Relationship between Creep Property and Loading-Rate Dependence of Strength of Artificial Methane-Hydrate-Bearing Toyoura Sand under Triaxial Compression

Abstract

Methane hydrate is anticipated to be a promising energy resource. It is essential to consider the mechanical properties of a methane hydrate reservoir to ensure sustainable production, since its mechanical behavior may affect the integrity of the production well, the occurrence of geohazards, and gas productivity. In particular, the creep property of methane-hydrate-bearing sediment is thought to have great significance in the long-term prediction of the mechanical behaviors of a reservoir. In earlier studies, triaxial compression tests were conducted on artificial methane-hydrate-bearing Toyoura sand under three axial-loading conditions, i.e., constant-strain-rate test, constant-stress-rate test, and creep (constant-stress) test. In this paper, the time-dependent properties of the methane-hydrate-bearing Toyoura sand observed in these tests were quantitatively discussed and found to be almost in agreement. The creep life obtained from the creep tests had a reasonably strong correlation with the loading-rate dependencies of strength, obtained from the constant-strain-rate tests and constant-stress-rate tests based on a simple hypothesis. The findings are expected to be used to develop a constitutive model considering the time-dependent behaviors of hydrate-bearing soil in future studies, and to improve the reliability of long-term prediction of the geomechanical response to gas extraction from a reservoir.

1. Introduction

Methane hydrate consists of cagelike crystal structures made up of hydrogen-bonded water molecules surrounding a guest molecule of methane. Because vast amounts of natural methane hydrate exist in marine sediment worldwide and in permafrost regions, methane hydrate is anticipated to be a promising energy resource [1,2,3,4].

The prediction of the geomechanical response to gas extraction from a reservoir is an important research issue for the sustainable production of methane hydrate since the mechanical behaviors of a methane hydrate reservoir may affect the integrity of the production well, the occurrence of geohazards, and gas productivity [5,6,7,8]. Some simulation studies concerning the mechanical behaviors of a methane hydrate reservoir have been reported. Rutqvist et al. [9] analyzed the geomechanical response during depressurization production from hydrate-bearing permafrost deposits. Kimoto et al. [10] analyzed the seabed ground deformation induced by methane hydrate production. Klar et al. [11] analyzed the mechanical behavior of horizontal wells in hydrate-bearing sediments during methane hydrate extraction. Such simulations require constitutive models for hydrate-bearing sediments.

A constitutive model should be developed on the basis of experimentally obtained mechanical properties. An experimental method for performing triaxial compression tests on artificial methane-hydrate-bearing sediment samples has been developed [12], and the mechanical properties of methane-hydrate-bearing sediments have been partially clarified [13,14,15,16,17,18,19,20,21,22,23,24]. However, the time-dependent behaviors of methane-hydrate-bearing sediments have not been fully clarified, although they are thought to have great significance in predicting the long-term behaviors of sediment over a time scale of decades. Thus, few models consider the time-dependent behaviors of methane-hydrate-bearing sediments appropriately based on experimentally obtained properties [25,26,27], although many constitutive models for methane-hydrate-bearing sediments have been proposed in earlier works [10,11,28,29,30].

One of the methods of investigating the time-dependent behavior of a geomaterial is to measure the loading-rate dependence of its mechanical properties. Miyazaki et al. [18,21,23,24] found that the axial-strain-rate dependence of methane-hydrate-bearing sand is as strong as that of frozen sand, and is stronger than that of water-saturated sand and many other geomaterials. This finding suggests that the time-dependence of methane-hydrate-bearing sediment is significantly strong for a geomaterial. Creep is also a time-dependent behavior and is thought to be closely related to the loading-rate dependence of mechanical properties. However, the creep property of methane-hydrate-bearing sediment has not been clarified sufficiently [21,22,24].

This study aims to provide organized basic data concerning the time-dependent properties of methane-hydrate-bearing Toyoura sand, and to search for quantitative relationships between the loading-rate dependencies and the creep property [18,21,22,23]. In this paper, the methods and results of three types of triaxial compression tests conducted on artificial methane-hydrate-bearing Toyoura sand are first presented: constant-strain-rate test, constant-stress-rate test, and creep (constant-stress) test. The experimental procedure developed by Masui et al. [12] was generally followed in the tests. Based on the review of the test results, the time-dependent behaviors observed in the tests were quantitatively compared and the relationship between them is discussed. Moreover, some constitutive models presented in earlier works are reviewed from that viewpoint.

