Ge 360102

LIPKIN, J., BENNETT, R. H. & MCTIGUE, D. F. (1986). Giorechnique 36, No. 1.11-25

Consolidation under an isotropic total stress increase : part II, experimental results

for marine clay

J. LIPKIN,* R. H. BENNETT? and D. F. McTIGUE$

Deformation and internal pressure changes have been measured in a large sample (of the order of 1 m3) of remoulded, reconsolidated marine sediment subjected to a series of step-like, 6.9 MPa changes in hydrostatic pressure. Undrained surface displacements of 0.24.4 mm were observed in response to each increment in external pressure. The surface then slowly rebounded with a characteristic time of about lo6 s. The excess pore pressure induced by each step in pressure at the boundary was of the order of from - 1 kPa to -2 kPa (suction) and likewise relaxed as external fluid diffused into the sample. Predictions based on a poroelastic material response model agree qualitatively with these observations when values of material properties are estimated from independent measurements. The experimental data can also be used to determine parameter values. Such a procedure yields very good fits to the data and indicates permeability, drained bulk modulus and solid bulk moduli of the order of lo-l6 m*, 10 MPa and 10 GPa respectively, in reasonable agreement with independent measurements.

Des changements de dbformation et de pression interne ont et& measures dans un grand &chantillon (de I’ordre de 1 m3) de sidiment marin remani& et reconsolidt soumis g une s&ie de modification de pression hydrau- lique par paliers de 6,9 MPa. Des d&placements non- drain&s superficiels compris entre 0,2 et 0,4 mm ont 8t& observks en rCponse B chaque augmentation de pression externe. Puis la surface s’est lentement restauree au tours d’un temps caractkristique d’environ lo6 s. Les surpressions induites & la limite lors de chaque palier de pression etaient de I’ordre de - 1 kPa a -2 kPa (suction) et se relichaient de faGon analogue au fur et B mesure que du fluide externe se diffusait dans l’&chantillon. Des prkvisions bashes sur un modtle de rkponse d’une mat&e porotlastique s’accordent de faGon qualitative lorsque les valeurs des propriCt&s des matitres sont estimCes B partir de mesures indkpen- dantes. Les donnies exp6rimentales peuvent s’employer aussi pour dkterminer les valeurs des paramttres. Une telle procbdure donne des rttsultats tris compatibles avec les don&es et indique une perm&abilit&, un module de masse drain&e et des modules de masse solide de l’ordre de lo-l6 m*, 10 MPa et 10 GPa respectivement.

Discussion on this Paper closes on 1 July 1986. For further details see inside back cover. * Sandia National Laboratories, Livermore. t Naval Ocean Research and Development Activity. $ Sandia National Laboratories, Albuquerque.

11

Ceci s’accorde assez bien avec les mesures indbpen- dantes.

KEYWORDS: clays; compressibility; consolidation; elasticity; pore pressures; soil properties.

INTRODUCTION An in situ heat transfer experiment (ISHTE) has been under development for several years as part of the US Subseabed Disposal Program (SDP) (Hollister, Anderson & Heath, 1981). It is intended that this experiment will be fielded over a one-year period at a water depth of approximately 6000 m in the central North Pacific Ocean. The experiment will involve the emplace- ment of a heat source and associated instrumentation in the sea floor to a depth of 1 m. The instrumentation will be capable of making in situ measurements of the sediment thermal, mechanical and chemical responses to this heat source. The data acquired will be used to assess the valid- ity of some of the numerical modelling techniques being used in the SDP feasibility study (Percival, 1983).

A large-scale simulation experiment has been completed as a prelude to the fielding of ISHTE. The details and purposes of this simulation experiment have been described by Percival (1982); however, it is only necessary here to note that the experiment made use of a temperature- controlled pressure vessel to cool and pressurize a large volume (approximately 1 m3) of remoulded, reconsolidated marine sediment. Simulated deep ocean conditions of 55.2 MPa hydrostatic pressure and 4°C were achieved in this way before carrying out the experiment. These conditions were then maintained for 30 days while a heater experiment was conducted in the sediment, after which the sediment was returned to atmospheric pressure.

In this Paper data obtained during the isothermal phases of the simulation experiment (i.e. during pressurization and depressurization) are presented and compared with the predictions of the poroelastic material response model presented by McTigue, Lipkin & Bennett (1986). The particular data considered are time-resolved measurements of

12 LIPKIN, BENNETT AND McTIGUE

(a) the displacement of the sediment-water interface

(b) the sediment pore pressure at two interior points in the sample volume.

A great deal of important information can be extracted from these data. Indeed, it will be shown that the simulation experiment provided a unique opportunity to examine marine sediment physical properties under simulated deep ocean conditions.

By fitting the predictions of the analytical model to the experimental data for undrained displacement jumps, asymptotic (late time) displacements, pore pressure jumps and relaxation rates, values of four sediment material constants can be estimated. Use of this procedure, however, also requires independent knowledge of four additional material constants (McTigue et al., 1986). By way of review (from part I), the following eight parameters are regarded as fundamental in the material model

initial porosity fluid bulk modulus elastic shear modulus first solid bulk modulus second solid bulk modulus drained bulk modulus permeability fluid viscosity

&, p, K, and G are assumed to be known. However, values for the solid bulk moduli K,’ and K,” are difficult to obtain directly, and only a few have been reported in the literature. There- fore K,’ and K,” are regarded as material constants whose values are to be determined from the displacement and pore pressure data. In addition, the permeability k and drained bulk modulus K are found.

