We have conducted triaxial deformation experiments along different loading paths on prism sediments from the Nankai Trough. Different load paths of isotropic loading, uniaxial strain loading, triaxial compression (at constant confining pressure, Pc), undrained Pc reduction, drained Pc reduction, and triaxial unloading at constant Pc, were used to understand the evolution of mechanical and hydraulic properties under complicated stress states and loading histories in accretionary subduction zones. Five deformation experiments were conducted on three sediment core samples for the Nankai prism, specifically from older accreted sediments at the forearc basin, underthrust slope sediments beneath the megasplay fault, and overthrust Upper Shikoku Basin sediments along the frontal thrust. Yield envelopes for each sample were constructed based on the stress paths of Pc-reduction using the modified Cam-clay model, and in situ stress states of the prism were constrained using the results from the other load paths and accounting for horizontal stress. Results suggest that the sediments in the vicinity of the megasplay fault and frontal thrust are highly overconsolidated, and thus likely to deform brittle rather than ductile. The porosity of sediments decreases as the yield envelope expands, while the reduction in permeability mainly depends on the effective mean stress before yield, and the differential stress after yield. An improved understanding of sediment yield strength and hydromechanical properties along different load paths is necessary to treat accurately the coupling of deformation and fluid flow in accretionary subduction zones.
 Devastating thrust-type earthquakes and tsunamis recur in subduction zones. One of the key outstanding questions for these regions is what controls tsunami- and seismo-genesis. The updip limit for seismogenesis, and the conditions that allow propagation of earthquake ruptures to shallow depths, is especially important for tsunami generation [e.g.,Lay et al., 2012]. The updip limit is hypothesized to correspond to a change in frictional behavior from velocity strengthening to velocity weakening a at critical temperature of 100–150°C associated with the transformation of smectite to illite [e.g., Hyndman and Wang, 1993; Hyndman et al., 1995; Vrolijk, 1990]. However, this simple hypothesis is not supported by measurements of the velocity dependence of friction in experiments on illite and other clay-bearing materials [Saffer and Marone, 2003; Brown et al., 2003]. Many workers suggest that depth-dependent changes in earthquake characteristics and tsunami generation depend not only on frictional behavior, but also on a multitude of factors including the consolidation characteristics of sediments, cementation processes, dehydration reactions accompanied by solid-fluid phase transitions such as smectite-illite and opal A-quartz, pore pressure generation, fracture permeability, and thermal gradient [e.g.,Byrne et al., 1988; Marone and Scholz, 1988; Moore and Vrolijk, 1992; Moore and Saffer, 2001; Ma and Beroza, 2008; Ide et al., 2011; Ma, 2012].
 The consolidation state of sediments in accretionary subduction zones change as they undergo burial, underthrusting, underplating, and exhumation. It is essential to document the different deformation mechanisms and consolidation states to explain the observations of both brittle and ductile deformation in the sediments [e.g., Moore, 1986]. Because fluid pressurization and fluid flow plays important roles in the deformation of sediments, it is also necessary to address the effects of deformation on fluid generation and hydraulic properties. For example, Zhu and Wong  report that the permeability evolution of porous rocks depends on the deformation mechanism; a slight decrease in permeability is observed with increasing porosity in brittle faulting regime, while a significant reduction in permeability with decreasing porosity in cataclastic flow regime. However, this and most other laboratory studies have measured permeability evolution during conventional triaxial deformation tests at constant Pc, and relatively few studies discussed the effects of stress states or stress history on permeability evolution. Crawford and Yale  measured the permeability of siliciclastic and carbonate rocks along different stress paths, and found that permeability evolution largely depends on rock type and deformation micromechanisms, and that critical state theory can account for the evolution of permeability in siliciclastic rocks but not in carbonate rocks. For sediments, the consolidation state at the onset of shear is a crucial factor in permeability evolution, as well as for the mode of deformation [e.g., Karig, 1990; Bolton et al., 1998]. Apparently, a better description of the evolution of hydraulic and mechanical properties with deformation is needed for modeling coupled deformation and fluid flow in accretionary subduction zones.
 The purpose of this paper is to consider the evolution of strength and hydraulic properties of sediments that are deformed along different stress paths over the range of stress conditions in accretionary subduction systems. First, we describe the results of experiments along different stress paths on three different samples from the Nankai accretionary subduction zone, which were collected during the Integrated Ocean Drilling Program (IODP) Nankai Trough Seismogenic Zone Experiment (NanTroSEIZE) Stage 1 Expeditions. Second, we discuss the effect of deformation on hydraulic properties in terms of stress state and history. Third, from the experimental results, we construct yield envelopes based on the critical state soil mechanics theory to estimate in situ stress states, strengths, and deformation modes.
2. Geological Settings and Experimental Samples
 The Nankai Trough is located off southwest of Japan, where the Philippine Sea Plate is subducting beneath the Eurasian Plate at a rate of 4–6 cm/year (Figure 1a) [Seno et al., 1993; Miyazaki and Heki, 2001]. The Integrated Ocean Drilling Program (IODP) Nankai Trough Seismogenic Zone Experiment (NanTroSEIZE) focuses on direct sampling, in situ measurements, and long-term monitoring in the region off the Kii Peninsula. The experiment proceeds in multiple stages, each consisting of multiple drilling expeditions, in order to understand the mechanics of seismogenesis and rupture propagation along plate boundary faults. During Stage 1 Expeditions 314, 315, and 316, logging data and core samples were successfully obtained from eight sites (Figure 1b) [Tobin et al., 2009]. The three samples, discussed in this paper, were collected from the following three major regions of the NanTroSEIZE transect: the Kumano forearc basin, the shallow tip of the megasplay fault, and the frontal thrust region (Figure 1 and Table 1). Sample 315-C0002B-63R-1 is Late Miocene, old accretionary prism silty claystone taken from a core depth below the seafloor (CSF) of 1034 m in forearc basin region (Figure 1c) [Expedition 315 Scientists, 2009]. The age of this specimen is estimated to be between 5.59 and 5.90 Ma, and the most likely depositional environment is the trench wedge although this interpretation is uncertain due to poor core recovery and strong tectonic overprint [Expedition 315 Scientists, 2009]. Sample 316-C0004D-48R-1 is early Pleistocene (∼1.67 Ma), slope sediment of silty claystone taken from 360 m CSF on the footwall of the megasplay fault (Figure 1d) [Expedition 316 Scientists, 2009a]. The burial depth of sample 316-C0004D-48R-1 before underthrusting is inferred to be ∼52 m, which is the present thickness of the slope sediments that overlie the sample, below the megasplay (Figure 1d); however, the estimated burial depth should be considered to be a minimum because some of the slope sediments may not have been underthrusted, and additional compaction may have occurred after underthrusting. Sample 316-C0006F-8R-1 is a Pliocene-Pleistocene Upper Shikoku Basin (USB) silty claystone taken from 457 m CSF on the hanging wall of the main frontal thrust (Figure 1e) [Expedition 316 Scientists, 2009b; Screaton et al., 2009b]. The total displacement of the present frontal thrust is estimated to be as much as 6 km [Moore et al., 2009], although this large displacement has likely been distributed among multiple faults of the frontal thrust region, as multiple thrusts are observed at Sites C0006 and at C0007, the latter site located ∼700 m seawards from the former [Screaton et al., 2009a]. At both frontal thrust regions (Sites C0006 and C0007) and the megasplay fault region (Sites C0004 and C0008), significant amount of erosion associated with fault activity is suggested by observation of slump scars and mass transport deposits, and analysis on cores samples [Moore et al., 2009; Screaton et al., 2009a, 2009b; Strasser et al., 2011; Kimura et al., 2011; Conin et al., 2011].
