Tension Cracks Research Articles

An enriched improved complex variable element-free Galerkin method for efficient fracture analysis of orthotropic materials

The fracture problem of orthotropic materials has been widely concerned by researchers in the fields of mechanics and engineering. The meshless method using nodes to discrete the problem domain is an effective way to analyze cracked structures. In this paper, an enriched improved complex variable moving least squares (EICVMLS) approximation, in which a group of intrinsic enrichments is introduced into the conventional ICVMLS adopting a well-defined weighted complex variable error norm, is proposed for capturing the crack-tip fields in orthotropic media accurately. Then, an enriched improved complex variable element-free Galerkin (EICVEFG) method is developed to simulate fracture behavior in orthotropic media. The visibility criterion is used to model the discontinuity behavior around cracks and the M−integral is considered to evaluate stress intensity factor (SIF). The stress field and the displacement field at the crack tip, the SIF for different crack inclinations, and different directions of orthotropy axes are investigated to verify the validity of the proposed method. In addition, the effects of linear basis functions and enriched basis functions on the results are compared in this study. The numerical results reveal that the established EICVEFG approach can achieve higher accuracy than the extended finite element method (XFEM) and traditional meshless methods such as the element-free Galerkin (EFG) method and the meshless finite volume (MFV) method. Similarly, the EICVEFG method has been proved to offer a higher convergence rate by parameter studies (including dimensionless factor dmax, integral size, and the number of integral cells in M−integral).

A solution for the frictional resistance in macro-block limit analysis of non-periodic masonry

This paper proposes a general equation to assess the crack inclination upper threshold when non-periodic textures characterise masonry walls. The proposed formulation introduces the computation of the frictional resistance at the macro-block interface by evaluating two masonry quality indexes, i.e., vertical and horizontal lines of trace. The proposed equation is adopted in conjunction with a macro-block limit analysis formulation in which the failure mechanism is parametrised and formulated according to the upper bound limit analysis theorem, coupled with a heuristic solver that is able to minimise the load multiplier and identify the geometry of the associated macro-block. The proposed analytical model is verified in a number of case studies by comparing advanced DEM simulations and numerical results arising from the literature.

Infrared precursor of pre-cracked coal failure based on critical slowing down

In order to study the precursor information of infrared radiation temperature of coal containing macro-cracks during load bearing damage, infrared monitoring tests of coal instability damage under different crack inclination angles are designed. Based on the critical slowing down theory, the variance and autocorrelation coefficients of the infrared radiation temperature series are calculated to reflect the damage precursors and provide a theoretical basis for early warning of coal and rock dynamic hazards. The results show that the infrared radiation sequences of pre-cracked coals have a critical slowing down effect. The autocorrelation coefficient and the variance of MIRT curve can be more accurate to find the precursor time of instability. In the critical slowing down analysis, the variance is more stable, and the lag step has a great influence on the autocorrelation coefficient. The infrared precursory information of the coal is mostly about 80% to 85% of the peak stress or instability time, and the horizontal fracture will make the failure precursory appear in advance.

Numerical and experimental investigation of mixed‐mode crack growth in aluminum alloys

AbstractFatigue crack growth in Al 2024 and Al 7050 specimens was assessed experimentally and numerically. In the experimental investigation, various specimen configurations and loading conditions were used to achieve pure mode I, pure mode II, and mixed mode I/II, I/III, and I/II/III. Sample configurations were as follows: first, compact tension shear (CTS) specimen to reproduce pure mode‐I and pure initial mode‐II loading conditions; second, surface crack tension (SCT) specimen to analyze the behavior of semielliptical surface cracks in mode‐I and mixed‐mode conditions; and third, hollow cylindrical (HC) specimen with initial semielliptical surface crack to analyze fatigue crack growth under complex stress state. In the numerical study, finite element method (FEM) simulations were performed by means of FRANC3D and ABAQUS solver. The numerical predictions were validated with the experimental results. These predictions resulted to be accurate estimation of the crack growth across the broad range of the investigated loading conditions.