2. Testing Method

The testing method used in earlier works [12,18,21,22,23] is described in this section.

2.1. Specimen Preparation

The specimens were prepared by freezing cylindrical unsaturated sand specimens consisting of Toyoura sand (average particle size: 0.230 mm, uniformity coefficient: 1.38, fine fraction content: 0%). The water saturation was adjusted to 0.60. The average porosity of the host specimens was 38%. The dry density calculated using the weight of sand used and the size of each host specimen was 1.68 g/cm³ on average, corresponding to a relative density of 96%, indicating that the sand particles in the host specimens were well compacted. Each host specimen was 50 mm in diameter and 100 mm in length.

The testing apparatus used for synthesizing methane hydrate in the host specimens, as well as for axial loading under triaxial compression, is drawn schematically in Figure 1. Refer to Miyazaki et al. [19] for the specifications and the system employed in the apparatus. Methane hydrate was synthesized in the pore space of the specimen by the following procedure. First, a frozen host specimen was set in the triaxial cell. Then, a cell pressure of 1 MPa was applied, and methane supplied from a methane gas cylinder was percolated through the specimen from its lower end, replacing the pore air, at a temperature of 268 K or less. The methane gas pressure was increased to 8 MPa at a rate of approximately 0.7 MPa/min, while the cell pressure was increased to 9 MPa at the same rate to maintain the effective confining pressure at 1 MPa. Then, the temperature inside the triaxial cell was raised to 278 K. The cell pressure, pore gas pressure, and temperature were then kept constant for 24 h in order to form methane hydrate in the pore space of the host specimen. After that, water was injected into the specimen to replace the gaseous methane remaining in its pore space. The cell pressure, pore pressure, and temperature were kept constant during the water substitution process. Over 4 × 10⁻⁴ m³ of water passed through the specimen during the water substitution process. We hereafter refer to a water-saturated specimen of the densely packed sand sediment containing synthesized methane hydrate prepared by the above procedure as a hydrate-sand specimen.

2.2. Axial Loading

Axial loading was conducted on all specimens while maintaining the pore pressure at 8 MPa (drained condition), the confining pressure at 9 MPa, and the temperature at 278 K. Thus, the effective confining pressure was continuously maintained at 1 MPa. Since the conditions of pore pressure and temperature are within the methane hydrate stability zone, the effect on the mechanical properties of the methane hydrate dissociation during axial loading is thought to be negligibly small. Results of three types of axial-loading tests are presented in this paper: constant-strain-rate test, constant-stress-rate test, and creep (constant-stress) test, the conditions of which are shown in

Table 1. Conditions of constant-strain-rate tests.

Axial-Strain Rate Ce	Methane Hydrate Saturation Sh
0.1%/min	39%, 40%, 41%, 41% (15%, 16%, 21%, 31%, 34%, 35%, 48%) *
0.05%/min	37%, 37%, 45%
0.01%/min	43%, 43%
0.005%/min	43%
0.001%/min	42%, 41%

* S_h values in parentheses were used to derive Equation (1).

,

Table 2. Conditions of constant-stress-rate tests.

Differential-Stress Rate Cs	Methane Hydrate Saturation Sh
1 MPa/min	39%, 42%, 42%
0.1 MPa/min	44%, 50%
0.01 MPa/min	44%, 48%, 50%

and

Table 3. Conditions of creep tests.

Creep Stress σcr	Methane Hydrate Saturation Sh
1 MPa	42% *, 42% *
2 MPa	48% *, 48% *
3 MPa	40% *, 45% *, 47% *
4 MPa	39% *, 50% *
4.5 MPa	41%, 42%, 42% *
5 MPa	36%, 41%, 45%, 48%
5.5 MPa	36%, 39%, 48%

* The specimens indicated by asterisks did not exhibit final rupture.

, respectively. The axial strain ε_a was calculated by dividing the axial displacement, measured with two 25 mm linear variable differential transformers (LVDTs), by the initial height of the specimen. In this paper, a positive strain value denotes compression. In the constant-strain-rate tests, the axial strain ε_a was increased at a rate C_e ranging from 0.001 to 0.1%/min. In the constant-stress-rate tests, the differential stress Δσ (= σ_a − σ_r) was increased at a rate C_s ranging from 0.01 to 1 MPa/min, where σ_a and σ_r are the axial and radial stresses, respectively. In the creep tests, the differential stress Δσ was increased to a predetermined creep stress σ_cr. In this paper, constant-strain-rate and constant-stress-rate tests are inclusively referred to as constant-loading-rate tests.

