不同开采方法下深海能源土离散元模拟

天然气水合物以胶结及孔隙填充等形式存在于深海能源土中,开采时因其分解会劣化地层力学特性进而引发海底事故,使得人们对能源土开采过程进行中力学特性的变化愈发重视。在前期室内试验的基础上,将一个温度-水压-力学二维微观胶结模型引入离散元商业软件PFC2D中,通过对排气、排水性较好的土体进行升温及降压法开采进行数值模拟,并将模拟结果与相同条件下的室内试验结果对比,验证了该胶结模型的适用性。进一步分析了颗粒接触分布与颗粒平均纯转动率（averaged pure rotation rate, APR）在水合物分解时的变化情况。升温分解过程中随温度升高,颗粒总接触分布各向异性程度增大;胶结接触逐渐减少并始终保持主方向为水平方向,无胶结接触增多并始终保持主方向为竖直方向;APR值逐渐增大且正负值分布逐渐趋于集中。降压分解过程中随反（水）压降低,颗粒总接触由各向同性分布逐渐发展为主方向为竖直方向的各向异性,APR值较小且分布均匀;恢复反压后,试样进一步破坏,颗粒总接触各向异性更加明显,APR值增大且正负值呈集中分布。     

孔隙填充型能源土的宏微观力学特性真三轴试验离散元分析

天然气水合物沉积物因其作为绿色新型能源且具有广阔的开发前景而备受全球瞩目。水合物在水合物沉积物（俗称能源土试样）中有不同的赋存型式,如孔隙填充型和胶结型等。针对孔隙填充型水合物的赋存形态,生成特定饱和度的能源土试样。开展了同一 平面上不同中主应力系数（b = 0、0.25、0.50、0.75、1.00）的真三轴排水试验的三维离散元模拟,将微观参数接触组构及剪切滑移率的演化规律与材料的宏观力学响应相结合,分析了中主应力对孔隙填充型能源土的宏微观力学响应的影响。结果表明：强接触处组构张量的大、中、小主值随b的变化规律与大、中、小主应力及大、中、小主应变随b的变化规律表现出良好的相关性。三向应力状态下的破坏强度接近Lade-Duncan破坏准则。能源土试样剪切滑移率随着中主应力系数的增大而增大;当处于三轴拉伸状态时,试样的剪切滑移率最大。     

考虑水合物胶结厚度的深海能源土粒间胶结模型研究

天然气水合物被公认是解决当前能源危机的潜在新型能源而备受关注。含水合物的海底土体称为深海能源土。水合物在能源土中有不同的赋存形式（如填充型水合物和胶结型水合物等）,由于胶结型水合物对整体强度的贡献比其他存在形式更大,尤其是饱和度较低的情况。针对于胶结型水合物的赋存形式进行研究,水合物作为胶结物质存在于土颗粒之间,胶结厚度会在一定范围内变化。为真实地反映此现象,通过对能源土试样的电镜扫描图片整理分析,获得水合物饱和度与粒间胶结厚度的函数关系。基于前期已经完成的不同粒间胶结厚度下胶结力学特性的试验研究成果,为探究胶结厚度变化对能源土体宏观力学特性的影响,建立了考虑水合物胶结厚度的能源土粒间胶结模型,并介绍此模型中相关胶结参数及其确定方法。     

DEM simulations of methane hydrate exploitation by thermal recovery and depressurization methods