CSF: core depth below seafloor, σv′: in situ effective vertical stress, σv0′: effective vertical preconsolidation pressure, OCR: overconsolidation ratio, (σ′v0/σ′v), p′y: yield effective mean stress, p0′: effective mean preconsolidation pressure, M: slope of critical state line, and C0: unconfined compressive strength. The in situ effective overburden pressure is calculated from the shipboard measurement of bulk density assuming that pore pressure is hydrostatic. The information on mineral compositions is from Expedition 315 Scientists , Expedition 316 Scientists [2009a, 2009b], and Guo and Underwood .
Conducted on PPS.
Uniaxial strain loading, undrained Pc reduction, drained Pc reduction
 The current consolidation state and past loading history of sediments and sedimentary rocks can be predicted from their elasto-plastic deformation behavior. Provided the sediment has been consolidated by axi-symmetric sediment loading where vertical stress is the maximum principal stress, the consolidation state of the sediment is simply described byOCR, a ratio between the preconsolidation stress, σv0′, which is the maximum vertical effective stress at the onset of yield determined in a consolidation experiment, and the present in situ effective vertical stress σv′, i.e., OCR = σv0′/σv′. Sediments are considered to be normally consolidated if OCR = 1 and overconsolidated if OCR > 1. If OCR < 1, sediments are considered underconsolidated [Jones, 1994]. Overconsolidation can be achieved by (1) an increase in σ′v0 due not only to greater overburden in the past but also the chemical effects of cementation and creep [e.g., Jones, 1994; Karig and Hou, 1992; Karig and Ask, 2003; Morgan and Ask, 2004], and (2) a decrease in σ′v due to erosion and/or an increase in pore pressure. Underconsolidation can only be achieved when an excess pore pressure has not been completely dissipated after an additional load has been applied. It should be noted that the sediments become overconsolidated if an excess pore pressure develops after the sediments are normally consolidated. Thus, the development of an excess pore pressure can render the sediments underconsolidated or overconsolidated, and for such states the mechanical response is different, i.e., the former is weak and ductile, while the latter is brittle [e.g., Jones, 1994].
 Although OCR is a useful parameter to describe the state of consolidation, it is theoretically applicable only to the situation in which sediments undergo uniaxial strain, and where the vertical stress is the maximum principal stress. The critical state concept of soil mechanics is very useful in describing the stress states and stress history for the deformation of marine sediments and porous sedimentary rocks. Critical state soil mechanics can describe the deformation of soils using the three parameters of effective mean stress, p′, differential stress, q, and specific volume (or volumetric strain). Herein, we use an axial-symmetric stress and strain model, and definep′ and q by
where σ1 and σ3 are the maximum and minimum principal compressive stresses and Ppis pore pressure, and where compressive stress and shortening strain are taken as positive. Although the three-dimensional space ofp′, q, and volumetric strain is a perfect description of the concept of critical state soil mechanics, the two-dimensional relationships ofq-p′ and volumetric strain-p′ are widely used. Two-dimensionalq-p′ space is often used to describe the stress states in nature and experiments (Figure 2a).
 The critical state is defined as the state where plastic deformation can occur without producing a change in strength and volume [Roscoe et al., 1958]. The critical state is represented as a straight line in q-p′ space and expressed by
where Mis the slope of the critical state line. The critical state line bounds deformation mode; brittle deformation on the left side of the critical state line, ductile deformation on the right side of the critical state line. The modified Cam-clay model developed byRoscoe and Burland  is often used to describe the yield envelope having an elliptic shape as
where p′0 is a reference effective mean pressure.
 In modified Cam-clay model, the yield envelope is the same as the plastic potential, which is orthogonal to the plastic strain vector (Figure 2a); a behavior that is often referred to as following an “associated flow rule” or “normality.” There are some types of soils, rocks, and concretes that do not satisfy normality, and deformation of these materials is described by a “non-associated flow rule” that can better describe dilatancy and hardening. In practice, “normality” should be verified if a Cam-clay model is used to describe the deformation of a material. The plastic strain vector consists of two components, plastic volumetric strain,εpp, and plastic shear strain, εqp (Figure 2a). For axial-symmetry, the volumetric strainεp and shear strain εq are expressed by
where εa and εr are axial strain and radial strain, respectively. From Hooke's law, the elastic volumetric strain εpe and the elastic shear strain εqe are linearly related to the effective mean stress and differential stress,
where B′ and G′ are the bulk modulus and shear modulus in terms of effective stress. It is noteworthy that the effective pressure, and thus these elastic parameters, are valid descriptors when the Biot-Willis coefficient is 1 (i.e., the grains are incompressible and all pores are connected). We did not check that the Biot-Willis coefficient is close to 1 for the samples used in this study, but this was verified for similar sediment core samples taken from the NanTroSEIZE transect [Kitajima and Saffer, 2011].
4. Experimental Methods
 Cylindrical test specimens with a diameter of 19 mm and lengths of 11–32 mm were trimmed using a razor blade from the whole-round core samples (∼75 mm diameter); in all cases the cylinder axis is vertical and parallel to the axis of the whole-round sample (Table 1). Although the sample geometry does not satisfy the ideal ratio of height to diameter for triaxial deformation tests, i.e., 2–2.5 for soil and 1.5–2 for rock, these samples were the best ones that could be prepared from a limited number of cores marked by moderate lithification and fissility. All experiments were conducted using a modified variable strain rate triaxial deformation apparatus (MVSR, Figure 3a) [Heard, 1963; Chester, 1989]. The gear-driven axial shortening was applied at a constant axial displacement rate of 5 × 10−6 mm/s to produce an axial strain rate of ∼10−7 s−1.
