Discrete Element Modelling of Metane Hydrate Soil Sediments using Elongated Soil Particles Yanxin Yu a, 1 (yanxin.yu.@alumni.ucl.ac.uk) Yi Pik Ceng a (yi.ceng@ucl.ac.uk) Xiaomin Xu b (xuxiaominzju@gmail.com) Kenici Soga b (ks0@cam.ac.uk) a. Civil, Environmental and Geomatic Engineering, Cadwick Building, University College London, Gower Street, London, WC1E BT, United Kingdom b. Geotecnical and Environmental Researc Group, Department of Engineering, University of Cambridge, Trumpington Street, Cambridge, CB 1PZ, United Kingdom ------------------------------------------------------------------------------------------------------- 1 * Corresponding autor: Yanxin Yu (yanxin.yu.@alumni.ucl.ac.uk) 1 Present address: 1. Cina Oil And Gas Group Limited, Suite 0, /F., Sino Plaza, - 1 Gloucester Road, Causeway Bay, Hong Kong 1 ------------------------------------------------------------------------------------------------------- 1 1-1 -
Abstract In tis Discrete Element Modelling researc, triaxial compression tests of particle assemblies were simulated to study te mecanical beaviour of metane ydrate sediments wit two different ydrate formation patterns: pore-filling and cementation. Te soil particles were modelled using sperical or elongated particles (two aspect ratios 1. and.0). Hydrates were modelled as smaller particles and were placed eiter inside te pores in a random manner (te pore-filling case) or around te soil particle contacts (te cementation case). Compared to te pure soil samples, te ydrates essentially influenced te mecanical beaviour of te ydrate-bearing soil samples, and te beaviours varied due to te different ydrate growt patterns. Te beaviour wit elongated soil particles is muc closer to tat of te natural ydrate-bearing sandy sediments retrieved from te Nankai Troug tan te beaviour wit sperical particles. Te observed macroscopic strengt beaviour is also explained 1 by te microscopic contact-type related contributions (soil-soil contact, soil-ydrate contact and 1 ydrate-ydrate contact) to te deviatoric stresses. 1 Keywords 1 Metane ydrate, Soil, DEM, Saturation, Particle sape, Anisotropy 1 1 1 1 - -
1. Introduction Metane ydrate develops and exists in te pores of soil sediments under deep seabeds or permafrost regions under conditions of low temperature and ig pressure. Te investigation on te geomecanical beaviour of metane ydrate bearing soils as attracted increasing interest, as metane gas is a potential energy source tat can be extracted by dissociating te ydrates in-situ from te ydrate-bearing sediments [1, ]. Among all te known ydrate distribution patterns, te most typical patterns considered for coarse grained ydrate bearing sediments are te pore-filling and te cementation patterns, as sown in Fig. 1. In te pore-filling pattern, ydrates freely grow in te pores witout connecting two or more soil particles togeter [1, ]. On te oter and, in te cementation case, ydrates nucleate at inter-granular contacts along te soil particle surface. Te existing soil skeleton structure is bonded by te ydrates, 1 wilst te soil-soil contacts are not bonded [1, ]. In bot patterns, te soil skeleton, wic as been 1 formed by consolidation under ig pressure, is not broken by te growt of ydrates inside te pores. 1 1 Fig. 1. Pore-scale ydrate distribution patterns of ydrate-bearing sediments: (a) pore-filling, (b) cementation - -
Te mecanical beaviour of ydrate-bearing soil sediments is dependent on te ydrate growt pattern, ydrate morpology and ydrate saturation [-1]. For example, two ydrate formation patterns were prepared by Masui et al. [1]: te strong bond sample (cementation pattern) and te weak bond sample (considered as te pore-filling pattern). Toyoura sand was used as te sediment sand. In bot cases, wit stiffness at 0% stress level ( E 0 ), peak strengt (maximum deviator stress) and dilation angle at peak strengt increased wit ydrate saturation; owever, te ydrate samples wit te cementation pattern indicated a greater effect of ydrate tan te ydrate samples wit te pore filling pattern. In tis paper, te Discrete Element Metod (DEM) was used to study te mecanical beaviour of te ydrate-bearing soil wit different growt patterns. DEM allows to model of te granular materials by explicitly considering teir true particulate nature [1]. Two typical types of microscopic 1 ydrate distribution patterns inside soil pores were modelled: (i) pore-filling and (ii) cementation (see 1 Fig. 1), using te discrete element code Particle Flow Code Tree Dimensions Version.0 (PFC D.0) 1 [1]. In te pore-filling model [1-1], ydrates nucleate on sediment grain boundaries and grow 1 freely into pore spaces witout bridging two or more particles togeter. In te cementation model [1, 1 1], ydrates nucleate at inter-granular contacts and te existing soil skeleton structure is cemented by 1 te ydrates, wile te soil-soil (s-s) contacts are not bonded. In most of te previous DEM studies 1 simulating te beaviour of metane ydrate soils [1-0], it was assumed tat all te soil and ydrate 1 particles were speres. However, it is well known tat te sape of soil particles as a large influence 0 on its mecanical beaviour [1, 1, ]. In tis study, elongated soil particles were used to - -
