by

Que

en's

Uni

vers

ity L

ibra

ries

on

05/0

4/13

. Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

Model parameters of the reference soil as reported by Alonso et al. (1990) are summarized in Table 1. An axisymmetric single element model was used to simulate the triaxial tests on the soil. The isotropic compressive loading was simulated in a strain-controlled condition in all directions. The wetting path was simulated by decreasing the soil suction from 0.2 MPa to zero at constant net mean stress.

Net Mean Stress (MPa)

0.1 0.2 0.3 0.4 0.5 0.6 0.7

Su

ctio

n (

MP

a)

0.00

0.05

0.10

0.15

0.20

0.25

A

B FD

C E

1 32

FIG. 1. Stress Paths in Case 1 Reported by Alonso et al. (1990)

Net Mean Stress (MPa)

0.1 0.2 0.3 0.4 0.5 0.6 0.7

Sp

ecif

ic V

ou

lme

1.6

1.7

1.8

1.9

2.0

FLAC ResultsAlonso et al. (1990)

A

B

ED

F

C2,3

12 3

1,2 3

1

FIG. 2. Comparison of Predicted FLAC Results with the Analytical Results Reported by Alonso et al. (1990)

Figure 2 shows an overall satisfactory agreement between the predicted FLAC

results and Alonso’s analytical data (BBM) with respect to both magnitudes and trends. However, the FLAC results slightly overpredict the collapse volumetric deformation. Results in Figure 2 also indicate that some swelling occurs as a result of wetting at low


Geo-Congress 2013

Dow

nloa

ded

from

asc

elib

rary

.org

by

Que

en's

Uni

vers

ity L

ibra

ries

on

05/0

4/13

. Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

stress levels whereas collapse occurs at higher stress levels.

TABLE 1. BBM Model Parameters used in FLAC Simulations

Model Parameters

G (MPa)

M λ κ p0

*

(MPa) κs k r

β (MPa-1)

RSa 10 1 0.2 0.02 0.2 0.008 0.6 0.75 12.5 CKb 3.3 0.82 0.14 0.015 0.055 0.01 1.24 0.26 16.4

a RS: Reference soil (Alonso et al. 1990) used for model verification b CK: Compacted kaolin (Josa et al. 1988) used in numerical example NUMERICAL EXAMPLE After the implementation of the BBM in FLAC was verified, the model was used to study wetting-induced deformations of an example embankment model. A compacted kaolin soil with well-documented properties (Josa 1988) was selected as the compacted fill of the example embankment. The compacted kaolin was low to moderately plastic (wP = 26.9%, wL = 38.7%; USCS Classification: ML). The BBM model parameters for the compacted kaolin were calibrated by Alonso et al. (1990) as summarized in Table 1. Model Grid, Boundary Conditions and Modeling Procedure The example embankment was 10 m high with a 1V:2H slope. The foundation soil was assumed to be the same as the embankment fill with a thickness of 5 m in a saturated condition. Figure 3 shows the finite difference grid of the embankment geometry in the example. The side boundaries of the model were fixed in the horizontal direction but allowed for vertical displacement of the embankment. The bottom boundary was fixed in both horizontal and vertical directions.

The embankment soil was modeled using the BBM with an initial suction value of 200 kPa for which the soil at the foundation level of the embankment was slightly overconsolidated. A Mohr-Coulomb model was used for the foundation soil with a saturated friction angle of 21.1°. In the first stage of analysis, the foundation soil was brought to equilibrium under gravitational stresses. The 10 m embankment fill with an initial suction value of 200 kPa was then constructed on the foundation soil by 5 lifts and the deformations of the entire model under gravity loading were calculated. Finally, the wetting-induced deformation of the embankment was calculated by decreasing the soil suction to zero to represent a completely saturated condition as the worst-case scenario for the embankment design.


Geo-Congress 2013

Dow

nloa

ded

from

asc

elib

rary

.org

by

Que

en's

Uni

vers

ity L

ibra

ries

on

05/0

4/13

. Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

FIG. 3. Finite Difference (FLAC) Grid of the Example Embankment-Foundation Model

Results and Discussion

Figures 4 and 5 show displacement vectors in the embankment-foundation model at equilibriums under self-weight loading and full saturation stages, respectively. Under self-weight loading, the settlement at the top of the embankment at its centerline is 51 mm. After the embankment becomes fully saturated, the settlement at the top (centerline) reaches 154 mm. The wetting-induced deformation in this paper is defined as the deformation due to wetting beyond the magnitude attained after self-weight equilibrium. Hence, the predicted wetting-induced settlement at the top of the embankment at its centerline is 103 mm. Results in Figure 5 indicate that not only the magnitudes of the displacement vectors increase as a result of wetting, but also the displacement vectors of the embankment slope tend to move outward. The horizontal displacement at the toe of the embankment slope reaches 64 mm as compared to a mere 10 mm under self-weight loading. Excessive lateral deformation of the slope could result in slope failure. In the example shown in Figure 5, the wetting-induced horizontal displacement of the embankment slope is fairly large, which indicates a high probability of embankment slope failure.

