Nonlinear constitutive models of rock structural plane and their applications

Structural planes play an important role in controlling the stability of rock engineering,and the influence of structural planes should be considered in the design and construction process of rock engineering.In this paper,mechanical properties,constitutive theory,and numerical application of structural plane are studied by a combination method of laboratory tests,theoretical derivation,and program development.The test results reveal the change laws of various mechanical parameters under different roughness and normal stress.At the pre-peak stage,a non-stationary model of shear stiffness is established,and threedimensional empirical prediction models for initial shear stiffness and residual stage roughness are proposed.The nonlinear constitutive models are established based on elasto-plastic mechanics,and the algorithms of the models are developed based on the return mapping algorithm.According to a large number of statistical analysis results,empirical prediction models are proposed for model parameters expressed by structural plane characteristic parameters.Finally,the discrete element method(DEM)is chosen to embed the constitutive models for practical application.The running programs of the constitutive models have been compiled into the discrete element model library.The comparison results between the proposed model and the Mohr-Coulomb slip model show that the proposed model can better describe nonlinear changes at different stages,and the predicted shear strength,peak strain and shear stiffness are closer to the test results.The research results of the paper are conducive to the accurate evaluation of structural plane in rock engineering.

Experimental Evaluation of Ductile Fracture of Sheet Metals under Plane Stress States

With the application of lightweight materials such as advanced high-strength steel and aluminum alloy in the automotive industry, it is necessary to quantitatively evaluate the ultimate deformation capacity of materials under various plane stress states for the digital simulation of these materials. Conventional Nakajima test can only provide three regular plane stress states, such as tension, plane strain tension and bulging, and FLC curve is affected by deformation path, mold lubrication and other variables. More importantly, Nakajima test cannot provide shear, tension shear, which are extremely important loading conditions in automobile collisions. Therefore, the research work of this paper focuses on the evaluation of the ultimate ductile fracture behavior of sheet metals under various conditions of plane stress states. The four variables Mohr-Coulomb model was established to study the ductile fracture of metal sheets under plane stress states. Beginning with the recorded minor and major strain distributing on the deformation area of uniaxial tension samples, Moving Regression Algorithm was deployed to reveal the inherent relationship among the key parameters involved in the M-C model, which also provided an experimental technique for monitoring the instantaneous changing of triaxiality over the whole loading period. Three or four typical types of uniaxial-loading specimens were well designed to determine the M-C curve. As a result, M-C curve and the transformed major stain vs. minor strain curve provide further information about the material arrest to the ductile fracture in the area of shear loading, in comparison with the conventional FLD test.

The stress state of geological structure and mining dynamic disaster in Fuxin basin

Further evidences show that most mining dynamic disasters are mainly oc- curred nearby NNE and near SN geological structures.In-situ stress measurement in Fuxin basin shows that the orientation of major compressed stress is near EW.At this stress field,geological structures with deferent strike have deferent stress state and dis- place mode.NNE and near SN geological structures are compressed to thrust and come into being high stress zone.NWW and NEE geological structures are tensile to separate and not prone to being low stress zone.NW structure is intervenient of them.So NEE and near SN structures are easy to occurre mining dynamic disasters and NWW and NEE structures is 'safety' comparatively.The mining dynamic disaster is controlled by stress state of geologic structure,which is determined by its strike.

On Plane Stress State and Stress Free Deformation of Thick Plate with FGM Interface under Thermal Loading

This paper demonstrates the plane stress state and the stress free thermo-elastic deformation of FGM thick plate under thermal loading.First,the Sneddon-Lockett theorem on the plane stress state in an isotropic infinite thick plate is generalized for a case of FGM problem in which all thermo-mechanical properties are optional functions of depth co-ordinate.The proof is based on application of the Iljushin thermo-elastic potential to displacement type system of equations that reduces it to the plane stress state problem.Then an existence of the purely thermal deformation is proved in two ways:first,it is shown that the unique solution fulfils conditions of simultaneous constant temperature and linear gradation of thermal expansion coefficient,second,proof is based directly on stress type system of equations which straightforwardly reduces to compatibility equations for purely thermal deformation if only stress field is homogeneous in domain and at boundary.Finally,couple examples of application to an engineering problem are presented.

