散体颗粒介质变形局部化宏–细观机制研究

散体颗粒是自然界中广泛存在的一类特殊的介质,受内部组构影响,散体颗粒介质在外荷载作用下发生明显的变形局部化效应,这也是岩土力学领域一直研究的热点问题之一。然而目前对于其机制研究方面大都局限于细观统计参数的分析,忽视了宏观现象与细观机制的内在联系。本文以砂土颗粒介质为例,运用离散元法对其在直剪试验过程中的宏–细观力学特性及变形破坏机制进行系统分析,并取得一些有意义的认识。根据数值试验中试样在不同法向应力下剪应力比的发展,从颗粒运动角度探讨试样宏观抗摩擦特性变化趋势的细观机制;发现描述细观组构的各向异性参数及主方向与宏观上剪应力比的发展具有同步性,反映试样宏细观演化的统一性;通过对于颗粒旋转的统计分析,揭示颗粒间摩擦作用是维持细观力学结构相对稳定的重要因素;通过对力链网络的形态演化分析,发现试样大主应力方向与各向异性主方向一致,力链密集程度随剪切过程下降,试样孔隙度随之上升;提出不同法向应力下的2种主要力链结构的力学模型,通过稳定性分析与能量累积释放理论解释宏观力学参数波动情况的原因,揭示散体颗粒介质变形局部化和体应变剪胀的细观机制。     

Application of Micromechanics Model to Study Anisotropy of Soils at Small Strains

A micromechanics model is used to analyse the stiffness anisotropy of soils at small strains. Five material constants for a cross-anisotropic elastic material are related to micromechanics variables such as fabric anisotropy, contact stiffness, particle radius, and the number of contacts in a given volume of particulate assembly. The analytical results from the model are compared with the published experimental data on small-strain stiffness anisotropy in order to estimate typical soil fabric conditions of sands and clays. The relationship between the small-strain shear modulus obtained from triaxial tests and shear tests is examined using the micromechanics model. The analysis shows that, when a soil is stiffer in the horizontal direction, the shear modulus evaluated from the conventional triaxial drained tests underestimates G_vh and G_hh. The opposite is true when a soil is stiffer in the vertical direction. When a soil is sheared in undrained condition, the measured shear modulus is closer to G_vh than G_hh, especially when the soil is stiffer in the horizontal direction. The effect of soil anisotropy on the stiffness measured from different stress paths in triaxial condition is investigated.     

Effect of the particle size ratio on macro- and mesoscopic shear characteristics of the geogrid-reinforced rubber and sand mixture interface

As a new type of material for civil engineering projects, the rubber and sand mixture is widely used in roadbed fillers, offering environmental benefits over traditional tyre disposal methods. This study uses a large-scale direct shear apparatus to examine the interface shear properties of the geogrid-reinforced rubber and sand mixture, considering different particle size ratios (r), rubber contents, and normal stresses. Based on indoor tests, direct shear models of the mixture with different values of r are established in PFC^3D, revealing the meso-mechanical mechanism of the mixture in the direct shear process. The results show that when r is greater than 1, incorporating a certain amount of rubber particles can increase the shear strength of the mixture. The r values of 15.78, 7.63, and 3.98 correspond to an optimal rubber content of 30%, 10%, and 20%, respectively. When r is less than 1, mixing rubber particles can only reduce the shear strength of the mixture. When the rubber content is low, the smaller the value of r, the greater is the thickness of the shear band. Furthermore, the normal and tangential contact forces are greater. The fabric anisotropy evolution law of the mixture is consistent with the change in the contact force distribution.     

松砂不稳定行为的数值模拟研究

针对松散砂土的不稳定行为和静态液化现象，开展了一系列的双轴剪切试验离散元数值模拟，从宏细观的角度研究了松砂不稳定行为的各种影响因素及其发生机理。通过数值模拟发现，砂土的不稳定行为不仅与初始孔隙比有关，而且与土体结构的各向异性和围压有关。当加载方向与由颗粒接触法向所表征的结构各向异性主方向不共轴时，不稳定行为的发生会同时伴随着各向异性主方向的旋转。两个方向的角度差愈大，不稳定行为愈容易发生，颗粒的细观运动和细观结构重组现象也愈剧烈。不稳定状态点处的剪切荷载主要由颗粒间法向接触力承担，切向接触力仅起次要作用。     

