Consolidation and strength evolution of Dollard mud: Measurement report on laboratory experiments

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Delft

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Delft UniversityofTechnology

Department of Civil Engineering

Hydraulicand Geotechnical EngineeringDivision HydromechanicsSection

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Consolidation and strength evolution of

Dollard mud

Measurement report on laboratory experiments

L.M. Merckelbach report no. 4-99

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1999

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The work reported herein has been financially supported by the Netherlands Tech-nology Foundation (STW) and the Commission of the European Communities, DG XII, MAST3-COSINUS Project (Contract No. MAS3-CT97-0082).

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Hydromechanics Section, Faculty of Civil Engineering and Geosciences, Delft University of Technology, P.O. Box 5048, 2600 GA, the Netherlands. Tel. +31 15 278 40 70; 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 having dredged large amounts of mud. Some authorities relate the navigable depth to a 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.

A research project is conducted to develop a model to describe the consolidation behaviour and strength evolution of mud layers. The third series of experiments for this project, executed at Delft University of Technology,are described in this report. The analysis of the data is left for future work.

The sediment at ion and consolidation of Dollard mud was simulated in segmented consol-idation columns. By using segments well-defined and undisturbed samples of the mud bed

were obtained

.

For this reason, more accurate shear vane measurements of the samples could

be done than if conventional consolidation columns had been used.

Four segmented consolidation columns and one conventional consolidation column were set up. To study the time evolution of the strength of the mud bed, the segmented columns were dismantled at different times. After the dismantling, shear vane tests were carried out and density measurements were done with a conductivity probe. The density profiles of the mud layer in the conventional column were measured with a 'Y-ray densimeter. Pore water pressures were measured at several times. From these measurements effective stresses and permeabilities were calculated. Various rheological parameters were derived from four different types of shear vane measurements. Flow curves were also measured.

It turned out that significant segregation occurred, resulting in a mud bed formed on top of a layer of approximately 5-8cm with a relatively large coarse silt fraction and high densities. For the mud layer it turned out that the effectivestresses could be approximated by a power law. Furthermore, the rheological parameters turned out to be approximately linearly interrelated, even though the parameters were derived from different types of rheological experiments. Both the relationships between peak shear stress and density, and between peak shear stress and effective stress show time dependency.

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Contents

1 Introduction 3

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2 Experiments2.1 Experimental set-up 44

2.2 Measurement techniques . 6

2.3 Mud preparation

...

7

3 Results 10

3.1 Mud-water interface settiement 10

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33.3.2 Density profilesPartiele size distributions per segment. . . 1011

3.4 Excess pore water pressure profiles 11

3.5 Effective stress data 11

3.6 Permeability data. 12

3.7

Shear stress data

.

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45 AcknowledgementConcluding remarks 1418

References 19 List of Symbols 20

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A Figures 22 B Density measurement 45

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2

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Chapter 1

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Introduetion

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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 bot tom 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 kg/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 related to 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 inlower costs.

Presently, a research project, which is financed by The Netherlands Technology Founda-tion, is conducted to develop a mathematical model of strength evolution in a mud bed. This model 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 introduced into a mud sample. During the period from April 28th until July 19th 1997, a first series of experiments was carried out at the Uni-versity of Oxford and reported in Merckelbach (1998b). A second series of experiments was carried out at the Hydromechanics Laboratory of Delft University of Technology, Department of Civil Engineering and Geosciences during the period from April 14th until July 17th 1998 and reported in Merckelbach (1998a). In both experiments Caland-Beer Channel mud was used.

A third series of experiments was also carried out at the Hydromechanics Laboratory of Delft University of Technology during the period of October 12th 1998 until January 13th 1999. The results are reported herein. However, the analysis of the data will be left for future work. It is noted that the data reported herein are also available on CD-ROM.

This report is organized as follows. In Chapter 2 the experimental programme is discussed and the measurement techniques used. In Chapter 3 the results are presented. Concluding remarks are stated in Chapter 4.

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Chapter

2

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Experiments

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The laboratory experiments described here, follow up the experiments on Caland-Beer Chan-nel mud, described in Merckelbach (1998a). Again, the aim is to simulate the formation of a mud layer formed by deposition from a suspension and to study the self-weight consolidation behaviour and strength evolution of this mud layer. Therefore, the experimental set-up used in earlier experiments, was reused, albeit with some minor modifications. This time we used a different type of mud, so that the data would not be restricted to one type of mud. Of the marine types of mud available in The Netherlands, we chose Dollard mud, since we expect that Dollard mud has a composition that differs most from that of Caland-Beer Channel mud.

2.1

Experimental set-up

A brief description is given here only. For a more detailed description of the experiment al set-up and procedures, the reader is referred to (Merckelbach, 1998a).

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We used consolidation columns to simulate the deposition and the consolidation behaviour. Four segmented columns and one conventional column were set up. The columns were 1.6 m high and they had an inner diameter of 10 cm.

The segmented columns were designed such

that

at some time, the consolidating bed could be sliced into well defined samples of 10 cm in diameter and 5 cm in height. Accurate shear strength measurements were done on these samples with a miniature vane.

So-called column segments were used to obtain the samples. In Figure 2.1, a sketch of a column segment is presented. In fact, only the consolidated bed at the time of dismantling needs to be covered with column segments, so that the remaining part of the column was constructed in one piece. One step of the dismantling procedure is shown in Figure 2.2. The procedure was repeated until all segments were isolated.

The drawback of this procedure is that after dismantling a column, the consolidation experiment could not be continued. Studying the strength evolution requires multiple, equally set-up columns. Therefore, four segmented columns were set up. Subsequently, these columns were dismantled after 9, 29, 63 and 95 days of consolidation.! Throughout this report the segmented columns are labelled as TDLxx, where xx denotes the duration of the particular experiment in days, and the conventional column is labelled TDLC.

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lThe measurements on Caland-Beer Channel mud were done on days 9,24,58 and 95.

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column section

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b~ '4 • I 18cm

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a complete segment

Figure 2.1: A base plate, a column section and a complete segment

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a) ~ I

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c) upper section lower section b) a) Set-up during consolidation.

b) Lower section after removal of upper section. The column section of the uppermost segment is pusbed on to the base plate (1), then, the segment is slided aside (2).

c) The removed segment with the sample, ready for the shear vane test.

Figure 2.2: A schematic picture of the dismantling of a segmented column

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2.2

Measurement techniques

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Basically three parameters were measured: pore water pressure, density and bed strength. In each cohunn pore water pressure ports were let into the column at twelve discrete levels. Tubes connected the pressure ports to a pressure measuring unit. A pressure measuring unit is a device that controls the actual conneetion between the pressure transducer and the pressure ports by means of valves, with a maximum of 24 pressure ports per transducer. Hence, three pressure measuring units were used to serve all five columns. The accuracy of the pore water pressure readings is 10 Pa.