investigate te stress-strain and volumetric responses by performing a series of DEM drained triaxial compression tests, and to make a comparison between te pore-filling and cementation models wit bot sperical and elongated soil particles. A microstructure study of contact-type related contributions to te deviatoric stresses was conducted to gain insigts into te mecanical beaviour during te deformation process. DEM Sample Preparation Due to te computational limitation, te initial size of te cylindrical samples was set to. mm in eigt and 1. mm in diameter, wit an aspect ratio of. Te soil sample was initially prepared by generating,000 spere particles wit diameters ranging from 0.1mm to 0.mm (following Gaussian distribution) in a cylindrical region wit rigid frictionless walls. Tis size range followed tat of Masui et al [1], altoug te sample size was muc smaller tan a typical triaxial sample. During tis 1 assembly generation stage, te initial value of porosity and inter-particle friction are set to 0. and 1 0., respectively. Te radius expansion metod was adopted to facilitate te creation of tis initial 1 porosity during te initial sample preparation state at zero confinement. Once te DEM assembly as 1 been generated, a numerical servo-control mecanism was activated to compress te specimen to reac 1 a desired isotropic stress state (e.g. 1 MPa, MPa and MPa in tis study). 1 Considering te development of natural ydrate bearing sediments in very deep underground, it 1 is assumed tat ydrates are formed after te geostatic stresses are carried by te soil skeleton. 1 Hydrate particles were randomly generated in te void space of te consolidated soil sample, until it 0 reaces te desired ydrate saturation ( S ). Fig. sows an example of te sample preparation - -
process of te pore filling case. In tis study, te case of S = 0% was te maximum number of ydrate particles tat could be created in te void space witout breaking te soil skeleton. Te total number of soil and ydrate particles was more tan 0,000 wit a saturation of 0%. Note tat te ydrate saturation ratios reported in tis study is a lower bound approximation, due to geometric nature of te aggregates of te ydrate speres (i.e. pores created witin te aggregates). It could be easily extrapolated to a iger saturation of te natural ydrate bearing soil sediments [1]. Fig.. DEM ydrate-bearing soil samples In order to acieve a uniform distribution of te ydrate particles in te cementation case, six directions of gravitational forces were applied in stages. For a given saturation, te desired amount of ydrate particles was evenly divided into six groups. Eac of tem was ten assigned wit a certain 1 direction of gravity. Hydrate particles ten dropped along te gravity direction until tey stopped at te 1 soil-soil contacts, and ten gradually accumulated along te soil particle surfaces. It was cecked to 1 ensure tat eac ydrate particle ad made at least two contacts wit eiter soil particles or oter ydrate 1 particles [1, 1]. Once te system reaced an overall equilibrium state, all tese ydrate-soil and - -
ydrate-ydrate contacts were ten be bonded. Te process was repeated for te next group of ydrate particles wit a different gravity direction. Note tat te soil skeleton was carefully kept undisturbed during tis wole process using a special subroutine in written in te FISH commands of PFCD. Te parameters for te DEM simulations are listed in Table 1. For example, te elastic modulus of MPa was cosen for te soil particles [, ]. In tis study, te selection of Young s modulus (E) for ydrate particle is based on te ydrate-soil elastic modulus ratio, wic is defined as te ratio between te Young s modulus of ydrate particle and tat of soil particle. Brugada et al. (0) ad performed a parametric study on tis issue, and concluded tat te value of 0.1 is suitable for modelling te mecanical beaviour of metane ydrate. Similar or even lower ratio as also been used in oter references, depending on te contact model used []. Te normal contact stiffness k n was set to be proportional to te particle elastic modulus ( E ) and te particle diameter (D). Te bonding strengt c 1 was determined suc tat te cementation effect was apparent but not too strong [1, ]. 1 Property Soil Metane ydrate Particle size D (mm) (Gaussian distribution) 0.1-0. 0.0 Density (kg/m ) 00 00 Elastic Modulus E c (MPa). Normal contact stiffness k n (N/m) DE c DE c Sear contact stiffness k s (N/m) 0.k n 0.k n Inter-particle friction 0. 0. - -
Bonding strengt, B n =B s (N) x 1 Table 1: Input parameters used in te DEM model To examine te particle sape effect, eac sperical soil particle inside te consolidated specimen were replaced by elongated clump particles wit te same volume. As sown in Fig., two aspect ratios were cosen for te elongated particles: 1. (-ball clump) and.0 (-ball clump). Note tat te replacement of soil particles would alter te original soil fabric. In order to minimize tis effect, te replacement process of all soil particles was performed one after anoter, rater tan all at once. Tere was also a certain time interval between eac sub-replacement, to allow te updated system maintaining equilibrium wit a minimized disturbance. By doing so, after all te particles were replaced, te sample maintained te same void ratios under te controlled confining pressure (e.g. void ratio e of te 1 consolidated sample was 0. at 1 MPa confining pressure). Hydrate particles were ten added into te 1 soil samples using te same preparation process as mentioned above. After te sample preparation, a 1 series of properly designed undrained triaxial compression tests were conducted on te consolidated 1 samples wit ydrate particles inside te pores. - -