Methane hydrate (MH, also called fiery ice) exists in forms of pore filling, cementing and load-bearing skeleton in the methane hydrate bearing sediment (MHBS) and affects its mechanical behavior greatly. To study the changes of macro-scale and micro-scale mechanical behaviors of MHBS during exploitation by thermal recovery and depressurization methods, a novel 2D thermo-hydro-mechanical bonded contact model was proposed and implemented into a platform of distinct element method (DEM), PFC2D. MHBS samples were first biaxially compressed to different deviator stress levels to model different in-situ stress conditions. With the deviator stress maintained at constant, the temperature was then raised to simulate the thermal recovery process or the pore water pressure (i.e. confining pressure for MH bond) was decreased to simulate the depressurization process. DEM simulation results showed that: during exploitation, the axial strain increased with the increase of temperature (in the thermal recovery method) or decrease of pore water pressure (in the depressurization method); sample collapsed during MH dissociation if the deviator stress applied was larger than the compression strength of a pure host sand sample; sample experienced volume contraction but its void ratio was slightly larger than the pure host sand sample at the same axial strain throughout the test. By comparison with the laboratory test results, the new model was validated to be capable of reproducing the exploitation process by thermal recovery and depressurization methods. In addition, some micro-scale parameters, such as contact distribution, bond distribution, and averaged pure rotation rate, were also analyzed to investigate their relationships with the macroscopic responses.     

A densification mechanism to model the mechanical effect of methane hydrates in sandy sediments

Recent pore-scale observations and geomechanical investigations suggest the lack of true cohesion in methane hydrate-bearing sediments (MHBSs) and propose that their mechanical behavior is governed by kinematic constrictions at pore-scale. This paper presents a constitutive model for MHBS, which does not rely on physical bonding between hydrate crystals and sediment grains but on the densification effect that pore invasion with hydrate has on the sediment mechanical properties. The Hydrate-CASM extends the critical state model Clay and Sand Model (CASM) by implementing the subloading surface model and introducing the densification mechanism. The model suggests that the decrease of the sediment available void volume during hydrate formation stiffens its structure and has a similar mechanical effect as the increase of sediment density. In particular, the model attributes stress-strain changes observed in MHBS to the variations in sediment available void volume with hydrate saturation and its consequent effect on isotropic yield stress and swelling line slope. The model performance is examined against published experimental data from drained triaxial tests performed at different confining stress and with distinct hydrate saturation and morphology. Overall, the simulations capture the influence of hydrate saturation in both the magnitude and trend of the stiffness, shear strength, and volumetric response of synthetic MHBS. The results are validated against those obtained from previous mechanical models for MHBS that examine the same experimental data. The Hydrate-CASM performs similarly to previous models, but its formulation only requires one hydrate-related empirical parameter to express changes in the sediment elastic stiffness with hydrate saturation.     

A state-dependent critical state model for methane hydrate-bearing sand

Methane hydrate exists in the pores of methane hydrate-bearing sand (MHBS) and is considered to be a potentially significant source of methane and thus energy for mankind. However, before conducting a large-scale extraction of methane from MHBS, it is crucial to simulate the mechanical behaviour of MHBS and evaluate its stability during drilling and methane production. In this paper, a state-dependent critical state model for MHBS is presented. The critical state of MHBS is discussed, and critical state line formulations are introduced as functions of hydrate saturation. A simple nonlinear bonding and linear debonding law is incorporated considering the cementing mechanism of hydrate. A modified state-dependent dilatancy is proposed to account for the effects of stress level, internal state (density), bonding strength and hydrate saturation. Determination of the model parameters is described in detail. The proposed model is employed to predict results of drained triaxial compression tests on MHBS. Satisfactory performance is demonstrated, i.e., the model can adequately capture the stress–strain and volume change behaviours of MHBS over a wide range of hydrate saturations, confining pressures and densities using a unified set of parameters.     

