Shear Modulus of a Carbonate Sand–Silt Mixture with THF Hydrate

Abstract

The maximum shear modulus (G_max) is an important factor determining soil deformation, and it is closely related to engineering safety and seafloor stability. In this study, a series of bender element tests was carried out to investigate the G_max of a hydrate-bearing carbonate sand (CS)–silt mixture. The soil mixture adopted a CS:silt ratio of 1:4 by weight to mimic the fine-grained deposit of the South China Sea (SCS). Tetrahydrofuran (THF) was used to form the hydrate. Special specimen preparation procedures were adopted to form THF hydrate inside the intraparticle voids of the CS. The test results indicate that hydrate contributed to a significant part of the skeletal stiffness of the hydrate-bearing CS–silt mixture, and its G_max at 5% hydrate saturation (S_h) was 4–6 times that of the host soil mixture. Such stiffness enhancement at a low S_h may be related to the cementation hydrate morphology. However, the G_max of the hydrate-bearing CS–silt mixture was also sensitive to the effective stress for an S_h ranging between 5% and 31%, implying that the frame-supporting hydrate morphology also plays a key role in the skeletal stiffness of the soil mixture. Neither the existing cementation models nor the theoretical frame-supporting (i.e., Biot–Gassmann theory by Lee (BGTL)), could alone provide a satisfactory prediction of the test results. Thus, further theoretical study involving a combination of cementation and frame-supporting models is essential to understand the effects of complicated hydrate morphologies on the stiffness of soil with a substantial amount of intraparticle voids.

1. Introduction

Gas hydrate is emerging as one of the future energy sources, but its dissociation can cause significant environmental hazards such as the release of methane (a potent greenhouse gas), the instability of the seafloor, etc. Past studies have revealed that hydrate morphology is a crucial factor governing the mechanical behaviour of hydrate-bearing sediments. In coarse-grained soil, the following three hydrate morphologies are commonly assumed: pore-filling, load-bearing and cementation [1]. As hydrate formation in sediments depends on many factors, such as the geological conditions and the fluid conductivity of the sediments, the transportation mechanism of gas, etc., many complex hydrate morphologies can exist including segregated veins, nodules and lenses in fine-grained soil and heterogeneous hydrate patches in coarse-grained soil under high effective stress [2,3]. Moreover, it is a significantly difficult task to identify the occurrence of paleo-gas hydrate in fossil sediments. Based on long-term field data, recent studies have shown that clathrite-like structures and the geochemical properties of pore water are useful indicators that provide helpful information for understanding the formation and dissociation of gas hydrate [4,5]. Recent field explorations in the South China Sea (SCS) have reported that high methane hydrate saturation can be found in fine-grained sediments containing foraminifera (carbonate fossils containing a significant proportion of intraparticle voids) [6]. Compared with the small interparticle voids of a fine-grained soil matrix, hydrates tend to form in the larger intraparticle voids of foraminifera. As such, the distribution of hydrates is heterogeneous, depending on the spatial variability of foraminifera instead of being evenly distributed in the voids.

Different laboratory methods have been adopted to form hydrate in soil specimens, resulting in different hydrate morphologies, e.g., excess gas method [7,8], excess water method [9,10], ice seed method [11,12], etc. However, two other methods are used for fine-grained soils of low permeability. In the first method, under high pressure and low temperature, methane gas was injected and reacted with ice powder, with an average particle size of 250 μm, to form hydrate powder. Then, it was mixed with fine-grained soil [13,14,15]. However, no bonding is formed between hydrate and soil particles in this method. This study adopted the second method, where tetrahydrofuran (THF) was used to replace methane gas [16,17,18]. THF hydrate is often adopted as a good substitute for methane hydrate owing to the similarities in the mechanical and thermal properties. As THF is miscible with water at room temperature, it is easier to control the hydrate saturation and its distribution by adding the estimated amount of THF/water solution to the desired location of the specimen. The objective of the study was to model the hydrate accumulation inside the interparticle voids of CS rather than the field hydrate formation process. Only CS was soaked in the THF/water solution to achieve this ends and details of laboratory procedures will be presented in the next section. It should be noted that THF hydrate discomposes into liquid without gas during dissociation; thus, one of the limitations is that no gas dissociation can be modelled from THF hydrate.

