A gradient elasticity theory for second-grade materials and higher order inertia

岩石工程基本术语标准GB/T-50279-98AAbsorbed water 吸着水Abutment 桥台Acoustic emission of rock 岩石声发射Acoustic prospecting 声学探测Active earth pressure 主动土压力Active fault 活断层Activity index 活动性指数Aging 老化allowable bearing capacity 容许承载力allowable settlement 容许沉降alluvial fan 冲积扇alluvial soil 冲积土alternating load 交变荷载anchoring, bolting 锚固ancher slab wall 锚定板墙additional stress, superim/posed stress 附加应力adverse geologic phenomena 不良地质现象aeolian deposit 风积土aeration zone water 包气带水aggregate for concrete 混凝土骨料anticline 背斜aquifer 含水层artesian pressure head承压水头artificial fill 人工填土attitude 产状average thickness method平均厚度法BBack analysis 反演分析Base course 道路基层Bearing capacity factor 承载力因数Bearing stratum 持力层Bedrock 基岩berm 反压平台(反压马道)Biotcon solidation theory 比奥固结理论Bishop’s simplified method of slices 毕肖普简化条分法Blasting 爆破block theory 块体理论body force 体积力borrow area 取土场boulder(stone block) 漂石(块石)Boussinesq theory 布辛涅斯克理论Bridge pier 桥墩Brittle failure 脆性破坏Bulk modulus 体积模量Buoyancy 浮托力buttress retaining wall 支墩式挡墙by/pass seepage 绕渗CCalifornia Bearing Ratio(CBR) 加州承载比Cantilever retaining wall 悬臂式挡墙Capillary water 毛细管水Categorization of geotechnical projects 岩土工程分级Cement stabilization 水泥加固Central load 中心荷载(轴心荷载)Cerruti’s solution 色卢铁解答channel, canal 渠道check dam 谷坊chemical grouting 化学灌浆coarse aggregate 粗骨料coarse/grained soil 粗粒土cobble 卵石(碎石)coefficient of collapsibility 湿陷系数coefficient of compressibility 压缩系数coefficient of consolidation 固结系数coefficient of curvature 曲率系数coefficient of deformation due to leaching 溶滤变形系数coefficient of permeability 渗透系数coefficient of secondary consolidation 次固结系数coefficient of self/weight collapsibility 自重湿陷系数coefficient of uniformity 不均匀系数coefficient of viscosity 粘滞系数coefficient of volume compressibility 体积压缩系数coefficient of weathering 风化系数cohesion 粘聚力cohesionless soil 无粘性土cohesive soil 粘性土collapsibility 湿陷性collapsibility test of loess 黄土湿陷试验collapsible soil 湿陷性土combined bolting and shot crete 喷锚支护compactibility 压实性compaction by rolling 碾压法compaction grouting method 挤密喷浆法compacting machinery 碾压机械compaction test 击实试验composite ground 复合地基composite slip surface 复合滑动面comprehensive engineering geological map 综合工程地质图compressibility 压缩性compression index 压缩指数compressive strength 抗压强度concentrated load 集中荷载(点荷载)concrete faced rock fill dam 混凝土面板堆石坝cone penetration test(CPT) 静力触探试验confined water 承压水consistency limit 稠度界限consolidated/drained triaxial test 固结排水三轴试验consolidated quick shear test 固结快剪试验consolidated/undrained triaxial test 固结不排水三轴试验consolidation 固结consolidation curve 固结曲线consolidation grouting 固结灌浆consolidation settlement 固结沉降consolidation test 固结试验constitutive relation of soil 土的本构关系(本构模型)constrained grain size 限制粒径constrained modulus 压缩模量contact pressure 基底压力(接触压力)contour map of groundwater 地下水等水位线图control of under groundwater 地下水控制core of rock 岩芯core recovery 岩芯采取率core wall 心墙corner/points method 角点法Coulomb/Navier strength theory 库仑/纳维强度理论Coulomb’s earth pressure theory 库仑土压力理论Counter fort retaining wall 扶壁式挡墙Crack growth 裂纹扩展Creep 蠕变Critical edge pressure 临塑荷载Critical height of slope (土坡)临界高度Critical hydraulic gradient 临界水力梯度Critical void ratio 临界孔隙比cross/hole method 跨孔法curtain grouting 帷幕灌浆cushion 垫层cutting 路堑cutoff wall 截水墙cyclic load周期荷载DDarcy’s law 达西定律Debris flow 泥石流Deep mixing method 深层搅拌法Deep soil stabilization 深层土加固Deep well method 