Failure Patterns Of Specimens Research Articles

A Stress‐Driven Double‐Phase–Field Framework for Tensile Fracturing Processes in Transversely Isotropic Rocks

ABSTRACTWe present a double‐phase–field framework for tensile fracturing processes in transversely isotropic rocks. Two distinct phase‐field variables are introduced to represent smeared approximations of tensile fractures along the weak bedding planes and through the anisotropic rock matrix, respectively. Driving forces that control fracture propagation in the phase‐field framework are constructed as a stress‐based formula with a recently developed tensile failure criterion that distinguishes the two failure modes in transversely isotropic rocks. For numerical implementation, we adopt a staggered integration scheme and decouple the governing equations so that the displacement field and phase‐field variables can be updated in sequence for a given loading step. The finite element formulation of the proposed framework is introduced in detail in this paper and is implemented in an in‐house finite element code. The numerical implementation is then validated by reproducing the uniaxial tension test results of Lyons sandstone. After that, we conduct simulations on a pre‐notched square plate loaded in tension to demonstrate the features of the proposed framework. Finally, we conduct simulations of three‐point bending tests of Pengshui shale and show that the proposed model can reproduce the force–displacement curves and failure patterns of specimens with different bedding plane orientations observed in laboratory experiments.

Mechanical behaviour of rock containing a persistent joint under uniaxial compression at different strain rates

Understanding the mechanical behaviour of jointed rock during seismic events is crucial for ensuring the stability of rock engineering. A series of uniaxial compression tests were conducted on granite specimens containing a persistent joint at strain rates (10−5–0.05/s). Acoustic emissions (AEs) were monitored to detect the rock fracturing, and the strain field on the specimen surface was measured by the digital image correlation technique. Three failure patterns of specimens were observed: rock splitting, joint slipping and mixed rock splitting–joint slipping. The shapes of typical strain–stress curves for the three patterns are different, but they are all characterised by multiple stress drops indicating significant rock fractures. When significant fractures occur, the frequency range of AEs expends and the dominant frequency of AEs becomes much larger. The specimen strength is affected by the strain rate, but this effect differs for different failure patterns of specimens. The joint inclination could influence the mode and profile of fractures near the joint, and the specimen strength and joint stiffness significantly decrease with increasing joint angle. This study could help better understand the behaviour of jointed rocks subjected to seismic loads.

Effects of content and size of aggregate on the mechanical responses of concrete at cryogenic temperatures

The meso-structure of concrete, which determines its apparent performance, is closely related to the maximum aggregate size (MAS) and aggregate volume. At cryogenic temperatures, due to the freezing of pore water, the internal structure of concrete is changed, leading to some difference in the role of coarse aggregate particles. In this study, the meso-mechanical modeling method was adopted based on the continuous grading aggregate model to investigate the influence of content and size of aggregate at cryogenic temperatures. The uniaxial compressive and uniaxial tensile behavior of concrete cubic specimens (sized by 150 × 150 × 150 mm3) with various aggregate volumes (15 % ∼ 45 %) and MAS values (12 mm ∼ 36 mm) were simulated with consideration of cryogenic temperatures effects. The variation of compressive strength, tensile strength, elastic modulus, and fracture to energy with maximum aggregate size and aggregate volume fractions at cryogenic temperatures was investigated, and the related influencing mechanism was analyzed. The numerical results demonstrated that the failure patterns of specimens at cryogenic temperature show some differences compared with those at ambient temperature. Besides, it was indicated that the effect of maximum aggregate size and aggregate volume on the elastic modulus and the energy to fracture is consistent with those at ambient temperature. At cryogenic temperatures, the compressive strength is improved with the increase of maximum aggregate size. For the smaller aggregate volume fraction (15 % ∼ 30 %), the tensile strength at cryogenic temperatures tends to increase as the increase of maximum aggregate size, while an opposite trend appeared at larger aggregate volume. Additionally, as the increase of aggregate volume fractions, the compressive strength decreases first and then increases at cryogenic temperatures, while the tensile strength and elastic modulus exhibit a trend of increase. It is concluded that cryogenic temperatures can enhance the influence of maximum aggregate size on tensile strength, but weaken the influence of aggregate volume fractions on strengths.