Fig.. Replacement of sperical soil particles by elongated clumps. Numerical simulation results After te sample preparation, a series of drained triaxial compression tests were performed at different ydrate saturations, confining pressures and wit ydrate growt patterns in te tree different particle sape samples. Te analysis was conducted and te comparisons were made..1 Stress-strain responses and stiffness Te stress-strain responses of te sperical soil model under a confining pressure of 1 MPa are illustrated in Fig. (a), as a reference. Tree different samples are sown: (a) S = 0%, (b) pore-filling model wit S = 0% and (c) cementation model wit S = 0%. Te maximum deviator stress increased wit ydrate saturation from 1. MPa (S =0%) to. MPa ( S =0%) in te pore-filling 1 model (by about 0% increase), and from 1. MPa ( S =0%) to.0 MPa ( S =0%) in te 1 cementation model (an increase of almost 00%). Tere is a ardening effect of ydrate saturation in 1 te case of bot ydrate growt patterns. However, for te same amount of increase in te ydrate - -
saturation, bot te elastic stiffness and peak strengt of te pore-filling sample were smaller tan tose of te cementation sample, sowing te significant influence of te ydrate growt pattern. Fig. (a). Comparisons of deviatoric stress as a function of axial strain between pore-filling and cementation cases at S =0% (Sperical soil model) Fig. (b). Experimental stress-strain beaviours of Metane ydrate bearing soils wit different ydrate saturations: (a) week bond samples; (b) strong bond samples (after Masui et al. [1]). - -
At large strain - critical state, te pore filling model exibited smaller sear strengt (about 0% decrease) tan te pure soil sample S =0%, as sown in Fig.. Te cementation model did not sow suc reduction (it increased by about 0%). In te pore filling model, bot soil and ydrate particles moved togeter at large strain, wit te ydrate particles involved in transmitting te main contact forces in te matrix. Te muc softer ydrate particles in te matrix weakened te overall strengt of te system. On te oter and, in te cementation model, it was observed tat some ydrate particles kept bonded wit te soil particles. Tis essentially made larger and irregular saped aggregated particles, wic led to greater sear resistance tan te sample wit sperical particles only. Te experimental data presented by Masui et al [1] is sown in Fig. (b) for comparison. A strong bond sample (cementation pattern) and a weak bond sample (normally considered as te pore-filling pattern) were prepared by Masui et al. (00) in teir syntetic metane ydrate 1 specimens. Te sediment sand is Toyoura sand. Te triaxial compression test results under te initial 1 isotropic effective confining stress of 1 MPa for te strong bond samples and te weak bond samples 1 are sown in Figure. Te constant searing rate was 0.1%/min under drained conditions. Te peak 1 strengt increased wit te ydrate saturation. In Figure (a) for te strong bond model, te peak 1 strengt increase began even at a low ydrate saturation; wile in Figure (b) for te weak bond 1 model, te obvious increase in peak strengt started from S =.%. And at te same saturation, te 1 stiffness and peak strengt of te strong bond case sowed a iger value tan tose of te weak bond 1 case. In addition, at te large strain, te iger saturation samples of te weak bond case exibited a 0 lower strengt tan te relatively lower saturation sample; wile te strong bond model did not sow - -
tis penomenon obviously. It is possible tat, due to te existing weak bonding between te particles in te weak bond samples, te residual strengt of ig saturation samples was still larger tan te S =.% sample. Altoug tis observation does not coincide exactly wit te caracteristics of te DEM pore-filling model, te simulation results are qualitatively comparable beaviour wit te experimental data. Fig. (a) sows te stress-strain relationsips of tree samples of different particle sapes wen tere is no ydrate. Fig. (b) illustrates te degradation of te secant Young s modulus E sec as a function of te axial strain of te tree samples. Bot stiffness and strengt increased wit te increase in aspect ratio. Te initial stiffness increased dramatically from about MPa in te spererical soil sample to 1 MPa in te -ball clump soil sample, an increase of around 1%. Peak strengt increased by about 0% from te spere soil sample to te -ball clump soil sample. Te critical 1 state strengt increased wit te increase in aspect ratio as well (by about 0%). 1 1 (a) Deviatoric stress (b) Degradation of secant Young s modulus - 1 -
