Laboratory experiments on consolidation and strength evolution of mud layers

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.~i~;(

TU

Delft

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De/ft University of Tecnnoloqv

Department of Civil Engineering

Hydrau/ic and Geotechnica/EngineeringDivision HydromechanicsSection

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Laboratory experiments on consolidation and

strength evolution of mud layers

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L.M. Merckelbach

report no. 1-98

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1998

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The work reported here in has been financially supported by the Netherlands Tech-nology Foundation (STW) and the Commission of the European Communities.

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,,' , ' " ~

TU Delft

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HydromechaniesSection,Facultyof Civil Engineering and Geosciences,Delft Universityof Technology,P.O. Box5048,2600 GA,the Netherlands.Tel. +31152784070; Fax +31 15 278 59 75;E-mail:l.merckelbach@ct.tudelft.nl

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Abstract

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Many harbours in the world suffer from high siltation rates in their basins. To guarantee safe shipping, harbour authorities have to maintain the navigable depth by dredging large amounts of mud. Some authorities relate the navigable depth to the depth at which the

density is equal to a certain value, e.g. 1200 kg/m3. However,the shear strength might be a

more direct criterion to relate the navigable depth to,

Presently, a research project, which is financed by The Netherlands Technology Foun-dation, is being conducted to develop a model that can be used to translate results from laboratory experiments to field conditions. To gain knowledge that is required for the mo-del formulation, a first series of laboratory experiments was carried out at the University of Oxford and reported herein

Continuous bulk density profiles were measured with a very accurate, non-destructive X-ray densimeter, which is available at the University of Oxford. At discrete levels the pore water pressure was measured. From these quantities accurate effective stress data and fairly accurate permeability data could be obtained. Itturned out that both effective stress and permeability can be related to volume fraction of solids according to a power law. The concept of a fractal structure also implies power laws between the quantities mentioned. The fractal dimension obtained equals 2.71

±

0.05.

In contrast with the density and pore water pressure measurements, the va.ne tests are destructive. In order to study the evolution of yield stress in time, the three columns were started under the same initial conditions. After 8, 13 and 24 days, a constant shear rate vane

test was carried out. The peak shear stress, calculated from the torques measured, shows a more or less linear relationship with the effective stress, and apparently exhibits a yield stress at ze.ro effective stress, the so-called true cohesion. Because of the linear relationship with the effective stress, the peak shear stress reduced by the true cohesion can also be described by a power law holding for a fractal dimension of 2.71.

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The results of this study indicate that the structural properties that determine effective

stress, permeability and peak shear stress, can be characterized by a fractal dimension.

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Contents

1 Introduction 4

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2 Experimental programme 5 2.1 General overview . . . 5 2.1.1 Mud preparation . . . 6

2.1.2 X-ray density measurements . 7

2.1.3 Pore water pressure measurements 7

2.1.4 Yield stress measurements . 10

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3 Data processing methods 14

3.1 Method applied to density profiles 14

3.2 Determination of permeability. . . 16

3.3 Method applied to the vane tests . 17

3.3.1 Conversion from torques to shear stress 17

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4 Results 18

4.1 Mud-water interface settlement 18

4.2 Density profiles . . . 18

4.3 Excess pore water pressure profiles 18

4.4 Effective stress data 18

4.5 Permeability data. 19

4.6 Vane test data 19

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5 Analysis 20

5.1 Quality of the data. . . 20 5.2 Behaviour of the measured quantities with time. 21

5.2.1 Interface height with time 21

5.2.2 Density profiles . . . 21 5.2.3 Effective stress data . . . 21 5.2.4 Interpretation of the effective stress data with the concept of fractal structure. 22

5.2.5 Analysis of the results of the vane tests 26

5.3 Reproducibility of the settling experiments 30

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6 Conclusions 34 References 36

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A Figures 37 2

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List of Figures 63 List of Tables 66 List of Symbols 67

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3

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Chapter

1

In

trodue

ti

o

n

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Many harbours in the world suffer from high siltation rates in their basins. To guarantee safe shipping, harbour authorities have to maintain the navigable depth by dredging large amounts of mud, which involves substantial costs.

Typical for these basins is that a bottom is hard to define since the density increases gradually from the water surface to deep in the bed. Some authorities relate the navigable depth to the depth at which the density of the mud is equal to a certain value, e.g. 1200 kgf m3. _{However,the (shear) strength seems to be a more relevant parameter for defining}

the navigable depth. Although density and shear strength of mud are interrelated, this

relationship is not unique and may be time dependent. Both parameters are reflected in the

consolidation behaviour. A definition of the navigable depth based on shear strength might give rise to a change in the dredging strategy and possibly result in lower costs.

Presently, a research project, which is financed by The Netherlands Technology Foun-dation, is being conducted to develop a model that can be used to translate results from laboratory experiments to field conditions. The model formulation requires knowledge of consolidation and strength evolution processes. In this respect, important parameters are effective stress, permeability and (peak) shear stress. These parameters can be calculated from measurable quantities as bulk density, pore water pressure and torques exerted onto a vane. During the period from April2Sth until July 19th 1997,a first series of experiments was carried out at the University of Oxford, Department of Engineering Science, Soil Mechanics Group, under supervision of Dr G.C. Sills. The results and interpretation are reported herein.

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Outline

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In Chapter 2 the experimental programme is discussed. The methods used for post-processing the measured quantities are described in Chapter 3. In Chapter 4 the results of the measu-rements are presented. Subsequently,the results are analysed in Chapter 5. Finally, the conclusions of this study are presented in Chapter 6.

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4

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Chapter

2

Experimental

programme

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2.1

G

en

e

ra

l o

v

e

r

view

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The acrylic settling columns that were used in the experiments were 40 cm high and had an inner diameter of 10.2 cm. The columns were placed in a non-climatised cellar of which the average temperature was 20

±

3°Celsius.

The mud tested was dredged from the Caland-Beer Channel in the Rotterdam harbour area. During the consolidation tests the followingquantities were recorded: the mud-water interface level as function of time; density profiles; and pore water pressures at a number of discrete levels. At the end of each test, yield stress profiles were measured.

The mud-water interfacelevelwas read from a cm scaleplaced along the columns. The density profiles of the mud in the columns were measured with an X-ray profiler,which is dis-cussed in Section 2.1.2. Total stress profiles were obtained by integration of density profiles.

Pore water pressure measurements were carried out by using pore pressure transducers, see Section 2.1.3. By subtracting pore water pressure from total stress, effective stress profiles were calculated. Moreover,from two consecutive density profiles and hydraulic gradients cal-culated from the pore water pressure measurements the local permeability could be estimated, as explained in detail in Section 3.2. Finally, yield stress was measured with a constant shear rate vane tester. Each column was subjected to the vane test at a different time so that the development of the yield stress with time could be estimated.

The details of the experiments are given in Table 2.1. In this table Pw refersto the pore water density,Pi to the initial bulk density, hi to the initial height of the mud layer and Td

to the duration of the experiment. The tests are identified by Tn, where

n

is the duration of the test in days. The measurement schedule is given in Table 2.2. In this table the numbers denote the time after start of the test in days. The symbols mean:

o density measurement only,

• density measurement and pore water pressure measurements and

*

density measurement, pore water pressure measurements followedby vane test (the end of the experiment).