FIG. 4. Displacement Vectors in the Embankment under Self-Weight Load (m)


Geo-Congress 2013

Dow

nloa

ded

from

asc

elib

rary

.org

by

Que

en's

Uni

vers

ity L

ibra

ries

on

05/0

4/13

. Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

FIG. 5. Displacement Vectors in the Embankment after Full Saturation (m)

Figure 6 shows velocity vectors and a contour map of shear strain rates within the embankment following full saturation. The velocity vectors in the embankment also indicate the tendency of the slope to move outward. The magnitudes of shear strain rate within the embankment show a coalescing potential slip surface, which together with a zone of larger strains at the top of the embankment, indicates that the embankment slope is on the verge of failure.

FIG. 6. Shear Strain Rate and Velocity Vectors in the Embankment after Full Saturation

Figure 7 shows the settlement of the embankment at the top at different stages of the analysis. The embankment surface at the center settles approximately 50 mm under self-weight loading. After the embankment becomes fully saturated, the settlement reaches approximately 150 mm. The magnitude of the wetting-induced settlement of the embankment surface is hence approximately 100 mm. Results in Figure 7 also indicate that after complete saturation of the embankment, the settlement of the embankment surface at its centerline is approximately 50 mm larger than that at the edge, resulting in a measurable amount of differential settlement at the top of the embankment fill. This amount of differential settlement at the top of the embankment could lead to significant damages to the structures and pavements constructed on the embankment.


Geo-Congress 2013

Dow

nloa

ded

from

asc

elib

rary

.org

by

Que

en's

Uni

vers

ity L

ibra

ries

on

05/0

4/13

. Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

Distance to Embankment Centerline (m)

0 2 4 6 8 10

Set

tlem

ent

(mm

)

0

50

100

150

200

250

300

Self-WeightWetting-InducedFull Saturation

FIG. 7. Settlement of the Embankment Surface

Settlement (mm)

0 100 200 300 400

Em

ban

kmen

t H

eig

ht

(m)

0

2

4

6

8

10

Self-WeightWetting-InducedFull Saturation

FIG. 8. Settlement of the Embankment Centerline along Height

Figure 8 shows the settlement of the embankment centerline along its height at different stages of the analysis. These results suggest that the maximum values of the fully-saturated and self-weight settlement in the embankment both occur at approximately 6 m above the foundation level. In addition, the magnitude of wetting-induced settlement increases significantly over the bottom 6 m of the embankment but stays essentially constant along the remaining top portion of the embankment (only 5 mm of reduction in magnitude over the top 4 m as compared to the maximum value). A typical characteristic of unsaturated soils when subjected to wetting is that they exhibit swelling behavior at low stress levels and collapse at high stress levels. The magnitude of the net mean stress at 6 m above the foundation level approximately equals to the preconsolidation pressure of the soil in saturated condition


Geo-Congress 2013

Dow

nloa

ded

from

asc

elib

rary

.org

by

Que

en's

Uni

vers

ity L

ibra

ries

on

05/0

4/13

. Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

as shown in Table 1. In the elastic region, the soil experiences swelling with relatively small deformations whereas the collapse settlement occurs in the soil at higher overburden pressures after yielding occurs. CONCLUSIONS The Barcelona Basic Model (BBM) describing the elasto-plastic behavior of unsaturated soils was implemented in FLAC and was verified against analytical results reported in the literature. The implemented BBM in FLAC showed a promising capability for use in studying the behavior of unsaturated soils subjected to wetting.

The verified BBM model was used to study the wetting-induced response of an example embankment constructed using a clayey soil. A fully saturated condition was assumed as a worst-case scenario for embankment design. The results showed that the top surface of a 10 m-high embankment could settle by approximately 100 mm after full saturation. In addition, wetting-induced deformation could also result in a measurable amount of differential settlement in the embankment fill due to larger net mean stresses toward the center of the embankment. This differential settlement could lead to significant damage in the structures and pavements constructed on the embankment. Furthermore, it was shown that excessive horizontal deformation at the toe as a result of wetting could lead to slope failure in the embankment. REFERENCES Alonso, E. E., Gens, A. and Josa, A. (1990). “A constitutive model for partially

saturated soils.” Geotechnique, Vol. 40 (3): 405-430. Itasca Consulting Group, Inc. (2005). “Fast Lagrangian Analysis of Continua (2D)

Version 5.0.” Itasca Consulting Group, Inc., Minneapolis. Josa, A. (1988). Un modelo eslastoplastico para suelos no saturados. Ph.D. Thesis,

Universitat Politencnica de Catalunya, Barcelona. Lawton, E. C., Fragaszy, R. J. and Hetherington, M. D. (1992). “Review of

wetting-induced collapse in compacted soil.” Journal of Geotechnical Engineering, Vol. 118 (9): 1376-1394.

Rutqvist, J., Ijiri, Y. and Yamamoto, H. (2011). “Implementation of the Barcelona Basic Model into TOUGH-FLAC for simulations of the geomechanical behavior of unsaturated soils.” Computers & Geosciences, Vol. 37: 751-762.


Geo-Congress 2013

Dow

nloa

ded

from

asc

elib

rary

.org

by

Que

en's

Uni

vers

ity L

ibra

ries

on

05/0

4/13

. Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

Zheng 2013-Numerical Modeling of Wetting-Induced Settlement of Embankments

Documents

Transcript of Zheng 2013-Numerical Modeling of Wetting-Induced Settlement of Embankments