Evolution model and failure mechanisms of rainfall-induced cracked red clay slopes:insights from Xinshao County,China

Red clay landslides are widely distributed worldwide,resulting in severe loss of life and property.Although rainfall-induced red clay slopes have received extensive attention,the role of cracks in the evolutionary process of red clay slopes and their connection to failure mechanisms is still poorly understood.A comprehensive approach integrating field investigation,laboratory tests,and numerical simulations was conducted to study the 168 red clay landslides in Xinshao County,China.The results show that red clay is prone to forming cracks at high moisture content due to its low swelling and high shrinkage properties.The failure mode of red clay slopes can be summarized in three stages:crack generation,slope excavation,and slope failure.Furthermore,the retrospective analysis and numerical simulations of the typical landslide in Guanchong indicated that intense rainfall primarily impacts the shallow layer of soil within approximately 0.5 m on the intact slope.However,cracks change the pattern of rainfall infiltration in the slope.Rainwater infiltrates rapidly through the preferential channels induced by the cracks rather than uniformly and slowly from the slope surface.This results in a significant increase in both the depth of infiltration and the saturated zone area of the cracked slope,reaching 3.8 m and 36.2 m^(2),respectively.Consequently,the factor of safety of the slope decreases by 13.4%compared to the intact slope,ultimately triggering landslides.This study can provide valuable insights into understanding the failure mechanisms of red clay slopes in China and other regions with similar geological settings.

Coupling Effect of Cryogenic Freeze-Thaw Cycles and Chloride Ion Erosion Effect in Pre-Cracked Reinforced Concrete

Chloride (Cl−) ion erosion effects can seriously impact the safety and service life of marine liquefied natural gas(LNG) storage tanks and other polar offshore structures. This study investigates the impact of different low-temperaturecycles (20°C, –80°C, and −160°C) and concrete specimen crack widths (0, 0.3, and 0.6 mm) on the Cl−ion diffusion performance through rapid erosion tests conducted on pre-cracked concrete. The results show thatthe minimum temperature and crack width of freeze-thaw cycles enhance the erosive effect of chloride ions. TheCl− ion concentration and growth rate increased with the increasing crack width. Based on the experimental modeland in accordance with Fick’s second law of diffusion, the Cl− ion diffusion equation was modified by introducingcorrection factors in consideration of the freeze-thaw temperature, crack width, and their coupling effect.The experimental and fitting results obtained from this model can provide excellent reference for practical engineeringapplications.

Review on Dynamic Modeling and Vibration Characteristics of Rotating Cracked Blades

As one of the most important parts in the engine,the structure and state of the rotating blade directly affect the normal performance of the aeroengine.In order to monitor engine crack failure and ensure flight safety,it is necessary to carry out research on the dynamic modeling of the cracked blade and breathing crack-induced vibration mechanisms.This paper summarizes the current research status on the dynamics of cracked blade,and the related topics mainly include four aspects:crack propagation path,mechanical model of open and breathing cracks,dynamic modeling methods of cracked blades such as lumped mass model,semi-analytical model and finite element model,and dynamic characteristics of cracked blades.The review will provide valuable references for future studies on dynamics and fault diagnosis of cracked blade in aeroengine.

IDENTIFICATION OF CRACKED ROTOR BY WAVELET TRANSFORM

The dynamic equation of cracked rotor in rotational frame was modelled, the numerical simulation solutions of the cracked rotor and the uncracked rotor were obtained. By the wavelet transform, the time frequency properties of the cracked rotor and the uncracked rotor were discussed, the difference of the time frequency properties between the cracked rotor and the uncracked rotor was compared. A new detection algorithm using wavelet transform to identify crack was proposed. The experiments verify the availability and validity of the wavelet transform in identification of crack.

Influence of non-dimensional strength parameters on the seismic stability of cracked slopes

Cracks in rock or soil slopes influence the stability and durability of the slopes. Seismic forces can trigger slope disasters, particularly in the cracked slopes. Considering the nonlinear characteristics of materials, the more generalized nonlinear failure criterion proposed by Baker is adopted. The influence of non-dimensional strength parameters on the stability of cracked slopes under earthquakes is performed using the upper bound limit analysis. The seismic displacement is calculated by adopting the logarithmic spiral failure surface according to the sliding rigid block model. Based on the existing studies, two methods for the stability analysis of cracked slopes under earthquakes are introduced: the pseudo-static method(with the factor of safety(Fs) as an evaluation index), and the displacement-based method(with the seismic displacement as an evaluation index). The pseudo-static method can only determine the instantaneous stability state of the cracked slope, yet the displacement-based methodreflects the stability variation of cracked slopes during earthquakes. The results indicate that the nondimensional strength parameters affect the factor of safety and seismic displacement of slopes significantly. The non-dimensional strength parameter(n) controlling the curvature of strength function shapes on the slope stability is affected by other parameters. Owing to cracks, the effect of non-dimensional strength parameters on seismic displacement becomes more significant.

