Yoneda et al.
Progress in Earth and Planetary Science(2024) 11:3
https://doi.org/10.1186/s40645-024-00606-1

Progress in Earth andPlanetary Science

Open Access

RESEARCH ARTICLE

Empirical evaluation of the strengthand deformation characteristics of naturaland synthetic gas hydrate‑bearing sedimentswith different ranges of porosity, hydrate
saturation, effective stress, and strain rate
Jun Yoneda1* , Kiyofumi Suzuki2, Motoi Oshima1, Michihiro Muraoka2 and Yusuke Jin1

Abstract
Evaluating the mechanical properties of gas (primarily methane) hydrate-bearing sediments is essential for commercial production as a next-generation resource and understanding the global carbon cycle. Triaxial and uniaxial
compression tests have been conducted on synthetic gas hydrate and natural core samples recovered from deepsea beds using pressure coring techniques. The results show that four factors are vital in establishing the strengthof hydrate-bearing sediments: hydrate saturation, effective confining stress, porosity, and strain rate. However,no study has evaluated these factors in a unified and quantitative manner, and even if the physical propertiesof the reservoir are known in detail from logging, predicting the strength has been challenging. In this study, pressure cores were drilled and recovered from the Eastern Nankai Trough in April 2018 after Japan’s second offshore
production test, and triaxial or uniaxial compression tests were performed on 12 pressure core samples brought backto the laboratory. The mechanical properties of the hydrate-bearing sediments were classified with previous obtained
results from 53 pressure cores and 223 synthetic cores, and empirical equations for triaxial compressive strengthand deformation modulus were proposed as functions of gas hydrate saturation, effective confining pressure, porosity, and strain rate. The obtained equations were found to correlate well with the experimental data and can predict
the strength and deformation modulus from logging data.
Keywords Methane hydrate, Pressure core, Strength, Stiffness, Young’s modulus, Triaxial test, Uniaxial test

*Correspondence:
Jun Yoneda
jun.yoneda@aist.go.jp
1
National Institute of Advanced Industrial Science and Technology (AIST),
Tsukisamuhigashi 2‑17‑2‑1, Toyohira‑ku, Sapporo, Hokkaido 062‑8517,
Japan
2
National Institute of Advanced Industrial Science and Technology (AIST),
Onogawa 16‑1, Tsukuba, Ibaraki 305‑8569, Japan

1 Introduction
Methane hydrate is an ice-like crystal that contains
methane molecules inside a cage comprising water molecules (Sloan 2003). Owing to its ability to exist stably at low temperatures and high pressures, methane
hydrate has been identified in nature at the bottom ofdeep seas and underground in permafrost regions. Two
major natural gas hydrates morphologies exist, as follows: hydrate‐bearing sediments composed of sand or siltwith hydrate‐filled pores and shallow type gas-hydrate infine-grained muddy sediments appearing as chunks, nodules, veins, lenses, and fracture fillings. Such as hydrates© The Author(s) 2024. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which
permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to theoriginal author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images orother third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line
to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory
regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of thislicence, visit http://creativecommons.org/licenses/by/4.0/.

Yoneda et al. Progress in Earth and Planetary Science(2024) 11:3

have the potential to become unconventional natural gas
resources. Hydrates in sand are expected to be produced
through conventional oil and natural gas drilling techniques, and methods are being developed to exploit thisproduction. National projects for methane hydrate development have been launched in various countries since the2000s, which have included exploration, coring, and field
production tests. Depressurization, currently the mostpromising methane hydrate production method (Kurihara et al. 2008; Nagao 2012; Yamamoto and Nagakubo2021), involves drilling a well in a reservoir where hydrate
exists, using a pump to depressurize the in situ formation pressure (pore pressure) to pressure and temperature conditions outside of hydrate stability, decomposing
the hydrate into methane gas and water, and retrieving
the products from the well. During this process, solid
methane hydrate, which has its own strength (Durham
et al. 2003), is converted into liquid water and gaseous
methane, resulting in reduced strength. Furthermore, inthe example of Nankai Trough, as the depressurization
method reduces the pore water pressure from approximately 13 MPa to the bottom hole pressure of 3 MPa,maximizing gas productivity, there is a concern that theeffective stress born by the soil skeleton will increase,resulting in consolidation. As large frictional forces could
occur between the well and formation, understanding
the mechanical properties of the formation is necessary
to evaluate the integrity and survivability of the resident
production wells (Shin and Santamarina 2016; Yoneda
et al. 2018). When considering the global glacial cycle,
some studies have considered consider methane hydrate
decomposition as a trigger for large-scale submarine
landslides (Paull et al. 2007; Elger et al. 2018). Therefore,
assessing geohazards caused by methane hydrate is critical for geoscience researchers, as methane released into
the atmosphere is a greenhouse gas.
More than 200 triaxial compression tests have been
performed using synthetic gas hydrates (Yun et al.
2007; Miyazaki et al. 2011a, b; Hyodo et al. 2005, 2013a,
b, Masui et al. 2005). Yun et al. (2007) performed triaxial compression tests on artificial samples with tetrahydrofuran (THF) hydrate to show the effects ofhydrate saturation (hydrate occupancy in the porespace) on strength and deformation properties. Masui
et al. (2005), Miyazaki et al. (2011a, b), and Hyodo et al.
(2005, 2013a, b) conducted triaxial compression tests
for synthetic methane hydrate-bearing sediments todetermine the effects of hydrate saturation under various drainage conditions and effective confining pressures. Miyazaki et al. (2010) proposed an empiricalequation to estimate the strength from confining pressure and hydrate saturation. In this scenario, hydrate
was formed from moist sand by injecting high-pressure

