Shear Strain Curves Research Articles

Analysis of strength characteristics of loess before and after freezing using a hollow cylinder torsional shear apparatus

This paper aims to comprehensively analyze the influence of the principal stress angle rotation and intermediate principal stress on loess's strength and deformation characteristics. A hollow cylinder torsional shear apparatus was utilized to conduct tests on remolded samples under both normal and frozen conditions to investigate the mechanical properties and deformation behavior of loess under complex stress conditions. The results indicate significant differences in the internal changes of soil particles, unfrozen water, and relative positions in soil samples under normal and frozen conditions, leading to noticeable variations in strength and strain development. In frozen state, loess experiences primarily compressive failure with a slow growth of cracks, while at normal temperature, it predominantly exhibits shear failure. With the increase in the principal stress angle, the deformation patterns of the soil samples under different conditions become essentially consistent, gradually transitioning from compression to extension, accompanied by a reduction in axial strength. The gradual increase in the principal stress axis angle (α) reduces the strength of the generalized shear stress and shear strain curves. Under an increasing α, frozen soil exhibits strain-hardening characteristics, with the maximum shear strength occurring at α = 45°. The intermediate principal stress coefficient (b) also significantly impacts the strength of frozen soil, with an increasing b resulting in a gradual decrease in generalized shear stress strength. This study provides a reference for comprehensively exploring the mechanical properties of soil under traffic load and a reliable theoretical basis for the design and maintenance of roadbeds.

Post-Cracking Shear Stiffness Model of Reinforced Concrete Beams

Macro diagonal cracks can significantly reduce the stiffness of slender reinforced concrete (RC) beams, which results in excessive deflection compared with limitations from design specifications. To evaluate the post-cracking stiffness of slender RC beams with diagonal cracks, a shear degradation model that considers shear deformation is proposed. Based on the variable angle truss model, this study deduced the strut angle formula based on the minimum energy principle. Then, the relationship between the stirrup yielding shear stiffness and elastic shear stiffness was modeled. Finally, the calculation procedure was developed by quantifying the stiffness degradation tendency. The comparison between the experimental results of deflection and the proposed analytical method showed good agreement. Additionally, the proposed method can capture the full-range features of shear strain curves.

Digital Image Correlation Analysis of Strain Fields in Fibre-Reinforced Polymer–Matrix Composite under ±45° Off-Axis Tensile Testing

This study presents an experimental investigation of an in-plane shear of a glass lamina composite using a ±45° off-axis tension test. Typically, the shear stress curve, shear modulus, and in-plane shear strength for composite lamina-type materials are identified. Previous research indicated that a loading rate affects the strength of this composite. This study extends the existing literature by utilising a non-contact optical digital image correlation (DIC) method to measure strain distribution during the test. Two cross-head displacement rates were examined. The obtained strain maps reveal an uneven distribution resembling fabric texture. As the deformation progresses, the differences in the strain pattern increase. Subsequently, a quantitative analysis of the differences between regions with extreme (minimum and maximum) strain values and regions with average values was conducted. Based on these measurements, shear stress–strain curves, indicating variations in their courses, were constructed. These differences may reach several percent and may influence the analysis of numerical simulations. The DIC results were validated using strain gauge measurements, a commonly utilised method in this test. It was demonstrated that the location of the strain gauge installation impacts the results. During the tests, the occurrence of multiple microcracks in the resin was observed, which can contribute to the nonlinearity observed in the shear stress–shear strain curve.

The Effect of Rigid Inclusions on the Dynamic Response of Highway Embankment

Soft soils are widespread in many areas of the East-West highway of Algeria, covering large areas. Construction projects such as highway embankments, airfields, roads, and railways in such areas experience several problems due to their low strength and permeability. This study used a fully dynamic analysis to evaluate the dynamic response of a highway embankment. The numerical analysis was carried out using the FLAC 2D version 8.10 software. The main objective was to evaluate the effect of rigid inclusions on the dynamic response of highway embankments by monitoring settlement, shear-strain curves, and maximum soil accelerations and displacements at different depth points. The obtained results showed that the configuration of the rigid inclusions significantly influences the dynamic response of the model. For instance, the settlement at 0.9m is 16% higher than at 0.2m from rigid inclusion.

