基于神经网络和平直节理接触模型的细观参数标定方法

近年来,颗粒流程序离散元分析方法在岩石工程领域广泛应用,它从细观角度最大限度地还原了岩石等材料力学行为的本源,但颗粒流模型的细观参数与岩石材料的宏观参数并不相同,其标定过程复杂、耗时。为此,基于平直节理接触模型,以单轴压缩、直接拉伸和双轴压缩等数值模拟试验测试岩石材料宏观力学参数;对模型细观参数进行正交设计,并通过多因素方差分析研究宏细观参数之间的关系;采用BP (back propagation)神经网络建模对细观参数进行标定并校核标定结果,校核结果表明细观参数标定精度普遍高于90%,且总体误差较小,证明了标定方法的可行性。结合花岗岩在室内常规试验下的应力-应变曲线和破坏特征,验证了神经网络的反演方法在标定岩石材料细观力学参数工作中的有效性。     

基于三维离散元堆积碎石土细-宏观力学参数相关性研究

以室内三轴压缩试验为基础,运用PFC3D离散元软件生成含有不同形状碎石块的1∶1堆积碎石土数值模型,标定得到相应的细观参数(相对误差控制在10%以内)。改变细观参数,定量探讨其与宏观力学参数(粘聚力和内摩擦角)关系,得到细观参数与粘聚力、内摩擦角的细-宏观参数关系式,并对其可靠性进行了验证。研究发现,(1)粘聚力与接触粘结力、颗粒摩擦系数呈线性正相关;同时受粘结力比值M=σc/τc的影响,当M1时,粘聚力随着M的增加而线性增加;M≥4时,粘聚力趋于稳定。(2)内摩擦角与颗粒摩擦系数呈对数关系,与接触粘结力呈抛物线关系。(3)细-宏观参数关系式是在含水率为7%室内试验结果基础上研究得出,将关系式运用到含水率为9%和11%的室内试验结果进行标定验证:依据含水率为9%和11%室内试验得到的c和φ值,运用细-宏观参数关系式计算得到细观参数,经验证其数值-室内试验结果相对误差在10%以内,说明通过细-宏观力学关系式得到的细观参数符合精度要求,关系式可靠。为后续土石混合体数值试验研究者进行细观参数标定工作提供了参考依据。     

单轴压缩下断续节理岩体动态损伤本构模型

断续节理将对工程岩体的强度及变形等力学特性产生显著影响,损伤力学中视节理为岩体的一种宏观损伤,因而采用损伤张量来刻画其对岩体的影响。目前学术界提出了用节理的几何、强度及变形等3类参数来描述节理的物理力学性质,而目前的岩体损伤张量计算方法都只涉及前2类参数,均没有涉及其变形参数即法向及切向刚度。为此,在前人研究的基础上,基于断裂及损伤理论提出了考虑节理法向及切向刚度的单轴压缩下单条断续节理引起的损伤张量计算公式,进而通过考虑节理间相互作用给出了单组单排或多排节理岩体损伤张量计算公式。其次,以岩石细观动态损伤模型为基础,结合宏细观损伤耦合观点提出了一个能够同时考虑节理几何、强度及变形参数的断续节理岩体动态损伤本构模型。最后,利用该模型讨论了节理参数及载荷应变率等对岩体动态力学特性的影响,认为节理长度减小及摩擦角增大将导致岩体动态峰值强度及弹性模量增大;岩体动态峰值强度及弹性模量则随着节理法向及切向刚度的增大分别减小或增大;而当节理法向及切向刚度按照同一比例增大时,岩体动态峰值强度及弹性模量则是增大的。岩体动态峰值强度与载荷应变率呈正相关。     

基于TCK模型的非贯通节理岩体动态损伤本构模型

提出在岩体动态损伤本构模型中应同时考虑宏、细观缺陷;基于能量原理和断裂力学理论推导得出了同时考虑节理几何及力学特征的宏观损伤变量(张量)的计算公式;基于综合考虑宏、细观缺陷的复合损伤变量(张量)及完整岩石动态损伤Taylor-Chen-Kuszmaul(TCK)模型,建立了相应的单轴压缩下节理岩体动态损伤本构模型;利用该模型讨论了节理内摩擦角及节理长度对岩体动态力学特性的影响规律。研究表明,试件动态峰值强度随着节理内摩擦角的增大而增大,随着节理长度的增加而减小。     