Different Toppling Bank Slope Failures under Hydrodynamic Action during Impoundment of the Miaowei Hydropower Station Reservoir

Toppling is a common deformation and failure phenomenon in the reservoir bank slopes of hydropower projects. This paper studies the genesis and evolution of different toppling bodies during water impoundment at the Miaowei Hydropower Station Reservoir on the Lancang River in southwest China. Toppling properties were determined and second failure characteristics analyzed in different reservoir impoundment stages. Different degrees of toppling deformation were primarily affected by the transverse bending stress, while the regional tectonic stress has been shown to have a significant effect on the transverse bending of the rock layers. Combined with the on-site investigation and monitoring results, the failure mechanisms of the different toppling deformation bodies were analyzed. The second failure of the toppling rock mass caused by the reservoir impoundment process is mainly the hydrodynamic splitting along fractures, wave impaction and softening on the slope foot. The transverse bending effect of gravity is transmitted upward through joint misalignment, rotation and slip, accelerating the speed of secondary toppling failure and forming a compression-shear failure along the toppling tension crack. A model to predict the scope and time of failure in the toppling deformation banks under the action of reservoir hydrodynamics was proposed.

Critical Inclination of Failure Surface and Seismic Active Earth Thrust for a Broken Slope Backfill

This paper presents an analytical approach, based on the limit-equilibrium state, to determine the critical inclination of failure surface and active earth thrust for a cohesive-frictional backfill with a broken slope and a surcharge load at a constant distance from a retaining wall under the seismic condition. A combined analysis using Mononobe-Okabe’s and Culmann’s methods within a trial and error procedure is performed in this study. The influences of several parameters such as wall height, surcharge magnitude, cohesion, and internal friction angle of the backfill, adhesion between the wall-backfill interface, tension cracks, horizontal and vertical seismic acceleration coefficients have been investigated on the critical inclination of failure surface and the active earth thrust. Additionally, the performance of the proposed approach is explored by geotechnical software (Geo5) and two available methods in the literature. All of the results and the detailed comparisons are given in tabular and graphical forms.

Oblique Crack Propagation of Brittle Rock under Uniaxial Compression and Its Influencing Factors

With the development of infrastructure in China, the slope rock mass is affected by external forces such as roads. Tunnel excavation will cause a series of engineering problems, which are essentially caused by the instability caused by the propagation of internal cracks in the rock mass. At the same time, in practical engineering, the rock mass is formed through long-term geological structure, and its internal cracks have a variety of properties. Based on granite samples as the research object, two different angles of sample shapes, cylindrical and circular, are prefabricated. The uniaxial compression test is studied to analyze the law of inclined crack propagation in rock under uniaxial compression. Combined with the theory of fracture mechanics, the influence mechanism of crack inclination and sample shape on crack propagation in rock mass is discussed. The test results show that under uniaxial compression, the stress-strain curves of granite samples can be divided into four stages: compaction, elasticity, plasticity, and residual deformation. For the cylindrical sample, the crack initiation occurs at the tip. The compressive strength of the sample decreases with the increase in the prefabricated crack angle, and the crack initiation angle increases with the increase in the prefabricated crack angle. The fracture of the sample changes from shear slip failure to split shear failure of the penetrating rock mass with the increase in the crack angle. For the disk sample, the crack initiation location gradually increases from the tip to the middle with the increase in the crack angle, and the crack initiation angle increases with the increase in the crack angle. The peak load of the sample decreases first and then increases with the increase in the crack angle and is the minimum at 60°. The fracture mode of the sample is mainly tensile failure. When the crack dip angle is between 30° and 60°, the tensile and shear composite failure of the sample occurs, and the influence mechanism of crack dip angle and sample shape on the crack propagation path is analyzed. The research results have important theoretical significance for engineering design, construction, and stability maintenance.

Fatigue Crack Arrest Induced by Localized Compressive Deformation.

