Axial Strain Accumulation Research Articles

Effect of torsional shear stress on the deformation characteristics of clay under traffic load

The soft clay under the road ground will suffer cyclic torsional shear stress encountered traffic load in addition to axial stress, which will cause further deformation of clay. To investigate the effect of torsional shear stress on the cumulative axial strain of clay, a series of undrained tests under cardioid stress path were performed on K0 consolidated undisturbed samples by using a hollow cylinder apparatus (HCA). The effect of vertical cyclic stress ratio (VCSR) and shear stress ratio (η) on the deformation and degradation characteristics of clay was investigated. The results indicate that there is inconsistency between the strain path and stress path. The increase in η further accelerates the accumulation of axial strain, which resulted from the degradation of clay induced by torsional shear stress. Considering the VCSR and η, a calculation method of degradation index was developed. Furthermore, a cumulative axial strain prediction model of clay under the cardioid stress path was established considering the degradation. This model addresses the limitation of traditional prediction models by considering the impact of torsional shear stress on cumulative axial strain.

Effect of compaction and moisture content on the deformation characteristics of unsaturated sandy soils varying fines content

ABSTRACT This research explores how the dynamic behaviour under cyclic compression loading affects compaction characteristics. Three types of sand, varying in fines content, are compacted under different saturation ( S r ) and compaction ( D c ) levels. Suction-controlled drained cyclic loading tests are conducted to predict axial strain accumulation, with initial suction measured for each compacted state. The study seeks to understand the correlation between axial strain accumulation and initial suction across soil types. Findings indicate that initial soil suction, influenced by saturation, significantly impacts axial strain under cyclic loading. Lower saturation enhances particle bonding, increasing initial suction and reducing strain accumulation. Moreover, an increase in fines content results in greater strain accumulation. Despite that, sands with elevated fines (18.8%) can achieve similar soil performance through effective compaction with precise saturation control. This underscores the role of saturation in moisture regulation during compaction, particularly for sands with higher non-plastic fines content, in achieving effective compaction.

Use of a novel magnetically actuated compression system to study the temporal dynamics of axial and lateral strain in human osteochondral plugs

The high water content of articular cartilage allows this biphasic tissue to withstand large compressive loads through fluid pressurization. The system presented here, termed the “MagnaSquish”, provides new capabilities for quantifying the effect of rehydration on cartilage behavior during cyclic loading. An imbalanced rate of fluid exudation during load and fluid re-entry during recovery can lead to the accumulation of strain during successive loading cycles - a phenomenon known as ratcheting. Typical experimental systems for cartilage biomechanics use continuous contact between the platen and sample, which may affect tissue rehydration by compressing the top layer of cartilage and slowing fluid re-entry. To address this limitation, we developed a magnetically actuated device that provides full lift-off of the platen in between loading cycles. We investigated strain accumulation in cadaveric human osteochondral plugs during 750 loading cycles, with two dimensional profiles of the cartilage captured at 30 frames per second throughout loading and 10 min of additional free swelling recovery. Axial and lateral strain measurements were extracted from the tissue profiles using a UNet-based deep learning algorithm to circumvent manual tracing. We observed increased axial strain accumulation with shorter inter-cycle recovery, with static loading serving as the extreme case of zero recovery. The loading waveform during the 750 cycles dictated the pace of the recovery during the extended free swelling period, as shorter inter-cycle recovery led to more persistent axial strain accumulation for up to five minutes. This work showcases the importance of fluid re-entry in resisting strain accumulation during cyclical compression.

An empirical formula for the accumulative deformation of saturated clay under different cyclic loading frequencies

Road and subway tunnels in soft clay soils subjected to traffic loading often cause lager settlement. It can pose danger to the surrounding buildings and structures. Hence, it is necessary for engineers to correctly predict the long-term deformation of saturated clay foundations under cyclic loading. In this paper, a series of dynamic triaxial tests were carried out on Nanning clay to investigate the effect of loading frequency and cyclic stress on axial strain accumulation of clay under undrained condition. Results show that loading frequency has a great effect on the axial strain accumulation of clay. Based on the experimental results, an empirical formula for calculating the accumulated deformation of saturated clay under cyclic loading was presented.