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Table 2.1:Overviewof theexperimental conditions

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T8 T13 T24 units Pw 1.017 1.017 1.017 lOJkg/rn" Pi 1.133 1.133 1.133 103kg/m3 hi 0.354 0.354 0.354 m

Td

8 13 24 day

Table 2.2: Measurement schedule

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T8 10 2

•

3

•

4

•

5 06 7 8 9 10 11 12

*

T13 0

•

•

•

•

•

•

T24 0

•

•

•

0

•

•

13 14 15 16 17 18 19 20 21 22 23 24 T8 T13

_*

T24 0

•

•

*

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The mud that was used was Caland-Beer Channel mud (Port of Rotterdam2.1.1 Mud preparation , The Netherlands). It was dredged on April 7th 1997. lts density! was about 1.25x 103kg/m3. A fewproperties of

the Caland-Beer Channel mud are listed in Table 2.3. A partiele size distribution is presented in Figure 2.1

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Table2.3: Properties of Caland-Beer Channel mud

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density of solids (x 103kg/m3)

sodium adsorption ratio (-)

cation exchange capacity (cmol/kg) specific surface (m2/g) humus (%) 2.5278 ±0.006 70 20.1 96 3.99

The mud used in the experiments was diluted to a density of 1.133x103 kg/rn". The

diluent was tap water to which "sea" salt (normally used for aquaria) was added, until it

had a density of 1.017x 103kg/rn", which was the same as that of the expelled pore water

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lThe density of the slurry as it wassupplied by the dredgingcompany. This density is generaJlynot equal to the in-situ density.

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100.00

....

80.00 I::l Cl) u r-. Cl) 0. til _60.00 ~ S Cl) .E:

_....

_40.00 CIl "3 S ;::l 20.00 U 0.00 1

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Caland-Beer Channel mud, present measurements

-+--Caland-Beer Channel mud (van Kessel,1997)--)E-

-10 100 1000

Equivalent spherical diameter d (IJ.m)

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Figure2.1:Partiele size distribution

in the mud container. Before the mud was introduced into the columns, it had been mixed

thoroughly for at least half an hour.

2.1.2

X-ray density measurements

The X-ray density profiler, which is available in the soil mechanics laboratory ofthe University

of Oxford, provides a method to measure the density distribution in a column in a

non-destructive manner. The main points of this technique are discussed briefly. For further

information the reader is referred to Been (1980).

For X-rays of sufficient energy, the absorption of X-rays passing through soil ean be

uniquely related to the density of the soil. A collimated beam of X-rays is directed at the

settiement column, and, after passing through the soil,reaches a detector. The count rate

produced by the detector is linked to the soil density by

N

=

No

exp(-IJ.Pb9d), where

N

is

the count rate,

No

a reference value, IJ. the absorption coefficient,Pb the bulk density of the

mud, 9 acceleration due to gravity and d the diameter of the column.

Owing to inevitable random variations in intensity of the X-ray source, the count rate

varies slightly, even for constant densities. Therefore, the count rate is averaged over 10

seconds to obtain higher accuracy. The claimed accuracy is ±0.002 x 103kg/m3. The energy

level of the X-rays was set at 160 keV.

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2.1.3

Pore water pressure measurements

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Pore water pressures were measured at several points along the column wall. The exact

positions of the pressure ports are tabulated in Table 2.4. At those positions holes with

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column wall

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-

Enot >=: Tube e 0 _a >.

s

>

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25rnrn 10 mm

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Figure 2.2: Schematicdiagramof a pressureport

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diameter 1.0 cm were drilled in the columns. Each hole was provided with a vyon plastic

filter, punched out of a large piece of material. The vyon was placed so that the innersurface

of the column was as smooth as possible. On the outside of the column the holes were provided

with so-called enots to which tubes were connected. A schematic diagram of a pressure port

is given in Figure 2.2.

All pressure ports were connected to a pressure measuring unit via tubes, inner diameter

2 mm and made of hard plastic. On this pressure measuring unit one pressure transducer was

mounted which could be connected to each of the tubes separately, like a whirligig principle,

see Figure 2.3. Besides connections with the pressure ports, each pressure measuring unit

had a conneetion with the calibration reservoir. This reservoir could be traversed in vertical

direction. Fixing the reservoir at known levels,a linear relationship between the transducer

output in J.LV and the water height was found via a regression analysis. In Figure 2.4 an

example of a calibration plot is shown.

In total three columns were set up. Two pressure measuring units were available,one with

11 pressure port connections and one with 22 pressure port connections. The 22-ports unit

was equipped with a PDCR 830 pressure transducer, which was brand new. The ll-ports unit

was equipped with an older type PDCR 810 pressure transducer. This transducer had been

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Bottom view Side view

t

to volt-meter

0

pressure transducer

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0

revolving disc Bolt

/

@

l

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₀

₀

A A

-,

fixed disc to pressure ports section A-A

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Figure 2.3:Schematic diagram of a pressure measuring unit

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20000

,---

,--

,

---",--

--

---,--

----,---,

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11easurements

*

y =14.03045x

+

4390.5

=

r>:

..../"x ....

>'

16000

f- /lI!/

..:::

-~ 14000

f- /~/

fr

/x

/

~ 12000

f- ///~///

~ 10000

f- ///~/

]

8000

f- //~/ «l ~/ ~

₆₀₀₀

f-////w.//

----4000

L-

---L_---

L_

---L_

-

--

L_

1

--

~

o

p2 =

0.9999964

~ 18000

f-200

400

600

Level (mm); x

800

1000

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Figure 2.4: Example of a calibration plot

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used several times before and some scale could be observed on the sensor. Both transducers were calibrated for fresh water.

It

was found that the PCDR 830 was indeed more stable than the PDCR 810, but the latter was still accurate enough to use.

For accurate pore pressure measurements it is crucial that nowhere in the system air bubbles are present. Furthermore, long tubes, more than 0.5 m,say,significantly increase the time that elapses until a reading becomes stable. If it takes too much time to get a stable

value, a reading might be erroneously considered stable. The accuracy is ab out 1 mm head of water or 10 Pa.

Table2.4:Locations ofthe pore water pressure ports incm from the bottom

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Port1

#

h (cm)0.5 2 2.5 3 4.5 4 6.5 5 8.5

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67 10.512.5 8 14.5 9 17.5

10

20.5

11 30.5

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2.1.4

Yield stress measurements

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The yield stress was measured with a shear vane tester. The apparatus was driven by a stepper motor that drives the vane at a constant speed of 0.4 degree per second. Between the rod of the vane and the stepper motor a torque transducer is mounted, that produces an output in mV, which is recorded by a data logger on a PC. A schematic representation is

shown in Figure 2.5.

The transducer output has a linear relation with the torsion of the transducer cello The tors ion of the cell has a linear relation with the torque that is exerted on the cell (and the

vane). A calibration procedure is necessary to convert transducer output from voltage to torque. To that end various known torques were exerted on the torque transducer so that the

transducer output could be related to the torque by means of aregression analysis. Figure 2.6

shows how the torques are applied by using weights (sachets filled with lead shots).