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methane gas (excess gas method) and replacing themethane gas with water. Their results showed goodcorrelation with the natural core samples from the
Nankai Trough under hydrate saturations of less than
40% (Masui et al. 2007). In studies of synthetic hydratebearing sand, the increase in strength caused by thepresence of hydrates was assumed to be reflected in theapparent cohesion, and the friction angle was considered to be constant (Waite et al. 2009).
In the past decade, advancements in pressure core technology have enabled the recovery of natural gas hydratebearing sediments for analysis without incurring pressure
loss; furthermore, triaxial compression testing of naturalcores has been realized, leading to a better understanding of hydrate mechanical properties (Priest et al., 2015,
Yoneda et al. 2015a, 2017, 2019a). In addition, cores collected from the Nankai Trough (Yamamoto 2015), Indian
Ocean (Collett et al 2019), and Gulf of Mexico (Flemings et al 2020) have also been tested, and equations havebeen proposed to estimate the strength from the effective
confining pressure and hydrate saturation (Yoneda et al.
2017), as well as examine the dependency of the strength
on the strain rate (Yoneda et al. 2022). Priest and Hayley (2019) compared previous results from synthetic
and natural samples to estimate how the morphology isaffected by differences in hydrate formation processes
and carefully explained the dependence on hydrate saturation, effective confining pressure, and clay content.
Despite this progress in the understanding of mechanicalproperties, the equation used to estimate the strength inprevious studies could not be used directly in the present
numerical simulations (Kimoto et al. 2010; Rutqvist et al.
2009; Klar et al. 2013; Yoneda et al. 2018), as they require
the strength of hydrate-free sediments. Furthermore,parameters for the deformation modulus, primarily usedin simulations of ground deformation associated withhydrate production, are challenging to obtain owing toa lack of proposed datasets. In this study, pressure cores
were recovered in the same area in which the second
offshore production test was conducted in the Nankai
Trough in April 2018 (Yamamoto et al 2019, 2021), andtriaxial or uniaxial compression tests were performed on
12 pressure core samples at the onshore laboratory. Subsequently, the mechanical properties of the hydrate-bearing sediments were investigated from 309 test results,
which include results from previous studies, and strength
predictions were made based on the gas hydrate saturation (Sh), strain rate (­ Rea), porosity (n), and effective confining pressure (σc’), parameters, on which the strength ishighly dependent. In addition, the proposed equation isverified by comparing the predictions of strength (qmax)
and deformation (elasticity) modulus (E50), using logging
data along with laboratory test results.

Yoneda et al. Progress in Earth and Planetary Science(2024) 11:3

2 Materials and methods
Two coring wells (AT1-CW1 and AT1-CW2) were
drilled in March and April 2018 after the completion of
the second offshore production test in the Daini–Atsumi
Knoll of the Nankai Trough in May–June 2017 (Yamamoto et al. 2021). The drilling vessel CHIKYU performed
the coring, using a high-pressure–temperature corer(HPTC) III developed by JOGMEC (Nishioka et al. 2018).
AT1-CW1 was drilled 10 m south of the P2 production
well, and AT1-CW2 was drilled approximately 20 m
west of the P3 production well at a location less affectedby production testing to confirm the impact of production (Fig. 1). During production in the testing of well
P3, which was closely located to CW2, the pressure was
reduced from 12 to 6 MPa (Yamamoto et al. 2021). Two

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weeks later, a depressurization of approximately − 1 MPa
was observed in the hydrate layer of monitoring wellMT3, which is approximately 20 m away (Ouchi et al.
2022). Similarly, CW2 was also approximately the same
distance from MT2, and the impact of the production
was an increase of approximately 1 MPa in effective
stress. Here, the methane hydrate in CW2 had not yet
begun to dissociate. In general, the strength of granularmaterials tends to increase when they undergo compression (increased effective stress) because of an increase inbulk density. For an effective stress increase of 1 MPa, theimpact on the mechanical properties of the hydrate-bearing sandy layer is inferred to be small, as stress conditions
are considered to be within the elastic region, based on
past research (Yoneda et al. 2019b; Fang et al. 2021). This

Fig. 1 Coring wells (CW1 and CW2) map at the AT1 site at the Eastern Nankai Trough [Reprinted from Yamamoto et al. 2019, Fire in the ice(Newsletters of National Energy Technology Laboratory of U.S. Department of Energy.)] The wells, named P, P2, and P3 for the gas production tests
carried out in 2013 and 2017, are located on the Northwest slope of the Daini–Atsumi Knoll. The sand-dominant turbidite sequences contain gas
hydrate, which are described as pore-filling and/or load-bearing type morphology

Yoneda et al. Progress in Earth and Planetary Science(2024) 11:3

study used samples from the AT1-CW2 well, obtainingpressure cores with an average length of cores of 2.5 m.
This coring was performed 25 times (runs). During thecoring, the pressure inside the core was maintained at or
above the borehole pressure in 23 of the runs. The pressure in the remaining two runs were slightly decreased,
but within the hydrate stability boundaries. Thus, approximately 100% of the pressure cores was successfully performed, and 50.35 m of pressure core was recoveredfrom the hydrate-concentrated zone at depths of 1286.5–
1343.7 m and 1356.6–1362.7 m with a high recovery rateof 76%. The measured depth represents the water depth
plus height of the rotary table, which is a reference level:rotary table 28.5 m, seabed 994.5 m. The X-ray images,
P-wave velocities, and gamma-ray bulk densities of therecovered pressure cores were measured using a pressure
core analysis and transfer system (Schultheiss et al. 2006)
onboard the drilling vessel after examining the pressure–temperature history. Furthermore, three types of sorting
were performed with onboard Pressure core Nondestructive Analysis Tools (PNATs) (Yoneda et al. 2015a, b; Jinet al. 2016), namely quantitative degassing, cryo core, andstorage chamber. In this analysis, 14.6 m of high-quality

