# Predicting the permeability of sediments entering subduction zones

## Abstract

Using end-member permeabilities defined by a worldwide compilation of sediment permeabilities at convergent margins, we compare permeability predictions using a geometric mean and a two-component effective medium theory (EMT). Our implementation of EMT includes a threshold fraction of the high-permeability component that determines whether flow occurs dominantly in the high- or low-permeability component. We find that this threshold fraction in most cases is equal to the silt + sand-sized fraction of the sediment. This suggests that sediments undergoing primary consolidation tend to exhibit flow equally distributed between the high- and low-permeability components. We show that the EMT method predicts permeability better than the weighted geometric mean of the end-member values for clay fractions <0.6. This work provides insight into the microstructural controls on permeability in subducting sediments and valuable guidance for locations which lack site-specific permeability results but have available grain-size information.

## Key Points

- Effective medium theory predicts permeability better than geometric mean for clay fractions <0.6
- The silt + sand fraction is usually abundant enough to form connected flow paths
- End-member permeabilities are globally valid functions of porosity

## 1 Introduction

The permeability of sediments entering subduction zones exerts important controls on generation and dissipation of excess pore pressures. These processes alter the consolidation state and frictional properties of the sediments and thus influence the localization of the plate boundary fault, stresses acting on the fault, the amount of sediment that is accreted or subducted, and the generation and propagation of seismic slip [*Davis et al.,* 1983; *Moore and Saffer*, 2001; *Saffer and Tobin*, 2011]. Sediment permeability distribution also guides fluid, thermal, and chemical cycling within subduction zones [*Kastner et al.,* 2014]. Laboratory measurements on cores collected during scientific ocean drilling expeditions (Ocean Drilling Program (ODP) and Integrated Ocean Drilling Program (IODP)) have aided characterization of sediment permeability distribution. Because the sampling and measurements are time intensive, they are not practical to conduct at all margins. Thus, it would be highly beneficial to predict permeabilities from more easily obtained parameters such as grain-size distribution and porosity.

Previous studies using ODP and IODP data [*Gamage et al.,* 2011; *Daigle and Screaton*, 2015] have shown that particle size is the main factor controlling permeability-porosity in marine sediments. This result is consistent with laboratory and numerical studies [*Schneider et al.,* 2011; *Reece et al.,* 2013; *Daigle and Reece*, 2015] that have demonstrated that the fraction of clay-sized particles relative to larger particles strongly influences permeability because the addition of clay-sized particles to an assemblage of silt or larger particles tends to decrease the permeability of the mixture up to a threshold clay fraction. Below this threshold clay fraction, the larger grains form a series of connected, higher-permeability pathways for fluid flow at the grain scale, while above it the larger grains tend to be isolated, and the overall permeability is controlled by the permeability of the clay matrix. The threshold clay fraction has been estimated at 80% by mass in sediments from the Nankai Trough [*Reece et al.,* 2013], but it is likely to be variable and dependent on the particle size distribution and grain shapes in an analogous manner to the percolation threshold [e.g., *Moldrup et al.,* 2001; *Consiglio et al.,* 2003]. The permeability of marine sediments may therefore be analyzed in terms of a two-component mixture consisting of clay-sized particles and larger particles but such an analysis must capture the intricacies of flow in sediments above or below the threshold clay fraction.

