Mechanical behavior of rock under uniaxial tension:Insights from energy storage and dissipation

Many rock engineering projects show that the growth of tensile cracks is often an important cause of engineering disasters,and the mechanical behavior of rocks is essentially the transmission,storage,dissipation and release of energy.To investigate the tensile behavior of rock from the perspective of energy,uniaxial tension tests(UTTs)and uniaxial compression tests(UCTs)were carried out on three typical rocks(granite,sandstone and marble).Different unloading points were set before the peak stress to separate elastic energy and dissipated energy.The input energy density ut,elastic energy density ue,and dissipated energy density ud at each unloading point were calculated by integrating stress-strain curves.The results show that there is a strong linear relationship between the three energy parameters and the square of the unloading stress in UCT,but this linear relationship is weaker in UTT.The ue and ud increase linearly with the increase in ut in UCT and UTT.Based on the phenomenon that ue and ud increase linearly with ut,the applicability of W_(et)^(p) index in UTT was proved and the relative energy storage capacity and absolute energy distribution characteristics of three rocks in UCT and UTT were evaluated.The tensile behavior of marble and sandstone in UTT can be divided into two stages vaguely according to the energy distribution,but granite is not the case.In addition,based on dissipated energy,the damage evolution of three types of rocks in UCT and UTT was discussed.This study provides some new insights for understanding the tensile behavior of rock.

Mechanical response and dilatancy characteristics of deep marble under different stress paths:A sight from energy dissipation

Dilatancy is a fundamental volumetric growth behavior observed during loading and serves as a key index to comprehending the intricate nonlinear behavior and constitutive equation structure of rock.This study focuses on Jinping marble obtained from the Jinping Underground Laboratory in China at a depth of 2400 m.Various uniaxial and triaxial tests at different strain rates,along with constant confining pressure tests and reduced confining pressure tests under different confining pressures were conducted to analyze the mechanical response and dilatancy characteristics of the marble under four stress paths.Subsequently,a new empirical dilatancy coefficient is proposed based on the energy dissipation method.The results show that brittle failure characteristics of marble under uniaxial compression are more obvious with the strain rate increasing,and plastic failure characteristics of marble under triaxial compression are gradually strengthened.Furthermore,compared to the constant confining pressure,the volume expansion is relatively lower under unloading condition.The energy dissipation is closely linked to the process of dilatancy,with a rapid increase of dissipated energy coinciding with the beginning of dilatancy.A new empirical dilatancy coefficient is defined according to the change trend of energy dissipation rate curve,of which change trend is consistent with the actual dilatancy response in marble under different stress paths.The existing empirical and theoretical dilatancy models are analyzed,which shows that the empirical dilatancy coefficient based on the energy background is more universal.

Energy dissipation of a ring-like metal rubber isolator

Metal rubber （MR） is a kind of homogeneous poroelastic damping material made of metal wire. In this paper, by ana- lyzing the forces on the MR isolator and the MR element, the hysteresis loops of the force and deformation are studied and verified by experiments. The results show that the force and displacement hysteresis loop of the MR isolator is described by the force and deformation hysteresis loops of the MR elements. In addition, the relationship between the energy dissipation coefficient of the MR element and that of the MR isolator is derived. The energy dissipation coefficient is programmed and calculated by MATLAB using experimental data, and the results are compared with the theoretical value. It is the basis for the design and applied research of the MR isolator in a future study.

Gravity field recovery from GOCE orbits using the energy conservation approach

The sum of the dissipative energy and energy constant of the GOCE satellite is found by a priori gravity field model at first, and the GOCE dissipative energy is obtained by computing the adjacent epoch difference via the differential method. Then, a gravity field model GOCE-ECPO1, which up to the degree and order 80, is recovered by the energy conservation approach from the 103-day precise orbital data of the GOCE satellite collected from November 1, 2009 to January 12, 2010. Finally, the model is compared with existing models EGM96, ITG-CHAMP05S, EIGEN-GRACE2010S, EIGEN-6C and GO CONS GCF 2 DIR_R3. The results show that at the same order and degree, the accuracy of model GOCE-EBPO1 is higher than those of models EGM96 and ITG-CHAMP05S, but lower than those of models EIGEN-GRACE2010S, EIGEN-6C and GO_CONS_GCF 2 DIR_R3, which is mainly caused by the pole gap.

