Dynamic notched semi-circle bend(NSCB) method for measuring fracture properties of rocks:Fundamentals and applications

Rocks are increasingly used in extreme environments characterised by high loading rates and high confining pressures.Thus the fracture properties of rocks under dynamic loading and confinements are critical in various rock mechanics and rock engineering problems.Due to the transient nature of dynamic loading,the dynamic fracture tests of rocks are much more challenging than their static counterparts.Understanding the dynamic fracture behaviour of geomaterials relies significantly on suitable and reliable dynamic fracture testing methods.One of such methods is the notched semi-circle bend(NSCB)test combined with the advanced split Hopkinson pressure bar(SHPB)system,which has been recommended by the International Society for Rock Mechanics and Rock Engineering(ISRM)as the standard method for the determination of dynamic fracture toughness.The dynamic NSCB-SHPB method can provide detailed insights into dynamic fracture properties including initiation fracture toughness,fracture energy,propagation fracture toughness and fracture velocity.This review aims to fully describe the detailed principles and state-of-the-art applications of dynamic NSCB-SHPB techniques.The history and principles of dynamic NSCB-SHPB tests for rocks are outlined,and then the applications of dynamic NSCB-SHPB method(including the measurements of initiation and propagation fracture toughnesses and the limiting fracture velocity,the size effect and the digital image correlation(DIC)experiments)are discussed.Further,other applications of dynamic NSCB-SHPB techniques(i.e.the thermal,moisture and anisotropy effects on the dynamic fracture properties of geomaterials,and dynamic fracture toughness of geomaterials under pre-loading and hydrostatic pressures)are presented.

A SEMI-CIRCLE THEOREM FOR UNSTABLE PERTURBATION IN TROPICAL CYCLONE-SCALE VORTICLES

In this paper, we discusses the spectrum distribution of baroclinic disturbances in tropical cyclone-scale vortices with the assumption that the basic flow does not vary with height. The semi-circle theorem for the unstable perturbation is obtained and the upper bound of growth rate can be estimated. The upper bound of instability growth rate increases with the increase of the maximum basic-state tangential wind speed, angular speed, inertial parameter, absolute vorticity, radial gradient of absolute vorticity and static stability. The upper bound of instability growth rate is greater for vortices of larger horizontal scale and smaller vertical scale and lower wave-number disturbances.

The influence of multi-metal-veins on fractures propagation investigated by the experiment and simulation

Fracture propagation is affected by multi-metal-veins formed by geological diagenesis in shale during the hydraulic fracturing.However,the influence of multi-metal-veins on fractures propagation remains unclear.To solve the problem,based on the semi-circle bending(SCB)test and the extended finite element(XFEM)theory,the interaction between multi-metal-veins and fractures is investigated.The experimental results reveal that the fractures usually deflect at the upper or lower interfaces between metal veins and rocks(e.g.the specimen S-2),which is different from the propagation behavior of fractures in calcite veins.Meanwhile,the fracture toughness of the specimen S-1 is 24.40%higher than that of the specimen S-2,indicating that the increasing of total thickness of multiple metal veins in-creases the resistance to the fracture vertical propagation.The simulation results show that the increasing of the number,total thickness of veins,the modulus difference between veins and rock,the approach angle and the notch angle all increase the resistance of the fracture passing through metal veins.The maximum deviation distance(Dmax)of the fracture decreases with the number of veins,while thickness combination types of metal veins do not affect Dmax.The reduction of the notch angle leads to the more tortuous fracture propagation path.Finally,we propose a new comprehensive fracture network pattern.Fracture networks are divided into two categories,including orthogonal fracture networks and sub-orthogonal fracture networks,and then divided into six sub-categories further.The research results will provide reference for hydraulic fracturing of shale reservoirs containing multi-metal-veins.

Effect of Flat Plate Leading Edge Pattern on Structure of Streamwise Vortices Generated in Its Boundary Layer

The use of leading edge with different geometrical patterns will affect the development of boundary layer flow on a flat plate and its heat transfer properties. In this work, the effects of three patterns namely saw-tooth, semicircular and slots with same wavelength and amplitude were examined. The experiments were carried out for Reynolds number based on wavelength of patterns ranging from 1540 to 3850. For all cases, after each valley, an oval shape region was formed containing a counter- rotating vortex pair. It is also shown that for the flat plate with slots, another vortex was visualized between each valley.

斜交型不稳定谱点分布侧半圆定理及其增长率上界的估计(英文)

Based on the theoretical analysis on the unstable spectrum distribution of heterotropic perturbation, the semi–circle theorem of such spectrum distribution is obtained — the spectrum distributed within an upper semi–circle domain with radius R0 and taking origin as its circle center in the complex plane, and the upper bound estimation of growth rate is given simultaneously. It is found that the smaller the horizontal scale of perturbation is, the higher the model top located, the greater the estimated value of upper bound of such growth rate is. Also the increase of vertical shear of wind and latitude have the positive contribution to the increase of such growth rate. Finally when stratified stability decreases, the relative maximal growth rate increases, while the maximal growth rate decreases instead.

Limit Theorems and Large Deviations forβ-Jacobi Ensembles at Scaling Temperatures

Letλ=(λ_(1),...,λ_(n))beβ-Jacobi ensembles with parameters p_(1),p_(2),n andβwhileβvarying with n.Setγ=lim_(n→∞)n/p_(1)andσ=lim_(n→∞)p_(1)/p_(2).In this paper,supposing lim_(n→∞)log_(n)/β_(n)=0,we prove that the empirical measures of different scaledλconverge weakly to a Wachter distribution,a Marchenko–Pastur law and a semicircle law corresponding toσγ>0,σ=0 orγ=0,respectively.We also offer a full large deviation principle with speedβn^(2)and a good rate function to precise the speed of these convergences.As an application,the strong law of large numbers for the extremal eigenvalues ofβ-Jacobi ensembles is obtained.

联合监控均值和方差的累积和控制图优化设计

为了提高监测均值和方差微小偏移的敏感度,围绕生产过程质量控制,建立同时监控均值和方差的累积和控制图。模型考虑均值和方差的变化,针对生产过程中的微小偏差,提出了一个新的累积和控制图,并给出了基于马尔可夫链理论的新控制图的平均链长计算方法。编程求解后对比文献中各控制图的平均链长数据以及更换变量数值改进控制图,通过计算变动比率得出新控制图的检测力度在不同偏移力度下都明显优于其他控制图方法。