Constitutive models of sands play an essential role in analysing the foundation responses to cyclic loads, such as seismic, traffic and wave loads. In general, sands exhibit distinctly different mechanical behaviours under monotonic, regular and irregular cyclic loads. To describe these complex mechanical behaviours of sands, it is necessary to establish appropriate constitutive models. This study first analyses the features of hysteretic stressstrain relation of sands in some detail. It is found that there exists a largest hysteretic loop when sands are sufficiently sheared in two opposite directions, and the shear stiffness at a stress-reversal point primarily depends on the degree of stiffness degradation in the last loading or unloading process. Secondly, a stress-reversal method is proposed to effectively reproduce these features. This method provides a new formulation of the hysteretic stress-strain curves, and employs a newly defined scalar quantity, called the small strain stiffness factor, to determine the shear stiffness at an arbitrary stress-reversal state. Thirdly, within the frameworks of elastoplastic theory and the critical state soil mechanics, an elastoplastic stress-reversal surface model is developed for sands. For a monotonic loading process, a double-parameter hardening rule is proposed to account for the coupled compression-shear hardening mechanism. For a cyclic loading process, a new kinematic hardening rule of the loading surface is elaborately designed in stress space, which can be conveniently incorporated with the stressreversal method. Finally, the stress-reversal surface model is used to simulate some laboratory triaxial tests on two sands, including monotonic loading tests along conventional and special stress paths, as well as drained cyclic tests with regular and irregular shearing amplitudes. A more systematic comparison between the model simulations and relevant test data validates the rationality and capability of the model, demonstrating its distinctive performance under irregular cyclic loading condition.

The liquefaction and weakening of saturated sands under cyclic stress loading is a major concern in earthquake engineering. This study proposes a model based on initial cyclic shear strain (gamma c,i) to predict the excess pore pressure generation in undrained saturated sands. Here, gamma c,i is defined as the average cyclic shear strain prior to the significant accumulation of excess pore pressure. To calibrate and validate the model, a series of undrained stress-controlled cyclic triaxial (CTX) tests were conducted on Fujian sand with 10 % Kaolin clay (FS-10) and Silica sand no.7 with 5 % Kaolin clay (SS7-5). The FS-10 and SS7-5 specimens displayed typical flow liquefaction and cyclic mobility as they approached initial liquefaction. A critical excess pore pressure ratio (ru,c) is introduced to characterize the effects of liquefaction failure modes on excess pore pressure generation. The model also incorporates reduction factors related to small-strain secant shear modulus and reference shear strain to account for variations in calculating gamma c,i. Ultimately, the initial cyclic shear strain-based model exhibited a strong correlation with experimental data under different confining pressures and loading cycles. In addition, it provides a critical initial cyclic shear strain for assessing soil liquefaction in engineering practices, particularly for improved ground with complex stress states.

Modelling the cyclic response of granular materials is key in the design of several geostructures. Over the years, numerous constitutive models have been proposed to predict the cyclic behaviour of granular materials. However, pertaining to the hypoplastic constitutive models, one of the significant limitations is their inability to accurately predict the geomechanical response during the unloading and reloading phases. This study introduces an extension of the MS-IS hypoplastic model designed to enhance the predictions during non-monotonic loading conditions. Addressing the limitations observed in the hypoplastic models during the unloading and reloading phases, the proposed model incorporates an additional stiffness feature. This new stiffness function is integrated into the foundational framework to enhance the model's overall stiffness response. For the unloading phase, the introduction of a stiffness degradation factor aims to modify the volumetric response and account for the realistic stiffness degradation. Additionally, for the reloading phase, stiffness is now a function of the mean effective stress. The novel model's performance is validated against experimental data, encompassing diverse loading and boundary conditions.

In this research, the reactions of geogrid reinforcement on the dynamic performance of medium-dense coral sand with various cyclic stress ratios were investigated using stress-controlled undrained dynamic triaxial tests. The results indicate that the insertion of geogrid decreases the dynamic deformations, and pore pressure build-up rate, and impeded the liquefaction of coral sand. The liquefaction resistance of coral sand increases with the increase in the number of reinforcement layers. The liquefaction resistance of coral sand reinforced with three-layer and two-layer geogrid increases by 333% and 6% compared to unreinforced ones. The geogrid reinforcement layers can effectively resist the complete stiffness degradation of coral sand under cyclic loading. The coral sand stiffness decays at an accelerated rate as the cyclic stress ratio increases, whereas increasing the number of reinforcement layers reduces the coral sand stiffness degradation rate, especially for three-layer geogrid reinforced coral sand at low cyclic stress ratios. Generally, the geogrid as a reinforcement material to coral sand is considered a better alternative to enhance the engineering properties of coral sand and offers significant prospects in coastal and marine engineering construction with coral sand.

This paper addresses the cyclic behaviour and stiffness degradation of subgrade soils subjected to stress-controlled cyclic loading, with particular emphasis on soils that are prone to mud pumping or subgrade instability. With continuous passage of trains over weak, saturated, low-plastic subgrade foundations, the finer fraction of the soils tends to fluidise (i.e., behave like a fluid) and migrate upwards, thereby, fouling the ballast and hindering the long-term performance of the rail track infrastructure. This leads to significant costs associated with annual track maintenance. Through a series of undrained cyclic triaxial testing varying the cyclic stress ratio (CSR, representing the axle loads) and loading frequency (simulating train speeds), the authors noted a significant upward migration of finer fraction coupled with internal moisture redistribution within the failed specimens. Further analysis revealed the instability of specimens was caused by early softening behaviour, and it is accompanied by a sharp reduction in the specimen stiffness. To tackle this, the stiffness was evaluated in terms of axial dynamic modulus and strain energy per cycle was evaluated to better understand the fluidisation behaviour. A novel quasi-linear relationship between threshold residual strain and number of cycles is proposed to serve as a practical guide.

