Major Principal Strain Research Articles

Water effect on subcritical crack growth and fracture behavior of marble

Understanding the fracture properties and subcritical crack growth of rocks in aqueous environments is significant for the effective assessment of the long-term stability of the masonry buildings, cultural heritage structures, and art sculptures. We use double torsion techniques to systematically investigate the subcritical crack growth behavior of marble under air, fluid, saturated and saturated + fluid test conditions. In the fluid condition and the saturated + fluid condition, the load reductions during the relaxation test are larger than other conditions, reaching 12.81% and 12.26%, respectively. There is a water-weakening effect on both the subcritical crack growth index (SCI) and KIC, but the water weakening sensitivity in KIC is lower than that of SCI. Compared to the air condition, the SCI values of the marble decreased by 43.69% under the fluid condition, 17.64% under the saturated condition, and 38.09 % under the saturated + fluid condition, respectively. The introduction of water during the relaxation test results in an immediate increase in the crack velocity and the major principal strain of the specimen, as evidenced by the appearance of the Ⅳ region on the KI-V curve. Scanning electron microscope images show that the most triangular pits and dissolution pits are present in the marble under fluid and saturated + fluid conditions, leading to a more pronounced deterioration of the mechanical properties. The test results highlight the significant impact of water on subcritical crack growth in marble. In particular, during rainfall, both dry and saturated marble masonry buildings are more prone to cracking due to the introduction of water.

Characteristic analysis of bionic-induced structures with negative stiffness inspired by the growth and deformation differences of branches

Negative stiffness (NS) structures with curved beams easily experience beam fracture in small-scale designs, limiting their repeatability and energy absorption. The induced energy absorption structure (IEAS), which achieves negative stiffness by altering load transfer paths, is designed inspired by the growth and deformation of tree branches. By means of the variation method of geometric parameters, a unique asymmetric buckling deformation mode is realized in IEAS. The NS and energy absorption characteristics in IEAS are analyzed based on load distribution and major principal strain theory. Compression results demonstrate that the asymmetric buckling mode exhibits higher energy absorption and specific energy absorption compared to symmetric linear buckling, effectively improving structural toughness. Through gradient analysis of geometric parameters and comprehensive analysis of induced structure layouts, the asymmetric buckling mode is successfully implemented in multi-layer IEAS. The multi-layer IESA exhibits excellent ability of energy absorption and toughness, making it have potential applications in areas that require small-sized designs with high energy absorption capabilities.

Blast Absorption Capacity of Brittle Mineral Foam: an Experimental Evaluation

Cellular materials, such as aluminum foam, have proven to be effective energy absorbents. They can be used as the crushable core for blast mitigation sacrificial cladding. In this paper insights into the blast response of a brittle mineral foam-based sacrificial cladding are presented. The experimental set-up used consists of a rigid steel frame (1000 mm × 1000 mm × 15 mm) with a square cavity of 300 mm x 300 mm in the center. An aluminum plate, representing the structure, with a total surface of 400 mm × 400 mm and a thickness of 2 mm is clamped into the steel frame. Two synchronized high-speed cameras in a stereoscopic configuration are used to capture the dynamic response of the aluminum plate at a frame rate of 20000 frames per second. The transient deformation fields are computed using a three-dimensional digital image correlation technique. The blast load is obtained by detonating 20 g of C4 placed at a distance of 250 mm from the center of the tested aluminum plate. The absorption capacity of the brittle mineral foam is assessed by comparing the out-of-plane displacement, the velocity, the acceleration and the major principal strain of the thin aluminum plate with and without the protective mineral foam. Two foam configurations with different thicknesses are considered: 60 mm and 120 mm. It is shown that adding the brittle mineral foam reduces the out-of-plane displacement together with the displacement velocity and acceleration of the aluminum plate at least by a factor of two. Post-mortem analysis of the foams shows that mitigation of the blast load in the present set-up and under the considered loading is partially obtained by crushing of the cell walls but mostly though the growth of cracks in the specimen.