Hydrodynamic Coefficient Investigation on a Partial Permeable Stepped Breakwater Under Regular Waves

Traditional breakwater takes the advantage of high protection performance and has been widely used.However,it contributes to high wave reflection in the seaside direction and poor water exchange capacity between open seawater and an inside harbor.Consequently,a partially permeable stepped breakwater(PPSB)is proposed to ensure safety and good water exchange capacity for an inside harbor,and a 3-D computational fluid dynamics(CFD)mathematical model was used to investigate the hydrodynamic coefficients using Reynolds-Averaged Navier-Stokes equations,Re-Normalization Group(RNG)k-εequations,and the VOF technique.A series of experiments are conducted to measure the wave heights for validating the mathematical model,and a series of dimensionless parameters considering wave and PPSB effects were presented to assess their relationships with hydrodynamic coefficients,respectively.With the increase in the reciprocal value of PPSB slope,incident wave steepness and permeable ratio below still water level(SWL),the wave reflection coefficient decreases.The wave transmission coefficient decreases with an increase in the reciprocal value of the PPSB slope and incident wave steepness;however,it increases with the increase in the permeable ratio below SWL.With increases in the reciprocal value of the PPSB slope,permeable ratio below SWL and incident wave steepness for relatively high wave period scenarios,the wave energy dissipation coefficient increases;however,it decreases slightly with increases in the incident wave steepness for the smallest wave period scenarios.Furthermore,simple prediction formulas are conducted for predicting the hydrodynamic coefficients and they are well validated with the related data.

Propagation of Waves in a Two-Temperature Rotating Thermoelastic Solid Half-Space without Energy Dissipation

The present paper is concerned with the propagation of plane waves in an isotropic two-temperature generalized thermoelastic solid half-space in context of Green and Naghdi theory of type II (without energy dissipation). The governing equations in x – z plane are solved to show the existence of three coupled plane waves. The reflection of plane waves from a thermally insulated free surface is considered to obtain the relations between the reflection coefficients. A particular example of the half-space is chosen for numerical computations of the speeds and reflection coefficients of plane waves. Effects of two-temperature and rotation parameters on the speeds and the reflection coefficients of plane waves are shown graphically.

Pseudocritical Rapid Energy Dissipation Analysis of Base-Load Electrical Demand Reduction on Nuclear Steam Supply System

Effect of pseudocritical rapid energy dissipation (PRED) from Pressurizer in nuclear steam supply system of Pressurized Water Reactor, where a single event as common cause failure, of considerable reduction of base-load electricity demand causes the temperature of the reactor coolant system (RCS) to increase, and corresponding pressure increases in pressurizer and steam generators above set-points. The study employed the uses of MATLAB/Simulink library tools, to experimentally modelled pressure control as PRED, where the momentum of transport of kinematic viscosity fraction above pseudocritical point dissipated as excess energy, to maintain the safety of the Pressurizer and RCS and keep the water from boiling. The result demonstrated the significance of pressure vector and Prandlt number as heat transfer coefficients that provided detailed activities in 2-D contour and 3-D graphics of specific internal energy and other parameterization of fluid in the pressurizer.

基于修正耗散能的水工混凝土损伤分析

能量耗散是混凝土变形破坏的本质属性,以能量研究岩体和混凝土等准脆性材料的破坏是一条可行的途径。然而,现有的以能量定义损伤变量的损伤分析结果与混凝土实际的破坏演变过程并不一致。本文通过建立损伤变量与耗散能之间的新关系,认为导致混凝土损伤的并非是全部耗散能,而是其中的一部分。因此,将耗散能分为两部分,一部分是引起混凝土损伤的耗散能,另一部分是混凝土在荷载作用下功-能转化过程中的其他耗散能。通过引入损伤耗能修正系数λ,定义损伤变量,并根据实测试验曲线确定λ值,建立了损伤演化方程。针对实测试验曲线的损伤分析结果表明,采用该方法计算的损伤演化过程与试验曲线更为吻合。将该方法应用于水工混凝土规范给出的应力应变曲线,揭示了水工混凝土损伤演化过程中损伤变量和等效塑性应变的变化规律,可为开展水工混凝土的损伤分析研究提供可行的途径。