On evaluation of shear modulus parameter (G0) in SANISAND constitutive model

The SANISAND constitutive model has been widely employed for the simulation of sands cyclic behavior. The shear modulus constant (G0) in SANISAND should be theoretically estimated from maximum shear modulus of soil (Gmax). To estimate G0, however, majority of calibration studies have used triaxial tests data in the shear strain levels larger than those associated with Gmax. This technical note aims to demonstrate how the selection criteria forG0 parameter affects the SANISAND model predictions , particularly in terms of G-reduction (shear modulus -shear strain) curve of sands. First, experimental G-reduction curves for four sands are compared with SANISAND predictions based on the values of G0 parameter estimated from triaxial tests. Then, a new calibration set of SANISAND for a single sand is proposed based on the G0 value estimated from Gmax, obtained from resonant column tests. The results confirm that the numerical shear stiffness values fall significantly lower than the experimental values in small strain ranges when the G0 constant is estimated from triaxial tests. However, the G0 constant estimated from Gmax appropriately predicts the experimental G-reduction curve of the sand in a wide shear strain range.

Observed responses of saturated sand under constant deviatoric stress path considering influence of loading amplitude

The soil in embankment dams and slopes may accumulate irreversible deformation due to water level variations. During this process, the soil skeleton experiences a constant deviatoric stress path, along with cyclic mean effective stress. In this work, triaxial drained tests were conducted on saturated sand under a low rate of strain to investigate the strain response along such stress paths, considering the influence of loading amplitude. The test results demonstrated that the volumetric strain of the saturated sand varied when the consolidation stress conditions were different. When the consolidation deviatoric stress was increased from 300 kPa to 900 kPa, the effect of cyclic load amplitude on the volumetric strain was strengthened, while the cumulative effect was weakened. The shear strain curves under different loading amplitudes were parallel to each other regardless of the consolidation stress condition. However, the cumulative shear strain showed great differences. The accumulation of shear strain was increased with the enhancement of loading amplitude. When the consolidation deviatoric stress was held constant at a low stress level, the effect of loading amplitude on volumetric strain was greater than that on shear strain. However, with the enhancement of stress level, the effect on shear strain was significantly enhanced.

Site response analysis of liquefiable soil employing continuous wavelet transforms

Propagation of the earthquake motion towards the ground surface alters both the acceleration and frequency content of the motion. Acceleration–time record and Fourier amplitude spectrum of the motion reveal changes in the acceleration and frequency content. However, Fourier amplitude spectrum fails to give frequency–time variation. Wavelet transforms overcome this difficulty. In the current study, site response analysis of a liquefiable soil domain has been investigated employing wavelet transforms. Three earthquake motions with distinct predominant frequencies are considered. It is revealed that the moment soil undergoes initial liquefaction, it causes a spike in the acceleration–time history. From the analysis, frequency of the spikes is found to be greater than the predominant frequency of the acceleration time history recorded at the ground surface. Interestingly, the spikes belong to the sharp tips of the shear stress–shear strain curve. Immediately after the spike, acceleration deamplification is observed. Post-liquefaction deamplification (filtering) of the frequency components is also observed.

Contribution of CFRP to the shear strength of retrofitted lightly-reinforced concrete panels