Bulk densities of the bed in the segmented columns were measured with a conductivity probe after dismantling and the shear vane tests. The bulk density of the bed in the con-ventional column was measured with a non-destructive "'(-raydensimeter, which was provided by the dredging company H.A.M. Several density profiles were measured of the conventional column. From these density profiles, together with the corresponding pore water pressure profiles, the permeability could be estimated. Regarding the set-up used in earlier experi-ments, the traversing system of the "'(-raydensimeter hasbeen automated, so that continuous density profiles could be measured. The accuracy of the density measurements is

±

5 kg/m3. The vertical resolution is about 1.7 cm. The improved "'(-ray densimeter system is discussed in more detail in Appendix B.

Rheological measurements were done with a UDS 200 rheometer, manufactured by Physica GmbH. Two devices were used: a five-bladed vane, 2.0 cm high and 1.0 cm in diameter, for

strength measurements and a concentric cylinder geometry for the flow curve measurements. The vane tests were carried out on the samples confined in the isolated segments. On each sample four different vane tests were carried out:

Rate controlled 1: The rotation speed was set at 1.0 rpm and the torque was recorded over a range of two complete revolutions. The data are characterized by four parameters: peak shear stress, rpeak, the peak angle 4>peak,the residualshear stress, rresiduab and the tangent to the curve in the origin, ~. See Figure 2.3 for the definitions.

Rate controlled 2: The rotation speed was set at 0.10 rpm and the torque was recorded over a range of 35 degrees. The data are characterized by three parameters: peak shear stress, rpeak, the peak angle 4>peak'and the tangent to the curve in the origin, ~. See Figure 2.3 for the definitions.

Stress controlled: The applied torque was increased from 0.01 mNm until 10 mNm loga-rithmically in a time interval of 300 s and the rotation angle was recorded. However, each measurement was aborted shortly after the materialstarted to flow. The data are characterized Dy two parameters: the yield stress, ryield, ani the yield angle, t/>yïeld.See Figure 2.4 for the definitions.

Oscillating, rate controlled: The vane was oscillated with an angular frequency ranging from 0.6 rad/s to 30 rad/s, and a rotation angle amplitude of 1.0 mrad. The storage modulus G' and the loss modulus Gil were recorded. The data are also characterized by two parameters: the storage modulus G' and the loss modulus Gil for an angular frequency of 1.57 rad/s. See Figure 2.5 for the definitions.

For experiment TDL63 and TDL95 only, oscillating vane tests were also carried out directly after the rate controlled vane test at

n

= 1 rpm.

In

this way the residual storage modulus and the residualloss modulus were measured.

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800700 600 ...-.. ~

e:_

500 ril ril

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200 RotatioD aagle(rad)

100 Tresidual

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0 2 4 6 8 10 12

Rotation angle (rad)

Figure2.3: A typical recording of a rate controlled measurement.

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500

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Tyield

--

ril ril ~ 300 ~ ril s-. ~ Q) 200 ..c:: 00

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100 <Pyteld 0 0 0.5 1 1.5 2 2.5 3 3.5 4

Rotation angle (rad)

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_{Figure2.4: A typical recording of a stress controlled measurement.}

2.3

Mud preparation

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The mud that was used, originated from the Ems-Dollard Estuary, The Netherlands. It

was

dredged in September 1998, near Nieuwe-Staten Zijl. lts bulk density was about 1400 kg/m3• A few properties of Dollard mud are listed in Table 2.1. The corresponding properties of

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Angular frequency

(rad/s)

Figure 2.5: A typical recording of an oscillation measurement.

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Caland-Beer Channel mud are also presented. Partiele size distributions are presented in Figure 2.6

Table 2.1: Properties of Dollar mud and Caland-Beer Channel mud

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_{2.6362 ±0.006} 42 18.0 108.23 3.05 2.5278 ±0.006 70 20.1 96 3.99

Dollard Caland-Beer Channel

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density of solids (x 10 kg/m) sodium adsorption ratio (-)

cation exchange capacity (cmol/kg) specifi.c surf ace (m2/g)

humus (% by weight)

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The mud used in the experiments was diluted to a density of approximately 1075 kg/m3. The diluent was tap water with NaCl added, until the water had a density of 1003.5 kg/m3, which is equal to the density of the pore water. Before the mud suspension was introduced into the columns, it had been mixed thoroughly for one hour.

An overview of the initial conditions is presented in Table 2.2.

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100.00 80.00 60.00 ~ 40.00 20.00 0.00 1

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TDL9 TDL29 TDL63 TDL95 TDLC

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.."'- Cumulative mass, Dollard mud

--+-Cumulative mass, Caland-B~r Channel mud ....•.... Mass density, Dollard mud -Mass density, Caland-Beer Channel mud ....•....

10 100

Equivalent spherical diameter d (J.'m)

Figure

2.6:

Partiele size distribution

Table 2.2: Properties of the mud suspensions introduced

den-Initial height (m) den-1.531 1.532 1.532 1.533 1.532 1003 1003 9 1000

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Chapter

3

Results

3.1

Mud-water

interface settlement

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The level of the mud-water interface was measured at different times during the experiments.

The measurements are shown in Figure A.1 (logarithmic time scale) and Figure A.2 (linear time scale). The interface dropped from 1.53 m (initial height) to about 0.65 m within one day. Subsequently, the settling velocity gradually decreased. Significant deformations did not occur anymore after about 50 days. The correspondence between the interface heights of the different cohunns is good. The discrepancy between the interface heights around 0.4 days is artificial and caused by missing data points.

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3.2

Density profiles

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In contrast with the conventional column, in which several density profiles were measured,

only one density profile was measured of each segmented column. In Figures A.3 through A.6 the density profiles of the four segmented columns (TDL9, TDL29, TDL63 and TDL95) are shown together with the corresponding density profile of the conventional column.

In all columns exceptionally high densities were measured in the lowest 8 cm of the bed.

The reason for these high densities is probably that coarse silt and fine sand particles seg-regated in the initial dilute suspension and settled very quickly Partiele size distributions, determined from samples taken from different segments are in support of this, see also

Sec-tion 3.3.

The correspondence between the density profiles measured with the conductivity probe and the "(-ray densimeter is quite good for the experiments of TDL29 and TDL63. Unfor

-tunately, the density measurement with the "(-ray densimeter of day 9 failed. Therefore, the measurement of day 8 is shown instead. The difference in height of the interface is mostly the result of the difference in time of measuring.

More serious deviations are observed between the density measurements after 95 days.

The discrepancy is most likely the result of the presence of gas bubbles. A number of gas bubbles with a diameter up to about 5 mm were observed during the dismantling of TDL95.

In contrast with the conductivity probe, the density data obtained with the "(-ray densimeter are not point measurements, but are averaged over the cross-section of the column. Therefore, if gas bubbles were present, it is likely that densities measured with the "(-ray densimeter are more reduced than densities measured with the conductivity probe.

