Cyclic Stress Paths Research Articles

Long-term behaviour and degradation of calcareous sand under cyclic loading

Calcareous sand has been used as the main filling material in numerous reef constructions. Therefore, understanding its long-term dynamic engineering geological characteristics under cyclic applications of traffic or wave loading is crucial to the design and prediction of the serviceability of reef infrastructures. Considering this, seven monotonic triaxial tests and 33 high-cycle (25,000 cycles) drained triaxial tests were conducted on calcareous sand with various mean effective stresses (p’) and cyclic stress ratios (ζ). The results show that the development of the accumulated axial strain (ε1acc) has a strong correlation with the positional relationship between the cyclic stress path and critical strength line (CSL) or static strength envelope (SSE) in the p’-q plane. The critical cyclic stress ratio ζc, that represents the cyclic stress path reaching the CSL, is proposed. When ζ>ζc, the growth rate of ε1acc with ζ increases drastically. Moreover, when the cyclic stress path approaches the SSE, ε1acc enters an incremental collapse state. The increase in p’ diminishes the dilatancy of the volumetric strain εv. However, this response of εv reverses from decreasing to increasing with increasing ζ. The resilient modulus (Mr) increases with the number of cycles (N) due to the initial densification. If εv dilation occurs, Mr will decrease with N as particles lose contact. A single parameter for the cyclic stress path ratio (ψ) considering the effects of p’, ζ, and SSE is proposed. Additionally, empirical formulas for calculating the ultimate ε1acc and Mr are established. Furthermore, particle degradation significantly worsens ε1acc and εv, but has a more profound effect on the compressibility of εv. This degradation is also detrimental to Mr. A certain deviation trend of the predicted values from the measured values is found to correspond with the relative particle breakage.

Undrained anisotropy and cyclic resistance of saturated silt subjected to various patterns of principal stress rotation

Although the undrained anisotropic behaviour of sand has been extensively studied, little is known about undrained anisotropy and liquefaction susceptibility of silt soil. This paper presents a systematic experimental study on the undrained response of a silt soil under different patterns of principal stress rotation, including the 90° jump of principal stress and the continuous rotation of principal stress. Particular attention has been focused on the influence of the cyclic stress path and the influence of cyclic stress ratio (CSR) on the pore pressure ratio ru and the deviatoric strain amplitude γqa. A remarkable finding of this study is that, for all loading patterns investigated, the pore pressure ratio ru is uniquely related to the deviatoric strain amplitude γqa, rather than to the CSR. Based on the experimental data, an explicit expression is proposed to relate γqa and ru, which can be used to predict the onset of failure as well as the build-up of pore water pressure at a specific strain level. The study also found that the relationship between the CSR and the number of cycles required to failure (Nf) is dependent on cyclic loading patterns and stress paths. However, by defining a unit cyclic stress ratio (USR) as a new index for cyclic resistance, a virtually unique relationship between USR and Nf can be established for all cyclic loading patterns and stress paths considered.

Undrained Cyclic Laboratory Behavior of Sandy Soils

The complex cyclic shear stress path experienced by the soil during an earthquake, which could also induce liquefaction phenomena, can be approximated in the laboratory only by using sophisticated testing apparatuses. Cyclic triaxial tests have been widely used, especially for coarse grained soils, as in this study. In the framework of the design for the seismic retrofitting of the ‘‘Ritiro viaduct’’ foundations along the A20 motorway connecting Messina with Palermo (Italy), a soil liquefaction study was also carried out. With this aim, a detailed geological and geotechnical characterization of the area was performed by in situ and laboratory tests, including seismic dilatometer Marchetti tests (SDMTs), the combined resonant column (RCT) and cyclic loading torsional shear tests (CLTSTs), and undrained cyclic loading triaxial tests (CLTxTs). In particular, the paper presents the results of cyclic triaxial tests carried out on isotropically consolidated specimens of a sandy soil. The seismic retrofitting works include the reinforcement of the foundation and replacement of the decks with newly designed type and structural schemes, mixed steel, and concrete with continuous girder. During the investigation, data were acquired for the characterization of materials, for the definition of degradation phenomena with the relative identification of possible causes, and for the estimation of the residual performance characteristics of the building. The structural campaign of investigations necessary to determine all of the key parameters useful for a correct definition of the residual performance capabilities of the work was divided into two phases: One in situ and one in the laboratory.