Low-rise buildings with thin Reinforced Concrete (RC) walls that do not comply with the minimum web shear reinforcement prescribed by current earthquake-resistant codes can be found in some Latin American countries. Previous experimental studies evidence that Carbon Fiber Reinforced Polymers (CFRP) strips may be used to retrofit RC walls for shear forces. The two models available in the literature to predict the contribution of CFRP to the shear strength of RC walls exclude key variables for assessing the seismic performance of lightly-reinforced concrete walls retrofitted with CFRP. In this research, a model for predicting the contribution of CFRP to the shear strength of lightly-reinforced concrete panels is initially developed. A model to correlate the contribution of CFRP to shear strength of lightly-reinforced concrete panels with that of thin and lightly-reinforced concrete walls is also proposed. The experimental program includes cyclic diagonal compression tests on fourteen lightly-reinforced concrete panels: one plain concrete panel and thirteen panels reinforced internally with web shear reinforcement-ratio equal to 0.11%; twelve retrofitted with CFRP, and one RC panel retrofitted with a concrete overlay conventionally reinforced with a welded-wire mesh. The CFRP configuration were diagonal or horizontal with one strip, and diagonal or horizontal with three strips. Three volumetric ratios of CFRP were studied in this research: 0.02%, 0.06% and 0.09%. The effectiveness of the configuration and volumetric-ratio of CFRP on performance of retrofitted panels was evaluated in terms of cracking patterns, failure modes, shear strength and energy dissipation capacity obtained from shear-strain curves measured during cyclic diagonal compression tests. The model proposed to predict the contribution of CFRP to the peak shear strength of retrofitted lightly-reinforced concrete panels depends on the properties, volumetric ratio and configuration of CFRP on the panel.

A Monotonic Smeared Truss Model to Predict the Envelope Shear Stress—Shear Strain Curve for Reinforced Concrete Panel Elements under Cyclic Shear

In previous studies, a smeared truss model based on a refinement of the rotating-angle softened truss model (RA-STM) was proposed to predict the full response of structural concrete panel elements under in-plane monotonic loading. This model, called the “efficient RA-STM procedure”, was validated against the experimental results of reinforced and prestressed concrete panels, steel fiber concrete panels, and reinforced concrete panels externally strengthened with fiber-reinforced polymers. The model incorporates equilibrium and compatibility equations, as well as appropriate smeared constitutive laws of the materials. Besides, it incorporates an efficient algorithm for the calculation procedure to compute the solution points without using the classical trial-and-error technique, providing high numerical efficiency and stability. In this study, the efficient RA-STM procedure is adapted and checked against some experimental data related to reinforced concrete (RC) panels tested under in-plane cyclic shear until failure and found in the literature. Being a monotonic model, the predictions from the model are compared with the experimental envelopes of the hysteretic shear stress–shear strain loops. It is shown that the predictions for the shape (at least until the peak load is reached) and for key shear stresses (namely, cracking, yielding, and maximum shear stresses) of the envelope shear stress–shear strain curves are in reasonably good agreement with the experimental ones. From the obtained results, the efficient RA-STM procedure can be considered as a reliable model to predict some important features of the response of RC panels under cyclic shear, at least for a precheck analysis or predesign.

Cyclic behavior of sand under non-uniform shear stress waves

During an earthquake, soil deposits are often subjected to complex stress/strain time histories that are quite different from the simplified ones used in laboratory tests for evaluation of the stress-strain-strength of these soils. To mimic the stress/strain time histories experienced at different depths of a mildly sloping soil deposit, a series of direct simple shear tests were conducted on Ottawa F65 sand specimens. The trends observed in these experiments were then used to estimate the lateral spreading of mildly sloping saturated deposits of the same sand subjected to various base motion time histories measured in the centrifuge tests conducted as part of an international research project (Liquefaction Experiment and Analysis Project, LEAP-2015 and LEAP-2017).In each CDSS test, after imposing the initial stress state, the specimen was subjected to non-uniform stress waves that resembled the shear stress time histories likely to develop in the LEAP-2015 and LEAP-2017 centrifuge specimens. A total of 17 CDSS tests were performed on specimens with relative densities of approximately 66%. Initial vertical and shear stresses were imposed on each soil specimen to correspond to the state of stress in a mildly sloping soil layer at two depths of about 4 m and 3 m. A ramped sinusoidal shear stress wave similar to the ramped sinusoidal base motion used in the LEAP centrifuge experiments was employed. The test results displayed a consistent trend between the peak cyclic stress ratio and the permanent shear strain that developed in the soil. The effects of overburden stress on the magnitude of permanent deformations were observed. Smaller initial vertical stress resulted in a more dilative response and smaller permanent shear strain. The observed permanent shear strain vs. peak cyclic stress ratio curves were then used to predict the lateral spreading of mildly sloping deposits tested in the LEAP-2015 and LEAP-2017 centrifuge experiments. Reasonably close correlation between the predicted and measured displacements were obtained. The developed dataset, made publicly available on DesignSafe-CI, can be used for calibration, evaluation, and further development of constitutive models for liquefiable soils.

