Undrained Cyclic Loading Research Articles

An optimization DEM modelling method for soil-fibre undrained cyclic loading tests model based on the influence range of fibre

The computational cost of discrete element modelling is high owing to the limitations of particle size and contact in fibre modelling. This paper proposes an optimised discrete element method (DEM) for a hybrid model of soil and fibres based on the fibre influence range. First, a relative velocity state function is established based on the relative motion state between the fibres and soil particles under undrained cyclic loading. Subsequently, the influence range of the fibres is determined using the relative velocity function based on the first few cycles of the undrained cyclic loading numerical tests. Cluster and clump models of the fibre are then generated based on the influence range of the fibre. Finally, a symmetrical shape of the optimised model is developed by extracting the distribution length of the edge curve of the influence range along the vertical direction of the axis. In this study, the proposed optimised DEM was validated through a series of undrained cyclic loading numerical tests on fibre-reinforced soil. The results of the optimised model were highly consistent with those of the traditional model, and the computational time was significantly reduced. The cyclic loading timing for determining the range of influence of the fibre was analysed. The optimised model based on the influence range of the 15th cycles not only restored almost the same results but also saved the calculation cost by nearly eight times. The optimised model established based on the influence range after the 15th cycles had a slight influence on the results. In addition, the applicability of the optimised model is discussed. This paper provides new insights into the establishment of a hybrid model of soil and fibres.

Dynamic characteristics of compacted landfill waste material from cyclic triaxial tests

This study conducted a series of cyclic and monotonic triaxial tests on reconstituted landfill waste material from a closed landfill site in Sydney, Australia, to assess its dynamic behaviour under various testing conditions. Specifically, the effects of cyclic deviatoric stress, loading frequency, and effective confining stress on the cumulative plastic axial strain, resilient modulus, and damping ratio under undrained cyclic loading conditions were investigated. Results indicated that the plastic deformation, resilient modulus, and material damping are significantly influenced by dynamic stress and confining stress, with a lesser impact from loading frequency. Notably, as the number of loading cycles increased, the cumulative plastic axial strain and resilient modulus exhibited an increase, whereas the damping ratio decreased. Furthermore, increasing cyclic deviatoric stress led to an increase in both cumulative plastic axial strain and damping ratio, while an increase in confining stress resulted in a decrease in these parameters. Conversely, the resilient modulus showed an increase with rising cyclic deviatoric stress and confining stress. The influence of loading frequency on cumulative plastic axial strain and resilient modulus was minor, and its effect on the damping ratio was rather negligible. The study observed that initial loading cycles caused rearrangement and reorientation of waste components and the mobilisation of fibres with tensile forces as loading progressed, suggesting that these landfill waste samples behaved comparably to fibrous soil with randomly distributed fibres. Through nonlinear regression analysis, an empirical relationship for cumulative plastic axial strain incorporating cyclic deviatoric stress, confining stress, number of cycles, and frequency was derived. This research contributes valuable insights into the behaviour of compacted landfills as railway subgrades, providing a foundation for informed decision-making in the design of transport infrastructure over closed landfill sites.

Total stress model of clay considering small strain characteristics

Saturated soft clay has the characteristics of high compressibility, low strength, and high structural sensitivity. Its small strain characteristics have a significant impact on the deformation development and long-term bearing capacity of ocean engineering foundations. A total stress model for undrained cyclic loading of clay considering small strain characteristics was created based on the Overlay model. The proposed model was used to simulate the static or dynamic triaxial test results of over consolidated Chicago clay, remoulded normally consolidated Georgia kaolin, and normally consolidated clay Malaysia kaolin, respectively. The results verified that the model can simulate the static shear characteristics of clay. The model can also simulate the weakening of soil strength and strain accumulation under cyclic loading, and is suitable for analyzing the response of ocean engineering foundations under long-term cyclic loading.