Bond behavior between recycled aggregate concrete and steel rebar subjected to biaxial lateral pressure

Eighty-four pull-out tests were carried out to study the bond behavior between recycled aggregate concrete (RAC) and steel rebar, considering different levels of recycled coarse aggregate (RA) substitution and biaxial lateral pressure. The effects of these two parameters on bond strength and peak slip were analyzed, the bond-slip constitutive relation between RAC and steel rebar under biaxial lateral pressure was established, and the energy of bonded interface was also analyzed. The results show that the failure patterns of specimens without lateral pressure were splitting failure, while the failure patterns of specimens with different biaxial lateral pressure can be classified as splitting-pull out failure. With an increase of lateral pressure, the relative bond strength, peak slip and bond energy gradually increased, whereas the relationship between RA replacement percentages and these parameters could not be clearly observed. In addition, the relative bond strength and peak slip approximately increased linearly with the increase of lateral pressure. Finally, based on the experimental results, a modified expression for bond-slip prediction was developed, taking into account damage, and the obtained results show that the predicted curves fit well with test data.

Experimental study on seismic behavior of dense-steel-column sandwich wall

This paper describes an experimental study on the seismic behavior of the dense-steel-column sandwich walls. Six full-scale specimens which are |-shaped, L-shaped, and T-shaped with or without diagonal braces were tested under low-frequency cyclic load. With the same axial compression ratio, the failure pattern of specimens without diagonal braces is as follows. There was no obvious failure phenomenon at the beginning of the test. As the increase of the horizontal displacement, the steel columns buckled in succession, and the buckling was local in the lower part. As the further increase of the horizontal displacement, the local buckling range of the columns extended till the specimen finally failed. With the same axial compression ratio, the failure pattern of specimens with diagonal braces is as follows. The braces locally buckled under the cyclic load at the beginning of the test. As the increase of the horizontal displacement, the buckling range of braces extended. As the horizontal displacement increases, the braces were fractured and the columns buckled in succession in the bottom until the specimen finally failed. The experimental results show that the diagonal braces can increase the specimens' shear stiffness and shear strength, while the braces can also improve the specimens' ductility and energy dissipation performance. The shear strength of the L-shaped wall is increased by 62.02% with the braces. The ductility coefficient of the T-shaped wall is increased by 110.58% with the braces. Additionally, it is also noted that the seismic performance of the L-shaped and T-shaped walls with end flanges is better than that of the |-shaped wall.

Study on dynamic compressive mechanical properties of freeze-thaw concrete

In this paper, the split Hopkinson pressure bar (SHPB) equipment was adopted to investigate the dynamic compressive mechanical properties of C40 concrete under various loading speeds after freeze–thaw cycles. The range of freeze–thaw times was 0 to 125 times. The range of loading speed was 4 to 10 m/s, and the tested peak strain rate ranged from 39.87 to 163.35 s−1. During the experiment, pulse shaper and lubricating oil were applied to make the test results more accurate. Based on the obtained results, this paper discussed two fundamental assumptions of one-dimensional wave propagation and dynamic stress equilibrium. A general equation was developed to express the dynamic compressive strength in dependency of the freeze–thaw times. The test results showed that the dynamic compressive strength of concrete increased first and then decreased with the increase of freeze–thaw times. The dynamic compressive strength also increased gradually with the increase of loading velocity. In addition, this paper discussed the difference and relationship between failure patterns of specimens and revealed the changing rules of stress versus strain curve, dynamic compressive strength, and dynamic impact factor (DIF). Two influence coefficients were introduced to quantify the effects of freeze–thaw damage and hydration on the dynamic compressive strength. Theory of statistical damage and Weibull distribution were employed to establish a constitutive model of freeze–thaw concrete. The results showed that the model can effectively describe the dynamic compressive mechanical responses of freeze–thaw concrete under impact loading, and gave some suggestions to concrete structural design, structural health detection, structural performance evaluation and so on in cold areas.

