1 Introduction

Natural gas hydrates (NGHs) have been considered as a promising and new strategic energy resource due to the wide distribution and vast reserves in nature (Sloan, 2003). The safe extraction of natural gas from hydrate reservoirs inherently involves coupled multiple physics (Wan et al., 2023) and basically requires a thorough understanding of mechanical properties of hydrate-bearing sediments (Wan et al., 2022). To deepen this understanding, natural cores of hydrate-bearing sediments have been collected from different regions along the continental margin. Examples include the Blake Ridge and the Gulf of Mexico (Winters, 2000; Yun et al., 2006), the Nankai Trough (Priest et al., 2015; Yamamoto, 2015), the Krishna-Godavari Basin (Yun et al., 2010; Yoneda et al., 2019a), the Ulleung Basin (Kwon et al., 2011; Lee et al., 2013), and the northern South China Sea (SCS) (Kuang et al., 2019; Wei et al., 2021). These natural cores have been well tested, but all the cores are of high costs. Joint measurements on a single core are preferred to acquire various geotechnical properties such as hydraulic permeability (Jang et al., 2019), compressibility (Priest et al., 2019; Yoneda et al., 2019b), and shear strength (Yoneda et al., 2015). Alternatively, remodeled samples are widely adopted in the laboratory by using natural sediments as the host for artificial NGHs, exploring mechanical properties of hydrate-bearing sediments.

Mechanical properties of marine sediments depend on the consolidation history (e.g., under consolidated, normally consolidated, and over consolidated). Over consolidated sediments (i.e., the effective overburden stress currently experiencing is lower than the maximum effective over-burden stress ever experienced in the history) are normally encountered in the shallow depth below the seabed, while hydrate-bearing sediments at deeper depths below the seabed are generally under consolidated. For example, Winters (2000) found that shallow sediments in the Black Ridge exhibit over consolidated behaviors, but the sediments at depth are obviously under consolidated. The low degree of consolidation at greater depths may be a result of high sedimentation rates and/or the presence of free gas and NGHs. Lee et al. (2013) reported that the average porosity of natural cores acquired from the Ulleung Basin ranges from 0.65 to 0.71, and these high porosities are mainly due to the extensive presence of diatom remains. Priest et al. (2014) claimed that the under consolidated state of marine sediments in the Krishna-Godavari Basin may be caused by varieties of factors such as the increasing water content due to hydrate dissociation, the overpressure due to low hydraulic permeability of the sediments, salinity of pore water, and hydrate veins. In these factors, the presence of NGHs is considered to be the most important one. Yoneda et al. (2019b) reported that the consolidation curve of natural hydrate-bearing sediments recovered from the Krishna-Godavari Basin is higher than that of natural hydrate-free sediments, demonstrating that the presence of NGHs can hinder the consolidation process and reduce the deformation of hydrate-bearing sediments. Besides the presence of NGHs, the overpressure due to the low hydraulic permeability of marine sediments in the Krishna-Godavari Basin is another important factor leading to under consolidation (Tanikawa et al., 2019). Under consolidated marine sediments with high porosities have significant impacts on the submarine slope stability during hydrate dissociation induced by natural factors and human activities. Priest et al. (2014) found that hydrate dissociation during the production of NGHs has a great potential to trigger seafloor instability in the under consolidated sediments.

Hydrate reservoirs in the northern SCS are mainly composed of fine-grained sediments, and high porosities have been observed (Liu et al., 2015; Li et al., 2019). The hydraulic permeability of these fine-grained sediments is normally low, leading to a prolonged consolidation process since the excess pore pressure is difficult to dissipate. Yoneda et al. (2019b) found that the complete consolidation time of fine-grained sediments is much longer than that of coarse-grained sediments when subjected to the same excess pore pressure. Wei et al. (2021) reported a similar result that the complete consolidation time of fine-grained sediments is the longest among the test sediments when the excess pore pressure is the same. Santamarina et al. (2015) reported that the consolidation coefficient of natural hydrate-bearing sediments is a hundred of times larger than that of hydrate-free sediments. Lei et al. (2020) found that the complete consolidation time of hydrate-bearing coarsegrained sediments becomes longer when the hydrate saturation is larger. To summarize, the presence of NGHs in pores stiffens hydrate-bearing sediments and reduces the excess pore pressure generated when subjected to an external loading. The reduced excess pore pressure will shorten the complete consolidation time according to the consolidation theory (Gibson et al., 1967). On the contrary, the presence of NGHs in pores lowers the hydraulic permeability of hydrate-bearing sediments (Liu et al., 2020; Zhang et al., 2020) and reduces the dissipation rate of excess pore pressure. The reduced dissipation rate lengthens the complete consolidation time. However, the double-edged sword effect of NGHs on consolidation properties of hydrate-bearing sediments has not been fully understood.

