Cyclic Load Ratio Research Articles

A New Method for Predicting Dynamic Pile Head Stiffness Considering Pile–Soil Relative Stiffness Under Long-Term Cyclic Loading Conditions

Under long-term horizontal cyclic loading, the evolution characteristics of the loading and unloading stiffness of piles are an important representation of pile–soil interaction. However, research in this area is limited, particularly regarding the impact of factors like pile–soil relative stiffness. In this study, laboratory tests with a long-term horizontal cyclic loading strategy were conducted to study various factors, including different cyclic amplitude ratios (ζb), cyclic load ratios (ζc), and pile–soil relative stiffness (T/L) in sandy soil, on dynamic pile head stiffness. The results show that the normalized cumulative displacement increases with the number of cycles and the ratio of T/L but tends to decrease as ζc increases. As ζb increases, the normalized cyclic loading stiffness also rises, while it has little effect on the normalized cyclic unloading stiffness. On the other hand, as ζc or T/L increases, the cyclic loading stiffness increases while the unloading stiffness decreases. Based on these observations, prediction formulas for normalized cumulative displacement and cyclic loading and unloading stiffness were established and confirmed with test results. The findings of this study provide methodological references for establishing models of pile–soil interaction under cyclic loading and for predicting loading and unloading stiffness under different influencing factors.

Assessment of accumulated lateral displacement of a flexible pile due to cyclic lateral loads in saturated sand

Pile foundations, which support offshore structures, are primarily subjected to cyclic lateral loads. The accumulated lateral displacement of the pile foundation is a critical parameter that affects the overall stability of the structure. This study presents a series of cyclic lateral loading tests conducted on flexible model piles installed in saturated sand with varying relative densities and cyclic loading characteristics. Based on the experimental results, a model is proposed to predict the accumulated lateral displacement of a pile under cyclic lateral loads. The proposed model takes into account the number of load cycles and the cyclic load ratio (the ratio of the minimum to maximum cyclic load) and is validated using experimental data. The results show that the accumulated lateral displacement increases exponentially with the number of load cycles and is influenced by the cyclic load ratio and the relative density of the sand. The proposed model provides an accurate prediction of the accumulated lateral displacement of piles installed in saturated sand and can be used to design pile foundations for offshore structures.

Inclination Effect of Cyclic Load Synchronous with Lateral Static Load on Pile Group in Sandy Soil

In general Pile foundations are often subject to more than one load in nature. Two loadings, when simultaneous, cause serious problems in the bearing capacity. Therefore, the major objective of this study is to assessment the performance of piles under inclined cyclic loads simultaneous with static lateral loads in sandy soil with a relative density of 70%. A laboratory investigates were conducted to determine effect of several factors on group pile performance model (2×2), including: the ratio of spaces between piles (i.e. 3D, 5D, 7D), influence of inclination angles of cyclic loading (i.e. 0°, 10°, 20°, 30°), the cyclic load ratio (i.e. 20%, 40%, 60% and 80%) and the effect of the presence of a static lateral load on the cyclic load. In light of the findings, the presence of the static load with the inclined lateral cyclic load has a positive effect on the deep foundations where the lateral deflection was reduced by an average of 54% for the three spaces. Also the lateral deflection at combined lateral loading decreases with increasing pile spacing, the percentages of decreases in the lateral deflection were (16%, 73%, 75% ) for spacing (3D, 5D, 7D ) respectively

Predicting the Effect of Surface Waviness on Fatigue Life of a Wire + Arc Additive Manufactured Ti-6Al-4V Alloy.

This paper reports the effect of as-deposited surface conditions on the fatigue strength of an additively manufactured titanium alloy, Ti-6Al-4V (WAAM Ti64). First, the local stress concentration caused by the surface waviness was quantified using a metrology technique and computer modelling. Fatigue tests were conducted under bending loads at a cyclic load ratio of 0.1. The applicability of two predictive methods was the focus of this study. The traditional notch stress method was unable to predict the correct S-N curve trend slope, which could be attributed to the early crack initiation from the troughs on the as-built surface, with crack propagation being the dominant failure mechanism. By treating the troughs as small cracks, the fracture mechanics approach delivered good predictions at every applied stress level. Surface machining and polishing may not always be practical or required; it depends on the applications and service load levels. This research demonstrated that the fracture mechanics approach can be used for predicting the fatigue life of WAAM titanium alloys in as-built conditions and, hence, can be a tool for decision making on the level of surface machining.

