Long-term Cyclic Loading Research Articles

Long-Term Drained and Post-liquefaction Cyclic Behaviour of Offshore Wind Turbine in Silty Sand Using Element Tests

Offshore wind turbine (OWT) structure foundations and soil are subjected to long-term cyclic loading from wind and waves. Loads due to earthquake also act on the OWT system in seismically active areas. The long-term dynamic behaviour of the OWT is challenging due to the complex nature of dynamic loads. The soil stiffness changes due to the application of cyclic loading, which leads to a change in the natural frequency and response of the OWT system. Therefore, the assessment of long-term dynamic behaviour soil surrounding the foundation of the OWT structure is essential due to the operational condition and seismic event. In this study, element tests are conducted utilizing cyclic triaxial test apparatus to examine the long-term drained and post-liquefaction long-term cyclic behaviour of silty sand. Secant shear modulus and damping ratio are estimated under drained condition due to 10,000 load cycles. Silty sand behaviour at liquefied phase and post-liquefaction long-term cyclic behaviour phases are investigated at different effective confining pressure, relative density, and shear strain rate. Based on the element tests, a numerical model is proposed predicting the long-term fundamental frequency of OWT to avoid resonance.

Present problems of vibration isolation in heavy mining machines at long-term cyclic loads

Abstract. An integrated approach was used, including the construction of a mathematical model and the results of lengthy industrial tests of heavy mining machines with rubber elastic bonds. The issues of vibration isolation of heavy machines operating in extreme conditions, i.e. with prolonged cyclic loads and the influence of an external aggressive environment inherent in mining and processing enterprises. As an example, we con-sider vortex mixers with a vibration isolation system containing rubber elements. During long-term operation, the mass of the mixer does not remain constant; its increase is associated with the sticking of the initial product on the moving parts of the ma-chine. The location of such machines in the sinter factory at + 10.4 m, as well as the change in time of rotational symmetry of the drum rotation imposes certain requirements on the vibration isolation system: the system must be "soft" and stable in time, i.e. during 9-10 years of operation, its stiffness and dissipative parameters should not go beyond the permissible values. In order to reduce the aging effect, type 2959 rubber based on natural caoutchouc with a reinforced protective group was used, while the instability of the main mechanical parameters was taken into account in the developed theory of vibration isolation of machines. On the basis of the developed simulation model and the Boltzmann-Volterra integral relations with kernels of relaxation and aftereffect, an equation was worked out, which made it possible to take into account the rubber viscoelastic properties in full volume; in this equation, stiffness operator of elastic suspension in the machine is written by using fractional exponential function of the Yu. Rabotnov's type; on the basis of the mathematical model, the basic parameters of the machine under the study were calculated; in particular, for the vortex mixer, the time dependences of amplitude of the mixer housing vibrations and coefficient of vibration isolation efficiency were calculated with taking into account aging of elastic link material in the ma-chines; the calculation results were compared with the results of industrial tests of the vortex mixer operation lasting for 16 years. The theory and method for calculating vibration isolation systems with rubber elastic links for heavy mining machines were developed with taking into account material structure changes due to the effects of aging. The paper considers an example of calculating the mixer vibration isolation system taking into account rubber aging; the magnitude of the change in time of the main mechanical parameters was obtained experimentally over 16 years. This made it possible to determine temporary changes in the amplitude of oscillations of the mixer body and the coefficient of efficiency of the vibration isolation system. It was shown that the mixer vibration isolation system remained effective for 9-10 years, after which the mechanical characteristics of the rubber went beyond the permissible values and the system lost its functional pur-pose, and the amplitude of the mixer body exceeded the existing sanitary standards.

