deformation and strength of embankments on soft dutch soil

Proceedings of the Institution of Civil Engineers

http://dx.doi.org/10.1680/geng.9.00086

Paper 900086

Received 12/11/2009 Accepted 09/02/2011

Keywords: computational mechanics/embankments/failures

ICE Publishing: All rights reserved

Geotechnical Engineering

Deformation and strength of embankmentson soft Dutch soilDen Haan and Feddema

Deformation and strength ofembankments on soft Dutch soilj1 Evert den Haan PhD

Geotechnical Researcher, Deltares, Delft, The Netherlandsj2 Antoine Feddema BEng

Senior Consultant/Manager, Deltares, Delft, The Netherlands

j1 j2

Embankment and dyke stability in the Netherlands has always been evaluated by effective stress analysis. The

subsoil of most of these structures is organic, weak and soft, but the internal friction angle of these soils is

surprisingly high. Empirical methods are used to obtain acceptable, reduced values of friction angle from triaxial tests

for use in stability analyses. It appears possible, however, to do full justice to the peculiar combination of low

strength and stiffness and high friction angle by means of the finite-element method using a viscous version of the

Cam-clay model. All parameters of the model are found from a single test in a constant-rate-of-strain K0 oedometer.

The approach is illustrated by two case histories, after first providing insight into the peculiar properties of the Dutch

soils, and the manner in which they are dealt with.

NotationCÆ creep factor

c9 cohesion

e voids ratio

h height

h0 initial height

K0 lateral earth pressure at rest

K0,nc virgin compression value of K0

k permeability

M critical-state strength parameter

p9 isotropic effective stress

p9c0 initial equivalent yield stress

p9eq equivalent isotropic effective stress

p90 initial value of equivalent stress

q deviatoric stress

su undrained strength

su=� 9p undrained strength ratio

t time

tage age of deposit

tcreep creep duration

�nat natural strain

�vol volumetric strain

k* cam-clay swelling factor

º* cam-clay compressibility factor

�* creep factor

� Poisson ratio

� 9ax axial effective stress

� 9p vertical yield stress

� 9rad radial effective stress

� 9v0 initial vertical effective stress

�9 internal friction angle

1. IntroductionDutch organic soils and peat, although weak and soft, have

surprisingly high values of the effective strength parameters and

undrained strength ratios. Their internal friction angles, �9, can

far exceed the 30–358 range that is common in sands, and

generally become higher as the organic content increases. For

example, peat has �9 values of up to 908, and in organic clays

values of 40–608 are common. �9 is an important parameter in

the Netherlands, as the effective stress approach is used almost

exclusively in stability analyses. To obtain reasonable factors of

safety, �9 is determined at strains far below failure, and the true

strength of the material is not accounted for. For a realistic

assessment it is necessary to combine (low) stiffness and (high)

strength parameters in one analysis, and the finite-element

method is the obvious means to achieve this.

Good results have recently been obtained with finite-element

calculations of the deformation of embankments constructed on

soft Dutch soils. This will be illustrated by two case histories.

The constitutive model used was a viscous version of the

modified Cam-clay model. The necessary soil stiffness and

strength parameters were determined from oedometer tests in

which a constant rate of strain was applied, and lateral stress was

measured.

The paper starts off by giving the background to the high strength

1

parameters of Dutch organic soils and peat, and the way in which

Dutch engineers have dealt with this in the past. Then the

constitutive model and the parameter determination are described.

Finally the two case histories are presented.

2. Strength of Dutch soft soilsDutch organic soils and peat, although weak and soft, have

surprisingly high values of the effective strength parameters and

undrained strength ratios. Figure 1 shows stress paths from

undrained triaxial compression tests on samples covering a wide

range of organic contents. For comparison, test results are also

shown for a loose and a dense sand. The organic soils were

sampled below the crest and the toe of the Lek river dyke, and

were reconsolidated to the in situ stresses. The heavily com-

pressed crest samples are normally consolidated, and Table 1

provides the characteristics of these tests. The internal friction

angles �9 far exceed the 30–358 that is common in sands, and are

higher as the soil becomes softer and more organic. Peat, for

example, has values up to 908, and organic clay from 408 to 608.

The application of such values in Bishop slip circle analysis

would yield unrealistically high factors of safety, but the methods

of parameter determination developed by Dutch engineers for

their effective stress slip analyses yield much lower values. The

high triaxial strengths and the positive effect of organic content

remained largely unnoticed up to the 1990s.

The undrained strength ratios su=� 9p are also high: 0.44 and 0.40

for the organic clays in Figure 1, and rather than failing, the peat

dilates and continues to increase its shear resistance. The lightly

stressed toe material also dilates during shear and is clearly

overconsolidated.

Data for Queenborough organic clay from Jardine et al. (2003)

are included in Table 1. The values of �9 and su=� 9p are

somewhat smaller than for the Dutch organic soils, but the �9

value is also quite high.