Study of mechanical behavior and strain localization of methane hydrate bearing sediments with different saturations by a new DEM model

This paper presents a numerical investigation into mechanical behavior and strain localization in methane hydrate (MH) bearing sediments using the distinct element method (DEM). Based on the results of a series of laboratory tests on the bonded granules idealized by two glued aluminum rods and the available experimental data of methane hydrate samples, a pressure and temperature dependent bond contact model was proposed and implemented into a two-dimensional (2D) DEM code. This 2D DEM code was then used to numerically carry out a series of biaxial compression tests on the MH samples with different methane hydrate saturations, whose results were then compared with the experimental data obtained by Masui et al. [9]. In addition, stress, strain, void ratio and velocity fields, the distributions of bond breakage and averaged pure rotation rate (APR) as well as the evolution of strain localization were examined to investigate the relationships between micromechanical variables and macromechanical responses in the DEM MH samples. The numerical results show that: (1) the shear strength increases as methane hydrate saturation S_MH increases, which is in good agreement with the experimental observation; (2) the strain localization in all the DEM MH samples develops with onset of inhomogeneity of void ratio, velocity, strain, APR, and distortion of stress fields and contact force chains; and (3) the methane hydrate saturation affects the type of strain localization, with one shear band developed in the case of 40.9% and 67.8% methane saturation samples, and two shear bands formed for 50.1% methane saturation sample.     

一个深海能源土弹塑性本构模型

天然气水合物赋存在低温高压环境中,会在土颗粒间形成胶结从而增大深海能源土抗剪强度。基于损伤力学理论,将结构性砂土本构模型推广应用于深海能源土分析中,模拟计算了三轴固结排水剪切试验,再根据应力-应变曲线关系定量反演初始屈服系数与水合物饱和度之间的函数关系,并修正了原有的结构性砂土破损规律,建立了深海能源土弹塑性本构模型。另外,根据该模型模拟了另外一组深海能源土三轴剪切试验和等向固结压缩试验。计算结果表明：新建立的深海能源土本构模型可以有效模拟深海能源土剪切强度随水合物饱和度之间的增长关系;随着水合物饱和度的增加,三轴压缩试验中深海能源土峰值强度及割线模量(E50)逐渐增加,等向固结压缩试验中屈服强度增加,与试验结果有较好的一致性,表明了该模型的合理性。     

三维离散元单轴试验模拟甲烷水合物宏观三轴强度特性

填充型水合物的砂性能源土试样可视为特殊的散粒体材料,即砂粒和水合物颗粒混合物,具有明显的非连续特征。为研究填充型水合物的能源土力学特性,初步探索了甲烷水合物在不同温度、反压条件下加荷模式的离散元模拟方法。离散元模拟中,将水合物块体视为由大量颗粒通过强胶结作用凝聚而成的整体,室内试验中的内部孔隙水压作用转化为水合物颗粒间的胶结力,故需要合理确定颗粒间胶结模型参数来实现反压的影响作用。通过参数反演建立了宏观强度、刚度参数与平行胶结模型的微观胶结参数间的宏、微观关系,基于已有室内甲烷水合物三轴试验资料,确定了给定温度和反压条件下的微观胶结参数取值,随后进行离散元单轴压缩试验。离散元单轴压缩试验模拟获得的水合物强度特性,与室内三轴试验结果符合较好;通过建立的宏、微观参数间的关系,实现了不同温度、反压下的水合物加荷模式的模拟。为进一步提出深海能源土离散元数值试验成样方法--孔隙填充水合物生成技术,形成含填充型水合物的能源土试样,研究其力学和变形特性奠定基础。     

Characterization of clastic rock using a biconcave bond model of DEM

This paper presents a biconcave bond model to investigate the effect of the cementation between grains on the mechanical behavior of rock. The proposed model considers the shape of the bonds among particles that have a biconcave cement form, based on observations of microscopic rock images. The general equations of the proposed model are based on Dvorkin theory. The accuracy and efficiency of the bond model is improved in three ways. After the biconcave bond model is implemented in the discrete element method software Particle Flow Code in 2 Dimensions, a series of numerical uniaxial compression tests were performed to investigate the relationships between the micro‐ to macro‐parameters. The simulations revealed that the biconcave bond model reflects the effect of micro‐parameters, such as the elastic modulus and Poisson's ratio of the cement, on the macroscopic deformation of cemented granular material. Variations in the bond geometry caused extremely diverse macro‐mechanical behaviors. Experimental results concerning rock demonstrate that the biconcave bond model accurately captures the mechanical behavior of intact rock and supports an innovative method for investigating the relationships between the micro‐ and macro‐parameters of cemented granular material. Copyright © 2016 John Wiley & Sons, Ltd.     