The vane consisted of four blades. The dimensions of the vane were 4 cm in height and 2

cm in diameter. This 2:1 ratio is the standard for vane measurements.

Before the yield stress could be determined, each column was disconnected from the

pressure tubes and instalied in a special holder. The measurements, divided into two stages,

were staggered in vertical direct ion to reduce the influence between the measurements, see

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mo

-tor

0

ar::

-

-~ )~ transducer rod ~

m

vane

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Figure 2.5: Schematic diagram of the shear vane tester

t

11

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transducer

J

,

c---

iron 'T' ___ cotton wire

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Figure 2.6: Calibration of shear vane tester

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Side view Plan view

-

_...

z

=

2 cm n

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_D

3

...

z

=

6 cm n 3 ~

...

z

=

10 cm n 3

D

...

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z

=

14 cm n3

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_...

'"

...

'"

a

a

n Z

=

18 cm

_a

3

D

...

z

=

22 cm n 3

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_{Figure 2.7.} Figure 2.7: Measurement positions with shear vane test

Since the traversable height was much smaller than the column height, the rod of the vane

was extendable. Before the vane was advanced to a deeper level, a section of rod (8.0 cm) was fixed between the first and the second piece by hand. It is very likely that unavoidable

vibrations inherent to this procedure had an adverse effect on the accuracy of subsequent measurements.

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Chapter

3

Data processing methods

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_3.

₁

_M

_ethod

_applied

_t

_{o density profiles}

Each file with output data generated by the X-ray profiler contains a column with height levels and a column with count rates. In Figure 3.1 an example is given. Although the count rate in air is much higher, the region of interest is in between 0 and 1 counts per second, since

in this region the count rates corresponding to both water, ab out 0.8 s-1, and mud, about 0.6 s-l are present. Exceptionallow count rates corresponds to material with a.high mass, such as a rig.

In the past it was found that t

h

e height of the c

o

lumn read from the figure did not alway

s

correspond to the physical height. This was ascribed to inaccurate recordings of the height. Therefore, the first step was to rescale the height levels. (The top and bottom of the column can be easily discerned and the physical height can be measured.)

The count rate relates to density as (Been,

1

9

80)

(3.1)

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where

N

is the count rate,

No

count rate for vacuum (zero mass), J..Lan absorption coefficient,

d the inner diameter of the column, Pbthe bulk density and 9the acceleration due to gravity. Conservation of mass gives

(3.2) where the subscript i refers to the initial condition and h is the height of the water surface,

which is equal to the initial height if no significant gas product ion occurs. With (3.1), equation (3.2) can be written as

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In

h

N

Pighi= -- In -_-dz.

J..Ld 0 No

(3

.

3)

The count rate is normalized by a reference count rate

Nr

e

f

,

N =

N /

s.;

dimensional inconsistencies then are avoided if the right-hand side of (3.3) is expanded, yielding

In No 1

!o

h

P·gh· =--h - - InNdz I I J..Ld J..Ld 0 . (3.4) 14

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0.85

Normalized count rate -

-0.8 -0.75

I-1

-0.7 f- I

-I

s

) 0.65 I- -'-" ~ 0.6 I- -0.55

l-J

-I

0.5 f-0.45 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Normalized count rate (-)

Figure 3.1: Output generated by X-rayprofiler

In this way the integral in (3.4) can be evaluated numerically, without knowing the unknowns

No and

/J.

Subsequently, one needs a calibration measurement to determine the two unknowns. If there was a distinct water layer above the mud layer, this water was used as calibration

sample. Otherwise, a sample of water with known density was placed on top of the column.

The calibration density Pc was determined with a commercially available densimeter. With (3.1) the equation for the calibration sample can be formulated:

(3.5)

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where Ncis the count rate corresponding to the calibration sample. Combining (il.4) and(3.5) the following expressions for

No

and J.L are found:

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N, - N. [pc(hln(Nc) -

I)]

0- cexp h h ' Pi i - Pc 1[hln(Nc)-I] J.L =

d

Pighj - Pcgh ' (3.6) (3.7) where I=

!oh

InNdz. (3.8)

With these expressions the count rate profile can be easily transformed into density profiles.

It is noted that both

No

and J.L depend on the energy level of the X-rays. Since this

energy level needs to be set at approximately 160 keV by hand for each measurement, these parameters have to be determined for each measurement. Common values found are

No

:::= 5-7

and J.L :::=0.19 - 0.21.

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Z

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Vw Vetf Vs

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Figure 3.2:Definitionsketchof partieleand fluidveloeities

3.2

Determination

of permeability

The motion of the pore water relatively to the particles can be modelled with Darcy's law,

which is written as

1 oPe

ePw(vw

-

v

s) =-k-!)",

Pw9 oz (3.9)

whereVw is the velocity of the fluid,Vs is the velocity of the particles, k is thepermeability of the soil,Pw is the density of the Huid,9 is the acceleration due to gravity,

z

vertical ordinate and Pe is the excess pore pressure defined by the difference of the pore-water pressure and the steady-state (hydrostatic) pore-water pressure:

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_Pe =P - Pss· (3.10)

The difference of the fluid velocity and the partiele velocity (vw - vs) is usually called the effective velocity,Vetf, see also Figure 3.2.

For reasons of continuity the volume flux of the mixture equals zero,so that,

(3.11) Using (3.10) and (3.11), equation (3.9) yields (Been, 1980)

k

op

Vs =--;:l

+

k.

Pw9UZ

(3.12) The averaged partiele velocity at a certain level, i.e. the settie rate, can be estimated as follows. A column is divided in N imaginary levels. Each levelcorresponds to a certain percentage of the total mass that is in between the bottom and that level. This percentage

must be constant with time. Then, from two consecutive density profiles,the settlement rates of the levels can be calculated. The pressure gradient ~ is calculated from the corresponding

pore water pressure profiles for the averaged height of the two levels. With these parameters and (3.12), the local permeability can be calculated.

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3.3

Method applied to the vane tests

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The data of the vane test were logged onto a PC with a sampling frequency of 1.0 Hz. To reduce the amount of data and to smooth the rather spiky profiles, every 10 data points were replaced by their average.

It turned out that during the strength measurements in a column and the calibration

session, the transducer output in m

V

corresponding to zero torque was not constant. Thus,

a torque which was different from zero, was recorded for a rotation angle equal to zero.

Therefore, all measurements of were corrected by a torque Tc such that the initial torque for

each measurement was equal to zero. The applied corrections are listed in Table 3.1. The

parameter z refers to the depth of the middle of the vane with respect to the mud-water

interface.

Table 3.1: Torque corrections in mNm

z

=

2 cm z

=

6 cm z

=

10 cm z

=

14 cm z

=

18 cm z

=

2< T8 -0.291 0.160 -0.323 -0.038 -0.048 T13 -0.774 -0.270 -0.753 0.034 -0.300 0.1.: T24 0.222 0.760 0.427 0.844 0.674 2cm 32

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3.3.1

Conversion from t

o

rques t

o

shear stress

In order to be able to relate shear stress to torque it is assumed that the shear stress is

uniformly distributed over the height of the vane and that bath end surfaces ofthe cylinder

contribute to the total torque. In a formula this reads

(3

.