The Influence of Shear Angles on the Split Hopkinson Shear Bar Testing

Dynamic material characterization is one of important factors in the development of modern transportation industry to overcome two main challenges, i.e. lightweight and crashworthy vehicles. The most commonly used apparatus to characterize the material in high strain rates is the Hopkinson bar. The Hopkinson bar can be conducted into several loading conditions such as compression, tension, shear, torsion and multiaxial. This paper focuses on the split Hopkinson shear bar testing, especially on the effect of the shear angles on generating the shear stress – shear strain curves, shear strain rates, and final shear strains. Four geometries of specimen were studied, i.e. circular hat-shaped (CHS), flat hat-shaped (FHS), punch (P) and double-notch (DN). This research is conducted with three main considerations, i.e. the same kinetic energy (7.34 Joule), the same shear area (±25 mm2), and the shear angles were varied as ±2.5°, 5°, 7.5°, 10° and 15°. This study shows that each testing has its own advantages and disadvantages and they generate different strain rate, strain rate gradient, final strain, and shear stress – shear strain relations which is not desirable. In term of shear angles, authors recommend using a shear angle of appoximately 5°. This shear angle generates the best purity on the shear loading among other shear angles and also the flow stress variation (among four tests) are quite acceptable ±16.4%.

Non-linear performance analysis of free headed piles in consolidating soil subjected to lateral loads

The analysis of laterally loaded pile is complex due to its site specific behaviour. Whereas most of the analytical methods provides only a generalized solution to it. Behaviour of piles in clay depends on site specific factors like subsoil condition, type of super-structure and the load transfer from it, construction duration and ground improvement process. The present study deals with the assessment of lateral load behaviour of pile based on the results of conventional and instrumented field load tests. The pile was designed based on the results of laboratory and field geotechnical investigations. The diameter and depth of bored cast in-situ pile were fixed as 600 mm and 16 m from the natural ground level respectively. The deflection profile obtained using inclinometer for various lateral loads on piles tested during different phases of site development were analyzed. The pile bending moment, shear force and soil reaction profile were established from the inclinometer data. The results obtained from the experimental data were found to be comparable with that of analytical method. The non-linear lateral load-displacement curves obtained from the load test conducted at different period of consolidation induced by site development process were analyzed. The curves thus obtained were transferred into a non-dimensional kh/khmax versus shear strain curve for the formation of equation explicit to the specific site. A site specific equation was proposed for the estimation of lateral load-displacement curve with respect to degree of consolidation of the surrounding soil subjected to surcharge load induced by the site development process.

Cyclic shear characteristics of marine cement soil under stress path with bidirectional shear stress

Under seismic loading, marine soil experiences horizontal shearing in two directions with different shear directions and amplitudes. It is therefore of considerable practical relevance to study the deformation behavior of marine cement soil under bidirectional shear loading. In this study, a series of cyclic simple shear tests were carried out to investigate the undrained deformation behavior of marine cement soil. The cyclic strain, stiffness softening, and cyclic strength were found to be significantly related to the phase difference and cement content. Cyclic shear strain accumulation increases as the number of cycles increases, and the emergence of inflection on the shear strain curve can be considered a suitable failure criterion for cement soil. The turning strain decreases as the cement content increases, and the phase difference decreases. With a decrease in cement content and an increase in phase difference, the rate of cyclic degradation and development of shear strain significantly increased. It was observed that the cyclic strength of cement soil increases with the cement content and decreases as the phase difference decreases.