It should be noted that sediment permeability is perhaps the single most important mechanical parameter that arises in the radionuclide trans- port and porewater convection analyses that are being done for generic sub-sea bed waste reposi- tories (Seabed Programs Division 6334, 1983). An independent determination of permeability made from in situ measurements at high pressure and low temperature is thus a valuable result that can provide increased confidence in existing laboratory data. In addition, the data and analysis presented here provide a unique opportunity to explore effects of fluid and solid compressibility on the deformation of a saturated marine sediment. These effects are commonly neglected in classical soil mechanics. However, it will be shown that obtaining an understanding of the sediment response observed in the simulation

experiment demands careful treatment of the relative compressibilities of the fluid and solid sediment constituents.

Sediment characteristics and sample preparation are reviewed in the following section. The instrumentation used to obtain surface displacement and pore pressure data is described in the next section, and the data are presented and compared with analytical predictions in the fourth section. Discussion and conclusions derived from this study are given in the final section.

SEDIMENT CHARACTERISTICS AND SAMPLE PREPARATION

The sediment used in the ISHTE simulation experiment was dredged from the floor of the North Pacific Ocean about 1500 km north-west of Hawaii. The water depth in the area is about 5800 m. The sediment is approximately 65% clay and approximately 35% silt, with the clay frac- tion dominated by illite. The in situ porosity is about 0.75.

Sample preparation was carried out by the University of Rhode Island Marine Geo- mechanics Laboratory (Silva, Jordan & Cri- scenzo, 1984). The sediment was first sieved to remove manganese nodules. It was then reconsti- tuted to a thick slurry by adding sea water and mixing. A reinforced steel tank was specially fab- ricated to contain the sediment sample during its consolidation as well as during the simulation experiment. This tank was 1 m in diameter with a fixed height of 1 m plus a detachable sleeve that increased the height to 1.5 m to accommodate the additional sediment volume needed before consolidation. A highly permeable drainage fabric and an adjacent layer of filter material were used to line the tank before it was filled with the sediment slurry. In the filling process, the sediment slurry was poured into the tank in layers approximately 0.2 m thick. After each layer had been added, the tank was sealed and a 30 kPa vacuum was applied for 1200 s to remove any air that may have been trapped in the slurry during the mixing process. This procedure was carried out continuously for 43.2 x lo3 s (12 h). After the full height of 1.5 m had been reached, the top of the tank was covered by filter material and drainage fabric.

Reconsolidation was directed towards re- turning the sediment to its in situ porosity. This was accomplished by loading the sample with steel plates placed on the top surface. The load was increased in three increments over 60.5 x lo4 s (7 days) to a maximum stress of 12.9 kPa. After an additional 51.8 x lo4 s (6 days), the entire tank was placed in a cold box at 5°C and consolidation was allowed to proceed for 6.22 Ms (72

CONSOLIDATION UNDER STRESS INCREASE 13

days). At this time, the load was removed, the sediment surface rebounded and, after an additional 259 x lo4 s (3 days), the final state was reached. The sample was then trimmed to the fixed height of the tank (1 m).

The trimmed material was sampled radially for water content. These measurements indicate the degree of uniformity in the sediment sample before the simulation experiment. As anticipated, the water content was lower near the drained boundaries of the tank, but the variation was small. The porosity at the centre was 0.76, and that at the boundary was 0.73, a change of about 4%. Post-test water content analyses show variations of the same order (Silva er al., 1984).

INSTRUMENTATION

General All the instrumentation used in the ISHTE

simulation experiment was attached to a steel frame developed by the Applied Physics Labor- atory of the University of Washington, Seattle, Washington (Miller, Miller & Olson, 1984). This frame was in turn mounted on the sediment tank so that the instruments could be positioned relative to the rigid structure. In addition to the instrumentation discussed in this Paper, the experiment included the use of a resistance heater, thermal sensors (both thermocouples and thermistors), a thermal conductivity probe and a porewater sampler. Miller er al. (1984) present details related to the development and calibration of the thermal instrumentation.

Sediment surface displacement Figure 1 is a schematic drawing of the device

used to obtain a time-resolved measurement of the displacement of the top surface of the sediment. The sensing element in this device was a

LVDT electrical leads

/ (in oil-fllled tube)

linear variable differential transducer (LVDT) made by Shaevitz Engineering, Pennsauken, New Jersey, which was modified so that its electrical output would be insensitive to hydrostatic pressure.

Space limitations on the instrumentation frame required remote positioning of the LVDT. A lever arm-sediment follower arrangement was therefore developed so that displacements could be measured near the centre of the sediment tank. Such positioning of the follower was important for obtaining data during the thermal part of the experiment. However, the resulting closeness of the follower to the heater implant arm suggests a possible source of error in the isothermal displacement data. A discussion of such measurement errors is deferred to the final section.