Figure 2 plots �9 of normally consolidated organic Dutch soils

against their bulk density. Each bar in the figure is based on

numerous tests. A consistent trend exists. Bulk density correlates

n.c.

o.c.

High-organic clayLow-organic clayDense and loose sand

Peat

0

50

100

150

200

0

p�: kPa

q: k

Pa

Lateral tensionboundary

10050

Figure 1. Effective stress paths of Dutch soft soils in undrained

triaxial compression illustrating the high angle of internal friction.

(Reconsolidation to field stresses. n.c., normally consolidated

material under dyke crest; o.c., overconsolidated material adjacent

to dyke)

Bulk density: kN/m3 Water content: % �9: degrees su=� 9v0 su=� 9p

Peat 10.4 309 83 0.74 0.62a

High-organic clay 12.8 170 54 0.53 0.44a

Low-organic clay 14.7 76 44 0.49 0.40a

Queenborough clay 14.6 85 35–38 0.53 0.30–0.33

a Assuming OCR ¼ 1.2.

Table 1. Characteristics of triaxial tests on Dutch (Figure 1) and

Queenborough organic soils

2

Geotechnical Engineering Deformation and strength ofembankments on soft Dutch soilDen Haan and Feddema

to some extent with organic content, and indications of the latter

are shown. The very high �9 value of peats with organic contents

above 20% is due to the effects of fibre tensioning. The fibres in

peat are orientated predominantly in the horizontal plane, and

during triaxial compression the fibres extend and reinforce the

matrix of granular and humified organic material in which the

fibres are embedded. Landva and La Rochelle (1983) describe

this mechanism at length, and the �9 ¼ 908 condition in peat has

often been reported. It occurs when the pore pressures during

shear increase to equal the cell pressure.

Coutinho and Lacerda (1989) show similar relationships as in

Figure 2 for Brazilian (Juturnaiba) organic soil. However, the

organic content–bulk density relationship of those soils differs

from the average Dutch relationship, and points to more pre-

compression of the former.

Bulk density and water content are the mainstays of correlations

with compressibility and strength parameters in Dutch organic

soil practice. These usually suffice, and only rarely are the

organic content, degree of humification or Atterberg limits

determined. Most of the relatively uncompressed peats are fibrous

and pseudo-fibrous, whereas deep, buried peat can be amorphous.

A puzzling feature of Figure 2 is that, despite the very different

structures of peat and organic clay, the trend is quite uniform

across such a large range of organic contents. Jardine et al.

(2003) in their study of the Queenborough clay explain the

increase of the shear strength parameters by colloidal organic

material affecting the surface behaviour of clay particles.

Colloidal activity is also expected in amorphous, humified peat,

but less so in fibrous peat, and so the uniform trend in the figure

is surprising.

The current Dutch test and design methods and the evaluation of

stability are briefly discussed below, before turning to the

alternative method using finite-element calculations with param-

eters from a constant rate of strain (CRS) K0-oedometer.

3. Dutch methodsKeverling Buisman (1934) developed the Dutch cell apparatus

(Figure 3) from earlier somewhat similar devices in use by

Ehrenberg, and by Terzaghi (see also De Boer, 2005, from which

it appears that the first triaxial tests ever, by von Karman in 1910

on marble and sandstone (Vasarhelyi, 2010), went unnoticed by

the soil mechanics pioneers). The Dutch cell differs from the

triaxial apparatus mainly by the cross-section of the piston being

equal to that of the sample. Samples were 15 cm high and 6.6 cm

in diameter, and free drainage occurred through porous platens.

Radial drainage also occurred through folds in the loose-fitting

rubber membrane. The membranes were tailor-made, and in-

cluded rubber flanges that were clamped into the upper and lower

plates; corrections were made for the uplift on the sample from

the annular gap around the piston. Pore pressures were not

measured, and back-pressure was not used.

The test was performed in multiple stages, in each of which the

vertical load was increased, and the cell pressure was first allowed

to equilibrate and was then lowered by draining off droplets of

water from the cell. This increased the deviator stress and

induced shear straining, the lateral component of which caused

the cell pressure to increase gradually and to arrest the shear

strains. In older procedures the cell pressure was lowered to near

failure, but later, when large numbers of tests had to be

performed, a standard of �3 kPa was adopted. A stage was

considered complete when the rate of vertical strain had subsided

to 10 �m per hour. The horizontal strains in the sample were

quite limited, and in essence a near-K0 condition was imposed.

The c9 and �9 values that were deduced from four consecutive

stages were low, but were satisfactory in the sense that factors of

safety near 1 were obtained for dykes considered to be on the

verge of failure. Effective stress analysis was nearly always used

φ�:

deg

rees

2018161412

35%10%

0

20

40

60

80

10

Bulk density: kN/m3

From Figure 1Betuwe railway, AlblasserwaardHigh-speed railway, Rijpwetering

60% 20% Organic contents

Figure 2. Internal friction angle �9 of Dutch organic soils as

function of bulk density Figure 3. The Dutch cell apparatus

3


in embankment analysis, although a quick cell test procedure

existed in which consolidation was not allowed, and which

basically yielded undrained strength.