Using an energy-based approach and a wide range of marine silt content (SC), along with simulating different field conditions, a systematic experimental study was conducted through a series of strain-controlled cyclic triaxial tests on the undrained cyclic response of saturated Konarak carbonate sand-silt mixtures that originated from the northern coasts of the Oman Sea. The results revealed that the trend of variation in capacity energy (cumulative dissipated energy required to initiate liquefaction, Wliq) of sand-silt mixtures versus variation in SC was highly dependent on the relative density (Dr). Using the concepts of equivalent intergranular void ratio (e*) and equivalent interfine void ratio (ef*), a new relationship was proposed to estimate the Wliq of the Konarak sand-silt mixtures under different field conditions. To take into account the effects of SC, the energy-based pore water pressure model model proposed by Jafarian et al. (2012) was revised with modified calibration parameters. Similarly, as there exists a distinct relationship between energy dissipation and the excess pore water pressure generation during cyclic loading, a significant correlation is also observed between energy dissipation and stiffness degradation for carbonate soil.

Monopile foundations of offshore wind turbines embedded in soft clay are subjected to the long-term cyclic lateral loads induced by winds, currents, and waves, the vibration of monopile leads to the accumulation of pore pressure and cyclic strains in the soil in its vicinity, which poses a threat to the safety operation of monopile. The researchers mainly focused on the hysteretic stress-strain relationship of soft clay and kinds of stiffness degradation models have been adopted, which may consume considerable computing resources and is not applicable for the long-term bearing performance analysis of monopile. In this study, a modified cyclic stiffness degradation model considering the effect of plastic strain and pore pressure change has been proposed and validated by comparing with the triaxial test results. Subsequently, the effects of cyclic load ratio, pile aspect ratio, number of load cycles, and length to embedded depth ratio on the accumulated rotation angle and pore pressure are presented. The results indicate the number of load cycles can significantly affect the accumulated rotation angle of monopile, whereas the accumulated pore pressure distribution along the pile merely changes with pile diameter, embedded length, and the number of load cycles, the stiffness of monopile can be significantly weakened by decreasing the embedded depth ratio L/H of monopile. The stiffness degradation of soil is more significant in the passive earth pressure zone, in which soil liquefaction is likely to occur. Furthermore, the suitability of the accumulated rotation angle and accumulated pore pressure design criteria for determining the required cyclic load ratio are discussed.

Marine clay may experience stiffness degradation and catastrophic failure when subjected to complex ocean dynamic loadings. This can result in instability, destruction, or capsizing of offshore structures. In this study, marine clay was regarded as a non-Newtonian fluid with shear-thinning behaviour, and the mechanism of progressive stiffness degradation during cyclic loading was discussed from the perspective of fluid dynamics. A series of cyclic direct simple shear tests were conducted on undisturbed marine clay obtained from three offshore sites. Further, the stiffness degradation and flow characteristics under different plasticity index (I-P) and cyclic stress ratio (CSR) conditions were investigated and quantified using the stiffness degradation index (delta) and average flow coefficient (kappa), respectively. The results revealed that the decrease in delta with the increasing number of cycles (N) in a semi-log scale can be categorised into three modes: (1) linear (nonfailure), (2) fast-linear-fast (failure), and (3) linear-stable (failure). Consequently, a two-parameter model was proposed to predict the delta of failure marine clay from different sea areas with varying I-P and CSR values. Moreover, with the increase in N, kappa of the nonfailure marine clay increased gradually in a very limited range, thus exhibiting illiquidity characteristics; by contrast, kappa of the failure marine clay exhibited a slow linear-exponential-rapid linear growth pattern, thus indicating a change in liquidity from weak to strong. Finally, a unified model linking the stiffness degradation and flow characteristics of marine clay under different types and conditions was proposed, where kappa at the cyclic failure state (the failure criterion is a double-amplitude shear strain of 15%) was denoted as kappa(f). Evidently, all data points of kappa/kappa(f) similar to delta were distributed in a narrow range, and a virtually negative exponential relationship was observed between kappa/kappa(f) and delta.

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.

Skirt-pile foundations have gained widespread attention in the field of offshore engineering due to their ease of installation and high bearing capacity. In this study, the ultimate bearing capacity, pile bending moment distribution and development, cumulative deformation characteristics, and cyclic stiffness development of skirt-pile foundations were investigated using physical model tests. The experimental results indicate that the ultimate bearing capacity and deformation resistance of the foundation can effectively be improved by increasing the skirt diameter. The cumulative deformation of the skirt-piles exhibited rapid development during the initial stages of cyclic loading, eventually stabilizing. Under long-term cyclic loading, the existence of the skirt can share the bending moment, which then affects the internal force distribution of the pile foundation along the axis. The pile foundation's cyclic stiffness reduces as the loading cycles increase and increases as the skirt diameter and length grow. Meanwhile, the horizontal cyclic stiffness decreases as the number of cycles increases, stabilizing after 3000 cycles. This study can not only deepen the understanding of the deformation laws of skirt-pile foundations in clay soil but also offers some references for the design of offshore pile foundations.