The effects of changing the deviatoric and spherical stresses during cyclic loading on the drained response of a sand

Changing the deviatoric and spherical stresses could affect the accumulative deformation behaviour of soils under cyclic loading. Drained cyclic triaxial loading tests were performed on saturated sand to study the dependence of cyclic loading-induced axial and volumetric strain accumulations on changing the deviatoric and spherical stresses in between loading cycles. The change in the stresses was simulated by changing cell pressure and axial load along different stress paths. The variation of axial and volumetric strain accumulations before and after changing the stresses is compared and discussed. It is found that changing the stresses could have different impacts on the axial and volumetric strain accumulations, as the accumulations are affected by different mechanisms. The axial strain accumulation after changing the stresses is affected by the average stress ratio and precedent stress history. The volumetric strain accumulation is hardly affected by changing the stresses unless an increase in the average stress ratio is caused. Both axial and volumetric strain accumulations show independence on the stress path of the disturbance. For the samples with decreasing average stress ratio, the strain accumulation direction after changing the stresses cannot be fully described using Modified Cam Clay flow rule.

Monotonic and cyclic undrained behaviour and liquefaction resistance of pumiceous, non-plastic sandy silt

Experimental data related to the mechanical behaviour of crushable pumiceous soils are limited compared with those for hard-grained soils. The main focus of previous studies has been on pumiceous sands, whereas pumiceous silts have not been investigated to date. In this paper, several series of monotonic and cyclic triaxial tests were performed to investigate the undrained behaviour and liquefaction resistance of a natural volcanic-ash derived, non-plastic pumiceous silt from northern New Zealand. Particle crushing due to sample reconstitution and triaxial testing was analysed by quantifying the changes in grain-size parameters and pumice contents. The main results can be summarized as follows. (1) The pumiceous silt showed a contractive response, even at medium to high relative densities, leading to high flow liquefaction susceptibility. (2) When subjected to cyclic undrained loading, the silt exhibited similar trends in terms of excess pore water pressure and axial strain accumulation to those established for hard-grained soils as opposed to those for pumiceous sands. (3) The liquefaction resistance of both medium-dense and dense samples was within the lower range compared to published cyclic resistance curves of both hard-grained soils and pumiceous sands. (4) The material did not undergo significant particle crushing after testing. Result (4) was considered to be the main factor that contributed to the fact that, in general, the cyclic undrained behaviour of the pumiceous silt was close to the trends established for those of hard-grained soils.

Cyclic resistance of fly ash influenced by anisotropic stress condition, sand contents, and gravel content

A series of cyclic triaxial tests were performed to study the effect of anisotropic stress, sand content (in a fly ash-sand mixture), and addition of gravel on the cyclic resistance of fly ash. The results indicated that the failure mode of pure fly ash in the presence of isotropic stress was cyclic mobility and that the cyclic resistance of pure fly ash was significantly lower than that of clean Nakdong River sand for given test conditions. The cyclic resistance of pure fly ash decreased when the effective confining stress increased from 100 to 200 kPa, as expected. The failure of pure fly ash conducted in the absence of stress reversal was due to the initial axial strain accumulation and subsequent sudden runaway deformation, and this failure mode differed dramatically from that of fly ash conducted under symmetrical stress reversal. An increase in the anisotropic ratio resulted in a decrease in the cyclic resistance of pure fly ash. Nakdong River sand and gravels were added to pure fly ash and it was examined whether the cyclic resistance of fly ash increased. Addition of sand was observed to decrease the cyclic resistance for 10% and 20% sand content by volume, regardless of the amount of increase in the dry density of the samples. Furthermore, the cyclic resistance of fly ash-gravel mixtures was greater than that of pure fly ash by approximately 17%.