The cell test has now been replaced by multi-stage triaxial

testing, using isotropic consolidation and undrained shear. To

avoid the high �9 values, the stages are terminated at axial strains

between 2% and 5%, and the stress envelopes at these strains are

taken to represent failure. The exact strain value to use has

become a matter of debate, and even confusion, and Den Haan

and Kruse (2006) explain how the disturbance during preceding

stages produces increased values of c9 and reduced values of �9.

The undrained approach to strength is now being investigated as

an alternative for limit equilibrium methods. The possible merits

of the simple shear test are also under investigation, as this test

closely mimics failures in peat, which tend to follow horizontal

shear planes.

The effective stress approach and the reduced friction angles are

also used in finite-element calculations. The soft and viscous

nature of organic soils has been modelled by specialised creep

models, for example in Plaxis by the soft soil creep model

(Vermeer and Neher, 1999), and in a similar model that is

included in the Imperial College finite-element program (Bodas

Freitas, 2008). The former has led to poor matches with field

measurements of embankment deformations when using the

reduced friction angles. An alternative method of parameter

determination has been developed that seems to give much

better matches. Before discussing this, it is necessary first to

describe briefly the creep model used in the finite-element

calculations.

4. The creep model for soft viscous soilThe creep model combines modified Cam-clay (Roscoe and

Burland, 1968) with the isotache description of soil compress-

ibility (e.g. Den Haan, 1996). Figure 4 illustrates the model for

triaxial conditions, and makes use of the parameters in Table 2

for Sliedrecht peat. Figure 4(a) shows the well-known modified

Cam-clay ellipse drawn through the present (p9, q) stress state in

A, p9 being the isotropic effective stress (� 9ax=3þ 2� 9rad=3) and q

1412108642

100010010

p �eq 10: kPa (log scale)

1/2x

1/2( */ *)λ μ x

1/2( */ *)λ μ x

0

0·2

0·4

0·6

0·8

1·0

1

Volu

me

stra

in

A

B

C

ln(10) *λ

ln(10) *κ1

1

Stress decreases

1/2x

Creep ratedecreases

p �c0

Reference isotacheCreep rate */(day)μ

p �0

(b)

0

2

4

6

8

10

12

14

0p�: kPa

(a)

q: k

Pa

p �eq

M

h

v

A

Figure 4. Illustration of the finite-element creep model: (a) p9–q

plot with modified Cam-clay ellipse as plastic potential surface

through state point (A, present stress state; h, rate of volumetric

creep strain; �, rate of shear creep strain); (b) isotaches in p9–�vol

space with p9eq and �vol determining rate of volumetric creep

Depth: m-G.L. Bulk density:

kN/m3

Water content:

%

k* º* �* � M �9: degrees K0,nc OCR

2.9 10.5 500 0.05 0.29 0.027 0.2 2.39 58.6 0.29 2.8

Table 2. Characteristics of Sliedrecht peat, Betuwe railway,

km 16.7

4


the deviatoric stress (� 9ax � � 9rad). However, the ellipse is now

used as a plastic potential surface rather than as yield surface.

The outward normal at any point on the ellipse defines the

direction of the rate of change of the viscoplastic or creep strain

vector, with the horizontal component forming the volumetric

part and the vertical component forming the distortional part.

The height of the ellipse is determined by the Cam-clay M-

parameter, and the cut-off on the p9 axis is the equivalent stress

p9eq: The latter is used in the isotache graph (Figure 4(b)) to

determine the magnitude of the volumetric creep strain rate.

Isotaches are simply a collection of lines in stress–strain space

on which the rate of strain is constant. The slope of the lines,

º* ¼ ˜�vol/˜ln(p9), is similar to the Cam-clay parameter

º ¼ �˜e/˜ln(p9). The volumetric creep rate @�vol,vp/@t is con-

stant on each line. The viscoplastic nature of soil compression is

such that, at constant p9, volume decreases with time, but at an

ever-decreasing rate. This is reflected in Figure 4(b) by lower

lines having a lower rate of strain. The vertical spacing of these

lines is determined by the creep parameter �* ¼ �˜�vol/

˜ln(@�vol,vp/@t ). This parameter is similar to the well-known

CÆ ¼ ˜�vol/˜log(t ) creep parameter. The creep strain rate is read

off at the present values of p9eq and volumetric strain. Elastic

strains are given by the Cam-clay swelling factor k* and Poisson

ratio �. Elastic strain rates are calculated and added to the creep

strain rates, and by integration in time and space the strains and

deformations are obtained.