The behavior of monopile embedded in sand under scour and cyclic loading conditions

The large-diameter monopile, as one of the most used foundations of offshore wind turbines, is subjected to severe sea conditions, such as the cyclic lateral loads induced by wind and waves, as well as the scour induced by the flushing currents. The combined cyclic lateral loads and scour introduces additional complexity and is encountered in offshore wind turbines as well as other offshore structures. In this study, the experimental tests and numerical simulation methods are adopted to investigate the behavior of monopile subjected to the combined cyclic lateral loads and scour. Firstly, the static and one-way cyclic lateral load tests are conducted to investigate the influence of scour conditions and the characteristics of cyclic lateral loads on the lateral displacement and bending moment of monopile. Subsequently, the three-dimensional numerical model is established by employing the stiffness degradation material model, reasonable comparisons between the numerical results and the experimental results suggest that the numerical model can be used as a reliable complement of the model tests. Finally, a series of parametric studies are carried out to investigate the effect of cycle numbers, scour conditions and cyclic load ratio on the accumulated deformation and lateral bearing capacity of monopile. It is found that the accumulated deformations are dependent on the cyclic load characteristics and scour depth, the one-way cyclic load and scour have opposite effects to the lateral capacity of monopile. A framework to predict the accumulated deformation of monopile subjected to the combined scour and long-term cyclic lateral load is developed, which can be served as a basis for the practical design of monopile.

Stiffness of granular soils under long-term multiaxial cyclic loading

Geotechnical infrastructures may be subjected over their lifetime to long-term loading cycles of varying amplitude, frequencies and direction as a result of the combination of environmental and operational processes. Soil elements surrounding the foundations of these geotechnical systems are in turn subjected to complex six-dimensional stress paths, invariably involving rotation of principal stress axes. Changes of the soil's mechanical properties can lead to changes of the overall structure dynamics, as well as to an accumulation of irreversible deformations. However, the evolution of the soil's response and stiffness under complex long-term cyclic loading scenarios is neither well known nor adequately understood. In contrast to the conditions imposed by standard laboratory tests, this research used a hollow-cylinder torsional apparatus (HCTA) to explore the evolution of the small-strain stiffness of a granular soil under long-term multiaxial drained stress cycles (up to about 6 × 105). Granular soil samples were subjected to stages of regular low-amplitude stress cycles at different anisotropic stress levels interspersed by periodic large-amplitude cyclic loops. A high-resolution local strain measurement system was employed to determine the vertical Young's modulus and shear modulus, both attained in a HCTA at different stages of the testing. It was found that low-amplitude multiaxial stress cycles, involving continuous rotation of principal stress axes, caused a degradation up to about 20% of these elastic soil properties. Within 104to 2 × 104cycles, the degraded stiffnesses reached a stable value, which was maintained up to at least 8 × 104cycles. The stiffness degradation was more pronounced for the shear modulus than the vertical Young's modulus of the soil.

A p–y Model for Large Diameter Monopiles in Sands Subjected to Lateral Loading under Static and Long-Term Cyclic Conditions

The design of large diameter monopiles subjected to cyclic lateral loading is of interest in many applications, such as, for example, in the offshore wind energy industry. Engineering design methods to estimate the deflection of these structures are required for this purpose. In the present work, a p–y model for large diameter monopiles subjected to lateral loading is proposed. The model considers a pile in cohesionless soil subjected to static and long-term cyclic loading. Its formulation features the consideration of nonlinear relations for the ultimate soil resistance pu and the initial subgrade modulus Epy0 among the soil depth and a cyclic factor that accounts for the effect of the soil density and loading amplitude. A relation is also proposed to account for a base shear force at the tip of the monopile. The proposed relations were employed and solved under the beam on nonlinear Winkler foundation (BNWF) approach and were adjusted to simulate a number of three-dimensional (3D) finite-element (FE) models accurately, accounting for variations on pile geometry, soil properties, and loading conditions. In the end, the performance of the proposed relations was evaluated through the comparison with a field test and a centrifuge test.

Evaluation of Deformation and Permeability Behavior of Amygdaloidal Basalt under a Triaxial Cyclic Loading Creep Test

Amygdaloidal basalt is a typical rock mass in the dam foundation of the Baihetan hydropower project in southwest China. With rising and drawdown of the reservoir water level, the permeability and creep deformation characteristics of the amygdaloidal basalt are much complicated in the long-term cyclic loading processes. A cyclic loading-unloading creep test on the amygdaloidal basalt was performed to evaluate its deformation and permeability behavior. The results showed that Poisson’s ratio and elastic modulus of the rock specimen varied significantly under different loading processes with a relatively large irreversible deformation. The permeability and strain rates of rock changed in two phases under lower deviatoric stresses, while there are three typical stages of strain growth with the final stress level of 121.8 MPa. For axial stress of 128 MPa, the creep deformation and creep rate in the axial direction are smaller than these in the lateral direction. Before the sample failure, the lateral deformation accelerates earlier than the axial deformation. The results also suggested that the permeability of the rock specimens decreases considerably during each loading process and then tends to be constant with time. No apparent change in steady permeability is observed with variation of stress. For 128 MPa axial stress, the permeability first decreases, then tends to be in a stable value, and at last increases during the sample failure.