An additional consideration associated with the use of an LVDT in a simulated deep ocean environment is the need to isolate it from the potentially detrimental effects of extended expo- sure to sea water. In the present application, this isolation was accomplished by mounting the LVDT in a plastic tube with a very flexible latex bladder on one end to permit access of the lever arm. The tube and bladder were filled with mineral oil, and the required electrical connec- tions were made through oil-filled lines to the pressure vessel feed throughs. Excitation and signal voltages were transmitted through these lines, and the signal voltages were recorded at preprogrammed intervals on an Esterline Angus (Indianapolis, Indiana) data logger. The same data logging system was used to record pore pressure data during the experiment. The record- ing interval was varied depending on the fre- quency of the changes expected to occur in a particular phase of the one-month experiment. An interval of 9 x 10’ s was used for the

s!/ LVDT housing

Heater Implant tube LVDT body (flxed)

LVDT core rod (movable)

Fig. 1. Schematic diagram of the sediment surface displacement measuring system

14 LIPKIN, BENNETT AND McTlGUE

Tubing to pressure Differential

Porous transducer (porewater) pressure

Cone angle = 5-3”

conducttng cable

+D

electronic signal conditioner

Fig. 2. Schematic diagram of the deep ocean piezometer probe

3.9 x lo5 s (4.5 days) pressurization phase. The time required for each individual pressure change during this phase was approximately 2 x lo3 s, with hold times at constant pressure after each step of the order of 2 x lo4 s; the 9 x 10’ s data logging interval was therefore adequate to capture the essential features of the sediment response during this phase of the experiment.

Before pressurization, the sediment and the salt water above it were cooled to 277 k 1 K. This temperature was maintained with excellent stability throughout the simulation experiment. Bench testing of the LVDT revealed that its voltage output at a given displacement depended on ambient temperature. It was therefore essential to calibrate this device at a temperature equal to that used in the experiment. Such a calibration was carried out following the simulation experiment using a controlled temperature environment chamber. The calibration factor obtained in this way, 0.333 V/mm, was used to convert LVDT voltage output to sediment surface displacement.

Pore pressure (piezometer) probe The piezometer probe consists of an 8 mm dia.

titanium tube attached .to a tip having a cone angle of approximately 5.3”. Details regarding the choice of probe tip design can be found in Bennett & Faris (1979). A porous stone, which allows porewater pressure to be transmitted to the pressure sensor, is fastened between the titanium tube and the probe tip (Fig. 2). Pore pressure is transmitted through the porous stone to an internal tube attached to the pressure sensor. The differential pressure sensor is pressure balanced by a similar internal tube that runs from the pressure sensor to the top of the porous stone retainer. The pressure sensor is enclosed in a

stainless steel housing that is pressure compen- sated to in situ hydrostatic pressure (Fig. 2). The stainless steel pressure sensor housing is separat- ed from the titanium probe components by high dielectric polycarbonate material. The total lengths of the piezometer probes can be changed depending on the experimental design objectives. Only one pore pressure measurement at a presel- ected depth below the sediment-water interface (mud line) is possible with each piezometer probe.

A variable reluctance differential pressure transducer measures the excess porewater pressure (differential above hydrostatic) directly. A 5 kHz sine wave is supplied to the differential transducer by a carrier oscillator in the signal conditioner unit, producing an alternating current output from the Wien bridge-type transducer cir- cuitry whose amplitude is proportional to the transducer imbalance. The alternating current signal is amplified, demodulated and filtered by the signal conditioning unit, producing a k5 V direct current output level corresponding to the full-scale range of the transducer (f68.9 kPa). Solid state signal conditioning electronics are enclosed (at atmospheric pressure) in a stainless steel capsule located directly above the pressure sensor capsule. Data were recorded with both analog strip charts and a data acquisition system with a hard copy printer for the duration of the experiment.

Testing and calibration of pressure transducers The pressure transducers were tested at high

hydrostatic pressure (68.9 MPa) over a period of 2.7 Ms (31 days) before the ISHTE simulation experiment to determine sensor characteristics and long-term stability (Bennett, Burns & Lambert, 1982). The pressure sensors exhibit a


Displacement gauge

piezometer probe

Far field piezomeler probe

-Steel tank

Porous stone

fT3.* cm 35.9cm y ,ITcm j

Fig. 3. Positions of piezometer probes in the sediment tank

zero shift during pressurization but display excellent long-term stability under high pressure. A correction can be made for the zero shift and applied to the pore pressure measurements observed during pressurization. The two piezometer probes were calibrated at laboratory ambient conditions before use in the simulation experiment. Immediately following the experiment, the pressure sensors were again checked and calibrated (McTigue, Lipkin & Bennett, 1985).

Piezometer insertion data Pore pressures were monitored with two

piezometer probes placed at different positions in the sediment sample. The near field piezometer monitored pore pressures 0.015 m from the heater (skin to skin) and 0.17 m below the mud line. The far field piezometer measurements were monitored 0.26 m below the mud line and 0.34 m from the heater (skin to skin), as depicted in Fig. 3. Each probe was inserted separately.

During probe insertion, soil deformation occurs and excess porewater pressures are generated. The maximum pressure occurs at the probeesoil interface and decays at a characteristic time which depends on the probe size and sediment properties (Randolph & Wroth, 1979). Nor- malizing the excess pressure using the initial and final values obtained during decay and plotting the data as a function of time reveals significant differences in the decay curves (Fig. 4). Applying the logarithmic fitting method from consolidation theory (Lambe & Whitman, 1969), t,,, is approx-

imately 1.2 x lo3 s for the near field probe and 3.7 x lo3 for the far field probe. The induced excess pore pressure at the far field probe has a time delay of approximately 36 s, whereas the near field probe has a nearly instantaneous decay of pressure following insertion. Furthermore, the maximum pore pressures generated differ significantly: 6.6 kPa and 12.9 kPa for the near and far field probes respectively. These discrepancies suggest that the sediment near the heater may have been altered or disturbed by insertion of the heater and various other probes before the simulation experiment. The effect of introducing a short drainage path near the heater is treated approximately in the analysis in part I, and is discussed extensively by McTigue et nl. (1985).