Influence of Recycled Cement Paste Powder on Early-Age Plastic Shrinkage and Cracking of Cement-Based Materials

Cement-based materials, especially those with low water-cement ratios, often experience premature cracking due to plastic shrinkage in the early curing stages. In this study, the development mechanism of early-age plastic shrinkage of cement paste, and the crack shrinkage control effect of recycled cement paste powder on cement paste, was quantitatively investigated using non-contacting two-dimensional digital image technology. The influence of different replacement rates (5%, 10%, 20% and 30%) of recycled cement paste powder on the major principal strain and crack patterns of cement paste was investigated. Furthermore, the mechanism of recycled cement paste powder on the early-age plastic shrinkage of cement-based materials was explored. The results show that the addition of recycled cement paste powder could suppress the early-age plastic shrinkage of cement paste. An appropriate replacement ratio (10%) of recycled cement paste powder shows a 33.3% time delay in crack appearance and a 28.0% reduction in the major principal strain. However, the higher replacement ratio of 30% shows an adverse effect on the major principal strain, with an increase of 35.1%. The core mechanism of the appropriate recycled cement paste powder on plastic shrinkage reduction lies in its porous nature, which allows for water absorption and release and regulates the moisture state inside the pores. This quantitative research of the major principal strain development of the early-age plastic shrinkage of cement paste can facilitate a better understanding of plastic shrinkage reduction in recycled cement paste powder on cement paste.

Role of particle rotation in sheared granular media

When granular assemblies are subject to external loads or displacements, particles interact with each other through contact and may exhibit translations and rotations. From a micromechanical perspective, particle rotations are an essential mechanism influencing the macroscopic behavior of granular materials. In this study, biaxial shearing tests were conducted on assemblies of dual-sized circular particles at different confining pressures. A high-precision image analysis method was developed to extract the particle-level motion of all the particles, including the rotational behavior. Experimental results showed that most of the particles exhibited rotations. Particles within the shear band exhibited more significant rotations and were characterized by low connectivity (number of contacts per particle). In contrast, the particles outside the shear band rotated lesser, only in the beginning stage of shearing. Every rotation in either direction is accompanied by an opposite rotation of almost the same magnitude in the neighboring region, and rotation clusters have been observed. Rotations in both directions are normally distributed within the assembly, and the average particle rotation is zero. The average rotations in both directions evolve symmetrically with major principal strain. Generally, the rotation rate (degrees per incremental strain) is observed to be maximum at the start of the shearing, and gradually it becomes constant toward the end of the shearing. The average value of the absolute cumulative rotation observed for whole particles is 18.6° at the end of shearing, i.e., 20% deviatoric strain. Smaller size particles tend to exhibit 67% higher rotations than bigger particles. Confining pressures have no significant effect on the rotational behavior of circular particles.

Numerical Simulation Study of ground surface subsidence caused by filling mining on surface buildings and facilities in a mining area: a case study

The filling mining method is planned to be adopted in Chentaigou Iron Mine. There are many significant buildings and facilities in the mining area, making it necessary to evaluate the influences of underground mining on the surface buildings and facilities. The main purpose of this research was to evaluate the extent of the surface subsidence basin and the degree of damage of buildings and facilities after filling mining by numerical simulation. To this end, a three-dimensional numerical model of the whole mining area was established. Secondly, a Discrete Fracture Network (DFN) in 3DEC numerical simulation software was adopted to obtain the strength parameters of each representative elemental volume (REV). Furthermore, FLAC3D numerical simulation software was utilized to evaluate the range of influence of the surface subsidence basin after filling mining. Finally, the maximum major principal strain on the surface was calculated. The results show that the surface subsidence basin of underground mining in this iron mine undergoes slow expansion then rapid expansion. Expansion of the surface subsidence basin is restricted by fault F1. After the mining orebody, the maximum major principal strain of surface meets design requirements, and the surface buildings and facilities are deemed safe.