The inter-particle coefficient of friction at the contacts of Leighton Buzzard sand quartz minerals

A series of micro-mechanical tests was carried out in order to investigate the inter-particle coefficient of friction at the contacts of quartz minerals of Leighton Buzzard sand. For this purpose, a custom-built inter-particle loading apparatus was designed and constructed, the main features of which are described briefly in this paper. This apparatus is capable of performing shearing tests at the contacts of soil minerals of a particle–particle type in the range of very small displacements, from less than 1 μm to about 300 μm, and very small normal loads, between about less than 1 N and 15 N. The laboratory data showed that the effects of the normal force and the sliding velocity on the coefficient of dynamic friction are not significant, while dry and saturated surfaces had similar frictional characteristics. The steady state sliding was mobilized within a range of 0.5–3.0 μm of horizontal displacement, and the coefficient of static friction was very similar to the corresponding coefficient during constant shearing. Repeating the inter-particle shearing tests on the same particles and following the same shearing track indicated a small reduction in the inter-particle coefficient of friction after the first shearing, which is possibly related to plastic deformation and damage to the asperities.     

Experimental investigation of inter-particle contact evolution of sheared granular materials using X-ray micro-tomography

The inter-particle contact evolution of two sheared granular materials, i.e., a spherical glass bead (GB) specimen and an angular Leighton Buzzard Sand (LBS) specimen, is investigated non-destructively using X-ray micro-tomography. A miniature triaxial apparatus is developed for the testing with in-situ scanning. Full-field X-ray CT images of the two specimens are obtained at different shearing stages. A series of image processing and analysis techniques in combination with a particle-tracking approach is developed to detect the inter-particle contacts and to determine the contact gain, the contact loss, and the contact movement during each shear increment. It is found that the average coordination number (CN) experiences a strong change in the pre-peak shearing stage, and tends to reach a steady value after the peak. As the shear progresses, the average CN of the particles with different sizes follows the same trend as the overall average CN. Additionally, as the shear progresses, the branch vectors of the specimens, which, prior to shearing, are nearly isotropically distributed for the rounded GB and concentrated along the horizontal direction for the angular LBS, are found to show a directional preference towards the loading direction. The contact gain and the contact loss, which contribute to this directional preference, and the contact movement, which leads to the attenuation of the directional preference, are shown to be the two competing factors determining the evolution of the fabric anisotropy of granular materials. The higher degree of fabric anisotropy in the shear bands is shown to be mainly attributed to the higher percentages of contact gain and contact loss when compared to that of the entire samples.     

Insight on bulk shear strength parameters of clay using discrete element approach incorporating physics-based interparticle force model

This paper aims to provide insight on factors affecting the bulk shear strength parameters of clay, i.e., the cohesion and internal friction as well as the effects of memory of preconsolidation pressure. A unique Discrete Element Method (DEM) model is built on platy particles with customized particle interaction force model. The particle interaction force model considers non-contact forces (such as the long-range electrostatic repulsion, short-range van der Waals attraction) as well as the direct contact force. The long-range electrostatic forces are calibrated by measurement with Atomic Force Microscope (AFM). Parameters for direct particle contacts of the regular DEM contact model, such as the contact stiffness and the friction coefficient, are calibrated by use of experimental consolidation and direct shear testing data. Computational simulations are conducted on digital clay specimen subjected to virtual direct shear tests. The predicted experimental responses of the digital specimens are consistent with typically observed in experiments including the shear stress-shear strain relationship, volumetric contraction and dilation, shear band formation, etc. From the stress–strain curves, the soil strength parameters are obtained with common experimental criteria. The DEM simulation results show that higher preconsolidation pressure drives more particles to overcome non-contact force into direct contacts and consequently bonding by van der Waals force. Consequently, the bulk cohesion of clay increases with increasing preconsolidation pressure. The results show that bulk cohesion strength is mainly attributed to the attractive interparticle force as well as the interlocking of platy particle, while the bulk internal friction angle is affected by the particle friction coefficient and particle fabric. Overall, the simulation results indicate the experimentally observed macroscopic shear strength parameters c and φ are linked to the microscope characteristics of soil particles and their mutual interactions. The results offer insight on the microscopic properties of particles on the bulk macroscopic strength behaviors. Besides, this work demonstrates a new strategy for simulation-based prediction of bulk soil strength parameters, by incorporating microscale characterization of the interparticle interactions and particle fabric into the particle-based DEM model.     