Fig.. Deviatoric stress and degradation of secant Young s modulus as a function of axial strain of tree soil models ( S =0%) Fig. sows te stress-strain relationsips of different ydrate saturation samples for a given particle sape (Fig. a for ball clamp and Fig. b for ball clamp). Results suggest tat te ydrate-bearing samples wit elongated particles exibited a similar trend in te mecanical response to te samples wit sperical particles, as sown in Fig. at te peak state. Fig. sows te effect of particle sapes on te stress-strain relationsips for a given ydrate growt pattern. In bot te pore-filling model and te cementation model, te stiffness and peak strengt of te ydrate-bearing soil samples (at S =0%) only sligtly increased wit te increasing aspect ratio of te soil particles. Tis percentage increase was not as evident as te no-ydrate case (see Fig. ). Tis was because te ydrate particles in te pores greatly dominated te beaviour at te peak state. 1 Fig. (a) also sows tat, wen comparing te cases wit te same 0% ydrate saturation, te 1 critical state strengts of te pore-filling models wit different saped soil particles were almost te 1 same. Tis suggests tat te soft ydrate particles are totally dominating te beaviour at te critical 1 state, removing all te sape effect of te soil particles. In te cementation model (Fig. (b)), on te 1 oter and, te critical state strengts were not te same. Tis indicates tat te soil particles are still 1 contributing to te critical state sear resistance even under te influence of ydrate particles in te 1 cementation samples. As sown in Fig., tere is now no obvious increase in te critical state 1 strengt wit te cementation models wen te soil particles became elongated. Tis revealed two 0 compensating penomena. Wen te soft ydrate particles lost te bonded contacts, tey were easier - 1 -
to be involved in te searing wen soil particles were more elongated. However, due to te large number of remaining bonded ydrate particles, te critical state skeleton of te cementation model was still iger tan tat of te pore-filling model. (a) -ball clump (aspect ratio 1.) (b) -ball clump (aspect ratio.0) Fig. Comparisons of deviatoric stress as a function of axial strain between pore-filling and cementation samples at S =0% (elongated soil particles at aspect ratios 1. and.0) (a) Pore-filling S =0% (b) Cementation S =0% - 1 -
Fig.. Comparisons of deviatoric stress as a function of axial strain of tree soil models at S =0%: (a) pore-filling model, (b) cementation model Te degradation curves of secant Young s modulus of te tree soil models ( S = 0%) are plotted in Fig. (a) and (b). Fig. (a) sows tat, in te pore-filling samples wit elongated soil particles, te increases of te initial stiffness (axial strain = 0.1%) from tat of te samples wit sperical soil particles were % (-ball clump) and % (-ball clump). Similarly, in te cementation samples as sown in Fig. (b), te increases were 1% (-ball clump) and % (-ball clump). After adding many ydrate particles to te elongated soil particle samples, te extra increase in te stiffness due to te added ydrate particles was not as evident as te increase in stiffness due to a cange in te sape of pure soil particles (Fig. (b)). Tus, te sape of soil particles ad more influence on stiffness tan te ydrate saturation. Tese suggested tat: (1) stiffness generally increased wit 1 ydrate saturation regardless of te soil particle sape; and () te cementation model exibited a 1 similar effect on stiffness compared to te pore filling model in terms of te initial stiffness at ig 1 ydrate saturation (please see Yu et al, 01 for furter detail), wereas te sape of te soil particles 1 significantly governed te magnitude of stiffness. Terefore te DEM simulations wit elongated 1 ydrate-bearing soil samples compared better to te stiffness values of te syntetic samples in te 1 experimental study of Masui et al. [1]. Furter researc is required to obtain a quantitatively 1 comparable model, for example, on factors suc as te input contact stiffness values of te soil 1 particles and of te ydrate particles, or te sape and morpology of te ydrate particles. - 1 -
(a) Pore-filling S =0% (b) Cementation S =0% Fig.. Degradation of secant Young s modulus te tree ydrate-bearing soil models ( S = 0%) Te comparative impact of te tree soil particle sape models wit two different ydrate growt patterns can be seen more clearly in Fig., as te mid-strain stiffness E 0 is plotted against various ydrate saturations. Fig. suggests tat: (1) Te iger aspect ratio of soil particles, te iger te mid-strain stiffness E 0, especially wen te aspect ratio was.0 (around 0% increase); () E0 increased wit ydrate saturation, te rate of stiffness increase was iger wen te saturation was iger. Tis trend of increase were similar regardless of soil particle sapes; () at te same ydrate saturation, E 0 of te cementation model was always iger tan tat of te pore-filling model. Te increase in E 0 of te pore-filling models became more apparent only wen ydrate saturation was 1 iger tan 0%, wile te increase in te stiffness of te cementation models started to increase 1 immediately wit ydrate saturation. But tere was an exception wen te soil particles ad a ig 1 aspect ratio of.0, were E 0 of te pore-filling model increased even wen te saturation was low. - 1 -