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probe is consistently higher than the density measured with the '"(-ray densimeter.Furthermore, it is noted that the density near the bot tom measured with the conductivity Unfortu-nately, the confidence in data obtained with both methods is low, because i) the range for which the '"(-ray densimeter in the present set-up could be ealibrated was limited to 1000 -1300 kg/m3, and ii) the samples taken from the lowest segment to calibrate the conductivity

probe, were too thick to measure the density with either the DMA35N density measurement system or density measurements based on the evaporation of pore water. The problem with the lat ter method was

that

because of the high viscosity, the volume of the sample could not be determined accurately. Fortunately, these data are not of great importance, since the bed in the lowest 5 to S cm consisted mostly of coarse silt or fine sand, see also Section 3.3.

In Figure A.7 all density profiles measured in the conventional column are collected. This figure shows the development of the density distribution of the conventional column (TDLC) with time.

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_3.3

_{Partiele size distributions per segment}

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Mud samples of a number of segments of experiment TDL29 and of all segments of TDL95 were analyzed for the partide size distribution. Here,

z

denotes the height above the base of the column. The mass density and cumulative mass percentages are shown in Figures A.S through A.H.

The results of both experiments are consistent. The partiele size distributions for

z ~

10 cm are almost equivalent and the coarse silt and fine sand fractions are almost completely

absent. For 0 ~

z

<

5 cm, i.e. the lowest segment, the coarse silt fraction and the fine sand

fraction spectacularly increased at the expense of the day and fine silt fractions. This result is in agreement with the measured density profiles. The region 5 ~

z

<

10 cm ean be regarded as a transit ion zone.

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3.4

Excess pore water pressure profiles

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The excess pore water pressure profiles are shown inFigures A.12 through A.16. The results of the pore water pressure measurements of the segmented columns do not show any anomalies. The dissipation of the excess pore water pressure with time ean dearly be observed.

3.5

Effective stress data

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Generally, the effective stress is defined as the tot al stress minus the pore water pressure. Total stresses are easily obtained by integration of the density profiles. The effective stress data are shown in Figures A.17 through A.20. Figures A.17 and A.1S, in which the effective stress is plotted against the partiele volume fraction, show that a power law relationship exists between effective stress and partiele volume fraction if the partiele volume fraction is smaller than ab out 0.16. For larger values the relationship seems to deviate, which is most likely a result of segregation.

The accuracy of the effective stress data, which depends on the accuracy of both the pore water pressure measurement and the density measurements, is estimated at ±15 Pa.

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Permeability was calculated from Darcy

3.6

Permeability data

's law:

1 élpe

k=---Va

8z'

(3.1)

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wheresure gradient. The settling velocity is calculated from two consecutive density profiles. TheVs is the settling velocity of the solids, k is the permeability and ~ the excess pres-excess pressure gradient used in (3.1) is the average of the pres-excess pressure gradients pertain

-ing to these two density profiles. The calculation procedure is described in more detail by Merckelbach (1998b).

Since the calculation of permeability requires at least two density profiles, the permeability data are available only for the conventional column (TDLC). The permeability data are presented in Figure A.21. The time indicated for each series of measurements is the average of the times of the two density profiles used in the calculation.

The permeability data for specific times seem to relate to the partiele volume fraction according to a power law if c/>p

<

0.16. However, the proportionality factor fluctuates signifi-cantly. Itis noted that the validity of both the effective stress and permeability power laws

is restricted to the range

<pp

E [0.08:0.16].

The permeability data for

<pp

>

0.16 show serious scatter, which can be explained as

follows. The determination of the permeability by the method used here, becomes inaccurate ifthe settling velocity approaches zero, which follows from (3.1). From Figure A.7 it can be seen that the density remained more or less constant in time for

p ~ 1260

kgjm3

==

~p ~

0.16

,

implying very low settling veloeities and with that inaccurate data. The accuracy for

<pp

<

0.16is estimated at ±3.0 x 10-

7

mis.

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3.7

Shear stress data

Rate controlled shear vane tests

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The peak shear stressesshear vane test at 0=1.0 rpm and 0

(Tpeak)

and the peak angles=0.1 rpm, are shown in Figures A.22 through A

(<Ppeak),

measured with the rate controlled.25. The segments are numbered starting from the interface and ending at the bottom. Note that each segment has a height of 5.0 cm.

The peak shear stresses increased with increasing depth and time, except for the peak shear stresses measured in the lowest segment. The peak shear stress measured in the lowest segment was initially higher than measured in the other segments, but increased much more slowly with time. The peak shear stresses obtained at a rotatien speed of 0 = 1.0 rpm were generally higher than those obtained at a rotatien speed of 0 = 0.1 rpm. Peak angles, on the other hand, did not change significantly and are more or less constant at 0.2 rad, irrespective of depth and time.

The residual shear stresses (TresiduaI) and the initia! curve gradients (~ 14>=0) are shown in

Figures A.26 through A.29. The residual shear stresses for 0 = 0.1 rpm were not determined, since these tests only covered the first 35 degrees. The residual shear stresses for 0 = 1.0 rpm and the initial curve gradients also increased with depth and time, as expected. However, the residual shear stresses measured in the lowest segment were also initially larger than the residual stresses measured in other segments, and increased much more slowly with time. The

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initial curve gradient forThe initial curve gradient data points show some scatter, which is probably caused by the

n

=0.1 rpm was generally larger than the gradient for

n

=1.0 rpm. fitting procedure based on only two data points.

Stress controlled shear vane tests

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The yield stresses

(Tyield)

and the yield angles

(t/>yïeld),

measured with the stress controIled shear vane test, are shown in Figures A.30 through A.33. The yield stresses also increased with increasing depth and time, except for the measurements of the lowest segment. The yield angles remained more or less constant at 0.2 rad. It is noted that the measurement of the yield stress and angle of the lowest segment for TDL63 is not available.

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Oscillating shear vane tests

The storage moduli (G') and the loss moduli (G") at w = 1.57 rad/s are shown in Figures A.34 through A.37. The residual storage and loss moduli were measured for only TDL63 and TDL95,

and

are shown in Figures A.36 and A.37.

Both the storage moduli and the 1088 moduli increased with increasing depth and time, except for the measurements of the lowest segment. The similarity between corresponding G'-curves and G"-curves is remarkable, for all segments. The curves of the residual moduli are similar to the (ordinary) moduli in all but magnitude.