13)

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where T is the measured torque, T the shear stress, l the height of the vane and r the radius

of the vane. With the values for the used vane, l =0.04 mand r =0.01 m, equation (3.13)

gives

(3

.

14)

As can be seen in (3.14), the contribution of one end surface of the cylinder is about

8%

(112),

which is relatively small.

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Chapter 4

Resu

l

ts

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The results presented in this ehapter are analysed in Chapter 5. The figures ean be found in Appendix A.

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4.1

The mud-water interface settlement was measured at different times during the

Mud-water interface settiement

experiments. The results are shown in Figure A.I.

4.2

Density profiles

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The vertical density distribution for experiment T8 are shown in Figures A.2 through A.5. The vertical density distribution for experiment T13 are shown in Figures A.6 through A.12 and for experiment T24 in Figures A.I3 through A.I9. The development of the density profiles with time are presented in Figures A.20, A.21 and A.22 for experiments T8, Tl3 and T24 respectively. In order to avoid too much cluttering, all data series are running averages over 20 values. The drawback of the averaging procedure is that sharp transitions in the profiles may not be presented entirely correctly. Moreover , the density distributions of the three columns together for 1,3, 8 and 10 days are shown in Figures A.23 and A.24. The data series in these figures are also running averages over 20 values.

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.3

E

x

cess pore water pressure profiles

The pressure profiles are shown in Figures A.25, A.26 and A.27,

4

.4

Effective stress data

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The effective stress data for experiment T8 are represented in Figures A.28 through A.3I. The data for experiment TI3 are given in Figures A.32 through A.38 and for experiment T24 in Figures A.39 through A.45. At first sight, these figures may seem a little bit confusing.

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In fact the effective stress data are represented in two different ways. The first way is the representation of effective stress against volume fraction. This representation uses the lower axis (volume fraction) and the left-hand axis (effective stress). The symbol used is

'

+

'

.

Notice that both axis are in logarithmic scale.

The second representation is effective stress against void ratio. This representation is added since in soil mechanics it is very common to plot the effective stress data in this way.

This representation uses the upper axis (effective stress) and the right-hand axis (void ratio). The symbol used is '.'.

4.5

Permeability data

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The permeability data for experiment T8 are presented in Figure A.46. The data are collected from all available density and pore water pressure profiles, as explained in Section 3.2. As done

for the effective stress data, the permeability is shown as a function of the volume fraction (primary axes) and as a function of the void ratio (secondary axes). The permeability data for experiment TI3 are shown in Figure A.47, and the data for experiment T24 are shown in Figure A.48.

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4.6

Vane test data

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The results of the vane tests for experiments T8, TI3 and T24 are shown in Figures A.49,

A.50 and A.51, respectively. The symbol

z

in the keys of these figures refers to the level below the mud-water interface at which the centre of the vane was positioned.

The measurement data as presented in Figures A.l through A.51, are available onCD-ROM.

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19

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Chapter 5

Analysis

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_5.

₁

_Q

_u

_ali

_ty

_of

_t

_{he data}

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The accuracy of the X-ray technique is approximately 0.002 x103 kg/rn''. The small spikes

that can be observed in Figures A.2 through A.19 are within the margin of accuracy, However,

sometimes doubtfullarge spikes or shifts occasionally occur, see Figures A.16 and A.19. The large fluctuations in the uppermost part of the mud layer for experiment T24, day 20 and day 24 are ascribed to local gas production which reduces the density significantly. It was observed that in the upper 1.0-1.5 cm the color of the mud changed from almost black in ochre, indicating chemical activity.

The excess pore water pressure profiles shown in Figures A.25, A.26 and A.27 have a rea-listieappearance: initially the total weight of the suspension is borne by the pore water, which cannot be expelled quickly because of the low permeability of the mud layer. When the conso-lidat ion process proceeds the pore water is expelled slowly and the mud particlesjaggregates start to take over the load: effective stress develops and excess pore water pressure decreases.

However, some readings seem to be doubtful. Shifts occur in the profiles pertaining to T13,

day 1 and T13, day 8,see Figure A.26. Explanations for the deviations could be the use of a transducer of less quality (experiment T13), the use of long tubes (experiment T8), a vertical shift of the transducer during the readings, or a combination of the given explanations. The profiles for T24 do not show this peculiarity.

Since the effective stress is calculated from the density measurements and the pore water pressure measurements, it is expected that the accuracy of the effective stress data is less,

or at most equal to the accuracies of the density and pore water pressure measurements.

Therefore, the accuracy of the effective stress is at best 10Pa, which corresponds to 1 mm water head. If one presurnes an abnormal progress of the effective stress curves, it can be mostly reduced to the doubtful pore pressure curves, see for example Figure A.36 (volume fraction against effective stress).

The permeability profiles are expected to be of significantly less quality than the ones for density, pore pressures and effective stress, since the (local) permeability is an average of a slice of mud and the result of an averaged partiele velocity obtained from two consecutive density measurements and interpolated pore water pressure profiles. Despite all these averages

a

I

I

I

20

I

I

.

I

the results seem rat her realistic. The accuracy of kis estimated to be ±1.5 .10-7 mis, which

is approximately 25%.

The error sourees in case of the vane measurements are twofold. Firstly, the transducer

output was relatively inaccurate. This is due to the fact that the torque transducer was

designed for much stiffer soils. The error in the measured torques is estimated ± 0.2 mNm,

see Figure A.49. Secondly, the torques were corrected for zero torque at zero rotation, see

also Section 3.3. The latter error souree is not easily quantified, but the corrections were of

the same order, see also Table 3.1

The relative error of the vane test of T8 ranges from 40 to 100%,which makes the data

almost useless. The relative error drops to approximately 20% for the test of T13 and to 10%

for the test of T24, so that only the vane test results of T13 and T24 are more or less reliable.

I

I

5.2

Behaviour of the measured quantities with time

5.2.1

Interface height with time

I

In Figure A.l the height of the water-mud interface with time is shown. This figure shows

that there is a discrepancy between the curves. Experiment T8 settled more quickly than

experiments T13 and T24. Furthermore, experiment T24 settled more quickly than T13,

but it seems that the curves of experiment T13 and T24 converge when time increases.

This could not be proved since the consolidation process in T13 had to be terminated for

the strength measurement. Sills

(1994)

also reports experiments that show discrepancies in

interface heights in the early stage which vanish when the consolidation process proceeds.

I

5.2.2

Density profiles

To illustrate the development of the bulk density density with time the development of the

bulk density is shown in Figures A.2 through A.19. The tendency is more or less the same

for all three experiments: the bulk density increases fastest at the bottom and more gently

higher in the column, but in the uppermost 2-3 cm of the bed the increment in density is again

larger. This latter effect is almost certain due to oxidation (Sills, personal comrnunication).

The maximum density reached in 24 days is approximately 1.22x103 kg/rn".