Fatigue crack growth behavior in an aluminum alloy Al–Mg–0.3Sc produced by wire based directed energy deposition process

AbstractAdditive manufacturing (AM) of Al–Mg–Sc alloys has received considerable interest from the aerospace industry owing to their high specific strength and suitability for AM processes. This study has investigated the fatigue crack growth behavior in an Al–Mg–0.3Sc alloy made by wire and arc additive manufacturing. Tests were conducted with two different crack orientations at cyclic load ratios of 0.1 and 0.5. At the lower load ratio, the horizontal crack showed a faster growth rate owing to the smaller grains and coarser second‐phase particles that the crack tip had encountered when it propagated along the material build direction. The anisotropy in crack growth rate was mainly caused by the grain size effect. When the applied stress intensity factor range exceeded the value of 10 MPa m1/2, an isotropic crack growth rate between the two crack orientations was measured. This is due to the microstructural influence being overcome by the governing parameter of fracture mechanics. At the higher load ratio of 0.5, crack growth rate is isotropic, and the threshold stress intensity factor range was much lower than that tested under load ratio 0.1. Finally, the modified Hartman–Schijve equation has been successfully employed to represent the crack growth rates in all three regions.

Influence of Horizontal Loading in Changing the Ultimate Uplift Bearing Capacity of Monopile Foundation of Offshore Wind Turbine

Throughout their lifespan, monopile foundations supporting offshore wind turbines inevitably experience horizontal loads from waves, winds, and currents, resulting in cumulative deformation. It has been believed that deformation caused by horizontal loading weakens the interaction between the pile and the soil, leading to a reduction in the ultimate uplift bearing capacity of the pile foundation. However, there is a scarcity of literature investigating this issue, particularly regarding monopiles used in offshore wind turbine installations. Therefore, this study aims to explore the impact of horizontal cyclic loads on the ultimate uplift bearing capacity of monopile, focusing on the pile–soil interaction. To achieve this, a series of 1 g model tests were conducted on a rigid model pile embedded in silt with varying relative compaction. The test results indicate that the ultimate uplift bearing capacity of the pile is significantly diminished after experiencing horizontal cyclic loading, and the extent of reduction is closely linked to the amplitude of the horizontal deformation. A semi-empirical model is developed to predict the ultimate uplift bearing capacity of the pile foundation following horizontal cyclic loading. The key findings of this study are as follows: (1) The earth pressure in the active zone gradually decreases with an increasing number of cycles, while the earth pressure in the passive zone experiences a slight increase under horizontal cyclic loading. (2) The position of the pile rotation center under horizontal cyclic loading is approximately 0.84 times the depth at which the pile is buried, and this relationship appears to be independent of soil density and cyclic load ratio. (3) The variation of earth pressure corresponding to the horizontal deformation of the pile in the active zone can be divided into three phases: a rapid decline phase, a slow decline phase, and a stable phase. (4) The reduction in the ultimate uplift capacity is influenced by the cyclic ratio and number of cycles but does not appear to have a significant relationship with soil density.

Lateral response of monopile reinforced by cement-improved soil in clay to monotonic and cyclic loadings: Laboratory model test and theoretical investigation

A systematic study was performed in laboratory model tests to assess the response of cement-improved reinforced monopiles to lateral monotonic and cyclic loading in clay. The overall load‒deflection behavior and profile of the bending moment was fully studied in monotonic tests, in addition to the p-y curves of the reinforced and unreinforced piles. Cyclic loading tests were carried out at different cyclic magnitude values and load ratios, and the cement-improved soil reinforcement range was also varied. This study provides several insights into the ongoing development of the deflection, unloading stiffness and bending moment of cement-improved soil reinforced piles as cycling progresses, which can provide empirical design recommendations for cement-improved soil reinforced monopiles subjected to lateral cyclic loading. Based on the typical p-y curve models of pile in soft clay and stiff clay, by considering the proportion of soil resistance shared by cement-improved soil and soft clay around a pile under lateral load, the modification factors of two parameters pu and y50 are derived, and then a modified p-y curve model of cement-improved soil reinforced piles in soft clay is established.