The radial variation in porosity described in the foregoing also may have contributed to the difference in response at the far field probe. Post- test analyses for water content show a porosity of 0.74 in the vicinity of the near field probe and 0.73 in the area of the far field probe. Extensive correlations of undrained shear strength and water content (Williams, 1982) indicate that this small decrease in porosity can increase the undrained shear strength by as much as 50%.

COMPARISON OF CALCULATED AND

MEASURED RESPONSES

A computer code was written to predict the surface displacement and the internal pore pressure based on the analytical solutions given in part I. The cumulative response to a succession of


I I I 1 4

0.1 1.0 10.0 100 1000

Term? ml”

Fig. 4. Normal&d dissipation of pore pressure induced by piezometer insertion

external pressure increases is calculated by super- position. Early time approximations are used for each step until the elapsed time, normalized by the relaxation time, exceeds 0.02. Because the relaxation time is approximately lo6 s and the typical ramp time for each pressure increment is approximately lo3 s, the early time approx- imation is employed well past the ‘corner’ at the end of each external load step.

A pressure-dependent fluid bulk modulus K, was used in these calculations. Over the range of pressure encountered in the ISHTE simulation experiment, from 0 MPa to 55.2 MPa, K, for sea water at 4°C increases about 16%, from 2.14 GPa to 2.49 GPa (Riley & Skirow, 1975). Such an increase affects the undrained volumetric behaviour of the sediment, i.e. the sediment stiffness increases during pressurization. The variation in K, is small between successive load steps, however, and the effects of previous steps decay exponentially with time. Thus, the solution for constant properties is used and K, is updated to the current value to calculate the contributions of all previous load increments to the present deformation. This results in a very slight overesti- mate of K, when fitting the model to the data. Further, it is assumed that the sediment always rests on the bottom of the tank, so that the measured displacement represents twice the sym- metric displacement. This assumption has been examined in detail by McTigue et al. (1985).

The displacement and pore pressure responses of the sediment are dominated by three factors, K, , B and c, defined in part I. The magnitude of the jumps in surface displacement scales with p,, L/K,, where p. is the external pressure and L is half the sample length. The undrained modulus

K, can be written in terms of the fundamental parameters

K, =

K 1 - K,JK,” 1+&.3--

KS’ K, 1 - K/K,’

K,’ 1 - K,JK,” ’ + ” z 1 _ KJK ’ f s

The jumps in pore pressure difference scale with (1 - B)p, In this case, B is very close to unity, and approximately

1 _ B ~ 9. K 1 - WKs” K, 1 - KJK,”

Finally, the relaxation rate for both the displacements and the pore pressure depends on the consolidation coefficient c, which scales with kK/,u. The overall pattern of the computer simulations, then, depends primarily on these three parameters.

The first calculation of interest is to model the experiment using the best available estimates of material properties obtained from independent tests. These values are given in Table 1 along with the sources used to obtain them. The fluid properties K, and p are well established and are available in extensive tables (Riley & Skirow, 1975). The solid bulk moduli K,’ and K,” are usually assumed to be equal Few measurements for clays are reported in the literature; that given by Skempton (1961) is adopted. Representative drained properties are given by Baladi & Akers (1981). Permeability and porosity measurements for the marine sediment used in the ISHTE simulation have been reported by Silva et al. (1984).

Calculations based on the set of parameters


Table 1. Independent estimates of material properties

Parameter Symbol Value Source

Viscosity Fluid bulk modulus Porosity Shear modulus Drained bulk modulus Solid bulk modulus Permeability

K,‘, K,” k

1.66 x 10m3 Pa s 2.14 x lo9 + 6.41~ Pa 0.75 6.0 x lo5 Pa 2.0 x 10’ Pa 5.0 x 10” Pa (lG3.0) x 10-16m2

Riley & Skirow (1975) Riley & Skirow (1975) Silva et al. (1984) Baladi & Akers (1981) Baladi & Akers (1981) Skempton (1961) Silva et al. (1981)

given in Table 1 are shown in Figs 5-8 along with the data measured in the simulation experiment. In Fig. 5 the maximum calculated displacement is seen to be 1.4 mm, while the observed value is 1.6 mm. However, it is quite evident that the computed undrained modulus K, is too small and the relaxation rates are too large. In Fig. 6 results for the surface displacement during depressurization show undrained displacements that are only slightly too large, and relaxation rates that are again too fast, particularly at late time when the cumulative relaxation from previous steps con- tributes significantly. The large displacement associated with the last depressurization step is ascribed to expansion due to exsolution of air. The model does not account for this phenome- non. In Figs 7(b) and 8(b) the calculated pressures are quite different from the data; 1 - B is clearly far too large.

The model fails to represent the data using independent estimates of the material properties. This suggests the possibility of seeking a set of parameters that yields a good fit, thus using the data to determine material properties. If the

parameter sensitivity is high, a good fit should be attainable using reasonable values for the material properties.

Fitting the model to the experimental data was carried out by trial and error, varying several parameters about their nominal, independently measured values. This approach cannot guar- antee that a good fit yields a unique set of parameters. However, experience gained through numerous calculations strongly suggests that the data can be matched for only one, well- constrained set of material parameters.

K,, p, & and G are regarded as known, and k, K, K,’ and K,” are varied to find a good fit. Although the displacement history is dominated by only two parameters, K, and c, it was found that the four primary parameters regarded as unknowns all act in concert in affecting the calculated displacements. The same is found for the pore pressure trends, which again depend prin- cipally on 1 - B and c. Thus, each data set is used to determine values for all four primary vari- ables.