The deformation characteristics of a kaolin clay under intermittent cyclic loadings

Metro train loading or machine vibration is characterized by intermittent cyclic loading interspersed with resting periods between loading cycles. The deformation of soft clay subjected to such unique cyclic loading may be different from that under consecutive cyclic loading, as reconsolidation occurs during the resting or drainage period. A series of cyclic triaxial tests were performed on a kaolin clay under both intermittent and consecutive cyclic loading patterns. The effects of including drainage periods between loading cycles on the deformation characteristic of the clay are investigated under different cyclic stress amplitudes, resting periods, consolidation confining pressures and over consolidation ratios. The results indicate that including drainage periods between loading cycles improves the cyclic resistance of the clay during subsequent loading cycles. However, compared with those under continuous cyclic loading, the overall axial strain and excess pore water pressure accumulation are much greater under the intermittent loading patterns, and the shorter the duration of resting period, the greater the overall accumulation. This means that including reconsolidation between loading cycles would enlarge the final deformation of soft clay. For the normally consolidated samples, the strain accumulation after reconsolidation highly depends on that developed in the first cyclic loading stage. Excess pore water pressure accumulated during each cyclic loading stage is negligible at given cyclic stress in over consolidated clay, whilst the axial strain accumulates notably in the first cyclic loading stage, but marginally after that. This may be attributed to the attenuation adjustment of microstructure in soil as cyclic loading continues.

Influence of stress history on the cyclic behavior of compacted soils in the frozen state: Deviator stress history

Observation of the cyclic behavior of compacted soils in a frozen state is required for assessing the dynamic stability of subgrades or embankments induced by earthquakes or traffic in cold regions, in which the compacted frozen soils have often experienced deviator stress history before applying cyclic stress. Therefore, strain-controlled monotonic triaxial tests followed by stress-controlled cyclic triaxial tests were carried out on compacted frozen soils to investigate the influence of deviator stress history on the cyclic behavior of such soils. The results shows that nonlinear and accumulated behaviors are represented in the stress-strain response of frozen soils regardless the amounts of residual strain induced by stress history. Although the volume fluctuations along with the general path are observed in the cyclic loading sequence, the general path seems consistent with volume changes during the monotonic loading stage, which potentially indicates that the plastic flow characteristics of this frozen soil are independent of the axial loading models (monotonic or cyclic loading). Moreover, an increase in the residual strains induced by stress history led to a decrease in the axial strain accumulation rate and to an increase in cyclic stiffness due to strain hardening induced by preloading. A previously proposed model for predicting the changes in the accumulated strain with the cyclic loading process was found to be applicable to compacted frozen soils regardless of the amounts of residual strain induced by stress history.

Ti–6Al–4V microstructural functionally graded material by additive manufacturing: Experiment and computational modelling

In this study, a functionally graded material (FGM) was fabricated using a powder bed fusion additive manufacturing technique. The FGM evaluated was Ti–6Al–4V, due to its importance in the medical device and aerospace sectors. The microstructure at selected build locations was analysed using both scanning electron microscopy (SEM) and electron backscatter diffraction (EBSD) techniques, where a gradient was observed both in terms of grain morphology and texture intensity. In addition, nanoindentation on the FGM sample shows a near quadratic shaped smooth gradient elastic modulus profile, with peak values at the midpoint of the gauge length. A tensile test to failure was conducted on the FGM sample with the aid of digital image correlation for surface strain analysis. Results show a gradient of local maximum principal strain in the highly {0001} textured section, while the reference sample in the control group shows a near-uniform strain distribution throughout the whole gauge length. A crystal plasticity finite element (CPFE) model was developed to explain the effect of texture on the mechanical properties adopting the microscopy-informed texture intensity gradient. Despite exhibiting higher elastic modulus (in the transverse direction, as measured via nanoindentation) the mid-section of the gauge length had a higher concentration of strain when loaded in the axial tensile direction, corresponding to build direction. The microscopy and computational modelling show that this apparent contradiction was explained via a high intensity of {0001} texture in the mid-section, leading to favourable conditions for axial strain accumulation.

Axial strain accumulation projection model for sand in cyclic loading

Strain accumulation analysis is important to understand the deformation mechanism of soil structure subjected to cyclic loading. An empirical model is a superior choice for the description of strain accumulation. However, the ambiguity and sensitivity for the physical meaning of the parameters in the empirical model hindered the understanding of the strain accumulation mechanism. Compared with conventional empirical models by directly fitting experimental data, this study proposed a new approach to formulate an empirical model of strain accumulation using the intrinsic relationship between the reloading process in cyclic loading and the monotonic loading process. All axial strain accumulation increments of silica powder during cyclic loading with constant cyclic stress amplitude were projected onto the corresponding monotonic loading stress-strain curve, and the evolution of strain accumulation was described by the projection modulus, which was regarded as an intrinsic parameter of the projection stress-strain curve. An empirical formulation for describing the connection between projection modulus and stress levels was proposed. In addition, the prediction model of total axial strain in cyclic loading was presented by combining the accurate representation of elastic and plastic moduli during primary loading. Finally, discussions on the intrinsic relation mentioned above were enhanced by presenting more experimental evidence. This paper provided novel insight into the mechanism of strain accumulation in cyclic triaxial conditions by linking strain accumulation with a unified stress-strain relation. However, limited by the triaxial stress conditions in this study, it is recommended to extend this projection method to other cyclic load tests.