A state-of-the-art review of mechanical characteristics and cracking processes of pre-cracked rocks under quasi-static compression

The mechanical characteristics and failure behavior of rocks containing flaws or discontinuities have received wide attention in the field of rock mechanics.When external loads are applied to rock materials,stress-induced cracks would initiate and propagate from the flaws,ultimately leading to the irreversible failure of rocks.To investigate the cracking behavior and the effect of flaw geometries on the mechanical properties of rock materials,a series of samples containing one,two and multiple flaws have been widely investigated in the laboratory.In this paper,the experimental results for pre-cracked rocks under quasistatic compression were systematically reviewed.The progressive failure process of intact rocks is briefly described to reveal the background for experiments on samples with flaws.Then,the nondestructive measurement techniques utilized in experiments,such as acoustic emission(AE),X-ray computed tomography(CT),and digital image correlation(DIC),are summarized.The mechanical characteristics of rocks with different flaw geometries and under different loading conditions,including the geometry of pre-existing flaws,flaw filling condition and confining pressure,are discussed.Furthermore,the cracking process is evaluated from the perspective of crack initiation,coalescence,and failure patterns.

APPLICATION OF WAVELET TIME-FR EQUENCY ANALYSIS TO IDENTIFICA-TION OF CRACKED ROTOR

Based on the simple hinge crack model and the local flexibility theorem, thecorresponding dynamic equation of the cracked rotor is modelled, the numerical simulation solutionsof the cracked rotor and the uncracked rotor are obtained. By the continuous wavelet time-frequencytransform, the wavelet time-frequency properties of the uncracked rotor and the cracked rotor arediscussed. A new detection algorithm that uses the wavelet time-frequency transform to identify thecrack is proposed. The influence of the sampling frequency on the wavelet time-frequency transformis analyzed by the numerical simulation research. The valid sampling frequency is suggested.Experiments demonstrate the validity and availability of the proposed algorithm in identification ofthe cracked rotor for engineering practices.

Experimental Dynamic Analysis of a Breathing Cracked Rotor

Crack fault diagnostics plays a critical role for rotating machinery in the traditional and Industry 4.0 fac- tory. In this paper, an experiment is set up to study the dynamic response of a rotor with a breathing crack as it passes through its 1/2, 1/3, 1/4 and 1/5 subcritical speeds. A cracked shaft is made by applying fatigue loads through a three-point bending apparatus and then placed in a rotor testbed. The vibration signals of the testbed during the coasting-up process are collected. Whirl orbit evolution at these subcritical speed zones is analyzed. The Fourier spectra obtained by FFF are used to investigate the internal frequencies corresponding to the typical orbit characteris- tics. The results show that the appearance of the inner loops and orientation change of whirl orbits in the experiment are agreed well with the theoretical results obtained previously. The presence of higher frequencies 2X, 3X, 4X and 5X in Fourier spectra reveals the causes of subharmonic reso- nances at these subcritical speed zones. The experimental investigation is more systematic and thorough than previ- ously reported in the literature. The unique dynamic behavior of the orbits and frequency spectra are feasible features for practical crack diagnosis. This paper provides a critical technology support for the self-aware health man- agement of rotating machinery in the Industry 4.0 factory.

Use of double edge-cracked Brazilian disk geometry for compression-shear fracture investigation of rock

A new specimen geometry-the double edge-cracked Brazilian disk and a relevant fracture analysis byweight function method are proposed for the investigation of rock fracture caused by compression-shear loading. Notonly can the mixed mode fracture with any ratio of KⅠ/KⅡ be achieved, but also the pure mode Ⅱ crack extensioncan be obtained. The combined mode fracture analysis for this geometry shows that diametral compression in the far-field can induce a compression-shear stress state in the singular stress field ahead of crack tips. Experimental investi-gations conducted on marble specimens show that the pure mode Ⅱ crack extension can be obtained when the dimen-sionless crack length a＞0.7 and the inclined crack angle 5°≤ψ≤40°. Normalized mode Ⅰ and mode Ⅱ stress inten-sity factors decrease from -0.45 and 2.47 at ψ=5° to -1.65 and 1.52 at ψ=40°, respectively. The strains at threepoints of specimen are also measured in order to investigate the influence of stress singularity on initial crack exten-sion. The results show that the principal orientations of strain at three points are very stable in the loading process.The derived formulae are quite explicit, and the specimen geometry is easy to fabricate and convenient to achieve thepure mode Ⅱ crack extension. Therefore, it can hopefully be used to obtain mode Ⅱ fracture toughness of rock.