On the cyclic stability diagram of offshore wind turbine supported on multiple foundations in saturated dense sand

This study explored the issue of cyclic loading on a tripod suction bucket foundation system in silty sand through three-dimensional (3D) finite element (FE) models by developing a cyclic stability diagram, in which the response is presented in terms of the average load ratio (ALR) and the cyclic load ratio (CLR), and three regions are identified: (1) no cyclic load effects, (2) cyclic load effects, and (3) severe load effects after approximately 1000 one-way load cycles. The simulations, based on dynamic FE analysis, enabled the identification of the ‘’self-healing’’ phenomenon due to enhanced stiffness degradation of a foundation in tension by incorporating the correct estimate of the soil-foundation interface and geometric nonlinearities. In addition, an approximating expression for the calculation of the accumulated rotation of offshore wind turbine (OWT) supported on multiple foundations is provided as a function of ALR and CLR utilizing modified least-squares method (MLSM). The proposed expression leads to notable improvements in the prediction of induced rotation of OWTs such that the coefficient of determination, R2, was obtained ranging from minimum value of 0.89 to a maximum value of 0.99. This study suggests that the salient features of multiple foundations must be considered in the design process of offshore wind turbines.

A model test study on the parameters affecting the cyclic lateral response of monopile foundations for offshore wind turbines embedded in non-cohesive soils

Abstract. During their service life, monopiles supporting offshore wind turbines are subjected to a large number of lateral cyclic loads resulting from complex environmental conditions such as wind and waves varying in amplitude, direction, load eccentricity and frequency. The consequential accumulation of displacements and rotations of the foundation structure with cyclic loading is one key concern in the design of monopiles. Nevertheless, the relevant offshore guidelines do not provide suitable procedures for predicting such deformations. Although there are several methods for this purpose in the literature, some of them produce very different or even contradictory results, which prevents a consistent approach to dimensioning. This paper briefly summarizes the current standardization regarding design of monopiles for cyclic lateral loading and provides some examples of possible prediction models from the literature. To highlight the need for further research, the predictions according to different approaches are compared and evaluated by a calculation example and a parameter study. Further, the results of a small-scale 1 g model test campaign on the load-displacement behaviour of monopile foundations subjected to lateral cyclic loading and the influencing parameters are presented, evaluated and compared with the findings of other research groups. In this way the test results can help to support or improve model development and provide insight into key issues relevant to monopile design. The parameters that have been assessed include the cyclic load magnitude, cyclic load ratio, load eccentricity, soil relative density, the grain size distribution of the non-cohesive bedding material and the pile embedment length.

Model tests on jacking installation and lateral loading performance of jacket foundation in sand

The long-term dynamic behavior of pile under cyclic loads is important for the stability and safety characteristics of jacket supported offshore wind turbine. In this study, large-scale indoor model tests were carried out on the jacking installation and lateral loading of jacket foundation in sand. For the process of pile installation, it shows that the linear growth of pile tip resistance during installation can be divided into two stages, and its critical depth (the depth at which the growth rate of pile tip resistance begins to decrease significantly) is 11D (diameter). The jacking resistance of latter pile is significantly greater than that of former pile. Under static load, the maximum bending moment point of front row pile is higher than that of back row pile. The depth of bending moment reverse point is also 11D for front and back row piles. Under cyclic loads, the displacement at tower top undergoes two stages: rapid growth stage and slow growth stage. The friction resistance of back row pile increases first and then decreases along depth, showing an oblique “V” shape. The natural frequency varies with different load frequencies and cyclic load ratios. The evolution trend of system damping ratio and natural frequency is roughly opposite.

Behaviour of soilbags subjected to monotonic and cyclic vertical loading

Soilbags have been successfully used in the reinforcement of building foundations that can function as the base isolation. A series of unconfined compression tests under monotonic and cyclic loading were conducted to investigate the static bearing capacity and the dynamic deformation behaviour of stacked soilbags. The results of monotonic loading tests demonstrate that the ultimate compressive strength and the tangent compression modulus of soilbags tend to relatively stable values of around 0.7 MPa and 6.73 MPa, respectively, when the number of layers exceeds three. Under cyclic loading, the accumulated vertical strain of stacked soilbags increases nonlinearly under the application of cyclic loading, reducing with each loading cycle and even reaching a relatively stable state where the vertical strain is primarily elastic, which can be described with an empirical formula with respect to the static vertical stress, the cyclic load ratio and the number of loading cycles. The resilient moduli of stacked soilbags change slightly during cyclic loading period, and increase with the increasing static vertical stress and the decreasing cyclic load ratio. The outcomes of this study demonstrate the feasibility of soilbags as the base isolation as they have prominent bearing capacity and stable deformation behaviour under cyclic loading.