 All experiments were conducted at room temperature. A screw-driven, piston cylinder pressure generator and a pressure transducer in the pore pressurization system were used to (1) keep pore pressure constant, (2) measure pore volume change, and (3) conduct pulse-decay permeability measurements. A 1-mm-thick Berea sandstone wafer was placed at the upper end of each sample, at the pore fluid access port, in order to facilitate uniform pore fluid access and prevent the sample from squeezing out to the pore pressure port. The experimental sample and the Berea sandstone wafer were isolated from the silicone fluid confining medium using a polyolefin tube (0.3 mm wall thickness) lined with silver foil (0.05 mm thick); the sample was saturated with distilled water for at least 12 h before pressurization. Distilled water is used as the pore fluid medium because the sample is considered to be in a fresh condition, having been preserved in the moisture-controlled refrigerator right up to the time of the experiments, and because we believe any salts in the original samples remain so the addition of extra salts using salt water as a pore fluid is not necessary.
 Confining pressure and pore pressure were measured by pressure transducers with an accuracy of 0.07 MPa and 0.02 MPa. The axial differential force and axial displacement were measured with a force gauge inside the pressure vessel (accurate to 0.2 MPa) and a displacement transducer (accurate to 8 × 10−4 mm) at the top of the loading system, respectively. The volume of pore fluid displaced from the sample was determined from the displacement of the piston in the pressure generator measured by a displacement transducer (accurate to 1.5 × 10−4cc in terms of volume). Porosity is computed from this volume change of pore fluid assuming incompressible grains. Room temperature was also recorded because the pressure and displacement measurements are temperature-sensitive, and the experiments lasted several weeks. The data were recorded by computer at intervals of 1 to 600 s, depending on the type of experiment being conducted.
 Different stress paths of (1) isotropic loading, (2) uniaxial strain loading, (3) triaxial loading at constant Pc, (4) undrained Pc reduction, (5) drained Pc reduction, and (6) triaxial unloading at constant Pc were achieved in the MVSR apparatus (Figure 2b). It is important to note that we employ these different stress paths not for reproducing the loading path and history in nature, which are unknown, but for understanding the evolution of hydromechanical properties along different stress paths. Each experiment usually included either a series of load paths of (1), (3), (4), (5), and (6) or a series of load paths of (2), (4), (5), and (6) (Table 1). During isotropic loading (σ1 = σ2 = σ3), the confining pressure was incremented stepwise while keeping a constant pore pressure of 10 MPa. When confining pressure is increased, pore volume is decreased and an excess pore pressure is developed within the sample. By draining excess pore pressure, consolidation proceeds. After a few hours to several days when pore pressure approaches equilibrium, permeability and axial shortening were measured, and then confining pressure was increased to achieve another step of consolidation. Axial shortening of the sample was determined during isotropic loading by displacing the upper piston to the hit point, i.e., the point at which differential loading initiates, for each consolidation step. Following the isotropic loading, conventional triaxial compression loading at constant confining pressure (σ1 > σ2 = σ3 = const.) was conducted. Confining pressure and pore pressure were kept constant and the differential axial load was developed by shortening at a constant displacement rate.
 In uniaxial strain consolidation, the axial load was applied at a constant displacement rate. Based on equation (5), a condition of no radial strain (εr = 0) was achieved by manually controlling the confining pressure so that the volumetric strain remained equal to the axial strain (εp = εa). By frequently monitoring and controlling both strains and stresses, the ratio of εp/εa of 0.99–1.01 was achieved at any moment of uniaxial loading. Note that the stress path for uniaxial strain loading is an outcome of the experiment because the strain condition is constrained, while isotropic loading and triaxial loading constrain the stress paths. The stress path is expressed by the slope of Δq/Δp′, e.g., an Δq/Δp′ of 0 represents isotropic loading, and an Δq/Δp′ of 3 represents triaxial loading.
 Undrained and drained Pc reduction was conducted following uniaxial strain loading or triaxial loading. In this load path, the axial loading was kept at a constant displacement rate, and the confining pressure was manually reduced. In undrained Pc reduction tests, the reduction rate of confining pressure was manually controlled so that pore pressure remained constant. An undrained Pc reduction test was introduced as a “modified undrained test” by Tembe et al. , and, in the approximation of incompressible fluid and grains, is equivalent to a conventional undrained shear test, in which confining pressure is kept constant and pore pressure varies with shear. In the undrained Pc reduction test, where pore pressure is maintained constant, the total volume of the pores does not change so a very small amount of plastic strain occurs as compensation for a recovery of elastic strain due to a decrease in the effective mean stress. A yield envelope for a soil is usually constructed based on (1) yield points determined in multiple drained triaxial shear tests at different Pc, or (2) the stress path of an undrained shear test. The former method requires conducting multiple tests, so the latter is advantageous, particularly for a limited number of sediment core samples. The undrained Pc reduction test also facilitates permeability measurement. Pulse-decay permeability measurements can be conducted during undrained Pc reduction in which pore pressure is constant, while permeability cannot be measured in conventional undrained tests where pore pressure is increased. For the reasons above, we chose to conduct undrained Pc reduction as an efficient means to construct yield envelopes and understand permeability evolution for stress paths along the yield envelope. Note that as confining pressure is reduced during Pc reduction, the sample eventually reaches the critical state, after which confining pressure cannot be reduced without allowing either a decrease in pore pressure or sample dilation. After achieving critical state further Pc reduction was conducted under a drained condition, where the pore fluid was allowed to drain into the sample to keep pore pressure constant while confining pressure was slowly decreased.
 To make permeability measurements, the axial shortening rate was set to zero and the sample was allowed to equilibrate until the rate of increase in pore pressure indicated a volume strain rate of less than 10−7 s−1(i.e., slow enough to drain excess pore pressure from the experimental samples so that the transient pulse-decay method for permeability determination would be accurate). The transient pulse decay method involves an abrupt increase in pore pressure at one end of the sample and then monitoring the subsequent evolution in pore pressure at either one end or both ends of the sample during equilibration [e.g.,Brace et al., 1968; Hsieh et al., 1981]. This method is more practical than steady state flow methods especially for low permeability samples such as shale [e.g., Kwon et al., 2004]. Hsieh et al.  and Neuzil et al. present analytical solutions for the transient pulse-decay method, and a graphical method for analyzing experimental data in order to obtain the hydraulic properties of the sample, i.e., hydraulic conductivity and specific storage. The analytical solutions for dimensionless hydraulic head (pore pressure) in the upstream and downstream reservoirs, as a function of time after the step change, are given by
where , , , and ϕm are the roots of .