深井法Degree of compaction 压实度Degree of consolidation 固结度Degree of saturation 饱和度Delayed elasticity 弹性后效Densification by explosion 爆炸加密法Densification by sand pile 挤密砂桩Density 密度Depletion coefficient 疏干系数Developing chart of exploratory drift 坑硐展示图Dewatering method 降水法Differential settlement 沉降差dike, levee 堤dilatancy 剪胀性dilatancy of rock 岩石扩容diluvial fan 洪积扇diluvial soil 洪积土direct shear test 直剪试验disaster geology 灾害地质学dislocation 位错dispersion coefficient 弥散系数dispersive clay 分散性粘土disturbed soil sample 扰动土样diversion tunnel 导流洞down/hole method 下孔法drainage method 排水法dynamic consolidation 强夯法dynamic load 动荷载dynamic penetration test 动力触探试验dynamic simple shear test 动单剪试验dynamic triaxial test 动三轴试验EEarth dam 土坝Earth material 土料Earth pressure at rest 静止土压力Earthquake engineering 地震工程学Earthquake subsidence 震陷earth/rock dam 土石坝earthwork 土石方工程eccentric load 偏心荷载effective grain size 有效粒径effective porosity 有效孔隙率effective stress 有效应力effective stress analysis 有效应力分析elastic strain 弹性应变electrical prospecting 电法勘探electro/osmosis 电渗法embankment 路堤engineering geologic columnar profile 工程地质柱状图engineering geologic exploration 工程地质勘探engineering geologic drilling 工程地质钻探engineering geologic evaluation 工程地质评价engineering geologic map 工程地质图engineering geologic mapping 工程地质测绘engineering geologic profile 工程地质剖面图engineering geology 工程地质学environmental geotechnics 环境岩土工程equipotential line 等势线equivalent opening size (EOS) 等效孔径excavating machinery 挖掘机械excavation 挖方excess pore water pressure 超静水压力expanded polystyrene (EPS) 聚苯乙烯发泡材料expansive soil 膨胀土FFabric sheet reinforced earth 铺网法Factor of safety 安全系数Failure strength 破坏强度Fall of ground 冒顶Fatigue strength 疲劳强度Fault 断层Field identification of soil 土的现场鉴别Field observation 现场观测Fill 填方Filter 反滤层Final settlement 最终沉降Fine aggregate 细骨料fine/grained soil 细粒土fissured clay 裂隙粘土fissure water 裂隙水flat jack technique 扁千斤顶法flow line 流线flow net 流网fold 褶皱fraction 粒组fracture mechanics 断裂力学fracture zone 断裂破碎带free face 临空面frees welling ratio 自由膨胀率free water 自由水freezing method 冻结法french drain 盲沟fresh rock 新鲜岩石friction/resistance ratio 摩阻比frost heave 冻胀frost/heave capacity 冻胀量frost heaving pressure 冻胀力frozen soil 冻土Ggap/graded soil 不连续级配土general shear failure 整体剪切破坏geo composite 土工复合材料geo drain, prefabricated strip drain 塑性排水带法geo fabriform 土工模袋geogrid 土工格栅geologic environment 地质环境geologic environment element 地质环境要素geologic structure 地质构造geo mechanical model test 地质力学模型试验geomembrane 土工膜geomorphology 地貌geophysical exploration 地球物理勘探geostatic stress 自重应力geosynthetics 土工合成材料geotechnical centrifugal model test 土工离心模型试验geotechnical engineering 岩土工程geotechnical engineering investigation 岩土工程勘察geotextiles 土工织物gradation 级配grain size 粒径grain size distribution curve 粒径分布曲线gravelly soil 砾类土gravitational water 重力水gravity retaining wall 重力式挡墙Griffith’s strength criterion 格里菲斯强度准则Ground fracturing 地裂Ground treatment 地基处理Groundwater 地下水Groundwater dynamics 地下水动力学Groundwater hardness 地下水硬度Groundwater monitoring 地下水监测Groundwater pollution 地下水污染Groundwater recharge 地下水补给量Groundwater regime 地下水动态Groundwater storage 地下水贮存量groin, spur dike 丁坝grouting 灌浆grouting test 灌浆试验guide adit 导洞HHardness degree of rock 岩石坚硬程度Heaving of the bottom 基坑底隆胀Hydraulic fill 水力冲填Hydraulic fracturing technique 水力劈裂法Hydraulic gradient 水力梯度Hydraulic tunnel 水工隧道Hydrogeological drilling 水文地质钻探Hydrogeological investigation 水文地质勘察Hydrogeology 水文地质学Hydrostatic