Microscale characterization of energy dissipation mechanisms in liquefiable granular soils

This study utilizes the discrete element method (DEM) to present a microscopic energy monitoring approach to characterize energy dissipation mechanisms in seismically loaded soils. Numerical simulations were conducted on saturated deposits of granular particles subjected to seismic excitations, modeled using a transient fully-coupled continuum–fluid discrete-particle model. The onset of liquefaction is illustrated through macroscopic and microscopic response patterns. A novel in-depth look at the individual microscale energy components both before and after the onset of liquefaction is presented. Local microscopic energies are also presented and are compared with local macroscopic energies calculated from stress–strain loops. Finally, an assessment of existing hypotheses to quantify liquefaction potential based on energy consideration is presented through a discussion of a number of simulations that resulted in liquefaction.     

基于耗散能量的饱和黄土动孔压模型

通过一系列不排水动三轴试验探究了饱和黄土振动液化过程中孔隙水压力和累积耗散能量的演化模式,并讨论了围压、动应力幅值和固结应力比对其演化过程的影响。结果表明：饱和黄土的孔隙水压力和耗散能量随着循环荷载作用逐渐累积。固结围压抑制孔隙水压力增长而消耗更多能量;更大的动应力幅值使得孔隙水压力增长更快而消耗能量更少;等压固结下,孔隙水压力增长至围压从而触发初始液化,而偏压固结下,通常先达到振动液化应变标准而孔隙水压力并没有增长至围压水平,并且固结应力比越大,液化时孔隙水压力越小,消耗能量也更少。归一化孔隙水压力u/σ₀’与累积耗散能量W/W_f之间关系受围压、循环应力比和固结应力比影响较小,可统一用双曲线模型表示。     

Macroscale friction of granular soils under monotonic and cyclic loading based upon micromechanical determination of dissipated energy

Macroscopic frictional behavior of granular materials is of great importance for studying several complex problems associated with fault slip and landslides. The main objective of this study is to model the macroscale frictional behavior of granular soils under monotonic and cyclic loadings based upon micromechanical determination of dissipated energy at particle contacts. This study is built on the general observation that the externally computed energy dissipation should be equal to the total internal energy dissipation derived from inter-particle sliding and rolling, energy losses from inter-particle collisions, and damping. For this purpose, the discrete element method is used to model a granular soil and determine the stored, dissipated, and damping energies associated with shear loading for applied monotonic and cyclic velocities. These energies are then related to the friction by an application of the Taylor-critical state power balance relationship. Also, the contributions of the different modes of energy dissipation (normal, shear, and rolling) to the total frictional resistance were studied. By changing the inter-particle friction, the simulations showed that the macroscopic friction was nearly constant, the slip friction increased almost linearly with increasing inter-particle friction, and the difference between the two was attributed to the non-energy dissipating dilatancy component. By providing a clear relationship between energy dissipated by micro-scale mechanisms versus the traditional engineering definition based on macro-scale (continuum) parameters, this study provides a means to develop a better understanding for the frictional behavior of granular media.

     

On the initiation and movement mechanisms of a catastrophic landslide triggered by the 2008 Wenchuan (M<Subscript>s</Subscript> 8.0) earthquake in the epicenter area

The Niumiangou landslide (~7.5 × 10⁶ m³) was the largest that occurred in the town of Yingxiu (the epicentral area) during the 2008 Wenchuan earthquake. This landslide originated on a steep slope (~30°) that was located directly above the rupture surface of the responsible fault and then traveled ~2 km after flowing down the axes of two gently sloping (<12°) valleys. Evidence at the site indicates that the landslide materials were highly fluidized and underwent rapid movement. To examine the initiation and movement mechanisms of this landslide, we performed a detailed field survey, conducted laboratory tests on samples taken from the field, and analyzed the seismic motion. We conclude that the landside materials were displaced due to seismic loading during the earthquake and that liquefaction may have been triggered in saturated layers above the sliding surface with progressive downslope sliding, which resulted in the high mobility of the displaced materials. The liquefaction of colluvial deposits along the travel path due to loading by the sliding mass enhanced the mobility of the displaced mass originating in the source area. Using an energy-based approach, we estimated the dissipated energy in our cyclic loading test and the possible energy dissipated to the soil layer on the slope by the earthquake. We infer that the seismic energy available for the initiation of the slope failure in the source area may have greatly exceeded the amount required for the initiation of the liquefaction failure. The slope instability might have been triggered several seconds after the arrival of seismic motion.     