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cores was stored in a pressure chamber and transported
to the Hokkaido Center of AIST Sapporo. X-ray images,
P-wave velocity measurements, and gamma-ray bulk
density tests using PNATs were performed on the corestransported to the laboratory, confirming that no disturbances or other significant changes occurred owing totransportation.
Figure 2 shows the results of the wireline logging performed after coring and the various physical properties of
the cores analyzed in this study. Table 1 shows the sample list for this study. The core grain size distribution thatwas chosen for the mechanical tests is shown in Fig. 3. A
laser-based grain size analysis [Microtrac MT3300 EX(Nikkiso Co. Ltd.)] was conducted with the same technique used using in Ito et al. (2015), with the results
expressed as volume percentages. The sand and mudalternation of the turbidite layer was 0.5–1 m at 1290–
1320 m, and the sand layer at 1320–1380 m was thicker.
The depositional age in the gas hydrate-reservoir sediments was 0.45–0.85 Ma (Egawa et al. 2015). The P-wave
velocities at 1340–1345 m were greater than 3000 m/s
in both the logs and cores. The maximum methane
hydrate saturation (Sh) was approximately 80% based on

Fig. 2 Results of logging and core analyses. Logging data were acquired by JOGMEC. (Yamamoto et al. 2019, Ouchi et al. 2022). P- and S-wave
velocities, bulk density, porosity, resistivity, and hydrate saturation are shownYoneda et al. Progress in Earth and Planetary Science(2024) 11:3

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Table 1 Core sample list
Sample ID:

Core top (m)measured depth
Seabed: 994.5 m
Rotary table:
28.5 mPorositynHydratesaturation
Sh(%)

Test type

Strain rate: %Rεa

Effective confiningpressure: (MPa)
σc ’

Mean
particle
size: (um)AT1-CW2-4P-2(43.5–52.5)

1295.25

0.432

0.3

Triaxial CU

0.01–0.05

1.6

6

AT1-CW2-6P-2a(5–12)

1300.88

0.454

9.1

Uniaxial

10

9

AT1-CW2-20P-2a(209–218)

1335.56

0.611

21Uniaxial

10

0

92

AT1-CW2-22P-3(31–40.7)

1340.07

0.402

55

Triaxial CD

0.0001–0.001

2.0

88

AT1-CW2-22P-3(40.7–50.2)

1340.16

0.410

55.1

Uniaxial

0.0001–0.001

088

AT1-CW2-22P-3(50–60)

1340.26

0.416

54

Triaxial CD

0.01–0.1

2.0

77

AT1-CW2-22P-3(85–93)

1340.69

0.482

35.9

Uniaxial

0.0001–0.001

039

AT1-CW2-23P-2b(25–33)

1342.69

0.421

54.9

Uniaxial

0.01

0

88

AT1-CW2-23P-2b(33–41)

1342.77

0.458

39.7

Uniaxial

0.25–1

085

AT1-CW2-23P-2b(41–49)

1342.85

0.479

50.3

Uniaxial

0.01–0.1

085

AT1-CW2-23P-3b(56.2–66)

1343.93

0.466

59.1

Uniaxial

10

0

85

AT1-CW2-24P-1(5–13)

1357.74

0.439

36.6

Uniaxial

1

0

53

Sand

Percent finer by weight (%)

100

Silt

Clay
AT1-CW2-4P-2(43.5-52.5)
AT1-CW2-6P-2a(5-12)
AT1-CW2-20P-2a(209-218)
AT1-CW2-22P-3(31-40.7)
AT1-CW2-22P-3(40.7-50.2)
AT1-CW2-22P-3(50-60)
AT1-CW2-22P-3(85-93)
AT1-CW2-23P-2b(25-33)
AT1-CW2-23P-2b(33-41)
AT1-CW2-23P-2b(41-49)
AT1-CW2-23P-3b(56.2-66)
AT1-CW2-24P-1(5-13)

90
80
70
60
50
40
30

(1)

Sample loading

(2)
(3)

20

(7)

(4)

10
0

(6)

1

0.1

0.01

0.001

0.0001

Grain size (mm)Fig. 3 Grain-size distribution curves for the core samples
(5)

(8)
(9)

the logging data. Of the sand layer samples, 10 were ingood shape with high P-wave velocities and no cracking exhibited. Two samples [AT1-CW2-4P-2(43.5–52.5)
and AT1-CW2-6P-2a(5–12)] were used to determine themechanical strength of the muddy portion of the alternating sand and mud layers, with a total of 12 samples
evaluated. An analysis plan was developed based on X-ray
computed tomography (CT) images, P-wave velocity,and gamma-ray density data from pressure cores stored
in 1.2 or 0.35 m pressure chambers and cut to 10 cm inlength for testing. The cut core samples were loaded into
a conveyance chamber and connected to the transparent
acrylic cell triaxial testing (TACTT) system (Yoneda et al.
2013a, 2015a, b). Figure 4 shows the TACTT schematic
diagram. In this system, the core sample is inserted into
the rubber sleeve of the triaxial chamber and is readyfor testing. The temperature and pressure are constantly
monitored, with the methane hydrate maintained within(10) (11)(1) Load cell (2) Core sample (3) Transparent acrylic cell (4) Camera(5) Conveyance chamber (6) Displacement transducer(7) Top cap & pedestal with piezo elements (8) Ball valve(9) Syringe pump for upper bound of sediment(10) Syringe pump for lower bound of sediment(11) Syringe pump for cell pressure

Fig. 4 Diagram of transparent triaxial acrylic cell testing (TACTT)
systemits stability boundaries. A syringe pump is connectedto the top and bottom of the specimen after installation to monitor the pore fluid flowing in and out of theYoneda et al. Progress in Earth and Planetary Science(2024) 11:3

specimen. Cell (confining) and pore pressures are controlled for the triaxial compression tests to apply an effective confining pressure. Outside the acrylic triaxial cell,eight cameras are used to measure the specimen’s initial
volume and volume changes using image processing. The
top cap and pedestal above and below the specimen contain hollow cylindrical-shaped piezo-crystals that allow
the vertical measurement of the P- and S-wave velocitiesof the core sample. When performing uniaxial compression tests, the confining and pore pressure bypasses are
opened, and compression is performed with zero effective confining pressure. In this study, sand layer samples
were subjected to drained conditions, whereas mud layer
samples were subjected to undrained conditions. BothPage 6 of 18

tests were conducted at a temperature of 10 °C and waterpressure of 10 MPa. As methane hydrate-bearing sediments are dependent on the strain rate, here, alternatingstrain rates were used for the axial loading, permitting
the acquisition of the stress–strain curves corresponding
to the strain rate.