The best fits obtained for surface displacements

? z V X E -a- i

E x Z-,2- :

/ /

-16-

I I

0 IO 20 30 40 T&me: s X 1 O4

Fig. 5. Comparison of sediment surface displacement data and model predictions during the pressurization phase of the experiment (magnitudes of the model parameters used are given in Table 1)

LIPKIN, BENNETT AND McTIGUE

Time. s X 10“

Fig. 6. Comparison of sediment surface displacement data and model predictions during the depressurization phase of the experiment (magnitudes of the model parameters used are given in Table 1)

are shown in Figs 9 and 10 for the pressurization and depressurization phases respectively. Simi- larly, the best fit for the far field pressure data is shown in Fig. 11. The values of the material properties required for these three fits are given in Table 2. It is evident that the parameter values obtained for these three cases are generally quite consistent among themselves, and they are all within an order of magnitude of the independent parameter estimates summarized in Table 1. The drained bulk modulus K, solid modulus K,’ and permeability k are all smaller than the independent measurements by factors of 2-3. The second

Far field

solid modulus K,” is commonly assumed to be equal to K,‘, but the sensitivity to this parameter is very high, and it was found that good fits could be obtained only with distinctly different values. This observation is usually ascribed to uncon- nected porosity in the soil (e.g. Biot & Willis, 1957). It should be noted that the required K,” values are close to, but greater than, the fluid modulus K,.

It is particularly interesting to note the apparent stiffening exhibited by both the data and the calculations for surface displacement during pressurization. The last eight external pressure

0

-10

m

5 - m 20

ii a,

?z -30 0

Y 2 (0 a,

-40

a

- 50

- 71 I

0 10 20 30

Ttme: s x 1 O4

(a)

L I

20 30

Time’ s X 1 O4

(b)

Fig. 7. (a) Sediment pore pressure changes measured by the far field piezometer during the pressurization phase of the experiment and (b) a comparison of far geld piezometer data and model predictions during the pressurisation phase of the experiment (magnitudes of the model parameters used are given in Table 1)


I 0 10 20 30

Time: s X 1 O4

(a)

-60

. I 1

10 20 30

Time: s X 1 O4

(b)

Fig. 8. (a) Sediment pore pressure changes measured by the near field piezometer during the pressurization phase of the experiment and (b) a comparison of near field piezometer data and model predictions during the pressurization phase of the experiment (magnitudes of the model parameters used are given in Table 1)

increments are all of the same magnitude (6.9 MPa), yet the undrained displacements associated with each become successively smaller (Fig. 5). The model results show the same trend due to the pressure-dependent increase in K,, but the degree of apparent stiffening seen in the data is under- estimated.

Model calculations for the far field pore pressure capture the essential.features of the measured response, although the computed undrained jumps are too small for the earliest and latest external increments. The pressure data are prob- ably ‘noisier’ than the displacement data. Pore

-16-

I I I

0 10 20 30

Time: s X 1 O4

0 1 2 3 4 5 6

Time. s X 1 O4

Fig. 9. Comparison of sediment surface displacement Fig. 10. Comparison of sediment surface displacement data and beat-fit model predictions during the preasuriza- data and best-fit model predictions during the depres- tion phase of the experiment (magnitudes of the model surization phase of the experiment (magnitudes of the parameters are given in Table 2) model parameters are given in Table 2)

pressures were measured at single points, and thus may reflect material inhomogeneities and other local effects. In contrast, the displacements that were measured result from strains integrated over the entire body, and thus they tend to be very smooth.

Despite the apparent success in modelling surface displacement and far field pore pressure histories, a serious problem is revealed by calculations for the near field pressure. Fig. 12 shows model results for the near field using the parameters obtained by fitting the far field data. There is clearly a large discrepancy between the model

I‘- Data 1

-_

I I


-71 I I I 0 10 20 30

Tfme: s X 1 O4

Fig. 11. Comparison of far field piezometer data and best-fit model predictions during the pressurization phase of the experiment (magnitudes of the model parameters are given in Table 2)

and the data. The model predicts a maximum cumulative pressure difference of about -8 kPa, while the test reached only -3 kPa. Further- more, the measured cumulative pressure difference in the far field (- 6 kPa) exceeds that in the near field (- 3 kPa). This observation cannot be represented by the model. Since the excess pore pressure relaxes by the diffusion-like process of fluid flow, the characteristic time for the relaxation scales with 12/c, where 1 is the drainage path length. In the experimental configuration (Fig. 3), the minimum drainage path from the far field probe is 0.14 m (to the side boundary), while that for the near field probe is 0.17 m (to the top boundary). Thus, the relaxation time for the near field is expected to be longer, and the cumulative

I I 1

0 10 20 30 Time: s X 1 O4

Fig. 12. Comparison of near field piezometer data and model predictions based on the parameters determined by fitting data for the far field probe (Fig. ll), pressurization phase of the experiment (magnitudes of the model parameters are given in Table 2)

pressure difference larger. The opposite is observed.

A second possible influence on the far field measurements may have entered through the radial variation in porosity discussed previously. However, while a small change in porosity can have a significant effect on the shear strength, its effect on the elastic properties and permeability is expected to be small. Indeed, on the basis of typical variations in drained bulk modulus with porosity (Hamilton, 1971), the modulus in the denser far field region may have been as much as 15% greater than that in the near field. The permeability may have been decreased as much as 25% relative to the near field (Silva & Calnan, 1981). These effects are partially offsetting and

Table 2. Material properties determined bv fitting models to data*

T I _

Cylinder model

K(x 106Pa) K,’ ( x 10’0 Pa) K,” ( x 109 Pa) k Cx IO-"II?)