密实散粒体剪切破坏能量演化的离散元模拟

砂土等散粒体在剪切过程中的能量存储及耗散是其宏观力学响应的深层原因,但因量测难度较大而研究较少。将考虑抗转动的接触模型引入离散元软件PFC2D,基于热力学第一定律建立各种能量量测方法,并在平面应变双轴压缩试验中采用该方法统计密实散粒体在剪切过程中的能量演化规律。采取了4种耗散类型,即滑动-滚动（S-R）、滑动-非滚动（S-NR）、非滑动-滚动（NS-R）和非滑动-非滚动（NS-NR）。结果表明：密实散粒体加载时能量耗散以滑动摩擦为主;且小应变加载阶段,外力功主要转化为弹性应变能,但同时也存在均布于试样的耗散能;随着应变的增加,外力功的转化形式逐渐过渡为以耗散能为主,且集中分布在带状区域内;各个加载阶段的摩擦耗散均存在各向异性。     

DEM study of fabric features governing undrained post-liquefaction shear deformation of sand

In an effort to study undrained post-liquefaction shear deformation of sand, the discrete element method (DEM) is adopted to conduct undrained cyclic biaxial compression simulations on granular assemblies consisting of 2D circular particles. The simulations are able to successfully reproduce the generation and eventual saturation of shear strain through the series of liquefaction states that the material experiences during cyclic loading after the initial liquefaction. DEM simulations with different deviatoric stress amplitudes and initial mean effective stresses on samples with different void ratios and loading histories are carried out to investigate the relationship between various mechanics- or fabric-related variables and post-liquefaction shear strain development. It is found that well-known metrics such as deviatoric stress amplitude, initial mean effective stress, void ratio, contact normal fabric anisotropy intensity, and coordination number, are not adequately correlated to the observed shear strain development and, therefore, could not possibly be used for its prediction. A new fabric entity, namely the Mean Neighboring Particle Distance (MNPD), is introduced to reflect the space arrangement of particles. It is found that the MNPD has an extremely strong and definitive relationship with the post-liquefaction shear strain development, showing MNPD’s potential role as a parameter governing post-liquefaction behavior of sand.     

Experiment and Study on Mechanical Property of Sandstone Post-peak Under the Cyclic Loading and Unloading

Engineering research has shown that the surrounding rock of deep roadways experienced many times of post-peak cyclic loading and unloading. So studying on rock mechanical characteristics of post-peak loading and unloading is helpful to control the deep surrounding rocks. The test using RMT-150B rock mechanics testing system, to experiment on the mechanical properties of sandstone of post-peak cyclic loading and unloading. The results show that: the stress–strain curves of post-peak cyclic loading and unloading have significant plastic hysteretic loops. The area of plastic hysteretic loops gloss back. The enveloping outer enclosure of cycle loading curve is the similar as the stress–strain curves of strain softening stage when the samples failure, which shows that post-peak failure of rocks have significant memory. With the increase of cycles, the cumulative deterioration parameters are gradually increased, and the ultimate bearing capacity, elastic of loading section of samples and cumulative deterioration parameters conform with the exponential attenuation function with constant term. With the increase of surrounding pressure, the total energy, dissipated energy and elastic energy of samples are gradually increased. With the increase of cycles, the total energy, dissipated energy and elastic energy of samples all are gradually decreasing, the rate of reduction decreases gradually. The samples exist in vertical splitting and transverse shear combination failure under the post-peak uniaxial cycles, or exist in shear failure under the post-peak triaxial cycles. The shear plane exists slip traces.     