 The parameters pu and pd are the pore pressures in the upstream and the downstream reservoirs, hu and hd are the hydraulic heads in the upstream and downstream reservoirs, and P and H are the initial differences in pore pressure and hydraulic head at time t = 0. The parameters A, l, K, and Ssare the cross-sectional area, the length, the hydraulic conductivity, and the specific storage of the sample, andSu and Sd are compressive storages of the upstream and downstream reservoirs, respectively, defined as the change in volume of fluid in the reservoir per unit change in hydraulic head in the reservoir. The specific storage of the sample has a unit of m−1, while the compressive storage has a unit of m2.
 The one-end pulse-decay method was used in the MVSR apparatus, in which the pore pressure system was connected only to the upper end of the experimental sample, and the downstream face of the sample was an impermeable boundary (Figure 3a). For this case γ = 0, and the analytical solution for dimensionless hydraulic head (pore pressure) in the upstream reservoirs is given by
 Pore pressure was quickly increased by ∼1 MPa and monitored until reaching equilibrium, since analytical solutions with different hydraulic conductivities and different storage capacities show almost the same behavior as the equilibrium is achieved in the single-end case [Hsieh et al., 1981]. The normalized pore pressure data were matched with the analytical solutions to compute the hydraulic conductivity and specific storage of each sample [Neuzil et al., 1981]. The compressibility of the upstream reservoir, Cu, was determined as a value of 9.11 × 10−9 (m3/MPa). The compressive storage of the upstream reservoir, Su, was computed to be 8.92 × 10−11 (m2) from the relationship, Su = ρwgCu, where ρw is the density of pore fluid and g is gravity.
 We also conducted two-end pulse decay permeability measurements on a sample during isotropic loading up to 50 MPa. For these, we used a different apparatus for measuring porosity and permeability (PPS) in which no differential axial loading was applied, but both ends of the sample were connected to the pore pressure system (Figure 3b). In this apparatus, double-ended pulse-decay is conducted by increasing the pore pressure of the upstream reservoir by ∼1 MPa att = 0 and monitoring the pore pressure of both the upstream and downstream reservoirs. The compressibility of the upstream and downstream reservoirs, Cu and Cd, were determined by dedicated calibration tests to be 7.96 × 10−9 m3/MPa and 8.51 × 10−9 m3/MPa, respectively, and the compressive storages, Su and Sd were determined to be 7.79 × 10−11 m2 and 8.33 × 10−11 m2, respectively.
5.1. Evolution of Strength Along Different Stress Paths
 The results of the deformation experiments are presented for sample 315-C0002B-63R (Figure 4), 316-C0004D-48R-1 (Figure 5) and 316-C0006F-8R-1 (Figure 6). Each figure includes plots of (1) stress-strain behavior, (2) stress evolutions inq-p′ space, (3) permeability vs effective mean stress, and (4) volumetric strain vs log σ1. The different stress paths used in each experiment are differentiated on the diagrams by color.
 For uniaxial strain loading, two or three stages of strength evolution can be distinguished by the changes in the stress strain response (Figures 4a, 5a, and 6a) and the slope of Δq/Δp′ (Figures 4b, 5b, and 6b). Differential stress first increases significantly with axial strain up to ∼2% shortening (Δq/Δp′ = 1.3), and then remains almost constant (Δq/Δp′ = 0). At a later stage, two samples (316-C0004D-48R-1 and 316-C0006F-8R-1-a) show further strengthening with strain (Δq/Δp′ = 0.6). The stages of stress-strain response probably represent an initial elastic response, followed by yielding with cement breakage, and then normal consolidation [e.g.,Karig, 1993; Morgan and Ask, 2004; Ask and Morgan, 2010]. Although cementation is implied by the slope change of Δq/Δp′, there is no clear evidence for cementation in the volumetric strain – log σ1′ relationships (e.g., sharp increase in σ1′ followed by slight decrease in σ1′) (Figures 4d, 5d, and 6d) [e.g., Holtz and Kovacs, 1981; Jones, 1994; Morgan et al., 2007]. Various responses seen within each stage could reflect yielding of sediments that have undergone a complicated stress history. This should be considered in future studies to understand the evolution of yield envelopes and consolidation states during changes in loading condition, e.g., isotropic, uniaxial, triaxial compression and extension [Yasufuku et al., 1991], and the effect of cementation on consolidation state.
 Under triaxial loading, the sample of 316-C0006F-8R-1 continuously strengthened with a slight change in the slope of the stress-strain curve at an axial strain of 6% (Figure 6e). Differential stress increases with a steeper slope in the stress-strain curves during undrained Pc reduction, and decreases during drained Pc reduction (Figures 4a, 5a, 6a, and 6e). This can also be seen in a q-p′ diagram so that q increases during undrained Pc reduction and decreases during drained Pc reduction with decreasing p′ (Figures 4b, 5b, 6b, and 6f). Strength (q) reaches a maximum at the transition from undrained to drained conditions, which could demark the critical state.
 The preconsolidation pressure σ′v0 is determined from the intersection point of the two lines that are tangential to the elastic portion and the normal consolidation portions in a logarithmic plot of volumetric strain versus σ1′ (Figures 4d, 5d, 6d, and 6h) [Holtz and Kovacs, 1981]. It turns out that all samples have a larger preconsolidation pressure than the in situ overburden pressure σ′v, which was calculated from the shipboard measurement of bulk density assuming that pore pressure is hydrostatic [Expedition 315 Scientists, 2009; Expedition 316 Scientists, 2009a, 2009b]. Thus, all samples are overconsolidated and OCR ranges 1.43–2.80 (Table 1).
5.2. Permeability Measurements
 In this section, we first validate the pulse-decay permeability measurements and strain rates used in the tests, and then show the results of permeability measurements conducted along different stress paths.