Effective medium theory (EMT) provides a framework for predicting the transport properties of disordered, composite materials based on the relative abundances, end-member properties, and the degree of connectivity among the different components [*Kirkpatrick*, 1973; *McLachlan*, 1988; *David et al.,* 1990]. The use of EMT in porous media has historically been focused primarily on prediction of electrical conductivity and dielectric permittivity [e.g., *Bruggeman*, 1935; *Kirkpatrick*, 1973; *Sen et al.,* 1981], but many studies have also demonstrated the applicability of EMT to predicting permeability [e.g., *Dagan*, 1979; *Poley*, 1988; *David et al.,* 1990; *Renard and de Marsily*, 1997; *Fokker*, 2001]. However, no previous studies have attempted to predict the permeability of mixtures of clay-sized and larger particles while incorporating the concept of the threshold clay fraction. In the formulation of *McLachlan* [1987, 1988], the electrical conductivity of a binary medium may be determined by considering one phase as inclusions within the other phase, with a critical fraction of the higher-conductivity phase separating regimes in which conductivity is dominated by flow through the higher- or lower-conductivity phases. This formulation is consistent with observations that the permeability of marine sediments depends on the presence or absence of percolating pathways through the silt + sand-sized fraction. On the other hand, previous work has shown that the weighted geometric mean of the end-member permeabilities can successfully predict the permeability of the mixture in some cases, although it is not clear that this is generally true [e.g., *Dagan*, 1979; *Schneider et al.,* 2011; *Daigle and Reece*, 2015]. Using end-member permeabilities defined by a worldwide compilation of sediment permeabilities at convergent margins [*Daigle and Screaton*, 2015], we show that the EMT formulation of *McLachlan* [1988] provides a better permeability prediction when the clay-sized fraction is <0.6. When the clay-sized fraction exceeds 0.6, the weighted geometric mean provides a better permeability prediction. We also show that the silt + sand-sized fraction of these sediments is a good approximation of the critical fraction in the EMT model for clay fraction <0.6, indicating that larger particles are present in sufficient abundance to form percolating pathways. For larger clay fractions, the better performance of the geometric mean indicates that the critical fraction is close to 0.5, suggesting that the larger particles cannot always form percolating pathways.

## 2 Background and Methods

*Daigle and Screaton* [2015] made a compilation of 317 permeability measurements from 25 years of scientific ocean drilling at and seaward of convergent margins worldwide. This compilation included eight measurements of sediments from pelagic sites in the equatorial and southern Pacific Ocean that will eventually be subducted, 80 measurements of permeability and particle size distributions of sedimentary inputs within 20 km seaward of subduction zones, and 72 measurements of sediments that have been subducted or underthrust beneath the overriding wedge (Figure 1). Sample depths were generally <1 km, and permeabilities were measured in the direction parallel to the borehole axis (i.e., vertical). These measurements were assigned either to “reference” or to “underthrust” structural domains. Permeability-porosity relationships were determined based on the relative fractions of clay-sized and larger particles. These relationships showed that sediments with >80% clay-sized particles (<4 µm diameter) by mass and sediments with >5% sand-sized particles (>62.5 µm diameter) exhibited significantly different permeability-porosity trends from sediments with <80% clay-sized particles and <5% sand-sized particles. In addition, the relationships that were determined on the basis of particle size were found to be consistent with permeability-porosity behavior of deeper analog sediments recovered from depths as great as 5 km. This was interpreted as evidence that diagenesis does not significantly alter the permeability-porosity behavior of sediments, and that particle size is the most important factor determining permeability-porosity behavior. *Daigle and Screaton* [2015] observed that samples obtained using the extended core barrel (XCB) system were prone to significant coring-induced disturbance, which may have affected laboratory permeability measurements. Therefore, in the present study we exclude XCB samples.

Several models have been investigated to describe the permeability of mixtures of clay-sized and larger particles. The weighted arithmetic and harmonic means are known to define upper and lower bounds, respectively, on the permeability of composite materials [*Dagan*, 1979]. These bounds correspond to media in which the high- and low-permeability components are arranged in layers parallel and perpendicular to flow, respectively. *Hashin and Shtrikman* [1962] derived upper and lower bounds for homogeneous, two-component mixtures, with a permeability range that is slightly narrower than that defined by the weighted arithmetic and harmonic means. *Schneider et al.* [2011] showed that the permeability may be approximated by the weighted geometric mean of the end-member permeabilities. These models all provide acceptable results when the end-member permeability contrast is small (less than an order of magnitude [*Daigle and Reece*, 2015]), but in general the permeabilities predicted by these models can vary widely (Figure 2a), limiting their predictive capability.