Comparison of Deformation Behavior of Saturated Sand under Constant and Variable Deviatoric Stress

The cyclic triaxial tests were carried out on Fujian standard sand under two stress paths, the constant deviatoric stress path (CDS) and constant stress-ratio path (variable deviatoric stress, VDS), and the influence of cyclic deviatoric stress on the development characteristics of saturated sand was preliminarily discussed. Under the condition of the same consolidation stress state and amplitude of cyclic spherical stress, the amplitude of deviatoric stress under the two stress paths was different. The test results indicated that cyclic deviatoric stress had significant effect on the volumetric and shear strain in soil. When the consolidation deviatoric stress was relatively small, the volumetric and shear strain curves under these two stress paths almost coincided. However, the cyclic deviatoric stress had a stronger effect with an increase in the consolidation deviatoric stress. During the loading and unloading stages, the slope of the volumetric strain curve under the VDS path was smaller than that under the CDS path. The accumulated volumetric strain under the VDS path was greater than that under the CDS path. In the loading stage, the growth rate of shear strain under the VDS path was greater than that under the CDS path, but the opposite relationship was observed in the unloading stage. The presence of cyclic deviatoric stress accelerated or slowed down the accumulation of shear strain. These phenomena were related to the positional relationship between the stress state of soil and the critical state line.

Factors Influencing the Mechanical Characteristics of a Pile–Soil Interface in Clay Soil

A series of direct shear tests using a large-scale constant-normal-stiffness direct-shear testing system was conducted to study the factors that influence the mechanical characteristics of a pile–soil interface in clay soil. Interfaces of different roughness (R = 0, 2, 4, and 6 mm) were tested in clay soil with four different water contents with four normal stresses under different shear rates during shearing. Results for the interfacial shear behavior are presented as shear-stress–shear-strain curves, shear strength, and parameters. The results show that (i) the higher the roughness, the higher the shear strength of the pile–soil interface.The larger the normal stress, the smaller the roughness effect on the shear strength and parameters of the pile-soil interface; and (ii) the higher the water content of the clay soil, the lower the shear strength of the pile–soil interface, with maximum cohesion at a water content of 25%. The main influence that increasing the water content has on the shear strength of the pile–soil interface is changing the coherence, while the shear rate in this test range has less effect on the shear strength of the pile–soil interface. Overall, the mechanical characteristics of the pile–soil interface are influenced by roughness, water content, and shear rate, and close attention should be paid to those three factors when analyzing test results.

The impact of CIP content on the field-dependent dynamic viscoelastic properties of MR gels

Magnetorheological (MR) gels are one of the categories of magnetic smart materials, whose mechanical properties changed significantly in the presence of a magnetic field. This paper present dynamic viscoelastic properties of MR gel under various of magnetic flux density and Carbonyl iron powders (CIPs) weight fraction. The test to understand the dynamic rheological properties are carried out using oscillatory shear. Firstly, the MR gels are prepared by dispersing the CIPs into polyurethane (PU) matrix with a mechanical stirrer. Experimental data are obtained by changing the magnetic flux density from 0 mT to 480 mT at room temperature of 25 ℃. The elastic stress of MR gels with different CIPs content was studied under different magnetic flux density in oscillating test environment. The study results display that the elastic stress increases with strengthening extra magnetic flux density and the shape of elastic stress—strain curves are different under various magnetic flux density. Initial modulus, magneto-induced modulus and MR effect of MR gels with different contents of CIPs were obtained by magnetic field scanning. The results show that a higher magnetic-induced storage modulus can be obtained at higher CIPs weight fraction. The critical values and static elastic yield stress of MR gels with different CIPs content are also obtained by shear stress vs shear strain curves at the different magnetic flux density.