 For comparison, permeability measurements using one-end and two-end pulse decay methods were made on specimens taken from the same whole-round core sample, 316-C0006F-8R-1, at the same condition ofp′ = 8 MPa during isotropic loading (Figure 7). For one-end pulse decay, the normalized pore pressure data are well matched to an analytical solution whereβ = 0.8, and t = 1900 at αβ2 = 1. From the relationships of α = Kt/l2Ss and β = SsAl/Su, we calculated Ss = 7.97 × 10−6 m−1 and K = 6.70 × 10−12 m/s. The intrinsic permeability k is calculated to be 6.86 × 10−19 m2 from the relationship k = Kρwg/μ, where ρw and μare the density and the dynamic viscosity of pore fluid, respectively. For two-end pulse decay, the experimental data matches an analytical solution ofβ = 0.3 and t = 4400 at αβ2 = 1. The specific storage, hydraulic conductivity, and intrinsic permeability were calculated to be Ss = 7.48 × 10−6 m−1, K = 2.31 × 10−12 m2, and k = 2.36 × 10−19 m2, respectively.
 The calculated value of hydraulic conductivity, or permeability, from the two-end pulse decay measurement is three times lower than that from the one-end pulse decay measurement, whereas the values of specific storage are almost the same. This is seen in measurements at all pressure conditions. It is worth noting that errors in pulse-decay measurements of permeability and hydraulic conductivity, caused by fitting curves, are generally less than 3%. Differences of the three subsamples of 316-C0006F-8R-1 (a, b, and c) trimmed from the same whole-round core sample could lead to the variation in permeability, but a great difference between samples exist only in hydraulic conductivity, or permeability, not in specific storage. This result probably reflects the inaccuracy in determining axial strain (and radial strain), because the relationshipsα = Kt/l2Ss and β = SsAl/Sushow that hydraulic conductivity depends on sample length while the specific storage depends sample volume (the product of length and cross-sectional area). In the triaxial deformation apparatus (MVSR), we can estimate the axial and radial strains from the measured axial displacement and pore volume change. On the other hand, in the other apparatus (PPS), which has no axial loading system, we could not measure axial displacement, and thus the hydraulic properties of sample 316-C0006F-8R-1-c, which was isotropically loaded on PPS, were calculated on the basis of an assumption that the deformation behavior, and thus the ratio ofεr to εain this experiment, are the same as those in the experiment on sample 316-C0006F-8R-1-b, which was isotropically loaded on the MVSR.
 The specific storage of a sample can be written as a function of water compressibility and the coefficient of compressibility of the sample,
where b is water compressibility and a is the coefficient of compressibility. The values for specific storage range from 3 × 10−6 to 3 × 10−5 [m−1]. With n = 0.4, a is calculated to be 1.06 × 10−9 [Pa−1]. To ensure the pore pressure is equilibrated during deformation experiments, Lee  suggested that the strain rate used for the CRS (constant rate of strain) test should satisfy the relationship,
where εa′ is the axial strain rate and Cv is the coefficient of consolidation. From the relationship Cv = k/μa, the maximum strain rate that should be used is εa′ < 0.1 k/l2μa = 4.23 × 10−5. The axial strain rate of 10−7 s−1, used herein, satisfies this condition.
 All experimental samples indicate that permeability decreases with effective mean stress during loading, while it stays almost the same during undrained Pc reduction and slightly recovers during drained Pc reduction (Figure 4c, 5c, 6c, and 6g). Permeability ranges from 10−17 to 10−19 m2 at an effective mean stress of 1–20 MPa and further decreases to ∼10−20 m2with pressurization to 50 MPa (316-C0006F-8R-1-c,Figure 8a). A closer look at the two experiments, 316-C0006F-8R-1-a and 316-C0006F-8R-1-b, reveals that the reduction rate of permeability depends on the stress paths (Figures 6c and 6g). During uniaxial strain loading, permeability continuously decreases with a log linear relationship. During isotropic loading, permeability quickly decreases at effective pressures less than 5 MPa, and stays almost constant thereafter. The fastest reduction in permeability is observed during triaxial loading. Interestingly, however, the two experiments with different loading paths show the same permeability at the final point of loading, i.e., p′ = 17 MPa and q = 6.5 MPa (Figures 6c and 6g).
 We have presented the results of 5 triaxial deformation experiments on three sediment core samples from different parts of the Nankai accretionary prism. Here we summarize the effects of stress states and paths on hydromechanical properties, construct yield envelopes for the prism sediments, and predict their in situ stresses and strengths. All of this can be represented well in q-p′ space using a critical state soil mechanics (modified Cam-clay) model.
6.1. Relationships Between Hydraulic Properties and Stress States
 We focus on the results of the three experiments on samples from the 316-C0006F-8R-1 core to understand the effects of stress states and load paths on hydraulic properties (Figure 8). Although volumetric strain decreases similarly with increasing effective mean stress regardless of load path (Figure 9a), permeability evolves differently along each load path. As already shown in the previous section, permeability decreases with a log linear relationship throughout uniaxial strain loading, and the greatest reduction in permeability is observed during triaxial loading (Figure 8a). It is less obvious, but the effect of stress path on permeability also can be seen as slight differences in slope of porosity-permeability relationships (Figure 8b). As the two experiments with different loading paths (316-C0006F-8R-1-a and 316-C0006F-8R-1-b) show the same permeability at the final point of loading, permeability is dependent on the stress state and best described as a state function inq-p′ space (Figures 8c and 8d). Porosity evolution depends on both the effective mean stress and the differential stress, and contours of porosity in q-p′ space are sub-parallel to the predicted yield envelope (black curve), which is determined separately from the experimental results discussed in the next section (Figure 8c). On the other hand, permeability evolution is more complicated and its dependence on stress state changes at the yield envelope (Figure 8d). Before yield, changes in permeability largely depend on the effective mean stress, whereas after yield, permeability evolution depends on both the differential and effective mean stresses. This transition across the yield envelope is also seen by the two trends observed in porosity-permeability relationships (Figure 8b). First, permeability quickly decreases with small change in porosity and then porosity decreases with slow change in permeability. Different trends across yield point have been observed in a previous study on sandstones [Zhu and Wong, 1997], however, the transition of permeability-porosity relationship on sandstones across the yield point is opposite from our findings, and permeability of sandstones decreases quickly after yield in the ductile deformation regime. The difference is probably due to different rock types and starting porosity. More experimental work is necessary to fully understand the permeability evolution of mudstones over a wide range of stress states and along different stress paths.
