Investigation of the influence of intermediate principal stress on the dynamic responses of rocks subjected to true triaxial stress state

Precisely understanding the dynamic mechanical properties and failure modes of rocks subjected to true triaxial stress state(σ_1 σ_2 σ_3, where σ_1, σ_2, and σ_3 are the major principal stress, intermediate principal stress, and minor principal stress, respectively) is essential to the safety of underground engineering. However, in the laboratory, it is difficult to maintain the constant true triaxial stress state of rocks during the dynamic testing process. Herein, a numerical servo triaxial Hopkinson bar(NSTHB) was developed to study the dynamic responses of rocks confronted with a true triaxial stress state, in which lateral stresses can maintain constant. The results indicate that the dynamic strength and elastic modulus of rocks increase with the rise of intermediate principal stress σ_2, while the dynamic elastic modulus is independent of the dynamic strain rate. Simulated acoustic emission distributions indicate that the intermediate principal stress σ_2 dramatically affects dynamic failure modes of triaxial confined rocks. As σ_2 increases, the failure pattern switches from a single diagonal shear zone into two parallel shear zones with a small slant. Moreover, a recent triaxial Hopkinson bar experimental system using three bar pairs is also numerically established, and the measuring discrepancies are identified between the two numerical bar systems. The proposed NSTHB system provides a controllable tool for studying the dynamic triaxial behavior of rocks.     

一种考虑主应力空间的岩石非线性真三轴强度准则

为评估岩石的真三轴强度特性,首先根据常规三轴试验岩石强度的变化规律,提出基于偏应力极值的非线性强度准则,并与12种岩石试验强度和4种典型岩石强度准则进行对比,发现该强度准则的预测值与试验强度非常接近,相关性系数R~2均在0.98以上,平均相对误差(MAPE,E_(MAP))均小于4%(除7号岩石为6.83%);该强度准则、指数准则、H-B准则、MM-C准则和D-P准则对所有12种岩石预测E_(MAP)的平均值分别为2.32%、2.43%、5.28%、7.39%和13.74%,说明该强度准则能够很好地预测不同类型岩石的强度,其预测精度略优于指数准则(岩石力学界认为预测精度较高的强度准则),远好于其他3种强度准则。在上述所建常规三轴强度准则的基础上,通过引入中主应力参数和罗德应力参数,构建考虑中主应力效应的真三轴强度准则,并与8种岩石的真三轴试验强度进行对比,该强度准则很好地反映了大主应力随中主应力的增加呈先增大后减小的变化规律,所得R~2均在0.9以上,其中5种岩石的R~2大于0.96;除了13和14号岩石(E_(MAP)分别为7.79%和4.84%),其余6种岩石的平均相对误差E_(MAP)均小于4%,说明该强度准则能够较好地预测岩石的真三轴试验强度,很好地反映了中主应力效应,具有良好的普遍适用性。子午面和偏平面的应力空间特征也说明该强度准则很好地反映了岩石的静水压力效应和中主应力对大主应力的影响规律。     

Creep properties and permeability evolution in triaxial rheological tests of hard rock in dam foundation

Triaxial creep tests were carried out under seepage pressure by using rock servo-controlled triaxial rheology testing equipment. Based on experimental results, rock rheological properties influenced by seepage-stress coupling were studied, and variations of seepage rate with time in complete creep processes of rock were analyzed. It is shown that, when the applied stress is less than failure stress level, the creep deformation is not obvious, and its main form is steady-state creep. When applied stress level is greater than or less than but close to fracture stress, it is easier to see the increase of creep deformation and the more obvious accelerative creep characteristics. The circumferential creep deformation is obviously higher than the axial creep deformation. At the stage of steady-state creep, the average of seepage flow rate is about 4.7×10⁻⁹ m/s at confining pressure (σ ₃) of 2 MPa, and is about 3.9×10⁻⁹ m/s at σ ₃ of 6 MPa. It is seen that the seepage flow rate at σ ₃ of 2 MPa in this case is obviously larger than that at σ ₃ of 6 MPa. At the stage of creep acceleration, the seepage flow rate is markedly increased with the increase of time. The variation of rock permeability is directly connected to the growth and evolution of creep crack. It is suggested that the permeability coefficient in complete creep processes of rock is not a constant, but is a function of rock creep strain, confining pressure, damage variable and pore water pressure. The results can be considered to provide a reliable reference for the establishment of rock rheological model and parameter identification.     