The deformation and shear strength of soil are closely related to the safety of engineering structures and seafloor stability during hydrate exploitation. Thus, the mechanical properties of hydrate-bearing soils have been reported in the past literature, e.g., the stress–strain behaviour and shear strength of hydrate-bearing sand [19], the dynamic shear modulus and damping ratio of hydrate-bearing sand [20], the effects of hydrate on the rheological properties of mudflow [21], shear wave velocity and maximum shear modulus (G_max) of hydrate-bearing sand [22], etc. Clayton et al. [22] conducted a series of resonant column tests on sand-sized geomaterials. The results showed that cementation morphology has more significant influence on the shear moduli of the host sand than pore-filling morphology. Similarly, Liu et al. [20] carried out resonant column tests on THF hydrate-bearing sand. The results revealed that effective stress and hydrate can enhance the shear modulus, while high hydrate saturation would suppress its enhancement. However, the effects of hydrate accumulated inside the intraparticle voids on the soil stiffness of fine-grained sediments with carbonate fossils are not well understood. In this study, special laboratory procedures were applied to form hydrate in the intraparticle voids of the CS–silt mixture. The bender element test was used to study G_max of the THF hydrate-bearing CS–silt mixture with the hydrate filling the intraparticle voids. The effects of this type of hydrate morphology on the G_max of fine-grained soil mixtures have rarely been reported in the literature. Furthermore, the effects of hydrate on soil stiffness were compared and discussed using theoretical frame-supporting and cementation models.

2. Materials and Methods

The tested soil mixture was formed by mixing a carbonate sand (CS) and a nonplastic silt in a ratio of 1:4 by dry weight to mimic the fine-grained sediment of the SCS. The CS was a marine sediment consisting of angular and shelly carbonate particles, which had similar chemical compositions and mechanical properties to that of foraminifera. As CS particles contain a substantial proportion of intraparticle voids, one of the objectives of this study was to model the hydrate accumulation in the intraparticle voids of the tested soil mixture. The silt was a crushed quartz.

Table 1. Physical properties of the tested soils.

Soils	Specific Gravity, Gs	Diameter Range (mm)	d50 (mm)	Maximum Void Ratio	Minimum Void Ratio
Nonplastic silt	2.63	<0.075	0.043	1.176	0.560
Carbonate sand (CS)	2.77	0.5−1.0	0.750	1.336	0.957
Soil mixture	-	<0.075, 0.5−1.0	0.050	1.010	0.476

summarises the basic physical properties of the tested soils. The average particle size (d₅₀) and the effective particle size (d₁₀) of the soil mixture were 50 and 17 μm, respectively. Figure 1 shows the particle size distribution (PSD) for CS, silt and the CS–silt mixture. The PSDs of two fine-grained sediment samples taken from the SCS [23] are also presented in the figure for comparison. The CS–silt mixture was a gap-graded soil, and the range of particle sizes was consistent with that of SCS sediments. Despite the fact that the tested soil mixture did not contain any fraction of clay, the fines content was similar to the marine sediment samples taken from the SCS. Ma et al. [24] found that fines play a dominant role in the soil matrix of a mixture if the CS content is less than 60%. To focus on the effects of the intraparticle voids of CS on the stiffness of the CS–silt mixture, only the fines content but not the soil plasticity was modelled correctly in this study. Moreover, the permeability of soil decreases with increasing clay content. To minimise the effects of the permeability of the soil on hydrate formation in the specimen, clay was not included in the soil mixture. Further study will be required to investigate soil mixtures with some fractions of clay, which more closely represent natural marine sediments.