Evaluation of permeability damage for stressed coal with cyclic loading: An experimental study

Permeability and its evolution directly control the flow behaviors of the subsurface energy fluid extractions. Coalbed is known as a fractured, dual-porous media, and whose permeability is directly related to effective stress and the manner of stress loaded and unloaded. Coal has been historically treated as a transverse isotropic media and the permeability can also be influenced by the sorption induced deformations. As a cleat-rich porous medium, coal is potentially bearing various loading paths, such as fracturing, mining and natural geological tectonics activities. The permeability variation under cyclic loading and different stress paths is crucial for the engineering design for both mining and gas extractions from coal seams. The pulse-decay method was employed to estimate the permeability of cylinder coal specimen. An average permeability damage concept with a complete loading-unloading cycle is introduced to quantify the effects of maximum stress, loading path, holding time period, and gas type on permeability evolution. It was demonstrated that the permeability hysteresis occurred during the cyclic loading-unloading, and that the average permeability damage was subject to the loading-unloading paths. The average permeability damage for the coal specimen is more sensitive to maximum loading stress and the loading-unloading path compared to gas injection pore pressure and the holding period. Gas adsorption induced swelling dramatically reduced the initial permeability and average permeability damage during cyclic loading. The permeability evolution was analyzed through poroelastic theory coupled with the matrix shrinkage concept. When applied to permeability and stress relationship, Biot's coefficient should be cautiously applied for coal reservoir because it could be larger than unity when the adsorption induced non-elastic swelling is considered, and it even could be negative when the irreversible cleats closure is considered.

Experimental investigation of accumulation deformation properties of frozen silt clay under different cyclic stress-paths

The long-term serviceability of infrastructures in cold regions is inevitably affected by such dynamic loads in practical works as earthquake loading and vehicle loading. In order to study the deformation characteristics of frozen soil under the seismic loading, namely P-waves and S-waves coupled action, different cyclic stress paths were simulated by using triaxial testing equipment with bidirectional cyclic loading function. The results indicate that the cyclic shear stress was main factor in the development of permanent axial strain of frozen sample, while the cyclic normal stress had limited impact. In the case of same stress path, the clockwise rotational-direction of the cyclic stress path is more conducive to the accumulation of the axial permanent strain. In addition, the residual strain generated is greater in the loading process than in the unloading one under the similar conditions. The synchronous vibration of normal stress and shear stress makes the elastic strain maintain larger value than the reverse synchronous vibration, but the asynchronous vibration makes the residual strain keep larger than the synchronous vibration under the condition of the same number of loading cycle.

Effects of the principal stress rotation in numerical simulations of geotechnical laboratory cyclic tests

Cyclic stress paths in geotechnical experiments can generate considerable principal stress rotation (PSR) in the saturated soil. The PSR without changes of principal stress magnitudes can generate additional excess pore water pressures and plastic strains, thus accelerating liquefactions in undrained conditions. This paper simulates a series of laboratory tests considering the PSR using two types of sand. The impact of PSR is taken into account by using an elastoplastic soil model developed on the basis of a kinematic hardening soil model with the bounding surface concept. The soil model considers the PSR by treating the stress rate generating the PSR independently. The capability of this soil model is verified by comparing the numerical predictions with and without PSR, as well as experimental results. The comparative results indicate that the simulation with the soil model considering the PSR can better reproduce the test results on the development of shear strain, reduction of effective confining pressure and liquefaction than the soil model without PSR. Therefore, it is important to consider PSR effects in simulations of geotechnical experiments under cyclic loadings.

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.

Relating fragmentation, plastic work and critical state in crushable rock clasts

Grain breakage during compression and shearing is one important mechanism responsible for irrecoverable changes of the mechanical properties of granular materials. Here we present results of triaxial tests on limestone fragments under some monotonic and cyclic stress paths and we investigate the relationships between the progression of grain breakage, the plastic work and the evolution of the critical state line. Using the plastic work concept, we propose a method for determining grain shape and grain breakage indices, and we show how grain breakage influences the critical stress state, and hence the mechanical behaviour. The validity of the relationships is then verified on different granular assemblies (granite fragments and quartz sands), although further tests remain necessary to validate them under more generic stress paths.