The tangents of the loss angles, defined by

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(3.2)

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are shown in Figure A.38. It appears that tan 5 remains more or less constant for all segmentsbut the lowest one, with

an

averaged value of about 0.154. The loss angles determined from the residual moduli are also more or less constant for all segments but the lowest one, however,

the averaged value isslightly larger. Flow curve measurements

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Flow curve measurements were obtained with a concentric-cylinder device. The measured shear stresses are presented as function of the shear rate in Figure A.39 and Figure AAO. For shear rates larger than approximately 5 s-l, the mud can be considered as a Bingham fluid. The dynamic differential viscosity is, which is a constant for Bingham fluids, is about 40.10-3 Pa s for bulk densities of 1200 kg/m3 and about 80.10-3 Pa s for bulk densities of

1230 kg/m3• The Bingham yield stresses vary slightly more and are not very weIl reproduced. The Bingham yield stresses are about 24 Pa for bulk densities of 1200 kg/m3 and about 45

Pa for bulk densities of 1230 kg/m3•

The dynamic apparent viscosity is plotted against the shear rate on double logarithmic scales in Figure A.4l. For shear rates higher than 4 S-I, the dynamic viscosity is

approx-imately proportional to the reciprocal value of the shear rate. The dynamic viscosities for bulk densities of about 1230 kg/m3 are generally higher than the dynamic viscosities for bulk densities of about 1210 kg/m3.

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Chapter 4

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Concluding

remarks

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The following remarks can be made concerning the present experiments.

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Experimental set-up

It was the second time that segmented consolidation cohunns were used. The segmented columns were designed such, that after some time of consolidation the mud bed could be sliced into well defined samples. Accurate and sensitive shear vane tests were carried out on these samples. The design again proved to be satisfactory.

The procedures and instrumentation with respect to the density measurements with the conductivity probe, the pore water pressure measurements and shear strength measurements were the same as for earlier experiments on Caland-Beer Channel mud. The recommendations regarding the traversing system of the 'Y-raydensimeter and the calibration procedure, as they were put forward after evaluation of the earlier experiments, have been followed, so that in the present set-up accurate and continuous density profiles could be measured.

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Results

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The results on the interface settlement, density measurements and effective stress data show a good correspondence between the different experiments, which means that the reproducibility of the experiments can be considered quite good.

All density profiles show a spectacular increase of the density near the bottom, which is very unusual for mud layers. Partiele size distributions, determined for several heights in the bed, indicate that a significant amount of the coarse silt fraction had segregated. The high densities that are observed near the bot tom, were attributed to the occurrence of segregation.

In earlier experiments on Caland-Beer Channel mud and Combwich mud (Merckelbach,

1998b; Merckelbach, ~a; Merckelbach et al., 1999) it was found that the effective stress followed a power law'

6r

tHepartiele volume fraction. For the present experiments this seems to be true if the data points pertaining to the lowest 8 cm of the bed are excluded, see Figure 4.1. It was shown that the partiele size distribution of the bed, ranging from 10 cm of the base and higher, was more or less invariant with the height. From this, it seems likely that a power law relationship between effective stress and partiele volume fraction requires a constant partiele size distribution throughout the bed.

The rheological experiments showed that the parameters that can be related to strength, all increased with depth and time, if the measurements of the lowest segment are left out of

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1000 • .-~

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...__,c, 100 Day 2

b

_{Day 8}

•

_•

Day 11

_•

Day 18

_•

Day 23 • Day 29

_•

Day 39

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•• 111 Day 63 10 0.1

rpp (-)

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Figure 4.1: Effective stress data of TDLC as function of

rPp,

excluding the data points pertaining to the lowest 8 cm of the bed

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consideration. However, this general behaviour is not only qualitative: all parameters are more or less linearly related, see Figure

4.2.

Furthermore, it

was

observed that the

rotatien angle

at which the peak shear stress was reached in the rate controlled measurements, was practically the same as the rotation angle at the yield point in the stress controlled measurements. Moreover, these angles remained constant with respect to dep th and time.

H the peak shear stress (or any other shear strength parameter) is related to the bulk

density, it can be seen that the relationship between peak shear stress and density is time dependent, see Figure 4.3. H, for instance, the strength evolution for p = 1200 kg/m3 is considered, we see that the peak shear stress increased with about a factor 3 from 9 to 95 days. The time effect seems to be most distinct during the early stage of consolidation.

Figure 4.4 shows the relationship between peak shear stresses and effective stresses. Leav-ing the data points of the lewest segment out of consideration, i.e. of each curve the data point with the highest effective stress, an approximately linear relationship can be observed.

Generally, the peak shear stress increases with time for a given effective stress. The data will be further analyzed in future work.

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400

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~ ~ El cd ~

₂₀₀

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100

0

0

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20000

--

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'-" .... ~ ~_~ El

10000

«!_.... «! 0..

5000

0

0

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--+- T,~S,

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rpm --*- ,

0=1.0

r m - - .- - peak,

0=0.

t>

rpm

----B

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T,

8, 0=0.1

rpm

--.--~, 0=0.1

rpm

100

200

390

400

500

T peaki

0 = 1.0

rpm

600

700 --+- Tyield X

10

--*- G'

-

-

.- - G"

--

-

-

B

--

--

G'

₁₁ 8 --.-- Gres 100

200

390

400

500

T peaki

0 = 1.0

rpm

600

700

Figure 4_2: Dependencies between rheologïcal strength parameters

16

_.

800

I

I

₈₀₀

700

600

..-..._ro

500

0..

--

_..-:

400

'"

'"

f-o.

300

200

100

0

1000

\3'...

Day 9

----.:

!

g:~~~

Day 95

8

~

·..·

::

~

J,'

,

"

_-:

.:

.

::~~

.

l-/)<- ----

---

-

--

--

-

---~

~~

.~~

.." ..

.

J

3·

ll-:;;1

ft'

I

I

I

1100

1200

1300

1

400

p (kgfm3)

1500

1600

1700

I

Figure 4.3: Peakshear stress against density

I

I

800

700

600

..-..._ro

5

00

0..

--

400

~

'"

f-o.

300

200

100

0

0

----

Day 9

--)f--

Day 29

--

.

--

Day 63

....13....

Day 95

-

..

I

100

200

300

400

(1'

(Pa)

500

600

700

800

I

Figure 4.4: Peak shear stress against effective stress

I

I

Chapter

5

I

Acknow ledgement

I

This work was funded jointly by the Netherlands Technology Foundation (STW) and the Commission of the European Communities, Directorate Genera! for Science, Research and Development, under contract No MAS3-CT97-0082 (COSINus-project). It was carried out in the framework of the Netherlands Centre for Coastal Research (NCK).

I

I

I

I

I

I

18

I

I

References

I

I

BEEN,K. 1980.Stress-etmin belunnour of a cohesiue soil deposited under water. Ph.D. thesis,

Oxford University.

MERCKELBACH,L.M. 1998a. Consolidation and strength eoolution of Calend-Beer Chan

-nel mud. Tech. rept. no. 7-98. Hydraulica Section, Delft University of Technology, the

Netherlands.

I

MERCKELBACHL,.M. 1998b. Laboratory ezperiments on consolidation and strength euolution

of mud layers. Tech. rept. no. 1-98. Hydraulics Section, Delft University of Technology, the Netherlands.