3 Results
Figure 5 shows the uniaxial compression results for alternating strain rate compression tests. In this figure, theinterpolated stress–strain relationship for each strain
rate is illustrated as dotted and dashed lines. The strain
rates in Fig. 5A and B correspond to 0.0001%/min and0.001%/min. Deformation occurs over several months

Fig. 5 Alternating strain rate uniaxial compression test results. a Core sample AT1-CW2-22P-3(85–93). Compression strain rate Rεa = 0.001%/min
to 0.0001%/min. b AT1-CW2-22P-3(40.7–50.2). Compression strain rate Rεa = 0.001%/min to 0.0001%/min. c AT1-CW2-23P-2b(41–49). Compression
strain rate Rεa = 0.1%/min to 0.01%/min. d AT1-CW2-23P-2b(33–41). Compression strain rate Rεa = 1%/min to 0.25%/min

Yoneda et al. Progress in Earth and Planetary Science(2024) 11:3

at 0.0001%/min, a prolonged loading rate for laboratory
testing, and this has not been tested in previous studies.
However, such a rate is assumed to be similar to real-field
deformation, in which depressurization is applied to thereservoir over periods of days to months. The compressive strength of 0.0001%/min is approximately half thatof 0.001%/min. The sample in Fig. 5B has a higher peakstrength than in Fig. 5A owing to higher hydrate saturation and lower porosity. Figure 5C shows the compression results for 50.3% hydrate saturation at 0.1%/min and
0.01%/min. Figure 5D shows the compression results for
39.7% hydrate saturation at 1%/min and 0.25%/min. As
the strain rate increases, the strength increases. Sand has
little strain rate dependence compared to hydrate-bearing sediments (Miyazaki et al. 2007). Meanwhile, studies
have reported the strain rate dependence of hydrate sediments on synthetic methane hydrate-bearing sediments(Miyazaki et al. 2007). Hydrates have also been found to
be strain rate dependent (Durham et al. 2003). Strain rate
alternating compression tests have previously been conducted on a few pressure cores collected offshore Indiaand in the Gulf of Mexico, confirming, along with thepresent results, that natural hydrate deposits are strain
rate dependent (Yoneda et al. 2019a, 2022).
Figure 6 shows the results of two triaxial compression
tests conducted at strain rates of 0.1, 0.01, 0.001, and
0.0001%/min. Effective confining pressure was applied
as the stress estimated in situ (σc’ = 2 MPa). Two samples were taken from a single sand layer with near-equal
porosity and hydrate saturation. Strain rate dependence
can be observed under triaxial stress conditions. Volume
change is correlated with the stress–strain relationship,
confirming a shift from compressive to dilative behavior for strain softening in the case of sediments withhigher compression rates [AT1-CW2-22P-3(50–60)].
Sediments with smaller compression rates [AT1-CW222P-3(31–40.7)] exhibited an initial change in volume
followed by constant volume, a result that was correlated with the convergence of deviator stress. Thus, strain
rate dependence and hydrate considerably influence thedeformation of hydrate-bearing sediments.
Because sand does not have cohesion, the unconfined compression test results can be considered a
direct effect of increased strength owing to the presence of hydrate. The fact that the deviator stress is zero
toward the end of the compression test (Fig. 5a and b)
implies that the measurement of a deviator stress inthe early stages of compression is a direct strengthening effect of the presence of hydrates. The triaxial compression test creates a stress–strain relationship underconfined conditions, which confirms the strengtheningof hydrate-bearing sediment with confining pressure.

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Fig. 6 Alternating strain rate triaxial compression test results. Stress–
strain curves for AT1-CW2-22P-3(50–60) and AT1-CW2-22P-3(31–40.7)
and volumetric strain versus axial strain are illustrated

Based on these results, the effect of confining pressure
on the strength and stiffness of hydrate-bearing sediments is discussed in the next section.
Next, we consider the strain-rate dependence. Previous studies have demonstrated that the dependence of sand on time is small (Miyazaki et al. 2007,
Nakashima 2019, Yoneda et al. 2019a). Therefore, thetime-dependence of hydrate-bearing sediments is amanifestation of the nature of the hydrate, which carries the load between soil particles during compaction.
Ice is also a strain rate-dependent material that exhibits viscous behavior, such as creep, which is attributed
to the friction inside the ice. Mechanisms responsible
for that friction include proton rearrangement towing
to water molecule rotation (Kneser et al. 1955), dislocation motion of water molecules (Perez et al., 1976),
ice crystal-grain boundary sliding, and lattice diffusion creep (Poirier 1985). In the case of slow loading,the main cause of friction is a considered to be grainboundary sliding or lattice diffusion creep. Lattice diffusion creep is the deformation caused by the generation and diffusion of micro-voids between crystals at alevel smaller than the grain boundaries. Higher strain
rates can result in greater strength, as the micro-voidis less likely to spread, whereas slower strain rates canresult in lower strength owing to the creep phenomenon. Methane hydrate also demonstrates strain ratedependence because of the effects of grain boundary
sliding and micro-void diffusion.

Yoneda et al. Progress in Earth and Planetary Science(2024) 11:3

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4 Discussion
4.1 Strength

Figure 7A and B displays the relationship between
strength and strain rate as a double-logarithmic graph.
In addition to the compression test results from the six
samples from this study, the results from 5 natural and12 synthetic samples are also shown in the figure. The
hydrate-bearing sediments have a greater line slope inany strain region (Fig. 7A) and hydrate-free sedimentsshows flat slope line (Fig. 7B). In double-logarithmic
graphs, previous studies have reported that strength
increases linearly with a strain rate (Durham et al. 2003;
Miyazaki et al. 2007; Yoneda et al. 2022). Miyazaki et al.
(2007) proposed an equation for the relationship between
hydrate saturation using this slope as the strain ratedependence parameter m. Subsequently, by adding thestrain rate dependence for the case of 100% (massive)
hydrate to the comparison, it was revealed that the strain
rate dependence of the strength of hydrate-bearing soil
involves the hydrate volume fraction and the following
equation is proposed (Fig. 8).

m = 0.52nh ,(1)where m represents the strain rate dependence, and nh is
the hydrate volume content (dimensionless), calculated
as nh = n × Sh . The new formulation parameter m, by
including the test results of this study, was confirmed tobe the same as the previous formula (Yoneda et al. 2022).