A reference isotache is defined on which the rate of volu-

metric creep strain is equal to �*/(1 day). The initial yield

equivalent stress p9c0 is on this line as shown, and an OCR

value is given by the ratio of p9c0 and the initial value of the

equivalent stress p90:

A loading increment during a multi-stage test on a laboratory

sample is shown schematically in the isotache graph. The initial

position A is on the reference isotache, and because consolidation

is rapid, strains are at first essentially elastic, which brings the

state to point B on an isotache where rates of strain are high.

Creep then occurs along BC, rapidly at first but quickly diminish-

ing with time. At any point on BC the rate of creep is by

approximation equal to �*/tcreep where tcreep is the creep duration.

So the rate at B would be infinite (or, rather, very high), and after

one day C is reached, where the rate is �*/(1 day). This is why

the reference isotache corresponds to the common one-day

laboratory compression curve, and its cut-off equals the usual

preconsolidation pressure. For the same reason, the use of

OCR ¼ 1 in calculations produces unrealistically high rates of

strain, equal to those after 1 day of loading on laboratory-sized

samples. In situ stress–strain develops along lower isotaches than

can be measured in the laboratory, owing to the larger timescale

and larger drainage distances, and therefore OCR values should

be well above 1, even for normally consolidated soil. In the latter

case, OCR can be derived from the isotache on which creep rate

equals �*/tage, where tage is the age of the deposit under the in

situ value of p9.

5. Parameter determinationAll parameters of this creep model can be determined from the

constant rate of strain (CRS) K0 oedometer test (Den Haan and

Kamao, 2003). This concerns not only the compressibility para-

meters k*, º*, �* and �, but also the critical-state strength

parameter M. Figure 5 is a schematic diagram of the CRS K0

oedometer, which is placed in a triaxial cell to make use of piston

control, logging and back-pressure facilities. Horizontal stress is

measured by strain gauges placed on the back of a section of the

oedometer ring, which has been turned down to membrane thick-

ness. Pore pressure is measured underneath the sample, and drain-

age is to the triaxial cell space. Sample diameter is 63 mm, and

sample height is 20–35 mm. Correction for wall friction is possible

by measuring the vertical load at both the top and the bottom.

Figure 6 shows the result of such a test on peat from Sliedrecht,

the first of the cases to be presented further on. By measuring not

only vertical stress and strain but also the horizontal stress, the

complete stress–strain–strain-rate relationship is known, so that

the creep model can be fitted to the results. The test procedure

Loadcell

Triaxialcell

space

Sample

Horizontalstress

Loadcell

Pore pressure

Figure 5. Schematic diagram of constant rate of strain K0

oedometer

5


150100500

0·2

0·4

0·6

0Time: h

(a)

Vert

ical

str

ain

Unloading

Relaxation

200100

Measured

Calculated

0

100

200

300

0

p�: kPa(b)

q: k

Pa

(d)

1000100101

MeasuredCalculated

0

0·2

0·4

0·6

0·1σ �v: kPa

Vert

ical

str

ain

σ� h

σ� v,

: kPa

σ �v

σ �h

15010050

MeasuredCalculated

0

100

200

300

400

500

0Time: h

(c)

15010050

MeasuredCalculated

0

0·2

0·4

0·6

0·8

1·0

0Time: h

(e)

K0

Figure 6. Test result and fit, CRS K0 oedometer test on Sliedrecht

peat

includes an unload–reload loop to assist in determining k* and �,

and a relaxation phase to assist in determining �*.

The interaction of the various model parameters is such that, for

normally consolidated states and constant rate of strain,

M ¼ 3

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� K0,ncð Þ2

1þ 2K0,ncð Þ2þ 1� K0,ncð Þ 1� 2�ð Þ(º�=k� � 1)

1þ 2K0,ncð Þ 1� 2�ð Þº�=k� � 1� K0,ncð Þ 1þ �ð Þ

s1:

so that M can also be obtained using reasonable estimates of

K0,nc, º*/k* and �.

Table 2 provides the characteristics and parameters of the test on

Sliedrecht peat. The strains are quite high, up to 65%, and in this

6


case natural strains were used in the fitting exercise. Natural

strain is defined by the integration of infinitesimal increments of

compression relative to the present height,

�nat ¼ð h

h0

� dh=h

¼ �ln h=h0ð Þ

¼ �ln 1� �ð Þ2:

At small strains, the natural strain is very similar in magnitude to

the normal (linear) strain �. However, at larger strain levels,

natural strain is numerically increasingly larger than linear strain,

and this has the effect of straightening the concave stress–strain

curve, which often develops at higher stresses well in excess of

the yield stress (as in Figure 6(d)). The friction angle found from

the fit is quite high, and the question is whether this value

coincides with the triaxial compression value. The answer to this

question is obtained from a project where numerous CRS K0

oedometer tests and triaxial tests were performed. In this project,

‘Ground-breaking methods of dyke safety evaluation’ (Van

Duinen, 2008), which was performed for Rijkswaterstaat (the

national public works authority), three dyke cross-sections were

thoroughly investigated. Samples were obtained using the Bege-

mann continuous stocking sampler (Begemann, 1971). The

triaxial and CRS K0 oedometer tests performed for this project

have been used to compare M values: see Figure 7. The figure is

limited to triaxial tests on material taken from under the crest of

the dyke, and which was reconsolidated at approximately the in

situ stresses. It therefore concerns normally to slightly over-

consolidated behaviour. It includes the relevant data of Figure 1.