MERCKELBACH,L.M., SILLS,

G

.

C.,

& KRANENBURG,

C.

1999. Laboratory experiments on consolidation and strength evolution of mud layers. To be published in: Proc. Intercolt

'98 Seoul.

I

I

I

I

I

19

I

I

I

List of Symbols

A

cross sectional area m2

A

calibration constant kg m-3 V-I

I

A

calibration constant Pa

B ca1ibration constant kg m-3

B ca1ibration constant

c concentration gil

Cs concentration of ca1ibration sample gil

e void ratio

I

G'

storage modulus Pa

Gif _{loss modulus Pa}

I electrica1 current Amp

kl calibration constant g 1-1

k

2 calibration constant g 1-1 V-I

k permeability m s-1

I

1

height of vane m

1 distance between electrodes m

Pe excess pore water pressure Pa

r radius of vane m

r resistivity Om

R

resistance

n

I

t time s

T measured torque mNm

Us velocity of the particles m S-1

V voltage volt

V

o

voltage measurement of clear water volt

l's

voltage measurement of sample volt

I

z

vertica1 ordinate m

'Y

shear rate S-1

6 108sangle rad

'TJ dynamic differential viscosity Pa s

I

p density kg m-3

Pb bulk density of the mud kg m-3

Pf density of the pore water kgm-3

Ps density of the solids kgm-3

I

al

effective stress Pa

I

'T shear stress Pa

t amplitude of shear stress Pa

'Tpeak peak shear stress Pa

'Tresidual residual shear stress Pa

'Tyield yield stress Pa

r/> rotation angle rad

I

~ amplitude of rotation angle rad

r/>peak peak rotation angle rad

r/>yiels yield rotation angle rad

r/>p volume fraction of solids

w

angular frequency radjs

I

11 angular velocity radjs

I

I

I

I

I

I

21

I

I

Appendix A

I

Figures

I

I

1.6

1.4

1.2

.--..

₁

S ._... ~ _0.8 ...c eo .~

0

.

6

-'=

0.4

0

.

2

0

0

.

01

0.1

1

10

time (day)

I

TDL9 -+-TDL29 --M--TDL63 --.- -TDL94 ····8···· TDLC _.•.

-100

Figure A.1: Interface heights against time

I

I

I

_1.6

1.4

1.2

..-..

₁

S ..__, +"

_0.8

,.Q bD

.

~

0.6

..Q

0.4

0

.

2

0

0

10

I

TDL9-TDL29 -,,*-TDL63-- .--TDL94....g.... TDLC _.•.

-20

30

40

50

60

time (day)

I

Figure A.2: Interface heights against time

J

0.6

0

.

5

0.4

..-.. S

_0.3

..__, ..t::!

0

.

2

0.1

0

1000

1300

1400

p (kg/m3)

1700

70

80

90

100

I

Day 9, TDL9-+-Day 8, TDLC···

1200

1600

1100

I

Figure A.3: Density profiles TDL9

I

23

'

.

.

'

I

0.6

0.5

0.4 .~

...

_.

_...

_,

----

_S

0

.

3

.._ ~

0.2

0.1

0

1000

1100

1200

Day 29 TDL29 ~ Day 29, TDLC .

I

1300

1400

p (kg/m3)

1500

1600

I

Figure A.4: Density profiles TDL24

0.6

0.5

0.4

..._{.................}

----

S

_0.3

.._ -e

0.2

0.1

0

1000

1100

Day 63 TDL63 ~ Day 63, TDLC .

1200

1300

1400

P (kg/m3)

1500

1600

I

Figure A.5: Density profiles TDL58

24

1700

I

J

0

.

6

0

.

5

0.4

--

S

₀

_.

₃

-e

0

.

2

0

.

1

0

1

000

Day 95 TDL95 ---+-Day 95, TDLC .

I

1100

1200

1300

1400

P (kg/m3)

1500

1600

1700

J

Figure A.6: Density profiles TDL95

I

0

.

6

0

.

5

0

.4

8'

₀

_.

₃

....__" ..c::

0

.

2

0

.

1

Day 2, TDLC --Day 8, TDLC ----Day

11

,

TDLC -- ---Day 18, TDLC . Day 23, TDLC _._. -Day 29, TDLC -.-. -Day 39, TDLC -Day 63, TDLC ---Day 95, TDLC ----

--I

Figure A.7: Density profiles TDLC

I

25

I

I

80.00

I

60.00 40.00

I

20.00 30

<

z

<

35 cm -+-15

<:

z

<

20 cm --M--5

<:

z

<

10 cm --

.--0

-

$ z

<

5 cm ····8···· 0.00 L_ __J_~~~~~~~L_~~~~ .. ~~ .. ~~~~ 1

I

10 100

Equivalent spherical diameter d (J.'m)

Figure A.S: Partiele size distribution, mass density, TDL29

I

100.00 80.00 60.00 ~ 40.00 20.00 0.00 1 30

<

z

<

35 cm -+-15

<:

z

<

20 cm -,"*-5

<:

z

<

10 cm - -.

-0

-

$

z

<

5 cm ····B···· 1000

I

r

r

...

.

' )I'

Q

,)1, l/('

.

-

-

/

a .a···a e..a a-···c:t·ci 10 100

Equivalent spherical diameter d (J.'m)

Figure A.9: Partiele size distribution, cumulative mass percentage, TDL29

I

26

I

I

100.00 80.00 60.00 ~ 40.00 20.00 0.00 1

I

I

30

<

z

<

35 cm -+-25

<:

z

<

30 cm

-"*-20

<:

z

<

25 cm . -15

<:

z

<

20 cm ····a···· 10

<:

z

<

15 cm _.•. -5

<:

z

<

10 cm _.e. .-O-~

z

<

5 cm --

.-..

10 100

Equivalent spherical diameter d (~m)

Figure A.IO: Partiele size distribution, maas density, TDL95

,

100.00 80.00 60.00 ~ 40.00 20.00 0.00 1 , , , _

...

..

-.-

--.

-

--

-.-

-

....

.

-

--,

,, , , ,

•

, , ,

,

, , r 30

<

z

<

35 cm -+-25

<:

z

<

30 cm

-"*-20

<:

z

<

25 cm --.- -15

<:

z

<

20 cm ····a···· 10

<:

z

<

15 cm _ .•.

-5

<:

z

<

10 cm _.e.. -O-~

z

<

5 cm --. -1000

t

10 100

Equivalent spherical diameter d (~m) 1000

Figure A.ll: Partiele size distribution, cumulative maas percentage, TDL95

I

I

I

1.6

1.4

1.2

1

.-S

_0.8

-e

0.6

0.4

0.2

0

0

100

200

Day2-Day 9 -....

-I

-

....

--

...

_-

...

--

.

----

.

_...