In experiment T24, some peculiar phenomena can be observed, see Figures A.13 through

A.19. In contrast with T8 and T13, the density somewhat above the bottom hardly increased

during the first three or four days. Moreover, the additional increment in the uppermost part

of the bed turned into a significant decay of the density after 20 days. In this part of the bed

the chemical have changed, as mentioned earlier.

I

I

5.2.3

Effective stress data

I

In Figures 5.1, 5.2 and 5.3, a selection of available effective stress data is shown. These figures

show that the maximum effective stress increases with time, as expected. Moreover, the curves

coincide to a large extent. However, some discrepancies can also be observed. In Figures 5.1

and 5.2 this is indicated by an arrow labeled with 'A'. Here, the volume fraction of solids

21

I

I

Day 3,

epp -

a' Day 8,

epp -

a' 100

I

----

ro 0...

--b 10

I

ep

p (-)

0.1 1L_ ~ L_ __ _L __ ~_J __ L_~~L_ ~ 0.01

I

Figure5.1: Selectionofeffectivestress data, experimentT8

increases at low effective stress. This is in accordance with the bulk density profiles,which

show an increase in density in the uppermost centimeters of the mud layer. The discrepancy

indicated by the arrow labeled with 'B' is possibly due to errors in the pore water pressure

profile of T13, day 8,see also Section 5.1. The curve T24, day 10,see Figure 5.3,looks very

similar to the curve T13, day 10 in Figure 5.2. The curves for experiment T24 for longer

consolidation times show extreme scatter for low effective stress and low volume fraction.

Again,this can be explained with the density profiles. For consolidation times longer then 20

days, the uppermost centimeters of the mud layer are subjected to chemieal changes. In this

thin layer an extreme reduction in density was observed.

Also remarkable is that the curves for 20

<

a'

<

100 Pa appear moreor less as a straight

line.

I

I

5.2.4

Interpretation

of the effective stress data with the concept of fractal

structure

I

Introduction

The concept of fractal structure has been introduced in the seventies by Mandelbrot (1982).

In recent years the fractal concept has been found to be relevant to a broad rangeof physical

systems and phenomena, including sedimentation of cohesive sediment aggregates, where in

certain cases aggregates may be considered as fractal structures.

A fractal structure obeys geometrie sealing relationships. A feature of a fractal structure

is that it looks the same under different magnifications,i.e. they are invariant to a change in

length scale (self-similarity). An important parameter is the fractal dimension D. The

self-I

22

I

I

Day 8,

<Pp -

a' Day 10,

<Pp -

a' 100 Day 13,

<Pp -

a'

I

_";;l B 0.. .__. -b 10

I

1 0.01 0.1

<Pp (-)

I

_{Figure 5.2: Selection of effective stress data, experiment TI3}

I

I

10 •• Day 10,

<pp - a'

Day 20,

<pp

-

a' Day 24,

<Pp -

a' " 100

"

I

:1

• I!Jo'++!~ 1L_ ~ ~ __ ~~ __ ~~~~+L_ ~ 0.01

<Pp (-)

0.1

I

Figure 5.3: Selection of effective stress data, experiment T24

23

I

I

I

similarity of a fractal and the meaning of the fractal dimension is illustrated by an example

(Meakin, 1988).

Consider a basic element of mI particles positioned in a fixed configuration. Form an aggregate with mI basic elements, that are positioned in a configuration corresponding to the configuration of the particles in the basic element. Repeat the procedure by using mI

aggregates to form a new aggregate. After each iteration the size of the aggregate is increased by a factor m2. As a result, the total number N of particles in a fractal aggregate ofsizeRa

scales as

N-[~:r

where Rp is the size of the primary particles, and D is the fractal dimension given by (5.1)

I

I

D = lnmi.

Inm2 (5.2)

I

The construction of a fractal structure in the plane with mI

=

5 and m2

=

3 is illustrated in Figure 5.4.

The fractal dimension of a fractal structure in three dimensions may be any number in the interval [1,3]. Very tenuous or stringy aggregates have aD close to 1. In the caseof pure coalescence of particles, D would be equal to 3. For many aggregation processesdimensions

varying from 1.8 to 2.8 are found, depending on the underlying physical mechanisms on mic ro-scale (Meakin, 1988;Jullien

&

Botet, 1987; Kranenburg, 1994).

It

is noted that the structure

of real aggregates is random rather than deterministic. This means that fractal properties are recovered only after averaging over sufficient aggregates.

With respect to cohesive sediments, a number of sealing relations can be given, see e.g. Kranenburg (1994). Without reproducing the derivations, the relations between yield stress ay of a volume-filling network and volume fraction, and permeability and volumefraction are

given here:

I

(5.3)(5.4)

I

The yield stress ay is assumed to depend on the strength of the connections between the

particles. If one assumes that consolidating mud layer is yielding continuously,ay should be

related to the effective stress.

Notice that both (5.3) and (5.4) are power-law relations, which are represented by a

straight line if plotted on double-Iogarithmic scales.

Application of the fractal concept to effective stress and permeability measure-ments

I

Let us try to determine the fractal dimension of the effective stress data present5.1, 5.2 and 5.3. Only data are considered for which holds that a'

>

10 Pa, to be sure thated in Figures these data correspond to a volume-filling network rat her than a suspension.

24

I

I

I

Iteration 1

cW

I

Iteration 2

I

+

Iteration 3

I

I

I

Figure 5.4: Construction of a fractal in the plane with D

=

1.46

I

25

I

I

The determination of D for experiment T8, see Figure 5.1 is rat her subjective, since a

clear straight line is hardly discernable. Possibly the effective stress has not been developed

enough.

More successful is the determination of D for experiment T13, day 10 and day 13. (It

was argued before that the data for T13, day 8 seem to be unreliable.) The slope of the

best fit line is estimated at 6.67. Equating the slope to the exponent in (5.3) yields a fractal

dimension D

=

2.70. Repeating the procedure for the data of T24 yields D

=

2.72. The

correspondence is remarkable. In Figure 5.5 a straight line corresponding to the averaged

dimension D =2.71 is added to the effective stress data.

As an indication of the validity of the fractal concept, lines corresponding to D=2.71 are

presented together with the permeability data in Figure 5.6. Although these data show sig

ni-ficant scatter, the correspondence is satisfactory, especially for experiment T24. However, one

could also suggest a dimension closer to 3 for experiment T13. Nevertheless, the results shown

in Figure 5.6 indicate that effective stress and permeability are not independent parameters,

but are interlinked.

I

I

I

5.2.5

Analysis of the results of the vane tests

The typical shape ofthe graphs oftorque versus rotation angle (T-(p) is shown inFigure 5.7.

In this figure the peak torque is indicated by 'A' and the residual torque by 'B'.

Peak torques

I

Peak shear stress, Tpealo can be calculated from the peak torque by using (3.14). In Figure 5.8

the peak shear stress data against height of experiments T8, T13 and T24 are represented

together with the effective stress data for the same points of time. The accuracy of the torque

measurements was estimated at ±0.2 mNm, which results in an accuracy of the shear stress

values of approximately ±8 Pa.