*McLachlan*[1988] to permeability. In this formulation, a heterogeneous medium made of a high-permeability and low-permeability component with permeabilities

*k*and

_{h}*k*, respectively, is modeled as a hypothetical homogeneous medium with permeability equal to the effective permeability

_{l}*k*of the original, heterogeneous medium. The permeability of the homogeneous medium is determined by assuming that the local spatial fluctuations of permeability in the heterogeneous medium sum to zero when averaged over the entire volume of the medium:

_{e}*f*is the volume fraction of the low-permeability component and

_{l}*f*is the critical volume fraction of the high-permeability component above which some connected flow pathways exist solely through the high-permeability component. When 1 –

_{c}*f*<

_{l}*f*, flow will mainly occur through the low-permeability component, while when 1 –

_{c}*f*>

_{l}*f*, flow will mainly occur through the high-permeability component. Note that

_{c}*f*is expressed in terms of volume fraction, while the threshold clay fraction is expressed in terms of mass fraction [

_{c}*Reece et al.,*2013;

*Daigle and Screaton*, 2015].

*Daigle and Screaton*[2015]:

*k*is permeability in m

^{2}and

*φ*is porosity (Figure 2b). Second, we assume that the porosities of the low-permeability and high-permeability components are equal to the overall porosity of the medium, so that the end-member permeabilities may be determined by the porosity of the sample. Third, we assume that the solid grain densities of the low-permeability and high-permeability components are approximately equal to each other, so that the volume fractions of the two components are equal to the mass fractions of clay-sized and larger particles, respectively. When

*f*is assigned a constant value of 0, 0.5, or 1, equation 1 reduces to the arithmetic mean, the geometric mean, and the harmonic mean, respectively (Figure 2c). In a physical sense, this means that when

_{c}*f*= 0, flow will travel predominantly through the silt + sand-sized fraction, and the sediment will retain higher permeability at larger clay fractions. Conversely,

_{c}*f*= 1 indicates that the silt + sand-sized fraction cannot form a connected flow path and flow will be forced to travel through the clay fraction, resulting in lower permeability at lower clay fractions. The theoretical limits of

_{c}*f*therefore correspond to the arithmetic and harmonic mean limits on permeabilities of mixtures [e.g.,

_{c}*Dagan*, 1979], and the geometric mean is simply a special case of EMT where

*f*= 0.5. In general, the use of equation 1 requires some assumption of reasonable values of

_{c}*f*.

_{c}## 3 Results and Discussion

To determine appropriate values of *f _{c}* for use in permeability prediction, we first determined iteratively the value of

*f*that best reconstructs the measured permeability for each sample using equation 1. Since

_{c}*f*is a threshold fraction of the high-permeability component, we compared these values to the mass fraction of silt + sand-sized particles determined for each sample. There is a remarkable trend defined by some of the samples in which

_{c}*f*is equal to the mass fraction of silt + sand-sized particles (Figure 3a). However, many of the samples yield

_{c}*f*= 0 or

_{c}*f*= 1; in particular, all of the deep analog samples and all except one of the underthrust samples lie on one of these two extremes. Most of the samples at the extremes have porosities <0.4 (32 out of 45) (Figure 3b), and so the difference between the permeabilities of the high- and low-permeability components in these samples is generally small; the inset in Figure 3b shows the ratio of the end-member permeabilities for a clay fraction of 0.5 and indicates that the end-member permeability ratio is less than 10 when porosity is less than 0.4. At lower porosities, the harmonic, geometric, and arithmetic means may fit the data equally well [e.g.,

_{c}*Daigle and Reece*, 2015], and the least squares optimization scheme we used to determine

*f*may tend to one of the two extremes when either can yield an acceptable result. We additionally cannot rule out the possibility that these phenomena are the result of either diagenetic alteration of flow pathways at the pore scale or deformation that creates a fabric [e.g.,

_{c}*Vannucchi and Tobin*, 2000]; depending on the orientation of the fabric, it could allow easier flow in either the vertical or horizontal directions, which would send

*f*to one extreme or the other. This may be the case in the higher-porosity samples with

_{c}*f*= 0 or 1.