Crack propagation mechanism in rock-like specimens containing intermittent flaws under shear loading

The rock masses, especially with existing discontinuous joints, are prone to shear failure when subjected to constant changing stress in the direction perpendicular to the free face, which may result in tunnel collapse and slope slip instability in the processes of rock engineering construction. To better understand the effect of various joint geometries on the shear behavior of rocks, the mechanism of crack initiation, propagation, and coalescence in rock-like materials (a kind of cement mortar) with intermittent flaws under shear loading is investigated using both laboratory experiments and numerical simulations. The component of moment tensor is utilized to investigate the temporal and spatial evolution of acoustic emission events and determine the geometry state of the cracks. The major principal stress and velocity field are presented to distinguish crack types and study the stress evolution associated with crack propagation. The results reveal that for specimens with various flaw dip angles the propagation direction of all newly generated cracks is basically parallel to the shearing loading, and the failure patterns of specimens are mainly controlled by tensile fractures. When the flaw inclination angle reaches 45°, the evolution of the thickness of newly generated micro cracks is controlled by the type of stress field, and after peak strength its variation mainly occurs near the tips of the pre-existing flaws. The secondary cracks obtained from the velocity field analysis mainly include tensile, compressive-shear, tensile-shear and pure shear cracks rather than simple tensile cracks, and the secondary cracks appear instantly and abundantly on both sides of the specimen. The work may shed light on the mechanism of slope slip, and provide guidance to the safe construction of engineering projects.

The evolution of dynamic energy during drop hammer testing of Brazilian disk with non-persistent joints: An extensive experimental investigation

Rock mass is well known as a discontinuous, heterogeneous, and anisotropic material. The behavior and strength of rock mass is heavily controlled by the condition and orientation of discontinuities (faults, joints, bedding planes) and discontinuity sets. Under dynamic loading conditions, rock bridges along non-persistent discontinuity planes may crack, and a fully persistent discontinuity may form, potentially affecting the stability of a rock structure. The study of the dynamic behavior of rock discontinuities has critical implications for civil engineering, the mining industry, and any other areas where rock mass is utilized as a structural foundation in areas prone to dynamic loading conditions, such as those formed during earthquake events. In this paper, cement-mortar-based Brazilian disks containing open, non-persistent joints were constructed and subjected to impact loading to investigate their impact energy behavior. The effect of some parameters, such as joint continuity factor (the relationship between joint length and rock bridge length), bridge angle, joint spacing, joint orientation, and impact angle were investigated to estimate the required Dynamic Energy for Crack Initiation (DECI), Dynamic Energy for Crack Coalescence (DECC) and failure pattern of specimens. The results of the experiments revealed an increasingly continuous joint reduces the DECI and DECC, while larger joint spacings past the middle value of those experimented increase the DECI and DECC. The bridge angle and loading direction do not affect DECI, but by increasing bridge angle DECC decreases, and it increases by increasing loading direction angle. Finally, an optimization analysis was conducted which showed that joint spacing and joint continuity factors significantly affects DECI, and joint continuity factor and loading direction have significant effect on DECC.

The Bond Strength on Over Lapping Bars Using Pullout Test

The behavior of reinforced concrete structures depends on sufficient bond strength between concrete and reinforcing steel. The perfect bond between the reinforcement surface and the concrete makes the transfer force work well. In this experiment, several forms of bars overlapped in the concrete and then tested pullout directly. This experiment is to get the tendency of the bond stress patterns that occur in overlapping bars. Another result of the study is the failure pattern of each specimen. The specimen size is 150í—150í—150 mm. In the center of the concrete cube is rib two overlapped bars. The reinforcement used plain and two ribs types of bars surface. The compression of concrete used is a minimum of 25 MPa. Furthermore, the specimen was subjected to a pullout test loaded in stages with 22 kN/minute speed. Loading stopped after the sample has collapsed. The pullout test uses the ASTM C234-91a standard. The failure pattern of plain reinforcement specimens with diameters of 12 mm, 16 mm, and 19 mm is a pullout or a slipped. The specimen with deform bar diameter 13 mm, 16 mm, and 19 mm occurs in splitting failure. The pullout test result, all samples in connection not yielded yet. The results show that the higher the bar diameter's development length, the higher the bond strength. The bond stress of the plain bar is smaller than the deform bar.