After axial loading, the methane hydrate in the specimen was dissociated by reducing the pore pressure. The initial volume of methane hydrate formed in the specimen, and thus the methane hydrate saturation S_h of the specimen, was calculated from the volume of released methane measured by a gas flow meter. The S_h for each specimen used in the constant-strain-rate tests, constant-stress-rate tests, and creep tests are also shown in Table 1, Table 2 and Table 3, respectively.

3. Review of Test Results

3.1. Constant-Loading-Rate Tests

In the constant-strain-rate test, the differential stress Δσ increases and the slope of the curve decreases until Δσ reaches a peak, then Δσ gradually decreases with the axial strain ε_a as shown in Figure 2. Masui et al. [12] noted that the strength (maximum differential stress) σ_fe increases with the methane hydrate saturation S_h due to the cementation effect of hydrate between sand particles. Miyazaki et al. [27] obtained the following approximate formula by least-squares regression:

σ_fe0.1 = σ_fe0 + 42.2 × S_h^3.24,

(1)

where σ_fe0.1 is a function of S_h expressing the strength at an axial-strain rate C_e of 0.1%/min, and σ_fe0 is 3.75 MPa, which is the average strength of the sand specimens. Note that some values of S_h in Table 1 are in parentheses; Miyazaki et al. [27] used these results to derive Equation (1).

The Δσ-ε_a curve for the hydrate-sand specimens depends on C_e [18,21,23,24]. Figure 3 clearly shows that, as C_e increases, the strength σ_fe increases and the axial strain at the peak strength ε_fe decreases. As noted by Miyazaki et al. [18], the time-dependence of a hydrate-sand specimen is stronger than that of a non-hydrate-sand specimen, because the axial-strain-rate dependence of the mechanical properties of the non-hydrate-sand specimens was hardly observed. Miyazaki et al. [18] also reported that the time-dependence of a hydrate-sand specimen is as strong as that of frozen sand and is stronger than those of most geomaterials such as rocks and soils. Parameswaran [31] presumed that the strain-rate dependence of frozen sand is governed by the liquid phase around the sand grains—namely, a quasi-liquid layer—and that this phase is associated with the melting of ice under pressure at the points where grains are in contact. Miyazaki et al. [18] suggested that the strong time-dependence of hydrate-sand specimens was caused by the local dissociation of hydrate occurring at the points where hydrate grains are in contact, similar to the pressure melting of ice.

In the constant-stress-rate test, the differential stress Δσ increases and the slope of the curve decreases until final rupture of the hydrate-sand specimen occurs as shown in Figure 4 [26]. The Δσ-ε_a curve for the hydrate-sand specimens depends on the differential-stress rate C_s. Figure 5 shows that, as C_s increases, the strength (differential stress at the final rupture) σ_fs increases and the axial strain at the final rupture ε_fs decreases [22].

3.2. Creep Tests

In the creep tests, Δσ was increased to σ_cr. We designate the point when Δσ reaches σ_cr as the starting point of creep. We hereafter refer to an increase in ε_a from the starting point of creep and the temporal derivative of ε_a as the creep strain ε_cr and creep-strain rate (dε_cr/dt), respectively. The relationship between creep strain ε_cr and elapsed time t for the hydrate-sand specimen with S_h = 41% and σ_cr = 4.5 MPa is shown in Figure 6 [22,24]. The creep strain ε_cr monotonically increased with the elapsed time t, while (dε_cr/dt), i.e., the slope of the ε_cr-t curve, changed with t as follows: first, (dε_cr/dt) decreased; second, it remained almost constant; and third, it increased. These three phases of creep are often referred to as primary creep, secondary creep, and tertiary creep, respectively. During secondary creep, (dε_cr/dt) did not remain exactly constant; it reached a minimum at a point during secondary creep, as indicated with a triangle in Figure 6. At the end of tertiary creep, as indicated with a square in Figure 6, the specimen could not withstand the creep stress σ_cr and finally ruptured. Note that not all the hydrate-sand specimens exhibited final rupture before 200,000 s had elapsed, as shown in Table 3.

The normalized creep stress σ_cr*, which is the ratio of creep stress to the strength σ_fe0.1, is often useful in comparing creep properties between geomaterials with different strengths. In this paper, since each specimen has a different value of S_h, we decided to calculate σ_cr* using the following equation:

σ_cr* = σ_cr/σ_fe0.1.