THF was used in this study to form hydrate in the soil specimens. The following procedures were used to ensure hydrate accumulation in the intraparticle voids of specimens. A given weight of the oven-dried samples of CS was first soaked inside a THF/water solution (21% THF by volume) under vacuum to saturate the intraparticle voids. After soaking, the weight of the wetted CS was carefully measured to determine the weight of the THF/water solution used in the soil specimen. The wetted CS was mixed thoroughly with the oven-dried silt. Then, the soil mixture was compacted on the pedestal of a triaxial test device to three different initial void ratios, as shown in Table 2, using the wet tamping method. Hydrate saturation (S_h), as shown in Table 2, is defined as the ratio of the volume of hydrate to the volume of void. In the solution consisting of 21% THF and 79% water by volume, all solution will form hydrate if the soil specimen is subjected to appropriate high-pressure and low-temperature conditions [25]. In other words, the hydrate-bearing specimens were dry specimens. The volume of hydrate was determined as the ratio of the weight of the THF/water solution in the soil specimen to the density of THF hydrate, which was taken as 0.981 × 10³ kg/m³ [26]. By adjusting the proportion of CS soaked in the THF/water solution, the percentage of intraparticle voids filled with hydrate was controlled to be between 25% and 100%. In addition, three control specimens without hydrate (S_h = 0) were compacted to the target initial void ratios, as shown in Table 2.

To verify that the intraparticle voids of the CS were saturated by the THF/water solution after soaking, a THF/water solution-soaked CS specimen was scanned by micro-CT equipped with a high-resolution X-ray tube (Type: XTH225/320 LC from Nikon, Tokyo, Japan). A CT imaging of a typical cross-section of a CS specimen, as shown in Figure 2. The grey, yellow and black colours represent soil particles, THF/water solution and air, respectively. It is depicted that the THF/water solution is either filled inside the intraparticle voids or on the surface of the CS particles. After mixing the THF/water-soaked CS with dry silt, it was postulated that the THF/water solution remains inside the intraparticle voids and on the surface of the CS particles of the CS–silt specimens. Nikitin et al. [27] observed that there was inevitable water migration during methane hydrate formation due to the cryogenic suction. However, the influence of the excess gas method in their study on water migration was omitted and in which a multiphase flow may cause water movement. In this study, it was assumed that there was negligible water migration in the specimens during hydrate formation when the temperature decreased to below 0 °C. Hence, it was reasonable to assume that hydrate was formed in the intraparticle voids and interparticle voids adjacent to the CS particles, as shown in Figure 3. The accumulation of hydrate inside the intraparticle voids of the CS–silt specimen agrees well with that observed in the field samples of hydrate-bearing sediment containing carbonate fossils taken from the SCS [28].

Table 2. Test conditions.

Specimen ID	Initial Void Ratio, e0	Percentage of Intraparticle Voids Filled with Hydrate	Effective Void Ratio, e′	Hydrate Saturation, Sh (%)	Effective Confining Stress, σc′ (kPa)
1	0.799	0	0.799	0	100, 200, 300, 400
2	0.799	100	0.510	24	100, 300, 500, 800
3 a	0.733	0	0.733	0	100. 200, 300, 400
4	0.733	25	0.672	5	100, 300, 500
5	0.733	50	0.593	12	100, 300, 500, 800
6 a	0.733	100	0.447	27	100, 300, 500, 800
7	0.666	0	0.666	0	100, 200, 300, 400
8	0.666	100	0.381	31	100, 300, 500, 800

^a Ji et al. [29].

Table 2. Test conditions.

Specimen ID	Initial Void Ratio, e0	Percentage of Intraparticle Voids Filled with Hydrate	Effective Void Ratio, e′	Hydrate Saturation, Sh (%)	Effective Confining Stress, σc′ (kPa)
1	0.799	0	0.799	0	100, 200, 300, 400
2	0.799	100	0.510	24	100, 300, 500, 800
3 a	0.733	0	0.733	0	100. 200, 300, 400
4	0.733	25	0.672	5	100, 300, 500
5	0.733	50	0.593	12	100, 300, 500, 800
6 a	0.733	100	0.447	27	100, 300, 500, 800
7	0.666	0	0.666	0	100, 200, 300, 400
8	0.666	100	0.381	31	100, 300, 500, 800

^a Ji et al. [29].