Tis migt be due to a cange in te sape of te pores wit elongated soil particles, making it easier for te ydrate particles to contribute to te increase in stiffness even at lower ydrate saturation. Fig.. Mid-strain stiffness E 0 at various ydrate saturations of tree soil particle model. Strengt Te comparative peak strengt q max (maximum deviatoric stress) against ydrate saturation was plotted in Fig.. Te peak strengt increased wit te aspect ratio in bot ydrate-bearing models. As ydrate saturation increased, ydrate particles in te pores played an essential role in sear resistance. As discussed before, te ydrate particles in te pores contributed significantly to te mecanical beaviours. Te increased aspect ratio of soil particles did not alter te influence of te ydrate particles, but te ydrate particles did strengten te matrices of te ydrate-bearing soil 1 samples in a similar manner regardless of te soil particles sape. - 1 -
Fig.. Peak strengt of tree soil models Te critical state strengt q cs sowed a different trend to te peak strengt, as sown in Fig.. Te impact of te compensating effect between te soil particle sape and te pore-filled ydrate particles in te cementation model can be seen more clearly in tis comparative Figure. In te pore-filling model, te critical state strengt decreased wit te increasing ydrate saturation. Tis was due to te involvement of te softer ydrate particles in te soil matrix at critical state. In te cementation model wit a low ydrate saturation of %, te critical state strengts were lower tan tose of ydrate-free soil sediments, and tose of te cementation models were always similar to tose of te pore-filling models regardless of particle sape. Tis suggested tat most of te inter-particle bonds of te ydrate particles broke, so te ydrate particles moved freely wit te soil particles 1 making te system similar to tat of te pore-filling cases. However, in te cementation model wit a 1 iger ydrate saturation, te critical state strengts increased wit ydrate saturation, as tere were 1 an increasing number of bonded contacts in te systems. For soil particles wit a lower aspect ratio, 1 te cementation effect was more dominant at te igest ydrate saturation. For soil particle wit a - 1 -
ig aspect ratio effect, te critical state strengt of te cementation model could still be similar to tat of te ydrate-free samples. Tis implies tat it was easier to break te cementation bonding in te elongated samples tan in te sperical soil sample. An example of bond breakage data is sown in section.. Fig.. Critical state strengt of tree soil models. Coesion and friction Te friction angle and coesion of samples wit a given ydrate saturation could be obtained by plotting te failure envelopes for te triaxial simulations under various confining pressures from 1- MPa (see Yu, 01). Te coesion values obtained from te failure envelopes were plotted against te ydrate saturations of te tree soil models in Fig. 1, and te friction angles (slope of te envelope) 1 were plotted against te ydrate saturation in Fig. 1. - 1 -
(a) Aspect Ratio 1.0 (b) Aspect Ratio 1. - 0 -
(c) Aspect Ratio.0 Fig. 1. Coesions of tree soil models Firstly, it is found (in Fig. 1) tat, by comparing te pore-filling model and te cementation model, te only contribution to te increase in te coesion was te bonding between ydrates and oter particles (ydrates and soils). Tus, te coesion values were zero for all te cases of te pore-filling model. Secondly, due to te increasing amount of bond breakage during searing, te coesion at te peak state was always iger tan tat of te critical state in te cementation model, wic was more significant at a iger saturation. Tirdly, at te same saturation, te peak state coesion increased as te soil particles were more elongated; owever, te aspect ratio of te soil particles did not cange te critical state coesion. In order to reduce from a iger peak coesion to a 1 similar critical state coesion, tere must be more breakage of te cementation bonding to samples 1 wit iger soil aspect ratio. Tis is consistent wit te pysical explanation given in te previous 1 section. - 1 -
(a) Aspect Ratio 1.0 (b) Aspect Ratio 1. - -
(c) Aspect Ratio.0 Fig. 1. Angles of friction of tree soil models Fig. 1 sows tat te peak friction angle of te S =0% sample evidently increases wit te aspect ratio. However, as te aspect ratio increased, te increase in te friction angles wit ydrate saturation became less obvious. Wen te aspect ratio was 1.0, te peak friction angle of te cementation model was larger tan tat of te pore-filling model. However, wen te aspect ratio was 1., te friction angle of te cementation model was similar to tat of te pore-filling model. In addition, wen te aspect ratio was.0, te friction angle of te cementation model was sligtly smaller tan tat of te pore-filling model. All tese are due to te coesion development wic resulted in a lower apparent friction. Tis is similar to te observation given by Waite et al. (00) 1 stating tat friction angle is largely independent of ydrate saturation. Hence, te simulation results - -