‘u{: 1 i5.2 MPa

Displacement Far field pressure

7.0 7.0 1.7 1.7 3.0 2.7 8.3 8.3 6.28 7.60 9.13 12.23 7.03 5.09 3.55 1.61 2.60 2.60 0,458 0.458 0.49995 0.49996 0.49997 0.49998

kpressurizati displacemeni

8.0 1.2 4.0

10.0 4.06 5.09

13.00 9.06 3.52 0,463 0.49993 0.49994

Displacement Far field Near field

pressure pressure

7.0 6.0 6.0 1.5 1.7 1.7 3.2 2.8 2.7 8.3 8.3 8.3 5.47 7.07 7.60 7.52 10.90 12.23 8.12 4.96 4.36 4.65 1.97 1.38 2.60 2.27 2.27 0,458 0.452 0.452 0.49994 0.49996 0.49996 0.49996 0.49997 0.49998

* p. K,, 4, and G are fixed to the values given in Table 1


result in a maximum decrease in the consolidation coefficient c of about 15% in the far field and, consequently, a similar decrease in the relaxation time. Calculations of the type shown in Fig. 11, when repeated for the near field pore pressure, indicate a relaxation time of the order of l/20 that observed in the far field. This can be ascribed only to an unexpectedly small value of the length scale 1.

These considerations strongly suggest the possibility that a shorter drainage path existed in the neighbourhood of the near field probe. In part I, the model for an annular region was developed to address this problem. Results using such a modified model are summarized in the following section.

APPLICATION OF ANNULUS MODEL

Smaller cumulative pressure differences at the near field probe, ostensibly further from a drained boundary than the far field probe, raise the possibility that free fluid may have penetrated the sediment near the centre of the tank. This seems likely since surface cracks were observed extend- ing from the heater probe as it was inserted into the sediment. A solution for the response of an annular porous body to external pressure changes was developed in part I to simulate the penetra- tion of free fluid near the centre of the sediment tank. Because the configuration of the cracks or gaps that may have been present in the sediment is unknown, the inner radius is arbitrarily taken to be equal to the radius of the heater probe. This results in a minimum drainage path to the near field pore pressure probe of 0.02 m (Fig. 3) and,

-8I 0 10 20 30

Time, s X 10“

Fig. 14. Comparison of far field piezometer data and annulus model predictions during the pressurization phase of the experiment (magnitudes of the model parameters are given in Table 2)

consequently, can be expected to lead to rapid relaxation of pore pressure changes in this area.

Figures 13-15 show the best fits obtained for the annulus model. The solutions for step changes in external pressure were used for these calculations, and the early time approximations were not employed. A reasonable representation of the displacement data can again be obtained cap- turing both the undrained step responses and the relaxation rates (Fig. 13). The far field pressure data are also well represented (Fig. 14). The material properties derived from both sets of calculations differ little from those obtained from the

x -8- E -i c

E g-12- s

:: 0

-16-

Time sXl@

Fig. 13. Comparison of sediment surface displacement data and annulus model best-fit predictions during the pressurization phase of the experiment (magnitudes of the model parameters are given in Table 2)

-3.51 I I 0.0 IO.0 20.0 30.0

Time. s X 1 O4

Fig. 15. Comparison of near field piezometer data and annulus model predictions during the pressurization phase of the experiment (magnitudes of the model parameters are given in Table 2)


solid cylinder model (Table 2). This is to be expected, because the surface displacement inte- grates over the entire sample and the far field probe should sense little influence from boundary conditions at small values of r/R,, where R, is the outer radius.

The principal difference in the annulus calculations is seen in the results for the near field pore pressure. The model is able to represent the essential features of the data (Fig. 15) including the maximum pressure difference attained and the relaxation rates. The calculated pressure jumps are notably larger than those measured during the middle portion of the test. Most importantly, however, it should be emphasized that the annulus model predicts smaller cumulative pressure differences at the near field probe, as observed. Material constants determined from this fit are shown in Table 2 along with those from the other fits.

SUMMARIZING REMARKS Calculations based on independent measure-

ments or estimates of material properties exhibit marked departures from the experimental data (Figs 5-S). To some extent, such discrepancies are related to parameter sensitivity in the poroelas- ticity model. There are several other factors, however, that may have contributed to the measured response. These are discussed briefly in the following paragraphs.

The sediment sample is idealized as a finite cir- cular cylinder that deforms freely in response to external pressure changes. There are two possible constraints, however, that may affect the actual experimental results. The first of these is due to the heater probe, which was fixed to a rigid structure and penetrated 0.33 m into the sample. If a no-slip condition or any sort of frictional resistance prevailed along the 12.7 mm radius probe, the surface displacement, which was measured at a radius of 38 mm, may have been restricted. The material would then appear to be stiffer than it actually is. It should be noted that the undrained bulk modulus determined by matching the model and data is of the order of 6 GPa, while conven- tional measurements for clays usually yield values about half as large.

In addition, it was noted that the model under- predicts the apparent stiffening observed in the undrained response. Assuming that no relaxation takes place during each pressure increment, the undrained modulus K, inferred from the surface displacement measurements increases from about 5 GPa to 13 GPa during pressurization. The model incorporates a pressure-dependent fluid modulus K, that gives rise to an increase in K,. However, for the calculations shown in Fig. 5, the

change in K, results in only a 44% increase in K,. It is possible that drag on the heater probe may manifest itself more strongly as the surface displacement increases, contributing to the apparent stiffening.