(2)

According to Equation (1), which was derived from the results of constant-strain-rate tests at C_e = 0.1%/min, σ_fe0.1 depends on S_h. For example, as represented in Figure 6, σ_cr of 4.5 MPa for the hydrate-sand specimen with S_h = 41% corresponds to σ_cr* = 75%. Miyazaki et al. [22,24] noted that ε_cr of the hydrate-sand specimen is larger than that of the non-hydrate-sand specimen at nearly equal σ_cr*, suggesting that the time-dependence of a hydrate-sand specimen is stronger than that of a non-hydrate-sand specimen as described above.

Figure 7 shows (dε_cr/dt) plotted against t for the test result shown in Figure 6. The (dε_cr/dt) decreased with t during primary creep, reached a minimum during secondary creep, and then increased with t during tertiary creep. As shown in earlier works [22,24,26,27], the slope of the log(dε_cr/dt)-log(t) relationship in primary creep varied with σ_cr in the range of −1 to −0.4; the slope approached −1 as σ_cr decreased. Hereafter, m is the slope of the log(dε_cr/dt)-log(t) relationship in primary creep.

There have been some experimental studies on the primary creep behavior of frozen sand. Ting and Martin [32] and Ting [33] showed that m ranged from −0.8 to −0.6 for frozen Manchester fine sand under uniaxial compression. Sales [34] reported that m decreased and approached −1 as σ_cr decreased for both frozen Ottawa sand and frozen Manchester fine sand under triaxial compression. In this sense, the primary creep behavior of hydrate-sand specimens closely resembles that of frozen sand. However, Sales & Haines [35] reported that m for Hanover silt and Suffield clay ranged from −1.1 to −0.9 and was nearly independent of σ_cr. It was reported that m is nearly equal to −1 for unfrozen sand [36], in agreement with our result for non-hydrate-sand specimens [22,24]. For reference, it is also reported that m is nearly equal to −1 for many types of rocks [37,38].

Some hydrate-sand specimens exhibited tertiary creep and some exhibited final rupture. The elapsed time until the creep-strain rate reached a minimum is hereafter expressed as t_mcr. The elapsed time until final rupture is hereafter referred to as the creep life t_fcr. Figure 8 shows that the minimum creep-strain rate (dε_cr/dt)_min decreases with increasing t_mcr and t_fcr, with a linear relationship between log((dε_cr/dt)_min) and both log(t_mcr) and log(t_fcr), and a slope of approximately −0.9. The ratio of t_mcr to t_fcr for the specimens that exhibited final rupture was approximately 0.5. The slope of the log((dε_cr/dt)_min)-log(t_mcr) relationship of a hydrate-sand specimen is almost equal to those of frozen Manchester fine sand (−0.8 to −1.2) [33] and Fairbanks silt (−1.1) [39]. As shown in Figure 9, (dε_cr/dt)_min increased with σ_cr*. The slope of the log((dε_cr/dt)_min)-log(σ_cr*) relationship of a hydrate-sand specimen was 9.6, which is nearly equal to that of frozen Manchester fine sand (9.0) [40]. It appears that hydrate sand and frozen sand have many common time-dependent properties.

4. Discussion

As reviewed in the previous section, the time-dependence of a hydrate-sand specimen is as strong as that of frozen sand, and is stronger than those of most geomaterials such as rocks and soils [18]. This is supported by the results of constant-strain-rate tests [18,21,23], constant-stress-rate tests [22], and creep tests [21,22] conducted on the hydrate-sand specimens. To date, the relationship between the results of these three tests has been qualitatively described. In this section, the relationship is quantitatively discussed.

4.1. Differential Stresses Versus Axial Strains in Three Tests

Figure 10 shows some of the relationships between the loading-rate dependence of strength and the creep behavior. In Figure 10, the following four Δσ-ε_a relationships are shown: σ_fe-ε_fe obtained from the constant-strain-rate tests (unfilled triangles), σ_fs-ε_fs obtained from the constant-stress-rate tests (unfilled squares), and σ_cr-ε_mcr (filled triangles) and σ_cr-ε_fcr (filled squares) obtained from the creep tests, where ε_mcr and ε_fcr are the axial strains ε_a corresponding to the minimum creep-strain rate and final rupture, respectively. Although a large variation can be seen in each Δσ-ε_a relationship, Δσ appears to be negatively correlated with ε_a. For some rocks, it has been reported that both ε_fe and σ_fe increase with C_e and that ε_mcr increases with σ_cr [38,41]. Thus, in this sense, the hydrate-sand specimens exhibited the opposite trend to these rocks. It appears that the σ_fe versus ε_fe plots are close to the σ_cr versus ε_mcr plots, and that the σ_fs versus ε_fs plots are an extension of the σ_cr versus ε_fcr plots. These quantitative agreements suggest that the creep property of the hydrate-sand specimens is closely related to the loading-rate dependence of strength, which is a typical time-dependent behavior.