pressure 静水压力IImmediate settlement 初始沉降(瞬时沉降) Impervious blanket 防渗铺盖Impervious layer 不透水层(隔水层)Inclined shaft 斜井Influence chart 感应图infra/red detection 红外探测initial collapse pressure 湿陷起始压力in/situ direct shear test of rock 岩石原位直接剪切试验in/situ test 原位试验intactness index of rock mass 岩石完整性指数(岩体速度指数)intact rock 完整岩石internal friction angle 内摩擦角interstrated water 层间水investigation stage 勘察阶段isochrone 等时孔压线isoline method等值线法JJet grouting method 高压喷射注浆法Joint 节理KKaiser effect 凯塞效应Karst 喀斯特(岩溶)Karst collapse 喀斯特塌陷Karst land feature喀斯特地貌K/consolidation K固结LLaminar flow 层流Land form unit 地貌单元Landslide 滑坡Landslide mass 滑坡体Land subsidence 地面下沉Laterite 红土Layer wise summation method 分层总和法Lime pile method 石灰桩法Lime soil pile 灰土桩Lime treated soil 灰土Limit equilibrium method 极限平衡法Linear shrinkage ratio 线缩率Line load 线荷载Liquefaction of sand 砂土液化Liquefaction potential 液化势Liquidity index 液性指数Liquid limit 液限Local shear failure 局部剪切破坏Loess 黄土loess/like soil 黄土状土longitudinal dike 顺坝long/term modulus 长期模量long/term stability 长期稳定性Lugeon unit 吕荣单位MMagmatic rock (igneous rock) 岩浆岩(火成岩) Marine soil 海积土Masonry retaining wall 砌体挡墙Maximum dry density 最大干密度Mechanical properties of rock 岩石力学性质Mechanics of granular media 散体力学Metamorphic rock 变质岩Method of slice 条分法micro/crack 微裂纹Mindlin’s solution 明德林解答Mini pile 微型桩Modified Griffith’s criterion 修正的格里菲斯准则Modulus of deformation 变形模量Modulus of elasticity 弹性模量(杨氏模量) Modulus of pressure meter 旁压仪模量Mohr/Coulomb law 摩尔库仑定律Monitoring of land slide 滑坡监测Monitoring of pore/water pressure 孔隙水压力监测Monitoring of settlement and deformation 沉降变形监测Monitoring of surrounding rock deformation of tunnel 洞室围岩变形监测Muck 淤泥mud pumping 翻浆冒泥NNatural angle of repose 天然休止角Natural building materials 天然建筑材料needle/punched geotextile 针刺土工织物New Austrian Tunnelling Method (NATM) 新奥法non/uniform settlement 不均匀沉降non woven geotextile 无纺土工织物normalization 归一化normally consolidation soil 正常固结土OOptimum moisture content 最优含水率Organic soil 有机质土Osmosic pressure method 渗透压法Outand cover method 明挖法Over break 超挖Overburden layer 覆盖层Overburden pressure 覆盖压力Over consolidation soil 超固结土Over consolidation ratio (OCR) 超固结比Over coarse/grained soil 巨粒土PPacked drain, fabric/enclosed drain 袋装砂井Parallel section method 平行断面法Parapet wall 防浪墙Particle size analysis 颗粒分析试验Passive earth pressure 被动土压力Peak strength 峰值强度Peat 泥炭Penetration resistance 贯入阻力Perched water 上层滞水Perennially frozen soil 多年冻土Permeability 渗透性Permeability test 渗透试验Phreatic line 浸润线Phreatic water 潜水Physical properties of rock 岩石的物理性质Piezo cone test (CPTU) 孔压静力触探试验Piezo metric head 测压管水头Pipe jacking method 顶管法Piping 管涌Plane strain test 平面应变试验Plastic failure 塑性破坏Plastic flow 塑流Plastic limit 塑限Plastic strain 塑性应变Plastic zone 塑性区Plasticity chart 塑性图Plasticity index 塑性指数Plate loading test 平板荷载试验Point loading test 点荷载试验Poisson’s ratio 泊松比poorly/graded soil 不良级配土pore air pressure 孔隙气压力pore pressure 孔隙压力pore pressure parameter 孔隙水压力系数pore pressure ratio 孔隙压力比pore water 孔隙水pore water pressure 孔隙水压力porosity 孔隙率pre consolidation pressure先期固结压力preloading method 预压法pressure bulb 压力泡pressure meter test (PMT) 旁压试验primary stress 初始应力(地应力)primary consolidation 主固结principle of effective stress 有效应力原理progressive failure 渐近破坏prototype monitoring 原型监测punching shear failure 冲剪破坏pump/in test 压水试验pumping test 抽水试验QQuicksand 流砂Quick shear test 快剪试验RRadial flat jack technique 径向扁千斤顶法Radial wells 辐射井Radius of influence 