Free torsional vibration of cracked nanobeams incorporating surface energy effects

This paper investigates surface energy effects, including the surface shear modulus, the surface stress, and the surface density, on the free torsional vibration of nanobeams with a circumferential crack and various boundary conditions. To formulate the problem, the surface elasticity theory is used. The cracked nanobeam is modeled by dividing it into two parts connected by a torsional linear spring in which its stiffness is related to the crack severity. Governing equations and corresponding boundary conditions are derived with the aid of Hamilton＇s principle. Then, natural frequencies are obtained analytically, and the influence of the crack severity and position, the surface energy, the boundary conditions, the mode number, and the dimensions of nanobeam on the free torsional vibration of nanobeams is studied in detail. Results of the present study reveal that the surface energy has completely different effects on the free torsionl vibration of cracked nanobeams compared with its effects on the free transverse vibration of cracked nanobeams.

Thermal effects on fracture toughness of cracked straight-through Brazilian disk green sandstone and granite

Cracked straight-through Brazilian disc(CSTBD) samples prepared using two rock materials were used for thermal treatment from room temperature to 700℃. Uniaxial splitting experiments were performed using an automatic electro-hydraulic servo press to study the evolution laws of physical and fracture properties of different deep rock materials under high-temperature geological conditions. The fracture characteristics were measured using an industrial camera and digital image correlation technology to analyze the effect of high temperature on fracture properties and failure modes of the CSTBD samples after different thermal treatments. The micro-damage properties of green sandstone and granite materials were obtained using a scanning electron microscope(SEM). The following conclusions were drawn from the test results:(1) With the increasing temperature, the fracture characteristics of green sandstone and granite change from brittle fracture to plasticity fracture, the longitudinal wave velocity of granite decreases sharply at 600℃, and the damage factor reaches 0.8748 at 700℃.(2) The fracture toughness of green sandstone and granite decreases with increasing temperature;however, the decreasing range of granite is larger than that of green sandstone.(3) As the temperature increases, the fracture morphologies of green sandstone and granite materials become rougher, whereas thermal damage cracks of granite and intergranular fractures inside sandstone as well as pores of sandstone increase.(4) The crack tip opening displacement and peak strain corresponding to peak load increase with the temperature.

Mechanism of fracture in macro- and micro-scales in hollow centre cracked disc specimen

The hollow centre cracked disc(HCCD) specimen is one of the suggested alternative methods for determining the fracture toughness of rock. This work aims to investigate the fracture mechanism in HCCD in macro- and micro-scales using numerical methods, extended finite element method(X-FEM) and particle flow code(PFC) modeling, respectively. In the X-FEM, heaviside and near-tip enrichment functions are employed to consider the presence of the crack in the model. In PFC modeling the movement and interaction of stressed assemblies of rigid spherical particles are modeled using the distinct element method(DEM). A numerical code called MEX-FEM based on XFEM has been developed to simulate the problems involving crack. The models of pure modes I and Ⅱ in macro-scale are simulated in micro-scale. The results show that dimensionless stress intensity factors(YI, YⅡ) for pure modes I and Ⅱ increase by increasing the crack length ratio. The angle at which the pure mode Ⅱ occurs decreases by increasing the crack length ratio. In mixed mode I-Ⅱ, The value of YI decreases by increasing the crack angle, while the value of YⅡ increases to a given crack angle and then it decreases. Moreover, the fracture in micro-scale, unlike the macro-scale, includes a combination of different modes of fracturing.

Fracture characteristics and ductility of cracked concrete beam post-strengthened with CFRP Sheet

The present paper concerns the fracture characteristics and ductility of cracked concrete beam externally bonded with carbon fiber-reinforced polymer (CFRP) sheet as well as the integration behaviors between CFRP/concrete interfacial debonding and concrete cracking.Three-point bending tests were carried out on the CFRP-strengthened cracked concrete beams with varying specimen depth and initial crack length.A straingauge method was developed to monitor the crack initiation and propagation in concrete,and the CFRP/concrete interfacial bonding behaviors,respectively.Clip gauges were used to measure crack mouth opening displacement (CMOD) and the deflection at midspan.Experimental results revealed that CFRP-strengthened specimen shows a higher load capacity under the same deformation level and a better inelastic deformation capacity compared with the unstrengthened one.For there are two manifest peak values in the obtained load versus displacement curve,the ductility of CFRP-strengthened concrete beams were investigated using index expressed as area ratio on the load versus displacement curve.The calculated results indicated that the contribution from CFRP sheet to the ductility improvement of specimen is notable when the deflection at midspan exceeded 10.5 times the first-crack deflection.