Size-dependent mechanical behavior of an intergranular bond revealed by an analytical model

The size of intergranular bonds significantly affects the macroscopic mechanical properties of geomaterials. A size-dependent bond contact model is desired in the distinct element method (DEM) for geomaterials formed by aggregates of bonded particles. This paper proposes an analytical solution of highly-precise stress fields of a biconcave bond between two identical disc-shaped particles under different loading paths based on Dvorkin’s solution. The Unified Strength theory is then introduced to obtain the initial failure domain in the bond. The proposed solution is consistent with results predicted by finite element simulations and experimental observations. The functions of bond stiffness with respect to all influencing parameters, i.e. bond width/thickness, particle radius and elastic parameters of bond material, are provided by the solution and empirically formulated by fitting a large number of analytical results. Additionally, the failure criterion or envelope under different combined loads is formulated for typical brittle bonds. The resulting failure criterion, approximated as an ellipsoid, depends on the size and material properties of the bonds. The proposed solution and equation can be implemented into a bond contact model used in DEM simulations of a geomaterial, where variation of bond sizes is significant and size-dependent contact model is important.     

A simple three‐dimensional distinct element modeling of the mechanical behavior of bonded sands

This paper presents a simple three‐dimensional (3D) Distinct Element Method (DEM) for numerical simulation of the mechanical behavior of bonded sands. First, a series of micro‐mechanical tests on a pair of aluminum rods glued together by cement with different bond sizes were performed to obtain the contact mechanical responses of ideally bonded granular material. Second, a 3D bond contact model, which takes into account the influences of bond sizes, was established by extending the obtained 2D experimental results to 3D case. Then, a DEM incorporating the new contact model was employed to perform a set of drained triaxial compression tests on the DEM bonded specimens with different cement contents under different confining pressures. Finally, the mechanical behavior of the bonded specimens was compared with the available experimental results. The results show that the DEM incorporating the simple 3D bond contact model is able to capture the main mechanical behavior of bonded sands. The bonded specimen with higher cement content under lower confining pressure exhibits more pronounced strain softening and shear dilatancy. The peak and residual strengths, the apparent cohesion and peak/residual friction angles, and the position and slope of the critical state line increase with increase in cement content. Microscopically, bond breakage starts when the system starts to dilate and the maximum rate of bond breakage coincides with the maximum rate of dilation. Bond breakage is primarily due to tension‐shear failure and the percentage of such failures is independent of both confining pressure and cement content. Copyright © 2015 John Wiley & Sons, Ltd.     

Discrete element analysis of uplift and lateral capacity of a single pile in methane hydrate bearing sediments

Methane hydrate (MH) is extensively found in outer continental margins where offshore infrastructures with pile foundations are also common. The presence of MHs significantly alters the mechanical properties of the host marine sediments, and therefore affects the behavior of piles inside. This paper presents an attempt to investigate the performance of a single pile in methane hydrate bearing sands in seabed using the distinct element method. A novel bond contact model was employed for sandy grains cemented by MHs at contacts, and calibrated from the triaxial compression tests on synthetic specimens of methane hydrate bearing sands. The response of the pile subjected to axial pullout loads and lateral loads was simulated under different subsurface conditions characterized by different saturation levels of MHs. The results show that the presence of MHs increases the uplift capacity of the pile by changing the failure mode of the soils from the perimeter failure to the conical failure. The uplift capacity of the pile significantly deteriorates as a result of de-bonding, while the onset of the rapid de-bonding triggers the softening of the uplift load. In addition, the lateral capacity of the pile largely increases due to the presence of MHs. The pile in methane hydrate bearing sands is considered flexible rather than rigid as a result of the increased deformation modulus of soils due to MH cementation between particles. The lateral load–displacement diagram of the pile in methane hydrate bearing sands is not as smooth as that in clean sands with an abrupt drop associated with the onset of de-bonding.     