Model Testing of Encased Stone Column Composite Foundations under Traffic Loads

In soft soil foundations, geogrid encased stone column composite foundation technology has been widely applied and developed in recent years due to its efficient treatment. In this study, eight groups of laboratory model tests were performed in a large-scale testing tank to investigate the bearing mechanism and stress characteristics of the composite foundation of geogrid encased stone columns under traffic loads with different cyclic load ratios. The stress at the bottom of the stone column and settlement of the composite foundation were measured and analysed. The test results show that cyclic shearing will cause the rearrangement of the soil particles at the column-soil interface, which will cause changes in the face pressure and effective stress state of the column-soil boundary. The cyclic load has a substantial influence on the accumulation settlement of the composite foundation and the development of the lateral stress state of the column. Based on the test results, the development law of the cumulative settlement is summarized, and the change mechanism of the column stress state is analysed and discussed.

Studies on Bearing Characteristic of Open-Ended and Close-Ended Pipe Piles under High-Speed Railway Loadings

The pile foundation under a high-speed railway (HSR) not only bears the self-weight of the superstructure, but also bears a long-term vertical periodic load during its service. In this study, a large-scale vertical dynamic load test and particle flow numerical simulation method were adopted to investigate the axial cyclic performances of open piles in sand. The results from the dynamic test show that under a dynamic load with cyclic load ratios of 0.1 and 0.2, the surface displacement of the pile decays rapidly as the pile distance increases. Moreover, the higher the vibration amplitude and frequency, the larger the surface displacement. The influence range of the soil around the pile is approximately six times of the pile diameter. It is also found that the external frictional resistance of the upper part of the pile decreases, whereas that of the middle part increases. In addition, the internal friction resistance of the lower part of the pile decreases and gradually stabilizes after approximately 200 cycles. The simulation results show that the influence range of the pile on the surrounding soil is approximately 5–8 times the diameter of the pile under the action of dynamic loading; the vertical displacement of the pile mainly occurs at the beginning of the cycles. The total settlement of the pile foundation increases with an increase in the cyclic load ratio. With an increase in the cycle period, the friction resistance values on the outside of the pile and middle part significantly decrease and increase, respectively. After 10 cycles, the resistance gradually stabilizes, and no evident changes in the internal friction resistance of the pile are observed.

Three-Dimensional Modeling of Monopiles in Sand Subjected to Lateral Loading under Static and Cyclic Conditions

Here, the results of a three-dimensional finite element study of the complex interaction of horizontal and moment loads (HM) on offshore monopiles as failure envelope, are reported. A new design criterion is described which is based on critical length, ultimate limit states, load characteristics and Eigen-frequency to ensure stable behavior of laterally loaded monopiles. Numerical analyses were performed to examine nonlinear interaction of a soil-pile system for 10,000 load cycles. The resulting framework can predict angular rotation due to cyclic loading. According to the loading level and duration of a load, elastic strains accumulate in the vicinity of a pile. Fairly intermediate two-way cyclic loading induced the largest rotations irrespective of the analysis performed (i.e., drained versus partially drained). Based on the regression coefficients of the non-dimensional frameworks used, accumulating rocking deformations of a pile at seabed level appear to be dependent on cyclic load ratio, drainage condition, and duration of loading. For safe design, sensitivity of the natural frequency of offshore wind turbine (OWT) at a monopile critical length as well as shorter lengths were also examined. The analytical model proposed here for determining the natural frequency of an OWT considers that soil-structure interaction (SSI) can be represented by monopile head springs characterized by lateral stiffness, KL, rotational stiffness, KR, cross-coupling stiffness, KLR, and parabolic soil stiffness variation with depth.

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.

An experimental study on the parameters affecting the cyclic lateral response of monopiles for offshore wind turbines in sand

The design of monopile foundations for offshore wind turbine structures is dominated by requirements resulting from serviceability and fatigue limit state. To fulfil these criteria, the load deflection-behaviour and therefore long-term accumulations of permanent deflections and rotations of the monopile foundation due to cyclic occurring wind and wave loads have to be predicted. In this paper a brief overview on current design code practice as well as other proposed methods for the prediction of accumulated deflections or rotations is given. Further, the results of a systematic model test study dealing with the response of monopiles to lateral cyclic loading in medium dense sand at different cyclic load ratios, load eccentricities and pile embedment lengths are described and evaluated. The observations of the model test study are supplemented by results of a second test series involving the visualisation of displacement fields around laterally loaded piles by means of particle image velocimetry. Based on the findings and the results of previous experimental investigations, recommendations regarding the prediction of displacement accumulations for large diameter monopiles in sand are given.