Strain energy dissipation during liquefaction of fibre-reinforced sand under undrained cyclic triaxial loading

Strain energy dissipation during liquefaction of fibre-reinforced sand under undrained cyclic triaxial loading

Evaluation of large axial strain of granular sand in post-liquefaction stage using DEM simulation

Field investigations in recent studies have revealed that significant damage to foundations often occurs in the post-liquefaction stage, during which sand undergoes substantial deformation. As a result, numerous researchers have dedicated considerable effort to studying the evolution of the axial strain at this stage. However, the accurate measurement of the exact value of this strain is challenging mainly owing to the limitations of the triaxial apparatus. In this study, the numerical method of discrete element method (DEM) is used to simulate undrained cyclic triaxial loading tests according to a large number of loading cycles. The mechanical behaviour of granular sand under different cell pressures was reproduced using the DEM method, wherein the liquefaction resistance increased with the cell pressure. The post-liquefaction axial strain exhibited a similar pattern of variation among the calculated cases at different cell pressures. The value of the double amplitude of the axial strain stabilised at a maximum value after a certain loading cycle. The microscopic characteristics derived from the DEM calculations, including the contact number and force chain network, were analysed to provide reasonable explanations. The sand fabric was re-established after a large number of loading cycles and controlled by cyclic loading, which helped stabilise the accumulated axial strain.

An activation mechanism for cyclic degradation of clays in bounding surface plasticity

AbstractDuring undrained cyclic loading, clayey soils experience substantial stiffness and strength degradation when subjected to shear amplitudes exceeding a critical threshold. This paper presents an enhanced bounding surface rate‐independent plasticity model, an evolution of the previous SANICLAY model, tailored to capture this specific behavior during cyclic loading. A distinguishing feature of the proposed model is the introduction of an activation mechanism. This mechanism triggers degradation modeling based on the applied cyclic shear amplitude. To measure this amplitude, the activation mechanism incorporates a novel state variable that serves as a proxy for the applied cyclic stress. The effectiveness of the proposed model is demonstrated by comparing it to experimental data from various materials subjected to cyclic shearing under undrained conditions. The study encompasses a broad range of constant strain or stress amplitudes. Compared to the reference model, the proposed model exhibits improved predictive accuracy for the stress‐strain response of clays at small amplitudes of cyclic loading and large number of cycles. Furthermore, it accounts for strength degradation due to cyclic loading.

Cyclic liquefaction in transitional and non-transitional tailings

Tailings have previously been identified as having the types of mixed mineralogies and gradings that can make them susceptible to having non-unique critical states and normally compressed states in laboratory element tests. This paper addresses how this mode of behaviour would affect their resistance to undrained cyclic loading, contrasting two triaxial studies, one on a tailings that has a conventional behaviour and one transitional. To demonstrate the influence of transitional behaviour it was necessary to create samples with as wide a range of initial specific volumes as possible, while trying keep the sample preparation methods the same for loose and dense samples. It was also necessary to examine the cyclic data in non-conventional ways, notably in the volumetric plane to highlight better the effects of initial sample specific volume. It is shown that, as previously determined for monotonic loading, the initial density has much less influence on the cyclic behaviour of a soil with transitional behaviour than it would for a conventional soil, and it is instead the stress history that is very much more important. Samples following their respective normal compression lines exhibit similar behaviour, but overconsolidation significantly enhances resistance and a sample that arrives at a given state by the undrained reduction of p′ due to cycling also has a much higher resistance.

Excess pore water pressure generation in poorly graded sands with varying particle shapes and relative densities

In this study, a series of cyclic triaxial tests were conducted on two poorly graded sands with different particle shapes. The experimental results were integrated with test results reported in the literature to construct a comprehensive database for investigating the effects of particle shape and relative density on excess pore water pressure (EPWP) generation. The sand types in the database were divided into three groups based on the particle shape: subrounded, subangular, and angular. The test results showed that the particle shape and relative density influenced the axial strain development and EPWP generation during undrained cyclic loading. As the relative density increased, the effect of the particle angularity on the shape of the EPWP generation curves decreased. The normalized EPWP generation curves of the subangular particles (C306 sand) exhibited a strong dependence on the relative density. However, the angular and subrounded particles exhibited a weaker influence than the subangular particles on EPWP change for different relative densities. A model was established to predict the EPWP generation with variations in the particle shape and relative density.