基于微观胶结厚度模型的深海能源土宏观力学特性离散元分析

首先,引入蒋明镜等提出的考虑水合物胶结厚度的深海能源土粒间微观胶结模型,用以反映能源土颗粒之间水合物微观胶结接触力学特性;其次,采用C++语言将模型程序化,并将其引入离散单元法中;然后,对选定的水合物饱和度经过实际二维离散元模拟调算,得出相应的水合物胶结尺寸,以修正水合物临界胶结厚度、最小胶结厚度及胶结宽度,进而确定水合物微观胶结参数;最后,根据所确定的胶结参数,针对不同水合物饱和度试样进行能源土宏观力学特性离散元双轴试验模拟,并从应力-应变、体变、剪胀角等方面与Masui等所进行的能源土室内三轴试验进行对比分析。结果表明：采用考虑粒间胶结厚度的水合物微观胶结模型,能够定性反映深海能源土的宏观力学特性,能源土试样的峰值强度、黏聚力和剪胀角均随水合物饱和度的增加而增加,但水合物饱和度对内摩擦角的影响规律不明朗;能源土试样的峰值强度、残余强度及体积剪缩量随着有效围压的增大而增大;剪胀角随有效围压的增大而减小。     

结构性黄土一维湿陷特性的离散元数值模拟

针对结构性湿陷性黄土大孔隙和胶结特性,应用离散元生成了不同含水率结构性黄土试样,研究试样的一维湿陷特性。首先,根据已有的结构性黄土试验资料和胶结颗粒材料离散元数值试验成果,建立胶结强度和初始饱和度之间的关系。其次,采用蒋明镜等提出的分层欠压法[1]和胶结模型[2]制得不同含水率结构性黄土离散元试样,然后进行不同含水率双线法和同一含水率4个压力下单线法湿陷试验的离散元数值模拟。数值模拟结果表明,提出的离散元分析方法能模拟天然结构性湿陷性黄土的主要力学性质,随着含水率的减少,结构屈服应力和最大湿陷压力增加,湿陷系数随着压力先增加后减小,湿陷起始压力为饱和试样的结构屈服应力,单线法湿陷后压缩曲线与饱和试样的压缩曲线接近。此外,模拟结果还表明,不同含水率结构性黄土离散元试样的最大湿陷系数与天然结构性湿陷性黄土相差较远,但在最大湿陷系数与孔隙比的比值上相接近;结构屈服对应着胶结的逐步破坏,湿陷伴随着大量的胶结破坏。提出了基于胶结点数目的损伤变量,研究了其在加载和湿陷过程中的变化规律。研究成果为认识黄土复杂力学特性和建立其本构理论提供了基础。     

Coupled modelling of hydro‐mechanical behaviour of unsaturated compacted expansive soils

The Barcelona basic model cannot predict the mechanical behaviour of unsaturated expansive soils, whereas the Barcelona expansive model (BExM) can only predict the stress–strain behaviour of unsaturated expansive soils without the water‐retention behaviour being incorporated. Moreover, the micro‐parameters and the coupling function between micro‐structural and macro‐structural strains in the BExM are difficult to determine. Experimental data show that the compression curves for non‐expansive soils under constant suctions are shifted towards higher void ratios with increasing suction, whereas the opposite is true for expansive soils. According to the observed water‐retention behaviour of unsaturated expansive soils, the air‐entry value increases with density, and the relationship between the degree of saturation and void ratio is linear at constant suction. According to the above observation, an elastoplastic constitutive model is developed for predicting the hydraulic and mechanical behaviour of unsaturated expansive soils, based on the existing hydro‐mechanical model for non‐expansive unsaturated soil. The model takes into consideration the effect of degree of saturation on the mechanical behaviour and that of void ratio on the water‐retention behaviour. The concept of equivalent void ratio curve is introduced to distinguish the plastic potential curve from the yield curve. The model predictions are compared with the test results of an unsaturated expansive soil, including swelling tests under constant net stress, isotropic compression tests and triaxial shear tests under constant suction. The comparison indicates that the model offers great potential for quantitatively predicting the hydraulic and mechanical behaviour of unsaturated expansive soils. Copyright © 2011 John Wiley & Sons, Ltd.     