Crack growth of plane stress state in hardening material

THE plane stress steady crack growth in power-law hardening materials is significant in theoretical research and practical application, especially in the application in aeronautic and aerospace industries. But people have not yet found any analytic solutions to it because of the mathematical difficulty of the problem.

Effect of three dimensional stress state on unstable fracture condition and crack opening level in a new crack growth model

A new model for the analysis of fatigue crack growth in the metal structures was proposed. This model shows a promising capability of explaining various fatigue phenomena. The new crack growth model is further completed by a continuous empirical formula for estimating the value of variable fracture toughness during crack propagation and a modified continuous equation for the crack tip stress/strain constraint factor used to calculate the stress intensity factor at the opening level. The prediction results are proved to agree well with the observed phenomena in test.

Mutual impact of true triaxial stress, borehole orientation and bedding inclination on laboratory hydraulic fracturing of Lushan shale

Unconventional resources like shale gas has been the focus of intense research and development for two decades. Apart from intrinsic geologic factors that control the gas shale productivity (e.g. organic matter content, bedding planes, natural fractures, porosity and stress regime among others), external factors like wellbore orientation and stimulation design play a role. In this study, we present a series of true triaxial hydraulic fracturing experiments conducted on Lushan shale to investigate the interplay of internal factors (bedding, natural fractures and in situ stress) and external factors (wellbore orientation) on the growth process of fracture networks in cubic specimens of 200 mm in length. We observe relatively low breakdown pressure and fracture propagation pressure as the wellbore orientation and/or the maximum in situ stress is subparallel to the shale bedding plane. The wellbore orientation has a more prominent effect on the breakdown pressure, but its effect is tapered with increasing angle of bedding inclination. The shale breakdown is followed by an abrupt response in sample displacement, which reflects the stimulated fracture volume. Based on fluid tracer analysis, the morphology of hydraulic fractures (HF) is divided into four categories. Among the categories, activation of bedding planes (bedding failure, BF) and natural fractures (NF) significantly increase bifurcation and fractured areas. Under the same stress regime, a horizontal wellbore is more favorable to enhance the complexity of hydraulic fracture networks. This is attributed to the relatively large surface area in contact with the bedding plane for the horizontal borehole compared to the case with a vertical wellbore. These findings provide important references for hydraulic fracturing design in shale reservoirs.

DUCTILE CRACK INITIATION AND STEADY-STATE PROPAGATION OF HIGH STRENGTH STRUCTURAL STEEL

The resistance to crack propagation at earlier stage for a high strength structural steel with certain ductility and its correlation to microstructures,stress states,deformation history and strain characteristics have been investigated.The resistance to crack propagation is mainly de- termined by the plastic constrain ahead of the crack tip,the elastic energy and plastic work absorbed in the stress-strain field.These are connected with the state function of triaxial stress.The deformation history and strain characteristic during deformation of material are described by the flow line in which the deformation history and strain characteristic restrain the crack initiation at stage Ⅱ and the crack propagation at stage Ⅲ.The strain hardening rate may sensitively reflect the stress distribution and micro-fracture mechanism in the interi- or of material.

The Stress-strain Analysis for the Linearly Elastic and Power Hardening of Strength Difference Plane Structure of Bars Jointed to a Rigid-body

The plane structure of bars jointed to a rigid-body is a complex and universal structure.Some other structure of bars can be considered as its special cases. Many material have different stress-strain relation in tension and compression, generally the relation is nonlinear. In this paper,we use the constitutive model of linearly elastic and power hardening of strength difference to analyze plane structure of bars. The displacement method is used to derive the universal expression of calculating stress and strain. The nonlinear equations for computing displacements of the rigid-body has been given and general computing program has been worked out. This problem has been solved satisfactorily.

THE ANALYSES OF THE THREE-DIMENSIONAL STRESS STRUCTURE NEAR THE CRACK TIP OF MODE Ⅰ CT SPECIMENS IN ELASTICPLASTIC STATE(Ⅱ)--THE ANALYSES OF THE STRESS STRUCTURE

Based on[1],the stress structures of the smooth region and shear lip of the specimens have been investigated in the paper.The characteristics of the stress structure in the smooth region have been found that the variable z can separated out;the stresses in the midsection can be obtained by the plane strain FEM results or HRR structure modified by the stress triaxiality.The effects of load level and thickness on the stress structure can be reflected by the distribution of CTOD along the thickness direction.The obtained expressions of the stresses are very simple and visualized.The analyses of the stress structure in the shear lip show that the stresses can be obtained by different methods of interpolation to a certain precise degree.A new degree parameter of the plane strain state has been put forward and studied.The parameter can reflect relatively well the variation of the kind and thickness of the specimen as well as the load level.The fracture parameter has also been investigated to be sure that it can be obtained by modified CTOD with the stress triaxiality.