Cyclic liquefaction resistance of MICP- and EICP-treated sand in simple shear conditions: a benchmarking with the critical state of untreated sand

In the present study, the undrained cyclic behaviour of biotreated sands using microbial and enzyme-induced carbonate precipitation was investigated for a wide range of initial void ratio after consolidation (e0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$e_{0}$$\\end{document}), initial effective normal stress (σN0′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma^{\\prime }_{{{\ ext{N}}_{0} }}$$\\end{document}) and calcium carbonate content (CC) under direct simple shear (DSS) testing conditions. The critical state soil mechanics framework for untreated sand was first established using a series of drained and undrained (constant volume) tests, which served as a benchmark for evaluating the undrained cyclic liquefaction behaviour of untreated and biotreated sands. The results indicated that the modified initial state parameter (ψm0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\psi_{{{\ ext{m}}_{{0}} }}$$\\end{document}) in DSS condition showed a good correlation with instability states and phase transformation under monotonic shearing. In undrained cyclic DSS loading condition, samples displayed cyclic mobility indicated by an abrupt accumulation of large strain or σN0′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma^{\\prime }_{{N_{0} }}$$\\end{document} transiently reaching zero or a sudden build-up of excess pore water pressure. The linkage between static and cyclic liquefaction was established for untreated and biotreated sand specimens based on the equivalence of characteristic soil states. The number of cycles before liquefaction (NL) for the biotreated sand specimens was mainly controlled by the cyclic stress ratio, e0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$e_{0}$$\\end{document}, σN0′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma^{\\prime }_{{{\ ext{N}}_{{0}} }}$$\\end{document} and CC. For a similar initial state prior to undrained cyclic loading, the biotreated specimens required a larger NL compared to the untreated sand. The cyclic resistance ratio at NL = 15 (CRR15) increased with decreasing ψm0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\psi_{{{\ ext{m}}_{{0}} }}$$\\end{document} for the untreated sand, while the CRR15 for biotreated sand increased with increasing CC and decreasing σN0′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma^{\\prime }_{{N_{0} }}$$\\end{document}.

Pumice sand behavior on undrained cyclic loading

Pumice sand behavior on undrained cyclic loading

Liquefaction mitigation of saturated sand using Air injection method under undrained cyclic loading

Liquefaction mitigation of saturated sand using Air injection method under undrained cyclic loading

Influence of pumice and fines contents on the extent of particle crushing in pumiceous sand-silt mixtures during undrained cyclic triaxial loading

Influence of pumice and fines contents on the extent of particle crushing in pumiceous sand-silt mixtures during undrained cyclic triaxial loading

Mechanism of the variation in axial strain of sand subjected to undrained cyclic triaxial loading explained by DEM with non-spherical particles

The mechanical response of sand is affected by the axial strain accumulated during undrained cyclic triaxial loading tests. However, the large deformation that occurs during the post-liquefaction stage is difficult to measure using testing apparatus. To address this limitation, this research utilizes the numerical method of DEM with non-spherical particles to simulate the undrained cyclic triaxial loading test on clean sand material. The validity of DEM is confirmed through laboratory test. A four-stage scheme for the development of axial strain in the liquefaction process is proposed and verified by analyzing the deformation features of sand specimens with different densities. Meanwhile, the macroscopic behavior is also described in conjunction with microscopic characteristics of sand particles, such as coordination number, force chain network and anisotropy degree of contact normal, which are calculated using DEM. In addition, the central value of variating axial strain at each cycle is analyzed to determine its variation feature via loading cycle. Due to the capability of DEM in describing the microscopic behavior of soil particle aggregation, it is found that the difference in the proposed four-stage scheme between compression and extension sides is the main cause of the central value of axial strain shifting monotonically.