Dynamic Response of Heavy-Haul Railway Tunnels in Fully Weathered Coastal Red Sandstone Strata with Base Rock Reinforcement: A Numerical Study

Xu, H.; Chen, C.; Shao, Z.; Wang, Z.; Cai, L.; Li, Z., and Xu, C., 2021. Dynamic response of heavy-haul railway tunnels in fully weathered coastal red sandstone strata with base rock reinforcement: A numerical study. Journal of Coastal Research, 37(1), 191–202. Coconut Creek (Florida), ISSN 0749-0208.Coastal fully weathered red sandstone exhibits poor cementation, and tunnels can easily develop large deformations undercrossing such rock masses under long-term cyclic loading. This article studies dynamic response of the base rock and tunnel lining structures under the dynamic load of heavy-haul train when different base rock reinforcing methods (curtain grouting reinforcement and cement-soil compaction pile reinforcement) are adopted. A tunnel undercrossing fully weathered red sandstone strata is taken as the research object, from which the rock mechanical strength parameters are obtained for a numerical model. The dynamic response of the base rock significantly decreases with the increased depth, and the inverted arch and arch foot are the most unfavorable stress locations, to which more attention should be paid. Base rock reinforcements enhance the integrity of rock mass, and the acceleration and peak stress of the rock base and lining structure significantly reduce when reinforcement is exerted. The effect of curtain grouting proved to be better, which is indicated by the reduction of acceleration and displacement of tunnel lining as well as the low value of peak acceleration and stress of the base rock.

Probabilistic Life Models for Steel Structures Subject to Creep- Fatigue Damage

When metal structures are subjected to long-term cyclic loading at high temperature, simultaneous creep and fatigue damage may occur. In this paper probabilistic life models, described by hold times in tension and total strain range at elevated temperature have been derived based on the creeprupture behavior of 316FR austenitic stainless steel, which is one of the candidate structural materials for fast reactors and future Generation IV nuclear power plants operating at high temperatures. The parameters of the proposed creepfatigue model were estimated using a standard Bayesian regression approach. This approach has been performed using the WinBUGS software tool, which is an open source Bayesian analysis software tool that uses the Markov Chain Monte Carlo sampling method. The results have shown a reasonable fit between the experimental data and the proposed probabilistic creep-fatigue life assessment models. The models are useful for predicting expended life of the critical structures in advanced high temperature reactors when performing structural health management.

The changing strength of carbonate silt: parallel penetrometer and foundation tests with cyclic loading and reconsolidation periods

This paper describes a centrifuge study using novel penetrometer tests (T-bar and piezoball) and model foundation tests to explore through-life changes in the strength of a reconstituted natural carbonate silt. The test procedures include episodic cyclic loading, which involves intervals of pore pressure dissipation between cyclic packets. These loads and the associated remoulding and reconsolidation cause significant changes in the soil strength and foundation capacity. Soil strength changes from penetrometer tests differed by a factor of 15 from the fully remoulded strength to a limiting upper value after long-term cyclic loading and reconsolidation. For the model foundation tests, the foundation capacity of a surface foundation and a deep-embedded plate were studied. The soil strength interpreted from the measured foundation capacity varied by a factor of up to three due to episodes of loading and consolidation, with an associated order of magnitude increase in the coefficient of consolidation. The results show a remarkable rise in soil strength over the loading events and provide a potential link between changes in soil strength observed in penetrometer tests and the capacity of foundations, allowing the effects of cyclic loading and consolidation to be predicted.