The localized compressive deformation (LCD) effect generated by an indentation process at the crack tip on the fatigue crack growth of the 7075-T651 aluminum alloy is reported. Eccentrically loaded single-edge crack tension specimens (ESE(T)) were pre-cracked at a crack length of about 20 mm by applying a constant amplitude fatigue loading. Subsequently, the LCD process was performed by using a semi-spherical indenter with a radius of 16 mm to compress the crack tip zone at different forces (5.0, 7.0, 12.5, 13.5, 15.5 kN), applied on the opposite surfaces of the specimens. The fatigue cracking process was continued on the compressed samples until an overall crack length of about 30 mm was obtained. The compressive load and the number of delayed cycles is discussed in terms of crack length and crack tip opening displacement (CTOD). A direct relationship between the compressive force induced by the LCD process and the delay of the crack propagation due to the crack arrest was observed. This effect became evident at a compressive force of 5.0 kN, where the crack propagation was arrested for about 9000 cycles in comparison with the non-LCD sample. However, when the force increased, the crack arrest also increased. The crack was considered to be completely arrested at a compressive load of 15.5 kN, since the crack did not grow after the application of more than 3 × 106 cycles.

The Instability of High-Steep Road Cutting Slope: A 3D Continuum-Discrete Coupling Method

In this paper, the 3D continuum-discrete coupling analysis method combined with the strength reduction theory is used to study the macrodeformation, stress law, and microfracture mechanism of a high and steep cutting slope of Zhongkai Expressway in Guangdong Province. The 3D continuum-discrete coupling slope model is established based on the finite difference software FLAC and the discrete element program PFC. Then, based on the correlations between stress tensor and force chain, displacement and shear strain increment, plastic deformation, and microfracture, the mechanism of slope instability is analyzed from macro- and microscales. The research shows the following: (1) the continuum-discrete coupling model is reasonable and effective in the three-dimensional slope stability analysis. (2) The coupling domain was penetrated by the shear band, and the upper part displacement of the coupling domain was large, whose direction was basically consistent with the shear band direction; thus, the slope slip surface was formed. (3) The microfracture can represent the macroscopic failure phenomenon, and the slope landslide can be interpreted as the result of shear fracture in slip direction, accompanied by the extension and penetration of tension crack.

Location of Tension Cracks at Slope Crests in Stability Analysis of Slopes

Over the conventional limit equilibrium method and limit analysis method, the finite element method is advantageous, especially for slopes involving complex failure mechanisms where the critical slip surfaces cannot be represented by log spirals and other similarities. In the presence of tension cracks at slope crests, however, the finite element method encounters difficulties in convergence while handling Mohr–Coulomb’s yielding surfaces with tensile strength cut-off. Meanwhile, the commonly used load-controlled method for the system of nonlinear equilibrium equations is hard to bring the slope into the limit equilibrium state. The two drawbacks drag down the finite element method in more extensive applications. By reducing the constitutive integration of plasticity with non-smooth yielding surfaces to the mixed complementarity problem, the convergence in numerical constitutive integration is established for arbitrarily large incremental strains. In order to bring the slope to the limit equilibrium state, a new displacement-controlled algorithm is designed for the system of nonlinear equilibrium equations, which is far more efficient than the load-controlled method. A procedure is proposed to locate tension cracks. Corresponding to the Mohr–Coulomb failure criterion with and without tensile strength cut-off, the failure mechanisms differ significantly, while the difference in the factor of safety might be ignorable.

