In order to study the cumulative damage and failure characteristics of long spiral belled pile under horizontal cyclic loading of offshore wind and waves, a series of indoor experiments on single piles under horizontal cyclic load were carried out. The cycle times as well as load amplitude at the same frequency were considered during the horizontal pseudo-static cyclic tests. On the basis of the distribution of pile deflection, bending moment, and Earth pressure around the pile, the pile-soil interaction was comprehensively discussed. The cumulative energy dissipation characteristics were introduced to describe the damage of test piles. Meanwhile, the effects of load amplitude and cycle times on the cumulative damage of long spiral belled piles were discussed. A power function model for energy dissipation coefficient prediction under multi-stage cyclic load was proposed. The results show that the horizontal peak bearing capacity of long spiral belled pile is increased by 57.2% and 40.4%, respectively, as compared with the straight pile and belled pile under the same conditions. The horizontal displacement mainly occurs at the upper part of the pile. Under the condition of limited cyclic times, the load amplitude has more significant effect on the bearing characteristics of the long spiral belled pile. In contrast to the straight pile and belled pile, the long spiral belled pile has better energy dissipation capacity, and the rank of the energy dissipation capacity of these three piles is long spiral belled pile > belled pile > straight pile. The power function model can well reflect the cumulative damage characteristics of long spiral belled pile under horizontal cyclic loading, and there is a good linear relationship between power function model parameters and load amplitude. The energy dissipation coefficient of long spiral belled pile with diverse cycle times at different mechanical stages of test pile is analysed. Then, the recommended power function model parameters according to different failure stages are proposed. The verification example indicates that the prediction results are close to the measured values with a calculation error of 22%. The prediction model can provide a certain reference for the application of long spiral belled pile in marine structures.
Pile foundations in the field of marine engineering are often subjected to horizontal cyclic loading caused by factors such as sea wind and waves. Local permanent cumulative damage at one or several places may appear at a pile under the horizontal cyclic loading, and crack or sudden fracture damage can occur after a certain number of cycles. The phenomena mentioned above can seriously affect the normal use of pile foundation and safety of the superstructure.
The bearing characteristics and deformation law of pile foundation under the horizontal cyclic load of sea waves are interesting topics for domestic and foreign scholars. Rao , Basack , Achmus , Liao , and Kong  studied the effects of cyclic load amplitude, cycle times, single pile size, and buried depth on the stress characteristics and deformation of single pile, and concluded that load amplitude, cycle times, and single pile size effect have great influence on the stress characteristics and deformation of single pile. Niemann [6, 7] has carried out centrifuge model tests and 1g model tests of single pile and group piles under lateral cyclic load in sand, and discussed the influence of pile group geometry, pile spacing, and cyclic load amplitude on the cumulative displacement of group piles. Cyclic load has a significant impact on the initial stiffness of p-y curve, and the initial stiffness decreases with the increase of cyclic times. Basack [8–10] developed a new lateral cyclic load application device for model pile foundation. Through comprehensive experimental research and finite element analysis, the bending moment distribution and bearing characteristic response of pile groups under horizontal cyclic load in soft soil area were studied, and the influence law of horizontal load parameters, namely, cycle times, frequency, and amplitude on degradation factors, was analysed. A series of summary and analysis were made on the lateral cyclic load of pile foundation in marine environment. According to previous research results, some design suggestions were put forward for pile foundation under cyclic load. Chen  carried out an experimental study on the pipe pile in soft soil area under static pressure and cyclic combined load, and explored the influence of static load, cyclic load, and load level. Three modes of cyclic characteristics of pile top displacement are given: rapid stability, gradual development, and severe failure. According to the cycle stability diagram, the cycle stability criterion is divided into stable region, metastable region, and unstable region, and the corresponding limit values are obtained according to the test results. Liu  studied the deformation characteristics of composite foundation supported by geogrid piles under cyclic loading through a series of model tests, and analysed the effects of load, geogrid layers, pile types, and other factors on the performance of composite foundation. The relationship between foundation settlement and cycle times is analysed by the numerical fitting method.