The results are plotted against bulk density, and cover a wide

range of soft Dutch organic soils. Plotted are M and �9 obtained

from the triaxial test, and by fitting the CRS K0 oedometer test.

Measured K0,nc values from the CRS K0 oedometer test are also

shown.

The high values of M and �9 are again conspicuous, just as in

Figure 1 (sin�9 ¼ 3M/(6 + M); by approximation �9 � 25M for

0.5 , M , 2.5). The agreement between triaxial M and M from

the CRS K0 oedometer test is reasonable. The very high strength

of the peat and the highly organic Gorcum light clay (GL), where

triaxial compression values tend to M ¼ 3 and �9 ¼ 908, is

underestimated, however, and this could be an indication of the

influence of organic fibres on strength, which would not be fully

developed in oedometric conditions. The measured K0,nc values

are also given in the figure. Their low values in the peats will be

noted; these indicate that partial fibre tension develops in the

horizontal plane.

The agreement in Figure 7 is considered sufficient to apply the

CRS K0 oedometer parameters, including M, in the creep model.

CRS K0 oedometer parameter sets have been determined for two

embankment construction projects, and applied in finite-element

calculations. The values of M and �9 from the tests are used

φ�

2018161412

M, triaxial tests M, fitted to oedometer tests K0,nc measured

0

0·5

1·0

1·5

2·0

2·5

3·0

10

Bulk density: kN/m3

K0,nc

M

Organic clayPeat

GLGL GL

61·9°

25·4°

36·9°

48·6°

90·0°

Figure 7. Comparison of M from triaxial compression tests and

M obtained from fitting CRS K0 oedometer tests by the creep

model, both as function of sample bulk density. Measured K0,nc is

also shown (GL: Gorcum light clay)

7


without any reduction, and are much higher than is usual in soft

soil. On the other hand c9 ¼ 0 is taken. The Cam-clay model

expects zero cohesion in normally consolidated conditions, and in

triaxial tests very little cohesion is measured.

6. Betuwelijn embankmentThe measured deformations of the Betuwelijn railway embank-

ment at km 16.7 near Sliedrecht have been analysed by means of

finite-element calculations in the project ‘Lateral ground stresses

on piles’, which was performed for CUR, the Dutch equivalent of

the UK’s Construction Industry Research and Information Asso-

ciation (CIRIA). The cross-section used in the finite-element

calculation was as shown in Figure 8. The finite-element mesh

consisted of 997 15-noded elements. An updated mesh analysis

was used (‘updated Lagrange’) to account for the large deforma-

tions. Seven CRS K0 oedometer tests were performed on samples

distributed over the 8.5 m depth of the soft layers. Figure 6 and

Table 2 provide data on one of these tests. In accordance with the

updated mesh technique, the compressibility parameters k* and

º* are taken with respect to natural strains. The bulk density of

the samples varied from 10.3 to 15 kN/m3, the water content

from 670% to 75%, and the M values found from the soft soil

model varied from 2.4 to 1.7. The correlation of M and bulk

density agreed with Figure 7, but no triaxial tests were performed

in this project. The finite-element calculation with these para-

meters gave good agreement with the measured horizontal and

vertical deformations, as shown in Figure 9. Only the initial

deformations after the first lift are heavily overpredicted, which

may be due to some uncertainty regarding the initial loading

sequence.

30252015105�14

�12

�10

�8

�6

�4

�2

0

2

4

6

0

Distance from centreline: m

Elev

atio

n: m

NA

P 1

5432

g.w.l.

Soft layers(fibrous and pseudo-fibrouspeat and high-organic clay)

Dense sand

Inclinometer

Settlement plate

Figure 8. Cross-section, Betuwelijn railway embankment, km

16.7 near Sliedrecht

100001000100100

1

2

1Time: days

Sett

lem

ent:

m

Meas.

Calc.

(a)

0·60·50·40·30·20·1

(b)

Stage 1 (71 days)Stage 5 (372 days)602 days

Calc.Meas.

