- k = (K x
µ) / (
x g), (2)
Constant flow permeability tests were conducted to determine vertical permeability values for core samples from Leg 180. In this test method, a constant flow is established across the sample and the resulting hydraulic gradient is measured. The tests were conducted using the Trautwein Soil Testing Equipment Company's DigiFlow K. The equipment consists of the cell (to contain the sample and the confining fluid) and three pumps (sample top pump, sample bottom pump, and cell pump). Bladder accumulators allowed deionized water to be used throughout the pumps while an idealized solution of seawater (25 g NaCl and 8 g MgSO4 per liter of water) was used as the permeant through the sample. ASTM designation D 5084-90 (1990) was used as a guideline for general procedures. The Leg 180 whole-round samples were stored in the plastic core liner and sealed in wax to prevent moisture loss. They were contained in a refrigerated environment (4°C) and in water until immediately prior to sample preparation. Immediately before testing, cores were trimmed to fit within the flexible wall membrane. The samples had a minimum diameter of 50.8 mm (2 in), and sample heights ranged from ~150 to 200 mm. The ends of each sample were trimmed to provide freshly exposed surfaces. Once encased within the flexible wall membrane, the samples were fitted with filter paper and saturated porous disks. Samples were placed in the cell, which was then filled with deionized water so that the membrane-encased sample was completely surrounded by this fluid. A small confining pressure of ~0.03 MPa (5 psi) was applied to the cell. All air bubbles were removed from the flow lines, and a backpressure of ~0.28 MPa (40 psi) was then applied in order to fully saturate the sample. Backpressure was achieved by concurrently ramping the cell pressure and the sample pressure to maintain a steady effective stress. Saturation was verified by measuring the change in pore water pressure in the porous material divided by the change in the confining pressure (ASTM, 1990).
Once the sample was fully saturated, cell fluid pressure was increased while the sample backpressure was maintained, thus increasing the effective stress on the sample. The maximum stress that the cell is able to sustain is ~1.03 MPa (150 psi), limiting the maximum effective stress to ~0.75 MPa (110 psi). The sample was allowed to equilibrate for at least 4 hr and generally overnight. Once the target effective stress was achieved, cell pressure and backpressure were maintained. Vertical sample displacement and cell fluid volume were monitored throughout testing.
After the target effective stress level was achieved, a brief constant gradient test was conducted to select an appropriate flow rate for the subsequent constant flow tests. During the constant flow tests, flow rates were maintained by two pumps, one on each end of the sample, ensuring that the volume of the sample remained unchanged. Throughout the permeation step, the head gradient was monitored to assure that gradients were not excessive (ASTM, 1990). Since fluid pressure in the closed hydraulic system is sensitive to temperature changes, testing was conducted within a closed cabinet with a fan to keep the internal temperature uniform. This kept temperature at ~27.5°C (±0.5°C). Temperature was monitored throughout the testing phase.
Two to three constant flow tests were performed at each effective stress. Once permeability values were obtained, cell pressure was increased and the sample was allowed to equilibrate overnight. At least two different effective stress steps were performed for each sample. If the permeability of the sample decreased significantly from step 1 to step 2 during permeation, more steps were performed. The maximum effective stresses reached in this study are well below in situ values. Therefore, we used the permeability results from the highest effective stress, and the values presented in this study should be considered maximum permeability values. However, in previous laboratory investigations (e.g., Bolton and Maltman, 1998; Bolton et al., 2000), it appeared that the largest decrease in permeability occurred as effective stresses were increased from 0 to 0.1 MPa; subsequently, permeabilities remained relatively constant.
Measurements were made of the sample's diameter and height before it was placed in the cell. Using these measurements, the specified flow rate (Q), and the pressure difference that was monitored by the testing equipment, hydraulic conductivity values were calculated for each sample using Darcy's Law:
where
These conductivity values were then converted to permeability (in square meters) using the following equation:
x g), (2)
where
= density (in kilograms per cubic meter), and
A viscosity of 0.001 Pa · s was used for this calculation.