The maximum shear modulus (G_max) was measured using a temperature controlled triaxial test apparatus with a pair of bender elements installed at the top cap and bottom pedestals of the triaxial cell, as shown in Figure 4a,b, in which dimethyl silicone oil was chosen as the medium to provide confining pressure and heat exchange. The experimental system (Nanjing TKA Technology Co. Ltd., Nanjing, China) consisted of a triaxial apparatus, two water pumps, a thermal controller, a temperature sensor, a wave generator, a power amplifier, an oscilloscope, a signal amplifier and a linear power supply. It is worth noting that the bender element on the top cap should be aligned carefully to keep it parallel to another one on the bottom pedestal for the accuracy of the shear wave measurement. In this study, only the time difference between the peak emitted wave and that of the received wave was chosen to calculate the shear wave velocity (v_s) in this study. The details regarding the interpretation of the bender element signals were reported by Ji et al. [29]. It should be noted that it is also possible to measure the damping ratio (ζ) of soil using the bender element test [30], i.e., the viscous behaviour of soil. In general, ζ is determined by viscoelasticity methods recommended in Sodeifian [31] and Liu et al. [20]. Cheng and Leong [30] proposed that ζ can be measured by applying the Hilbert transform method to the bender element test results. Although, bender element signals can be processed to study the viscoelastic behaviour of soil, this study focused only on small strain stiffness, i.e., the G_max of THF hydrate-bearing soil.

3. Results and Discussion

Table 2 shows that eight specimens were tested in this study. As the control of high pressure and low temperature was time-consuming, only two replicated tests have been carried out for each specimen ID 1 and 2 to verify the reproducibility of consistent specimens and reliability of test data. Figure 5 shows the measured shear wave velocity against the effective confining pressure for the host soil mixture (S_h = 0) and those with S_h ranging between 24% and 31%. The test results of six specimen ID are depicted in the figure for e₀ ranging from 0.666 to 0.799 and effective confining pressure ranging from 100 to 800 kPa. The measured v_s of specimen ID 1 and 2 (e₀ = 0.799) are the average values of two replicated tests. It is found that the measurements were within ±8% and ±5% of the average values for specimens ID 1 and 2, respectively. Those of the remaining four specimens were measurements of a single test. The test results of two other fine-grained soils are also shown in the figure for comparison [32,33]. Hardin and Richart [34] suggested that v_s can be related to the effective stress using the following equation:

$$v_s=a{\left({{\sigma }_c}^{\prime }\right)}^b$$

(1)

where σ_c′ is the effective confining stress, a and b are the two fitting parameters; b reflects the sensitivity of the effective stress on v_s. Equation (1) was used to best fit the data shown in Figure 5. It was found that b increased from 0.187 to 0.320, while the initial void ratio decreased from 0.799 to 0.666 for the dry soil mixture. As expected, a dense soil has more contact points or a higher coordination number, resulting in a greater contribution of the effective stress on v_s. Santamarina et al. [35] reported a value for b of approximately 0.25 for rough or angular sand and silt particles. The measured range of b for the tested soil mixture was consistent with this reference value. By adding S_h ranging between 24% and 31%, it was apparent that the v_s of the hydrate-bearing soil mixture was 3–5 times that of the host soil mixture. The increase in v_s reflects the increase in skeletal stiffness due to the presence of hydrate. In addition, b reduced to the range between 0.127 and 0.161. In other words, the hydrate-bearing soil mixture was less sensitive to the effective stress. Lee et al. [32] also observed a similar trend on remould clay-dominated sediments, where b decreased from 0.3 to 0.03 as the S_h increased from 0 to 100%. As expected, v_s of specimen with 100% S_h (all the voids filled with THF hydrate) is almost independent of the effective stress. Furthermore, Kim et al. [33] has also obtained similar results on CO₂ hydrate-bearing clayey silt where b decreases from 0.26 to 0.01 as S_h increases from 0 to 63%. It should be noted that at a S_h of 27–28%, the CO₂ hydrate-bearing clayey silt was less sensitive to the effective stress than the soil mixture tested in this study. The specimen preparation in this study resulted in some hydrates forming inside the intraparticle voids, leading to a lower amount of cementation than that found in Kim et al. [33] at a similar S_h.