核级石墨PFC2D模型的宏细观参数分析

颗粒流软件PFC能够很好地处理非连续介质力学的问题,模拟核级石墨的损伤和断裂过程具有独特的优势。在采用PFC^2D模拟核级石墨时,为了增加模拟的便捷性,实现了PFC^2D细观参数的快速标定。本文首先设计了四因素四水平的正交试验,分析了核级石墨的宏观参数与PFC^2D的细观参数关系;然后基于建立的核级石墨宏细观参数的关系,采用PFC^2D模拟石墨IG11的三点弯曲试验,并从位移场变形、荷载-位移曲线和断裂参数三个方面验证其宏细观参数关系的正确性。结果表明,弹性模量E随平节理模量E_c的增加线性增加;抗拉强度σ_t随平节理抗拉强度σ_b的增加线性增加;泊松比ν随平节理刚度比k_n/k_s的增加先增大后减小;数值模拟的位移场变化和荷载-裂缝口张开位移P-CMOD曲线与试验结果较吻合,此外,断裂参数的最大误差不超过3.57%。     

红砂岩单轴压缩宏细观参数映射关系研究

颗粒流离散元软件PFC2D在岩土工程中的应用十分广泛,存在的主要问题是如何标定其细观参数,目前大多使用"试凑法",此方法的缺点在于工作量大、效率低等,本文提出以反向传播算法(back propagation,BP)神经网络的方式代替此方法,利用PFC2D内置的FISH以及Python语言对其进行二次开发,使之自动运行并获取40组宏细观参数样本。结果表明:BP神经网络可以快速准确地建立宏细观参数映射关系,误差均保持在0.01以内,模拟得到的应力–应变曲线与室内试验曲线高度吻合,且无需大量的数据样本便可创建网络,效率较高;另外,经验证本文选用的平直节理模型,可以有效地解决平行粘结模型UCS/TS值偏小问题,确定平直节理模型可以更好地模拟岩石。     

MACRO AND MICROSCOPIC PARAMETER MAPPING RELATIONSHIP FOR RED SANDSTONE 1)

颗粒流离散元软件PFC2D在岩土工程中的应用十分广泛,存在的主要问题是如何标定其细观参数,目前大多使用"试凑法",此方法的缺点在于工作量大、效率低等,本文提出以反向传播算法(back propagation,BP)神经网络的方式代替此方法,利用PFC2D 内置的FISH 以及Python 语言对其进行二次开发,使之自动运行并获取40组宏细观参数样本。结果表明：BP神经网络可以快速准确地建立宏细观参数映射关系,误差均保持在0.01 以内,模拟得到的应力--应变曲线与室内试验曲线高度吻合,且无需大量的数据样本便可创建网络,效率较高;另外,经验证本文选用的平直节理模型,可以有效地解决平行粘结模型UCS/TS值偏小问题,确定平直节理模型可以更好地模拟岩石。     

岩石化学腐蚀-围压细观损伤本构模型与离散元模拟研究

基于Lemaitre应变等价性假设理论,假定受水化学-力耦合损伤的岩石微元强度服从Weibull分布,考虑化学腐蚀与围压耦合作用对岩石力学参数的影响,通过核磁共振技术与损伤力学理论,引入细观化学损伤变量与力损伤变量,并认为微元破坏符合SMP准则,建立岩石化学腐蚀-力耦合损伤本构模型,并采用理论推导的方法得出所需的模型参数。同时基于颗粒离散元方法,引入参数半径乘子来改变颗粒间的黏结接触尺寸,从而模拟水化学损伤,采用平直节理模型对水化学作用后的岩石进行三轴压缩模拟,得到了水化学作用和不同围压下的岩石三轴应力-应变模拟曲线。通过对比所构建的岩石化学腐蚀-力耦合损伤本构模型理论曲线、离散元模拟曲线和试验曲线,结果表明三者吻合度较好,能够很好地反映岩石在化学腐蚀和围压耦合作用下的力学特性与破坏特征,并通过离散元方法得到了岩石在三轴压缩过程中裂纹的产生与分布情况。     

胶结砂砾石层面直剪试验及破坏行为细观研究

本文采用宏观试验和细观模拟相结合的方法研究胶结砂砾石层面在剪切过程中的破坏行为．首先进行了不同法向应力作用下的胶结砂砾石层面直剪试验,获得了不同的剪切面破坏特征：随着法向应力的不断增加,剪切破坏面凹凸起伏程度、骨料脱落现象越发明显．其次为了深入探究层面破坏现象,按照室内试验采用的骨料级配粒径建立细观颗粒数值模型,结合物理试验对模型进行参数标定,并进行数值模型的层面直剪模拟和细观分析．结果表明,数值模型可以再现宏观直剪试验层面破坏特征;法向应力越大,层面区域颗粒发生错动和翻转的数量越多;层面破坏方式为颗粒间的张拉和剪切混合破坏,裂隙均集中在层面位置,随着法向应力的增加,裂隙的集中区域逐渐由“面”向“带”转变．     