自然老化服役后板式橡胶支座摩擦滑移性能试验研究

为了解自然老化服役后板式橡胶支座的摩擦滑移性能,取实际桥梁中服役10年的7个板式橡胶支座进行摩擦滑移试验,分析不同竖向压应力下支座摩擦滑移规律,研究自然老化板式橡胶支座的水平弹性刚度、摩擦系数及耗能能力等,并对比人工热老化支座的相关性能。结果表明:相同服役年限的自然老化板式橡胶支座老化程度并不相同;自然老化板式橡胶支座摩擦系数随着竖向压应力的增大而减小,水平弹性刚度随着竖向压应力的增大而增大;压剪作用对老化板式橡胶支座的耗能能力影响较小,但需要注意累积的摩擦滑移会使支座耗能能力降低。自然老化板式橡胶支座(试验值)相较于未老化支座(理论值)的表面摩擦系数有所降低,但水平弹性刚度明显增大;自然老化板式橡胶支座水平弹性刚度增大幅度远高于人工热老化的板式橡胶支座,人工热老化研究严重低估了自然老化对板式橡胶支座的危害。

黄河流域黏性泥沙群体沉速计算分析

针对黄河流域由黏性矿物组成的黏性泥沙群体沉降特征展开研究。基于泥沙颗粒受力分析和能量守恒定律,以处于稳态的泥沙颗粒为参照物,构建了泥沙颗粒水沙界面能量耗散物理图形;建立了考虑挟沙水流运动黏性系数和紊动黏性系数的泥沙群体沉速显式表达式,并采用黄河流域典型黏性泥沙红色砒砂岩颗粒开展了泥沙群体沉速试验研究。结果表明:红色砒砂岩组成的含沙水体中泥沙群体沉速整体随含沙量增大而减小并逐渐趋于定值;当垂向平均含沙量为0.34~0.45 kg/m^(3)时,泥沙群体沉速表现为随含沙量的增加而增大。采用试验数据对建立的公式进行验证,公式能较合理地表达水流黏性和尾流分离对泥沙颗粒沉降阻力的影响。研究结果可为黄河流域黏性泥沙淤积和输移规律研究提供参考。

连续弯段溢洪道糙条消能工整流特性试验研究

为探究糙条消能工在连续弯段溢洪道上导流效果影响因子排序和糙条导流特性,采取9因素3水平的正交试验设计方案进行物理模型试验,引入超高变异系数C v对导流效果进行评价;对影响水流结构的因子进行量纲分析及多元回归处理,建立评价导流效果的多因素影响模型。结果表明:糙条布设角度和糙条高度分别对2个弯段中水流结构影响最大,这2个因素直接影响糙条平衡水面差、稳定流态效果的优劣。剔除影响较小的共用因素,得出糙条消能工最优导流布置方案;各类函数模型中最大拟合优度为0.822,拟合方程对实测值进行对比验证,二者相对误差范围在2.78%~7.15%之间。研究成果可为连续弯段溢洪道整流分析提供理论参考。

孤立波与多排水平板相互作用的数值研究

利用FLUENT进行二维波浪水槽数值模拟,对孤立波作用下多排水平板的水动力特性开展研究。首先通过与试验结果的对比,验证数值模型在处理孤立波与水平板相互作用问题上的准确性;然后分析相对波高、板宽、相对板间隙和相对潜深等参数对多排水平板消浪性能的影响,通过分析流场和涡量场,讨论多排水平板结构的消波机理。研究结果表明:当相对板间隙j/B在0.02~0.10范围内时,多排水平板的消浪效果最好,优于单排水平板;多排水平板为水体交换提供了空间,并降低了结构受力,在减少施工用料的同时还具有良好的消浪能力。