_{c}For the remainder of the samples, the silt + sand-sized fraction appears to be a reasonable approximation of *f _{c}*, though there are some deviations, in particular a trend of

*f*clustering between 0.4 and 0.6 for silt + sand-sized fraction <0.4 (Figure 3a). Figure 4a shows permeability computed for all samples from equation 1 using

_{c}*f*equal to the silt + sand-sized fraction plotted against the measured values. Overall, the fit is good, with a coefficient of determination (

_{c}*R*

^{2}) of 0.846 and a 68% confidence interval of ±0.852 orders of magnitude (statistics determined using log

_{10}

*k*). Although samples from different geographical regions have different ranges of porosity and permeability, nearly all the samples lie on the trend. When

*f*is fixed at 0.5, equation 1 reduces to the geometric mean (Figure 2c), and it has been observed that the geometric mean often gives a good representation of the permeability of mixtures of silt and clay [

_{c}*Schneider et al.,*2011;

*Daigle and Reece*, 2015]. If we use

*f*= 0.5 in equation 1, we are able to reconstruct the measured permeabilities of all samples with

_{c}*R*

^{2}= 0.765 and 68% confidence interval of 0.984 orders of magnitude. While this fit is not as good as that shown in Figure 4a, it still can provide a reasonable permeability estimate, especially in samples with porosity <0.4 since the end-member permeabilities are close to each other in these cases, and the model is less sensitive to the values of

*f*. Thus, these differences in permeability estimation methods will likely be most important for investigations into shallowly buried sediments and early subduction processes, where porosity is >0.4. Investigations focused on deeper portions of subduction zones could opt for the simplest approach without significantly increasing error.

_{c}To provide guidance on specific cases in which the geometric mean may be used, we compared the root-mean-square (RMS) errors from the geometric mean and our EMT model for different porosity ranges and clay-sized fractions (Figure 4b). The EMT model yields lower RMS errors for all porosity ranges, although the difference with respect to the geometric mean is negligible for porosity <0.4. The geometric mean gives a better permeability prediction when clay-sized fraction is >0.6. Since the geometric mean is a special case of EMT where *f _{c}* = 0.5, the better performance of the geometric mean with respect to the general EMT suggests that the larger grains are not present in sufficient abundance to provide percolating pathways when clay-sized fraction exceeds 0.6. This is consistent with our observation in Figure 3a that

*f*appears to be larger than the silt + sand-sized fraction when the silt + sand-sized fraction is <0.4. Our implementation of the EMT model with

_{c}*f*equal to the silt + sand-sized fraction is therefore preferred when the clay-sized fraction is <0.6, while for larger clay-sized fractions

_{c}*f*= 0.5 and the geometric mean may be used. To provide global context for this result, we reviewed lithologic descriptions and grain-size results (where available) to categorize subduction zones where sediments <0.6 clay-sized fraction are likely to be subducting (Table S1). This includes margins where turbiditic or volcaniclastic sediments occur near the base of the incoming sediment column (e.g., Nankai-Ashizuri and Muroto, portions of the Aleutian Trench, Costa Rica-Osa, Northern Barbados, South Chile, and Java), or trench sediments are inferred to be subducted (e.g., Peru). Hemipelagic sediments tend to be borderline (clay-sized fraction around 0.6), and pelagic clays have higher clay-sized fraction. We note that accreted sediments and slope sediments generally have greater proportions of silt and sand sized material, and the EMT model will likely be appropriate for those sediments.