300

400

500

Pe

(Pa)

600

700

800

I

Figure A.12: Excess pore water pressure profiles TDL9

I

1.6

Day2-1.4

Day 9 -....

-Day

23 - -. --1.2

Day 29

...

.

•

.

...

1

.-S

₀

_.

₈

..__. ~

0.6

0.4

0.2

I

700

800

600

100

200

300

400

500

Pe

(Pa)

Figure A.13: Excess pore water pressure profiles TDL29

I

28

900

I

I

I

1.6 Day2-1.4 Day 9 ----Day 23 .·e·· 1.2 Day 29_{Day 39 _ .}...._••_..... -1 Day 63 -.•..

---

S _0.8

--

-e 0.6 0.4 0.2

I

800 100 200 300 400 500 600 700 Pe

(Pa)

Figure A.14: Excess pore water pressure profiles TDL63

I

1.6 Day2-1.4 Day 9 - ---Day 23 .·e·· 1.2 Day 29 .._{Day 63 -}._.._••_.._.... 1 Day 95 ...

---

S _0.8

--...c! 0.6 0.4 0.2

I

800 700 100 200 300 400 500 Pe

(Pa)

600

Figure A.15: Excess pore water pressure profiles TDL95

I

29

900

I

I

_1.6 Day2-1.4 Day 8 - ...-Day 11 --. --1.2 Day 18 ..._{Day 23 _.}._••_...._-. 1 Day 29 _ .•. -... Day 39 --..

-E

_0.8 Day 63 --...

----

Day 95 --.. --...c:= 0.6 0.4 0.2

I

I

100 200 300 400 500 600 700 800 900 Pe (Pa)

I

Figure A.I6: Excess pore water pressure profiles TDLC

Figure A.I7: Effective stresses TDL9, TDL29, TDL63 and TDL95

I

I

-

-1000

~~

...

rtt ...••

I

.. :':t~~

_xX

...

..

100 ++ ++ ++ -. .+ ." .+ Po. •• Day 2,

<pp -

u'

+

--

Day 8,

rpp -

u'

~b _{Day 11,}

_{rpp -}

_a' x

•

I

10 Day 18,Day 23,

rpp -

fp -

u'

a'

•

•

•

•

•

Day 29,

ePP -

u'

•

A Day 39,

rpp -

u'

•• A Day 63,

rpp -

a' A

•••

++ A xA + • ~ Day 95,

,pp -

a'

•

• \

.'

1 0.01 0.1 1

I

l/Jp (-)

Figure A.18: Effective stresses TDLC

I

12 ---~---~---~---~---~

6

TDL9,

a' -

e --.- -TDL29, a' - e ---TDL63 a' -

,

,

e ----TDL95, a - e ....•... 10

8

I

-. I

--2 , ,

~-...

•••·~IIk. ~~

..

•...•

-,

.

,

_,

'. '.

,

'.

,

\ 4

I

, ,

_{._}

...

-

...

o

200

400

600 800

1000

u' (Pa)

Figure A.19: Effective stresses TDL9, TDL29, TDL63 and TDL95

I

·

1

12 10 8 ... I 6 .._ Q,) 4 2 0 0 Day 2 u' - e -

,

,

Day 8 u - e ----

,

,

Day 11

,

u

,

-

e - -• -Day 18 u - e

_,

,

....•... Day 23

_,

u -

,

e _ .... -Day 29

_,

u -

,

e - ... Day 39

,

u -

,

e -- . -Day 63

_,

u -

,

e --....--. Day 95, u - e ---- -.

I

I

200 400 u' (Pa) 600 800 1000

I

Figure A.20:Effectivestresses TDLC

I

1e-05 Day 5 + Day 9.5

-

---Day 14.5

_•

-,

1e-06 ~ 20.5

•

+ ay 26 • x· ••

-I

Day 34

_•

₊

_•

_•

...[I) Day 51 •

_•••

--

Day 79

...

...

S 1e-07 _•

•

_• .._

•

..IC:

_•

•

1e-08

•

•

I

•

1e-09 0.01 0.1 1

if>p (-)

I

Figure A.21:Permeability data

I

I

Figure A.22: Peak shear stresses and peak angles, TDL9

I

Figure A.23: Peak shear stresses and peak angles, TDL29

I

I

Figure A.24: Peak shear stresses and peak angles, TDL63

I

800

_ Tpeak,

0=1.0

rpm

1.4

700

___._ ~eak,

0=0.1

rpm - ... - peak-

0=1.0

rpm

600

--G- ippeak,

0=0.1

rpm

1.2

I

,

..._

₅₀₀

1

..._ cd "'0 0.. cd

'"'

.._

400

0.8

.._ ~

_..,

~

_..,

~o.

300

0

.

6

-s.

0.

200

0.4

I

'

100

--

--::!=---.----~---~---~

__

_-.

0

.

2

0

0

0

1

2

3

4

5

6

7

8 9 Segment

#

I

Figure A.25: Peak shear stresses and peak angles, TDL95

I

I

₂₀₀

₂₅₀₀₀

~ Tresiduab

0=1.0

rpm

-

...

-

fil<l>=o, 0=1.0 rpm

20000

150

--9--

~ 1<1>=0,

0=0.1

rpm

I

";d ..--.

15000

~

e;_

c,_{.._} öi

100

0 ::1

_-!l

"0 fJ

.~

I

10000

.;

~

~ I I

50

I

5000

I

I

O-~-..

...

...,==-=-

c..=:..::'-=--'~--=-

-

--'---'--

-

'---'

O

o

1

234

5

6

789

Segment

#

Figure A.26: Residual shear stresses and ~; ItP=o, TDL9

150

"

.-~ 0.. .._ öi

₁₀₀

::1 "0 0gj ~

50

I

0

0

I

I

25000

20000

.-15000

_c,~ .._ 0

-!l

10000

_.;

_~

5000

0

9

~ Tresiduah

0=1.0

rpm

- ...- il<p=O' 0=1.0 rpm

--9-- ~I<p=o,

0=0.1

rpm

lil I I I I I I I I _....{!I g-- _"''''., ",,,,~

....

,,,.., " e'" '" ,

_

...

,

(I'..:"::-'" .. ~i--__.---_ ;~

..

1 2

3

4

5

6

Segment

#

8

7

Figure A.27: Residual shear stresses and ~; ItP=o, TDL29

I

I

₂₀₀

25000

- Tresiduah

fl=1.0

rpm

-~-

ft

14>=0' fl= 1.0

rpm

20000

150

--G-

~ 14>=0, fl=O.l

rpm

I

.- p---e .-~ I

15000

~ 0.. II 0.. .__.. I .__.. ëii

100

I 0 :::l I {l "'0

"i

.~

₁₀₀₀₀

~~ ~ ",;

'"

....

.

-...