Undrained dynamic response of naturally high-strength sensitive clay to bidirectional cyclic loadings under the plane strain condition

Soils beneath railway embankments can be considered under the plane strain condition. Excessive settlement has been observed on structured clays beneath railway embankments in the coastal areas of China. Compared with the cyclic behaviors of structured clay under the axisymmetric condition, the dynamic responses under the plane strain condition have been less studied. In this study, several one-way undrained cyclic true triaxial and cyclic plane strain tests were conducted on undisturbed structured clay. The test results show that the permanent major principal strain obtained from cyclic plane strain tests is smaller than that obtained from cyclic true triaxial tests under the same conditions, implying that the permanent major principal strain obtained from the cyclic true triaxial test is overestimated. Moreover, the cyclic minor principal stress has a significant influence on the permanent deformation and excess pore pressure in cyclic plane strain tests. Compared to the results of cyclic plane strain tests with the constant minor principal stress, the permanent major principal strain is lower by 9.2% and 20.1% when the ratios of the amplitude of the cyclic minor principal stress to that of the cyclic major principal stress (η) are 0.3 and 0.5, respectively. As η increases, the maximum excess pore pressure increases markedly, whereas the change in the minimum excess pore pressure is almost negligible. Furthermore, an empirical formula for predicting the permanent major principal strain under the plane strain condition considering the impacts of bidirectional cyclic loadings was established.

Variance-Based Sensitivity Analysis of the Biaxial Test on a Cruciform Specimen

Parameter identification is a key aspect in the modeling of the material’s mechanical behavior. The identification quality depends on the sensitivity of the test results to the values of the constitutive parameters. In this context, a variance-based sensitivity analysis is performed, in order to quantify the influence of the material parameters on the results of the biaxial test on a cruciform specimen; in particular the influence of the Swift hardening law parameters and the Hill'48 anisotropic yield criterion on the forces, the principal strains, strain path and thickness reduction. In general, it was concluded that the Swift hardening parameters influence the forces and the major principal strain value, while the anisotropy parameters have the most influence in the principal strains, strain path and thickness reduction along the surface of the cruciform specimen.

Fracture mechanism and energy evolution of sandstone with a circular inclusion

Understanding the stress distribution, deformation and fracture behavior around a circular hole or inclusion is critical for the stability assessment of rock structures such as tunnels and backfilled openings. In this study, the analytical solutions of stress and displacement distribution around a circular inclusion of different elastic properties were first derived based on the theory of elasticity. Then prismatic sandstones with a circular hole in different filling modes were prepared and tested in uniaxial compression tests . Progressive deformation and fracturing behavior around holes were analyzed by digital image correlation technique . Moreover, the energy evolution characteristics of specimens were studied to reveal its deformation and failure mechanism. The results show that after filling, the radial and tangential stress and displacement of the inclusion increase, while the stress and displacement around the surrounding rock of the hole decreases, thereby improving the strength and deformation properties . In addition, the crack types and initiation positions around the unfilled and filled holes are quite different due to the stress redistribution. Based on the energy evolution characteristics and the major principal strain fields, the stress-strain behavior is divided into five stages. It is found that the inclusion not only has passive supporting and energy absorption effects on the surrounding rock, but also has a similar crack arrest effect on the initiation and propagation of new cracks. Finally, the effects of inclusion elastic properties and lateral stress coefficient on the stress concentration characteristics around the filled hole were discussed.

Twin Shear Unified Strength Solution of Shale Gas Reservoir Collapse Deformation in the Process of Shale Gas Exploitation

The collapse deformation of shale has a significant influence on the exploitation process. Experimental analysis has indicated a correlation coefficient range from 0.9814 to 0.9981 and the established sample regression formula could be used to express the relationship between the dynamic elastic modulus and static elastic modulus of shale specimens. Based on the twin shear unified-strength theory, where coefficient b was considered to express the effect of intermediate principal stress, with the deduced regression formula, the unified solution of major principal strains describing a critical collapse of the shale shaft wall was derived. The results showed that the intermediate principal stress had a significant influence on the major principal strain, describing the critical collapse of the shale shaft wall. At the same depth, the critical collapse major principal strain increased with the increase in the b values. With the change in b value from 0 to 1, the calculated difference in critical collapse major principal strain with the same wellbore depth would change from 22.1% to 45.5%. With the change in b value from 0 to 1, the calculated difference in critical collapse major principal strain with the same wellbore temperature would change from 22.1% to 45.6%. The unified solution formula of the major principal strain, describing the critical collapse of the shale shaft wall expressed by the dynamic elastic modulus, could adjust the contribution of intermediate principal stress by changing the values of b, while considering the influence of temperature and confining pressure. The twin shear unified-strength solution of the shale gas reservoir collapse deformation could be used to effectively evaluate the shale gas reservoir stability during shale gas exploitation.