wit elongated soil particles reproduced a closer matc to te mecanical response of te natural sediments. Te critical states frictions owever sowed similar trends as te critical state strengt.. Volumetric responses Under te confining pressure of 1 MPa, te volumetric strain against axial strain relationsips are illustrated in Fig. 1. Fig. 1(a) sows te volumetric responses of sperical soil models: (1) S = 0%, () pore-filling model wit S = 0% and () cementation model wit S = 0%, corresponding to te stress-strain responses sown in Fig. (a). Te sediments initially sowed elastic contractive beaviour ten followed by a dilation. Te peak contractive value in te pore-filling model were similar to tat in te pure soil sample, wereas tat in te cementation model was larger due to a large number of bonding contacts wit te soft ydrate particles. Wen particles started to move relative to one anoter, dilation appened. Bot pore-filling and cementation ydrates caused a larger dilation 1 compared to te pure soil sample. Te rate of dilation of te cementation model was greater tan tat 1 of te pore filling model, meaning cementation enanced dilation. Te volumetric responses of te 1 tree ydrate-free soil samples, corresponding to te data sown in Fig., are illustrated in Fig. 1(b). 1 Te rate of dilatancy increases wit soil elongation. Te increased dilatancy rate also extended to 1 iger axial strain wen te soil particles were elongated, resulting in a iger critical state volume. - -
(a) Sperical soil model (b) Tree kinds of soil models Fig. 1. Volumetric response volumetric strain as a function of axial strain: (a) sperical soil model; (b) tree kinds of soil models ( S =0%) Fig. 1 sows tat te increase in te ydrate saturation enanced te dilative caracteristics of te ydrate-bearing sediments, and te increase was more obvious wen te saturation was iger. However, unlike te ydrate-free soil models (Fig. 1), te angle of dilation of te ydrate-bearing samples wit elongated soil particles (especially wit very ig ydrate saturation) was lower tan tat of te samples wit sperical soil particles. Tis implies tat searing of samples wit elongated soil particles triggers more bonding breakage tan tose wit sperical soil samples. In addition, for te pore-filling model, te angles of dilation for te cases wit ydrate saturation iger tan % 1 were very similar, sowing a relatively insignificant impact of te soil particle sape in tis model. 1 Tese findings suggest again tat te dilation was affected by several factors including (1) te ydrate 1 saturation, () te cementation bonds between particles, and () te soil particle sape. Hydrate - -
saturation effect in te pore-filling cases are more dominant tan te particle sape effect. Te particle sape effect is more apparent to te cementation model especially wen te ydrate saturation is ig. Fig. 1. Dilation angle as a function of ydrate saturation at different aspect ratios Te critical state granular void ratio e ln p projections were plotted in Fig. 1. Te granular void ratio is defined as te void ratio of te pores created by te soil particles after te ydrate particles are removed. It can be seen tat, in bot pore-filling and cementation models, te critical state granular void ratios of te elongated soil models were larger tan tose seen in te sperical soil model. In all te tree soil models, te ydrate effects on dilation produced iger critical state void ratios as te saturation increased. It is also suggested tat te ydrate-induced dilatancy was less evident at a ig confining pressure. As te confining pressure increased, te dilation caracteristic 1 tended to diminis in te pore-filling model. Te dilation beaviour was also weakened by te 1 confining pressure in te cementation model, altoug due to te remaining unbroken bonds it could 1 not be similar to te pore-filling cases. - -
(a) Pore-filling Aspect Ratio 1.0 (b) Cementation Aspect Ratio 1.0 (c) Pore-filling Aspect Ratio 1. (d) Cementation Aspect Ratio 1. (e) Pore-filling Aspect Ratio.0 (f) Cementation Aspect Ratio.0 Fig. 1. Critical State Line projection on Granular Void Ratio e ln p plane - -
. Bond Breakage Since te macroscopic data implies tat searing of samples wit elongated soil particles potentially triggers more bonding breakage tan tose wit sperical soil samples. Hence, an example of breakage data is sown in Fig. 1, wic consists of a comparison between te sperical soil sample and te elongated soil samples at S =0%. Tis is a typical saturation wit relatively ig number of ydrate particles bonding contacts, but allowing te freed ydrate particles to move in te pore space. Altoug te number of te contact bond breakage was very small in te initial state, it was evident tat bond breakage began to appen just after te elastic pase, and te percentage of bond breakage in total bonds increased steadily. Te percentages of bond breakage of te elongated soil samples were evidently larger tan tat of te sperical soil sample. 1 Fig. 1. Bond Breakage in te triaxial test of cementation model at S =0% 1 Discussions - -