Fig. 8 Strain-rate dependency parameter m vs. hydrate volume
fraction

From this, the maximum deviator stress at a given strain
rate Rεa is expressed as:

qmax = qmax1 · Rεma ,(2)where qmax is the maximum deviator stress, qmax1 is the
maximum deviator stress at a strain rate of 1%/min, andRεa is the strain rate in percent per minute. The variable
m is expressed as a function of nh.

Fig. 7 Strength (maximum deviator stress) versus compression strain rate. A Hydrate-bearing sediments. B Hydrate free sediments

Yoneda et al. Progress in Earth and Planetary Science(2024) 11:3

Figure 9 shows the results of drained triaxial compression tests of synthetic and natural gas hydrate sediments
at various previously reported strain rates. They wereconverted to compressive strength qmax1 at a strain rateof 1% using Eq. (2) and plotted relative to hydrate saturation. The results are shown for 309 test results, with 80 of
the results corresponding to the 53 natural core samples
and 229 of the results corresponding to the 223 artificial
core samples (see Additional file 1: Data S1). Two major
factors may account for the differences between artificial and natural hydrate-bearing sediments. One is thehydrate morphology in the pore spaces of sediments. The
other is the physical properties of the host sediments.
Regarding hydrate morphology, typical morphologies
have been established as cementing type (grain contact
and grain coating), pore-filling type, and load-bearing
type (matrix supporting) (Waite et al. 2009). The unsaturated system (excess gas method), where methane gas is
injected at high pressure into moist sand and temperature controlled to hydrate the meniscus, is recognized
for generating cementing-hydrate deposits (Clayton et al.
2005; Priest et al. 2005). Reportedly, when water is passed
through gas-saturated methane hydrate sediments, thehydrate morphology changes from cementing type topore-filling or load-bearing type (Choi et al. 2014). The

Page 9 of 18

triaxial compression strength and deformation modulus
of artificial methane hydrate using the excess gas method
plus water injection exhibit a strong correlation with thepressure core results (Yoneda et al. 2015a, b). To generate the artificial cores, we decided to include only thedrained triaxial compression from the data of the excess
gas method plus water injection, which demonstrated astrong correlation with the results of the natural cores. In
Fig. 9, for each effective confining pressure, a nonlinear
increase in strength occurs with increased hydrate saturation. In previous studies, the mechanical properties ofthe soils were frequently expressed in terms of the Mohr–
Coulomb failure criterion with Terzaghi’s effective stressprinciple (τ = c′ + σ tanφ ′ ), which is utilized in numerical simulations. Here, τ is shear stress, c’ is cohesion, σ’
is normal stress, and φ’ is the friction angle of the effective stress. This model can represent changes in strengthwith increasing effective confining pressure by expressing
strength in terms of the apparent cohesion and friction
angle. Figure 9 shows that hydrate-bearing sedimentswith zero effective confining stress exhibit uniaxial compression strength, indicating cohesion owing to the presence of hydrates. In practice, applying a compression test
to sediment after hydrate dissociation under unconfinedconditions is not possible. The sample could not evenFig. 9 Normalized strength evolution of previous studies with hydrate saturation at strain rate Rεa = 1%/min (Masui et al. 2005, 2007; Miyazaki
et al. 2007, 2011a, b; Yun et al. 2007; Hyodo et al. 2013b, 2017; Yoneda et al. 2015a, b, 2017, 2019a, 2021, 2022; Choi et al. 2018; Nakata et al. 2018;
Nakashima 2019; Priest and Hayley 2019; Xu et al. 2022). Plots are categorized by effective confining stress. The solid lines are predicted values basedon the proposed Eq. (7)Yoneda et al. Progress in Earth and Planetary Science(2024) 11:3

Page 10 of 18

stand on its own because it is an unconsolidated (coarse)
sediment. A uniaxial compressive strength of zero effective confining pressure indicates cohesion owing to theadhesion component at zero normal stress in the Mohr–
Coulomb failure criterion. The increase in strength issmaller for smaller effective confining pressures andlarger for larger effective confining pressure owing to
the increase in the peak friction angle corresponding to
the increase in the bulk solid (soil particles and hydrate
crystals) density caused by the hydrate. Previous studies have also shown that the angle of the failure shear
band increases with hydrate abundance in compression
tests under plane strain and triaxial conditions using athick acrylic observation window and X-ray CT, respectively (Yoneda et al. 2013a, b, 2016; Kajiyama et al. 2017).
Therefore, the presence of hydrate increases not only thecohesion but also the internal peak friction angle. Consequently, the following strength estimation equation
has been proposed (Yoneda et al. 2017) by modifying
the equations of Miyazaki et al. (2007) and Jung and Santamarina (2011), based on the triaxial testing results for acompression strain rate of 0.1%/min, which has been previously proposed based on the Mohr–Coulomb fracture
criterion.