高频循环剪切下结构与松砂接触面的土体特性

应用颗粒离散元分析理论,深入地研究了高频循环剪切荷载下松砂与结构的接触面土体响应特性,对各种颗粒因素和剪切条件对接触面土体孔隙率和体应变的影响进行详细分析.数值仿真分析结果表明,松砂颗粒摩擦系数和颗粒刚度越大,接触面附近土体剪缩性越不明显;松砂的颗粒刚度比对其力学性质影响不大;边界围压越大,松砂的剪缩性越明显;高频循环...     

Study of the micro-mechanical behaviour of the Opalinus Clay: an example of co-operation across the ground engineering disciplines

The high degree of scientific cross-fertilisation possible between the three geo-engineering disciplines soil mechanics, rock mechanics and engineering geology, is demonstrated by means of a micro-mechanical model of the Opalinus Clay. After a brief review of Terzaghi’s effective stress principle and the importance of micro-mechanical models in general, a conceptual study of a micro-mechanical model of a claystone is presented in some detail. The model is based on the Particle Flow Code (PFC) developed by Itasca Corp. It introduces into the model the pertinent composition and structure of the Opalinus Claystone established in the local engineering geology of Switzerland and SW Germany. This includes elongated clay platelets, various layers of densified water around the platelets, free water in the pores and a specific texture of the platelets after consolidation. The model is numerically subjected to a series of loading stages. It is shown that the micro-mechanical model reproduces a number of features which have been known for a long time in soil and rock mechanics but which are often intractable in conventional generic models. The features include non-linear stress–strain curves with pre-failure damage and post-failure strain softening, a non-linear increase of the particle contacts with loading, distinct clustering of deformations, clustering of micro cracks leading to the development of shear bands and hysteresis in cyclic loading. It is concluded that micro-mechanical models are promising tools for further development of our understanding of the mechanical behaviour of geological materials. They offer an excellent opportunity for scientific co-operation between engineering geologists and soil and rock mechanics engineers.     

Experimental study on sand anisotropy using hollow cylinder apparatus

This study investigated sand anisotropy experimentally using a hollow cylinder apparatus. The effect of the initial anisotropy on the shear behavior of sand was illustrated by conducting experiments on specimens with bedding planes and systematically varying the density, principal stress direction, and intermediate principal stress. The change in induced anisotropy during shearing was experimentally captured by re-shearing the specimens subjected to prior shear history. The experimental results revealed the following: (a) Anisotropy in sand, whether initial anisotropy developing during specimen preparation or induced anisotropy developing due to shear history, causes pseudo-density changes in the mechanical behavior, in which sand of the same density behaves as if it has a different density depending on the direction of shear. (b) The changes in induced anisotropy, due to shearing in the same direction as that of the prior shear, make the soil behave similarly to dense sand, whereas shearing in a direction perpendicular to the prior shear makes the soil behave similarly to loose sand. (c) The larger the prior shear, the more pronounced the pseudo-density changes that appear in the subsequent behavior. Moreover, the significance of induced anisotropy in liquefaction and compaction phenomena was experimentally demonstrated through single and double swing cyclic shear tests. The results obtained from the study will be useful for validating models that incorporate induced anisotropy.     

Micromechanical analyses of the effect of rubber size and content on sand-rubber mixtures at the critical state

This study presents a series of monotonic drained triaxial tests consisting of mixtures of sand (stiff) and rubber (soft) particles simulated by the discrete element method (DEM). Sets of mixtures were prepared with different rubber size ratio of 1, 2.5 and 5 and contents ranging from 0% to 30% by weight. The numerical samples were sheared up to large axial strains to reach a critical state. The slope of the critical state lines is strongly affected when the rubber size is the same as sand. When rubber size increases, the critical state lines shift downward with little effect on the slope. While it is generally accepted that, for the given range of rubber contents used in the study, the sand-rubber mixture strength increases when adding rubber particles, the results from this study suggest that said strength diminishes as rubber size is incremented. Micro-scale information, including coordination number, geometrical and mechanical anisotropy, was obtained for all the tests. Regardless of the rubber particle size, rubber-sand contacts represent an important contribution to the overall strength of the material; however, the rubber particle size dictates how said contribution takes place. These findings highlight the importance of understanding new geomaterials to practicing engineers that different size ratios and rubber contents have positive or negative effect of strength and deformability and the choice of a sand-rubber mixture has to be based on the project nature.     