6.2. Consolidation State
 All samples are overconsolidated, as indicated by the OCR of 1.43–2.8 (Table 1). It is important to note that the effect of sample disturbance on the estimation of effective vertical preconsolidation stress is probably small, because in the relationship of volumetric strain and vertical stress (Figures 4d, 5d, 6d, and 6h), the slope of elastic loading is almost the same as that of unloading (the data are not available for sample 315-C0002B-63R-1 because of quick unloading). As discussed above, overconsolidation reflects greater preconsolidation stress because the in situ effective vertical stress is computed assuming a hydrostatic pore pressure. Greater preconsolidation stress can be explained by (1) a maximum depth of burial greater than the current depth, (2) creep and cementation of the sediments, or (3) an in situ stress-strain history inconsistent with the uniaxial-strain loading in whichσv′ = σ1′. Further studies are required to evaluate the effects of creep and cementation on consolidation states and preconsolidation stress, and it was not the main scope of the present work to narrow down the cause of overconsolidation. Nevertheless, we can evaluate the amount of overburden at past maximum depths for samples 316-C0004D-48R-1 and 316-C0006F-8R-1 by considering their depositional and erosional history. Sample 315-C0002B-63R-1 is not considered here because it is older prism sediments with an unclear deformation history. At Sites C0004 and C0006 a large amount of material has been removed by submarine landslides and slope failures in association with the activity of the major faults in the megasplay fault and frontal thrust systems [Moore et al., 2009; Strasser et al., 2011; Kimura et al., 2011]. Assuming overconsolidation is entirely due to erosion, we can estimate the maximum total thickness of the removed material from values of the preconsolidation stress obtained in the deformation experiments.
 Sample 316-C0004D-48R-1 is underthrust slope sediment that is overlain by accreted sediments and younger slope sediments above the megasplay fault. There is an approximately 1 m.y. gap (unconformity from 1.5 to 2.5 Ma) between the accreted sediments and the overlying slope sediments [Expedition 316 Scientists, 2009a]. Supposing that the bulk density of removed sediment is the same as the averaged bulk density of slope sediment (∼1.66 g/cm3) and that the pore pressure is hydrostatic, the thickness of the slope sediments removed to produce a σv′ equal to the preconsolidation stress is 580 m. This is much larger than the thickness of eroded sediments estimated from 1) the porosity-effective stress relationship in the slope sediments (∼57 m) [Conin et al., 2011], 2) bathymetric and seismic data (∼90 m) [Strasser et al., 2011], or 3) consolidation experiments on slope sediments (∼75 m) [Lipik et al., 2011].
 Sample 316-C0006F-8R-1 is the accreted Upper Shikoku Basin (USB) sediment in the hanging wall of the frontal thrust, and overlain by accreted trench wedge sediments and slope sediments. The slope sediments and accreted trench wedge sediments are also overconsolidated [Dugan and Daigle, 2011; Guo et al., 2011]. Supposing that overconsolidation of the slope sediments is caused merely by erosion, and that the bulk density of the removed sediments is the same as the averaged bulk density of the slope sediment (∼1.80 g/cm3), then the thickness of the removed slope sediment is ∼100 m. The amount of erosion is not large enough to explain overconsolidation of both the accreted trench wedge and USB sediments. Some sediment may be removed at the lithological boundary between the accreted trench wedge sediments and the USB sediments where there is more than 1 m.y. gap from 1.46 to 2.87 Ma [Expedition 316 Scientists, 2009b; Screaton et al., 2009b]. Supposing that some USB sediments are removed at that boundary and have bulk density of 1.97 g/cm3, the thickness of the USB sediment removed to produce a σ′vequal to the preconsolidation stress for Sample 316-C0006F-8R-1 is ∼720 m. This is much larger than the thickness (∼90 m) of the removed USB sediments for a similar age gap observed in the USB sediments at an input site (Site C0012) that is estimated from the uniaxial consolidation tests (H. Kitajima and D. M. Saffer, Elevated pore pressure and anomalously low stress in regions of low frequency earthquakes along the Nankai Trough subduction megathrust, submitted toGeophysical Research Letters, 2012).
 Although the overconsolidation of the samples from C0004 and C0006 can be explained partly by maximum burial depths greater than the current depth, it is unlikely that this is the complete explanation. Thus, a number of possibilities should be considered to explain the overconsolidation of prism sediments. There have been strenuous efforts made to understand the strain and stress histories of prism sediments, including the use of borehole breakouts analyses, AMS (anisotropy of magnetic susceptibility) measurements, measurements of anelastic strain recovery (ASR), and microstructural observations. Along the NanTroSEIZE sites, borehole breakout analysis and ASR measurements in the shallower portion of accretionary prism give consistent results that indicate (1) the maximum horizontal stress is mostly perpendicular to the trench, except at Site C0002 where the maximum horizontal stress is almost parallel to the trench, and (2) that the maximum principal stress is vertical except at Sites C0001, C0002, and C0009 where the maximum principal stress shifts to a horizontal stress at depths greater than ∼1000 mbsf [Tobin et al., 2009; Saffer et al., 2010; Chang et al., 2010; Lin et al., 2010a, 2010b]. On the other hand, AMS analysis of prism sediments from Sites C0004 and C0006 suggests that deformation of sediments has been strongly affected by a large horizontal stress at our sample locations, which were at the hanging wall of the frontal thrust and the footwall of the megasplay fault [Kitamura et al., 2010; Louis et al., 2012]. The P wave velocity anisotropy also suggests the strong effect of horizontal stress, particularly on the footwall of the megasplay fault at Site C0004 [Louis et al., 2012]. These findings suggest that deformation in an accretionary prism is characterized by large magnitude of horizontal shortening and tectonic horizontal stress, which is not well treated by the OCRanalysis that is most appropriate for flat-lying sediments loaded by an overburden with small lateral strain [e.g.,Terzaghi et al., 1996].