Anisotropic and Noncoaxial Behavior of Soft Marine Clay under Stress Path Considering the Variation of Principal Stress Direction

The influence of the variation in the principal stress direction on the anisotropic and noncoaxial behavior was investigated through several hollow cylinder apparatus (HCA) tests that were performed on reconstituted soft clay specimens under a stress path with a fixed or continuous rotation of the major principal stress axis. In particular, the varying amplitude of the deviator stress (q) and intermediate principal stress coefficients (b) were focused upon. The results indicated that the shear stiffness and strength were strongly dependent on the fixed major principal stress angle. Furthermore, apparent noncoaxiality was observed between the orientations of the major principal strain increment and the major principal stress. Consequently, the noncoaxial behavior of the reconstituted soft clay was sufficiently and effectively described using rose and polar diagrams. Furthermore, the data fluctuation indicated that the noncoaxiality of soft clay was strongly dependent on both q and b during the pure principal stress rotation (PSR). The results obtained for undisturbed clay and sand are not expected to be applicable to reconstituted clay, because its behavior is in contrast to the former two. Regarding reconstituted soft clay, the degree of noncoaxiality was observed to increase during the second rotation (N = 2) compared with that during the first rotation (N = 1). However, this trend gradually weakened with an increase in q or b values. Moreover, regardless of whether N = 1 or 2, the degrees of noncoaxiality decreased with the increase in q for b = 0.5 whereas it increased with the increase in b values for N = 1. However, those for b = 1 were the smallest for N = 2. The results are expected to provide an experimental basis for the constitutive modeling of soft clay with fixed and continuous rotations of the major principal stress axes in ocean engineering.

Experimental Investigation on the Deformation and Noncoaxial Characteristics of Fiber-Reinforced Aeolian Soil under Traffic Load

The cumulative plastic deformation of a foundation associated with traffic loading causes subgrade instability, and eventually, failure of retaining structures. In the present study, hollow torsional shear tests were conducted on fiber-reinforced aeolian soil involving varying fiber contents, cyclic deviator stresses, cyclic shear stresses, and consolidation confining pressures using the Small-Strain Hollow Cylinder Apparatus, developed by GDS Instruments Ltd. (GDS SS-HCA). This enabled an investigation of the deformation characteristics and noncoaxial angle changes of fiber-reinforced aeolian soil under a heart-shaped stress path. The results indicate that fiber-reinforced soil deformation under cyclic loading involves axial (ɛz), radial (ɛr), circumferential (ɛθ), and shear (γzθ) strains, and deformation increases with increasing the cyclic number. The strain increases rapidly during the first 200 cycles and then gradually. The axial deformation decreases with increasing fiber content when the fiber content is less than 2‰ and increases when the content is more than 2‰. The plastic strain and total deformation decrease with increasing confining pressure but increase as the cyclic dynamic stress and cyclic shear stress amplitudes increase. Functional equations of the cumulative axial plastic strain and vibration numbers are proposed. The relationships between the model parameters, including the fiber content and cyclic torsional shear stress, are analyzed. The principal stress axis rotation causes variations between the major principal strain increment and the principal stress directions, representing the noncoaxial angle (β). The noncoaxial angle fluctuates during each loading cycle, exhibiting a V shape, for principal stress axis angles (ασ) from −90° to −45° and −45° to 30°, and decreasing at angles varying from 30° to 90°, with a maximum noncoaxial angle of approximately 30° per cycle.

Evaluation of 3D deformation field in siltstone with a pre-existing 3D surface flaw under uniaxial compression using X-ray computed tomography and digital volumetric speckle photography

The interior deformation or rupture of materials is usually derived from measuring the surface deformation of specimens. In this study, a set of uniaxial compression tests combined with in situ X-ray computed tomography (CT) was performed on siltstone specimens with a pre- existing three-dimensional (3D) surface flaw with various inclination angles (α = 30◦, 45◦, 60◦). The ratio of flaw depth to specimen thickness was 0.26. Based on the CT images of the specimens under different loads, the digital volumetric speckle photography procedure was applied to quantifying the 3D interior deformation of the specimens, and 3D displacement and major principal strain ε1 distribution in different sections were determined. The characteristics of internal strain before specimen fracturing indicated strain localization, which could describe the propagation mechanism of the single 3D surface flaw.