Tensile Properties and Tensile Failure Criteria of Layered Rocks

Rocks are less resistant to tension than to compression or shear. Tension cracks commonly initiate compression or shear failure. The mechanical behavior of layered rocks under compression has been studied extensively, whereas the tensile behavior still remains uncertain. In this paper, we study the effect of layer orientation on the strength and failure patterns of layered rocks under direct and indirect tension through experimental and numerical testing (RFPA2D: numerical software of Rock Failure Process Analysis). The results suggest that the dip angle of the bedding planes significantly affects the tensile strength, failure patterns, and progressive deformation of layered rocks. The failure modes of the layered specimens indicate that the tensile strength obtained by the Brazilian disc test is not as accurate as that obtained by the direct tension test. Therefore, the modified Single Plane of Weakness (MSPW) failure criterion is proposed to predict the tensile strength of the layered rocks based on the failure modes of direct tension. The analytical predictions of the MSPW failure criterion agrees closely with the experimental and numerical results. In rock engineering, the MSPW failure criterion can conveniently predict the tensile strength and reflect the failure modes of layered rocks (such as shale, slate, and layered sandstone) with satisfactory accuracy.

Performance of a U-shaped anchoring system for cable-stayed bridges

An innovative U-shaped anchoring system was previously proposed to prevent the cracking of cable-pylon anchorage zones of concrete pylons in long-span cable-stayed bridges. The anchoring system transfers the cable force to the concrete pylon in the form of radial pressure, which fundamentally prevents the tension cracking of the concrete pylon column. In this study, the mechanical performance of the U-shaped anchorage system was investigated using finite element analysis. Subsequently, the fatigue performance of the steel strand in the U-shaped saddle, the anti-sliding performance of the U-shaped saddle, and the corrosion resistance of the steel strand were experimentally studied. The results of finite element analyses indicate that the U-shaped anchorage system significantly avoids concrete cracking in the cable anchorage zones provided that the strength grade of concrete filler is no less than C30. The experimental results show that the steel strand with polyurea coating has sufficient fatigue resistance as well as adequate anti-corrosion performance, and the anti-sliding performance of the anchoring system is sufficiently good. These critical studies validate the superiority of the U-shaped anchoring system with polyurea-coated steel strands, which should observe wide engineering applications in long-span cable-stayed bridges.

The strain characteristics of cracked anchored soft rock under short-term creep

Abstract The short-term creep properties of cracked soft rock are the basis for analyzing and predicting the long-term deformation characteristics of engineering rock mass. Based on orthogonal test design and by means of physical testing and theoretical analysis, this paper systematically studies the short-term creep strain properties of soft rock mass with a vertical anchor form under different combinations of crack number, crack discontinuity degree and crack inclination. The results show the following: (i) as the stress increases, the growth rate of the instantaneous strain of the anchored soft rock slows down, the growth rate of the creep strain increases and the growth rate of the total strain decreases at first and before it then increases. Based on this, the idea is proposed that the stress corresponding to the turning stress of the total strain change rate, from small to large, is the turning stress of the strain rate. This stress value is approximately 50% of its uniaxial compressive strength (UCS). (ii) Statistical analysis shows that for the same cracked rock mass, the three characteristics of cracks have different effects on the instantaneous strain, creep strain and total strain of anchored soft rock, and a certain number of cracks under specific geometric conditions are beneficial to the long-term deformation control of anchored soft rock. (iii) A relative creep model based on mutation is proposed. Considering the effects of the test instrument, the model can be divided into the power function model, the logarithmic function model and the exponential function model, according to goodness of fit. All three models can describe the initial and stable creep stage of anchored soft rock with cracks.

A Study on Linear Shrinkage Behavior of Peat Soil Stabilized with Eco-Processed Pozzolan (EPP)