Energy Performance Contracting—Business opportunities would be infinite if the “two obstacles” were cracked

Energy Performance Contracting was introduced into China in the mid 1990s. Since western energy service companies came to China, their management pattern has undergone major changes. Why did such changes occur? Mainly because these companies encountered two difficulties in China: tax and financing.

Wave-induced flow of pore fluid in a cracked porous solid containing penny-shaped inclusions

An aim of current study is to analyze the contribution of reflected longitudinal waves to wave-induced fluid flow(WIFF) in the cracked porous solid.Initially,we investigate the time harmonic plane waves in cracked porous solid by employing the mathematical model proposed by Zhang et al.(2019).The solution is obtained in form of the Christoffel equations.The solution of the Christoffel equations indicates that there exist four(three dilatational and one shear) waves.These waves are attenuated in nature due to their complex and frequency-dependent velocities.The reflection coefficients are calculated at the sealed pore stress-free surface of cracked porous solid for the incidence of P1 and SV waves.It is found that three longitudinal waves contribute to WIFF and the contribution of these waves to the induced fluid in the cracked porous solid is analyzed using the reflection coefficients of these longitudinal waves.We analytically show that the fluid flow induced by these longitudinal waves is linked directly to their respective reflection coefficients.Finally,a specific numerical example is considered to discuss and to depict the impact of various parameters on the characteristics of propagation like phase velocity/attenuation,reflection coefficients and WIFF of longitudinal waves.

METHOD TO CALCULATE BENDING CENTER AND STRESS INTENSITY FACTORS OF CRACKED CYLINDER UNDER SAINT-VENANT BENDING

Using the single crack solution and the regular solution elf plane harmonic function, the problem of Saint-Venant bending of a cracked cylinder by a transverse force was reduced to solving two sets of integral equations and its general solution was then obtained. Based on the obtained solution, a method to calculate the bending center and the stress intensity factors of the cracked cylinger whose cross-section is not thin-walled, but of small torsion rigidity is proposed. Some numerical examples are given.

THE COMPLEX-VARIABLE-VARIATIONALMETHOD FOR ANALYSING FINITEINTERNALLY CRACKED PLATESAND ITS APPLICATION

In this paper, a whole field solution to finite internally cracked plates is derived by complex variable method, where the equations of equilibrium and compatibility, the single value condition of displacements and the traction-free condition on crack surfaces are satisfied exactly. The stress intensity factors of finite plates with central crack or eccentric crack or cracks emanating from a hole are calculated by using minimum potential energy principle to treat the boundary conditions excluding those on crack surfaces. As an application of the method to engineering problems, the computation about a finite rivet joint stiffened plate with cracks emanating from a hole is also performed. The numerical results show that the method presented in this paper gives rapid convergence and is much time-saving in computations.

NONLINEAR DYNAMICS OF A CRACKED ROTOR IN A MANEUVERING AIRCRAFT

The nonlinear dynamics of a cracked rotor system in an aircraft maneuvering with constant velocity or acceleration was investigated. The influence of the aircraft climbing angle on the cracked rotor system response is of particular interest and the results show that the climbing angle can markedly affect the parameter range for bifurcation, for quasi-periodic response and for chaotic response as well as for system stability. Aircraft acceleration is also shown to significantly affect the nonlinear behavior of the cracked rotor system, illustrating the possibility for on-line rotor crack fault diagnosis.

THE SOLUTION OF INTEGRAL EQUATIONS WITH STRONGLY SINGULAR KERNELS APPLIED TO THE TORSION OF CRACKED CIRCULAR CYLINDER

In this paper, the functions of warping displacement interruption defined on the crack lines are taken for the fundamental unknown functions. The torsion problem of cracked circular cylinder is reduced to solving a system of integral equations with strongly singular kernels. Using the numerical method of these equations, the torsional rigidities and the stress intensity factors are calculated to solve the torsion problem of circular cylinder with star-type and other different types of cracks. The numerical results are satisfactory.

AN APPROXIMATE ANALYSIS OF FREQUENCY RESPONSE OF A CRACKED HINGEDHINGED BEAM

A new method based on a modified line-spring model is developed for evaluating the natural frequencies of vibration of a cracked beam.This model in conjunction with the Euler-Bernoulli beam theory,modal analysis and linear elastic fracture mechanics is applied to obtain an approximate characteristic equation of a cracked hinged-hinged beam.By solving this equation the natural frequencies are determined for different crack lengths in different positions.The results show good agreement with the solutions through finite element analysis.The present method may be extended to analyze other cracked complicated structures with various boundary conditions.