Experimental evaluation of sandstone under cyclic coupled compression-shear loading: fatigue mechanical response and failure behavior

In this study, the inclined sandstone specimen is introduced into cyclic loading tests to fulfill the coupled compression-shear loading state. 21 cyclic coupled compression-shear loading tests are conducted on inclined specimens under different loading conditions, including maximum stress levels ranging in 0.80, 0.85, 0.90 and 0.95, and amplitude levels varying in 0.40, 0.50, 0.60 and 0.70. Our testing results systematically revealed the influence of cyclic loading parameters on fatigue mechanical response of rocks under coupled compression-shear loading, regarding the deformation characteristics, energy evolution, damage variable and failure mechanism. Under higher maximum stress or cyclic amplitude, inclined rocks are characterized by larger elastic modulus and higher dissipated energy, resulting in less irreversible strain, faster damage accumulation and shorter fatigue life. Furthermore, a fatigue life prediction method is proposed based on the energy dissipation, and its reliability is verified by comparing with experimental results. In addition, the progressive cracking behavior of rocks is analyzed during the fatigue tests by virtue of digital image correlation technique. Under cyclic coupled compression-shear loading, rock specimens are featured by a prominent shear-dominated failure along its short diagonal direction combined with local tensile damage along the loading orientation.

     

考虑场地动应力条件的饱和海洋粉细砂液化特性

确保地震荷载作用下海床场地的动力稳定性是海洋工程全寿命周期安全运行的重要保证,然而对复杂海域环境下饱和粉细砂的液化特性研究尚属少见。基于海域场地动应力计算方法,确定各试验工况的场地循环应力比CSR,并对试样施加与之对应的不排水循环荷载。试验结果表明：可液化的海洋粉细砂在考虑其场地动应力条件的循环荷载作用下出现不同的液化可能性;粉细砂呈循环破坏模式,将双幅轴向应变>5%作为循环破坏标准;海洋粉细砂的液化可能性与土体的埋深及动应力均不呈单一相关性,而是随着干密度的增大,液化振次逐渐增大,当干密度＞1.72 g/cm3时土体不再液化。该结果可为杭州湾区抗震区划及海洋工程结构抗震设计提供参考。     

Comparison of Numerical and Analytical Liquefaction Analyses of Tailings

The seismic performance of a tailings impoundment can be adversely affected by the behavior of the retained tailings. However, there remains considerable uncertainty in tailings liquefaction analysis. Twenty cyclic simple shear tests conducted on tailings from a gold mine in Quebec, Canada, were simulated numerically. The simulations indicated that the dynamic behavior of tailings could be modelled reasonably well, except that the weighted cyclic resistance curve of the tailings differed from that of clean sand which was used to develop the constitutive model (UBCSAND). An (N₁)_60-CS value of 10 blows/30 cm was estimated for the tailings based on calibration at a CSR of 0.10 for 15 cycles of loading. Numerical simulation of the behavior of a 20-m-high deposit of tailings during an earthquake (M_w = 5.9) indicated liquefaction of the upper 8 m of tailings. Liquefaction analysis using the Simplified method with published magnitude scaling factors (MSF) did not predict the occurrence of liquefaction. The use of MSF values calculated from the laboratory testing predicted liquefaction in the upper 8 m of tailings, corresponding quite well with the numerical simulation. The results indicate that both analytical and numerical methods can be used to evaluate the potential for tailings liquefaction under seismic loads.     

Numerical simulation of liquefaction behaviour of granular materials using Discrete Element Method

In this paper, numerical simulation of 3-dimensional assemblies of 1000 polydisperse sphere particles using Discrete Element Method (DEM) is used to study the liquefaction behaviour of granular materials. Numerical simulations of cyclic triaxial shear tests under undrained conditions are performed at different confining pressures under constant strain amplitude. Results obtained in these numerical simulations indicate that with increase in confining pressure there is an increase in liquefaction resistance.     

饱和砂土液化后大变形机制的离散元细观分析

采用颗粒流软件模拟了饱和砂土在不排水条件下的循环剪切试验,研究了不同因素对液化的影响,并进一步分析了饱和砂土液化后宏观变形的基本规律。在此基础上,从孔隙分布角度解释了砂土液化后的大变形的细观物理机制。通过自编程序对颗粒排列和孔隙分布的演化过程进行定量描述,给出孔隙率标准差作为液化后体积收缩势的度量,并研究了孔隙率标准差与液化后大变形的关系。离散元细观数值模拟再现了室内试验中的宏观现象,证实了室内试验中饱和砂土液化后的有限剪切大变形是客观真实的材料响应。土体体积收缩势的累积所导致的孔隙均匀化以及土颗粒间自由空隙增大正是饱和砂土液化后循环剪应变逐渐增大的细观机制。孔隙率标准差作为孔隙均匀化的量化指标,与循环剪应变各周次幅值有良好的相关性。     