The effects of unloading on undrained deformation of a kaolin clay under cyclic loading

Excavation induced unloading may induce additional shear stress in soils. Such additional shear stress or unloading history may affect the long-term deformation of soft clay under subsequent cyclic loadings. A series of undrained cyclic triaxial tests were performed on a kaolin clay to study unloading effect on cyclic behaviour of the soil. The effect of unloading sequence on deformation of the clay under cyclic loading was simulated by reducing cell pressure in between loading cycles. The dependence of axial strain accumulation on the amplitude of cell pressure reduction and unloading schemes was investigated under different initial confining pressures and cyclic loading frequencies. The results indicate that reducing confining pressure accelerates the strain accumulation during subsequent loading cycles and the greater the reduction in cell pressure, the greater the accumulated strain and excess pore water pressure. Such acceleration of axial strain accumulation after unloading would be attributed to the variation of stress state and the soil's ability in memorizing the unloading history. The direction of strain accumulation is controlled by the shear stress ratio rather than the amplitude of unloading. The final accumulated strain is not much affected by unloading schemes if the samples are the same in the initial confining pressure and the amplitude of unloading. An empirical model was developed to fit the axial strain accumulation both before and after unloading. The effects of cell pressure reduction on the parameters of the empirical model were also analysed.

Experimental study on the mechanical behaviour of bounded geomaterials under creep and cyclic loading considering effects of instantaneous strain rates

Rational evaluation of the long-term performance of large-scale foundations, tunnels and natural slopes located in seismically active areas necessitates accurate assessment of the strength and deformation characteristics of bounded geomaterials, such as natural rocks and cemented soils, under creep and cyclic loading conditions. In the present study, a unique approach for examining the induced instantaneous loading/strain rates during unconfined creep and cyclic loading was adopted to unveil the effects of creep and cyclic loading on the mechanical behaviour of laboratory-produced bounded geomaterial, namely Gypsum Mixed Sand (GMS). At first, a series of unconfined monotonic tests at six different strain rates ranging from 5.3E+0 to 2.1E-5%/min were conducted on GMS. Subsequently, the mechanical behaviour of the GMS was examined under unconfined creep/sustained loading at four different stress levels. Further, these results were compared with a number of unconfined cyclic loading tests performed at different stress amplitudes. Identical patterns of the variations of axial strain accumulation and instantaneous strain rates were observed during the creep and cyclic loading. Based on the relationships between the failure stress/strain and the corresponding instantaneous strain rate, the mechanical behaviour of the GMS specimens subjected to creep and cyclic loading was found to be similar to each other, and was distinctively different than those under monotonic loading condition.

Cyclic Properties of Artificially Cemented Gravel-Silty Clay Mixed Soils

The aim of this paper is to provide an insight into the effect of fine content (FC) on the artificially cemented gravel-silty clay mixed soils (CMS) in terms of strength, deformation, effective stress path and pore pressure response by undrained cyclic triaxial tests. In addition, some cyclic triaxial tests were also conducted on remolded gravel-silty clay mixed soils (RMS) under the same test conditions in order to evaluate the effect of cementation provided by the cementitious material. The corresponding cyclic responses, such as the generation and accumulation of axial strain, pore pressure and effective stress path, are compared across a range of CMS and RMS. A constant 5% percentage (by weight) of calcium oxide in mixed soils with four different ratios of fine content (13%, 30%, 50% and 70%) are tested under four types of confining pressures, 50 kPa, 100 kPa, 200 kPa and 300 kPa respectively. The results demonstrate that: an increase in fine content leads to decrease in both strength and liquefaction resistance, but accelerate the strain accumulation and pore pressure development. The cyclic responses of CMS exhibit “hysteresis” significantly compared with those of RMS due to the bonding strength between soil particles.