Post-cyclic undrained behavior of marine soft clay subjected to partially drained cyclic loading

Under long-term cyclic loading, marine soft clay in coastal areas is more likely to exhibit partially drained behavior than undrained behavior. The partially drained dynamic behavior of marine soft clay tends to exert a significant effect on the post-cyclic characteristics. Thus, this study conducted two series of monotonic shearing tests to investigate the mechanical behavior of marine soft clay after long-term (50,000 cycles) traffic loading in terms of variable confining pressure (VCP). The post-cyclic stress path, pore water pressure, and shear strength were discussed through comparison of the results with those of the standard monotonic shearing test (without cyclic loading history). Partially drained cyclic loading enhanced the post-cyclic shear strength and increased the brittleness of the specimen. The behavior of the pore water pressure and void ratio of post-cyclic soft clay were similar to those of clay during undrained cyclic loading to the reconsolidation process, that is, the specimen exhibited quasi-overconsolidation performance after partially drained cyclic loading. Subsequently, the relationships between the quasi-overconsolidation ratio (QOCR) and the total cyclic stress and strength ratios were developed, and the strength-dependent parameter of the latter relationship was determined through the standard undrained monotonic shearing test of overconsolidation soil.

Undrained cyclic loading behavior of stiff Eocene-to-Jurassic plastic, high-OCR clays

Assessing foundation response to cyclic loading is vital when designing transport infrastructure, such as road pavements and rail tracks, as well as offshore, port, and tall tower structures. While detailed guidance is available on characterizing many soil types’ cyclic behavior, relatively few studies have been reported on stiff, geologically aged, plastic clays. This paper addresses this gap in knowledge by reporting cyclic loading experiments on three natural stiff UK clays that were deposited and buried between the Jurassic Age and Eocene Epoch before geological unloading to their currently heavily over-consolidated states. High-quality samples taken at relatively shallow depths were reconsolidated to nominally in situ K0 stresses in triaxial and hollow cylinder apparatus before imposing cyclic loading. The completely stable, metastable, or unstable outcomes invoked by different levels of undrained cyclic loading are interpreted within a kinematic yielding framework that is compatible with monotonic control experiments’ outcomes. The cyclic limits marking the onset of significant changes in permanent strain accumulation, pore pressure development, and stress–strain hysteresis demonstrate that the weathered Gault clay offers the lowest cyclic resistance. The experiments show that energy considerations provide a promising way of evaluating undrained pore pressure generation and stiffness degradation. They also provide a basis for developing cyclic constitutive models and analysis procedures for cyclic foundation design in stiff, high-OCR, plastic clay strata.

Low amplitude strain accumulation model for natural soft clays below railways

An improved constitutive model for strain accumulation of natural clays under undrained cyclic loading is presented. The proposed model includes a formulation for the non-linear small-strain stiffness in the overconsolidated regime, along with a modified hardening law for cyclic accumulation to improve the tracking of strain accumulation at small stress amplitudes. To calibrate and validate the proposed model, a series of laboratory tests were conducted to study the cyclic response of natural Swedish clays, the effect of loading amplitude and pre-shearing history. Good agreement between predicted and measured accumulated axial strains and excess pore water pressures was obtained with different loading amplitudes. The findings reveal that the undrained pre-shearing has a substantial impact on the rate of accumulated strain, with pre-sheared samples exhibiting lower resistance values. The proposed and validated model opens up possibilities to study the monotonic and non-monotonic quasi-static response of soft clays below railway embankments over the lifetime of the structure, i.e. including the effects of construction, operation and decommissioning.