基于离散-连续耦合的尾矿坝边坡破坏机理分析

在连续介质力学有限差分数值模拟的基础上,选取有代表性的局部区域进行基于有限差分与离散元的离散-连续耦合分析。采用上述方法模拟了某尾矿坝边坡在尾矿冲填前后潜在滑移带附近的宏细观力学特征。模拟结果显示,对于耦合和非耦合模型中的连续域两种方法的计算结果基本一致,但离散域的存在可以对滑移带形成过程的细观力学特征,如力链分布、土体细观组构发展等进行分析,研究边坡破坏的细观机理。研究表明,在滑移带形成过程中,滑移带内外土体各向异性的发展明显不同：随着荷载的施加,潜在滑移带内土体颗粒发生了较明显的位移,应力主方向发生了明显转动。颗粒的转动改变了带内组构的分布,并逐渐形成剪切滑移带,造成边坡失稳。滑带外土体虽然应力主方向发生了一定的偏转,但剪应力变化不大。采用的离散-耦合分析方法可以分析边坡在渐进破坏过程中滑移带形成的细观力学机理。     

基于微观破损机理的胶结砂土三维本构模型研究

在岩土破损力学和临界状态土力学框架内,遵循宏微观土力学的研究思路,建立了胶结砂土三维本构模型。定义与重塑砂土屈服面几何相似但尺寸扩大的胶结砂土屈服面;采用经三维离散元验证的Lade-Duncan强度准则作为临界状态强度面;基于胶结材料微观力学理论并结合三维离散元模拟结果,获得具有微观力学机制的胶结破损规律;将胶结破损规律引入到重塑砂土的硬化规律和流动法则,得到胶结砂土的硬化规律和流动法则。将该本构模型应用于人工制备胶结砂土室内常规三轴压缩试验和等平均应力真三轴试验的模拟,初步验证了该模型的适用性。     

Linking inherent anisotropy with liquefaction phenomena of granular materials by means of DEM analysis

The liquefaction phenomena of sands have been studied by many researchers to date. Laboratory element tests have revealed key factors that govern liquefaction phenomena, such as relative density, particle size distribution, and grain shape. However, challenges remain in quantifying inherent anisotropy and in evaluating its impact on liquefaction phenomena. This contribution explores the effect of inherent anisotropy on the mechanical response of granular materials using the discrete element method. Samples composed of spherical particles are prepared which have approximately the same void ratio and mean coordination number (CN), but varying degrees of inherent anisotropy in terms of contact normals. Their mechanical responses are compared under drained and undrained triaxial monotonic loading as well as under undrained cyclic loading. The simulation results reveal that cyclic instability followed by liquefaction can be observed for loose samples having a large degree of inherent anisotropy. Since a sample having initial anisotropy tends to deform more in its weaker direction, leading to lower liquefaction resistance, a sample having an isotropic fabric potentially exhibits the greatest liquefaction resistance. Moreover, the effective stress path during undrained cyclic loading is found to follow the instability and failure lines observed for static liquefaction under undrained monotonic loading. From a micromechanical perspective, the recovery of effective stress during liquefaction can be observed when a threshold CN develops along with the evolving induced anisotropy. Realising that the conventional index of the anisotropic degree (a) is not effective when the CN drops to almost zero during cyclic liquefaction, this contribution proposes an alternative index, effective anisotropy (a×CN), with which the evolution of induced anisotropy can be tracked effectively, and common upper and lower bounds can be defined for both undrained monotonic and cyclic loading tests.     