糙条对溢洪道连续弯段水流特性的影响

为探究溢洪道连续弯段水流特性及糙条消能工水力学特性,通过开展27组正交模型试验,结合消能率和超高变异系数筛选最优工况,采用RNG k-ε紊流模型与体积分数法(volume of fluid,VOF)对布设糙条和不布设糙条的溢洪道进行水流特性数值模拟对比研究。结果表明:糙条的布设使溢洪道沿程水深增加且变化剧烈;糙条能够抑制菱形波和折冲水流的产生,通过改善两弯段流态使水面均匀性提升38.0%和44.7%;布设糙条后,两弯段纵向流速均值被降低了45.16%和44.83%,各断面凹岸纵向流速的最大值沿水深下移;糙条的存在加剧了水流紊动,使两弯段纵向紊动强度均值增加了117.98%和71.05%,纵向紊动强度集中在凹岸衰减、凸岸增强,且各断面凹岸的最大值沿水深上移;糙条增大了床面动水压力,减小了两岸压力差,对压力分布形式有显著改善效果,有助于保护底板和边壁不易被冲蚀。研究成果可为溢洪道连续弯段设计及安全运行提供参考。

超长溢流宽度大流量溢洪道泄洪水力特性研究

受地形、地质等因素的影响,超大库容、大泄量水利工程泄量分配与消能防冲问题十分复杂。尼雷尔工程采用堰上低水头、超长溢流宽度、大泄量溢洪道布置形式。为准确了解尼雷尔工程溢洪道实际泄洪能力和下游消能防冲与汇流等水力特性,通过模型试验与数值模拟相结合的方法,对不同方案下溢洪道的流量系数、消能率、坝后水流归槽情况、河道流速等进行了研究。研究结果表明:原设计低水头高堰溢洪道实际过流能力满足设计要求,采用数值模拟方法可以避免模型试验中缩尺效应的影响;坝面采用台阶高度1.5 m的消能方式消能效果最佳,护坦内部的侧向汇流也比较平稳顺畅,两侧来流在护坦内对撞消能后进入下游主河槽,坝后主河槽平均水深增大近30%,平均流速降低约20%。研究结果可为高坝大库容工程的泄洪消能设计提供参考。

孔隙率对矩形沟槽上垂直多孔屏障的波浪散射效应影响

The effect of porosity on surface wave scattering by a vertical porous barrier over a rectangular trench is studied here under the assumption of linearized theory of water waves.The fluid region is divided into four subregions depending on the position of the barrier and the trench.Using the Havelock’s expansion of water wave potential in different regions along with suitable matching conditions at the interface of different regions,the problem is formulated in terms of three integral equations.Considering the edge conditions at the submerged end of the barrier and at the edges of the trench,these integral equations are solved using multi-term Galerkin approximation technique taking orthogonal Chebyshev’s polynomials and ultra-spherical Gegenbauer polynomial as its basis function and also simple polynomial as basis function.Using the solutions of the integral equations,the reflection coefficient,transmission coefficient,energy dissipation coefficient and horizontal wave force are determined and depicted graphically.It was observed that the rate of convergence of the Galerkin method in computing the reflection coefficient,considering special functions as basis function is more than the simple polynomial as basis function.The change of porous parameter of the barrier and variation of trench width and height significantly contribute to the change in the scattering coefficients and the hydrodynamic force.The present results are likely to play a crucial role in the analysis of surface wave propagation in oceans involving porous barrier over submarine trench.

液舱晃荡对压载水型浮式防波堤消浪性能的影响

基于计算流体力学(CFD)方法,建立了波浪与压载水型浮式防波堤相互作用的数值模型,模拟分析了波浪场分布特征,探究了液舱晃荡对压载水型浮式防波堤消浪性能的影响.结果表明:压载水型浮式防波堤通过减小防波堤运动响应和增大对入射波能量的消耗来提升消浪性能;对比干砂型浮式防波堤,压载水型浮式防波堤消浪性能最高可提升21.9%;常见入射波浪频率接近液舱晃荡固有频率,引起舱内液体会发生共振现象,导致防波堤消浪性能减弱;在防波堤液舱内部加入竖向挡板,改变其液舱晃荡的固有频率,加入挡板后防波堤消浪性能最高可提升51.6%.结果有望为海岸防护工程领域提供新的思路和解决方案,为实际工程提供一定的参考.