Centrifuge modelling of pipe-soil interaction in clay with crust layer

Seabed in regions, such as the Gulf of Guinea and North West Shelf of Australia, may exhibit a crust layer where the undrained shear strength can be an order of magnitude higher than that of the immediately underlying sediment. This can complicate design of steel catenary risers, where fatigue depends on the cyclic vertical stiffness of the pipe-soil interaction. Potential punch-through of the riser into the underlying soft soil may invalidate design assumptions based on the pipe-soil stiffness within the crust layer. The long-term evolution of pipe-soil stiffness within the crust layer, which exhibits similar properties to an over-consolidated soil, is also poorly understood. This paper describes centrifuge model tests undertaken in a clay sample with a crust layer, simulating the punch-through process of a pipe under load control and investigating the pipe-soil stiffness during long-term cyclic loading tests under displacement control. Results confirm that the potential for punching-through the crust layer depends strongly on the relative ratio of pipe diameter to crust layer thickness. The long-term evolution of pipe-soil stiffness showed a steady increase after an initial remoulding stage in contractile soils (normally consolidated and lightly over-consolidated), but a steady reduction in the heavily over-consolidated, more dilatant, crust. The magnitude of pipe-soil stiffness changes (during both remoulding and reconsolidation) is governed by the over-consolidation ratio of the soil and the amplitude of the cyclic displacements. This study provides insights on the relevant cyclic stiffness to consider when assessing SCR fatigue life in over-consolidated soils and soils exhibiting a superficial crust layer.

Strain evolution of saturated clays under cyclic loadings in three-dimensional stress condition

The strain evolution of saturated clays under cyclic loadings has been studied by means of various laboratory testing methods, aiming for the accurate simulation of engineering conditions such as the consolidation states of clays, cyclic stress paths of external loadings and boundary conditions in situ. Considering that the subgrade clays are usually overconsolidated rather than normally consolidated, the drainage condition is normally partially drained instead of undrained under long-term cyclic loadings, and the cyclic stress paths are in three-dimensional stress state, this study explores the three-dimensional strain characteristics of both normally and overconsolidated clays in partially drained condition based on a true triaxial apparatus. Emphasis are put on the effects of cyclic stress ratio (CSR), overconsolidation ratio (OCR) and coefficient of cyclic intermediate principal stress (bcyc) on the accumulation of permanent strain components including major, intermediate, minor principal strains, and volumetric strain. Test results show that the relative magnitudes of strain components are strongly influenced by both bcyc and OCR, while the accumulated directions of strain paths tend to be identical for various bcyc values. The increase of bcyc leads to a linear growth of permanent volumetric strain for both normally and overconsolidated clays, while the permanent major principal strain shows a firstly increasing and then decreasing trend versus the increase of bcyc. For the normally consolidated and overconsolidated clays, the largest permanent major principal strains are achieved at around bcyc = 0.4 and 0.2, respectively. The accumulation of permanent intermediate principal strain is always promoted by the increase of bcyc. In addition, the development of permanent major principal and volumetric strains with cycle number is analyzed in the double logarithmic plane, which are found to be combined by two linear parts.

Numerical simulation on undrained cylic triaxial test of soft marine clay considering end restrictions of soil specimen

Soft marine clay is subjected to long-term cyclic loads such as waves or seismic loadings in marine environment. Numerous cyclic traixial tests have been conducted to investigate the dynamic behaviors of soft marine clay. However, due to the limitation of laboratory triaxial test, such as end restraints caused by friction between the loading caps, pedestal and the specimen, a perfect cyclic triaxial test is impossible in reality. In this study, taking two extreme boundary conditions into consideration, based on the “Cyclic Mobility (CM) Model”, an elastoplastic constitutive model and a soil-water coupled finite element-finite difference (FE-FD) code named as DBLEAVES, a series of numerical simulations on cyclic triaxial tests of soft marine clay are conducted. The influence of those factors such as, cyclic stress ratio (CSR), loading frequency and confining pressure are also discussed in detail. The results show that the CM Model can describe the mechanical behavior of clay under cyclic loading accurately. End restrictions have high influence on the cyclic response of clay by creating strain localization areas and extreme pore water pressure zone. This paper makes clear the significant influence of boundary conditions on the cyclic triaxial test results.