Experimental study on the cyclic response of Nanhai Sea calcareous sand in China

Considering that the foundation soil (calcareous sand) of offshore platforms is subjected to wave loadings of different heights in a long time, cyclic triaxial tests are conducted on the Nanhai Sea calcareous sand under different loading conditions, i.e., amplitude, initial effective confining pressure, frequency, and waveform. Test results indicate that the failure of Nanhai Sea calcareous sand under cyclic loading is not only governed by the gradual development of excess pore water pressure but also by the accumulation of axial strain. There is a dilative tendency in loose or dense Nanhai Sea calcareous sand inhibiting the full liquefaction, which leads to the failure type of cyclic liquefaction. The effect of loading conditions on the excess pore water pressure, the axial strain, the secant modulus, and the cycle numbers to failure was investigated. The effect of loading amplitude, effective confining pressure, and waveform is profound, while the effect of frequency is not obvious. The cycle numbers to failure at different cyclic stress ratios demonstrated that the liquefaction resistance of Nanhai Sea calcareous sand is larger than that of calcareous sand in other sea areas.

Effects of principal stress rotation and cyclic confining pressure on behavior of soft clay with different frequencies

Soft clay is subjected to complex cyclic stress paths involving a combination of cyclic vertical and horizontal stress with principal stress rotation caused by traffic load. In this study, three groups of tests, namely tests with principal stress rotation, cyclic confining pressure, and combination of principal stress rotation and confining pressure, were conducted at different load frequencies using Wenzhou soft clay with hollow cylinder apparatus to investigate the undrained cyclic behavior of soft clay. The development of pore water pressure, accumulative strain, axial stress–strain relationship, and resilient modulus were analyzed. Experimental results show that the different stress paths play important roles in the cyclic behavior. The principal stress rotation accelerates the degradation of the resilient modulus due to the accumulation of axial strain. The cyclic confining pressure constrains the development of axial strain, which results in a larger resilient modulus. A lower load frequency results in a larger pore water pressure, accumulative strain, and degradation of resilient modulus. These results provide reference for the assessment of settlement induced by traffic load on soft soils.

Laboratory-based characterization of shallow silty soils in southwest Christchurch

Cyclic triaxial test data are presented to characterize the cyclic response of silty soils at three no-liquefaction case history sites in southwest Christchurch. Stress-strain response and axial strain accumulation demonstrate nuanced, transitional responses of silty soils. Post-liquefaction reconsolidation volumetric strains are within the range expected for clean sands. However, there are clear differences in the post-liquefaction response of silts from that of sands. Low-plasticity silts undergo time-dependent reconsolidation whereas sands undergo immediate reconsolidation. Simplified liquefaction triggering procedures estimate significant liquefaction at these sites; yet, no liquefaction manifestations were observed during the Canterbury earthquake sequence. Laboratory estimates of cyclic resistance are consistent with estimates from simplified liquefaction triggering procedures, and both estimates are well below the estimated seismic demand. Thus, liquefaction is likely triggered at the element-level in the silty soil deposits. Post-liquefaction reconsolidation test results suggest water and ejecta may not necessarily accumulate in these stratified silty soils as they would accumulate in thick deposits of liquefiable clean sands. Thus, manifestations of liquefaction may not be observed at stratified silt/sand sites with delayed reconsolidation responses and lower hydraulic conductivities. Additional mitigating factors may also have contributed to the discrepancy between simplified procedure estimates of liquefaction and the lack of liquefaction observed at these sites.