,,~

,

EI' "". \

50

»> _.,"~ ,"" \,

I

~~

~-'

,

,

5000

~F~

~

..

~

..

...

0

0

0

1

2

3 4

5

6 7 8 9 Segment

#

I

Figure A.28: Residual shear stresses and ~; 14>=0,TDL63

I

200

25000

- Tresidual,

fl=1.0

rpm

-~-

i

l

4>=O' fl=l.O

rpm

20000

150

--G-

~ 14>=0, fl=O.l

rpm _I~ I

I

.-~ II

.-15000

~ ~ II

•

.__..0.. I I , ëii

₁₀₀

I I

,

0 :::l ,..d /

,

{l "'0

sr:

_I

,

.~

,

₁₀₀₀₀

~~ '" I

,

~

'"

'"

,-

.

I

,

,~--_.--

,,

50

.D"-;~..j!

,

,

I

...

:..,

....

,

5000

;::

...

•

0

0

0

1

2

3 4

5

6 7 8 9 Segment

#

I

Figure A.29: Residual shear stresses and ~;

IlP=o,

TDL95

I

I

₆₀₀ _~eld

-_G-

ield 1.4 500 1.2

I

_..-.. 400 ₁ ..-.. ] ~ 0.. .... .._ 300 0.8 .._ ~ "0Q; ~>. _0.6 .>' 200

i;1-I

100

_{----B----B----~---~---_G----B}

0.4 0.2 0 0 0 1 2 3 4 5 6 7 8 9 Segment

#

I

,

Figure A.30: Yield stresses and yield angles, TDL9

I

I

600 _~eld

-_G-

ield 1.4 500 1.2 400 _{1 ..-..} ..-.. _"'0 ~ 0.. ~.... .._ 300 0.8 .._ "0 "0 Q; Q; ~>. _0.6 .>' 200 i;1-0.4 100 0.2 0 0 0 1 2 3 4 5 6 7 8

9

Segment

#

I

I

Figure A.31: Yield stresses and yield angles, TDL29

I

I

I

600

_~eld -_G- ield

1.4

500

1.2

400

₁

--

CIS ] c, ....

--

-0

300

0.8

--

-0 Qi Qi ~>.

_0.6

.>'

200

-e-0.4

100

_{----e----B---_~---~----o}

0.2

0

0

0

1

2

3

4

5

6

7

8

9 Segment

#

I

Figure A.32: Yield stresses and yield angles, TDL63

I

600

- ;jÇeld --G- ield

1.4

500

1.2

I

.-

400

1

-

_"'0 CIS c, ~_....

--

-0

300

0.8

--

-0 Qi ~ ~>.

_0.6

.>'

200

"'$-0.4

I

'

100

_{~----e----B----~---~----G---_g}

0.2

0

0

0

1

2

3

4

5

6

7

8

9 Segment

#

I

Figure A.33: Yield stresses and yield angles, TDL95

I

I

_{50000 20000}

45000 -_--G- Storage modulus_{LOBS modulus}

..- 40000 (Ij ₁₅₀₀₀ ..-~ 35000 (Ij

I

0.. 00

-=' 30000 00

:;

_=' "'0 25000 10000

:;

0 "'0 S 0 Cl> 20000 S ~ 00 15000 00 ... 0 0 5000 ...:l ...

I

tr: 10000 5000 0 0 0 1 2 3 4 5 6 7 8 9 Segment

#

I

Figure A.34: Storage and 1088moduli forw

=

1.57 rad/s, TDL9

I

50000 20000

45000 -_--G- Storage modulus_{Loss modulus} ..- 40000

'"

15000 ..-0.. 35000 (Ij

-

c,

I

00

-=' ₃₀₀₀₀ 00

:;

_=' "'0 25000 ~ 10000

:;

0 I _"'0

E

I ₀ I Cl> 20000 I S ~ _II 00 00 ... ₁₅₀₀₀ I ₀ 0 I _...:l ... I 5000

I

tr: 10000 I I I 5000

---~

... ....m ...., 0 0 0 1 2 3 4 5 6 7 8 9 Segment

#

I

Figure A.35: Storage and 1088moduli for w

=

1.57 rad/s, TDL29

I

I

50000 20000

45000 -_--G- Storage modulus_{Loss modulus}

I

.-. 40000 --- Residual storage modulus

'Ó --- Residualloss modulus 15000

-0.. ₃₅₀₀₀ 'Ó

--

0.. Cl)

--::l ₃₀₀₀₀

_rg

:;

~ 25000 10000

:;

0 -e

E

0 ~ 20000

E

Cl)

I

'Ó 15000 Cl) f,.; 0 0 _{5000 ~} ... U') 10000 5000 0 0 0 1 2 3 4 5 6 7 8 9

I

Segment

#

Figure A.36:Storage andloss moduli forw

=

1.57 radJs, TDL63

I

50000 20000

- Storage modulus 45000 _{--G- Loss modulus}

-

40000 --- Residual storage modulus

'Ó --- Residualloss modulus ₁₅₀₀₀

-0.. ₃₅₀₀₀ 'Ó 0.. Cl)

--::l ₃₀₀₀₀ Cl)

I

:;

::l ~ 25000 10000

:;

0 _~

E

0 ~ 20000 SCl) 'Ó 15000 Cl) f,.; ₀ 0

...

₅₀₀₀ ~ U') 10000

I

5000 0 0 0 1 2 3 4 5

6

7 8

9

Segment

#

I

Figure A.37: Storage and 1088moduli forw

=

1.57 radJs, TDL95

I

I

I

I

I

0.5 -+- TDL9

_•

..--, _0.45 --*- TDL29 / ~ _{- -.- - TDL63}

_i

Q) ····B···-TDL95 •ei) ba 0.4 / ' --.-- TDL63 ~Residual~ ,/ s::: /' ~ _{- -e--- TDL95 Residual} ' / t . rn 0.35 " 00 t. ..9 '/ /, Q) 0.3 " _~c ..s:::_{.._,. i}I. _:

_.

_.

...

,

0

0

.

25

.

,

.._,. s::: ~ 0.2 s::: ~ _0.15 0.1 0 1 2 3 4 5 6 7

8

9 Segment

#

I

I

Figure A.38: Tangent of the 1088angle

I

I

I

I

I

60

~----

~---

~

----

--

~---~--

----

~--~

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~._._._._._._

.

:

:

::~:=

:

=

:

=:=

:

::=:~

50

~._.-.-

-

-

:

:: ...._.-

.

- ....

.

- .-

'

...

_-+ , _ - - - ., •• : •• : : ••: ••:•• .1'.-". . ::- :..:~:..:..:*:..: :.t: _---::::.:==::.:.::--+ ... _..__ • .A.--- ----9 40

.,..

I ... ~--

..

-

..