Thermal effects on the dynamic properties of marine sediment under long-term low cyclic stress

Thermal problems may be encountered in offshore engineering applications, such as pipeline engineering activities and submarine nuclear waste storage. However, few studies have focused on the behaviours of marine sediment involved temperatures, especially under long-term low cyclic loads. In this study, a series of undrained temperature-controlled triaxial tests were carried out to study the thermal effects on the dynamic properties of marine sediment from the South China Sea (SCS) under long-term low cyclic loading. The experimental tests were performed at different temperatures and cyclic stress ratios (CSRs). The dynamic deformation, pore pressure and degradation of the strength of the samples were measured and analyzed. Two modified models for predicting the pore pressure and degradation of marine sediment are presented based on the experimental data. The results indicate that the temperature-induced pore pressure increases with increasing temperature as a power function without draining and loading. The axial strain, loading-induced pore pressure and degradation index decrease with increasing temperature. The CSRs have a substantial influence on the axial strain and loading -induced pore pressure.

Long-Term Cyclic Loading Impact on the Creep Deformation Mechanism in Cohesive Materials

Long-term cyclic loading is observed in a wide range of human activities, as well as in nature, such as in the case of ocean waves. Cyclic loading can lead to ratcheting which is defined as progressive accumulation of plastic deformation in a material. Long-term cyclic loading causes a time effect (creep), which is a secondary compression effect. In this article, we conducted 15 triaxial tests on four types of cohesive materials in undrained conditions to evaluate the damage and failure mechanism. To characterize the strain and pore pressure development, we modified the Yanbu resistance concept. On the basis of the static creep tests, we concluded that the stress paths for undrained creep behavior have to take into account the pore pressure developed during long-term cyclic loading. Pore pressure build-up and plastic strain accumulation during long-term cyclic loading are dependent on the number of loading cycles. Finally, we proposed the failure criterion, which was based on the Modified Cam-Clay constitutive model.

The Effect of TiAl6V4 Particles on Tissue in Rats

Electron beam melting (EBM) is three-dimensional (3D) printing technologies that can manufacture multi-functional porous scaffolds with exact structures for the application of surgical operations. In the past decade, thousands of acetabular implants manufactured by EBM or SLM have been designed into acetabular cups with certain porosity for surgical operations. Particles of 3D printed porous Ti6Al4V implants will adhere between sintered interface and non-sintered interface of porous sample during 3D printing. However, the internal excess particles of complex structural parts are difficult to remove. During long-term cyclic loading, stress strain can cause residual Ti6Al4V particles to fall off. These detached Ti6Al4V particles are scattered around the implant and are contact with osteoblasts. In our study, we detected the influence of the differentiation concentration of Ti6Al4V particles on bone of rats. The influence of the differentiation concentration of Ti6Al4V particles on bone was evaluated by distal femoral defects in rats. Micro-CT and biochemical analysis were used to evaluate all of the rats after 12 weeks. Outcomes demonstrated that low concentration Ti6Al4V particles may improve the osteogenesis of SD rat through micro-CT. Serum markers implied that the differentiation concentration of Ti6Al4V particles didn’t influence on hepatic and renal functions. In conclusion, Low-dose residual particle does not induce a decrease in bone mineral density (BMD) of rats.

An Investigation into the Effect of Long-Term Cyclic Loading on the Natural Frequency of Offshore Wind Turbines

An Investigation into the Effect of Long-Term Cyclic Loading on the Natural Frequency of Offshore Wind Turbines

Spatial deformations of osteosynthesis systems. Message 2. Experimental results

Test procedure and a device for the spatial loading of full-scale bone specimens with fractures and fixation means and simultaneous measurement of mutual displacements arising in the fracture region due to the load are presented. The device allows us to apply longitudinal, transverse bending and rotational one-time and long-term cyclic loads to the specimen, simulating the action of loads when walking. The measurement of displacements was carried out by digitally photographing the fracture areas followed by computer image processing.The test results of the “tibia with simulated fracture - fixation plate” systems under spatial loading by three external forces are presented, which cause compression, bending and torsion. As a result of the tests, the values of mutual displacements and the angles of mutual rotation of parts of the fracture were measured.Comparison of test and calculation results using the relationships described in Message 1 shows the suitability of the method, which allows us to quickly and reliably assess the level of displacements in bone fractures under the spatial loading.