基于MMC模型的Q460C高强结构钢延性断裂性能研究

为研究Q460C高强结构钢的延性断裂性能,对处于不同应力状态的9个试件进行了单调加载断裂试验。采用修正加权平均(MWA)法获得了Q460C钢材直至断裂的全过程真实应力-真实应变曲线,通过编写MATLAB优化程序校准了VGM和MMC断裂预测模型的参数。借助VUMAT子程序将相关参数代入ABAQUS/Explicit求解器模拟各试件的断裂行为,评估了两种断裂模型对各试件断裂预测的相对精度。通过对已有文献中两个圆周缺口试件的断裂模拟,验证了该文校准的MMC模型参数对Q460钢断裂预测的普适性。研究结果表明:采用MMC模型进行数值模拟得到的荷载-位移响应与试验结果吻合度较好,尤其是对纯剪和剪拉试件的断裂模拟;带应力软化的MMC模型可准确且形象地再现各试件的起裂和裂缝扩展;该文校准的MMC断裂模型参数对Q460钢材断裂行为预测具有相对较好的适用性。

A review of rockburst:Insights from engineering sites to theoretical investigations

Rockburst has perennially posed a formidable challenge to the stability of underground engineering works,particularly under conditions of deep-seated high stress.This paper provides a comprehensive review of recent advancements in on-site research related to rockburst occurrences,covering on-site case analyses,monitoring methodologies,early warning systems,and risk(proneness)evaluation.Initially,the concepts and classifications of rockburst based on on-site understanding were summarized.The influences of structural planes(in various spatial distribution combinations),in-situ stress(particularly magnitude and direction of the principal stress),dynamic disturbances,and excavation profiles on rockburst were thoroughly assessed and discussed through the analysis of published rockburst cases and on-site survey results.Subsequently,a compendium of commonly employed on-site monitoring techniques was outlined,delineating their respective technical attributes.Particular emphasis is accorded to the efficacy of microseismic monitoring technology and its prospective utility in facilitating dynamic rockburst early warning mechanisms.Building upon this foundation,the feasibility of assessing rockburst propensity while considering on-site variables is verified,encompassing the selection and quantitative evaluation of pertinent indicators.Ultimately,a comprehensive synthesis of the paper is presented,alongside the articulation of prospective research goals for the future.

压缩剪切平面应变试样的应力状态响应

为模拟金属塑性变形过程中的压缩剪切应力状态的平面应变特征,构建了平面压缩剪切试样。通过数字图像相关(DIC)技术和有限元模拟表征变形区Y方向的应力状态分布特征及压缩断裂过程。DIC结果显示,在压缩实验过程中,变形区的应变场分布与有限元结果吻合良好,有限元结果可靠。有限元结果表明,通过改变试样的缺口倾角,可以定量控制应力三轴度的大小,并且主应变方向与缺口倾角方向一致。在变形区Y方向发生压缩剪切的平面应变,同时试样边缘位置相对于中心位置具有更低的Lode角参数,具有双向压缩加载特征,使得静水压力增大,应力三轴度进一步降低至-0.823。