Monotonic and cyclic tests on kaolin: a database for the development, calibration and verification of constitutive models for cohesive soils with focus to cyclic loading

A database with about 60 undrained monotonic and cyclic triaxial tests on kaolin is presented. In the monotonic tests, the influences of consolidation pressure, overconsolidation ratio, displacement rate and sample cutting direction have been studied. In the cyclic tests, the stress amplitude, the initial stress ratio and the control (stress vs. strain cycles) have been additionally varied. Isotropic consolidation leads to a failure due to large strain amplitudes with eight-shaped effective stress paths in the final phase of the cyclic tests, while a failure due to an excessive accumulation of axial strain and lens-shaped effective stress paths was observed in the case of anisotropic consolidation with $$q^{\text{ ampl }}< |q^{\text{ av }}|$$ . The rate of pore pressure accumulation grew with increasing amplitude and void ratio (i.e. decreasing consolidation pressure and overconsolidation ratio). The “cyclic flow rule” well known for sand has been confirmed also for kaolin: With increasing value of the average stress ratio $$|\eta ^{\text{ av }}| = |q^{\text{ av }}|/p^{\text{ av }}, $$ the accumulation of deviatoric strain becomes predominant over the accumulation of pore water pressure. The tests on the samples cut out either horizontally or vertically revealed a significant effect of anisotropy. In the cyclic tests, the two kinds of samples exhibited an opposite inclination of the effective stress path. Furthermore, the horizontal samples showed a higher stiffness and could sustain a much larger number of cycles to failure. All data of the present study are available from the homepage of the first author. They may serve for the examination, calibration or improvement in constitutive models dedicated to cohesive soils under cyclic loading, or for the development of new models.

Inelastic compaction and permeability evolution in volcanic rock

Abstract. Active volcanoes are mechanically dynamic environments, and edifice-forming material may often be subjected to significant amounts of stress and strain. It is understood that porous volcanic rock can compact inelastically under a wide range of in situ conditions. In this contribution, we explore the evolution of porosity and permeability – critical properties influencing the style and magnitude of volcanic activity – as a function of inelastic compaction of porous andesite under triaxial conditions. Progressive axial strain accumulation is associated with progressive porosity loss. The efficiency of compaction was found to be related to the effective confining pressure under which deformation occurred: at higher effective pressure, more porosity was lost for any given amount of axial strain. Permeability evolution is more complex, with small amounts of stress-induced compaction ( &lt; 0.05, i.e. less than 5 % reduction in sample length) yielding an increase in permeability under all effective pressures tested, occasionally by almost 1 order of magnitude. This phenomenon is considered here to be the result of improved connectivity of formerly isolated porosity during triaxial loading. This effect is then overshadowed by a decrease in permeability with further inelastic strain accumulation, especially notable at high axial strains ( &gt; 0.20) where samples may undergo a reduction in permeability by 2 orders of magnitude relative to their initial values. A physical limit to compaction is discussed, which we suggest is echoed in a limit to the potential for permeability reduction in compacting volcanic rock. Compiled literature data illustrate that at high axial strain (both in the brittle and ductile regimes), porosity ϕ and permeability k tend to converge towards intermediate values (i.e. 0.10 ≤ ϕ ≤ 0.20; 10−14 ≤ k ≤ 10−13 m2). These results are discussed in light of their potential ramifications for impacting edifice outgassing – and in turn, eruptive activity – in active volcanoes.

Biaxial Ratcheting Response of SS 316 Steel

Ratcheting is one of the challenging phenomena that needs to be investigated for the Fast breeder reactor (FBRs), to arrive at the optimum structural dimensions that are safe and yet do not have undue redundancy. Austenitic stainless steel is the principal structural material for Indian FBR. Preliminary assessment indicates that there is a need to demonstrate that the main load carrying vessel made of this material can provide sufficient safety margin against ratcheting under biaxial loading conditions. This exercise calls for carrying out many simulated experiments, particularly with biaxial tension torsion specimens to generate adequate data for developing robust constitutive models to predict ratcheting. Accordingly, many biaxial tension-torsion experiments for austenitic stainless steel pipes were conducted and the best results have been reported here. The mechanical behavior of this material has been reported for a given axial tensile stress superimposed with a given range of cyclic shear stress for many cycles of loading. Rectangular rosette is used for capturing the biaxial response. Important material responses like cyclic hardening and biaxial ratcheting have been experimentally observed. Maximum accumulation of 2700 μ axial strain has been observed for a loading condition of constant axial stress of 102 MPa super imposed with a cyclic variation of shear stress amplitude of 120 MPa over 2450 cycles. The amount of progressive accumulation of axial strain was found to be directly dependent on the number of cycles. The observed rate of axial strain accumulation found decreased with increase in number of cycles. All these results are presented in detail in this paper and important conclusions that are useful in modeling the observed behavior are discussed.