Effects of different concentrations of TiAl6V4 particles on MC3T3-E1 cells and bone in rats

Three-dimensional (3D)-printed porous Ti6Al4V implants have good mechanical properties and excellent biocompatibility. As such, these implants are widely used in orthopedics. Particles adhere between the sintered and nonsintered interfaces of the porous samples during 3D printing. These excess particles can be cleaned by blowing the particles and via ultrasound, but the excess internal particles of complex structural parts are difficult to remove. During long-term cyclic loading, stress and strain can cause residual Ti6Al4V particles in the pores of the implant to shed. These detached Ti6Al4V particles are in extensive contact with osteoblasts and scattered around the implant. In this study, we examined the effects of different concentrations of Ti6Al4V particles on osteoblasts and bones. MC3T3-E1 cells were used to evaluate the effects of different concentrations of Ti6Al4V particles on cells after 72 ​h on the basis of the expression levels of genes, involving osteopontin, alkaline phosphatase, bone morphogenetic protein-2 and runt-related transcription factor-2. Microtubule-associated protein 1 light chain 3 was used to detect the autophagy of MC3T3-E1 with different concentrations of Ti6Al4V particles. The distal femoral defects of rats were examined to examine bone growth with different concentrations of Ti6Al4V particles. All rats were accepted by micro-CT and biochemical analyses after 12 weeks. The results indicated that 10 and 100 ​μg/ml of Ti6Al4V particles may improve osteogenic differentiation. Micro-CT revealed that low concentrations of Ti6Al4V particles may improve the osteogenesis of the rats. However, the (cortical and trabecular) BMD of middle and high dose groups was no significant change compared with control group. In conclusion, low-dose residual particles do not inhibit osteoblast differentiation and do not decrease the bone mineral density of rats.

Calculation of monopile foundation in sand to long-term lateral cyclic load

Monopiles are widely used to support the upper structures of wind turbines in offshore engineering. Due to harsh environmental conditions, they are subjected to long-term lateral cyclic loading from waves and winds during the design life. A robust beam on the Winkler foundation model is presented to analyze the responses of monopile foundation under long-term lateral cyclic load, incorporating cyclic stiffness evolution of sand based on the results of drained cyclic triaxial tests. The reasonability of the model is proved by comparison with a published centrifuge model test. Furthermore, a parametric analysis is performed to study the effects of pile diameter, pile eccentricity, embedment depth and cyclic load amplitude to the accumulation of deformation at the pile head during the long-term lateral cyclic load, based on which an empirical expression for estimating the accumulated displacements of a long-term lateral loaded monopile under cyclic loads is given.

Assessment of Practical Methods to Predict Accumulated Rotations of Monopile-Supported Offshore Wind Turbines in Cohesionless Ground Profiles

Monopiles supporting offshore wind turbines can experience permanent non-recoverable rotations (or displacements) during their lifetime due to the cyclic nature of hydrodynamic and aerodynamic loading exerted on them. Recent studies in the literature have demonstrated that conventional cyclic p–y curves recommended in different codes of practice (API-RP-2GEO and DNVGL-RP-C212) may not capture the effects of long-term cyclic loads as they are independent of the loading profile and the number of applied cycles. Several published methodologies based on laboratory scaled model tests (on sands) exist to determine the effect of cyclic lateral loads on the long-term behaviour of piles. The tests vary in terms of the pile behaviour (rigid or flexible pile), number of applied loading cycles, and the load profile (one-way or two-way loading). The best-fit curves provided by these tests offer practical and cost-efficient methods to quantify the accumulated rotations when compared to Finite Element Method. It is therefore desirable that such methods are further developed to take into account different soil types and the complex nature of the loading. The objective of this paper is to compare the performance of the available formulations under the actions of a typical 35-h (hour) storm as per the Bundesamt für Seeschifffahrt und Hydrographie (BSH) recommendations. Using classical rain flow counting, the loading time-history is discretized into load packets where each packet has a loading profile and number of cycles, which then enables the computation of an equivalent number of cycles of the largest load packet. The results show that the loading profile plays a detrimental role in the result of the accumulated rotation. Furthermore, flexibility of the pile also has an important effect on the response of the pile where predictions obtained from formulations based on flexible piles resulted in a much lower accumulated rotation than tests based on rigid piles. Finally, the findings of this paper are expected to contribute in the design and interpretation of future experimental frameworks for Offshore Wind Turbine (OWT) monopiles in sands, which will include a more realistic loading profile, number of cycles, and relative soil to pile stiffness.