Determination of shear behavior and constitutive modeling of the 603 steel over wide temperature and strain rate ranges

A new double shear specimen (DSS) is used to study the plastic flow behaviors and constitutive models of the 603 steel under shear loading. Shear stress-shear strain curves are obtained over large ranges of temperatures (93–673 K) and shear strain rates (0.001–35,000 s−1). The stress state effect on the plasticity of the material has been studied particularly through the comparison of the test results with the experimental data under uniaxial compression. An obvious elevation of the flow stress levels and the strengthening of the work-hardening effect are observed in the compressive tests, indicating an important stress state effect on the plastic behaviors of the material. A constitutive model JC1 is determined by the present tests, which in numerical simulation shows much more precise prediction on the strain waves and the flow stress curves than the compression-based model, JC2. A shear dominated stress state is obtained in the shear zone, in which the stress triaxiality and the Lode angle parameter are both very low. Therefore, in this work the effects of stress state and strain rate have been decoupled successfully at high strain rates, and the stress state effect on the mechanical properties is largely avoided. It implies that without the consideration of the stress state effect, the equivalent stress-equivalent strain relation may fail to describe the plastic behavior of the material accurately. In engineering application, the actual stress/strain state must be considered in the determination or selection of the constitutive models to obtain a precise computation result.

Site Amplification Functions for Central and Eastern North America – Part I: Simulation Data Set Development

This paper presents the development of large-scale simulation-based data sets used to inform new site amplification models for Central and Eastern North America (CENA). Linear elastic, equivalent linear, and nonlinear one-dimensional site response simulations of site conditions in CENA are employed. An analysis tree is introduced to capture the range of expected CENA geologic conditions. Independent variables include the following: (1) representative and random shear wave velocity ( VS) profiles using data from the literature; (2) randomized, nonlinear shear modulus reduction and damping vs. shear strain curves with constraint on soil shear strength; and (3) outcrop ground motions representative of the VS= 3,000 m/s CENA reference rock condition. The resulting database of 1,747,278 simulations is conditioned on several parameters relevant to site amplification, which facilitates model development that is the subject of a companion paper. The database is openly available for use by other researchers.

Stiffness– and damping–strain curves of sensitive Champlain clays through experimental and analytical approaches

Stiffness degradation, G/G0, curves of Champlain clay at St-Adelphe, Quebec, and the associated variation of its damping ratio with shear strain are constructed in this study using the new combined triaxial simple shear (TxSS) apparatus. The apparatus offers the ability to obtain the stiffness (G/G0) and damping ratio of soils over a wide strain spectrum from 0.001% to 10%. The value of the small-strain stiffness of the tested clay is further confirmed through another series of piezoelectric ring-actuator technique (P-RAT) tests. Although, the stiffness degradation curve of the tested clay follows to some extent traditional curves suggested in the literature, the examined Champlain clay exhibits a different trend with respect to hysteresis damping, especially at large strains (>1%), and available analytical models could not successfully predict the damping behavior of the Champlain clay at such a strain level. A new constitutive model is therefore presented as a modification of the original Sig4 model considering the pore-water pressure built up with shear strain. Stiffness degradation and damping ratio versus shear strain curves of Champlain clays estimated using the proposed soil model are similar to their experimentally determined counterparts even at large shear strains where other models tend to misjudge the damping behavior of the clay.

Thermo-viscoplastic behavior and constitutive modeling of pure copper under high-strain-rate shear condition

A new double shear specimen (DSS) is used under the traditional Split Hopkinson pressure bar (SHPB) technique to study the constitutive behaviors of pure copper under dynamic shear loading. Shear stress-shear strain curves are obtained at 288–673 K and in a wide range of shear strain rates between 6000–45,000 s−1. A shear dominated stress state is obtained in the shear zone, in which the stress triaxiality and the Lode angle parameter are both very low. The influence of stress state on the plastic flow properties of the material is observed through comparison of the test results with the experimental data in compression. With the aid of finite element analysis (FEA), it's seen that the determined constitutive model JC1 can give much more precise prediction on the shear testing results than the compression-based model, JC2. The result implies that the commonly adopted compression or tension test data may not be suitable for description of shear dominated deformation conditions. In engineering application, the actual stress/strain state must be considered in the determination or selection of the constitutive models to obtain a precise computation result.