A second factor that could give rise to a large apparent undrained modulus K, is the assumption that the sediment always rested on the bottom of the tank. The calculated surface displacement represents the axial strain integrated over the entire sample length. If, however, the sediment were able to deform without settling over a time-scale that is comparable with or longer than the time of each pressure increment (about 1800 s), the measured displacements could be as little as one-half of the value calculated. Simplifying and conservative assumptions were used by McTigue et al. (1985) to estimate the likelihood of such an occurrence. These results suggest that a small gap between the bottom of the sediment sample and the sample tank would close on a time-scale that is much less than that of the pressure build-up and therefore would not contribute to the displacement of the top surface of the sample.

A third factor that results in a high apparent undrained bulk modulus is deformation of the steel tank. The surface displacements were measured relative to the tank, which was assumed to be rigid. However, the tank itself was also fully immersed in the external fluid and deformed with each pressure increment. For a bulk modulus of K,, = 180 GPa, the tank would shorten by about 0.01 mm with each pressurization step. Thus, the measured undrained displacements are about 3% low, making the material appear to be slightly stiffer than it actually is. This small correction is neglected.

Values for the modulus K, of clay particles used in the initial model calculations are another area of uncertainty. Slates are comprised of clays and have almost no porosity, so that moduli obtained from measurements on slates should provide a reasonable estimate for individual clay particles. Clark (1966) reports K, values for slate in the range 20-50 GPa. Another estimate for an aluminium silicate clay can be obtained by adopt- ing the modulus for metallic aluminium, 69 GPa. These values bracket that used by Skempton (1961), 50 GPa, which was used in the prelimi- nary calculations.

The sensitivity of the calculations to changes in the input parameters has been examined by varying each parameter about its nominal best-fit value while holding the other parameters constant. Because &,, K, and p are well known, and since the value of G has little influence on the deformation, the bulk moduli K, K,' and K,", and


i

3 E i; 1 o-6 -

E a,

;” 5

8

s fj 10-7 = ::

6 0

I I

10~8 j I 1 8 0’1 1.0 10.0 100.0

Drained bulk modulus K. MPa

(a)

7- I

6-

Baladi -

0’001 I I I I 0 010 0.100 1 1.000 1 10~000 1

Shear modulus G, MPa

ib)

Fie. 16. Predicted dependence of the consolidation coefficient on (a) the drained buik modulus and (h) the shear modulus

the permeability k, are regarded as unknowns. The permeability affects only the consolidation coefficient c, which varies linearly with k. Thus, the influence of variations in K, K,’ and K,” on the observable parameters c, 1 - B and K, are of particular interest. Figs 1618 show the results of these sensitivity calculations. The consolidation coefficient c varies only with changes in K, and c and K are approximately proportional near the nominal fit. The parameter c (Fig. 16) is quite insensitive to K,, and thus it does not vary with pressure. The undrained pore pressure difference scales with 1 - B (Fig. 17), which varies linearly with K and varies very strongiy with K,” as K,” approaches K,. The undrained modulus K, (Fig.

18) varies roughly linearly with K,’ near the nominal fit, and is very sensitive to K,“. These results are summarized qualitatively in Table 3.

In conclusion the analysis of the isothermal mechanical response of the sediment in the ISHTE simulation experiment shows that the dominant deformation processes are well under- stood. Fitting calculated results using a poroelastic model to surface displacement and pore pressure data determines a number of material properties. These results are of particular interest because they are derived from a very large sediment sample under simulated deep ocean conditions. Some of the inferred properties can be checked against independent laboratory measure-


Sohd bulk modulus K,": GPa 1 10 100 1000

10-z

10-z-

co I

10-b-

10-s ' I I , 0.1 1 10 100

DraIned bulk modulus K: MPa

Fig. 17. Predicted dependence of 1 - B on the drained bulk modulus and the solid bulk modulus KS”

ments, while others are uniquely determined in this analysis.

The sediment is modelled as a porous elastic material with compressible constituents. Such an analysis distinguishes this problem from many others in soil mechanics where the water and soil particles are assumed to be incompressible.

Indeed, the mechanical response data from the simulation experiment indicate that the undrained Poisson’s ratio of the sediment is v, z 0.49995. None the less, all the measured effects during pressurization and depressurization are due to the small difference in the compressibilities of the water and clay particles. The model shows that, because the water is more compressible than the solid, a change in external pressure results in a very small difference between the pressure in the sediment pores and that at the sediment boundaries. The sediment undergoes an undrained isotropic deformation, which relaxes as external water flows into the body. The material thus expands slowly until only the strain due to com- pression of the solid remains. This phenomen- ology is clearly seen in the data for surface displacement and pore pressure.

Calculations based on independently measured or estimated material properties show order-of- magnitude agreement with the data but fail to represent the detailed behaviour accurately. The parameter sensitivity is found to be quite high, however, and very good fits are obtained by varying the magnitude of the material properties over reasonable ranges. The best fits are found for values of permeability, drained bulk modulus and solid bulk modulus that are all within a factor of 2-3 of independent measurements.

Table 3. Sensitivity of derived parameters to changes in material properties

Parameter Sensitivity of parameter to the following

If, K..