Effect of shearing rate on the behavior of geogrid-reinforced railroad ballast under direct shear conditions

A series of large-scale direct shear tests were conducted to investigate the behavior of unreinforced and geogrid-reinforced ballast at different rates of shearing. Fresh granite ballast with an average particle size (D₅₀) of 42?mm and five geogrids having different aperture shapes and sizes was used in this study. Tests were performed at different normal stresses (σ_n) ranging from 35?kPa to 140?kPa and at different rates of shearing (S_r) ranging from 2.5 to 10.0?mm/min. The laboratory test results revealed that the shear strength of ballast was significantly influenced by the rate of shearing. The internal friction angle of ballast (φ) was found to decrease from 66.5° to 58° when the shearing rate (S_r) was increased from 2.5 to 10.0?mm/min. It is further observed that the interface shear strength has improved significantly when the ballast was reinforced with geogrids. The interface efficiency factor (α), defined as the ratio of the shear strength of the interface to the internal shear strength of ballast, varies from 0.83 to 1.06. The sieve analysis of samples after the testing reveals that a significant amount of particle breakage occurs during shearing. The value of breakage, evaluated in terms of Marsal's breakage index (B_g), increases from 5.12 to 13.24% with an increase in shearing rates from 2.5 to 10.0?mm/min. Moreover, the influence of aperture shape and size of geogrid on the behavior of ballast-geogrid interfaces was also examined in this study.     

Cohesiveness and hydrodynamic properties of young drinking water biofilms

Drinking water biofilms are complex microbial systems mainly composed of clusters of different size and age. Atomic force microscopy (AFM) measurements were performed on 4, 8 and 12 weeks old biofilms in order to quantify the mechanical detachment shear stress of the clusters, to estimate the biofilm entanglement rate ξ. This AFM approach showed that the removal of the clusters occurred generally for mechanical shear stress of about 100 kPa only for clusters volumes greater than 200 μm³. This value appears 1000 times higher than hydrodynamic shear stress technically available meaning that the cleaning of pipe surfaces by water flushing remains always incomplete. To predict hydrodynamic detachment of biofilm clusters, a theoretical model has been developed regarding the averaging of elastic and viscous stresses in the cluster and by including the entanglement rate ξ. The results highlighted a slight increase of the detachment shear stress with age and also the dependence between the posting of clusters and their volume. Indeed, the experimental values of ξ allow predicting biofilm hydrodynamic detachment with same order of magnitude than was what reported in the literature. The apparent discrepancy between the mechanical and the hydrodynamic detachment is mainly due to the fact that AFM mechanical experiments are related to the clusters local properties whereas hydrodynamic measurements reflected the global properties of the whole biofilm.     

Size effect on aperture and permeability of a fracture as estimated in large synthetic fractures

Synthetic fractures of from 0.2 to 12.8 m in size were created on a computer by a new spectral method to reproduce the ratio of the power spectral density of the initial aperture (the aperture when the surfaces are in contact at a single point) to that of the surface height determined for a tensile fracture of 1 m. First, the size effect on the standard deviation of the initial aperture was analyzed for fractures with and without shearing. Next, by taking aperture data at constant intervals to establish a flow area, water flow was simulated for fractures during both normal closure and closure after shearing, by solving Reynolds equation to determine the hydraulic aperture. When the fracture is closed without shearing and has the same mean aperture, the effect of the fracture size on the hydraulic aperture disappears if the fracture is larger than about 0.2 m, since beyond this size the standard deviation of the initial aperture is almost independent of the fracture size. When the fracture is closed after shearing, the hydraulic conductivity shows remarkable anisotropy, which becomes more significant with both shear displacement and closure. However, the relation between the hydraulic aperture normalized by the mean aperture and the mean aperture normalized by the standard deviation of the initial aperture is almost independent of both the fracture size and shear displacement when the shear displacement is less than about 3.1% of the fracture size, at which point the standard deviation of the initial aperture of the sheared fracture is almost independent of the fracture size.     

Experimental study on the clogging effect of dredged fill surrounding the PVD under vacuum preloading

Clogging effect surrounding prefabricated vertical drains (PVDs) is a typical problem when vacuum preloading is applied to a dredged fill foundation. A large-scale model test was designed to clarify the cause and mechanism of the clogging effect, and the basic physical and mechanical parameters of the soil in the clogging zone were tracked during the test. The results demonstrated that a clogging zone was formed around the PVD in the early stage of improvement with conventional vacuum preloading, and the boundary of the clogging zone was approximately 0.2–0.4 of the boundary radius. The clogging zone surrounding the PVD was formed because of the overall movement of the soil toward the PVD under the high vacuum pressure gradient, rather than fine particle migration. The soil in the clogging zone exhibited permeability anisotropy and equivalent ‘smear’ effect. The permeability ratio (k_h/k_v) was less than 1, and the ratio of horizontal permeability coefficients at the test distances of 45 cm and 10 cm were 9.6 at a depth of 20 cm and 8.9 at a depth of 80 cm. An analysis of the microstructure of the soil in the clogging zone demonstrated that the clay particles tended to be vertically oriented. The re-orientation of the clay particles reduced the horizontal permeability coefficient and led to the permeability anisotropy of the soil in the clogging zone. Thus, decrease in the horizontal permeability coefficient and equivalent ‘smear’ effect of the soil in the clogging zone affect the consolidation of dredged fill, which leads to the clogging effect. The permeability anisotropy also slightly affects consolidation.     