_{c}The general trend of *f _{c}* being equal to the fraction of silt + sand-sized fraction when the clay-sized fraction is <0.6 implies that flow does not occur predominantly in either the high- or low-permeability components in such cases but is instead distributed throughout the medium. Physically, this suggests that larger grains tend to be arranged such that they form connected flow pathways at the pore scale. This could be brought about either by the arrangement of the larger grains themselves or by stress shielding in which the larger grains form force chains that protect the clay fraction from consolidating [

*Mueth et al.,*1998;

*Schneider et al.,*2011]. This phenomenon becomes more important as clay-sized fraction increases, since it becomes more difficult to have connected flow pathways through the silt + sand-sized fraction. In these situations, stress shielding may preserve local regions of high-porosity clay associated with the larger grains, which act to promote fluid flow across the medium in the vicinity of the larger grains. Thus, when the clay fraction is small, flow can occur through the silt + sand-sized fraction (Figure 4c), but when the clay fraction increases, stress shielding may play an important role in providing preferential flow pathways (Figure 4d). There is a clay-sized fraction, however, above which the larger grains are not present in a sufficient quantity to form percolating flow pathways (Figure 4e). This clay-sized fraction appears to be 0.6 based on our data set.

Finally, we note that our assumption that the porosities of the low-permeability and high-permeability components are equal to the overall porosity of the medium may be an oversimplification. Previous studies of the permeability of marine shaly sands [*Revil and Cathles*, 1999; *Daigle and Reece*, 2015] have found that the end-member porosities are approximately equal in some cases, but it is not clear whether this can generally be assumed. If stress shielding resulted in less porosity loss in the clays during burial, the low-permeability end-member would have higher porosity, while the high-permeability end-member might have lower porosity than we assumed. Since the high-permeability end-member displays greater sensitivity to porosity (Figure 2b), our assumption may have resulted in a slight overestimate of permeability, particularly at lower porosities in consolidated samples. This effect may be slightly evident in Figure 4a in the samples from Nankai-Ashizuri and the Deep Analogs. However, enhanced porosity due to stress shielding is usually a highly localized phenomenon (e.g., Figure 4d and *Schneider et al.* [2011]). Sensitivity analysis additionally shows that a 0.1 reduction in the porosity of the high-permeability end-member decrease the overall permeability by less than half an order of magnitude at a clay-sized fraction of 0.2 (Figure S1), with even less sensitivity to the porosity of the high-permeability end-member when the clay-sized fraction increases. Therefore, the assumption is unlikely to significantly affect the results.

## 4 Conclusions

Permeability in marine sediments is controlled by the relative quantities of clay-sized and larger grains. We showed that the permeability of sediments entering subduction zones and underthrust sediments on the subducting plate may be modeled using EMT (equation 1) by considering the sediments as two-component mixtures of clay-sized grains and larger grains. The end-member permeabilities were determined from a global compilation of permeability-porosity trends from convergent margins worldwide [*Daigle and Screaton*, 2015]. We found that the critical high-permeability fraction (*f _{c}*) in equation 1 could be approximated as the silt + sand-sized fraction when the clay-sized fraction was <0.6. For larger clay-sized fractions, the geometric mean provided a better permeability prediction, suggesting that

*f*= 0.5 in these cases. Our model was able to predict measured permeabilities accurately in reference and underthrust sediments, as well as in deep marine sediment analogs. Our assessment of the variation of the critical high-permeability fraction from sample to sample indicated that the underthrust and deep analog sediments undergo processes that alter the pore-scale flow pathways either through either diagenesis or localized deformation. The fact that the geometric mean is a better predictor of permeability for clay-sized fractions >0.6 suggests that the larger grains cannot form connected, percolating pathways when their mass fraction falls below 0.4. Our work highlights the importance of the silt + sand-sized fraction in controlling the permeability of sediments at convergent margins.

_{c}## Acknowledgments

The data used in this study are available in the references provided in the caption of Figure 3. This research used samples and data provided by the Ocean Drilling Program and the Integrated Ocean Drilling Program. This material is based upon work at University of Texas supported by the Department of Energy under award number DE-FE0013919 and NSF EAR-0819769 at University of Florida. This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe on privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein to not necessarily state or reflect those of the United States Government or any agency thereof.

The Editor thanks two anonymous reviewers for their assistance in evaluating this paper.