An improved hypoplastic constitutive model of rockfill considering effect of stress path

An incrementally nonlinear hypoplastic constitutive model was introduced, which was developed without recourse to the concepts in elastoplasticity theory such as yield surface, plastic potential and the decomposition of the deformation into elastic and plastic parts. Triaxial drained tests on rockfill were conducted on a large scale triaxial apparatus under two types of stress paths, which were the stress paths of constant stress ratio and the complex stress paths with transitional features. Motivated by the effect of stress path, the Gudehus-Bauer hypoplastic model was improved by considering the parameter variations with different ratios of stress increment. Fitting parameter α presents a piecewise linear relationship with cosine of the slope angle θ determined by instantaneous stress path. The improved hypoplastic model can present peak stress increasing and volumetric strain changing from dilatancy to contractancy with the increase of transitional confining pressure σ _3t and the decrease of slope angle θ of stress path. Compared with the test data, it is shown that the model is capable of fully considering the effect of stress path on rockfill.     

Physical simulation of hot deformation of TiAI based alloy

In order to establish a model between the grain size and the process parameters, the hot deformation behaviors of Ti-49.5Al alloy was investigated by isothermal compressive tests at temperatures ranging from 800 to 1 100 ℃ with strain rates of 10^-3-10^-1 s^-1. Within this range, the deformation behavior obeys the power law relationship, which can be described using the kinetic rate equation. The stress exponent, n, has a value of about 5.0, and the apparent activation energy is about 320 J/mol, which fits well with the value estimated in previous investigations. The results show that, the dependence of flow stress on the recrystallized grain size can be expressed by the equation: σ = K1 drex^-0.56. The relationship between the deformed microstructure and the process control parameter can be expressed by the formula: lgdrex= -0.281 1gZ 3.908 1.     

Flow stress behavior of Cu13Zn alloy deformed at elevated temperature

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结构性吹填软土侧向变形真三轴试验研究

为了研究吹填软土在侧向变形条件下的力学与结构特性,利用真三轴试验机以及WF应力路径试验仪进行了不排水条件下的侧向卸荷试验,并与常规三轴试验结果进行了对比分析.试验结果表明：与常规三轴剪切试验应力-应变关系曲线表现的硬化特性不同,真三轴卸荷试验表现出应变软化现象.随着初始围压的增大,土体由剪缩向剪胀变化.由于中主应力的影响,真三轴卸荷状态下土体的结构屈服应力值明显大于WF卸荷状态以及常规三轴试验下的数值,其随着中主应力系数bd的增大而成非线性增长.真三轴侧向卸荷条件下土体抗剪强度指标大于WF卸荷条件,与常规三轴试验结果也明显不同,其内摩擦角增大,粘聚力减小.     

基于大三轴试验的粗粒土应力剪胀方程

摘要：采用大三轴剪切仪对三种不同相对密度的双江口心墙坝覆盖层料,进行了各向等压固结条件下的排水剪切试验。基于试验成果,提出了一个适用于粗粒土的经验型应力剪胀方程,并通过分析剪胀方程参数与围压之间的关系,给出了剪胀方程参数的确定方法。采用本文剪胀方程和Rowe剪胀方程分别对多种粗粒土三轴试验结果进行了预测,结果初步表明,和Rowe剪胀方程相比,本文剪胀方程能更好地模拟粗粒土的剪胀性。     

Mechanical characteristics of intact Middle Pleistocene Epoch loess in northwestern China

In order to research the mechanical characteristics of intact Middle Pleistocene Epoch loess, triaxial shear tests and isotonic compression test of intact Middle Pleistocene Epoch loess were conducted by improved SJ-1A triaxial shear equipment. According to test results, it can be found that the intact Middle Pleistocene Epoch loess has the properties of shear dilatancy and shear shrinkage. With the increase of confining pressure, stress-strain curve develops from softening to hardening. The failure mode of intact Middle Pleistocene Epoch loess is shear failure with the rupture angle between 55° and 61°. And it is better to determine the yield stress (p _y , q _y ) of the intact loess under different confining pressures by using the ɛ _v-q/p curve. Along with the increase of confining pressure, yield deviatoric stress q _y and yield spherical stress p _y present logarithmic relationship. Besides, the strength parameters, elastic modulus K and G of intact loess, are obtained, which are benefit for loess projects design.     