The G_max was evaluated using G_max = ρv_s², where ρ is soil density. Past studies [36,37,38] have revealed that the effective stress and the void ratio are the two most important factors controlling the G_max, and the following empirical equation is proposed:

$$G_{\max }=C_0\cdot F\left(e\right)·{\left(\frac{{\sigma }^{\prime }}{P_a}\right)}^h$$

(2)

where C₀ is a material parameter characterised by the particle size, shape, bonding and overconsolidation ratio. It increases with the increase in the particle size and sphericity and roundness of particle [39]. σ′ is the effective stress, F(e) is a void ratio function, P_a is a reference pressure taken as 1 kPa in this study and h is the exponent term for the effective stress. Different forms have been proposed for F(e). In this study, F(e) = (0.3 + 0.7e²)⁻¹, as proposed by Hardin [40], was adopted. Equation (2) was used to fit the measured G_max against the effective stress. To eliminate the influence of the void ratio, Figure 6 depicts the G_max normalised by F(e) as a function of the effective stress for the test results shown in Figure 5. For the hydrate-bearing specimens, F(e) was evaluated using the effective void ratio (e′), defined as the void ratio considering hydrate as the solid constituent. It is evident from Table 2 that the e′ was approximately 57–64% of the initial e of the host soil mixture, resulting in an increase of 50% of F(e) for hydrate-bearing CS–silt at an S_h between 24% and 31%. As expected, the normalized G_max of the hydrated-bearing specimens was at least one order of magnitude higher than that of the dry specimens. The best-fit values of C₀ and h and the corresponding R² are summarised in

Table 3. Best-fit values of the model parameters for Equation (2).

Soil	C0	h	R2
CS–silt mixture	2	0.57	0.92
CS–silt mixture with Sh = 24–31%	78	0.28	0.82
LB-E sand	12	0.42	0.99
LB-E sand with Sh = 10% (excess gas method)	1394	0.02	0.76

. The best-fit values of a hydrate-bearing Leighton Buzzard Grade E (LB-E) sand using the excess gas method are also shown in the table for comparison. On the one hand, with hydrate forming in the specimens, the value of exponent h decreased from 0.57 to 0.28. The reduction in the value of h implies that the contribution of the effective stress became less important with the addition of hydrate. In other words, the hydrate contributed to a significant part of the skeletal stiffness. On the other hand, the value of parameter C₀ increased sharply from 2 to 78, which may be due to the bonding effect of hydrate or larger and rounder coagulated particles of CS and silt bonded together by hydrate. Clayton et al. [22] studied the effects of the hydrate morphology on the small strain stiffness of the LB-E sand. Hydrate morphology is controlled by the specimen preparation method. In general, cementation hydrate morphology is formed by the excess gas method. The G_max of the hydrate-bearing sand containing 10% S_h was 6–13 times that of the host sand, as shown in Figure 6. The h value decreased from 0.42 to 0.02, and the C₀ value increased from 12 to 1394. An h value close to 0 indicates that the material is either solid or cemented soil. A small amount of hydrate (low S_h) bonding the interparticle contacts is sufficient to stiffen substantially the soil matrix of the host sand.

Figure 7 compares the effects of hydrate on the G_max of the tested soil mixture with those of two common hydrate morphologies found in sand: (i) cementation (from the excess gas method) and (ii) pore-filling (from the excess water method). The G_max was normalised by the effective stress factor (σ_c′/P_a)^h in which the exponent h was assumed as 0.5. The amount of hydrate formed in the pores of the specimen is reflected by the reduction in the effective void ratio, e′. It is apparent that cementation and pore filling have the greatest and least increase in the normalized G_max, respectively. The hydrate-bearing CS–silt mixture lies between cementation and pore-filling morphologies. Equation (2) is shown with different values for C₀ as the broken lines in the figure. It seems that C₀ = 6 can be used to best fit the hydrate-bearing sand with pore-filling morphologies as well as the host sand. Thus, the effects of hydrate on the G_max can be reflected by the increase in F(e) as a result of the reduction in e′. On the contrary, the best-fit parameters for the hydrate-bearing CS–silt were different from those of the host soil (see Table 3). This was because the accumulation of hydrates in the intraparticle voids of the CS and the interparticle voids of the soil mixture involved both cementation and pore-filling morphologies. Thus, all three parameters in Equation (2) were affected.