In this study, an oedometer test system is developed to conduct laterally confined consolidation tests on remolded hydrate-bearing sediments collected from the Shenhu area of the northern SCS, and effects of hydrate saturation on the consolidation properties of hydrate-bearing fine-grained sediments are explored in detail. How the average consolidation degree evolves with elapsed time is clarified, allowing the development of an empirical model to calculate the average consolidation degree of hydrate-bearing sediments.

2 Experimental Setup, Materials, and Procedures 2.1 Experimental Setup

A schematic diagram of the oedometer test system applied in this study is shown in Fig. 1. The test system consists of an oedometer cell, a pore pressure control system, an incubator, an axial loading system, and a data acquisition module. The pore pressure control system is used to inject pore fluid for hydrate formation. Low temperatures for hydrate formation are maintained by using the incubator, and the temperature can be well controlled within a range from −20℃ to 50℃ with an accuracy of ±0.1℃. The axial loading system, composed of a hydraulic jack, a reaction frame, and a force sensor, can provide a maximum loading of 30 kN. The oedometer cell is placed on the hydraulic jack but in the reaction frame. During the consolidation, settlement of the sample is measured by using a LVDT (Linear Variable Differential Transformer), and the accuracy is 0.001 mm. These experimental data are consistently monitored and automatically recorded by using the data acquisition module, and the minimum recording interval is one second.

The oedometer cell (Fig. 2) is made of stainless steel with an inner diameter of 61.8 mm and a maximum height of 50 mm after the piston installation. Upper and lower porous metal disks prevent fine particle migration from the sample into drainage lines and allow pore water drainage to be uniformly distributed in the cross section. A temperature sensor with a diameter of 1.5 mm is penetrated through the bottom pedestal into the sample at a depth of 1.5 cm, and temperature of the sample is measured with an accuracy of ± 0.1℃. A pair of bender elements with the same diameter of 2.0 cm are installed in the middle of the top and bottom pedestals to measure the velocity of compression wave (i.e., P-wave). The penetration depth of the bender elements into the sample is 2 mm.

2.2 Experimental Materials

Natural fine-grained sediments collected from the Shenhu area in the northern SCS are used to remodel specimens hosting NGHs in this study. The physical properties of these natural sediments are summarized in Table 1, and the natural sediments have been used to explore the undrained triaxial shear properties (Wei et al., 2023a, 2023b).

As synthesizing methane hydrate within fine-grained sediments in the laboratory is still a challenge, tetrahydrofuran (THF) is widely applied as an analogue of methane to study mechanical properties of hydrate-bearing finegrained sediments in the gas hydrate community (Yun et al., 2007; Liu et al., 2018; Kim et al., 2021). X-ray computed tomography images have shown that the morphology of THF hydrate within remodeled fine-grained sediments is similar to that of methane hydrate within natural fine-grained sediments (Liu et al., 2019), which allows for the acceptable differences in mechanical properties caused by the analogue (Lee et al., 2007; Hyodo et al., 2013). In this study, THF and self-made deionized water are used to prepare THF solutions with different concentrations (i.e., the ratio of THF over water weight), which inherently control the hydrate saturation.