影响半径Rankine’s earth pressure theory 兰金土压力理论Rate of settlement 沉降速率Rate of stripping 剥离比Rebound modulus 回弹模量Rebound of foundation 地基回弹Recharge area 补给区Recharge rate 补给率Recharge method 回灌法Reclamation 围垦工程Reinforced earth 加筋土Reinforced soil wall 加筋土挡墙Relative density 相对密度Relaxation time 松弛时间Relief well 减压井Remolded strength 重塑强度Remote sensing prospecting 遥感勘测Reserve of building material 建材储量Residual soil 残积土Residual strength 残余强度Resonant column test 共振柱试验Retaining wall 挡土墙(挡墙)Retardation 滞后Rheology 流变学Road pavement 道路路面Rock 岩石Rock burst 岩爆Rock classification 岩石分类Rock engineering 岩石工程Rock fall 岩崩Rock fill dam 堆石坝Rock mass 岩体Rock mass basic quality (BQ) 岩体基本质量Rock mechanics 岩石力学(岩体力学)Rock quality designation (RQD) 岩石质量指标Rolled fill earth dam 碾压土坝Rolling compaction test 碾压试验Root pile 树根桩Rose diagram of joints 节理玫瑰图Run off area 径流区rupture, fracture 断裂SSaline soil 盐渍土Sand drain 排水砂井Sandy soil 砂井土Saturation curve 饱和曲线Scale effect 尺度效应Seasonally frozen soil 季节冻土Secondary consolidation 次固结Secondary consolidation settlement 次固结沉降Sedimentary rock 沉积岩Seepage 渗流Seepage deformation 渗透变形Seepage failure 渗透破坏Seepage force 渗流力Seepage path 渗径Seismic prospecting 地震勘探self/boring pressure meter 自钻式旁压仪semi/infinite elastic body 半无限弹性体sensitivity 灵敏度settlement 沉降settlement calculation depth 沉降计算深度settlement curve 沉降曲线shea rmodulus 剪切模量shear strain 剪应变shear strength 抗剪强度sheet pile wall 板桩墙shield driving method 盾构法shot concrete 喷射混凝土shrinkage index 缩性指数shrinkage limit 缩限side ditch 侧沟simple shear test 单剪试验slaking 湿化slide/resistant pile 抗滑桩slip surface 滑动面slip zone 滑动带slope wash 坡积土sloping core 斜墙slow shear test 慢剪试验soft clay 软粘土soil 土soil dynamics 土动力学soil fabric 土的组构soil flow 流土soil mass 土体soil mechanics 土力学soil nailing 土钉soil sampler 取土器soil skeleton 土骨架soil structure 土的结构soldier pile 排桩special soil 特殊土specific gravity of soil particle 土粒比重specific grout absorption 单位吸浆量(比吸浆量)specific penetration resistance 比贯入阻力specific surface 比表面积specific water absorption 单位吸水量specific yield 给水度split test 劈裂试验(巴西试验)stability analysis 稳定分析stability number 稳定数stable crack growth稳定裂纹扩展standard penetration test (SPT) 标准贯入试验state of plastic equilibrium 塑性平衡状态steady seepage 稳定渗流stereo graphic projection 赤平投影stone material 石料storage coefficient 储水系数strain controlled test 应变控制试验strain hardening 应变硬化strain space 应变空间strain softening 应变软化strength envelope 强度包线stress concentration 应力集中stress controlled test 应力控制试验stress distribution 应力分布stress history 应力历史stress level 应力水平stress path 应力路径stress recovery method 应力恢复法stress relaxation 应力松弛stress relief method 应力解除法stress space 应力空间strip load 条形荷载structural block 结构体structural plane 结构面structural types of rock mass 岩体结构类型subsurface runoff 地下径流surcharge 超载surface force 表面力surface soil stabilization 浅层土加固surface water 地表水surface wave velocity method 表面波法surrounding rock 围岩surrounding rock stress 围岩应力(二次应力) Swedish circle method 瑞典圆弧法Swelling force 膨胀力Swelling index 回弹指数Swelling ratio 膨胀率Syncline 向斜TTailings dam 尾矿坝Tensile strength 抗拉强度Terzaghi’s consolidation theory 太沙基固结理论texsol, fibre soil 纤维土thaw collapsibility 融陷性thick wall sampler 厚壁取土器thin wall sampler 薄壁取土器thixotropy 触变性three phase diagram 三相图tie back wall, anchored wall 锚杆挡墙time factor 时间因数torsional shear test 扭剪试验total mineralization of ground/water 地下水总矿化度total stress 总应力total stress analysis 总应力分析transducer 传感器transient load 瞬时荷载transmissivity 