Comparing the shear stresses only, it can be seen that the shear stress increases with both

depth and time, as expected. In 24 days the peak shear stress in the top of the mud layer

increased to approximately 50 Pa, and would be likely to increase when the consolidation

process continued. Deeper in the bed the peak shear stress developed to more than 150 Pa.

Comparison with effective stress shows that peak shear stress is generally of the same

order of magnitude. However, the peak shear stress is mostly slightly larger than the effective

stress.

In Figure 5.90" is plotted against Tpeak' The figure shows a more or less linear relationship

between the two parameters and indicates the presence of a peak shear stress at-zero effective

stress, the so-called true cohesion, Tc. The curves for T13 and T24 can be represented by a

straight line according to Tpeak

=

Tc

+

ma', where Tc

=

24 Pa and m

=

0.6. The curve for

T8 can also be represented by a straight line with m equal to 0.74 or possibly slightly less

(0.5). However, the true-cohesion is approximately 15 Pa, which is significantly smaller. The

increase in true-cohesion which is observed for day 8 to day 13 may indicate a time effect.

Thus, if the peak shear stress is reduced by the contribution of the true-cohesion, the

result,

T'

,

is approximately linearly proportional to the effective stress. Therefore, the graph

I

I

I

26

I

I

I

1000 T8 Day 3 T8 Day 8 D = 2.71 .

I

~ 100 c,

---10

I

1 0.06 0.1 0.2

CPp (-)

_;1 13 Day

10

24 Day

10

1000 13 Day 13 " 1000 24 Day 20

I

D

=

2.71 ... 24 Day 24D

=

2.71 ...

"

... ~ 100 ~ 100 c, c,

---

---

,

1h

l

-b _~ I I

I

10 10 1L--_-4L _J 0.06 0.1

CPp (-)

0.2 1l-"___---"-L _J 0.06 0.1

CPp (-)

0.2

I

Figure 5.5:Effectivestress data, experimentTB,T13 and T24

I

27

I

I

le-05 1 T24 D

=

2.71 ...

r.

·le-06

\

~

\

... en ... ...

---

S

.

',

--

+

ff·4

+

'.

~ + + . +~+\+ le-07 ++ <I ~~ ++ .+ '+ le-08 0.06 0.1 0.2

<pp (-)

+

I

+ ~ le-06

₁

... ~ en

---

_S

i~

..+

--

.. + + ~ + +++ le-07

I

le-08 0.06 0.1 0.2

<pp (-)

I

_{Figure 5.6: Permeability data, experiment T13 and T24}

I

A

I

s-

Z

S

--

s-B

I

<p (rad)

I

Figure 5.7: Typical curve of torque versus rotation angle

28

I

Figure 5.8: Effective stress and peakshear stress against height

I

I

160

140

120

~

100

c, ..._.

80

-"

'"

~ ~o..

60

40

20

0

0

20

I

.:.:.:. ...;...,., -... ' ... T8 --fr -T13 ---T21-···o.... Tpeak =Tc

+

ca _._.

-40

60

80

100

120

140

160

180

a'

(Pa)

I

Figure 5.9: Effective stress against peak shearstress

29

I

I

I

/

I

100 I ~ c, ...__, -b

E

10 "1-/ / ma' T8 ---

-"

T, T8 --G -ma', T13

--T'

,

T13 ---.-ma' T24-···

"

T, T24 ···-0-··· D=2.71 -.-. / / / / / o

I

1L_ L_ ___L __ ~ __ ~ ~ 0.06 0.07 0.08 0.09 0.1

<pp (-)

0.2

I

Figure 5.10: ma' and T' against

rP

p

I

for T' against

<pp

on double-logarithmic scale should correspond to the line pertaining to the

fractal dimension

D

=

2.71. This is shown in Figure 5.10 in which also the effectivo stre

s

s data

averaged over the vane height are presented. The figure shows a good agreement between the T' and scaled a' data and a good correspondence to the line pertaining to the fractal

dimension D=2.71 for stress levels higher than 10 Pa.

I

Residual torques

As can be seen in Figures AA9, A.50 and A.51 the residual torque is hard to quantify,

especially for experiment T8. Nevertheless, for experiment T13 and T24 the residual torques were estimated with some difficulty. The residual shear stress Tres, which is calculated by using (3.14), is presented in Figure 5.11 as a function of height, together with the peak shear stress. The residual shear stress curves seem to look realistic, despite the relatively bad quality of the data. The average ratio of peak to residual value is approximately 204

±

004, which is

rather low. More common values found in the literature vary from 3 to 5. An explanation might be that the mud layer was still very soft.

I

5.3

Reproducibility of the settling experiments

I

The inevitable drawback of the vane test as described in this study is that the settling experi

-ment cannot be continued, because there are significant effects on the subsequent consolidation behaviour. To study the time effects, multiple columns have to be set up. The question that arises is to what extent different columns show the same behaviour, that is, if an experiment

30

I

I

0.3 Tpeak, T13 ___ 0.25 Tpeak, T24 ····0···· Tres, T13 - -Q Tres, T24 ... 0.2 .._0. ,.-...

S

_{0.15 'Q} ..__, -e 0.1 G.. "0 0.05 1---1 0 0 50 100 150 200 T (Pa)

I

I

I

Figure 5.11:Tpeakand Tresagainst height

I

can be reproduced.

Comparing the settling of the interface one could argue that the experiment

TI3

and T24 show similar behaviour, whereas experiment T8 slightly deviates from the other two, see

Figure A.1.

However, comparing density profiles measured for different experiments, but for corre -sponding time points, it can be seen from Figures A.23 and A.24 that there are significant

differences between all profiles. The figure for Day 1 shows that the initial conditions vary significantly between all three experiments. However, as time proceeds the density profiles for the lower 10 cm converge. The deviation between experiments T13 and T24 is not that large during the whole experiment, except for the discrepancy initially found at h =23 cm, which persisted throughout the experiment. These results suggest that for reproducible density profiles the similarity of initial conditions is of vital importance.

Unfortunately, control of the initial conditions is limited. Here the initial conditions

turned out to be significantly different. Alternatively, the reproducibility can also be assessed by comparing behaviour governing relationships such as the effective stress-volume fraction relationship and, if sufficiently accurate, the permeability-volume fraction relationship.

The permeability data are considered to be of too poor a quality, therefore weconcentrate

on the effective stress-volume fraction relation only. Again the data of Day 1, 3, 8 and 10 are used for comparison. The effective stress is presented as function of the volume fraction.

Linear scales are used rat her than logarithmic scales to facilitate the comparison of the data series. (Fractal dimensions are unimportant here.) In Figures 5.12 and 5.13 the effective stress relations are shown. For Day 1 the effective stresses are too small to be of significance. For Day 3 the effective stresses have developed much more for experiment T8 than for T13

I

I

I

31

Day 1 Day 3 100 100 T8 + _T8 + 90 _T13 )IE 90 T13 )IE T24

•

T24

•

80 80 70 70 "..__ 60 ~ ₆₀ cd c,

_e:,

"--'" -0 50 _b 50 40 40 30 30 20 20 10 10 0.05 0.1 0.15 0.2 0.05 0.1 0.15 0.2

c/>p (-)

c/>p (-)

I

I

I

I

I

Figure 5.12: Effective stress versus volume fraction for Day 1 and Day 3, comparison between

experiments

and T24. The differencesbetween the data of TI3 and T24 are relatively small.