Deformation and cyclic resistance of sand in large-strain undrained torsional shear tests with initial static shear stress

This paper presents the findings from an experimental study focusing on the undrained cyclic behavior of sand in the presence of initial static shear stress. A series of undrained cyclic torsional shear tests was performed on saturated air-pluviated Toyoura sand specimens up to single amplitude shear strain ($\gamma$_SA) exceeding 50%. Two types of cyclic loading conditions, namely, stress reversal (SR) and stress non-reversal (SNR), were employed by changing the amplitude of the combined initial static shear and cyclic shear stresses. The tests covered a broad range of initial states in terms of relative density (Dr = 20–74%) and the initial static shear stress ratio (α = 0–0.30). The following five distinct modes of deformation were identified from the tests based on the density state, the transient undrained peak shear stress, and the combined cyclic and static shear stresses: 1) static liquefaction, 2) cyclic liquefaction, 3) cyclic mobility, 4) shear deformation failure, and 5) limited deformation. Of these, cyclic liquefaction and static liquefaction are the most critical. They occur in very loose sand (D_r ≤ 24%) under SR and SNR, respectively, and are characterized by abrupt flow-type shear deformation. Cyclic mobility occurs under SR in loose to dense sand with D_r ≥ 24%. Contrarily, shear deformation failure typically occurs under SNR in sand with 24 < D_r < 65%, and limited deformation may take place in dense sand with D_r ≥ 65%. In this paper, a stress-void ratio-based predictive method is proposed to identify the likely mode of deformation/failure in sand under undrained shear loading with static shear. Furthermore, the cyclic resistance is evaluated at three different levels of $\gamma$_SA (i.e., small, $\gamma$_SA = 3%; moderate, $\gamma$_SA = 7.5%; and large, $\gamma$_SA = 20%). The results show that, independent of the density state, the cyclic resistance continuously decreases with an increase in α at the small $\gamma$_SA level, while it first decreases and then increases for both loose and dense sand at the moderate and large $\gamma$_SA levels.     

Investigation on physical and mechanical properties of bedded sandstone after high-temperature exposure

Uniaxial compression tests were carried out on bedded sandstone to explore the effect of exposure to high temperatures on the physical and mechanical properties of the specimens. The influences of testing temperature and bedding orientation on the physical and mechanical properties and failure behaviors of the bedded sandstone were analyzed. The results show that for sandstone with a constant bedding orientation, as the temperature increases, the P wave velocity first increases and then decreases, while the mass and density decrease. The mechanical properties of bedded sandstone, including its compressive strength and elastic modulus, first increase and then decrease with increasing temperature, and a thermal temperature of 400 °C was identified as the transition temperature, above which considerable changes in the mechanical properties were observed. In addition, the P wave velocity, strength, and elastic modulus also varied with increasing bedding orientation, which indicated that the bedded sandstone exhibits anisotropy in its P wave velocity, strength, and elastic modulus. The P wave velocity gradually increases with increasing inclination angle, and the fluctuation in the anisotropic degree of the P wave velocity remains small as the temperature increases. The strength and elastic modulus of the bedded sandstone exhibit U-shaped variations with increasing bedding orientation, and the anisotropy degree first increases and then decreases with increasing temperature. Furthermore, the failure modes are closely related to the designed heat treatment temperature and bedding orientation and can be generally classified into four categories: shearing across the rock matrix and bedding planes, shearing combined with tensile splitting, shearing along the bedding planes, and shearing combined with tensile splitting along the bedding planes. Finally, the effect of high temperatures on the mechanical properties of bedded sandstone was further revealed by means of SEM analysis from a microstructure point of view.