Liquefaction Resistance of Sandy Soils from Undrained Cyclic Triaxial Tests

Recent earthquakes frequently showed liquefaction of sandy soils. In these case one of the major challenges is the assessment of the residual strength of liquefied soil. Laboratory researches have clearly indicated that liquefaction susceptibility depend on many factors including soil grain size distribution, effective confining stresses and applied stress path in terms of cyclic shear stress amplitude. The complex cyclic shear stress path experienced by the soil during an earthquake can be reproduced in laboratory only by using sophisticated testing apparatuses. Cyclic triaxial tests have been widely used to asses soil liquefaction potential especially for coarse-grained soils, as in this study. In the framework of the design for the seismic retrofitting of the “Viadotto Ritiro” foundations along the A20 motorway connecting Messina with Palermo, a soil liquefaction study has been carried out. With this aim, a detailed geological and geotechnical characterization of the area has been performed by in situ and laboratory tests including the combined resonant column and torsional shear test and undrained cyclic triaxial tests (CTX). In particular, the paper presents the results of CTX, carried out on isotropically consolidated specimens carried out on specimens of a sandy soil to asses liquefaction strength. The results are plotted in terms of deviator stress q versus axial strain ea, cyclic stress ratio CSR and axial strain ea versus number of cycles Ncyc, effective mean stress p′ versus deviator stress q, cyclic stress ratio CSR and pore pressure ratio Ru versus number of cycles Ncyc. The results show that the cyclic resistance increases with the decrease in the initial confining stress and decreases as the silt content increases and confirme that the coarsest material has a lower tendency to liquefy.

DEM analysis of the onset of flow deformation of sands: linking monotonic and cyclic undrained behaviours

This study explores the link between the monotonic and cyclic undrained behaviour of sands using the discrete element method (DEM). It is shown that DEM can effectively capture the flow deformation of sands sheared under both monotonic and cyclic undrained loading conditions. When subjected to cyclic shearing, flow-type failure is observed for a loose sample, while cyclic mobility is observed for a dense sample. A strong correlation between the monotonic and cyclic loading behaviour that has been revealed experimentally is also confirmed in DEM simulations: (a) flow deformation occurs in the compressive loading direction when the cyclic stress path intersects the monotonic compression stress path prior to the monotonic extension stress path, and vice versa; (b) the onset of flow deformation in q– $$p^{\prime }$$ space is located in the zone bounded by the critical state line and the instability line determined from monotonic simulations. Hill’s condition of instability is shown to be effective to describe the onset of flow failure. Micro-mechanical analyses reveal that flow deformation is initiated when the index of redundancy excluding floating particles drops to below 1.0 under both monotonic and cyclic loading conditions. Flow deformation induced by either monotonic or cyclic loading is characterized by an abrupt change of structural fabric which is highly anisotropic. The reason why the dense sample dilated during monotonic loading but showed cyclic mobility (temporary liquefaction) during cyclic loading is attributed to the repeating reversal of loading direction, which leads to the periodic change of microstructure.

Stiffness Degradation and Plastic Strain Accumulation of Clay under Cyclic Load with Principal Stress Rotation and Deviatoric Stress Variation

AbstractIn certain field conditions, the soil element is subjected to cyclic stress paths with both principal stress rotation and deviatoric stress variation. To better understand the response of s...

Influence of shear stress level on cyclic deformation behaviour of intact Wenzhou soft clay under traffic loading

Under traffic loading, the soil elements in subgrade are subjected to a cyclic cardioid-shaped stress path in the 2τvh~(σv−σh) stress plane. This significantly differs from the conventional stress paths that have been simulated using the cyclic triaxial and simple shear apparatuses, as widely reported in the literature. To date, the influence of shear stress level on cyclic deformation behaviour of intact soft clay subjected to cyclic traffic loading were rarely considered in the existing experimental investigation. For this reason, a series of cyclic hollow cylinder experiments that mimic cardioid-shaped stress paths are carried out on intact samples of Wenzhou soft clay. A wide range of vertical stress levels combined with different shear stress levels (i.e., different cardioid-shaped stress paths) are simulated in the experiments. The results show that the shear stress level significantly influences the cyclic straining and exacerbates the potential of cyclic shear failure. The difference of cyclic tests with variable shear stress level increases as the vertical cyclic stress ratio value increases. Based on the test results, an allowable cyclic stress ratio is determined to be about 0.22, which may serve as the upper bound limit of cyclic traffic loadings on soft clayey deposit. For the hollow cylinder specimens used in this study, a resilient axial strain of 3% could be a proper failure criteria value. A simplified permanent strain model that considers shear stress is proposed for the deformation behaviour of soft clay under cyclic traffic loading.