Te abovementioned sections ave illustrated tat te macroscopic mecanical beaviour of metane ydrate sediments is igly dependent on ydrate distribution patterns, soil particle sape and ydrate saturation, from te initial state, peak state and towards to te critical state. Wit te elongated soil particles, te overall mecanical beaviour was found to be muc closer to te experimental results wit real metane ydrate sediments. Fundamentally, te elongated soil particles could form a more complex microstructure providing a iger searing resistance and experience a more complicated microstructure evolution process, comparing to te one wit spere soil particles. Te overall stress tensor can be decomposed into a number of contact-type related stress tensors, as well as te deviatoric stress []. For te metane ydrate bearing soils, tere are tree contact-type related contributions from: (1) te soil-soil (s-s) contacts; () te ydrate-soil (-s) contacts, and () te ydrate-ydrate (-) contacts. Herein, we attempted to study te micromecanics of different 1 caracteristics of deviatoric stress evolutions, as sown in Fig. and Fig., by investigating tese 1 contact-type related contributions. 1 1 Fig. 1 and Fig. 1 present te contact-type related contributions to te peak deviatoric stress ( q max ) and te deviatoric stress at critical state ( q cs ), respectively, for bot porefilling and 1 cementation cases wit spere soil particles. Te results sow tat te contributions of tree-type 1 contacts to te overall mecanical beaviour of ydrate bearing sediments depend largely on its 1 growt pattern and te trend observed in te peak strengt is different from tat in te critical state 1 strengt. At te peak state, Fig. 1(a) sows tat, for te pore-filling model, te contribution from all 0 tree types of contact increase wit te increasing of ydrate saturation. For example, te - -
contributions from s-s, -s and - contacts are 1.1MPa, 0.01MPa and.e-mpa at 0% ydrate saturation, and.0mpa, 0.1MPa and 0.01MPa at 0% ydrate saturation, respectively. In te cementation case, tere is a similar, yet muc stronger increasing trend, as sown in Fig. 1(b). Te contributions from s-s, -s and - contacts are.01mpa, 0.MPa and 0.00MPa at 0% ydrate saturation, and.1mpa, 0.MPa and 0.0MPa at 0% ydrate saturation, respectively. Interestingly, for bot pore-filling and cementation cases, te combined contributions from - and -s contacts remain in a relative low levels, wit te maximum values of 0.MPa and 0.MPa at S 0%, respectively. Tis implies tat te increases of q max in bot models are mainly due to te enancement of te interaction between soil-soil particles, rater tan te ydrate bonding effect. Fig. 1. Contribution of tree-type contacts to te peak deviatoric stress 1 At te critical state of te pore-filling model, as sown in Fig. 1(a), te contributions from te 1 s-s contacts reduce significantly wen ydrate saturation increases. At 0% and 0% ydrate 1 saturations, contributions from s-s, -s and - contacts are 0.1MPa, 0.0MPa and.0e-mpa, 1 and 0.MPa, 0.1MPa and 0.00MPa, respectively. Tese sow tat, at large deformation, te - 0 -
existence of a larger number of softer ydrate particles significantly reduced te contribution of te s-s contacts, wic is te major contribution to te deviatoric stress. For te cementation case, te contributions from te s-s contacts remain approximately constantly, wit 0.0MPa at 0% ydrate saturation and 0.1MPa at 0% ydrate saturation, respectively. Fig. 1. Contribution of tree-type contacts to te deviatoric stress at critical state Fig.s 0- present te effect of soil particle sape on q max and q cs for bot porefilling and cementation cases. For te pore-filling cases wit elongated soil particles, as sown in Fig. 0, te contribution of s-s contacts to q max remains approximately te same as te ydrate saturation increases, wen comparing te same soil particle sape model. At 0% ydrate saturation, te contribution of s-s contacts to q max increases significantly wit te increasing of soil particle aspect 1 ratio, wit 1.MPa,.0MPa and.mpa for spere particle, -ball clump and -ball clump 1 models, respectively. However, at 0% ydrate saturation, te effect of soil particle sape becomes 1 less pronounced, wit.0mpa,.mpa and.0mpa for spere particle, -ball clump and 1 -ball clump models, respectively. Te steady increasing in q max wit ydrate saturation is purely - 1 -
due to te added contributions from te -s and - contacts, wit 0.MPa, 0.MPa and 0.MPa for spere particle, -ball clump and -ball clump models ( S =0%), respectively. For te cementation case, as plotted in Fig. 1, te contribution of s-s contacts to q max increases significantly as te ydrate saturation increases for all tree cases wit different soil particle sape. However, te effect of soil particle sape on s-s contribution becomes less remarkable wen te ydrate saturation increases. For example, te s-s contributions for spere particle, -ball clump and -ball clump models are.01mpa,.mpa and.1mpa at 0% ydrate saturation, and.1mpa,.0mpa and.0mpa at 0% ydrate saturation, respectively. Fig. 0. Particle sape effect on te peak deviatoric stress (pore-filling case) - -
Fig. 1. Particle sape effect on te peak deviatoric stress (cementation case) Fig. and Fig. sow te effect of particle sape on te deviatoric stress at critical state. For bot pore-filling and cementation cases, te s-s contact contribution to q cs decreases wit te increase of ydrate saturation. Te iger soil particle aspect ratio, te greater te reduction. For instance, in te pore-filling case, te contributions from te s-s contacts at te critical state reduce from 1.01MPa, 1.1MPa and. at 0% ydrate saturation, to 0.1MPa, 0.MPa and 0.MPa at 0% ydrate saturation for spere particle, -ball clump and -ball clump models, respectively, as sown in Fig.. Interestingly, te latter is muc lower tan te ones in te cementation models, as sown in Fig., wit 0.MPa, 0.1MPa and 1.0MPa, respectively. Tese indicate tat, at large deformation, te existence of a larger number softer ydrate particle in te 1 cementation model plays a better role in preserving te soil particle structure tan tat in te 1 pore-filling model. - -
