Abstract
This paper presents the numerical simulations results carried out using Discrete Element Method (DEM) on the shear behaviour of Methane Hydrate (MH) bearing sand during monotonic loading. A series of triaxial drained loading tests were carried on an assembly of particles for different methane hydrate saturations. In this study, pore filling habit of MH leading to load bearing distribution is considered for the DEM simulation. In qualitative sense, the DEM simulations results have captured the shear behaviour of MH bearing sand similar to the laboratory experiments. The DEM simulation results highlights that MH saturation and confining pressure has a profound influence on the shear behaviour of hydrate bearing sand. Moreover, the evolution of micro-mechanical parameter (e.g. contact force) during shear loading has been presented and discussed.
INTRODUCTION
Recently, offshore seismic geologic survey has identified several locations of methane hydrate deposits around the globe. Methane hydrate or clathrates contains methane, the main constituent of natural gas. They form under high pressure and low temperature conditions. The methane hydrates are regarded as one of the most feasible sources for future energy compared with other known hydrocarbon deposits. However, there is significant hazard related to drilling and production operations for methane hydrate as the methane is approximately 20 times as effective as green house gas as carbondioxide (Hyodo et al. 2005; Collet & Dallomore, 2002) . In order, to produce methane gas from methane hydrate safely and without damaging the environment, we need to address a wide-range of geotechnical and environmental issues. It has been reported that methane hydrate production may collapse and leads to settlement or landslides on the seafloor. Moreover, marine substructures are vulnerable to these sea bed deformations and no attractive technology is currently available to recover methane economically from methane hydrate. This emphasises the need to understand the pore scale interactions between methane hydrate and soil grains which has a significant effect on the shear and volume change behaviour methane hydrate bearing sediments.
INTRODUCTION
The laboratory experiments such triaxial, direct shear and bending tests have been conducted recently on the shear behaviour of methane hydrate bearing soil sample (e.g. Masui et al 2005; Hyodo et al 2002 & 2013 and Song, 2010 . Detailed review of literature highlight that the shear strength, stiffness and dilation of hydrate bearing sand is influenced by hydrate saturation, initial confining pressure and temperature. Waite et al. (2009) concluded that stress-strain response of hydrate bearing soil is affected by the hydrate growth habit. He has described three models which show the microscopic distribution of hydrates in soils. (1) pore filling: hydrate nucleate on sediments grain boundaries and grow freely into pore spaces without bridging two or more particles. (2) load-bearing: Hydrate bridges neighboring grains and contributes mechanical stability to granular assembly by becoming part of the loading bearing force chain. (3) Cementation: Hydrate establish a bond on the interparticle contact points. It is to be noted that it is often difficult to control the hydrate formation, distribution, saturation, and pore habit challenges during laboratory experiments (Jung et al. 2012) . In this context, numerical simulations using DEM will provide valuable insight on the micromechanical behavior of MH sediment mixtures. This approach will be stemmed from the strict modeling of the particles at the grain scale level. The advantage of this method is that it has the flexibility in facilitating the isolation effects, the loading configurations and individual particle characteristics such as size, shape, roughness and physical properties in relation to the mechanical behaviour of the assembly. Brugada et al (2010) developed a DEM model to capture shear behavior of me-thane hydrate soil considering the pore filling distribution. It has been highlighted that hydrate contribution to the strength of the sediment is purely frictional nature. Jung et al (2012) carried out DEM simulations to explore the effects of hydrate distribution, saturation, sediment porosity, confining stress and pore habit. They concluded that mechanical properties of hydrate-bearing sediments can be expressed as function of hydrate saturation, initial porosity and effective stress. Jian et al (2013) developed a simple contact model to capture the cementing effect of methane hydrate sediment mixtures. They reported that the cohesion/cementation of hydrate bearing deposit increases with increase in hydrate saturation. In this study, the pore filling category which leads to the load bearing arrangements is considered for the DEM simulations. The effect of hydrate saturation and confining pressure on the yield envelope has been studied and reported.
DISCRETE ELEMENT METHOD
The Discrete Element Method (DEM) is an explicit finite difference program developed by Cundall and Strack (1979) . In DEM the equilibrium contact forces and displacement of a stressed assembly are computed through a series of calculations that trace the movements of the individual particles. The calculations performed in DEM alternate between the application of Newton's second law to the particles, and a force displacement (i.e. constitutive) law at the contacts (Fig.1 ). Newton's second law is used to determine the motion of each particle arising from the contact and body forces acting upon it, while the force displacement law is used to update the contact forces arising from the relative motion at each contact. (Itasca, 2004) The DEM software (e.g. TRUBAL & PFC2D & 3D) models the movement and interaction of the stressed assemblies of spherical particles. The distinct particles are displaced independently from one another and only interact at contacts or interfaces between the particles. The particles are assumed to be rigid and have negligible contact areas (contact occurs at a point), but they are, allowed to overlap at the contact points using the soft contact algorithm. PFC3D enables the investigation of features that are not easily measured in laboratory tests such as coordination numbers, inter-particle contact forces, and the distribution of normal contact vectors to be investigated, and it is also possible to compose bonded particles into agglomerates and simulate fracture when the bonds break. Hyodo et al. (2013) carried out a series of triaxial experiments on the methane hydrate bearing sand samples. The cylindrical specimen of 30mm diameter and 50 mm high was used for the testing program. Toyoura sand was selected as the MH bearing sand. Samples were prepared at an initial porosity of 0.4. The stress and temperature condition of the deep sea bed was considered to examine the mechanical behaviour of MH bearing sand. MH bearing sand was first mixed with predetermined amount of water to achieve the target MH saturation. The moist soil was then placed in a mold with each layer compacted by tamper. This specimen was then subjected to a series of process under specific temperature and pressures as shown in Fig 2. The methane gas was injected at stage (3) and the temperature was reduced to 1C where MH was stable (Fig.2) . A very high pore water pressures was then applied to the sample to consider the condition of the sea bed. More details on the sample preparation and testing procedure can be found elsewhere (e.g. Hyodo et al 2013; Hyodo et al. 2005) . A series of drained triaxial tests were then carried out to understand the behavior of MH bearing sand during shear loading. Fig. 3 shows the variation of stress ratio and volumetric strain with axial strains for samples with different percentage of MH saturation. It is evident from the figure that MH saturation has profound influence on the shear behavior of MH bearing sand. A marked increase in the initial stiffness and shear strength was observed with increase in the MH saturation. Moreover the volumetric strain changed from compressive to dilative and for S MH =53% significant dilative behaviour on the MH bearing sand has been observed. 
SHEAR BEHAVIOR OF MH BEARING SAND