To understand the effects of the hydrate morphology on the soil stiffness, a frame-supporting model, namely, the Biot–Gassmann theory modified by Lee (BGTL) [41], and the cementation model proposed by Dvorkin and Nur [42] were adopted in this study to estimate the G_max. In the BGTL model, hydrate is assumed to be one of the solid constituents, which reduces the porosity and changes the shear modulus of the soil mixture. A reduced porosity (φ_r) is defined as follows:

$${\phi }_{\mathrm{r}}=\phi \left(1-S_h\right)$$

(3)

where φ is the porosity of the soil mixture. The shear modulus of the soil mixture can be calculated from Equation (4) [39]:

$$G_{dry}=G_{sat}=\frac{G_{ma}{K}_{ma}\left(1-\beta \right)C^2{\left(1-{\phi }_{\mathrm{r}}\right)}^{2x}+G_{ma}{\beta }^{2}M{C}^2{\left(1-{\phi }_r\right)}^{2x}}{K_{ma}+4G_{ma}\left[1-C^2{\left(1-{\phi }_r\right)}^{2x}\right]/3}$$

(4)

where G_ma and K_ma are the shear and bulk moduli of solid phase, respectively; β is a Biot coefficient, which is a function of the porosity for unconsolidated sediments; x is a parameter depending on the degree of consolidation and differential pressure; C is a parameter depending on the clay content; M is a modulus that measures the variation in the hydraulic pressure needed to force an amount of water into a formation without any change in the formation’s volume. The formulae used to calculate the above parameters are given in Equations (A1)–(A6) in Appendix A. It should be noted fluid is not able to transmit shear waves, which has no effect on the shear modulus. Therefore, G_dry = G_sat in Equation (4).

In the cementation model [42], hydrate is assumed to form at the particle contacts. The effective bulk (K_dry) and shear moduli (G_dry) can be calculated using Equations (5) and (6), respectively:

$$K_{dry}=\frac{n\left(1-\phi \right)}{6}\left(K_c+\frac{4}{3}{G}_c\right)S_n$$

(5)

$$G_{dry}=\frac{3}{5}{K}_{dry}+\frac{3n\left(1-\phi \right)}{20}{G}_c{S}_T$$

(6)

where K_c and G_c are the bulk and shear moduli of hydrate, respectively, as shown in

Table 4. Elastic properties of the solid constituents.

Constituent	G (GPa) [43]	K (GPa) [43]
Quartz	45	36.6
Calcite	32	76.8
Hydrate	3.3	7.9

[43]. S_n and S_T are parameters that are proportional to the normal and shear stresses of a pair of cemented particles, respectively, which depend on the amount of particle contacts and the soil and particle moduli. The formulae for S_n and S_T are given in Equations (A7) and (A8), respectively, in Appendix B [42]. n is the average number of particle contacts, taken as 5.6 in this study. Equations (A15)–(A23) in Appendix B [44] were used to calculate n, which agreed with the findings verified by CT that n is taken reasonably between 4.8 and 7 for random dense packing [45].