2.3 Experimental Sample Preparation

Firstly, air-dried natural sediments are mixed with a certain weight of THF solution to acquire an initial sample with the solution content of 15% by weight. The concentrations of the THF solutions are set as 0 (i.e., deionized water), 0.060, and 0.104, which correspond to targeted hydrate saturations of 0 (i.e., hydrate-free), 30%, and 50%, respectively (Zhang et al., 2022). Then, the moist sediments are sealed in a Ziplock bag for at least 16 h. After the moisture curing process, the moist sediments are carefully scooped into a mold and compacted separately (4 layers in total, and scarification on the top is conducted after the first three compactions), remodeling a host sample with a diameter of 61.8 mm and a height of 40 mm. Porosity of the remolded host sample is controlled at about 0.60 (i.e., a void ratio of 1.5), modelling the high porosities found in the shallow natural sediments. Then, the host sample is saturated with THF solution for at least one day by using the vacuum method in the oedometer cell, followed by freezing down to 0℃ and maintaining for at least 24 h to promote THF hydrate formation. Finally, the sample temperature is adjusted to 4℃ and maintained for at least 24 h to eliminate any potential ice in pores prior to oedometer test. Note that the hydrate-free samples also experience the temperature adjustments in order to control variables.

2.4 Oedometer Test

The vertical stress applied on the sample ranges from 50 kPa to 10000 kPa over seven loading steps (i.e., 50, 100, 200, 400, 800, 1600, 3200, 6400, and 10000 kPa). The sample is allowed to consolidate at each vertical stress level, and consolidation is considered complete when the sample height stabilizes (e.g., the decrement per hour is smaller than 0.01 mm) after each vertical stress change. Settlement of the sample and weight of the drainage water are continuously measured throughout the test, and these measured values are combined to calculate the void ratio change.

3 Results 3.1 Laterally Confined Compression Characteristics

Laterally confined compression curves of the hydrate-free and hydrate-bearing samples are shown in Fig. 3. It is obvious that the void ratio e decreases with increasing vertical stress P, and the e-P curve gradually approaches an oblique line in semilogarithmic coordinates after a yield point. The vertical stress at the yield point is named as the yield stress P_y. In addition, the void ratio e increases with increasing hydrate saturation S_h when subjected to the same vertical stress P, and the slopes of all the oblique lines are barely dependent on the hydrate saturation S_h.

The effect of hydrate on the confined compression properties has been further confirmed by the compression index C_c$ {\mathrm{C}}_{\mathrm{c}} $, and the yield stress P_y, which are shown in Fig. 4. The compression index slightly increases with increasing hydrate saturation S_h, with values of 0.510, 0.526, and 0.552 for S_h = 0, 30%, and 50%, respectively. These values are well within the range from C_c = 0.45 to C_c = 1.371 for natural samples collected from the same area in the northern SCS (Jiang et al., 2023). This slightly change pattern is consistent with the results of tests on natural finegrained samples collected from the Krishna-Godavari Basin (Yoneda et al., 2019b). In addition, the yield stress P_y, increases with increasing hydrate saturation S_h, with values of 145, 157, and 202 kPa for S_h = 0, 30%, and 50%, respectively. It is obvious that the increasing rate of P_y is small when hydrate saturation is low (e.g., S_h<30%), and then the increasing rate becomes larger when hydrate saturation becomes higher (e.g., 30%<S_h<50%).

3.2 Coefficient of Volume Compressibility

Coefficient of volume compressibility m_v, is defined as the change in the unit volume of soils per unit increase in effective stress during compression, and it can be calculated as:

$ {m_v} = \frac{{\frac{{\Delta e}}{{\Delta P}}}}{{1 + {e_i}}} = \frac{{\frac{{{e_i} - {e_{i + 1}}}}{{{P_{i + 1}} - {P_i}}}}}{{1 + {e_i}}}, $

(1)

where the subscripts i and i +1 represent variables before and after the vertical stress change, respectively.

Fig. 5 shows the coefficients of volume compressibility m_v, for hydrate-free and hydrate-bearing samples at different levels of vertical stress P. It is shown that m_v-value of the hydrate-free sample decreases with increasing P le-vel. However, m_v-values of hydrate-bearing samples initially increase and then decrease with increasing P level in general, and the transitions occur at P = 200 kPa. In addition, m_v-values of hydrate-free and hydrate-bearing samples are almost same when subjected to the vertical stress larger than 800 kPa, indicating a negligible effect of hydrate saturation S_h on the compression process.