c′ = c′ sand + 1.6σt Sh ,φ ′ = φ ′ sand + αSh β ,(3)where c’ is the apparent cohesion, c’sand is the apparent
cohesion of the sand, σt is the hydrate tensile strength(Jung and Santamarina 2011), φ’ is the peak effective friction angle, φsand is the peak effective friction angle of thehydrate-free sand, and α and β are fitting parameters that
determine the degree of strength increase with increasing
hydrate saturation.
Here, the cohesion and peak friction angles of hydratefree sediments are needed to estimate the strength. However, it is nearly impossible to obtain the cohesion andpeak friction angle of hydrate-free sediments directly inthe actual field before laboratory testing. Therefore, weestimate the parameters by focusing only on hydrate-free
sediments from the experimental results in Fig. 10.
Figure 10 shows the relationship between the strength
representing the peak deviator stress under the drained
condition and the porosity of the hydrate-free sediments.
For comparison under the same effective confining pressure, regression analysis was performed based on the
results for 0.5, 1, and 3 MPa effective confining pressure.
The maximum strength is related to the porosity (voidratio, relative density) (Bolton 1986, Tatsuoka 1986).
These results show that for each effective confining pressure, the porosity decreases and the strength increases.
Meanwhile, in dense sand, there is a considerable degreeof interlocking between particles, and before shear failure can take place, this interlocking must be overcome in

Fig. 10 Maximum deviator stress of hydrate-free sediment vs.
porosity

addition to the frictional resistance at the points of contact (Craig 1997). The results for each effective confining
stress contain variation, which could be attributed to thedifferences in the particle size distribution and particle
shape. However, this effect was not larger than the effectof the porosity (Additional file 2: Fig. S1). Therefore, theincrease in strength (slope of the regression line) at each
effective confining pressure is summarized as a linear
function of the effective confining pressure. Informationon the grain size or shape was not treated as a parameterin the empirical equation, as the equation is currently difficult to determine from the logging and requires coring
and a large amount of grain analysis. Consequently, themaximum strength at Sh = 0 is expressed by the following equation using the porosity and effective confiningpressure,q(S h =0) = −6.8σc′ · n + C,

(4)Here, the proportionality constant C is calculated fromeach test result, such that each plot can be converted to a
specific porosity. Figure 11 shows the test results modified to represent 35%, 40%, and 45% porosity.
The strength increases nonlinearly near an effective
confining pressure of σc’ = 3 MPa. Dense sand has a large
peak friction angle at low-confining pressure, decreasing
as the confining pressure increases (Bolton 1986, Tatsuoka 1986). Furthermore, the peak friction angle of thedense sand decreases at high confining pressures owing
to particle crushing (Bolton 1986, Miura and Yamanouchi, 1977, Vesić and Clough, 1968). Equation (3) presents a linear approximation of this result, showing acomponent of the apparent cohesion csand. However, if
such a nonlinear increase in strength is linearly modeled to obtain c and φ, the low-confining pressure range
will be overestimated and the high-pressure range will be
underestimated, hindering correct evaluation. Therefore,
this study returns to the fact that the cohesive component

Yoneda et al. Progress in Earth and Planetary Science(2024) 11:3

Page 11 of 18

Fig. 11 Strength evolution versus confining stress based on Eq. (4)for different porosities of hydrate-free sedimentsof sand is originally zero, and a new evaluation is performed as the secant friction angle of each peak strength.
The secant friction angle represents the inclination ofa line from the origin to the intersection of a normal
stress at failure under Mohr–Coulomb failure criteria.
Figure 12 shows the difference between general Mohr–
Coulomb failure criteria for dense sand and the secant
friction angle for this study. The general Mohr–Coulomb
model would produce a cohesion component of the sand.
However, with the secant angle, the stress dependency of
the failure envelope can be expressed. Figure 13 summarizes the relationship between the secant angle and effective confining pressure at peak strength.

Fig. 12 Models based on Mohr–Coulomb fracture criterion. A Effective friction angle and cohesion for dense sand. B Secant friction angle

Fig. 13 Secant friction angle of hydrate-free sediments

Yoneda et al. Progress in Earth and Planetary Science(2024) 11:3

Page 12 of 18

Equation (5) is obtained to estimate the strength
increase, allowing the strength of the hydrate-free sediment to be estimated if the porosity and effective confining pressure are known,

φsand = (51 − 20n) + (2.7 − 50n)log10 (1 + σc′ )(5)Then, with csand = 0 from Eq. (3), we propose a newstrength estimation equation for hydrate-bearing
sediment,c = 1.6σt Sh , φ = φsand + αSh β(6)From the relationship between Eq. (6) and the maximum strength (qmax = σ1 − σ3 in the Mohr–Coulomb failure criterion), Eq. (7) can be obtained using Eqs. (1), (2),(5), and (6),qmax =

2(σc′ sinφ + ccosφ) mRεa ,1 − sinφ(7)

where c = 1.6σt Sh , σt = 0.5(MPa), φ = φsand + αSh β ,φsand = (51 − 20n) + (2.7 − 50n)log10 (1 + σc′ ),α = 20, β = 1.5, and m = 0.52nh = 0.52nSh . α, β, and σtwere determined by multiple regression analysis to havethe highest correlation. σt is the tensile strength of methane hydrate. In Jung and Santamarina (2011), the direct
measurement for the maximum strength was approximately 0.2 MPa: meanwhile, a previous study (Yoneda
et al. 2017) also adopted 0.2 MPa. However, Yoneda et al.
2019c and Kida et al. 2021 reported that the strength varies with hydrate crystal grain size. Here we treated σt as afitting parameter. The tensile strength of the hydrate estimated from this regression analysis was 0.5 MPa. Figure 9
overlays the proposed empirical formula. As an example,
the predicted values are shown for a porosity of 38% andeffective confining pressures of 0, 1, 3, 5, and 10 MPa.
Although the experimental values are not directly comparable because of the varying porosity, the increase instrength with increasing hydrate saturation is well represented for each effective confining pressure. Figure 14
shows a cross plot of the predictions calculated using
the porosity, strain rate, effective confining pressure, andhydrate saturation for all tests versus the experimental
data. The coefficient of determination for all results is0.95, permitting the estimation of the maximum strength
using only the parameters available from the logging data(bulk density, porosity, and hydrate saturation).
4.2 Deformation modulus

Figure 15 shows the deformation modulus and strain
rate relationship as previously conducted for strengthin Fig. 7. The deformation (/secant/elastic) modulus E50 is defined as E50 = (qmax/2)/ε50, where, ε50 is theaxial strain at half the maximum deviator stress. E50 isFig. 14 Predicted and measured maximum deviator stressfor synthetic and natural core samples

Fig. 15 Strain-rate dependency on the deformation modulus

defined in the standard (JIS A 1216 Method for unconfined compression test of soils, Eurocode 7, 5.9.3 Triaxial deformability testing) and is routinely used forelastic model analysis. The figure shows the results fordifferent hydrate saturations and effective confiningpressures. As the strain rate increases, the deformation
modulus also increases. Figure 16 shows the parameterm′, demonstrating the slope of the deformation modulus in the double-logarithmic graph of Fig. 15. Here, theresult for the hydrate free sediment is assumed to haveno strain rate dependence, and when approximated bya line passing through the origin, the deformation modulus is shown to be proportional to the hydrate volume
fraction, as expressed by m’ = 0.53nh.