岩石强度和变形真三轴试验研究

为了得到岩石在3向应力条件下的强度及变形特征,通过真三轴试验对岩石强度进行试验研究.结果表明:峰值强度(σ1)随着中间主应力(σ2)的增加有所提高,峰值强度的最大增加量达到65.8%;在中间主应力较低时,岩石呈现出塑性的特征,随着中间主应力的增加,岩石逐渐由塑性向脆性转变.所以岩石破坏不仅取决于最大主应力差(σ1-σ3),而且与中间主应力密切相关.     

缩尺效应对粗颗粒土静止侧压力系数影响规律试验

准确把握粗颗粒土静止侧压力系数K₀对分析以及设计土石坝等岩土工程有十分重要的作用。由于缩尺效应的存在,室内试验结果往往无法正确反映原级配粗颗粒土静止侧压力系数。为研究分析缩尺效应对粗颗粒土静止侧压力系数影响规律,找出消除其影响的方法,利用自行研制的大型K₀测试仪对某砂卵砾石料及堆石料进行了大量K₀试验。通过改变试样的颗粒最大粒径、缩尺方法,相对密实度等初始条件,研究了不同密实度条件下粗颗粒土静止侧压力系数随级配的演化规律。试验结果表明：相对密实度及缩尺方法不变时,粗颗粒土静止侧压力系数会随着颗粒最大粒径的增加而显著减小,因此,缩尺效应对粗颗粒土静止侧压力系数的影响无法忽略；缩尺方法对粗颗粒土静止侧压力系数有一定影响,相对密实度及颗粒最大粒径相同时,采用等量替代法缩尺后试样静止侧压力系数值最小,因此,采用等量替代法缩尺可减小缩尺效应对粗颗粒土静止侧压力系数的影响；相比颗粒最大粒径,相对密实度对粗粒土静止侧压力系数的影响更为显著,相对密实度越大的土样,颗粒最大粒径对粗粒土静止侧压力系数影响更明显。基于静止侧压力系数试验结果及前人的研究,建立根据室内试验结果反推现场粗颗粒土料静止侧压力系数的公式,以消除缩尺效应对粗颗粒土静止侧压力系数的影响。最后,利用K₀试验结果验证了该经验公式的准确性及适用性。     

Double pull specimen more suitable for measuring bond-slip relationship of FRP-to-concrete interface

A new "conceptual" design named "double pull" specimen was proposed in order to measure the bond-slip (δ-τ) relationship of fiber reinforced polymer (FRP)-to-concrete interface more accurately. A finite element analysis (FEA) was performed for preliminarily evaluating the suitability of the proposed conceptual double pull specimen. Through the FEA, it was indicated that the FRP-to-concrete interface of the proposed conceptual specimen might subject to a much higher load level than that of the most commonly used simple shear specimen, showing a great potential for measuring δ-τ relationship more accurately. In the light of the conceptual specimen, a kind of "practical" double pull specimen was developed and proved to be more suitable for measuring δ-τ relationship through an exploratory experimental study with 20 specimens. Consequently, an experimental program with 10 double pull specimens was performed for measuring the ultimate slip δ_u which was difficult to capture by using the existing specimens. It is shown that the range of δ_u is 0.31-0.52 mm based on the test results. The suggestion for improving the measure method is also put forward.     

Deformation behavior and microstructural evolution of Al-Zn-Cu-Mg-Sc-Zr alloy during high temperature compression

The deformation behavior of a new Al-Zn-Cu-Mg-Sc-Zr alloy was investigated with compression tests in temperature range of 380–470 °C and strain rate range of 0.001–10 s⁻¹ using Gleeble 1500 system, and the associated microstructural evolutions were studied by metallographic microscopy and transmission electron microscopy. The results show that true stress—strain curves exhibit a peak stress, followed by a dynamic flow softening at low strains (ɛ<0.05). The stress decreases with increasing deformation temperature and decreasing strain rate, which can be represented by a Zener-Hollomon exponential equation with the activation energy for deformation of 157.9 kJ/mol. The substructure in the deformed specimens consists of few fine precipitates with equaixed polygonized subgrains in the elongated grains and developed serrations at the grain boundaries. The dynamic flow softening is attributed mainly to dynamic recovery and dynamic recrystallization. Foundation item: Project(2006AA03Z523) supported by the National High-Tech Research and Development Program of China     