The characteristics shown in Fig. 5 indicate that the effects of hydrate saturation on the confined compression properties of hydrate-bearing samples are dependent on the stress level. Comparing with values of P_y shown in Fig. 4, it is observed that the decrease in m_v-value with increasing vertical stress level only occurs when the yield point has been arrived and passed. The stiffening effect of hydrates on hydrate-bearing sediments, hindering the confined deformation (Waite et al., 2009), is obvious when subjected to low vertical stresses. But the stiffening effect may vanish when the vertical stress is high enough.

3.3 Consolidation Properties

Fig. 6 shows the measured settlement h as a function of elapsed time t under different levels vertical stress P. It is evident that the complete consolidation time is barely dependent on the vertical stress P and hydrate saturation S_h in general although the curves for hydrate-free and hydrate-bearing samples are distinguishable when P = 50 kPa (Fig. 6a). According to the distinguishable curves shown in Fig. 6a, the final settlement after stabilization is observed to increase with decreasing hydrate saturation S_h. This is further confirmed by the experimental data shown in Fig. 6b where P = 100 kPa. However, as the vertical stress P increases further, the final settlement of hydrate-bearing samples is comparable with (Figs. 6c–6g) and even larger than (Figs. 6h–6i) that of hydrate-free sediments. In addition, the final settlement of hydrate-bearing samples with S_h = 50% is generally smaller than that of hydrate-bearing samples with S_h = 30% when the vertical stress is small (i.e., P<800 kPa). The final settlement difference between hydrate-bearing sediments with hydrate saturations of 30% and 50% has an overall negative trend with the vertical stress P.

3.4 Coefficient of Consolidation

The coefficient of consolidation c_v, is a parameter describing the rate at which the consolidation process evolves during an oedometer test, and it can be estimated from the time-settlement curve (Fig. 6) by using the graphical method, i.e., the square root time method (Mitchell and Soga, 2005). Fig. 7 shows the coefficients of consolidation (c_v) of hydrate-free and hydrate-bearing samples under different levels of vertical stress (P). It is shown that the coefficients of consolidation (c_v) of hydrate-bearing samples generally increase with increasing vertical stress when P<200 kPa. However, the coefficient of consolidation decreases and then stabilizes around 0.6 × 10⁻⁶ m² s⁻¹ when the vertical stress is larger than 800 kPa. On the contrary, the coefficient of consolidation of hydrate-free samples decreases with increasing vertical stress from 50 kPa to 400 kPa and then maintains relatively unchanged when P >400 kPa. This is consistent with the results obtained from the hydrate-free sediments recovered from the northern SCS (Jiang et al., 2023). In addition, when the vertical stress is larger than 800 kPa, the coefficients of consolidation c_v of hydrate-free and hydrate-bearing samples are almost the same, indicating that the effect of hydrate saturation S_h on the coefficient of consolidation c_v is dependent on vertical stress.

4 Discussions and Model Developments 4.1 Dependency of Yield Stress on Hydrate Saturation

The yield stress of hydrate-free samples mainly comes from the inner structural fabric generated due to sample preparation operations (e.g., solution mixing, compaction, scarification, and others). When hydrate forms in pores, the yield stress of hydrate-bearing samples comes not only from the inner structural fabric but also from the hydrate filling and cementing. Contribution of the inner structural fabric is assumed to be similar or identical whether there is hydrate or not, as the sample preparation operations have been well controlled. The hydrate filling effect mainly shrinks fluid-occupied pores and equivalently enhances the compactness, while the hydrate cementing effect mainly hinders soil particle adjustments when subjected to an external loading. These two effects of hydrate in pores can stiffen host sediments and make hydrate-bearing samples more difficult to be compacted than hydrate-free samples when subjected to the same external loadings. However, the efects may weaken and even partially vanish when the external loading is large.