K KS’ K," G k

Moderate Zero Zero Low Moderate Moderate Zero High Zero Zero Zero Moderate High Zero Zero

SolId bulk modulus K,‘, K,“: GPa

Fig. 18. Predicted dependence of the undrained hulk modulus on the solid bulk moduli


ACKNOWLEDGEMENTS The ISHTE simulation experiment was a col-

laborative effort of numerous individuals under the direction of C. M. Percival (Sandia National Laboratories). The successful execution of the experiment was in large measure due to the technical expertise of L. 0. Olson and the staff of the University of Washington Applied Physics Laboratory. Sample preparation and geotechnical analyses were carried out by the University of Rhode Island Marine Geotechnical Laboratory, co-ordinated by A. J. Silva. Technical assistance for the piezometer instrumentation was provided by J. T. Burns (Naval Ocean Research and Devel- opment Activity). Technical assistance for the sediment surface displacement instrumentation was provided by E. Boespflug (Sandia National Laboratories). An anonymous referee pointed out the potential influence of sample inhomogeneity due to lower water content near the drainage. This work was supported by the US Department of Energy under contract DE-AC04-76DPOO789.

REFERENCES Baladi, G. Y. & Ackers, S. A. (1981). Constitutive

properties and material model development for marine sediments in support of the subseabed disposal program. In Subseabed Disposal Program annual report January to December 1980, vol. II, part 1, pp. 621-781 (ed. K. R. Hinga). Report SANDIl- 1095/H, Sandia National Laboratories, Albu- querque. (Available from National Technical Information Service, US Department of Commerce, Springfield, Virginia.)

Bennett, R. H., Burns, J. T. & Lambert, D. N. (1982). Fabrication and testing of deep ocean piezometer system and components. In Subseabed Disposal Program annual report January to September 1981, vol. II, part 1, pp. 641-645. Report SAND82-0664/ II, Sandia National Laboratories, Albuquerque. (Available from National Technical Information Service, US Department of Commerce, Springfield, Virginia.)

Bennett, R. H. & Faris, J. R. (1979). Ambient and dynamic pore pressures in fine-grained submarine sediments: Mississippi Delta. Appl. Ocn Res. 1, 115- 123.

Biot, M. A. & Willis, D. G. (1957). The elastic toe% cients of the theory of consolidation. J. Appl. Mech. 24594-601.

Clark, S. P. (1966). Handbook of physical constants. Memoir 97, Geological Society of America, New York.

Hamilton, E. L. (1971). Elastic properties of marine sediments. J. Geophys. Res. 76, 579-604.

Hollister, C. D., Anderson, D. R. & Heath, G. R. (1981). Subseabed disposal of nuclear wastes. Science 213, 1321-1326.

Lambe, T. W. & Whitman, R. V. (1969). Soil mechanics. New York: Wiley.

McTigue, D. F., Lipkin, J. & Bennett, R. H. (1985). Isothermal mechanical response of sediments in the

ISHTE simulation experiment. Report SAND83- 1847, Sandia National Laboratories, Albuquerque. (Available from National Technical Information Service, US Department of Commerce, Springfield, Virginia.)

McTigue, D. F., Lipkin, J. & Bennett, R. H. (1986). Consolidation under an isotropic total stress increase: part I, model analysis for compressible constituents. Gtotechnique 36, No. 1, l-9.

Miller, J. B., Miller, V. W. & Olson, L. 0. (1984). ISHTE simulation APL-UW engineering report. In 1982 Subseabed Disposal Program annual report: thermal response studies October 1981 through Sep- tember 1982, pp. 81-168 (ed. C. M. Percival). Report SAND82-2717, Sandia National Laboratories, Albu- querque. (Available from National Technical Infor- mation Service, US Department of Commerce, Springfield, Virginia.)

Percival, C. M. (1982). Laboratory simulation of deep ocean in situ heat transfer experiment. In Oceans ‘82 Conference Record, pp. 679-684. Washington: Marine Technology Society and IEEE Council on Oceanic Engineering.

Percival, C. M. (1983). The Subseabed Disposal Program in situ heat transfer experiment (ISHTE). Report SAND80-1202, Sandia National Laboratories, Albu- querque. (Available from National Technical Infor- mation Service, US Department of Commerce, Springfield, Virginia.)

Randolph, M. F. & Wroth, C. P. (1979). An analytical solution for the consolidation around a driven pile. Int. J. Numer. Analyt. Meth. Geomech. 3, 217-229.

Riley, J. P. & Skirow, G. (1975). Chemical oceanography. New York: Academic Press.

Seabed Programs Division 6334 (1983). The Subseabed Disposal- Program: 1983 status report Report SAND83-1387, Sandia National Laboratories, Albu- querque. (Available from National Technical Infor- mation Service, US Department of Commerce, Springfield, Virginia.)

Silva, A. J. & Calnan, D. I. (1981). Geotechnical aspects of subseabed disposal of high level radioactive wastes. In Subseabed Disposal Program annual report January-December 1979; vol. II, appendix, pp. j35- 744. Report SAND80-2577/H. Sandia National Laboratdries, Albuquerque. (Available from Nation- al Technical Information Service, US Department of Commerce, Springfield, Virginia.)

Silva, A. J., Jordan, S. A. & Criscenzo S. J. (1984). URI technical report of the simulation experiment for in situ heat transfer experiment project. In 1982 Sub-

seabed Disposal Program annual report: thermal response studies October 1981 through September 1982, pp. 253-340 (ed. C. M. Percival). Report SAND82-2717, Sandia National Laboratories, Albu- querque. (Available from National Technical Infor- mation Service, US Department of Commerce, Springfield, Virginia.)

Skempton, A. W. (1961). Effective stress in soils, con- crete, and rocks. In Pore pressure and suction in soils pp. 4-16. London: Butterworths.

Williams, N. D. (1982). The effects of elevated temperature on the engineering-. properties of seapoor sediments. PhD thesis, University of California, Berkeley.

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