6.3. Yield Envelope Construction
 In view of the horizontal stress, we evaluate the consolidation state of the prism sediments in q-p′ space. As a first step, we construct yield envelopes for the undisturbed sediments in their natural state, i.e., at in situ conditions prior to core recovery and experimental testing. A yield envelope is usually determined by conducting either multiple drained triaxial deformation experiments at different confining pressures or undrained triaxial shear experiments. Instead, we use the stress paths determined during Pc reduction tests and apply the modified Cam-clay model to estimate the yield envelope for the undisturbed samples in situ. We first validate the application of the modified Cam-clay model to experiment results by checking whether yielding of the sediment samples satisfy the associated flow rule, i.e., plastic strain vectors are normal to the yield envelopes. Both plastic volumetric strain and plastic shear strain are calculated by subtracting elastic strain from total strain. As given byequation (7), the bulk modulus B′ is determined from the elastic part of the relationship between effective mean stress and volume strain, and the shear modulus G′ is determined from the elastic part of the relationship between differential stress and shear strain. The bulk modulus, B′, can be determined from the ratio of volumetric strain to the natural logarithm of effective mean stress, κ, by the equation,
 We assume that the deformation at the beginning of uniaxial strain loading, during triaxial unloading, and during isotropic unloading is perfectly elastic (Figures 9a and 9b). For sample 316- C0006F-8R-1, the elastic parameters are nearly the same regardless of the stress path, and they are determined asG′ = 340 MPa and κ= 0.03. Based on these elastic parameters, the plastic vector for each stress state during Pc reduction testing of the sample 316-C0006F-8R-1 is plotted inFigure 9c. The plastic potential is normal to the plastic vector, and the direction of the plastic potential mostly follows the stress paths during both undrained and drained Pc reduction consistent with normality. Taking into account the assumption of the Cam-clay model that the yield envelope is the same as the plastic potential [Wood, 1990], the stress paths during Pc reduction can be considered to be the yield envelope. Application of the modified Cam-clay model to construct the yield envelope is also verified by porosity contours that are parallel to the yield envelope (Figure 8c) because porosity contours may be considered to represent a set of constant porosity slices of a 3-D yield surface, projected onto 2-Dq-p′ space.
 The stress paths during undrained Pc reduction tests, and thus the yield envelopes determined for the three experimental samples, are well described by the modified Cam-clay model (equation (4)) with M = 0.75–1.10 (Figures 4b, 5b, 6b, and 6f and Table 1). However, the yield envelopes determined from the stress paths during Pc reduction are not yield envelopes for undisturbed sediments in situ because the samples have undergone additional consolidation from testing in the lab. Based on the assumption of the Cam-clay model that the yield envelopes expand self-similarly with increasing consolidation (decreasing porosity), a constantM is used with an effective mean preconsolidation stress, p′0(the same as a reference effective mean stress in the Cam-clay model) to define the in situ yield envelopes. As the vertical preconsolidation stress is estimated by the value at the intersection of the two lines that are tangential to the elastic and normal consolidation portions of the logarithmic plot of volumetric strain versusσ1′ (= σv′) (Figures 4d, 5d, 6d, and 6h), the effective mean stress at yield p′y may be determined similarly using the logarithmic plot of volumetric strain versus p′ (Figure 10a) [e.g., Wood, 1990; Atkinson, 2007]. The yield envelope for each sample in situ is constructed by drawing an envelope going through the yield point of p′y in q-p′ space with the value of M determined from Pc reduction, and p0′ is determined as the value of intersection of the in situ yield envelope with the p′ axis (Figures 10b–10d).
 We briefly discuss some limitations of the procedure for yield envelope construction presented above. We assume that the yield envelope is not inclined along the past loading paths in applying the Cam-clay model to our experimental data. That assumption is validated by the fact that the porosity contours, which are equivalent to a set of yield envelopes, are not inclined with thep′ axis, and that the value of p′yof uniaxial strain loading is lower than that of isotropic loading for sample 316-C0006F-8R-1. However,p′0determined from uniaxial loading and isotropic loading is different for sample 316-C0006F-8R-1 (Table 1). This difference probably reflects sample-to-sample variation and test reproducibility; however, another uncertainty exists in the application of the modified Cam-clay model to our experimental results. Although we use the modified Cam-clay model to better fit our Pc reduction stress path of all test samples, the original Cam-clay model (Figure 2a) also can fit the Pc reduction stress path with the exception of sample 316-C0004D-48R-1. No data of undrained Pc reduction is available at higherp′ (close to p0′), where the difference between the original and modified Cam-clay models is obvious, because we started the undrained Pc reduction at a non-isotropic stress condition. The importance of these factors should be tested in future work, but we suggest the basis of our analysis of the yield envelope construction is valid.
 Similar to the case of undrained Pc reduction, the stress path during drained Pc reduction is well matched to the modified Cam-clay yield envelope (Figures 4b, 5b, 6b, and 6f). When samples deform in a brittle fashion during the conventional triaxial drained tests, the differential stress increases up to the peak strength, followed by a stress drop to the residual strength. According to the Cam-clay model, the yield envelope and critical state line represent the peak strength and residual strength, respectively [e.g.,Wood, 1990; Atkinson, 2007]. From the fact that the Pc reduction rate was relatively quick (but slow enough to be perfectly drained within the samples), and that samples were deformed at small amounts of strain before reaching the critical state at any Pc, we interpret that the stress path of the drained Pc reduction test represents peak strength. The peak strength in the brittle deformation regime is presented as a part of the yield envelope bounded by the critical state line and the tensile cut-off line inq-p′ space (Figures 10b–10d). The tensile cut-off line represents the possible stress states for unconfined, uniaxial loading (Pc = 0). In other words, differential stress at the intersection of the yield envelope and the unconfined loading line is the unconfined compressive strength (UCS) (Table 1).
6.4. Estimation of In Situ Stress State and Strength
 As the consolidation state can be presented in q-p′ space (Figures 10b–10d), possible in situ stress conditions can also be understood in q-p′ space. The present in situ stress imposed on a sample should be within or on the yield envelope. The in situ effective vertical stress is estimated from the shipboard measurement of bulk density of the overburden sections assuming a hydrostatic pore pressure, while the horizontal in situ stress magnitude is unknown. We consider the following four representative relationships between the effective vertical stress σ′v, the maximum horizontal stress σH′, and the minimum horizontal stress σh′: (1) σh′ = σH′ < σv′, (2) σh′ < σH′ = σv′, (3) σh′ = σv′ < σH′, and (4) σv′ < σh′ = σH′. From equations (1) and (2) with the effective overburden pressure σ′v, the linear relationships between p′ and q are obtained for each case, and all four lines intersect at p′ = σv′ (Figure 11a). This point represents the isotropic stress condition, σ′h = σ′H = σ′v. More general stress states of (5) σ′h < σ′H < σ′v, (6) σ′h < σ′v < σ′H, (7) σ′v < σ′h < σ′H lie between the lines of (1) and (2), (2) and (3), and (3) and (4), respectively (Figure 11a). The three stress states, between (1) and (2), (2) and (3), and (3) and (4), is associated with conditions for normal faulting, strike-slip faulting, and thrust faulting, respectively [Anderson, 1951]. Given that the pore pressure is hydrostatic, the possible stress conditions of each sample in situ are bounded by the in situ yield envelope or the tensile cut-off line, and the lines (1) and (4) (Figures 11b–11d). If an excess pore pressure exists, the yield envelope is still the same but the region of possible in situ stress in q-p′ space changes. Specifically, the bounding lines (1) and (4) shift to the left by the amount of the excess pore pressure. We treat q as the difference between the maximum and minimum stresses, or the absolute difference between the vertical and horizontal stresses, i.e., q = σ′1 − σ′3 ≥ 0, and we also assume that the yield envelope in the stress condition where σ′v < σ′h is identical to that in the stress condition where σ′h < σ′v. It should be noted that this assumption must be tested by further experiments, such as by using triaxial extension tests to construct the yield envelope for the stress condition where σ′v < σ′h.