Energy-based approach to study liquefaction triggering in homogeneous and stratified soils under consolidated undrained cyclic loading

Pore water pressure development through seismic effect is one of the key reasons for liquefaction failures in the foundations, dams, bridges, slopes and other vulnerable geotechnical engineering structures. The energy dissipation theories have provided a remarkable understanding of the pore water pressure generation inside a soil skeleton. In the present study, a series of consolidated undrained cyclic triaxial tests have been performed to evaluate the normalized dissipated energy (Wn) required for triggering liquefaction in both homogeneous and stratified soil specimens (prepared using silt interlayer) to replicate the site conditions nearby marine or alluvial deposits. The generated hysteresis loops using cyclic loading facilitate the calculation of dissipated energy. Also, the test results indicated a significant variation in the dissipated energy of homogeneous specimens at different magnitudes of cyclic stress ratios (CSR) and relative densities (Dr). With an increase in the cyclic stress ratio from 0.14 to 0.20, the trend of dissipated energy was observed to be different when relative densitie of sand varied from 30% to 65%. In the stratified specimens, thickness (t) and location of the silt layer (d) in the given soil specimen were the major influencing factors for estimating the liquefaction potential in loose conditions. Additionally, the highest value of Wn,max was obtained as 0.51 for the stratified specimen with topt = 28 mm at a cyclic stress ratio of 0.14. Based on the trendline variations, empirical models have been developed to estimate the normalized dissipated energy (Wn) for both homogeneous and stratified conditions. The developed models for homogeneous specimens are functions of CSR and Dr, whereas, in the case of stratified specimens, t, d and σd/σ'c (σd = deviator stress, σ'c = effective confining stress) have been utilized to predict the Wn with an satisfactory R2 value above 0.90. From the analysis of liquefaction resistance curves, the energy-based approach used in this study has been observed to provide more realistic results than the pore pressure ratio and strain-based failure criteria.

Excess pore water pressure generation in fine granular materials under undrained cyclic triaxial loading

Understanding the mechanism of excess pore water pressure generation in subgrades is essential for not only designing but also further maintenance purposes. The primary goal of this research was to investigate excess pore water pressure generation in fine granular materials under cyclic loading. A series of undrained cyclic triaxial tests were performed to study the excess pore water pressure generation in two selected fine granular materials: (1) railway sand and (2) tailings. The excess pore water pressure response of these materials was evaluated in terms of density conditions, number of cycles, and applied cyclic stress ratios (CSR). As a result, excess pore water pressure accumulated over time due to cyclic loading. However, its accumulation was significantly dependent on the governing factors, i.e., densities, CSR values, and material types. The excess pore water pressure exhibited a slight increase at low CSR values, but a sharp increase was observed at higher CSR values, which ultimately led to a failure state after a certain number of cycles. In addition, under the same loading conditions, the samples that had higher relative compaction showed better resistance to cyclic loads as compared to those with lower relative compaction. Finally, a relationship between excess pore water pressure and cyclic axial strain of the fine granular materials was discovered.

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.

Elastoplastic modelling for long-term cyclic stability of soft clays with consideration of structure damage

The constitutive model of structured clays under cyclic loads is helpful to analyze the long-term stability of foundations, such as subgrade under traffic loads and foundation of an offshore gravity platform under wave loads. Responses of structured clays under cyclic loading depend on the applied cyclic stress and can be phenomenally divided into the cyclic stability, cyclic critical state and cyclic degradation. Among these three types, the cyclic stability is directly related to the long-term stability of structured soil foundations. To analyze the cyclic stability of structured soft clay, the constitutive responses under cyclic loads of different amplitudes are firstly discussed according to the shakedown theorem. Secondly, based on the modified Cam-clay model and the plastic hardening rule proposed by Li and Meissner, an elastoplastic two-surface model is herein developed to simulate the long-term responses of saturated structured soft clays under undrained cyclic loading. In the model, a special parameter for describing progressive damage of soil structure is introduced into the interpolation function of plastic modulus, which is related to the accumulated plastic deviatoric strain. The comparisons of theoretical computations with experiment data from some researchers are finally presented to demonstrate the simulation capability of this model. It is shown that the accumulated strain and the pore water pressure of soft clays under long-term undrained cyclic loading have been well simulated. Moreover, the impact of the cyclic stress ratio (CSR) on the cyclic stability is evaluated by using the empirical formula between the model parameters and the CSR. In addition, the method for calibrating the model parameters is also proved to be reasonable and feasible, thus enabling the model parameters to be determined rigorously.