RESEARCH ON BOND-SLIP BEHAVIOR BETWEEN CONCRETE AND STEEL REBAR UNDER UNIAXIAL LATERAL PRESSURE AFTER HIGH TEMPERATURES

The bond performance between concrete and steel rebar after high temperatures (HT) affects the safety evaluation of reinforced concrete structure. In practical engineering, the reinforced concrete is often subjected to lateral pressure (LP). Therefore, forty-eight pull-out tests of steel rebar embedded in concrete were carried out with HT and LP as parameters. The effects of LP on failure pattern, peak bond stress, peak slip and residual bond strength of specimens after HT were analyzed, and the empirical formula for peak bond stress with HT and LP was also established. The bond stress field of reinforced concrete under lateral pressure was deemed as linear superposition of concrete extrusion pressure in front of ribs and lateral pressure, and the bond strength of specimens with/without uniaxial LP were then calculated based on the microscopic transfer model and multi-axis strength failure criteria of concrete after HT. The results show that: LP and HT have significant effect on failure pattern of specimens. As LP increases, the peak bond stress, residual bond strength and peak slip gradually increase, but the peak slips of specimens with LP are smaller than those of specimens without LP when HT reaches 500 ℃. The theoretical calculations agree well with test results, indicating that it can predict the bond strength between concrete and steel bar after HT.

Experimental and numerical investigation on the effects of bedding plane properties on the mechanical and acoustic emission characteristics of sandy mudstone

Bedding planes have a strong influence on the mechanical characteristics of layered rocks. To study the effects of bedding plane properties on the strength, fracture and acoustic emission (AE) characteristics of rock, Brazilian tests of sandy mudstone with different angles between the bedding plane inclination and loading direction (the bedding plane-loading angle) were first conducted. Based on the cohesive zone model in ABAQUS, the effects of the number and strength of bedding plane on the fracture and crack distributions of specimens were then investigated through numerical simulation. The experimental results showed that with increasing bedding plane-loading angle, the failure strength of the disk specimens continuously increased. The characteristics of the AE count and crack distributions (RA-AF distribution) were predominantly affected by the failure pattern. The AE count distributions were divided into two types: unimodal distribution and multimodal distribution. The cracks that formed in the specimens were divided into three forms: tensile cracks, mixed cracks and shear cracks. The numerical simulation results showed that both the number and strength of the bedding planes strongly influence the fracture and crack distributions of specimens. With the increase in bedding plane strength, the failure patterns of the specimens under each bedding plane-loading angle transformed from layer activation failure to central failure under each bedding plane-loading angle tested. Furthermore, under each bedding plane-loading angle, the failure patterns of specimens with different numbers of bedding plane were the same, and the percentage of cracks on the bedding planes increased while the percentage of cracks within the rock matrix decreased.

Time-dependent behavior of rock-like specimen containing multiple discontinuous joints under uniaxial step-loading compression

Rock with multiple discontinuous joints widely exists in rock engineering, and its mechanical properties are complex, which greatly increases the difficulty of engineering design and construction. Time-dependent deformation characteristics and long-term strength evaluation of jointed rock masses remain poorly understood. In this work, the creep experiments of rock-like specimens with multiple discontinuous joints under uniaxial step-loading compression are carried out to explore the influence of joint geometry (rock bridge length, joint length, joint angle, and joint spacing) on creep strain, long-term strength, and failure pattern of specimens with multiple discontinuous joints. The following conclusions are drawn from the test results: 1) The deformation of jointed rock specimens has evident time-dependent effect, and the cumulative creep deformation increases as creep load increases; 2) The strength of jointed rock specimens under loading changes with time, and the ratio of long-term strength and creep peak strength ( σ∞/ σc) of the tested specimens ranges from 41% to 96%; 3) The distribution of initial joints affects the creep fracture modes of rock-like specimens. The rupture of rock-like specimens with different joints distribution is mainly caused by the growth of wing cracks and quasi-coplanar secondary cracks. Three different failure modes are observed from these specimens: i) tensile failure with cracks across the joint plane; ii) shear failure with cracks along the joint plane; and iii) tensile failure with cracks along the joint plane. Based on the principles of damage mechanics and fracture mechanics, a theoretical mechanistic model considering both the closure stage of pre-existing open joints and time-dependent propagation stage of new cracks is established. Considering the influence of joint length, joint angle and joint density, the evolution of creep strain of rock-like specimen with multiple discontinuous joints is analyzed. The theoretical model results agree well with the experimental results, which indicates that the established model can replicate the creep failure process of jointed rock mass. These theoretical and test results help us better understand the effect of multiple joints on the long-term behavior of rock mass.