 If the in situ stress state lies on the yield envelope for a sample in situ, we can say the consolidation state of the sample is normal consolidation because it is about to yield with any additional load. In other words, the “overconsolidation” indicated by an OCR greater than 1 can be considered as normal consolidation if the in situ stress state lies on the yield envelope because of a large horizontal stress. Thus, for more general stress states, the consolidation state should be understood in terms of the proximity of the in situ stress state to the yield envelope. More importantly, considering the possible in situ stress in q-p′ space relative to the critical state can indicate the likely deformation modes (brittle or ductile). For example, possible in situ stress states for sample 315-C0002B-63R-1 are mostly at mean stress greater than the critical state so yielding would be in the ductile regime (Figure 11b), while those for samples 316-C0004D-48R-1 and 316-C0006F-8R-1 occur in both the brittle faulting and ductile deformation regimes (Figures 11c and 11d). In light of this, OCR can be used as a parameter to indicate whether the sample is more likely in a brittle or ductile deformation regime, i.e., the greater the OCR is, the more brittle will be the deformation mode of the sample.
6.5. Implications for Deformation in Accretionary Prism
 We have presented the results of triaxial deformation experiments that employed different stress paths and used critical soil mechanics concepts (Cam-clay model) to understand the hydromechanical properties and in situ stress state of the accretionary prism sediments. Although the number of samples considered in this study was small, our analysis provided the following important insights into the deformation of accretionary prisms: (1) hydromechanical properties, as well as in situ stress states and deformation styles of the Nankai accretionary prism, can be described using critical soil mechanics concepts (Cam-clay model); (2) the shallower portion of the Nankai accretionary prism is “overconsolidated,” and the estimated in situ stress states, particularly near the major faults of the frontal thrust and megasplay fault, suggest the occurrence of both brittle and ductile (compactive) deformation; and (3) both the in situ sediment strength and the mode of yielding (brittle or ductile) are largely affected by the consolidation state and the in situ stress state.
 As discussed above, sediments can preserve records of stress and deformation history in different ways as a result of their elasto-plastic behavior for consolidation. Borehole breakout and ASR analysis document the current stress or strain, i.e., vertical stress is the maximum principal stress, while AMS data provide an implication for the past strain and thus stress, i.e., horizontal stress is the maximum principal stress. This transition of stress state, which is caused by a change in direction of the maximum principal stress from horizontal to vertical, is preserved in the microstructures of core samples from the region of the frontal thrust where deformation bands and shear fractures are both observed (Sites C0006 and C0007) [Expedition 316 Scientists, 2009b, 2009c]. Specifically, the deformation bands have a slip sense of reverse faulting associated with horizontal layer-parallel contraction, followed by the shear fractures with a slip sense of normal faulting. Interestingly, this is consistent with our prediction of deformation mode using inferred yield envelopes inq-p′ space, so that the in situ stress state falls in the ductile regime for σ′h > σ′v and in the brittle regime with σ′h < σ′v. Moreover, the observation of horizontal contraction (deformation bands) supports our interpretation that the apparent high preconsolidation stress is possibly caused by past loading with a horizontal maximum principal stress.
 The reconsolidation experiments, as presented herein, can provide us information such as about the preconsolidation stress (yield stress) and the yield envelope that can constrain (1) the past stress state when the sediments were subjected to the maximum consolidation, and when porosity was the lowest, and (2) the present stress state, sediment strength, and deformation style. A better reconstruction of the entire history of loading and deformation of the prism sediments can be achieved by combining all the information available, specifically through further study employing experiments and microstructural analysis. Experimental work on other samples, particularly from input sites (Sites C0011 and C0012), as well as samples from much deeper portions of the accretionary prisms and the underthrusting sediments that are to be sampled by drilling in coming years, would help our understanding of the complicated deformation history and seismicity in the entire subduction system. Comparisons of the microstructures in experimentally deformed samples, natural core samples, and ancient prism sediments from on-land outcrops, will also help us to understand the temporal and spatial characteristics of the deformation.
 The use of different stress paths can facilitate our understanding of the mechanical and hydraulic behavior of sediments recovered from the Nankai accretionary prism. The evolution of hydromechanical properties, and predictions of in situ stress state and the compressive strength of the prism sediments, are well described within q-p′ space using the critical soil mechanics concept, or a modified Cam-clay model.
 We consider the stress paths, observed during Pc reduction testing of NanTroSEIZE samples, track yield envelopes that are best described by the modified Cam-clay model. Yield envelopes for the sediments samples in situ, constructed from the experiment results, are used to constrain the in situ stress state, the unconfined compressive strength, and the mode of deformation. All samples tested in this study are “overconsolidated,” and for this reason the estimated in situ stress states indicate both brittle and ductile deformation modes are expected near the major faults of the frontal thrust and the megasplay fault.
 During consolidation, porosity decreases with both effective mean stress and differential stress as the yield envelope expands. Permeability depends solely on the effective mean stress within the yield envelope, but after the samples yield, permeability depends more on the differential stress than the effective mean stress. Differential stress reduces permeability more effectively, implying shear-enhanced mechanisms are involved in the reduction of permeability. The greatest change in permeability with both effective pressure and changing porosity occurs during conventional triaxial loading at constant Pc.
 This research used samples and data provided by the Integrated Ocean Drilling Program (IODP) and Ocean Drilling Program (ODP). We acknowledge the support provided by all crew, technicians, and scientists on board the D/V Chikyu during NanTroSEIZE Stage 1 Expeditions 314, 315, and 316. We thank Pierre Henry (associate editor), Julia Morgan, Maria Ask, an anonymous reviewer, and Thorsten Becker (editor) for comments that greatly improved this manuscript. H.K. was supported by a Schlanger Ocean Drilling Fellowship, which is part of the NSF-sponsored U.S. Science Support Program for IODP (USSSP-IODP) that is administered by the Joint Oceanographic Institutions (now the Consortium for Ocean Leadership). We also acknowledge Clayton Powell for his invaluable assistance in the laboratory.