Numerical modeling focused on Site 1108 to assess whether elevated pore pressures due to sedimentation are likely at the depth of the low-angle normal fault. Previous researchers (Gibson, 1958; Bredehoeft and Hanshaw, 1968) developed analytical models for this problem of estimating fluid pressures due to sedimentation. However, to model varying sediment rates and changes in storage properties through time, we used a one-dimensional numerical approach. This numerical approach was previously described by Screaton and Ge (2000), but the calculation of compressibility within the model has been improved.
In the absence of overpressures, we assume that porosity will decrease exponentially with depth, as has been observed by Athy (1930):
where
For the hydrostatic case,
the change in effective stress, 
e,
with depth is:
e
/ dz) = (s
- f)
x (1 - n) x
g, (4)
where
s
= grain density,
f
= fluid density, and
From Equations 3 and 4, dn
can be related to de:
e)
= (-b x n)
/ [(s
- f)
x (1 - n) x
g]. (5)
The coefficient of
vertical compressibility (
)
is defined as
= -dV / (V
x de),
(6)
where
Porosity is related to the volume change by
The expression for
as a function of n
follows from Equations 5, 6, and 7:
= (b x
n)
/ [(s
- f)
x (1 - n)2
x
g]. (8)
The sedimentation history was broken up into packets for which sedimentation rate, porosity parameters no and b, and permeability were assigned. The permeability remained constant for each packet throughout the simulation. Based on the sedimentation rate for each of the packets, the loading program calculated the additional thickness of each sediment layer added to the basin. As each new sediment layer was added to the basin, the layers beneath were moved down one row. Below the sediment layers, model layers were assigned low compressibility and porosities to simulate underlying crystalline rock. The bottom boundary condition of the model was no-flow and the top boundary condition was hydrostatic. The model was set up so that only nonsediment layers would be dropped from the bottom of the model.
For each sedimentation
step, the pore fluid pressures of each layer were calculated based on the
additional load of the new layers. When a porous medium with incompressible
grains is loaded, the stress is partitioned between the pore fluid and the
matrix. The loading efficiency, 
,
denotes the fraction of the stress added to the pore fluid and is defined as
follows (after Neuzil, 1986):
=
/ (
+ n
),
(9)
where
= the compressibility of the fluid. For highly compressible sediments, the
loading efficiency is near 1.
The updated pore pressures
were then input into SUTRA (Voss, 1984), which used the pore pressures as
initial conditions for transient fluid flow for the duration of the
sedimentation step. Once the pore pressures at the end of the sedimentation step
were calculated in SUTRA, they were transferred back into the loading program
and effective stress was calculated. Sediment porosity loss was calculated only
if the effective stress exceeded the previous maximum effective stress value.
Porosity loss was determined using a value from the previous sedimentation step
and vertical node spacing was reduced to maintain constant solid volume and to
ensure mass balance, while horizontal dimensions were held constant. The new
porosity was used to calculate
for the next time step using Equation 8. The calculated compressibility was also
used to assign specific storage, Ss, for each node to be
used in the SUTRA fluid flow simulation:
x g x
(
+ n).
(10)
Site 1108 was modeled to a depth of ~900 mbsf, the estimated depth of the low-angle normal fault zone. Values for the parameters no (= 70%) and b (= 1.6 × 10-3 m-1) in Equation 3 were selected based on the porosity data from shallow parts of Site 1108, with the assumption that shallow depths are least likely to be overpressured. The sediment column of Site 1108 was broken down into five sediment packets (Fig. F2). The initial thickness of each packet was calculated based on ages, porosities, and depths reported shipboard and assumed an initial porosity of 70% and conservation of solid volume. The top packet includes the 400 m that is inferred to have been removed by erosion. For the removed section, an average porosity of 50% was used. The sedimentation rate below the bottom of drilling (485 mbsf) was assumed to be the same as the overlying section, yielding an age at the bottom of ~4.4 Ma. The modeling was broken up into 75 sedimentation steps of 58.7 k.y. each.