循环荷载下岩石阻尼参数测试的试验研究

对岩石阻尼参数测试进行理论分析,利用MTS815FlexTestGT岩石力学试验系统,对细砂岩和粉砂质泥岩进行单轴压缩循环荷载下的试验研究。试验加载波形为正弦波,频率3Hz,加卸载振动循环30次,动应力范围1.0～6.5MPa(即2～12kN)。利用循环加卸载试验方法对岩石阻尼参数进行测试,得到岩石密度与加卸载循环塑性变形、滞回环面积、阻尼比、阻尼系数等的变化特征。在相同测试条件下,岩石密度越大,循环加卸载得到滞回环间的塑性变形则越小,相互滞回环间距为紧密型;反之则塑性变形大,滞回环间距为稀疏型;岩石密度越大,滞回环面积则越小,岩石发生的能量耗散则越小,反之则滞回环面积大,能量耗散也大;阻尼比随密度增加而减小,阻尼系数则大致增加,故可通过岩石密度初步定性判断其阻尼参数特征。

双层开孔消浪板结构消能性能分析

双层开孔消浪板是一种新型消能结构,其结构通过上层开孔板和下层实心板两部分来解决结构的消能问题.文中通过模型试验的方法来验证结构的消能性能,同时,对双层开孔消浪板结构在规则波作用下的消能系数随3个主要影响因子(相对板宽B/L,相对开孔A/A0,波陡H/L)变化的结果进行分析.通过分析和比较消能系数与影响因子之间的相互关系,证明双层开孔消浪板结构具有较好的消能效果.

坡面细沟侵蚀断面形态发育影响因素分析及动力特性试验

研究细沟形态发育过程对认识细沟侵蚀具有重要作用,该文采用6种坡度(2°、4°、6°、8°、10°、12°),5种流量(8、16、24、32、40 L/min)下的组合冲刷试验,系统研究了坡面细沟横纵断面形态发育影响机制及动力特性。结果表明:细沟宽深比变化范围为3.006~4.884,根据水力最佳断面,细沟水流远未达到稳定。横断面形态系数随坡度的变化范围为0.36~0.522,细沟横断面形态随流量、坡度以及冲刷历时均趋近于梯形水力最佳断面,即阻力最小的断面。随着流程长度的增加,横断面形态由宽深逐渐变窄,横断面形态系数也随之减小。细沟纵断面形态范围为0.60~11.26,且随坡度的增大而增大,与流量相关性不大。综合阻力系数及消能率均与细沟纵断面形态系数呈良好的幂函数关系。

不同循环加载条件下岩石阻尼比和阻尼系数研究

为了合理地描述岩石的阻尼行为,提出了考虑轴向和环向阻尼振动的岩石阻尼参数计算方法;通过动循环荷载、分级循环荷载和常幅循环荷载试验,对比分析了这3种不同应力路径下砂岩、砾岩及砂砾岩的阻尼特性,得到了阻尼参数对应力幅值、应变幅值的响应特性,揭示了常幅循环加载过程中阻尼比和阻尼系数随循环次数的演化规律;从熵守恒和能量守恒定律出发,建立了岩石阻尼比随循环次数演化的经验模型。结果表明:(1)动荷载下岩石的阻尼比与轴向应变幅值成线性递增,而阻尼系数恰好相反;分级循环荷载下岩石的阻尼参数都随应力幅值成线性递增。(2)疲劳破坏门槛值是岩石耗散能和阻尼比演化规律发生变化的分界点,在应力上限高于疲劳破坏门槛值时,耗散能、阻尼比及阻尼系数随循环次数都呈3阶段的变化规律,演化曲线呈半U型;在应力上限低于疲劳破坏门槛值时,呈现2阶段的发展规律,演化曲线呈L型;(3)通过砂岩的阻尼比试验,验证了所建模型能够描述砂岩在常幅循环荷载过程中阻尼行为。