-~-...---~---

..--·--- ~---~ ...-~

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20

r:

10

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O~

---L---

~L---~

---~---~--~

o

20

40

80

I

p

=

1202kg~m3

TDL29 (up

__._ p

=

1202

klLm ,

TDL29 (down

--...-p

=

123

kg~m3,

TDL29 (up

---p

=

1233k&Lm ,

TDL29Jdown

-_-p

=

121

kg~m3,

TDL 3 (up

....•.... p

=

1210k&Lm ,

TDL63J down

...

.•....

p

=

121

kg~m3

TDL 3 (up

_

.

•

.

-p

=

1210krLm ,

TDL63 (down

_

.

~

.

-p

=

123

kg~m3,

TDL95 (up

_

.

•..

p

=

1231krLm ,

TDL95 (down

_

.

....

.

.

p

=

123

kg~m3,

TDL95 (up

--

...

-p

=

1231kg/m ,

TDL95 (down

-

-

...

-I

_{Figure A.39: Flow curves: shear stresses}

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42

..

...

-100

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60~---~---~~---~---.---.

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50 40 30 20 10

._._._

.

_

.

~_

.

_

.

-.

_

.

_

.

-.-

._

.

_

._._

.

_

.

,

I

O

~

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

o

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I

2 4 6 8 10

'Y

(8

-

1)

P

=

1202 kg'm3 TDL29 (up _..._ p

=

1202

klim

,

TDL29 (down ~ p

=

123 kg~m3,TDL29 (up

-

-

-p

=

1233 k&Lm,TDL29 Jdown

-_

-p

=

121 kg'm3, TDL 3 (up ....•-_.. p

=

1210 kHLm,TDL63 (down

.

.

.

.

•

.

.

.

.

p

=

121 kg~m3 TDL63 (up

_

.

...

.

-p

=

1210 krLm , TDL63 (down

_

..

~

-

-p

=

123 kg~m3, TDL95 (up

_

.

....

.

-p

=

1231 krLm , TDL95 (down

_

.."...

-P

=

123 kg'm3, TDL95 (up -- ._ -p

=

1231 kg/m ,TDL95 (down

--

...

-Figure A.40: Flow curves: shear stresses, 0::;

l'

::;

10S-1

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I

0.10.1 1 10 100

l'

(8

-

1)

P

=

1202 kg~m3 TDL29 (up

---p

=

1202

~Lm ,

TDL29 (down

----p

=

123 kg~m3, TDL29 (up

--

-p

=

1233 k5Lm , TDL29 ~down

-_

-I

p

=

p1210 kNLm , TDL63 (down

=

121 kg~m3, TDL 3 (up

~

.

.

..

.

.

.,

•

~

....

.

.

.

.

p

=

121 kg~m3 TDL63 (up

_

.

•

.

-p

=

1210 krLm , TDL63 (down

_

.

~.-p

=

123 kg~m3, TDL95 (up

_

.•

..

p

=

1231 krLm , TDL95 {down

_

.

~

.. p

=

123 kg~m3, TDL95 (up --

...

-p

=

1231 kg/m , TDL95 (down ..

.,..

.

I

_{Figure A.4I: Flow curves: dynamic viscosities}

I

I

I

Appendix B

I

Density measurement

I

Density measurement

One of the basic parameters measured in the present experiments is density. The measurement technique used, depended on the type of column involved. The bulk density of the mud in the segmented columns was measured by using a conductivity probe, whereas the bulk density of the mud in the conventional column was measured by using a "(-ray densimeter.

The "(-ray densimeter used, was a LB370 densimeter, manufactured by Berthold GmbH. The measurement principle of the "(-ray densimeter, is based on the absorption of "(-rays by matter, similar to the absorption of X-rays, see Been (1980).

The souree of the LB370 is Caesium-137, a radioactive material that emits mainly photons

of high energy, so called ')'-rays. The souree is shielded by a lead housing

.

Locally the shield

can be opened to produce a narrow bundie of "(-rays. The "(-rays are passed through the consolidation column and detected at the other side by a Nal-crystal that converts gamma-photons to light-gamma-photons. The signal is enhanced by a photon multiplier tube. Subsequently, the light pulses are converted into an electric current. The electric current is manipulated by an electronic unit that eventually produces an output in Volts. A sketch of the "(-ray densimeter is shown in Figure B.l. The bulk density is related to the voltage by the relation

I

I

I

Pb=aV

+

b, (B.1)

where Pb is the bulk density, V the output of the "(-ray densimeter and aand bare calibration constants. It is noted that the usual exponential relationship between density and the count rate of pulses (Been, 1980) is dealt with within the electronic unit.

I

Procedure of measuring continuous density profiles

Continuous density profiles were obtained by traversing the "(-ray densimeter in the verti

-cal direction. Simultaneously traversing and measuring inevitably results in averaging the measurements in space and thus reducing the vertical resolution. A high vertical resolution requires a low traversing speed and a short observation time. Unfortunately, the readings of the "(-ray densimeter are relatively unstable. In order to obtain an accurate reading, the observation time should be sufficiently long, i.e. several minutes.

The traversing speed was set very low: 0.24016 mm/s, which is about one meter per hour. The signal of the "(-ray equipment was averaged over 10 seconds. Although this duration is much too short to produce an accurate density measurement, such a short time enables the

I

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screw-spindle

_\

NaI-crystal and

consolidation column

""" Caesium-137 source pboton

I

I

_{traversing plateau}

I

Figure B.l: Ascbematic representation of tbe 'Y-ray densimeter

detection of sharp transitions. If desired, the accuracy of the density measurements can be

increased

by

averaging in the vertical direction afterwards.

I

Calibration

I

During earlier measurements it was found that the values of the calibration constants a and

b varied slightly from day to day. Since calibration samples could not be used because of too

short a traversing range, calibration strips were used instead. These strips could be placed between the column and the housing of the source.

In order to determine the equivalent, additional density of each strip, the calibration constants a and b were determined by using four mud samples of known density before the consolidation column was set up. The containers in which the samples were put, were equiv-alent to a section of the consolidation column. A linear fit resulted in a =50.242 kg/m3/V and b

=

903.11 kg/m3, with

R2

=

0.9988. Subsequently, each strip was placed separately between the column section filled with water and the housing of the souree and by using (B.1) the additional density could be determined. In total three different strips were used, so that,

including a measurement without strips, four calibration points were available before each density measurement. The procedure to determine the additional density of the strips was repeated for water with different salinities. The effect of the salinity is within the accuracy of the measurements, see also Table B.l.

To determine the accuracy of the signal, the conventional column was filled with only water. The density of the water was 1003.5 kg/m3, measured with a hand held densimeter (Anton Paar DMA32N). Before the readings were taken, the 'Y-raydensimeter was calibrated. The readings are shown in Figure B.2. Some statistics are presented in Table B.2. The aver-aged density is practically equivalent to the density measured with the hand held densimeter. The absolute accuracy is of the order ±10 kg/m3, indicated by the minimum and maximum

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