Figure 8 compares the test results with the computed values of the BGTL and cementation models for an initial void ratio of 0.733. It was apparent that the measured G_max of the CS–silt mixture increased nonlinearly from 43 to 1100 MPa for an S_h ranging between 0% and 27%. The trend of the nonlinear increase in the G_max with respect to an S_h at a low regime of the S_h was consistent with the predicted tendency of the cementation model. For example, the predicted G_max increased from 1703 to 3565 MPa when the S_h increased from 0.5% to 5%. At a low S_h < 5%, a certain extent of hydrate accumulated at the interparticle contacts in the vicinity of CS particles, leading to a substantial stiffening of the soil matrix. Yu et al. [46] conducted a numerical simulation on the small strain behaviour of hydrate-bearing soil using the discrete element method. A contact bonding model was imposed between hydrate and soil particles to simulate the effects of cementation. The bonding effect may increase the contact number of the soil matrix, leading to a higher shear wave velocity (or G_max). The numerical results showed that the G_max increased nonlinearly with S_h, where the rate of increment decreased substantially with further increases in the S_h. Despite a similar nonlinear trend at the low regime of the S_h, the magnitude of the predicted G_max by the cementation model was much higher than the measured value. One of the limitations of the cementation model is that it is independent of the effective stress. However, the G_max is dependent on the effective stress. On the other hand, the BGTL model can account for the stress-dependent G_max. For the hydrate-free soil mixture (S_h = 0), under an effective stress of 100 and 300 kPa, the BGTL predicted a G_max of 33 and 86 MPa, respectively, which is consistent with the test results. However, BGTL cannot model the substantial increase in the G_max for 0 < S_h < 5%. Furthermore, both of the test results of Clayton et al. [22] using the excess gas method and this study fall between the cementation and BGTL models. Hence, hydrates play more than one role in the soil mixture. Figure 8 also shows that for a given S_h, the G_max of the specimens prepared by the excess gas method [22] is higher than that in this study. Some hydrates accumulated inside the intraparticle voids resulting in a weaker cementation effect for the CS–silt mixture, while the excess gas method tends to form a cementation morphology in the sand, enhancing significantly the stiffness of the soil matrix. Thus, a hydrate morphology is as important as the hydrate saturation and effective stress in governing the stiffness of hydrate-bearing soils.

Jung et al. [47] used the discrete element method to model the stress–strain behaviour of hydrate-bearing sand. Grain clusters and the parallel bond model were adopted to simulate the patchy hydrate and bonding effects between hydrate grains and mineral grains, respectively. The breakage of hydrate clusters was ignored in their study. According to the hypothesis shown in Figure 3, the hydrate morphology of the CS–silt mixture had two distinct features: (1) filling the intraparticle and interparticle voids; (2) cementation at the interparticle contacts. Due to the complex hydrate morphology, a hybrid model that incorporates features of both the cementation and frame-supporting models should be used to predict the observed G_max of the hydrate-bearing CS–silt mixture. The hydrate filling the intraparticle and interparticle voids plays a role in frame-supporting, while the hydrate occupying the interparticle contacts works as cementation. Various modelling techniques in the discrete element method may be used to numerically implement the concept of a hybrid model [46,47,48]. In this way, it is essential to quantify the proportions of hydrate filling the intraparticle and interparticle voids and those cementing at the interparticle contacts.

4. Conclusions

The maximum shear modulus (G_max) is an important factor determining soil deformation, and it is closely related to engineering safety and seafloor stability. The bender element test was conducted to investigate the effects of hydrate on the G_max of a CS–silt mixture in this study. By adopting special specimen preparation procedures, THF hydrate formed in the intraparticle voids of the CS grains and interparticle voids between the CS and surrounding silt particles. Both cementation and pore-filling hydrate morphologies contributed to the skeletal stiffness of the hydrate-bearing CS–silt mixture. At a low hydrate saturation (S_h), the cementation morphology played a dominant role, where the G_max of the hydrate-bearing CS–silt mixture increased by 4–6 times at an S_h of 5%. However, the G_max also depends on the stress for the range of S_h tested. This stress-dependent stiffness implies that the hydrate with a frame-supporting morphology also plays a significant role in the soil matrix. In other words, the difference in the hydrate morphologies determines the effect of the hydrate saturation and effective stress on hydrate-bearing specimens. Therefore, neither the existing cementation model nor the frame-supporting model, i.e., BGTL, could alone predict adequately the shear modulus of the hydrate-bearing CS–silt mixture. Thus, a hybrid model incorporating both cementation and frame-supporting models should be used. This type of hybrid model may be implemented numerically using the discrete element method. Further investigation is required to provide theoretical evidence for the effects of complicated hydrate morphology on the stiffness of the CS–silt mixture, which is essential for hydrate exploration and ocean engineering safety.