Discrete element modelling of cyclic behaviour of granular materials

Discrete Element Modeling (DEM) of cyclic behavior of granular material has been attempted to understand liquefaction behavior of sands. A series of cyclic biaxial tests in both undrained and drained conditions with constant stress and strain amplitudes were performed on assemblage of loose and dense systems. Tests are conducted on monodisperse (uniform) and polydisperse (well graded) samples. From this study, it has been shown that DEM can simulate the cyclic behavior of sands very satisfactorily. Characteristic features, i.e., occurrence of large plastic strains and changing over from contractile to dilative behavior beyond the phase transformation angle, anisotropy of reduced strength on the extension side etc are very well reflected in numerical simulations. Liquefaction of loose assemblage seems to be mainly due to continued and cumulative loss of co-ordination number under each cycle as there is a reversal of loading direction and hence a continuous reorientation of fabric. There is no cumulative loss of co-ordination number in dense states because the stress ratios are mostly higher than the phase transformation level where the fabric has reached a limiting orientation. Micro mechanical explanations to the macroscopic behavior of the disc assemblage under cyclic loading are presented in terms of the force and fabric anisotropy coefficients.     

不同含水率作用下砂岩的能量机制研究

水对岩石具有软化、溶蚀和水楔作用,为研究不同含水率作用下岩石的能量机制,利用MTS815岩石力学试验系统开展了5种含水率状态下砂岩的常规三轴压缩试验。结果表明：随含水率的增大,岩石吸收总能量的增速和总量减少;弹性能增速在储能阶段随含水率的增加而减小,但弹性能的释放速率则大致相当,岩石的储能极限随含水率的增大而减小;岩石变形破坏所耗散量随含水率的增加而较小,但不同含水率作用下岩石的峰前和峰后能量耗散速率则大致相当;岩石的耗散能比例可以反应内部的损伤状态,耗散能比例随时间变化呈现出先增大后减小,然后再稳定增长,最后急剧变大的规律;随着含水率的增大,声发射能率的集中程度和强度逐渐减小,声发射累计能量随含水率的增大而减小,表明随着含水率的增加,岩石的储能能力和应变能释放能力降低,岩石的脆性破坏特征减弱,塑性增强。     

On integration of a cyclic soil plasticity model

Performance of three classes of explicit and implicit time‐stepping integrators is assessed for a cyclic plasticity constitutive model for sands. The model is representative of an important class of cyclic plasticity models for soils and includes both isotropic and nonlinear kinematic hardening. The implicit algorithm is based on the closest point projection method and the explicit algorithm follows a cutting‐plane integration procedure. A sub‐stepping technique was also implemented. The performance of these algorithms is assessed through a series of numerical simulations ranging from simulations of laboratory tests (such as triaxial and bi‐axial compression, direct shear, and cyclic triaxial tests) to the analysis of a typical boundary value problem of geotechnical earthquake engineering. These simulations show that the closest point projection algorithm remains stable and accurate for relatively large strain increments and for cases where the mean effective stress in a soil element reaches very small values leading to a liquefaction state. It is also shown that while the cutting plane (CP) and sub‐stepping (SS) algorithms provide high efficiency and good accuracy for small to medium size strain increments, their accuracy and efficiency deteriorate faster than the closest point projection method for large strain increments. The CP and SS algorithms also face convergence difficulties in the liquefaction analysis when the soil approaches very small mean effective stresses. Copyright © 2001 John Wiley & Sons, Ltd.     

冻结粉土三轴压缩变形破坏与能量特征分析

对不同温度和不同围压下的青藏冻结粉土进行了三轴压缩与加卸载试验,得到冻结粉土应力-应变关系曲线、抗压强度等力学参数随温度与围压变化的关系。结果表明,冻结粉土典型应力-应变曲线在低围压下大致可以分为线弹性、峰前塑性变形与峰后软化3个阶段。当? 3 < 3.0 MPa时,应力-应变曲线具有明显的峰后软化现象,随围压的增大,软化现象逐渐减弱,当? 3 达到14 MPa,应变软化现象重新变得明显;冻结粉土的强度与变形模量均随围压的增加先升后降;低围压作用下冻结粉土体积随轴向应变的增加先缩后胀,而高围压下体积变形只有体缩;低围压下冻结粉土体积塑性变形耗散能先是随着体积塑性变形增大而增大,之后由于剪胀而减少,高围压下体积塑性变形耗散能始终增加;剪切塑性变形耗散能与塑性剪应变之间近似成抛物线的关系。     