Numerical study of inter‐particle bond failure by 3D discrete element method

The cohesive‐frictional nature of cementitious geomaterials raises great interest in the discrete element method (DEM) simulation of their mechanical behavior, where a proper bond failure criterion is usually required. In this paper, the failure of bond material between two spheres was investigated numerically using DEM that can easily reproduce the failure process of brittle material. In the DEM simulations, a bonded‐grain system (composed of two particles and bond material in between) was discretized as a cylindrical assembly of very fine particles connecting two large end spheres. Then, the bonded‐grain system was subjected to compression/tension, shear, rolling and torsion loadings and their combinations until overall failure (peak state) was reached. Bonded‐grain systems with various sizes were employed to investigate bond geometry effects. The numerical results show that the compression strength is highly affected by bond geometry, with the tensile strength being dependent to a lesser degree. The shear, rolling and torsion strengths are all normal force dependent; i.e., with an increase in the normal force, these strengths first increase at a declining rate and then start to decrease upon the normal force exceeding a critical value. The combined actions of shear force, rolling moment and torque lead to a spherical failure envelope in a normalized loading space. The fitted bond geometry factors and bond failure envelopes obtained numerically in this three‐dimensional study are qualitatively consistent with those in previous two‐dimensional experiments. The obtained bond failure criterion can be incorporated into a future bond contact model. Copyright © 2015 John Wiley & Sons, Ltd.     

基于弹性张量离散化的脆延转变本构模型研究

外部荷载作用下的裂隙扩展在空间上一般是非均匀的,引起岩石材料的衍生各向异性。将材料离散成大量随机分布的由力键连结的物质点,基于力键的方向性,且将局部弹性张量离散成一定数量的方向张量,理论推导出力键模量与宏观弹性参数之间的关系。通过考虑力键断裂效应,建立了各向异性弹性损伤本构模型。为了模拟中等孔隙率岩石在常规三轴压缩试验中脆性向延性转变的力学行为,在力键断裂效应中引入损伤抑制函数。通过模拟Tennessee大理岩和Indiana石灰岩的常规三轴实验,并与试验数据对比,验证了模型的合理性和有效性。     

DEM analyses of one-dimensional compression and collapse behaviour of unsaturated structural loess

Natural loess is a kind of under-consolidated and unsaturated loose granulates (silts) with its microstructure characterized with large voids and inter-particle cementation. This paper presents a distinct element method (DEM) to investigate its macro- and micro-mechanical behaviour (compression and collapse behaviour) under one-dimensional (1D) compression condition. A relationship between bond strength in DEM model and initial water content is used to develop a bond contact model for loess. Then, DEM structural loess samples are prepared by the multi-layer under-compaction method, and cemented with the bond contact model. The effect of water content and void ratio on compression and collapse behaviour of loess is numerically investigated by simulating 1D compression and wetting tests on the DEM material. The DEM results agree qualitatively with available experimental observations in literatures. The wetting-induced deformation is independent of the sequence of wetting and loading under 1D compression condition. The macroscopic yielding and collapse behaviours are associated with bond breakage on microscopic scale. Moreover, bonds break in one of the two failure types in the simulations, i.e. tensile failure and shear failure (compression-shear failure and tension-shear failure), with bonds broken firstly mainly due to tension followed by shear when the samples are compressed, while mainly due to shear when the samples are wetted under a certain pressure. In addition, the contact orientations and deviator fabrics of contacts under 1D compression and wetting were also investigated.