基于无应力状态法的异形钢箱拱塔施工过程线形控制

为进一步优化异形钢箱拱塔施工及安装方法,以某异形斜拉桥中采用的双肢非一致倾斜拱形桥塔为工程案例,考虑支架对结构线形的影响,分析了桥塔施工过程线形变化。针对钢箱桥塔内部板件变化复杂且规律性低、传统建模方法效率低下的问题,使用插值原理生成坐标并对号入座到节点逻辑编号,节点逻辑编号中自带单元信息,单元可以通过循环快速生成,形成了复杂钢箱结构快速建模方法;针对传统正装法在计算闭环结构时常发生的单元畸变导致算法不收敛现象,将无应力状态法与正装法相结合,解释了传统正装方法失效的原理,提出一种改进的闭环结构施工过程模拟的分析方法——无应力正装法,运用该方法分析了支架上的闭环结构施工过程中的3种线形方案,以合龙为目标精确计算了主塔结构在施工过程中的三向控制线形,顺桥向、横桥向和竖向最大变形分别为16,2 cm和9 cm,两肢间三向线形偏差分别为5,3.5,5 cm,同时计算了桥塔节段的安装线形,作为实际桥塔施工安装的重要定位依据,安装线形最大矢量位移值为2.8 cm,最终节段安装线形恰好落在零位置处,实现了合龙段的零偏差安装。无应力状态法在异形钢箱拱塔施工过程线形控制中的应用展示了其在保证施工精度和效率方面的优势,给桥塔安装提供了重要的定位基准。

煤矿井下主要地质构造附近应力特征研究

在断层、剪切带、褶皱等主要地质构造附近,应力状态和岩土条件往往会发生显著变化,造成突煤、冒顶、突水、瓦斯突出等矿山重大不稳定和安全隐患。为了解和量化主要地质构造附近的应力状态,对山西省东升煤矿断层附近区域进行综合现场监测,详细分析监测资料,识别断层附近应力异常,采用三维数值模拟研究了冲击地压的应力分布和应变能集中情况,为冲击地压危险性评价提供依据。

高应力断层构造区巷道冲击破坏特征研究

断层构造区静动载应力耦合作用加剧了井下断层区围岩冲击危险性,断层构造区巷道围岩应力分布规律及冲击动载响应特征存在显著特殊性。目前对于断层构造区的冲击研究主要集中于工作面采场附近,但对于断层构造区巷道冲击破坏鲜有研究。以陕西某矿深埋高应力断层构造区巷道为工程背景,分析了断层构造区巷道围岩变形破坏力学特征:①断层面存在明显应力阻隔效应,正断层附近存在上盘应力集中区和下盘应力降低区2个特殊应力区。巷道由于断层面影响,巷帮静载集中应力呈现非对称分布特征,远离断层面侧应力集中程度大于靠近断层面侧,该侧巷道围岩冲击破坏危险程度增大。②断层面对于应力波传递产生明显阻隔作用,正断层上盘动载响应大于下盘动载响应,由于巷道两帮应力非对称分布特征,右帮动载响应明显大于左帮。基于上述特征,提出了断层构造区巷道围岩“卸(大直径钻孔卸压)−支(梯次加固成层式吸能防冲支护)”协同防冲控制技术,工程试验结果表明:①巷道围岩采取“卸−支”协同防冲处理措施后,巷道两帮应力集中区往围岩深部转移3~5 m,应力峰值降低18.5%~20.3%,巷道帮部围岩应力集中程度显著降低。②采用“卸−支”协同防冲处理措施前,巷道顶底板及两帮变形量分别为856,334,325,567 mm,巷道围岩变形破坏严重,采用“卸−支”协同防冲处理措施后,巷道围岩变形量降低35.69%~62.03%,巷道围岩稳定性增强。③钻孔煤粉量显著低于临界粉煤量,巷道围岩动力显现降低。

Discussion on rotational tectonic stress field and the genesis of circum-Ordos landmass fault system

When the resultant of applied forces does not pass through the center of an active landmass, the landmass will rotate, giving rise to a rotational tectonic stress field. The motion of a fault along the principal stress plane is de-termined by the mechanic features of the plane. Tensile fractures occur on the faults in the direction of the principal extensional stress plane, and fault-depression basins will be formed under a long-term action. Thrusting and over-thrusting occur on faults in the direction of the principal compressional stress plane, or folds may be formed as a result. Information on geology shows that the North China landmass, which remained stable and intact for a long time, became disjointed in the Eogene period. In the course of disjunction, anticlockwise rotation took place in the Shanxi-Hebei-Shaanxi (Jin-Ji-Shan) landmass, giving rise to the fault-depression system in its periphery. In the Pliocene epoch the landmass lost stability and its eastern boundary moved westward. As a result, the Shanxi gra-ben system appeared and Ordos landmass was formed. Structural and mechanic features of the main faults around Jin-Ji-Shan landmass can be explained with principal stress plane of a rotational tectonic stress field.