Lin  applied the concept of strain superposition to evaluate the strain accumulation of laterally loaded piles in sandy soil, and found that soil properties, pile embedding mode, cyclic loading mode, and other factors can significantly affect the performance of horizontally loaded piles. Rosquoet et al. conducted centrifuge tests on sandy soil, and found that the maximum displacement was generated in the first cycle, and the cumulative deformation was mainly generated in the short-term cycle. Zhang et al. conducted a single pile model test in sandy soil foundation and also reached a similar conclusion. The cumulative displacement of pile top was mainly concentrated in the short-term cycle, and the short-term effect of the cycle was greater than the long-term effect. LeBlanc et al.  carried out unidirectional and bidirectional cyclic loading tests in dry sand with different dry densities. They believed that the cumulative stress and deformation of pile foundation under horizontal cyclic loading was related to the unloading stiffness, and the expression formula was given. Arshad  and Richards et al.  compared the model test of one-way and two-way cyclic loading and found that under the same load amplitude, the cumulative deformation caused by two-way cyclic loading was greater than that caused by one-way cyclic loading. Bolton , Alizadeh, Davisson , Little , Long , and Verdure  established a logarithmic function or power function model between the development trend of pile foundation’s cumulative deformation and the number of cycles under horizontal cyclic load through model tests and field tests. Luo et al. , based on numerical simulation, used the power function model to predict the cumulative deformation of pile foundation under different loads. Peralta et al.  carried out horizontal cyclic loading tests of rigid pile and flexible pile in sandy soil, discussed the influence law of cyclic number and load amplitude on accumulated damage and deformation of pile foundation, and presented the relationship between cumulative damage and deformation of rigid pile under long-term horizontal cyclic load and times of cyclic loading.
Many researchers have found that the cumulative deformation of single pile under horizontal cyclic loading mainly occurs in short-term cycle, and in the early stage of cyclic loading, the number of cycles and loading mode can obviously affect its bearing characteristics. The long spiral belled pile is made by improving the manufacturing technology and construction equipment of the spiral pile, setting an enlarged head at the pile end on the basis of the spiral pile. A new type of pile is formed, which increases the compaction between pile and soil beside pile due to the existence of enlarged head at pile end and thread of pile body, thus greatly improving the bearing capacity of pile. At present, the long spiral belled pile is widely used in engineering, but its application and research in marine structures are few. Therefore, it is of great significance to study the bearing and damage characteristics of long spiral belled piles under the approximate horizontal cyclic loads such as offshore wind and waves.
This study focuses on the pile-soil interaction and energy dissipation characteristics of offshore long spiral belled piles subjected to the horizontal cyclic loading. Three types of piles, namely, long spiral belled pile, straight pile with equal cross section, and belled pile, are selected. A set of single pile model tests under horizontal cyclic load were carried out with an indoor model box. As limited to the test conditions, the loading frequency is 0.01 Hz. Cyclic reciprocating loads with different load amplitudes are applied at the same frequency in the test. Through the distribution of pile deflection, bending moment, and Earth pressure around the pile, the influence of cyclic load amplitude and cycle times on the interaction between the long spiral belled pile and the soil around the pile is discussed. By analysing its hysteretic characteristics and skeleton curve, the cumulative energy dissipation characteristics are used to reflect the damage of test pile, and the influence of load amplitude and cycle times on the cumulative damage of long spiral belled pile is discussed. The power function prediction model of energy dissipation coefficient under multi-stage cyclic loading is put forward. It provides a reference for the application of long spiral belled pile in offshore engineering.
2.1. Manufacture of Model Pile
The test model pile is a precast concrete pile, and the similarity ratio is calculated by taking the long spiral belled pile with pile length L = 12m, pile diameter D = 0.6 m, and concrete strength C35 as the prototype. It is determined that the proportional constant SL is 10, the elastic modulus similarity ratio CE = 1/5, and the straight pile and belled pile are set as the control group. The geometric dimensions of the three indoor model piles designed based on the similarity ratio are shown in Table 1.
Enlarged head diameter (mm)
Reinforcement cage length (m)
Long spiral belled pile (LK)
Belled pile (KZ)
Equal cross section straight pile (ZZ)