Mechanical response of fully bonded bolts under cyclic load

The mechanical properties of a bolting system under cyclic loading were investigated experimentally by pullout tests. Bolts of different diameters were inserted into steel tubes and bonded together by resin or cement to prepare simulated bolting systems for further pullout tests. Uniaxial compression tests showed that cement has a comparatively higher stiffness and peak stress compared with resin. A monotonic pullout test was conducted to determine the safety threshold for cyclic loading and the stress distribution along the steel tube. Interesting results were observed for specimens that were tested under different cyclic loading patterns. For instance, the deformation–memory property of the bolting system under a cyclic disturbance was evaluated; the triggering mechanism of creep behavior under cyclic loading is discussed; contributing factors associated with a hysteresis loop during a cyclic process were investigated; and weakening factors, such as the amplitude, upper loading level, and lower loading level were considered. The influence of cyclic mode on the failure patterns of specimens with different bonding materials was analyzed. Dominating failure modes, such as reversed-cone shaped resin agglomeration, flake-shaped scrapping, and bolt–resin interface debonding for resin-bonded specimens were exhibited and these are discussed. An annulus-shaped bonding block, brittle collapse, and cement–tube interface debonding for cement-bonded specimens is displayed and elucidated.

Investigation on Mechanical Behavior of I-Section Steel Columns After Elevated Temperature

This paper presents the experimental and numerical investigations on mechanical behavior of I-section steel columns after elevated temperature exposure. A total of twenty-six compression tests were carried out, in which one was under ambient temperature and the other twenty-five were under heating and cooling phase to study the influence of high temperature (400, 550, 700, 850, 1000°C) and high temperature duration (0.5, 1, 1.5, 2, 2.5 h) on mechanical behavior of the specimens. The failure pattern, axial load versus strain relation, axial load versus displacement relation and ultimate strength of the specimens were presented and analyzed. The test results showed that, high temperature duration had limited influence on the ultimate strength and other mechanical behaviors of the specimens, while the ultimate strength decreases with the increase of the maximum temperature the specimens suffered and some other behaviors also changed. The failure pattern of specimens after high temperature did not change compared with that of specimens under ambient temperature. The finite element models that have the same geometry with the test specimens were set up to compare with the test specimens and the results predicted from finite element analysis showed good agreement with that measured in test. Therefore, parametric study was carried out to investigate the influence of different section geometry on the ultimate strength of I-section steel short columns after elevated temperature. A new relationship for the ultimate strength for I-section steel short columns after elevated temperature was developed and proved to be reliable and accurate. What’s more, the effect of slenderness ratio on the stability coefficient of the columns was also investigated in the parametric study.

Investigation of elastic constants and ultimate strengths of Korean pine from compression and tension tests

Korean pine (Pinus koraiensis) is a wood species recently adopted in China for the rehabilitation of traditional timber buildings. This paper investigates its mechanical properties with laboratory tests on typical specimens to obtain the moduli of elasticity, Poisson’s ratios, shear moduli, coefficients of mutual influence, crushing strengths and tension strengths in various directions. Highly different failure patterns of specimens in compression test were observed when loaded in different directions relative to the grain while only brittle failure mode was observed for tension specimens. The measured parameters of Korean pine were compared with those obtained from theory of orthotropic elasticity, the empirical formula and the Norris failure criterion, good agreements were reached for all examinations in general which indicate it is admissible to treat Korean pine as ideal orthotropic material.

Mechanical properties and constitutive equations of concrete containing a low volume of tire rubber particles

Uniaxial compressive tests were conducted for a low-volume tire rubber concrete (RC) with different rubber volume content levels and particle sizes (five of each). The influence of rubber content and particle size on the mechanical properties of RC was investigated, including axial compressive strength, elastic modulus, peak strain, ultimate strain, appearance of visible cracks and failure pattern of specimens. The mechanical analysis of test results was conducted based on uniaxial compressive stress–strain curves. Uniaxial compressive constitutive models of low-volume rubber concrete were established that included axial compressive strength, peak strain and constitutive parameters a and b. There was obvious regularity between constitutive parameters a and b, rubber content and rubber particle size. Moreover, the physical meanings of constitutive parameters a and b were given, and the established constitutive models were evaluated by tests. The test results demonstrate that the constitutive models have not only good predicting ability and high accuracy but also nice applicability within the limit of 50kg/m3 rubber content. The constitutive models were then improved by introducing the sand rate reduction factor k to reflect the influence of rubber additives. The improved constitutive models are able to predict the performance of concrete with low amounts of rubber.