4.2. Loading-Rate Dependence of Strength

The normalized strengths σ_fe* and σ_fs* and the normalized differential-stress rate C_s* are calculated as follows for each hydrate-sand specimen with a different value of S_h:

σ_fe* = σ_fe/σ_fe0.1,

(3)

σ_fs* = σ_fs/σ_fe0.1,

(4)

C_s* = σ_fe*/(σ_fe/C_e), for constant-strain-rate tests,

(5)

or

C_s* = C_s/σ_fe0.1, for constant-stress-rate tests.

(6)

As expressed in Equation (5), C_s* for the constant-strain-rate tests is the normalized strength σ_fe*, given by Equation (3), divided by the time to the peak strength (σ_fe/C_e), which corresponds to the average normalized differential-stress rate (differential-stress rate divided by σ_fe0.1) until the peak strength is reached at the axial-strain rate C_e. Realignment using the normalized differential stresses given by Equations (3)–(6) made it possible to quantitatively compare the loading-rate dependencies obtained in the constant-strain-rate tests and constant-stress-rate tests. As shown in Figure 11, plots of σ_fe* and σ_fs* versus C_s* are close to each other. The approximate curves in Figure 11 were calculated using the following expressions obtained by least-squares regression:

σ_fe* = 1.77 × (C_s*)^0.0732,

(7)

σ_fs* = 1.54 × (C_s*)^0.0562.

(8)

The determination coefficients of Equations (7) and (8) are 0.86 and 0.87, respectively.

4.3. Creep Life

Although a large variation can be seen in the relationship between creep life t_fcr and normalized creep stress σ_cr* in Figure 12 [21,22] as is often the case with a geomaterial, t_fcr tends to decrease with increasing σ_cr*.

Let us assume that the rupture of a hydrate-sand specimen progresses at a rate proportional to the nth power of the normalized differential stress σ*, where σ* is the differential stress divided by σ_fe0.1 and n is a parameter expressing the time-dependence of a hydrate-sand specimen, and that the final rupture of a specimen occurs when a state quantity D reaches a value D_f, where D is the time integral of (σ*)ⁿ given by

$$D={\displaystyle {\int }_t{(\sigma *)}^{n}dt}.$$

(9)

When σ* increases with t at a constant rate C_s*, by substituting

σ* = C_s* × t.

(10)

into Equation (9), we obtain

$$D=\frac{{(C_s*)}^n\cdot t^{1+n}}{1+n}=\frac{1}{(1+n)\cdot (C_s*)}{(\sigma *)}^{1+n}.$$

(11)

Considering the moment when final rupture occurs, we obtain

$$D_f=\frac{1}{(1+n)\cdot (C_s*)}{({\sigma }_f*)}^{1+n},$$

(12)

and thus,

$${\sigma }_f*={\left\{(1+n)\cdot D_f\cdot (C_s*)\right\}}^{\frac{1}{1+n}}.$$

(13)

Considering σ_fe* and σ_fs* expressed by Equations (7) and (8) as σ_f* in Equation (13), we obtain n and D_f. Using Equation (7) derived from the results of the constant-strain-rate tests, we obtain

n = 12.7,

(14)

D_f = 180.

(15)

Using Equation (8) derived from the results of the constant-stress-rate tests, we obtain

n = 16.8,

(16)

D_f = 121.

(17)

Since σ* remains constant at σ_cr* in the creep tests, by substituting

σ* = σ_cr*

(18)

into Equation (9), we obtain

D = (σ_cr*)ⁿ × t.

(19)

Considering the moment when final rupture occurs, we obtain the following relationship between the normalized creep stress σ_cr* and creep life t_fcr:

D_f = (σ_cr*)ⁿ × t_fcr,

(20)

and thus,

t_fcr = D_f × (σ_cr*)⁻ⁿ.