Fabric assessment of damaged anisotropic geo-materials using the multi-laminate model

Fabric or texture of intact geo-material affects its degree of anisotropy, and results in various mechanical properties in different orientations. It is a complicated problem, and it is important to consider fabric variations under different stress paths. Applied stresses change the fabric of the material, and change its rigidity and stiffness in different directions. Classic models are developed based on the invariants of stress tensor. These invariants do not carry the characteristics of the material in different directions, and most of the directional information of the material behaviour is being missed. To overcome these issues, a simple methodology was outlined to predict the behaviour of a geo-material in various orientations due to anisotropy. Multi-Laminate model, which is capable of considering the behaviour of material in different directions, was utilized as the framework of this study. Three damage functions and three ellipsoids were used to consider degradation of the material and spatial rigidity distribution around a point, respectively. The shape of the ellipsoids might be changed during the loading history due to fabric evolution. Model results were compared with some tests results. Mechanism of failure was predicted via investigating the damage functions. Fabric evolution was assessed, and rigidity variation of material under a cyclic stress path was investigated.

A new index for evaluating liquefaction resistance of soil under combined cyclic shear stresses

In geotechnical laboratory testing, a cyclic sine wave loading is applied to samples to simulate seismic loading. The shear stress amplitude in cyclic tests, the cyclic stress ratio (CSR) is always used to express the resistance of soil to cyclic loading. However, the cyclic strength of samples subjected to different cyclic stress patterns can exhibit quite differently. Apart from the possibility of the continuous rotation of the principal stress direction, the difference in shear stress due to cyclic changes induced by different cyclic stress paths is also an influential factor. A new parameter is presented in this paper, the equivalent cyclic stress ratio (ESR), which is defined as the ratio of the mean value of the maximum shear stress in a cycle to the initial effective confining pressure. With the hollow cylinder apparatus, several series of cyclic loading tests were carried out on Fujian fine sand and Qiantang silt. The ESR-based data all fall within a very narrow band in the half logarithmic coordinate, even when cyclic stress paths are different. Test results from Ishihara on Toyoura sand were also re-analyzed using the new index, and a similar correlation was evidenced for loose sand under various cyclic stress paths. For dense and very dense sands, the treatment can also narrow the discreteness of results. With this new index, the cyclic strength of soil obtained from relatively simple tests, e.g. cyclic triaxial tests or cyclic torsional shear tests can be easily used to predict the cyclic strength of soil subjected to combined cyclic shear stresses.

Cyclic Behaviors of Granular Materials under Generalized Stress Condition Using DEM

AbstractMost behaviors of granular materials have been studied under the limit conditions of stress paths such as cyclic triaxial compression and extension tests. Furthermore, the macrobehavior and micromechanical response of granular materials under more comprehensive cyclic loading tests in the generalized stress condition are not well understood. The objectives of this paper are to ensure the ability of the Discrete Element Method (DEM), to simulate the macrobehavior of granular materials under various cyclic stress paths of the generalized stress condition, and to explore the micromechanical response. To this end, four different cyclic stress paths under generalized stress simulations, following the stress-controlled method on a sample of spheres, were conducted. To check the validity of DEM results, the experimental results of the real sand under cyclic stress programs were used. The macrobehaviors, indicated by the stress–strain–dilation relationship and the directions of principal strain increment ...

Cyclic shear behaviour of fibre-reinforced mine tailings

ABSTRACT: In order to investigate techniques to improve the mechanical behaviour of mine tailings, an investigation of the cyclic shear response of fibre-reinforced mine tailings was carried out in the present study. Cyclic simple shear tests were conducted on fibre-reinforced and non-reinforced mine tailings. The tailings, produced from gold mining, were classified as sandy silt with traces of clay. Polypropylene fibres (zero and 0.5%) were added to the material. Under monotonic shear conditions, the addition of fibres unstiffens the material. Under shear stress-controlled cyclic conditions, fibres improved the material shear response and produced a stiffer material. Under shear strain-controlled cyclic conditions, no improvement was observed as a result of addition of fibres and there was no effect on material stiffness. The agreement of the strength envelopes of both monotonic and cyclic stress paths, under different cyclic loading conditions, allows the use of the same strength parameters for mixtures analysed under different loading conditions.