颗粒离散元模拟堆积碎石土变形的参数灵敏度分析

采用颗粒离散单元方法,实现任意形状块石的模拟,基于室内试验数据标定滑坡坡体物质的堆(残、坡)积碎石土的细观参数,并考虑试样尺度效应,对影响堆积碎石土宏观变形特征的细观参数进行虚拟试验敏感度分析。研究表明,1以三轴剪切试验获得测试数据并标定颗粒离散元细观参数具有相对误差在5%以内的可靠性;2虚拟模型1(101mm×200mm)与模型2(300mm×600mm)对标定的细观参数具有尺度效应,但其相对误差控制在9%以内;3离散元颗粒间的摩擦系数与碎石土的内摩擦角、抗剪强度及残余强度为非线性正相关,摩擦系数每增加0.1,峰值主应力差平均增加118.85kPa,残余强度平均增加90.44kPa;4围压越大,材料的剪胀性越弱,围压在100kPa~500kPa时,剪胀特征值K在3~6之间变化,随着围压增加,模型破坏时的粘结力以近线性增加;5杨氏模量越大,碎石土的抗剪强度越大,但两者之间并不成线性关系,且不同杨氏模量对材料的残余强度没有显著影响。     

On the orders of the best approximations of integrals of functions by integrals of rank σ

We study the values e _σ(f) of the best approximation of integrals of functions from the spaces L _p (A, dμ) by integrals of rank σ. We determine the orders of the least upper bounds of these values as σ → ∞ in the case where the function ƒ is the product of two nonnegative functions one of which is fixed and the other varies on the unit ball U _p (A) of the space L _p (A, dμ). We consider applications of the obtained results to approximation problems in the spaces S _p ^ϕ. __________ Translated from Neliniini Kolyvannya, Vol. 10, No. 4, pp. 528–559, October–December, 2007.     

Measurement of length-scale and solution of cantilever beam in couple stress elasto-plasticity

Owing to the absence of proper analytical solution of cantilever beams for couple stress/strain gradient elasto-plastic theory, experimental studies of the cantilever beam in the micro-scale are not suitable for the determination of material length-scale. Based on the couple stress elasto-plasticity, an analytical solution of thin cantilever beams is firstly presented, and the solution can be regarded as an extension of the elastic and rigid-plastic solutions of pure bending beam. A comparison with numerical results shows that the current analytical solution is reliable for the case of σ0 〈〈 H 〈〈 E, where σ0 is the initial yield strength, H is the hardening modulus and E is the elastic modulus. Fortunately, the above mentioned condition can be satisfied for many metal materials, and thus the solution can be used to determine the material length-scale of micro-structures in conjunction with the experiment of cantilever beams in the micro-scale.     

An experimental study of dynamic tensile properties of glass fiber at low-temperatures

Tensile impact experiments of EC8.0−24×7 glass fiber bundles at different low temperaturesT(14°C, −40°C and −10°C) and strain rates ɛ were carried out, and complete stress-strain curves were obtained. Within the range of the experiment temperatures and strain rates, it is found that the initial modulusE, the ultimate strength σ_max and the unstable strain ɛ _b of the glass fiber bundles all increase with ɛ at an identicalT. At an identical ɛ, with the decrease ofT, E and σ_max increase; but ɛ _b increases when 10°C>T>−40°C and decreases when −40°C>T>−100°C. The strain-rate- and temperature-dependent bimodal Weibull statistical constitutive theory was adopted for the statistical analysis of the experimental results, and the Weibull parameters of single fiber were obtained. The results show that the bimodal Weibull distribution function is suitable to represent the strength distribution of the glass fiber at low temperature and different strain rates. The differences in the mechanical properties between EC8.0−24×7 and EC5.5−12 ×14 glass fiber bundles were also discussed. Project supported by the National Natural Science Foundation of China (No. 19772058).     