(21)

The broken and solid curves in Figure 12 are calculated by substituting Equations (14) and (15) and Equations (16) and (17) into Equation (21), respectively. Although some experimental data are about two orders of magnitude larger than the predictions, the curves do not greatly differ from the plots of t_fcr-σ_cr* on the whole, suggesting that the results of the constant-strain-rate tests, constant-stress-rate tests, and creep tests are in reasonable agreement with the simple hypothesis described above. A lot of tests will be required to verify the hypothesis exactly.

Although creep life is an important characteristic in developing a time-dependent constitutive model, it requires substantial time and effort to obtain the creep life experimentally. In this section, the creep life was found to be reasonably predicted by the loading-rate dependence of strength, which can be obtained with relatively little time and effort.

4.4. Review of Constitutive Models Proposed for Methane-Hydrate-Bearing Sediments

The time-dependent properties of methane-hydrate-bearing sediments are important in predicting the long-term geomechanical response to gas extraction over a time scale of decades. When a constitutive model that does not take account of the time-dependent properties of methane-hydrate-bearing sediments is used in a numerical simulation, the long-term deformation of the seabed will be underestimated, because the increase in deformation of the seabed sediments due to the passage of time is ignored.

Many constitutive models for methane-hydrate-bearing sediments have been proposed. Hyodo et al. [28] presented an elastoplastic model for hydrate-bearing soil based on a modified Cam-Clay model [42], which considers the dependence of mechanical properties on pressure and temperature. Klar et al. [11] developed an elastic-perfectly plastic model for hydrate-bearing soil using the results of constant-strain-rate tests at C_e = 0.1%/min [12]. Uchida et al. [29] developed a constitutive model based on the concept of critical-state soil mechanics, and showed that predictions by their model fitted well with the stress–strain relationships and volumetric behaviors observed in constant-strain-rate tests at C_e = 0.1%/min for both artificial and natural hydrate-bearing soil [12]. The above-mentioned models are thought to be unable to express the loading-rate dependencies or the creep behaviors without modification, because they do not currently consider the strong time-dependence of hydrate-bearing soil. When these models are improved in the future by incorporating the time-dependent terms (viscous terms) of hydrate-bearing soil into their mathematical equations, the results presented in this and earlier studies [18,21,22,23,24,26,27] are expected to be used.

Few constitutive models take account of the time-dependence of hydrate-bearing soil based on experimentally obtained properties. Yoneda et al. [25] presented a visco-elasto-plastic model based on the modified Cam-Clay model [42] and reported that the strong strain-rate dependence of the mechanical properties of hydrate-bearing soil was well predicted by the model. Kimoto et al. [10] also developed an elasto-viscoplastic model with the material parameters determined using the results of triaxial compression tests on natural hydrate-bearing soil. These models seem to be able to express the loading-rate dependencies of hydrate-bearing soil. However, it is not clear whether these models can accurately predict the creep behavior of hydrate-bearing soil [22,24,26,27] and the relationship between the creep property and loading-rate dependence of strength, as shown in Figure 10, Figure 11 and Figure 12.

Okubo & Fukui [43] presented a constitutive model to express the time-dependent behaviors of some types of rocks. The model can be applied to various loading conditions such as constant stress rate, constant strain rate, constant stress (creep), and constant strain (stress relaxation). It was developed based on the same hypothesis that was assumed in this study. Thus, the model is thought to have the potential to be applicable to the time-dependent behaviors of hydrate-bearing soil. The results presented in this and earlier studies [18,21,22,23,24,26,27] are expected to be used in applying the model to hydrate-bearing soil in the future.

5. Conclusions

The results of three types of triaxial compression tests—constant-strain-rate test, constant-stress-rate test, and creep test—conducted on hydrate-sand specimens suggested that the time-dependence of methane-hydrate-bearing sediment samples is strong for a geomaterial. The time-dependent properties of the hydrate-sand specimens observed in these tests were quantitatively discussed and found to be almost in agreement with each other. The creep life obtained from the creep tests had a reasonably strong correlation with the loading-rate dependencies of strength obtained from the constant-strain-rate tests and constant-stress-rate tests based on a simple hypothesis describing, using the normalized differential stress, when the final rupture of a hydrate-sand specimen occurs. This suggests that the creep life of a hydrate-sand specimen can be estimated from the loading-rate dependence of strength instead of conducting a creep test, which requires substantial time and effort.

The findings in this study are expected to be used to develop or improve a constitutive equation considering the time-dependent behaviors of hydrate-bearing soil in future studies. Using such a constitutive model that considers the time-dependent property of hydrate-bearing soil will improve the reliability of long-term prediction of the geomechanical response to gas extraction from a reservoir.