Influence of cyclic loading on the tensile fracture characteristics of ultra-high performance engineered cementitious composites

Ultra-high performance engineered cementitious composite (UHP-ECC) with tensile strength of nearly 15 MPa and tensile strain capacity of nearly 8% exhibits high potential for improving the fatigue performance of modern infrastructures. In this study, monotonic loading tests were performed on UHP-ECC specimens subjected to different number of fatigue cycles and the influence of cyclic loading ratio on the fracture mechanism of UHP-ECC was investigated. In order to evaluate the effect of fatigue loading on the residual toughness of the material, the calculated pseudo strain-hardening (PSH) index was calculated for each loading mode. Furthermore, the fatigue tests at different stress levels were conducted and the corresponding relationship between stress level and fatigue life was compared with that published in literature. Based on the evolution of hysteresis curve, a fatigue damage prediction model was proposed. The thorough experimental investigations, combined with the numerical model, aim to provide useful reference for the future design of UHP-ECC structures subjected to repetitive loading.

The Effect of Vertical Loads and the Pile Shape on Pile Group Response under Lateral Two-Way Cyclic Loading

This paper is presented the lateral dynamic response of pile groups embedded in dry sand under influence of vertical loads and the pile shape in-group, which are subjected to the lateral two-way cyclic loads. The laboratory typical tests with pile groups (2×1) have an aluminum-pipe (i.e. circular, square) pile, embedded length to diameter of pile ratio (L/D=40) and spacing to diameter ratio (S/D) of 3, 5, 7 and 9 are used with different cyclic-load ratio (CLR) 0.4, 0.6 and 0.8. The experimental results are revealed that both the vertical and lateral pile capacity and displacement is significantly affected by the cyclic-loading factors i.e. (number of cycles, cyclic load ratio, and shape of pile) .In this study, important design references are presented. Which are explained that the response of the pile groups under cyclic lateral loading are clear affected by the attendance of vertical load and pile shape. Where, it is reduction the lateral displacement of group piles head and increase lateral capacity about (50) % compared without vertical loads. On the other side, the pile shape is a well affected to the pile response where the level of decline in lateral displacement at the pile groups head in the square pile is more than circular pile about 20 % at the same load intensity.

Fatigue Life Prediction for Specimens with an Open Hole with a Pre-Compressed Boundary Via the Nominal Stresses Under Regular Cyclic Loading

The method of predicting the fatigue life of structural elements containing open holes with a preliminary compressed material in the hole vicinity under cyclic loading is proposed. The method is based on the commonly accepted approach of the life prediction via nominal stresses. The presence of residual stresses caused by plastic deformation of the material in the hole zone is taken into account by adjusting the cyclic load ratio in calculations. The concept of “fictitious compression stresses” is introduced for this purpose; its value is determined by solving the contact problem in an elastoplastic formulation in a finite element package. A functional relation between the value of residual stresses and the fatigue life of specimens with pre-compressed hole surface is established. The calculation results via the proposed method are compared with fatigue test results for specimens with pre-compressed hole surface. Satisfactory correlation between calculated and experimental data is obtained. The advantage of the proposed method is the reduction of required input data to construction of the fatigue curve for standard specimens with a stress-free hole. Considering that for the same alloy with identical heat treatment such curves may differ for different material batches, testing of standard specimens under regular loading is mandatory. Despite a usual scatter in fatigue life experimental values, the proposed method allows one to obtain a reliable and conservative assessment of the effect of hole boundary zone pre-compression on the fatigue life at the design stage.

Combined static-cyclic multi-axial crack propagation in cruciform specimens

Two cracks, initiated from the opposite tips of a 45° inclined central notch, were considered in cruciform specimens made of Ti6246. A static load was applied along one arm of the specimen and a cyclic load (R = −1) was applied along the other arm. Crack propagation was carefully monitored by optical means for different ratios of static to cyclic load. The observed crack propagation was simulated using two numerical tools, involving two different mixed-mode crack propagation prediction methods. The experimental evidence shows that there is a switch in crack propagation direction from orthogonal to the cyclic load at low static load levels to orthogonal to the static load for high static load levels. Both numerical procedures were able to predict this switch, albeit at slightly different static to cyclic load ratios.