Mass-Stiffness Templates for Cubic Structural Elements Dedicated to Professor Karl Stark Pister for his 95th birthday

1 This paper considers Lagrangian finite elements for structural dynamics constructed with cubic displacement shape functions.The method of templates is used to investigate the construction of accurate mass-stiffness pairs.This method introduces free parameters that can be adjusted to customize elements according to accuracy and rank-sufficiency criteria.One-and two-dimensional Lagrangian cubic elements with only translational degrees of freedom(DOF)carry two additional nodes on each side,herein called side nodes or SN.Although usually placed at the third-points,the SN location may be adjusted within geometric limits.The adjustment effect is studied in detail using symbolic computations for a bar element.The best SN location is taken to be that producing accurate approximation to the lowest natural frequencies of the continuum model.Optimality is investigated through Fourier analysis of the propagation of plane waves over a regular infinite lattice of bar elements.Focus is placed on the acoustic branch of the frequency-vs.-wavenumber dispersion diagram.It is found that dispersion results using the fully integrated consistent mass matrix(CMM)are independent of the SN location whereas its lowfrequency accuracy order is O(κ8),whereκis the dimensionless wave number.For the diagonally lumped mass matrix(DLMM)constructed through the HRZ scheme,two optimal SN locations are identified,both away from third-points and of accuracy order O(κ8).That with the smallest error coefficient corresponds to the Lobatto 4-point integration rule.A special linear combination of CMM and DLMM with nodes at the Lobatto points yields an accuracy of O(κ10)without any increase in the computational effort over CMM.The effect of reduced integration(RI)on both mass and stiffness matrices is also studied.It is shown that singular mass matrices can be constructed with 2-and 3-point RI rules that display the same optimal accuracy of the exactly integrated case,at the cost of introducing spurious modes.The optimal SN location in two-dimensional,bicubic,isoparametric plane stress quadrilateral elements is briefly investigated by numerical experiments.The frequency accuracy of flexural modes is found to be fairly insensitive to that position,whereas for bar-like modes it agrees with the one-dimensional results.

基于结构受力状态理论的群桩基础承载力研究

目的 将结构受力状态理论应用于群桩基础的承载力判定,推广计算群桩基础安全容度和降低材料浪费的方法,为群桩设计提供有力依据。方法 依托沈阳航空航天大学图书馆现场静载试验,通过ABAQUS有限元模拟软件建立群桩基础模型,应用结构受力状态理论分析实测数据与模拟数据,精确判定群桩基础工作过程中的弹塑性分支荷载与失效荷载,并与当前规范理论获取的荷载判定结果进行对比。结果 在考虑群桩效应等不利因素的前提下,所判定的群桩承载力在保证安全的同时,相较于以控制沉降为40 mm方式得到的群桩基础设计荷载提高了21.6%,失效荷载比极限荷载大770 kN。结论 弹塑性分支荷载可以直接作为群桩基础的设计荷载,从极限荷载至失效荷载这一区间经证明群桩结构可以正常工作,可作为群桩基础的安全裕度使用,为研究群桩基础承载力提供了新方法。

二维圆弧阵列结构共面冲击下的平台应力研究

借助数值模拟和理论分析的方法研究了二维圆弧阵列结构在不同冲击速度下的共面平台应力.利用有限元分析软件ANSYS/LS-DYNA建立了二维圆弧阵列结构共面冲击下的有限元模型,并用压缩试验验证了有限元模型的可靠性.数值模拟结果表明该结构在低速冲击下呈现出“波浪”形坍塌,中速冲击下呈现出“一”字形加“波浪”形坍塌,高速冲击下表现为稳定的“一”字形坍塌.基于线性回归理论推导出不同变形模式间的临界速度表达式,发现其与相对密度呈线性关系.根据特征单元变形模式,推导出了预测二维圆弧阵列结构在不同冲击速度下平台应力的理论模型,理论值与有限元计算值吻合较好,最大相对误差为9.79%.此外,大量参数化计算后发现:同一结构参数下,二维圆弧阵列结构共面平台应力与冲击速度的平方呈线性关系,并随冲击速度的增大而增大;同一冲击速度下,其共面平台应力随着壁厚半径比的增大而增大;同一相对密度下,其共面平台应力随着圆弧角度的增大而增大.