Peat soil incorporated materials from fragmented organic constituents that originated in submerged wetlands. Peat soil has a particular index property that accounts for more than 75% of its organic content. Due to its low shear strength, high moisture content, high compressibility, low specific gravity, restricted bearing capacity, irregular shrinkage, and instability, peat soil is interpreted as a challenging soil for the building industry. The purpose of this study is to look at the index properties of Klias, Beaufort peat soil, and eco processed pozzolan (EPP), as well as to investigate the strengthening and stiffening effects of EPP stabilization treatment on peat soil and the association between EPP and linear shrinkage effects of peat. The linear shrinkage used to measure the shrinkage behaviour of peat soil consists of untreated samples, namely peat soil, and treated samples, which are peat soil in addition to EPP with a concentration of 20% and 30%, respectively. A scanning electron microscope (SEM) is employed to produce images of a sample by scanning the surface of an untreated peat sample and treated peat samples with EPP. High moisture content with an average of 580% was reported for the KBpt area. EPP can potentially help to reduce the shrinkage by almost 66.66%. Additionally, the results showed that by adding EPP as filler material to the peat soil, shrinkage behaviour decreases significantly for untreated peat soil and treated peat soil with EPP, with 4.29% reduced to 1.43% significantly. Correspondingly, the crystallization process occurred between peat soil and EPP, which contributed to the reduction of shrinkage and tension crack in peat soil and produced Muscovite, which is appeared and identified as mineral that important in rock-forming mineral. Doi: 10.28991/CEJ-2022-08-06-05 Full Text: PDF

Diagonal Tension Cracking Strength and Risk of RC Deep Beams

This study focuses on the shear serviceability of simple and continuous reinforced concrete deep beams. The test results of 81 simple deep beams (i.e., simply supported single-span deep beams) and 29 continuous deep beams, for which their diagonal tension cracking loads were reported, were collected from existing studies. On this basis, the diagonal tension cracking mechanism is discussed, and four existing models for diagonal tension cracking are evaluated. The evaluation results show the existing models fail to accurately reflect the influences of the main design parameters (including the shear span-to-effective depth ratio and main tensile reinforcement ratio) on the diagonal tension cracking strength. Therefore, a new equation for the diagonal tension cracking strength for simple and continuous deep beams is proposed. The proposed equation is verified to be superior to the existing models, showing an average value and a coefficient of variation for tested-to-predicted diagonal tension cracking strength ratios of 1.02 and 0.21, respectively. On the other hand, a probabilistic analysis is conducted to evaluate the diagonal tension cracking risk under service load, showing that 35% of deep beams exhibited a diagonal tension cracking load that is less than the service load, which indicated that diagonal cracks easily occur in RC deep beams under service loads.

Analytical Solutions for Active Lateral Earth Force

Analytical solutions are presented for the active force on a retaining wall from a single wedge of unreinforced soil, as obtained from a general Coulomb-type limit equilibrium analysis. The solutions can accommodate variable wedge geometry, pore pressure, shear-strength parameters, surcharge stress, applied loads, pseudostatic seismic coefficients, and a tension crack zone. Closed-form expressions are derived for the critical angle of the base failure plane and corresponding maximum effective normal force on the wall for a triangular soil wedge. Verification checks show exact agreement with existing analytical solutions for simplified conditions, including Coulomb and Mononobe-Okabe active earth force. A numerical example is provided to demonstrate the method for a gravity retaining wall.

Theoretical Analysis of Stress Intensity Factor for Two Asymmetric Cracks Emanating from Water Conveyance Tunnel

The water conveyance tunnel has been widely applied in tunnel engineering, which may be subjected to compressive stress and shear stress from rock and faults, respectively. The internal pressure caused by water in the tunnel will make the appearance of cracks and propagation, resulting in disasters. In order to study the effects of the cracks and compressive stress on the cracked tunnel model, a plane model containing a circular hole with two unequal cracks under the compression loads, shear stress and internal pressure was established in this study. Complex variable function and conformal mapping function were implemented to theoretically derive the stress intensity factors (SIFs) at the crack tip in the rock mass, the numerical simulation was conducted to validate the theoretical solutions. The results indicate that the numerical results using the ABAQUS code were in good agreement with the theoretical solutions. The effects of compressive stress, shear stress, internal pressure, crack length and crack inclination angle on model II SIFs were discussed, the initiation angle and initiation pressure of different rock materials were also studied. When the crack inclination angle changes from [Formula: see text] to [Formula: see text], the tunnel is easily destroyed. With the increase of the right crack length, the increasing rate of the SIFs increases quickly first and then linearly, however, the left crack length has a slight effect on SIFs. When the crack inclination angle is [Formula: see text], the crack initiation angle reaches the maximum value.