�16

�14

�12

�10

�8

�6

�4

�2

00

Horizontal displacement: mEl

evat

ion:

m N

AP

Figure 9. Deformations, measured and calculated, Betuwelijn

railway embankment, km 16.7: (a) centreline settlements;

(b) lateral deformations at inclinometer location

8


7. IJkdijkThe project ‘Macro Stability Experiment’ of the IJkdijk Founda-

tion was instigated to test innovative dyke stability monitoring

techniques (Van et al., 2009). A dyke, 6 m high and 100 m long,

was built at Booneschans and brought to failure: see Figure 10. A

cross-section of the dyke is given in Figure 11. It consists of a

sand core (1) covered by clay (2), and the subsoil consists of a

thin crust of clay (3), followed by 1–2 m of peat (4), a thin

Allerød sandlayer (5), (sand with a slight organic content) and a

base of stiff Pleistocene sand (6). The dyke was brought to failure

by filling the basin behind the dyke and digging a toe ditch

(phase I), then deepening and widening the ditch (phase II), and

finally by pumping water into the sand core of the dyke (phase

III). For this purpose infiltration tubes were installed as shown in

Figure 11, and connected to a pumping system.

The dyke failed a few hours into the pumping phase. Extra steps

were in place to ensure failure (emptying the ditch, and water-

filling of a row of containers on the crest), but proved unneces-

sary. The sand core and clay shell structure of the dyke is typical

of river dykes in the Netherlands, and water-filling of the core

mimics the effect of high river levels. A full description of the

project, including a limit equilibrium analysis of the failure, will

be given in Zwanenburg et al. (2012). Here a finite-element

analysis will be presented of the deformations occurring during

construction and up to the point of failure.

The peat layer was the dominant source of deformations. It was

modelled by the creep model described earlier. Average param-

eters were taken from six CRS K0 oedometer tests performed on

this peat. Bulk density varied between 9.9 and 11.4 kN/m3, and

water content between 285% and 625%. Table 3 gives the

parameters used. The M value is 2.6, and is therefore very high.

Small-strain compressibility parameters were used in this case.

The OCR in the peat was found by calibrating the calculation to

the oedometer tests: the first construction lift was applied drained,

and OCR was adapted by trial and error to obtain the same strain

in the peat as the average value in the tests at the calculated

vertical effective stress (�vert � 18% at � 9v ¼ 42 kPa). This

approach circumvents the rather large variation in yield stresses

found in the tests. The permeability of the peat (k) was

determined in the CRS K0 oedometer tests from the hydraulic

Figure 10. IJkdijk macro stability experiment dyke at Booneschans

directly after failure

151050�5�10�15�20�25�12

�10

�8

�6

�4

�2

0

2

4

6

�30

Distance from toe: m

Infiltration tubes

Pore pressure gauges

12 2

3

4

5

6

Elev

atio

n: m

NA

P I

I

II

III

g.w.l.

Inclinometer

Settlement plate

Figure 11. Dyke cross-section, IJkdijk macro stability experiment,

2008

9


gradient set up from the undrained base to the draining upper

boundary. It was found that k decreases as strain increases, and

this was formulated as

k ¼ k010��vol=C k3:

The parameters k0 and Ck were again taken as averages from the

six tests performed on the peat.

A finite-element calculation was performed using a fine mesh of

2054 15-noded elements. A small-strain analysis was applied, and

the construction phase deformations were incorporated in the

mesh. Figure 12 compares the results of the calculation with

measurements of

(a) construction-phase settlements below the crest

(b) pore pressures measured in the soft soils under the crest and

adjacent to the ditch, during construction and the failure

phases

(c) the horizontal deformations near the toe during the failure

phases.

The construction phase was modelled in eight lifts of undrained

load application and subsequent consolidation. The inclinometer

was placed after construction, and horizontal deformations are

taken from the null measurement of the inclinometer.

The construction phase settlements are reasonably well predicted,

as seen in Figure 12(a). Settlements were not measured during

the failure phases.

Figure 12(b) shows that the construction phase pore pressures in

the peat under the crest are predicted quite well. Had it not been

possible to let permeability decrease with increasing compression

as described above, the fit would not have been as good. The pore

pressures during the first lift are overpredicted, because the

thickness of this lift was taken as larger than in reality. This was

necessary to enable the infiltration wells to be included in the

finite-element mesh.

The pore pressures in the top clay under the crest are poorly

predicted, simply because the gauge is located close to the

assumed phreatic line. During the consolidation phases the

calculated pore pressures take on the phreatic value. The pore

pressures in the peat near the ditch are predicted reasonably well.

The horizontal deformations at the inclinometer location in

Figure 12(c) depart from the null measurement 37.35 days after

the start of construction, at which point the finite-element

calculation predicted a maximum of 0.185 m. Phase 0 in Figure

12(c) shows the horizontal deformation that accumulated during

the 5.8 days between the null measurement and the beginning of

phase I.