Ductility and Strength of Modified Recycled Aggregates Columns with Silica Fume and Hybrid Fiber

In order to make up for the defects of new and old aggregate, making full use of the function of silicon fume and hybrid fiber, cyclic loading tests were carried out on five concrete with recycled aggregate columns and an ordinary concrete frame column under the combined influence with different admixtures and its ratios (silica powder and hybrid fiber) . This text was focused on the properties and failure pattern of specimens, displacement ductility coefficient, ultimate displacement rotation and horizontal bearing capacity. The test results showed that a low content of silica powder could improve ductility performance, while the addition of hybrid fiber made the ductility to be further enhanced and improved the early strength by a larger margin than later stage. With the constitutive relation and adjusting the modification coefficient of concrete stress strain curve using MATLAB, It could be more accurate on the bearing capacity of the columns.

Dynamic Brazilian Tests of Granite Under Coupled Static and Dynamic Loads

Rocks in underground projects at great depth, which are under high static stresses, may be subjected to dynamic disturbance at the same time. In our previous work (Li et al. Int J Rock Mech Min Sci 45(5):739–748, 2008), the dynamic compressive behaviour of pre-stressed rocks was investigated using coupled-load equipment. The current work is devoted to the investigation of the dynamic tensile behaviour of granite rocks under coupled loads using the Brazilian disc (BD) method with the aid of a high-speed camera. Through wave analyses, stress measurements and crack photography, the fundamental problems of BD tests, such as stress equilibrium and crack initiation, were investigated by the consideration of different loading stresses with abruptly or slowly rising stress waves. The specially shaped striker method was used for the coupled-load test; this generates a slowly rising stress wave, which allows gradual stress accumulation in the specimen, whilst maintaining the load at both ends of the specimen in an equilibrium state. The test results showed that the tensile strength of the granite under coupled loads decreases with increases in the static pre-stresses, which might lead to modifications of the blasting design or support design in deep underground projects. Furthermore, the failure patterns of specimens under coupled loads have been investigated.

Experimental study on low cycle fatigue strength of beam-to-column connections in steel bridge bents with different plate assembling and material mismatching

This study examined the effects of inherent defects due to plate assembling and material mismatched condition between base and weld metal on the fatigue strength of beam-to-column connections. Low cycle fatigue tests were carried out on specimens with different plate assembling systems and material mismatched conditions. The test results revealed that the global load-displacement relationships from specimens with different plate assembling systems and material mismatched conditions are similar, meaning these effects involve only local behavior of specimens. However, the fatigue strength of the specimens strongly depends on the location of defects resulting from plate assembling and mismatched conditions. The specimen with the undermatched conditions and the existing defect located closer to the corner of beam-to-column connection tends to have lower fatigue strength. The fracture surfaces indicated that failure patterns of specimen are different regarding mismatched conditions. While the crack propagated through the weld metal for the undermatched condition, it propagated towards the boundary between base and weld metal for overmatched condition. Elasto-plastic shell analysis was performed under the same condition as the experiments. And it is found that when evaluating fatigue strength of beam-to-column connections, the effects of plate assembling system and material mismatched condition should be considered.

Meso-Level Numerical Study on Different Type of Fiber Reinforced Concrete

To investigate failure mechanism and toughening features of fiber reinforced concrete (FRC) with different reinforced fibers, meso-level numerical simulations have been conducted on FRCs incorporated with steel, glass and polypropylene fibers, respectively (which were named as SFRC, PPRC and GRC). The complete failure process of crack initiation, coalescence and development, interaction and final break have been simulated. By analyzing the failure patterns of specimens, also the spatial and temporal distribution of acoustic emission and loading - step curves, it can be concluded that both peak strength and toughness of SFRC and GRC can be greatly improved. However, for PRC, the improvement of peak strength is little while its toughness can be enhanced significantly.