Dissolution and Seepage Coupling Effect on Transport and Mechanical Properties of Glauberite Salt Rock

Potential high rates of aqueous dissolution are characteristic of salt rocks, and solute and mass flux through a soluble porous medium are functions of solute concentration gradients and pressure gradients. Due to different dissolution properties for different mineral components in glauberite salt rock, an interaction between mineral dissolution and solvent seepage arises, driven by the hydraulic pressure gradient in the rock. The originally almost impermeable glauberite rock becomes an increasingly permeable porous medium with dissolution, changing the transport and mechanical properties because of the progressive removal of solid sodium sulfate (Na₂SO₄), one of the constitutive components of glauberite salt rock. Glauberite is often found in bedded salt rock deposits, and the mineral glauberite has economic value and has been mined for many years in China. More economic and safe technologies, such as controlled solution mining, are inherently attractive. Thus, investigations into relevant physical and mechanical properties of glauberite in the context of solution mining have value, and to clarify glauberite behaviour, a series of experiments were performed. It is observed through experiments that the permeability of the rock mass during dissolution of glauberite is a function of the dissolution duration and the hydraulic pressure gradient applied to the system. For example, in laboratory tests, after 49, 53 and 70 h of dissolution, the relationships between permeability (k—cm²) and pressure gradient (Δp—MPa across the specimen of length 100 mm) of the glauberite specimens were observed to be k = 0.24 for a Δp of 0.10, k = 0.30 for a Δp of 0.12, and k = 0.41 for a Δp of 0.18, with the empirical functional relationship becoming gradually steeper with pressure. Also, the triaxial compression (mechanical) characteristics of glauberite salt rock change substantially after a period of dissolution: the compressive strength under a confining stress of σ₃ = 2.0 MPa changes initially from 46 to 11 MPa after 70 h of dissolution and seepage. Along with strength degradation, the Young’s modulus (stiffness) changed from 4.6 to 0.5 GPa. Evidently, coupled dissolution and seepage rate greatly impact both transport and mechanical properties of the rock as fabric evolves in a time-dependent manner.     

Effects of solid and slotted baffles on the convection characteristics of backward-facing step flow in a channel

This study investigates the enhancement of the laminar forced convection characteristics of backward-facing step flow in a two-dimensional channel through the installation of solid and slotted baffles onto the channel wall. The effects of the height of baffle H _b, inclination of baffle installation ϕ_b, height of slot in baffle H _t, inclination of slot in baffle ϕ_t, and distance between the backward-facing step and baffle D on the flow structure, temperature distribution and Nusselt number variation for the system at various Re are numerically explored. Results show that a slotted baffle can enhance the average Nusselt number for the heating section of channel plate by the maximum 190% when Pr=0.7, H _s=0.5, L=5, H _b ≤ 0.3, W _b ≤ 0.2, 0.1 ≤ D ≤ 0.5, 0° ≤ ϕ_b ≤ 45°, H _t ≤ 0.1, 0° ≤ ϕ_t ≤ 45° and 50 ≤ Re ≤ 400. As for the solid baffle, the enhancement may be up by 230%. The solid baffle might cause the re-separation of main stream, and consequently result in poor local heat transfer coefficient in the end region of heating section. This disadvantage can be obviously improved as the baffle is slotted. Besides the penalty of increase in pressure drop due to the baffle installation is much higher for the situation with solid baffle.     

Apparatus for Testing Concrete under Multiaxial Compression at Elevated Temperature (mac2T)

This paper describes a new test facility for determining material mechanical properties of structural concrete. The novel facility subjects 100 mm cubic concrete specimens to true multiaxial compression (σ₁ ≠ σ₂ ≠ σ₃) up to 400 MPa at temperatures of up to 300°C. Forces are delivered through three independent loading frames equipped with servo-controlled hydraulic actuators creating uniform displacement boundary conditions via rigid platens. Specimen deformation is calculated from displacements measured to an accuracy of 10⁻⁶ m using a system of six laser interferometers. The combination of stiff loading frames, rigid platens, an accurate and reliable strain measurement system and a fast control system enables investigation of the material response in the post-peak range. The in-house developed control software allows complex multi-stage experiments involving (i) load and temperature cycling, (ii) small stress probes and (iii) arbitrary (pre-defined) loading paths. The program also enables experiments in which the values of the control parameters and the execution of the test sequences depend on the response of the specimen during the test. The capabilities of the facility are illustrated in this paper by experiments determining the effects of different heat-load regimes on the strength and stiffness of the material and tests identifying the tangent stiffness matrix of the material and the associated changes in the acoustic tensor under multiaxial compression.     