Analysis of stress intensity factor for a crack emanating from elliptical hole subjected to compressive stress and shear stress

Underground caves often exist in karst areas, which will cause many difficulties in tunnel construction. The underground caves are often subjected to compressive stress, shear stress and internal pressure come from rock, faults and groundwater, respectively. The crack emanating from the cave will propagate under the effect of external forces, leading to the disaster of cave collapse and water gushing. To research the stability of crack emanating from the elliptical cave, a model of a plane containing an elliptical hole with a single crack under the compressive stress, shear stress and internal pressure was established. The theoretical solutions of stress intensity factors (SIFs) for crack tip were derived using complex variable function and conformal mapping function. The theoretical results were compared with the results of numerical simulation to verify the correctness of the theoretical solutions. The effects of crack length, ellipse shape, compressive stress, shear stress, internal pressure and crack inclination angle on SIFs were discussed. We can conclude that when the crack inclination angle is varied from 0° to 30°, the initiation pressure is small, and the cave is easily destroyed by groundwater. The flatter the elliptical hole, the easier the crack propagates. With an increasing of crack length, the value of SIFs at the crack tip increase quickly first and then increase linearly. When the crack inclination angle is 45°, the initiation angle of the crack reaches the maximum value.

Experimental Investigation of Failure Mechanisms of Granites with Prefabricated Cracks Induced by Cyclic-Impact Disturbances

Engineering rock mass is normally subject to cyclic–dynamic disturbances from excavation, blasting, drilling, and earthquakes. Natural fractures in rock masses can be reactivated and propagated under dynamic and static loadings, which affects the stability of rock mass engineering. However, fractured rock mass failure induced by cyclic-impact disturbances is far from clear, especially considering varying angles between the rock mass and the direction of impact loadings. This work investigated rock deformation and failure characteristics through cyclic impact tests on granite samples with cracks of different angles. A Hopkinson bar was employed for uniaxial cyclic impact tests on granite samples with the crack inclination angles of 0–90°. The magnetic resonance imaging technique was used to determine rocks’ porosity after cyclic impacts. The stress–strain curves, porosity, strength, deformation modulus, failure modes, and energy density of samples were obtained and discussed. Results showed that the crack inclination angles significantly affected the damage evolution and crack morphology of rocks. Under the constant cyclic impact, the dynamic deformation modulus and dynamic strength of rock samples first increased and then decreased with the increase in crack inclination angle. The failures of granite samples for inclination angles of 0 and 90° were dominated by tensile cracking, while those for the inclination angles of 30–60° were dominated by shear cracking. The energy density per unit time gradually decreased with the increase in impact cycles. The results can provide references for the stability analysis and cyclic-impact-induced failure prediction of fractured rock masses.

Stress intensity factors and T-stress for an edge cracked Brazilian disk specimen under diametrically distributed load

Analytical formulae of stress intensity factors (SIFs) and T-stress in an edge cracked Brazilian disc (ECBD) subjected to diametrically uniformly and parabolic distributed pressure were firstly derived with the weight function method (WFM). Meanwhile, these analytical expressions of SIFs and T-stress were verified to be very accurate through the comparative analysis with the existing results, which could be expediently used to calculate the SIFs and T-stress in ECBD specimens with normalized crack length less than 0.50. Furthermore, load distribution form and load distribution angle affecting SIFs and T-stress was also investigated, which indicated that their influences were closely related to the crack length and crack inclination angle. The values of YI and T* decreased with increasing load distribution angle, however, YII was increased for θ = 30°, a/D < 0.25. It was also found that load distribution form and distribution angle had almost no effect on SIFs for a/D > 0.35, but their effects on T-stress should be considered for large crack inclination angles. Moreover, the influence of uniformly distributed pressure on SIFs and T-stress was more significant than that of parabolic distributed pressure for a larger load distribution angle.