Fig.. Particle sape effect on te critical state deviatoric stress (pore-filling case) Fig.. Particle sape effect on te critical state deviatoric stress (cementation case) Te results sow tat te contributions of ydrates to te overall mecanical beaviour of ydrate bearing sediments depend largely on its growt pattern and te trend observed in te peak strengt is different from tat in te critical state strengt. For te peak strengt, ydrates gives pure additional strengt increment to te original soil strengt (soil-soil contact) in te pore filling case. In te cementation case, owever, te presence of ydrates not only adds strengt by its ydrate-soil - -
contact, but also enances te existing soil strengt (soil-soil contact), magnifying te effect of ydrates on te peak strengt. Tis is because te sape of ydrate bonded soil particles become irregular and bigger, wic leads to increase in dilatancy and peak strengt. At te critical state, many ydrate particles move around te soil voids by large deformation and start to interact more directly to soil particles. In te pore filling case, te presence of ydrates makes its critical strengt to decrease because free moving small ydrate particles move in between large soil particles by large deformation and teir soft nature contributes to te overall strengt. In te cementation case, owever, te effect of ydrates is more complex. Te detaced ydrate particles make te soil softer as discussed before. But te sape of te ydrate bonded soil particles also becomes irregular and tey are aggregated, making te soil stronger. Te two compensating effects create complex strengt variation wit ydrate saturation as sown in Fig.s 1 and. In tis study, 1 te ydrates are modelled as small particles. In reality, tey can disintegrate into even smaller 1 particles by searing. Hence, furter work is needed to understand te contribution of ydrates and 1 teir disintegration as searing continues. 1 1 - -
Conclusions In tis paper, te Discrete Element Metod (DEM) was employed to provide some insigts into te macro- and micro- mecanical beaviour of ydrate-bearing sediments wit two different ydrate distribution patterns: pore-filling and cementation. Te soil particles were modelled separately using sperical particles or elongated clumps wit two different aspect ratios, in order to investigate te influence of te soil particle sape effect on te mecanical beaviour of ydrate-bearing sediments. A series of drained triaxial compression tests were performed to study te effects of soil particle sape, ydrate saturation ( S ) and ydrate growt. Te effect of soil particle sape on te overall mecanical beaviour of ydrate sediments was found to be significant. Altoug te trends on increasing stiffness and strengt wit ydrate saturation were similar among different particle sapes, te magnitudes of stiffness and strengt were 1 greater in samples wit elongate soil particles tan in tose wit sperical particles. Te values 1 obtained from elongated soil particles gave closer matc to te experimental results reported by Masui 1 et al. (00). 1 Te ydrates not only strengtened te sediments skeleton in te initial and peak states, but also 1 induced te softening beavior in te critical state as te softer ydrates moved into te soil matrix. 1 Meanwile, te ydrate growt patterns greatly influenced te ydrate-bearing soil sediments. For te 1 pore-filling models, te soft ydrate particles totally dominated te beaviour of te critical state, 1 removing all te sape effect of te soil particles. Te cementation ydrate particles induced larger - -
stiffness and strengt tan te pore-filling ydrates. However te sape of te soil particles was still contributing to te critical state strengt given te great influence of te ydrate particles. Tis is due to te two contrasting penomena. Wen te soft ydrate particles lost te bonded contacts, it was easier for tem to be involved in te searing wen soil particles were more elongated. However, due to te large number of remaining bonded ydrate particles, te critical state skeleton of te cementation model was still iger tan tat of te pore-filling model. In general, te ydrate saturation effect in te pore-filling cases were more dominant tan te particle sape effect, wereas te particle sape effect was more apparent to te cementation model especially wen te ydrate saturation was ig. Acknowledgement Tis researc work was conducted under te collaboration between University College London (UCL) 1 and University of Cambridge during te period from 0 to 01. Te first autor would like to 1 tank te Ministry of Education of Cina, te UK Government Department for Business, Innovation 1 and Skills (BIS) and University College London (UCL), for te UK-Cina Scolarsips for 1 Excellence and all teir oter generous financial supports. 1 Reference 1 [1] Soga, K. & Lee, S.L. & Ng, M.Y.A. & Klar, A. 00. Caracterisation and engineering properties 1 of metane ydrate soils. Caracterisation and Engineering Properties of Natural Soils, Taylor and 1 Francis, Vol., pp.1-. - -
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