Laboratory Experiments

NUMERICAL SIMULATION USING DEM
In this study, DEM simulations similar to the laboratory experiments were carried out using PFC3D. The cylindrical soil specimen similar to the size of the laboratory experiments (diameter =30mm, height = 60mm) was prepared from 7941 spherical particles. The particle size varying from 0.07 -1 mm was considered for MH bearing sand (base sand). The MH bearing sand samples were prepared at an initial porosity of 0.4. In PFC3D during sample preparation the particles were randomly located inside the container without any overlap with the existing particles. The properties used for MH bearing sand are tabulated in Table 1 . The particles were generated using radius expansion technique incorporated in PFC3D. After generation the assembly was isotropically compacted to a desired initial confining pressure ( 3 ). Then the hydrate particles were randomly generated in the pores of the sand particles. The number of particles for different saturation was determined from initial void volume. In this study, the MH particles were assumed to be of uniform spherical particles having a size 0.04 mm. The random process was repeated until the total number of specified hydrates was created to reach desired hydrate saturation. The properties assigned for the MH particles are presented in Table 1 . It was observed that the initial porosity slightly decreases with the addition of MH particles. The samples with different hydrate saturation are presented in Fig. 4 . A linear force displacement contact model was used for the simulation program. Based on the laboratory experiments, Yoneda et al. (2010) has reported that the friction angle of MH bearing sand increases with MH saturation. In this context, the contact friction angle of the assembly has been varied to capture the shear behavior for different percentage of MH saturation. A series of drained triaxial tests were then carried out by applying a constant velocity at the top and bottom platen. Results of the numerical simulation are expressed using macroscopic stress parameters such as deviator stress (q) and mean p, which are defined as follows:
Effect of MH Saturation
Fig 5 shows the variation of stress ratio (q/p) and volumetric strain with axial strain for different percentages of MH saturation at an initial confining pressure of 5 MPa. It is evident from the figure that MH saturation has significant influence on the shear behavior of sand. The stress ratio increases with the increase in the methane hydrate saturation. The stress ratio exhibit a peak value around 2% axial strain thereafter remains constant with axial strain. The volumetric strain clearly captured the dilative behavior with MH saturation. It is seen that dilation of the MH bearing sand increases with increase in the MH saturation. Qualitatively, these results are very similar to the laboratory experimental results presented by Hyodo et al. (2013) . Moreover, axial strain corresponding to the peak stress ratio also increases with confining pressure. Fig.6 also presents the variation of volumetric strain with axial strain. It is seen that the dilation decreases with the increase in confining pressure. Fig. 7 shows the variation of peak deviator stress with confining pressure for different MH saturation. It is clear from the figure that deviator stress linearly increases with confining pressure. As stated earlier, peak deviator stress increases with MH saturation. Obviously, higher confining pressure leads to higher peak deviator stress. Moreover, significant influence of MH saturation on the peak deviator stress can be observed for confining pressure greater than 3 MPa. proportional to contact force magnitude. During shear loading contact force chain are developed along the major principal stress direction. It is evident from Fig.8 that the MH particles strongly contribute toload bearing along with MH bearing sand during shear loading. The mean contact force (the average value, overall contacts with non-zero normal force) of 1.01 MN and 1.20MN was observed at =1.8% for samples S MH = 0 and S MH = 35 % respectively. In fact, the increase of mean contact force with MH saturation is indirectly reflected in the corresponding increase of deviator stress.
Peak deviator stress with confining pressure

CONCLUSIONS
This paper has presented the DEM simulation results on the shear behavior of methane hydrate bearing sand. The pore filling type distribution of MH was considered for the DEM simulation program. Laboratory experiments clearly highlight effect of saturation on the shear behavior of MH bearing sand. DEM simulations carried out on samples similar to the laboratory experiments clearly captured shear behavior similar to the laboratory. It can be concluded from DEM simulations that the deviator stress and dilation significantly increases with increase in MH saturation. Moreover, confining pressure has a significant influence on the shear behaviour of MH bearing sand. The peak deviator stress increases linearly with increase confining pressure. It was observed the MH particles also contribute toward load bearing arrangement and this may be one of the reasons for increase in deviator stress with MH.

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