Fig. 8 shows the yield stresses (P_y) of hydrate-free and hydrate-bearing samples. It is shown that the P_y increment is 12 kPa when the hydrate saturation (S_h) increases from 0 to 30%, and when S_h further increases from 30% to 50%, the P_y increment becomes 45 kPa, which is 375% larger than the previous increment. This indicates that there is a threshold of hydrate saturation beyond which the hydrate effects on the yield stress become more pronounced. This is consistent with the conception of effective hydrate saturation (De La Fuente et al., 2020). This two-stage trend can be depicted by using the following fitting equation:

$ {P_y} = {P_0} + k<{S_h} - \xi {S_{hc}} >, $

(2)

where P₀ represents the yield stress of hydrate-free samples (generated due to the inner structural fabric); k is a fitting parameter, and ξ is a hydrate morphology dependent parameter; S_hc stands for the critical hydrate saturation beyond which hydrate effects on the yield stress become obvious, and its value generally ranges from 25% to 40% (Waite et al., 2009); < > is the Macaulay bracket which sets negative values of S_h − ξS_hc to be zero but performs no operations on the positive values. The dashed broken line colored blue in Fig. 8 is drawn by using the fitting equation with k = 2.3 × 10⁵ Pa and S_hc = 25%. Since the morphologies of THF hydrate within fine-grained sediments are mainly pore-filling and load-bearing/frame-building (Liu et al., 2019), the parameter ξ is as assigned a unit value in this study according to the criteria reported by Yan and Wei (2017). For cementing hydrate in pores, the parameter ξ is valued as zero.

4.2 Average Degree of Consolidation

The average degree of consolidation, U_t, is an important parameter describing the amount of the imposed external loading that has been transferred to the effective stress of soil, and it can be calculated as (Mitchell and Soga, 2005):

$ {U}_{t}=1-\frac{8}{{\text{π}}^{2}}\sum\limits_{m=1}^{\infty }\frac{1}{{m}^{2}}\mathrm{exp}\left(-{m}^{2}\frac{{\text{π}}^{2}}{4}{T}_{v}\right), $

(3)

where m is a positive odd number (i.e., m = 1, 3, 5, ···); T_v is the dimensionless index of the elapsed time which is formulated as:

$ {T_v} = \frac{{{c_v}t}}{{{H^2}}}, $

(4)

where H equals to half of the sample height in this study, where a double drainage condition is applied. Eqs. (3) and (4) are solved by using the finite difference method, and a Python code is developed to calculate the average degrees of consolidation (U_t) of hydrate-free and hydrate-bearing samples under different levels of vertical stress. The calculated results are shown in Fig. 10. It is obvious that the average degree of consolidation (U_t) of hydrate-free and hydrate-bearing samples increases with elapsed time, regardless of whether the vertical stress is low or high. However, the average degree of consolidation (U_t) rapidly (i.e., within 2 h) increases to unit when the vertical stress P is low (e.g., P = 50, 100, 200 kPa), while the average degree of consolidation cannot reach the final value until the elapsed time is 24 h when the vertical stress is 400 or 800 kPa. When further increasing the vertical stress to 10000 kPa, the increment of the average degree of consolidation U_t becomes slower but still faster than that corresponding to the low stress conditions.

An empirical Eq. (5) is given to ease the engineering application of Eq. (3):

$ {U_t} = 1 - a \cdot {{\rm e}^{ - bt}}, $

(5)

where a and b are two fitting parameters. The values of parameters a and b obtained by fitting the calculated data in Fig. 9 are summarized in Table 2. It is obvious that all a-values fall within a narrow range from 0.91 to 1.00 in this study, indicating that a = 1 is acceptable to some extent.

The variations of parameter b with the vertical stress P and hydrate saturation S_h are shown in Fig. 10. It is obvious that the overall trend of the parameter b changing with vertical stress P is consistent with that of the coefficient of consolidation c_v shown in Fig. 7. In addition, the dependency of b-values on hydrate saturation becomes weaker when the vertical stress is higher than 400 kPa (Fig. 10b), with relatively stable values range from 0.17 to 0.58, and the average of b-values is 0.43.

An empirical Eq. (6) is proposed to describe the hydrate saturation dependent parameter b under different vertical stress P.