Later on during the experiments the effective stress es develop more and more, so that the

relationship of effective stress against volume fraction becomes more meaningful. For Day 8

it can be seen that the relationship found for experiment T8 still differs much from the ones

found for T13 and T24. The curves for T13 and T24 almost coincide for both Day 8 and Day

10.

Summarizing it can be stated that experiments T13 and T24 show the same behaviour,

since their effective stress relations correspond very weIl. Differences found in density profiles

are almost certain due to different initial conditions. Experiment T8 seems to deviate from

experiments T13 and T24 in all aspects (settling of the interfaces, density profiles and effective

stress-volume fraction relation), but the differences are not that large, except for the extreme

values of effective stress. Comparing effective stress-volume fraction relations can relax the

constraint of practically equivalent initial conditions a bit.

I

I

I

I

32

I

I

I

I

I

₁₄₀ Day 8 + ₁₄₀ Day 10_T13 )IE

)IE T24

•

•

120 120 100 100

I

~ ~ c, 80 c, 80 ,,__.. ,,__.. b -b 60 60 40 40

I

20 20 0.05 0.1 0.15 0.2 0.05 0.1 0.15 0.2

<pp (-)

<p

p

(-)

I

Figure 5.13: Effective stress versus volume fraction for Day 8 and Day 10,comparison between

experiments

I

I

33

I

I

I

Chapter

6

Conclusions

I

I

The following conclusions can be drawn from the present study on consolidation and strength evolution of Caland-Beer Channel mud. The accuracies of the non-destructive X-ray den-sity measurements and the pore water pressure measurements are quite high, resulting in an accuracy of

±

5 Pa for the calculated effective stress. Although calculated from density measurements and pore water pressure measurements, the accuracy of the calculated per me-ability is only fair, because of the averaging procedures. The accuracy of the shear stresses determined from the vane tests is

±

8 Pa.

Since the vane tests are destructive, investigation of the strength evolution requires mul-tiple experiments. To that end experiments in three columns were started simultaneously with equal initial conditions. The reproducibility for TI3 and T24 is quite good, which is expressed by consistent interface settlement curves and a effective stress-void ratio relation. Experiment T8 behaved slightly different.

The effective stress data turned out to relate to the volume fraction of solids according to a power law. The application of the fractal structure concept to cohesive sediments also prediets a power law between the effective stress and volume fraction. The fractal dimension obtained is 2.71

±

0.05, which is close to 3, indicating a dense structure. It turned out that for the present experiments the fractal dimension is invariant with respect to time, depth and column.

A fractal structure also implies that the permeability depends on the volume fraction according to a power law. The tendency of the experimental permeability data corresponds satisfactorily to the prediction for a fractal dimension of 2.71. This might be an indication of the validity of the fractal concept for soft mud beds.

Plotting peak shear stress against effective stress shows that the mud used exhibits true cohesion. Within the accuracy of experiment al error the true cohesion is the same for the measurements of Day 13 and Day 24, but is significantly smaller for the measurement of Day 8. This indicates a thixotropie effect. Furthermore, the relationship between effective stress and peak shear stress seems linear, so that the peak shear stress reduced by true cohesion can also be described by a power law holding for the fractal dimension of 2.71.

I

I

I

I

34

I

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I

Acknow ledgements

I

This work was funded jointly by the Netherlands Technology Foundation (STW) and the

Commission of the European Communities, Directorate General for Science, Research and

Development, under contract No. MAS3-CT97-0082(COSINus-project).It wascarried out in

the framework of the Netherlands Centre for Coastal Research (NCK).

I

EspeciallyIwould like to thank Dr G.C. Sills from the Department of Engineering Science,

University of Oxford for the pleasant cooperation and instructive discussions. Iwould also like

to thank Dr R. Gonzalez and Mr C. Waddup from the same department for their assistance

with the experiment al set-up. Iwould also like to express my gratitude to Dr C. Kranenburg

from the Faculty of Civil Engineering, Delft University of Technology,for the many valuable

comments and suggestions.

I

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35

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I

References

I

BEEN,K. 1980. Stress-strein behaviour of acohesive soil deposited under water. Ph.D. thesis,

Oxford University.

JULLIEN, R., & BOTET, R. 1987. Aggregation and fractal aggregates. World Scientific

Publications, Singapore.

KRANENBURG,C. 1994. The Fractal Structure of Cohesive Sediment Aggregates. Estuarine,

Coastal and Shelf Science, 39, 451-460.

I

MANDELBROT,B.B. 1982. The fractal geometry of nature. Freeman, New York.

MEAKIN,P. 1988. Fractal aggregates. Advances in Colloid and Interface Science, 28, 249

-331.

SILLS,G.C. 1994. Hindered settling and consolidation in cohesive sediments. In: Intercoh.

I

VANKESSEL,T. 1997. Generation and transport of subaqueous [luid mud layers. Ph.D. thesis,

Delft University of Technology.

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I

36

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I

Appendix A

Figures

I

40

T8

-e-T13

---lOt-T24

-e-I

35

S

_u

--

_...:::::

.... 30

b.O 'ä)

::r:

I

25

20

~

--

--_J

--

----~--

--

--~---

~--

--~

o

5

10

15

Time (day)

20

25

I

Figure A.1: Interface height with time

I

I

37

I

I

I

0.4 0.35 0.3 0.25

S

_0.2 "-' -c 0.15 0.1 0.05 0 1.1 Day1

--I

1.12 1.14 }.16 1.18 p (10 kg/m3) 1.2 1.22

I

_{Figure A.2: Vertical densitydistribution, experiment T8}

I

0.4 Day2 --0.35 0.3 0.25

I

__.._

8

_0.2 "-' ~ 0.15 0.1

I

0.05 0 1.1 1.12 1.14 1.16 1.18 1.2 1.22 p (10 kg/m3)

I

Figure A.3: Vertical density distribution, experiment T8

38

I

0.4 Day8 --0.35 0.3 0.25

:§:

_0.2 -e 0.15 0.1 0.05 0 1.1 1.12 1.14 _1.16 1.18 1.2 1.22 P (10 kg/m3)

I

I

I

0.4 0.35 0.3 0.25

--

S _0.2

--

-C! 0.15 0.1 0.05 0 1.1 1.2 Day3-

-I

1.12 1.14 1.16 1.18 p (10 kg/rrr")

I

_{Figure AA: Vertical density distribution, experiment T8}

I

I

I

I

Figure A.5: Vertical density distribution, experiment T8

39

I

I

Figure A.6: Vertical density distribution, experiment T13

I

0.4 Day 2 --0.35 0.3

I

... 0.25

S

_0.2 .._.. ~ 0.15 0.1

I

0.05 0 1.1 1.12 1.14 1.16 1.18 1.2 1.22 P (10 kg/m3)