Non‐isothermal plasticity model for cyclic behaviour of soils

On the one hand, it has been observed that liquefaction‐induced shear deformation of soils accumulates in a cycle‐by‐cycle pattern. On the other hand, it is known that heating could induce plastic hardening. This study deals with the constitutive modelling of the effect that heat may have on the cyclic mechanical properties of cohesive soils, a relatively new area of interest in soil mechanics. In this paper, after a presentation of the thermo‐mechanical framework, a non‐isothermal plasticity cyclic model formulation is presented and discussed. The model calibration is described based on data from laboratory sample tests. It includes numerical simulations of triaxial shear tests at various constant temperatures. Then, the model predictions are compared with experimental results and discussed in the final section. Both drained and undrained loading conditions are considered. The proposed constitutive model shows good ability to capture the characteristic features of behaviour. Copyright © 2007 John Wiley & Sons, Ltd.     

Mechanical properties of cementitious sand and sand with small cyclic shear strain to assess aging effects on liquefaction

Liquefaction damage from earthquakes frequently indicates effects of sand aging on liquefaction resistance: Liquefaction damage in natural or aged reclaimed ground has been much less than that in young reclaimed ground. However, the mechanisms underlying aging effects remain unclear. Cementation and stress history of sand strongly influence aging effects: Cementation raises liquefaction resistance, whereas liquefaction history sometimes reduces liquefaction resistance. Small cyclic shear strain, from which the induced density change is almost negligible, was adopted as representing the stress history. To evaluate liquefaction resistance, initial shear modulus, and deformation characteristics of sand, we prepared specimens by adding cement and by applying a small cyclic shear strain. In cementitious sand, liquefaction resistance increased when cement contents exceeded 0.3% by mass. The initial shear modulus apparently increased at the same degree of cement addition as that which increased the liquefaction resistance. For sand with a small cyclic shear strain, the liquefaction resistance increased when the applied cyclic axial strain exceeded 0.01%. Application of small cyclic shear strain only slightly increased the initial shear modulus, but the linear elastic region tended to expand to greater shear strain. Shear properties of sand with small cyclic shear strain resembled those found for sand that had been consolidated for a long time.

     

Numerical modeling of changes in anisotropy during liquefaction using a generalized constitutive model

A constitutive model with rotation hardening was generalized from the triaxial compression state to a general stress state. With the generalized model, numerical simulations of cyclic and monotonic undrained triaxial tests were conducted to reproduce the phenomenon of continuous, orderly and rapid changes in anisotropy during liquefaction. The simulated results demonstrated that when sand enters the liquefaction stage, the yield surface in the stress space rotates quickly, causing continuous and rapid changes in anisotropy. Through comparison of the simulated and experimental results, the generalized constitutive model was shown to be able to capture the fundamental behaviors of sand demonstrated by the experimental data, and the rotational hardening rule adopted in the generalized model was proven suitable for describing the continuous, orderly and rapid changes in anisotropy that occur during liquefaction.     

分级循环荷载下岩石动力学行为试验研究

利用WDT-1500多功能材料试验机,对砂岩、砾岩和砂砾岩进行了分级循环荷载试验,研究了岩石的动弹性模量对应力幅值和应力水平的响应特性,得到了动弹性模量和耗散能随应力幅值、应力水平及含水率的变化规律。试验结果表明,分级循环荷载下岩石的能量耗散越多,动弹性模量越小;应力水平越高,动弹性模量和耗散能越大;含水率和应力幅值越大,动弹性模量越小,耗散能越大。讨论了邓肯-张模型能够描述分级循环荷载作用下岩石的应力-应变关系,构建了动弹性模量随应力水平、应力幅值及含水率变化的演化模型,探讨了模型参数的确定方法。根据能量耗散的经验法则,建立了耗散能演化模型,结果表明,该模型能够描述分级循环荷载过程中能量耗散行为。