Refined extraction of crack characteristics in large-scale concrete experiments based on digital image correlation

The accurate extraction of the crack patterns and measurements of crack kinematics are essential for understanding the mechanical behaviour in experiments on structural concrete as well as in the validation and further development of sound mechanical models. This paper presents important refinements of the authors' recently published automatic crack detection and measurement procedure (ACDM) based on surface displacement measurements obtained with digital image correlation (DIC). The proposed refinements are crucial for reliably assessing the crack behaviour in large-scale experiments with complex crack patterns, since the original methods of ACDM may fail or result in biased measurements at locations with closely spaced cracks, crack intersections or cracks with high morphological curvature. The main refinements are (i) a Canny edge-based crack detector, which is applied on the DIC major principal strain field and (ii) enhancements in the crack kinematic measurement to assess the reliability of the results. The latter includes the automatic selection of optimum reference points used in the crack kinematic measurement to increase its reliability and remove uncertain results. The refined ACDM procedure is validated using several large-scale 2.0 × 2.0 m shear panel experiments with highly complex crack patterns. Compared to the original ACDM, significantly thinner cracks can be detected with a much higher reliability of crack locations and crack kinematic measurements, particularly close to crack intersections and at closely spaced cracks. Additionally, two approaches for the statistical consolidation of the large amount of gathered data into characteristic crack properties in large-scale homogeneous concrete element experiments are proposed and compared. The results show that the statistical consolidation of the ACDM data using a 95%-quantile match well with the direct extraction of the best-fit homogeneous crack properties from the full-field DIC displacements. The consolidated data provides highly valuable insight into the mechanical behaviour, especially regarding crack phenomena.

Mechanical and fracture behaviors of compacted gold mine tailings by semi-circular bending tests and digital image correlation

The storage and handling of mine tailings (MTs) pose significant economic and environmental problems and finding suitable recycling or re-use alternatives for MTs is an on-going process. One of those alternatives is creating MTs-based adobes or compacted MTs, which then can be used in construction materials and ground stabilization applications Therefore, the fully understanding of the mechanical and fracture behaviors for the compacted MTs are significant for the applications. However, no study on such behaviors of the compacted MTs was documented in the literature. In this study, the investigations of the mechanical and fracture behaviors of the compacted MTs were carried out experimentally by using semi-circular bending tests (SCB) and digital image correlation (DIC). The SCB tests were conducted by using three-point bending instruments. Mode I fracture behaviors were therefore obtained by manually setting different notch depths with various loading span distances. The influences of notch depths and span distances on the Mode I fracture toughness, KI, were obtained by testing the notched SCB specimens. Additionally, the influences of notch depths and span distances on the fracture process zone (FPZ) and fracture energy were evaluated. Results showed that the measured Mode I fracture toughness was not evidently influenced by the notch depths and span distances. The fracture energy decreased with the increase of notch depth and span distance. Finally, the maximum major principal strains were found to increase with the increase of notch depths.

Direct measurement of geomembrane strain from aggregate indentations

High localized strain in geomembranes caused by indentations from coarse, uniform drainage aggregate is associated with long-term stress cracking and has been widely studied. A number of large-scale lab tests were carried out with direct measurement of the distribution of the major and minor principal (engineering) strain across the area of a large laboratory sample of geomembrane. This ‘grid-point’ method of strain estimation is compared to the method developed by Tognon et al. which has been recommended as the best available approach at this time. It has been found that the method by Tognon et al. tends to over- and under-predict geomembrane strain depending on the aggregate and protection layers used. Indentations with higher smaller ratios of membrane to bending strains tend to be underestimated. A correction factor is proposed based on the ratio of membrane to bending strains and fits the measured grid strain method used in this study well.