导水系数trench 探槽trench out method 挖沟法triangular method 三角形法triaxial compression test 三轴压缩试验(三轴剪切试验)triaxial extension test 三轴伸长试验truetriaxial test 真三轴试验tunnel 隧道tunnel lining 隧道衬砌turbulent flow 紊流UUltimate bearing capacity 极限承载力Unconfined compressive strength test 无侧限抗压强度试验Unconsolidated undrained triaxial test 不固结不排水三轴试验under/consolidated soil 欠固结土underground diaphragm wall 地下连续墙underground opening 地下洞室under lying stratum 下卧层underpinning 托换技术undisturbed soil sample 不扰动土样(原状土样)uniformly distributed load 均布荷载unit weight 容量up/hole method 上孔法uplift pressure 扬压力VVacuum preloading 真空预压法Valley terrace 河谷阶地Vane shear test 十字板剪切试验Varved clay 带状粘土Vertical shaft 竖井Vibro flotation 振冲法Void ratio 孔隙比Volumetric strain 体应变Volume shrinkage ratio 体缩率WWater bearing capacity 容水量Water content 含水率Water injecting test 注水试验Water retaining capacity 持水度Weak intercalated layer 软弱夹层Weak structural plane 软弱结构面Weathered crust 风化壳Weathered rock 风化岩石Weathered zone 风化带Weathering 风化作用Weathering degree of rock 岩石风化程度Well point 井点排水well/graded soil 良好级配土Winkler’s assumption 文克勒假定YYield 屈服Yield criteria 屈服准则。

• Motion follows from
Newton’s 2nd Law
Fi mi ai
Research
Equations of Motion
Newton’s 2nd Law
Fi mi ai
Equations of motion for one mass point (3 equations) Equations of motion for system of mass points (3n equations)
F k l L
xj
Force in 3D
F
Fi k xi x j L

x x
i
xi x j
j
Initial spring length L Current spring length l Spring stiffness k
Research
Elastic Energy
Research
20
Dynamics
Force is known for every particle. How do we determine motion xi t ?
• Kinematic relations
Velocity
v i (t ) d x i (t ) dt
Acceleration 2 d v i (t ) d x i (t ) a i (t ) dt dt 2
l
xj
F
L
Elastic spring energy gradient of Force = – energy
1 E W k (l L) 2 2
E Fi xi
Research

vibrations in hotter region carry energy (vibrations) to cooler regions. In a metal, electrons are free and thus dominate thermal conductivity. In a ceramic, phonons are more important.
T3 T2 T0
Thermal Expansion
• If the curve is not symmetric, the average position in which the atom sits shifts with temperature. • Bond lengths therefore change (usually get bigger for increased T). • Thermal expansion coefficient is nonzero.
THERMAL CONDUCTIVITY
K=kl+ke: Again think about band gaps: metals have lots of free electrons (ke is large), while ceramics have few (only kl is active).
heat flux (J/m2-s)
q k
ቤተ መጻሕፍቲ ባይዱ
dT
gradient
Fick’s First Law
dx k=thermal conductivity (J/m-K-s): Defines material’s ability to transfer heat.
Atomic view: Electronic and/or Atomic

186
The experimentally obtained cyclic stress-strain points at room temperature and 873K are plotted in Figure 1 in terms of the stable stress amplitude and plastic strain amplitude. The cyclic stress-strain relation is considered to follow Ramberg-Osgood equation:
Energy Materials 2014 The Chinese Society for Metals (CSM) and The Minerals, Metals & Materials Society (TMS) TMS, 2014
AN EXPERIMENTAL STUDY ON THE LOW CYCLE FATIGUE BEHAVIORS OF DOMESTIC IP ROTOR STEEL FOR 1000MW ULTRA-SUPERCRITICAL TURBINE
σ / 2 K ' (△ε p / 2) n
'
(1)
Where σ is the stress range of the stable hysteresis cycle Nf/2, △ε p is the plastic strain range, K ' is the cyclic strength coefficient, and n ' is the cyclic strain hardening exponent. Through curve fitting we obtain: RT: σ / 2 1017.21 (△ε p / 2) 0.0683 873K: σ / 2 498.99 (△ε p / 2) 0.0739 (2) (3)