Yoneda et al. Progress in Earth and Planetary Science(2024) 11:3

Page 13 of 18

The rate of increase is constant even when the effective confining pressure is changed. Therefore, thedeformation coefficient is expressed as the product of afunction of the effective confining pressure and porosity, the exponential function of the hydrate saturation
rate, and the strain rate,′

E50 = f (σc′ , n) · exp(aSh )Rεma ,(9)Then, the deformation modulus for hydrate-free sediment is expressed as:

E50 = f (σc′ , n) · Rεma .
Fig. 16 Strain-rate dependency parameter m vs. hydrate volume
fraction for the deformation modulus

Similar to Eq. (2) proposed for strength, the deformation modulus for any given strain rate, based on the
deformation modulus at 1% strain rate, is expressed by
Eq. (8),′E50 = E501 Rεma .

(8)Using Eq. (8), all results are converted to the Rεa = 1%
strain rate case (Fig. 17). Although the data varied widely,
the deformation modulus shows a log-linear relationshipwith the hydrate saturation.

(10)

Figure 18 shows the relationship between the deformation modulus and effective confining pressure of thesediment without hydrate. The figure plots are coloreddifferently for each porosity. Although there is somevariation owing to the different porosity and difference
grain size, the deformation modulus increases nearlinearly with increasing effective confining pressure.
The effect of the grain size is shown in Additional file 2:
Fig. S2. A large difference is seen in the results for theeffective confining pressure of 12 MPa; here, the higher
confining pressure results in a strain-hardening typestress–strain relationship, producing in a smaller deformation modulus. In addition, particle crushing might
be another factor.

Fig. 17 Deformation modulus vs. hydrate saturation under various effective confining stresses (Yun et al. 2007, Miyazaki et al. 2011a, b; Hyodo et al.
2013b; Yoneda et al. 2015a, 2015b, 2019a, b, c, 2021; Choi et al. 2018; Nakashima 2019)

Yoneda et al. Progress in Earth and Planetary Science(2024) 11:3

Page 14 of 18h.
E50 = (σc′ + 0.9)n−4.8 exp(1.7Sh )Rε0.53nS
aFig. 18 Deformation modulus versus effective confining stressfor hydrate-free sediments

Figure 19 shows the relationship between the deformation modulus and porosity. Larger porosity correspondswith lower strength, while smaller porosity correspondswith higher strength. An approximation of the magnitudeof the power is used to estimate the deformation coefficient of the porosity.
Therefore, the parameters with the highest coefficientsof determination were obtained by multiple regression
analysis, under the assumption that the coefficient of
deformation for hydrate-free sediments can be derived
from the following relationship,

E50_sand = (aσ c′ + b)·nc .

(11)

The results show that a = 1, b = 0.9, and c =  − 4.8, withthe coefficient of determination = 0.65.
Empirical Eq. (11) is substituted into Eq. (9) to obtain
the parameter α that is most correlated to the hydrate
saturation. The result was α = 1.7, and the estimatedequation for the deformation modulus is obtained as

Fig. 19 Deformation modulus versus porosity for hydrate-free
sediments(12)

Figure 17 shows the results predicted by Eq. (12) as
solid lines. Figure 20 shows a cross plot of the predicted
and measured values for all the test results. Although
the correlation coefficient is 0.24 and some variation isobserved, the deformation modulus could be estimatedfor hydrate-bearing sediments. The results for the synthetic samples correlate well, but the natural core samples are scattered. Studies have been reported on the
differences in the physical properties of host sediments,
with an emphasis on grain size distribution and clay content (Hyodo et al. 2017; Priest and Hayley 2019). These
differences, this may be due to the fact that it is very difficult to form the end faces with pressure core technology,
and it is extremely difficult to make the top and bottom
faces of the specimen parallel. Furthermore, natural corescan be heterogeneous, and it is presumed that the stiffness, which is more sensitive than the strength, has varied (Additional file 3).
More than a dozen simulators have been proposed to
predict seabed ground deformation during methane
hydrate production, and advanced numerical simulations
such as elasto-plastic and elasto-visco-plastic analyses
are available based on elastic analysis (White et al. 2020).
Most simulators use multiple time steps separated by ashort period to solve for kinetic hydrate dissociation.
In using the above equations, the strain rate of a previous time step can be applied. In this case, the deformation is overestimated in the increased strain rate step andunderestimated in the decreased strain rate step. Therefore, the analysis step should be as small as possible. We

Fig. 20 Predicted and measured deformation modulus
for hydrate-bearing and hydrate-free sediments

Yoneda et al. Progress in Earth and Planetary Science(2024) 11:3

believe that the ultimate results will have much less error
than an analysis that does not consider the strain rate.
The equations proposed in this study empirically predict the deformation modulus E50 and the peak strength.
Therefore, residual strength and dilatancy properties
after failure are not considered. In cases in which the formation is subjected to large deformation, stress–strain
relationships and dilatancy properties must be evaluatedusing a constitutive model based on the critical state soil
mechanics, such as the constitutive model for hydratebearing sediments, which is based on the Cam–Claymodel (Uchida et al. 2012).
Finally, Fig. 21 shows the depth profiles of the strengthand deformation modulus calculated using Eqs. (7) and(12) from the AT1-CW2 porosity, bulk density, P- andS-wave velocities, and hydrate saturation obtained from
logging. The vertical effective stress σv’ is the sum of
the bulk density from the seafloor. The confining pressure was assumed to be the mean effective stress. Here,σc’ = σv’ + 2K0σv’. The coefficient of earth pressure atrest (K0) was calculated using Poisson’s ratio (ν = (1/2
(Vp/Vs)2 − 1)/((Vp/Vs)2 − 1)) calculated from the P- andS-wave velocities; in elastic ratio, Poisson’s ratio andK0 = ν/(1 − ν) are related. If the P- and S-wave velocities are not measured in the reservoir, the equation
K0 = 1 − sinφ’ can be used (Jaky 1944, 1948). Furthermore,