Reasonable agreement is obtained between the measured and

predicted horizontal deformations during phases 0, I and II. The

calculation failed in phase II after applying 33% of the phase

(deepening the ditch), earlier than in reality, where failure occurred

in phase III. This is a satisfactory outcome, as the finite-element

plane-strain simulation does not account for the additional resis-

tance provided by the side planes at both ends of the failure

surface. With the thickness of the peat layer decreasing to 1 m at

the northern end of the failure zone, the end effects are expected to

be especially strong. Zwanenburg et al. (in review) calculate an

extra 15% of lateral shear resistance from the side planes.

It was envisaged that the vertical load on the subsoil in phase III

would be increased by gradually saturating the sand core. The

infiltration process in phase III is shown in Figure 13. A lower

infiltration tube placed in the top clay was operated separately from

the six infiltration tubes in the first sandfill layer. The figure shows

the infiltration pressures measured near the pumps at the southern

end of the embankment and the pore pressures measured in the

failed section of the sand core approximately at the level of the

infiltration tubes, and approximately 1 m higher. The infiltration

sequence was rather complicated, and pressure build-up was higher

than expected. Various pumping pauses further complicate affairs.

The discharged amount of water totalled about 200 m3, which is

expected to saturate the lower approximately 1.5 m of the sand

core, and to increase the vertical load by approximately 1 kPa.

In Figure 13 the development of the maximum horizontal

deformation of the toe-line inclinometer is also shown. There is a

clear correlation between the infiltration pressures in the final

phase before failure and the rate of increase of the horizontal

deformations. The additional weight of the water is very small,

and is not expected to contribute significantly to the failure. A

post-mortem trial pit constructed through the failure surface

revealed that core sand had penetrated the soft layers below the

crest. It is now postulated that failure was accelerated by both the

high infiltration pressures and the penetrating sand. The horizon-

tal thrust would be increased by both, especially if the infiltration

pressures could propagate into the penetrated sand.

Bulk density:

kN/m3

k* º* �* � M �9:

degrees

K0,nc OCR k0: m/s Ck

10.5 0.02 0.22 0.02 0.21 2.6 65.1 0.25 3.3 1.15 3 10�8 0.35

Table 3. Characteristics of IJkdijk peat, Booneschans

10


50454035302520151050

0·1

0·2

0·3

0·4

0·5

0·6

0Days after start of construction (13 August 2008 06:00)

Sett

lem

ent

unde

r cr

est:

m

Settlement plateCalculated

(a)

50454035302520151050

0·200·150·100·05

Allerød

In peat under crestIn top clay under crestIn peat near ditch

Mea

s.C

alc.

IIIIIIInc.

�3

�2

�1

0

1

2

3

4

5

6

7

Days after start of construction (13 August 2008 06:00)(b)

Tota

l hea

d: m

NA

P

�10

�8

�6

�4

�2

0

20

Horizontal displacement, inclinometer no. 53: m

Dep

th: m

NA

P

Full line: measurementSymbols: calculation

0: Start of phase II: End of phase I: filling basin, digging ditchII: End of phase II: ditch deeperIII: Phase III: infiltration in sand coreIIIA: During pause in infiltrationIIIB: Infiltration ends; failure imminent

IIIBIIIA0 III

Peat

Top clay

Clayshell

Pleisto-cenesand

(c)

Figure 12. Results of finite-element calculation, IJkdijk macro-

stability experiment, 2008: (a) construction phase settlements;

(b) pore pressures; (c) horizontal deformations during failure phase

11


The finite-element calculation failed before these rather compli-

cated processes occurred, after 0.33 of the ditch-deepening phase

had been applied. A finite-element calculation with a coarser

mesh of some 800 six-noded elements, however, did not fail even

in phase III, as detailed in an earlier paper (in Dutch) by Den

Haan and Feddema (2009). There, infiltration pressures were

applied by means of wells, and the sand penetration into the peat

was also modelled. A factor of safety (FS) was determined at the

end of phase III by undrained reduction of the Cam-clay M-

parameter, and FS ¼ 1.17 was found, whereas FS ¼ 0.85 would

be expected if the 15% side plane resistance was accounted for.

The coarse mesh has considerably fewer degrees of freedom than

the finer mesh, and this appears to offer additional resistance to

failure. To be sure mesh fineness was sufficient, a very fine mesh

of 4297 15-noded elements was also used. It produced essentially

the same results as reported in this paper.

8. DiscussionThe two finite-element calculations presented in this paper have

applied a creep model that is a viscous version of modified Cam-

clay, to embankments on soft organic clays and peat, with

parameters determined from constant rate of strain K0 oedometer

tests. The latter include the strength parameter M, which is quite

high in these soils, while cohesion is zero, and strain-dependent

permeability. The finite-element calculations with this model

appear to produce very satisfactory fits to the measured deforma-

tions and pore pressures, and the failure of the IJkdijk case is also

covered satisfactorily.