Verification of Wrinkle-Scaling Law Using Photogrammetry for Rectangular Membranes

This study verifies wrinkle-scaling law through photogrammetric measurement for a rectangular membrane subjected to shear and tensile loads. The wrinkle-scaling law treated in this study indicates that a wrinkle amplitude ratio during a formation and a dissipation process of wrinkle are determined by the ratio of a virtual shrinkage strain to a major principal strain, which is not affected by a membrane size. A formation and a dissipation process of wrinkles on five rectangular isotropic membranes with different sizes were measured by photogrammetry, and the relationship between the wrinkle amplitude ratio and the strain ratio was discussed. The results showed that the relationship between the wrinkle amplitude ratio and the strain ratio is linear, which represents the scaling law, regardless of the membrane size, while confirming the validity of the scaling law. This paper also presents a utilization method of the wrinkle-scaling law to a practicable situation using photogrammetric measurement.

Geosynthetic-reinforced soils above voids: Observation and prediction of soil arching

The assumption with the biggest impact on the design of geosynthetic-reinforced soils above voids is the presence and degree of soil arching, which affects the predicted applied stress on the geosynthetic. A series of centrifuge tests were conducted to investigate the soil arching in geosynthetic-reinforced soils with measurements of the soil stresses and observation of soil and geosynthetic deformation used to infer the arching behaviour. Detailed analysis of the results showed that arching significantly reduces the stress at the base of the soil when a void forms; this mechanism is due to stress redistributions and not the formation of a physical arch as suggested in some models. A new method to reliably predict this reduction is proposed by calculating the coefficient of lateral stress on vertical failure planes based on the observations of a continuous convex arc of major principal strains above the void, and the assumption that this is indicative of the stress behaviour.

Three-dimensional cyclic behavior of saturated clays: comparison between undrained and partly drained conditions

The cyclic response of subgrade clays under traffic loadings is likely to be partly drained rather than undrained, and the traffic-induced dynamic stress field is three-dimensional rather than axisymmetric. To compare the three-dimensional deformation behaviors of saturated clays between partly drained and undrained conditions, a large number of cyclic true triaxial tests were conducted. Experimental results show that a partly drained condition leads to a remarkable increase of permanent major principal strain ([Formula: see text]) compared to an undrained condition, and the differences of [Formula: see text] between the two drainage conditions are affected greatly by the factors of cyclic stress ratio (CSR), overconsolidation ratio (OCR), and coefficient of cyclic intermediate principal stress (bcyc). The increase of bcyc induces a linear reduction of [Formula: see text] in an undrained condition, while it causes an increase first followed by a decrease of [Formula: see text] in a partly drained condition. The clays undergo stiffness softening and hardening in partly drained and undrained conditions, respectively, and the effects of bcyc and CSR on the stiffness evolution are very different between the two drainage conditions. The mechanism of the complex [Formula: see text] and resilient modulus behaviors in a three-dimensional state and partly drained condition is further discussed. In addition, two different empirical models are employed to predict [Formula: see text] in partly drained and undrained conditions.

Can maxilla and mandible bone quality explain differences in orthodontic mini-implant failures?

Purpose: This study aimed to compare the risk of orthodontic mini-implant (OMI) failure between maxilla and mandible. A critical analysis of finite-element studies was used to explain the contradiction of the greatest clinical success for OMIs placed in the maxilla, despite the higher quality bone of mandible. Materials and Methods: Four tridimensional FE models were built, simulating an OMI inserted in a low-dense maxilla, control maxilla, control mandible, and high-dense mandible. A horizontal force was applied to simulate an anterior retraction of 2 N (clinical scenario) and 10 N (overloading condition). The intra-bone OMI displacement and the major principal bone strains were used to evaluate the risk of failure due to insufficient primary stability or peri-implant bone resorption. Results: The OMI displacement was far below the 50–100 µm threshold, suggesting that the primary stability would be sufficient in all models. However, the maxilla was more prone to lose its stability due to overload conditions, especially in the low-dense condition, in which major principal bone strains surpassed the pathologic bone resorption threshold of 3000 µstrain. Conclusions: The differences in orthodontic mini-implant failures cannot be explained by maxilla and mandible bone quality in finite-element analysis that does not incorporate the residual stress due to OMI insertion.