Structure and Electric Properties of （1-x）（Bi1/2Na1/2） TiO3-xBaTiO3 Systems

The structural, dielectric and piezoelectric properties of （1-x）（Bi1/2Na1/2） TiO3-xBaTiO3 ceramics were investigated for the compositional range, x=0.02, 0.04, 0.06, 0.08, 0.10. The samples were synthesized by a conventional solid-state reaction technique. All compositions show a single perovskite structure, and X-ray powder diffraction patterns can be indexed using a rhombohedral structure. Lattice constants and lattice distortion increase while the amount of BaTiO3 increases. The X-ray diffraction results show the morphotropic phase boundary （MPB） of （1-x）（Bi1/2Na12） TiO3-xBaTiO3 exists in near x=0.06-0.08. Temperature dependence of dielectric constant eT33/ε0 measurement reveals that all compositions experience one structural phase and two ferroelectric phases transition below 400℃： rhombohedral （or rhombohedral plus tetragonal） ferroelectric phase ←→ tetragonal antiferroelectric phase ←→ tetragonal paraelectric phase. Relaxor behaviors exist in the course of ferroelectric to antiferroelectric phase transition. Dielectric and piezoelectric properties are enhanced in the MPB range for （ 1-x）（Bi1/2Na1/2）TiO3-xBaTiO3.     

椭球颗粒体系宏细观特性的三维离散元分析

颗粒材料由大量不同形状的离散颗粒组成,其力学特性与构成颗粒体系的颗粒形状密切相关,目前关于颗粒形状对颗粒材料剪切强度的影响已有大量的物理试验或数值模拟试验研究,而非球形颗粒材料在复杂应力路径下的宏、细观力学特性认识还不够充分。本文采用离散单元法(DEM)对按一定级配生成的不同伸长率的椭球颗粒体系进行等σ₃(第三主应力)等b(中主应力比)的真三轴加载数值模拟试验,研究了椭球颗粒体系的三维宏、细观力学特性,并验证了常用三维强度准则对椭球颗粒体系的适用性。研究结果表明在三维加载路径下,不同于圆球颗粒体系宏、细观演化规律的一致性,椭球颗粒体系的宏观应力面与细观组构面演化规律不一致,宏观应力比与强接触网络组构偏值/均值比线性不为1,归因于椭球颗粒体系弱接触网络对宏观应力的贡献；椭球颗粒体系宏观体应变、细观法向接触力分布、接触数目及配位数分布等宏、细观指标与加载路径无关；随着椭球伸长率η增大,Mohr-Coulomb、Lade-Duncan、Mastsuoka-Nakai及施维成三维强度准则对φmax(峰值内摩擦角)~b关系预测准确度逐渐增大,其中Lade-Duncan准则能更好地拟合不同加载路径下椭球颗粒体系的数据点。本文的研究为提高人们对真实应力状态下椭球颗粒材料的宏、细观特性提供了一定的理论基础。     

Effects of heat treatment on microstructure and mechanical properties of Fe-Co-Ni-Cr-Mo-C alloy

A kind of Fe-Co-Ni-Cr-Mo-C alloy was designed for valve seat use. The effects of the quenching temperature, tempering time and tempering temperature on the mechanical properties and microstructure of the alloy were investigated. The results show that the hardness decreases, while tensile strength (σb), transverse rupture strength (σbb) and impact toughness(Kit) increase after the alloy is quenched and tempered. The best complex property (σb, 446 MPa; σbb ,793 MPa; Kic, 2.96 J/cm2 ) can be obtained when the alloy is quenched at 1 100 ℃ and tempered at 650 ℃. The results of X-ray diffraction and energy dispersive X-ray analysis (EDX) show that the major strengthening phases are carbides such as (Fe, Cr)7 C3 and Fe2 MoC. The obvious secondary hardening appears when the alloy is tempered at 550 ℃, which results from the precipitated carbides of Cr and Mo in the alloy from the matrix and the heat-resistant retained austenite .     