The determination of the strength parameters of soft organic clay

and peat has long troubled the geotechnical profession in the

Netherlands. The very high �9 value of these soils poses

problems both in laboratory strength testing and in stability

calculations. The procedure used in this paper – interpreting

constant rate of strain K0 oedometer tests within the framework

of a viscous version of modified Cam-clay to produce both

strength and compressibility parameters – is possibly a viable

alternative for Dutch practice.

The ability to predict vertical and horizontal embankment

deformations has a bearing on fill material consumption, on track

or road maintenance, and on deformations of foundations, piles

and utilities buried near the toe of the embankment. The ability

to faithfully predict pore pressures set up during construction can

further reduce the occurrence of failures during construction if

adequate surveillance and feedback are performed. The most

important function of calculations, however, is to predict failure,

and in this respect the adequate indication of failure of the IJkdijk

embankment is encouraging.

Predicting failure of dykes has become an important aspect of

geotechnical engineering in the Netherlands. Dyke authorities are

required to evaluate dyke safety every 5 years, and there are some

17 000 km of such dykes in the Netherlands! Evaluation is in

terms of the factor of safety and probability indices determined

from limit equilibrium analyses. Using the finite-element ap-

proach described in this paper, a dyke can first be built up, from

15:00:0013:00:0011:00:00�10

0

10

20

30

40

09:00:00

(Por

e) p

ress

ure:

kPa

0

20

40

60

80

100

120

140

160

Max

. hor

izon

tal d

efor

mat

ion:

mm

Lower infiltration tube (A)

Infiltration tubes in sandfill (B)

Pore pressure at base of sandfill (C)

Pore pressure 1 m above base ofsandfill (D)

Horizontal deformation

27 Sept. 2008

A

D

CB

50

60

70

80

Figure 13. Development of infiltration pressures and pore

pressures in sand core and of maximum lateral inclinometer

deformation, phase III failure stage, IJkdijk macro-stability

experiment, 2008

12


history as it were, to the present state, taking advantage of the

prolonged creep compression under the dyke and the accompany-

ing increase in shear resistance. Then a factor of safety can be

determined by one of various methods in which failure is

simulated. The most usual approach is the stepwise, undrained

reduction of the Cam-clay strength parameter M until failure

occurs, giving the factor of safety as the ratio of the available and

the reduced value of M.

However, the applied creep model has several limitations that

need to be considered. These are

(a) volume changes and pore pressures set up by rotation of the

stress tensor during construction and loading

(b) anisotropy of creep rates

(c) overconsolidation effects.

More general limitations lie in such matters as not modelling

localising deformations along shear surfaces during failure,

inadequate knowledge of the shape of the shear stress envelope in

principal stress space, the non-uniqueness of solutions when non-

associativity is assumed on the shear stress envelope (e.g. by

assuming zero viscoplastic volume change), and the inability to

model side plane resistance.

Stress tensor rotation occurs during embankment construction as

a result of load spreading. At the toe, for example, the initial

geostatic state with vertical major principal stress rotates over 908

to the passive state, and locations between crest and toe undergo

intermediate amounts of rotation.

In soft soils such rotations usually induce volume decrease and

pore pressure increase. These effects are not dealt with by the

creep model used here. Jardine et al. (1997) describe how, once

consolidation has occurred under the rotated stresses, undrained

loading without further rotation yields high undrained strength,

close to that which is obtained without any rotation. This is due

to the soil’s fabric gradually adapting to the rotated state of

stresses and strains. In dyke safety evaluation the failure loads

stem mostly from rising water levels, and as these are essentially

horizontal, they will induce fresh rotations of the stress tensor,

and appear so quickly as to be essentially undrained. This effect

is probably small, however: the IJkdijk finite-element model was

run with extreme water loading (water level in the basin behind

the dyke raised quickly to crest level), and it was found that

rotations were less than 108 in the zones in which shear failure is

expected to occur.

Modified Cam-clay is an isotropic model in the sense that the

yield ellipse remains orientated along the isotropic stress axis.

Developments are under way in which the ellipse rotates depend-

ing on the relative amounts of isotropic and distortional plastic

strains. Such anisotropic models appear to improve fits to meas-

ured soil behaviour, and have recently been adapted to account

for soil viscosity, as well as the specific behaviour of peat (Leoni

et al., 2010). This may provide an avenue for further improve-

ment of the approach presented here.

The creep model does not deal adequately with the overconsoli-

dated state. On unloading, rates of creep strain reduce strongly

and behaviour becomes essentially elastic, and only critical-state

strength is used. Embankments with a significant passive zone of

highly overconsolidated material may therefore be less amenable

to the approach described here.

The side plane and mesh size effects on the moment of failure in

the IJkdijk case have been noted, and in any calculation of failure

it will be necessary to take these effects into account.

Notwithstanding these limitations, and given that due care is

exercised, the procedure described in this paper should allow

successful application of the finite-element method to the calcula-

tion of deformations and strength of embankments on soft

organic soils.

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deformation and strength of embankments on soft dutch soil

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