$ {b_h} = \left\{ {\begin{array}{*{20}{c}} {\alpha \cdot {b_0} \cdot {{\rm e}^{ - {{\left[ {\log {{\left({P/\beta \cdot {P_y}} \right)}^\gamma }} \right]}^2}}}, \; \; P<4{P_y}} \\ { \;\;\;\;\;\;\;\;\;b \;\;\;\;\;\;\;\;\; \; \; \; \;, P \geqslant 4{R_y}} \end{array}} \right., $

(6)

where α, β, and γ are fitting parameters; Subscripts '0' and 'h' represent hydrate-free and hydrate-bearing samples. The fitting results for the hydrate saturations of 30% and 50% are shown in Fig. 11 as dashed curves colored black. Set α = 0.88, β = 1.00, and γ = 2.29 when S_h = 30%; set α = 0.60, β = 0.65, and γ = 2.08 when S_h = 50%; and set b₀ = 4.89 in this study. It is obvious that the empirical equation with proper parameter values can capture the basic physics underlying the changes.

By integrating Eqs. (2) and (6) into Eq. (5), the average degree of consolidation U_t of hydrate-bearing sediments can be calculated. The calculated curves are compared in Fig. 12 with corresponding data shown in Fig. 9. It is shown that the calculated curves generally agree with the corresponding data, especially for the conditions at low (e.g., 50, 100, and 200 kPa) and high (e.g., 3200, 6400, and 10000 kPa) vertical stresses. The agreement is not always good but acceptable for the conditions at median vertical stresses (e.g., 400, 800, and 1600 kPa). Note that the calculated curves overlap when the vertical stress is higher than 1600 kPa, mainly because of the constant values of parameter b in Eq. (6). If the variation of b-value can be depicted in more detail, the errors shown in Figs. 12f, 12g, and 12i may be reduced further.

5 Conclusions

In this study, oedometer (i.e., laterally confined consolidation) tests are conducted on remodeled hydrate-free and hydrate-bearing samples by using natural fine-grained sediments collected from the northern SCS as the host materials. Results are analyzed and used to explore the effects of hydrate saturation on the laterally confined compression characteristics and consolidation properties of hydrate-bearing sediments. Empirical equations for calculating the yield stress and the average degree of consolidation are developed and verified. Main conclusions are drawn as follows:

1) Vertical loading induces a reduction in void ratio, and the decrement of void ratio increases with decreasing hydrate saturation when subjected to the same vertical loading. Values of the compression index of hydrate-free and hydrate-bearing fine-grained sediments are quite similar, ranging from 0.510 to 0.552 when hydrate saturation increases from 0 to 50%. The yield stress of hydrate-free fine-grained sediments is 145 kPa, and the yield stress slightly increases to 157 kPa when hydrate saturation is 30% but sharply jumps to 202 kPa when hydrate saturation is 50%.

2) Both the coefficient of volume compression and the coefficient of consolidation for hydrate-bearing fine-grained sediments decrease with increasing vertical stress. However, as vertical stress increases, these two coefficients for hydrate-bearing fine-grained sediments firstly increase and then decrease to a relative stable level, and the transition occurs when the vertical stress is 200 kPa, which is no smaller than the yield stress. In addition, the effects of hydrate saturation on these two coefficients are minor when the vertical stress is high (i.e., >800 kPa).

3) The average degrees of consolidation of hydrate-free and hydrate-bearing fine-grained sediments increase with elapsed time. The duration of complete consolidation is short when subjected to low vertical stresses (e.g., 50 kPa, 100 kPa, and 200 kPa), while it is long when subjected to median vertical stresses (e.g., 400 kPa and 800 kPa). However, further increases in vertical stress (i.e., >800 kPa) may shorten the duration of complete consolidation, although it is still longer than that under low stresses.

Acknowledgements

This study is jointly supported by the Natural Science Foundation of Shandong Province (No. ZR2022YQ54), the Marine S&T Fund of Shandong Province for Laoshan Laboratory (No. 2021QNLM020002), and the Taishan Scholars Program (No. tsqn202306297).