Keywords

1 Introduction

Methane hydrate (MH) is a crystalline solid in which methane molecules are captured by cages formed by water molecules framework under high pressure and low temperature [1]. Methane hydrate bearing sediments (MHBS) is a soil deposit containing MH in its pores. The exploration of MH has attracted worldwide attention for its high energy density. However, MHs only exist stably under certain conditions and changes of pore pressure or temperature caused by gas exploitation may lead to MH dissociation, which may change the mechanical properties of MHBS and trigger a series of and geo-hazards. Therefore, a deep investigation on the mechanical behaviors of MHBS is necessary.

The mechanical behavior of MHBS is influenced by many factors, among which the formation of MHs in the pore of MHBS plays an important role. According to previous research, three formation habits of MHs have been summarized: pore-filling, cementation and load-bearing [2]. In the last decades, considerable laboratory tests have been conducted to study the mechanical properties of natural and artificial MHBS, such as triaxial compression tests [3, 4] and direct shear tests [5]. However, the mechanical behavior of MHBS is still insufficient, especially the microscopic mechanism related with the macroscopic behavior. The distinct element method (DEM) [6] is efficient to capture the evolution of microscopic particle interactions and thus was employed. In this study, a pore-filling types of MHBS was generated by a novel technique. The constant stress ratio (CSR) compression tests with different stress ratios are performed to analyze its volumetric strain and contact fabric.

2 Numerical Simulation

A new technique proposed by He and Jiang [7] was used to generate the pore-filling type MHBS samples. At first, a cubic sample with an initial void ratio of 0.84 was generated by multi-layer under-compaction method (UCM) [8]. The size of the sample is 5.445 × 5.445 × 5.445 mm3. The grain size distribution is similar to that of Toyoura sand.

After the generation, N particles with radius of Ra was randomly created in the pores of soil particles according to the MH saturation Smh which is defined by the ratio of MH volume Vmh to the total pore volume Vv. Subsequently, the particle with radius of Ra was replaced by a near-spheroidal cluster, which was formed by bonding n MH particles with radius r together. The void ratio of the cluster is ea. The number of MH clusters N can be calculated by:

$$ N = \frac{{V_{mh} }}{{\frac{4}{3}n\pi r_{{}}^{3} \times (1 + e_{a} )}} $$
(1)

In this study, the void ratio of the MH cluster ea is 0.82, the radius of the MH particle r is 0.024 mm and the number of MH particles in a cluster n is set to 60. When Smh = 10%, the number of MH clusters N is 1166. The parallel bond model (BPM) is employed in the cluster and the material parameters used in this paper is the same as in [9].

3 Numerical Results

In CSR tests, the intermediate principal stress σ2 and the minor principal stress σ3 were kept equal and the stress ratio η was maintained constant, i.e., σ2 = σ3 = ησ1. The load was applied step by step. In the first step, σ1 was set to 1.0 MPa and the latter σ1 was 1.15 times the former σ1 during the subsequent loading. To investigate the influence of stress ratio, three different stress ratio, i.e., 0.5, 0.7, 0.9, were used.

Figure 1 shows relationships between void ratio and major principal stress of MHBS with Smh = 10% under different stress ratios. The void ratio decreases when the major principal stress increases. And the compressibility of pore-filling type MHBS is low before yielding but higher after, though the yield point is not obvious. Besides, the void ratio is lower when stress ratio is higher, which indicates that the yield of the MHBS sample is related to stress path.

Fig. 1.
figure 1

Relationships between void ratio and major principal stress of MHBS with Smh = 10% under different stress ratios.

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Relationships between bond contact ratio and major principal stress of MHBS with Smh = 10% under different η is illustrate in Fig. 2. The bond contact ratio is defined as the ratio of bond contact number to initial bond contact number. The bond contact ratio decreases when the major principal stress increases.

Fig. 2.
figure 2

Relationships between bond contact rate and major principal stress of MHBS with Smh = 10% under different stress ratios.

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The fabric tensor is defined based on Satake [10] to describe the soil anisotropy:

$$ F_{ij} = \frac{1}{{N_{c} }}\sum\limits_{k = 1}^{{N_{c} }} {n_{i}^{k} n_{i}^{k} ,i = j = 1,3} $$
(2)

where Nc is the contact number,\( n_{i}^{k} \) is the component of the unit vector nk at a contact.

The fabric tensor for the strong contacts is described by [11]:

$$ F_{ij}^{\text{s}} = \frac{1}{{N_{c} }}\sum\limits_{s = 1}^{{N_{c}^{s} }} {n_{i}^{s} n_{j}^{s} ,i = j = 1,3} $$
(3)

where \( N_{\text{c}}^{s} \) is the number of the strong contacts and \( n_{i}^{\text{s}} \) is the component of unit vector ns at a strong contact.

The development of the eigenvalues of contacts (F11, F22, F33) for MHBS samples with Smh = 10% when η = 0.7 during the test is presented in Fig. 3(a). It can be seen that the minor principal fabric F33 slightly increases to a constant value while the major principal fabric F11 slightly decreases to a constant value. As for the eigenvalues of the strong contacts (\( F_{11}^{s} \), \( F_{22}^{s} \), \( F_{33}^{s} \)), shown in Fig. 3(b), \( F_{11}^{s} \) reaches a peak value then decreases, while \( F_{22}^{s} \) and \( F_{33}^{s} \) decrease to a minimum value then increase.

Fig. 3.
figure 3

The development of the eigenvalues of (a) contacts and (b) the strong contacts for MHBS samples with Smh = 10% when η = 0.7.

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