真三轴压缩下大理岩强度、变形与损伤特征数值

为研究真三轴条件下岩石的力学行为,采用离散元颗粒流程序,探析不同应力路径下大理岩试样的变形破坏过程、微裂纹演化机制及其中间主应力效应。结果表明：平行黏结模型能较准确地反映大理岩真三轴压缩下力学特性和破坏模式;中间主应力对峰值强度、弹性模量、破坏角和破坏模式演变的影响较为显著;八面体理论可较好地拟合出大理岩真三轴压缩中的破坏应力,所得的破坏强度包络线具有明显线性特征;结合应力-应变曲线形状,该大理岩在压缩过程中裂纹扩展可划分为4个阶段,即线弹性阶段、裂纹稳定扩展阶段、裂纹非稳定扩展阶段及峰后破坏阶段;随着中间主应力增大,应力-应变曲线峰后段的脆性破坏特征变强,试样从拉伸破坏向拉剪混合破坏转变,且中间主应变符号由拉转向压,岩石损伤演化与中间主应力间呈现出“对勾”型趋势。     

Microstructure and microwave dielectric properties of CaO-B2O3-SiO2 glass ceramics with various B2O3 contents

The effects of B2O3 addition on both the sintering behavior and microwave dielectric properties of CaO-B2O3-SiO2 (CBS) glass ceramics were investigated by Fourier transform infrared spectroscopy (FTIR),X-ray diffractometry (XRD) and scanning electron microscopy (SEM).The results show that the increasing amount of B2O3 causes the increase of the contents of [BO3],[BO4] and [SiO4],which deduces the increase of CaB2O4 and α-SiO2 and the decrease of CaSiO3 correspondingly.No new phase is observed throughout the...     

Effect of ZnO-B<Subscript>2</Subscript>O<Subscript>3</Subscript> glass addition on the microwave dielectric properties of BaO-Nd<Subscript>2</Subscript>O<Subscript>3</Subscript>-TiO<Subscript>2</Subscript>-Bi<Subscript>2</Subscript>O<Subscript>3</Subscript> system

The effect of ZnO-B₂O₃(ZB) glass addition on the sintering behavior, microstructures and microwave dielectric properties of BaO-Nd₂O₃-TiO₂-Bi₂O₃ (BNTB) system was investigated with the aid of X-ray diffraction, scanning electron microscopy and capacitance meter. It is found that the ZB glass addition, acting as a sintering aid, can effectively lower the sintering temperature of BNTB system to 850 °C. The dielectric constant of BNTB-ZB ceramics increases with the increase of soaking time and the value of dielectric loss decreased with increasing soak time. The optical dielectric properties at 1 GHz of ɛ=74, tan δ=4×10⁻⁴, and TCC=25 ppm/°c were obtained for the BNTB system doped with 25 wt% ZB glass sintered at 850 °C for 2 h, representing that the BNTB-ZB ceramics could be promising for multilayer low temperature co-fired ceramics applications.     

Experimental study on the mechanical and failure behaviors of deep rock subjected to true triaxial stress: A review

It has become an inevitable trend of human development to seek resources from the deep underground. However, rock encountered in deep underground engineering is usually in an anisotropic stress state (σ₁>σ>σ₃) due to the influences of geological structures and engineering disturbances. It is therefore essential to study the mechanical, seepage, and dynamic disaster behaviors of deep rock under true triaxial stress to ensure the safe operation of deep rock engineering and the efficient exploitation of deep resources. In recent years, experimental techniques and research on true triaxial rock mechanics have achieved fruitful results that have promoted the rapid development of deep rock mechanics; thus, it is necessary to systematically review and summarize these developments. This work first introduced several typical true triaxial testing apparatus and then reviewed the corresponding research progress on rock deformation, strength, failure mode, brittleness, and energy as well as the 3D volumetric fracturing (dynamic disaster) properties of deep rocks under true triaxial stress. Then, several commonly used true triaxial rock strength criteria and their applicability, the permeability characteristics and mathematical models of deep reservoir rocks, and the disaster-causing processes and mechanisms of disturbed volumetric fracturing (rockburst, compound dynamic disasters) in deep rock engineering were described. This work may provide an essential reference for addressing the true triaxial rock mechanics issues involved in deep rock engineering, especially regarding the stability of surrounding rock at depth, disaster prevention and control, and oil and gas exploitation.