A critical review of microscale mechanical testing methods used in the design of microelectromechanical systems

Microelectromechanical systems (MEMS) technologies are evolving at a rapid rate with increasing activity in the design, fabrication, and commercialization of a wide variety of microscale systems and devices. The importance of accurate mechanical property measurement for successful design was realized early on in the development of this field. Consequently, there exist many different techniques to measure quantities such as the Young's modulus (E), yield strength (σ _Y ), fracture strength (σ _F ), residual stress (σ _F ), and residual stress gradient (∇σ _R ) of microscale structures and materials. We review and critically compare several of the important techniques including the microtension test, axisymmetric plate bend test, microbeam bend test, M-test, wafer curvature measurements, dynamic (resonant) tests, fabrication of passive strain sensors, and Raman spectroscopy. We discuss the characteristics of typical test structures, and the common sources of structure-related errors in measurement. A rational approach for the selection of test techniques for the design of microsystems is suggested.     

On Aerodynamic Forces for Viscous Compressible Flow

The paper is aimed at reviewing and adding some new results to our recent work on a force theory for viscous compressible flows around a finite body. It has been proposed to analyze aerodynamic forces directly in terms of fluid elements of nonzero vorticity and density gradient. Let ρ denote the density, u the velocity, and ω the vorticity. It is demonstrated that for largely separated flows about bluff bodies, there are two major source elements: R _e(x) =−?u ²∇ρ·∇ϕ and V _e(x) =−u×ω·∇ϕ, where ϕ is an acyclic potential, generated by the solid body moving with unit velocity in the negative direction of the force considered. In particular, under mild conditions, the (unique) choice of ϕ enforces that the elements R _e(x) and V _e(x) decay rapidly away from the body. Four kinds of finite body are considered: a circular cylinder, a sphere, a hemi sphere-cylinder, and a delta wing of elliptic section—all in transonic-to-supersonic regimes. From an extensive numerical study carried out for these bodies, it is found that these two elements contribute to 95% or more of the total drag or lift for all the cases under consideration. Moreover, R _e(x) due to density gradient becomes progressively important relative to V _e(x) due to vorticity as the Mach number increases. The present method of force analysis enables effective analysis and assessment of relative importance of aerodynamics forces, contributed from individual flow structures. The analysis could therefore be very much useful in view of the rapid growth in numerical fluid dynamics; detailed (either local or global) flow information is often available. The paper is dedicated to Sir James Lighthill in honor of his great contributions to aeronautics on the occasion of the publication of his collected works. Received 3 January 1997 and accepted 11 April 1997     

Rheological and mechanical properties of silica colloids: from Newtonian liquid to brittle behaviour

Rheological and mechanical properties of aqueous mono-disperse silica suspensions (Ludox? HS40) are investigated as a function of particle volume fraction (ϕ _p ranging from 0.22 to 0.51) and water content, using shear rate tests, oscillatory methods, indentation and an ultrasonic technique. As the samples are progressively dried, four regimes are identified; they are related to the increasing particle content and the existence and behaviour of the electrical double layer (EDL) around each particle. For 0.22 ≤ ϕ _p ≤ 0.30), the suspensions are stable due to the strong electrostatic repulsion between particles and show Newtonian behaviour (I). As water is removed, the solution pH decreases and the ionic strength increases. The EDL thickness therefore slowly decreases, and screening of the electrostatic repulsion increases. For 0.31 ≤ ϕ _p ≤ 0.35, the suspensions become turbid and exhibit viscoelastic (VE) shear thinning behaviour (II), as they progressively flocculate. For 0.35 ≤ ϕ _p ≤ 0.47, the suspensions turn transparent again and paste-like, with VE shear thinning behaviour and high elastic modulus (III). At higher particle concentration, the suspensions undergo a glass transition and behave as an elastic brittle solid (IV, ϕ _p = 0.51).     

Bifurcation From Stability to Instability for a Free Boundary Problem Arising in a Tumor Model

We consider a time-dependent free boundary problem with radially symmetric initial data: σ_t − Δσ + σ = 0 if and σ(r,0)=σ₀(r) in {r < R(0)} where R(0) is given. This is a model for tumor growth, with nutrient concentration (or tumor cells density) σ(r,t) and proliferation rate then there exists a unique stationary solution (σ_S(r), R_S), where R_S depends only on the number . We prove that there exists a number μ_*, such that if μ < μ_* . . . then the stationary solution is stable with respect to non-radially symmetric perturbations, whereas if μ > μ_* then the stationary solution is unstable.