Page 15 of 18

the dynamic elastic modulus calculated from Vp using therelation E = ρVp2 (1 + ν)(1 − 2ν)/(1 − ν) is also shown in the
figure for reference. The deformation (elastic) modulus of
the core sample was approximately 1/10 of the dynamic
elastic modulus from the previous study (Yoneda et al.
2021). The deformation modulus becomes smaller thanthe dynamic modulus, as it is the secant modulus for the
average stiffness before the peak strength. In addition, thedynamic modulus is measured by sonic waves that passthrough the fastest zone, indicating waves through thestiffest zone. Meanwhile, the specimen starts to deformfrom the weakest zone. The figure shows the core test
results obtained in this study, modified as strength at astrain rate of 1%. It is confirmed that the proposed equation provides good prediction results for the deformation
modulus and strength.

5 Conclusions
Samples were recovered by pressure coring to clarify
the strength and deformation characteristics of methane hydrate-bearing sediments from the same site in
the Nankai Trough, where the second offshore gas production test was performed, and triaxial and uniaxial
compression tests under different strain rates wereconducted. The compression test results at an unprecedentedly slow strain rate of 0.0001%/min revealed

Fig. 21 Strength and deformation modulus prediction based on the proposed empirical equation and logging data. Hydrate saturation in Eqs. (7)and (12) were based on the prediction by Archie’s equation

Yoneda et al. Progress in Earth and Planetary Science(2024) 11:3

that the increase in strength owing to the presence of
hydrate was slight. However, the compressive strength
at a strain rate of 1%/min was approximately ten times
greater than the result for 0.0001%/min. In this case,the strain rate dependence is expressed in a log-linear
fashion, as in previous studies. Based on an evaluationof the strength and deformation parameters obtained
and the results of previous core tests, the empirical Eqs. (7) for strength and (12) for the deformation
modulus were proposed, allowing the prediction of thein situ compressive strength and deformation modulus
by setting the parameters obtained from the log: porosity, bulk density for calculating the effective stress,
hydrate saturation, and strain rate corresponding to anassumed strain rate. These predictions do not include
the effect of particle size and shape and may containerrors of ± 40%. Note that caution should be exercisedin practical use. This study allows predictions of thestrength and stiffness based on the parameters obtained
from the well-log. However, reference measurementsfrom coring and laboratory tests are required to yield
more accurate reservoir parameters. Finally, Eqs. (7)and (12) are reiterated and described.
Empirical Eq. (7) for the strength (maximum deviator
stress) of hydrate-bearing sediment.

qmax =

2(σc′ sinφ + ccosφ) mRεa ,1 − sinφPage 16 of 18

Additional file 2. Effect of grain size (Median) on the maximum deviator stress and deformation modulus under triaxial compression of gas
hydrate-bearing sediments.
Additional file 3. Borehole physical property data sheet for AT1-CW2.
Acknowledgements
We would like to express our sincere thanks to Japan Oil, Gas and Metals
National Corporation (JOGMEC), the operations team of JMH, and Geotek fortheir technical support and fruitful discussions during the pressure coring. We
extend special thanks to K. Yamamoto, and Y. Nakatsuka of JOGMEC for theirleadership contribution to the drilling program and to N. Tenma, J. Nagao, H.
Minagawa, S. Nagase, K. Yamada, K. Shinjo, and J. Watanabe of AIST for theirsupport during the onshore core analysis.
Author contributions
JY designed the experiments, analyzed the data and wrote the paper. KS
designed the coring process and analyzed the LWD data. MO and MM performed pressure core recovery and contributed to the writing of the paper. YJ
designed the core processing procedure and contributed to the developmentof a permeability testing apparatus and writing the paper.
Funding
This study was conducted as part of the activity of MH21-S R&D consortium asplanned by the Ministry of Economy, Trade and Industry (METI).
Availability of data and materials
The data set supporting the conclusions of this article is included within thearticle (and its additional file) as Additional file 1: Data set S1. The dataset supporting the conclusions of this article is also available in the repository site ofOpen Science Framework (OSF), [https://​osf.​io/​g6yv4/].

Declarations
Competing interests
The authors declare that they have no competing interests.

where σc′ = effective confining stress (MPa),φ = φsand + αSh β ,c = 1.6σt Sh ,σt = 0.5(MPa),φsand = (51 − 20n) + (2.7 − 50n)log10 (1 + σc′ ),α = 20, β = 1.5, and m = 0.52nSh , Rεa = strain rate (%/min), n = porosity, and Sh = hydrate saturation.
Empirical Eq. (12) for the stiffness (deformation modulus) of hydrate-bearing sediment.
′

E50 = (σc′ + 0.9)n−4.8 exp(1.7Sh )Rεma
where m′ = 0.53nSh .

Abbreviations
AIST	Advanced Industrial Science and Technology
CT	Computed tomography
JOGMEC	Japan Oil, Gas and Metals National Corporation
PNAT	Pressure core Nondestructive Analysis Tools
TACTT​	Transparent acrylic cell triaxial testing
THF	Tetrahydrofuran

Supplementary Information
The online version contains supplementary material available at https://​doi.​
org/​10.​1186/​s40645-​024-​00606-1.
Additional file 1. Data summary table of triaxial test results for gas
hydrate-bearing sediments.

Received: 27 March 2023 Accepted: 4 January 2024

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