I

Figure A.7: Vertical density distribution, experiment T13

40

I

Figure A.8: Vertical density distribution, experiment T13

I

0.4 Day 5--0.35 0.3 0.25 ...

8

_0.2 .__. ...c:: 0.15 0.1 0.05 0 1.1 1.12 1.14 }.16 1.18 1.2 1.22 P (10 kg/m3)

I

I

I

Figure A.9: Vertical density distribution, experiment T13

41

I

Figure A.1O:Vertical densitydistribution, experiment TI3

I

0.4 Day 10 --0.35 0.3 0.25

I

--

--

S

_0.2 ~ 0.15 0.1

I

0.050 1.1 1.12 1.14 }.16 1.18 1.2 1.22 P (10 kg/m3)

I

Figure A.ll: Vertical density distribution, experiment TI3

42

I

I

Figure A.I2: Vertical density distribution, experiment TI3

I

0.4 Day 1 --0.35 0.3 0.25

I

S

_--

_0.2 ..c:! 0.15 0.1

I

0.050 1.1 1.12 1.14 }.16 1.18 1.2 1.22 p (10 kg/m3)

I

Figure A.I3: Vertical density distribution, experiment T24

43

I

I

_{Figure A.I4: Vertical density distribution, experiment T24}

I

'

0.4 Day 3--0.35 0.3 0.25

I

S

_0.2

----

_-e 0.15 0.1

I

0.05 0 1.1 1.12 1.14

1.

₁₆ 1.18 1.2 1.22 p (10 kg/m3)

I

Figure A.I5: Vertical density distribution, experiment T24 44

t

Figure A.16: Vertical density distribution, experiment T24

,

0.4 Day 10--0.35 0.3 0.25

I

_...,

5

0.2 ..c: 0.15 0.1

I

0.050 1.1 1.12 1.14 }.16 1.18 1.2 1.22 P (10 kgjm3)

I

Figure A.17: Vertical density distribution, experiment T24

45

I

I

0.4 Day20 --0.35

I

0.250.3 ~ El _0.2 ___. ~ 0.15

I

0.1 0.05 0 1.1 1.12 1.14

1.

₁₆ 1.18 1.2 1.22 p (10 kg/m3)

I

_{Figure A.18: Vertical density distribution, experiment T24}

I

0.4 Day24--0.35 0.3 0.25

S

_0.2 ___. ~ 0.15 0.1 0.05 0 1.1 1.12 1.14

1.

₁₆ 1.18 1.2 1.22 P (10 kg/m3)

I

I

I

Figure A.19: Vertical density distribution, experiment T24

46

0.4 0.35

-

---0.3 --- -0.25

S

_0.2 '-" ~ 0.15 0.1

I

I

I

I

,

0.4 0.35 0.3 0.25

S

_0.2 '-" ~ 0.15 0.1 0.05

I

I

I

Day 1 Day 2 Day 3 Day 8

---

-

~-" , .J , .J

'

:::S

--

-

;'':-7_:''

<; -; I'-~ '- r '-,

-,

v, 'v \ " f'1 " .: ~ ..i .),...~ '\ ,/

-

\ \ ~ ( -,

,

-/ ... 0.05

o ~----~---~---~----~----

--~

----~

1.1

-

.

_

1.12 1.14 1.16 1.18 P (103kg/m3) 1.2

Figure A.20: Vertical density distribution with time,experiment T8

Day 1 Day 2 Day 3 Day 5 Day 8 Day 10 Day 13 "

o ~----~---~---~---~---~---~

1.1 1.12 1.14 }.16 1.18 P (10 kg/m3) 1.2

Figure A.21:Vertical density distribution with time,experiment T13

47

1.22

I

I

I

0.4 0.35 0.3 0.25 _...,

El

_0.2

--

~ 0.15 0.1 0.05 Day 1 --Day 2 --- -Day 3 -- - --Day 8 _._. -Day 10 -.-. -Day 20 --- -- -Day 24 --- ----":.:.:_-

-

-

~'t"".:....,_"_...":..

o

~----

~---

~

---

~----~--

--

--~--

--

--1.1 1.12 1.14 p (10}'~~jm3) 1.18 1.2 1.22

I

_{FigureA.22: Vertical densityclistribution withtime,experimentT24}

Day 1 Day 3

I

0.4 0.4 T8-- T8 --0.35 T13 - - - -- _0.35 T13 ---- -T24-·-··· T24-·-· ···-0.3 0.3 0.25 0.25

I

S

_--

_0.2

S

_--

_0.2 ~ ~ 0.15 0.15 :

:

~ 0.1 0.1 :,.' t»

I

0.05 0.05 -,, -,, '.~_."'.... 0 0 1.12 1.14 }.16 1.18 1.2 1.12 1.14 }.16 1.18 1.2 p (10 kgjm3) p (10 kgjm3)

I

Figure A.23:Verticaldensitydistribution for Day 1 and Day3,comparison between experiments

48

I

I

I

I

Day 8 Day 10 0.4 0.4 J J J T8

--

_T13 -

-

- -0.35 T13 - - --- _{0.35 T24} ... T24··· 0.3 0.3 .::'"-=--::,.:-.::'".::'"_::'".:-.=-.::.

/-

-0.25 0.25 ,"; "

S

_~ v t 0.2 0.2 '-'-. .__, " ~ ~ 0.15 0.15 f- , ,"

",

0.1 0.1 f- ','··~.I_, - "-0.05 0.05 f- ".~_',.._' --._'., " 0 0 .l_ 1.12 1.14 }.16 1.18 1.2 1.12 1.14 }.16 1.18 1.2 p (1O kg/m3) p (1O kg/m3)

I

I

_{Figure A.24: Vertical density distribution for DayB and Day 10, comparison between experiments}

I

0.4 0.35 0.3 0.25

----

_El 0.2 .__, ~ 0.15 0.1 0.05 0 0 Day 1--Day 2 ----Day 3 -- ---Day 8 _._.

-I

I

50 100 150 200 250 300 350 400 450 Pe

(Pa)

I

Figure A.25: Excess pore water pressure development,experiment TB 49

I

I

I

0.4 0.35 0.3 0.25

S

_{'-" 0.2} ~ 0.15 0.1 0.05 0 0

I

I

I

0.4 0.35 0.3 0.25

S

_{'-" 0.2} ~ 0.15 0.1 0.05

I

I

I

I

Day 1--Day 2 - ---Day 3 - --- -Day 5 . Day 8 _._ .-Day 10 -.- .-Day 13 ---- -50 100 150 200 250 300 350 400 450 Pe

(Pa)

FigureA.26: Excess pare water pressure develaprnent, experimentT13

Day 1--Day 2 ----Day 3 --- -Day 8 _._. -Day 10 -.-. -Day 20 --- -- -Day 24 ---- --lil_,

.

,

'.,

.

,

'

.

,

_'

_.

.

_'

_.

_,

..

'

.

,

_'

_.

o

~

--~--~--~~~~----~--~~--

~

~~--

~

o

50 100 150 200 250 300 350 400 Pe

(Pa)

FigureA.27: Excess pare water pressure development,experiment T24

50