Predicting onset of cyclic instability of loose sand with fines using instability curves

This study utilises the equivalent granular state parameter, ψ⁎, as a key parameter for studying static and cyclic instability and their linkage. ψ⁎ can be considered as a generalisation of the state parameter as first proposed by Been and Jefferies so that the influence of fines content in addition to stress and density state can be captured. Test results presented in this study conclusively showed that ψ⁎ at the start of undrained shearing and ηIS, the stress ratio at onset of static instability, can be described by a single relationship irrespective of fines content for both compression and extension shearing. This single relationship is referred as instability curve. However, the instability curve in extension shearing is different from that of compression. In this paper, the capacity of the instability curve in predicting triggering of cyclic instability was evaluated experimentally. An extensive series of undrained one-way (compression) and non-symmetric two-way cyclic triaxial tests, in addition to monotonic triaxial tests in both compression and extension were conducted for this evaluation. Furthermore, a published database for Hokksund sand with fines was also used. Test results show that cyclic instability was triggered shortly after the cyclic effective stress path crossed the estimated ηIS-zone(s) as obtained from instability curve(s) irrespective of whether instability occurs in the compression or extension side.

Cyclic shear response of fibre-reinforced cemented paste backfill

In order to investigate techniques to improve tailings backfill stability in stopes, the cyclic shear response of fibre-reinforced cemented mine tailings was studied. Cyclic simple shear tests were conducted on fibre-reinforced and non-reinforced cemented mine tailings. The tailings, produced from gold mining, are classified as sandy silt with traces of clay. Portland cement (5%) and polypropylene fibres (zero and 0·5%) were added to the material. Under monotonic shear conditions, the addition of fibres confers hardening behaviour to the cemented material. Under shear strain controlled cyclic conditions, fibres increased the shear stress values of the cemented samples after successive load cycles. The agreement of the strength envelopes of both monotonic and cyclic stress paths, under different cyclic loading conditions, allows the use of the same strength parameters of mixtures analysed under different loading conditions.

Undrained cyclic triaxial behavior of saturated clays under variable confining pressure

A laboratory study on the undrained dynamic behavior of saturated clays in cyclic triaxial tests with a variable confining pressure (VCP tests) is presented. Tests were performed on remolded clayey samples using a dynamic triaxial device where the deviatoric stress and confining pressure can be varied simultaneously. Various cyclic stress paths have been applied on the specimens through varying the ratios or phase differences between the cyclic deviatoric stress and cyclic confining pressure. Specifically, the stress paths used in the present study were designed to simulate the coupling effects of simultaneously varying shear and normal stresses in clays due to earthquakes and other vibration sources. Test results obtained from this study show that the undrained response of saturated clays is strongly influenced by the variation of confining pressure, in terms of pore water pressure, development speed of cyclic strain and magnitude of cyclic strength. It is found that when strong P-waves are propagating in soil layers, VCP tests are more appropriate for the simulation of in situ stress fields than the conventional cyclic triaxial tests with a constant confining pressure (CCP tests).

Experimental Evidences of the Effect of Fibres in Reinforcing a Sandy Gravel

Studies regarding fibre-reinforcement are restricted to clays, silty and sandy soils. No information is available on gravels. It is worth checking the effect of randomly oriented discrete fibres also on such soils to see if they can be beneficial and to get a better insight into the grain to soil interaction mechanism. In this paper, the effect of a small amount of fibres having high aspect ratio on a sandy gravel was analysed by means of tests carried out in a large triaxial apparatus. Specimens of both natural and fibre-reinforced sandy gravel were prepared by wet tamping at different relative densities, and were tested along monotonic and cyclic stress paths. The results show that the addition of a small amount of fibres causes a slight increase in peak strength and a larger increase in ultimate strength at small confining stress, with an overall more ductile behaviour. The cyclic tests at small confining stress and intermediate strain levels show that, for the lowest applied strain (of the order of 10−2%), the stiffness was larger for the reinforced specimens, with a much sharper decrease at larger strains and final values similar for the reinforced and non-reinforced materials.