Pile Group Foundation Research Articles

Optimal intensity measure selection and probabilistic seismic demand model of pile group supported bridges in sandy soil considering variable scour effects

Scour of pile group foundations is a common hazard for cross-river bridges and can produce considerable damage to piles in earthquake-prone regions. The fragility-based performance assessment for pile group supported bridges subjected to earthquake and scour hazards has drawn increasing attention from engineering practice and academic communities. Such assessment requires numerical models that are computationally efficient and accurate in describing the mechanical behavior associated with the complex soil-pile interaction of these soil-bridge systems. Additionally, selecting an optimal ground motion intensity measure (IM) is generally required for such assessments. However, modeling the pile group effect for seismically excited pile groups and the optimal IM for the scoured bridges have not been well addressed in previous related studies. To this end, a practical pile group effect modeling approach is adopted in this study and validated by a set of shake table tests on scoured pile group bridge available in the literature. Based on the validated numerical modeling approach for the soil pile interaction, a series of coupled soil-bridge models are generated considering the structural and soil parameter uncertainty and analyzed in the OpenSees platform. The optimal IM for various engineering demand parameters (EDPs) is identified from thirty-nine scalar IM candidates through the criteria of efficiency, practicality, sufficiency, and hazard computability. Finally, a straightforward form of probabilistic seismic demand model (PSDM), incorporating the effect of scour depth changes, is developed for pile group supported bridges. Results show that the increase of scour depth significantly increases the curvature demand of a pile group and statistically reduces the embedded depth of the belowground plastic hinge of the pile shaft. The rank of optimal IM candidates directly depends on the selection criteria of an optimal IM and the selection of EDP. In addition, the scour depth slightly affects the rank of optimal IMs. Generally, VSI, PGV, and Sv,1.0 are recommended for the probabilistic seismic demand analysis of pile group supported bridges in sandy soils with scour potentials.

Numerical analysis of load-transfer mechanism of stiffened deep cement mixing pile foundation

ABSTRACT To reveal the load-transfer mechanism of stiffened deep cement mixing (SDCM) piles, the three-dimensional numerical analysis of a pilot pile was first conducted using the finite element software Diana, which can simulate the Mohr-Coulomb friction interface. Comparisons show that the computed load-settlement curve and distribution law of the skin frictions agreed well with the measurements. Then, the numerical method was employed to model the group pile foundations with four SDCM piles. It shows that the bearing capacity increased with increasing pile spacing and core lengths. And most loading was shared by the stiffened cores. It indicates that negative skin frictions may arise at the bottom of a reinforced concrete pile cap or the end of a stiffened core. And there is a hysteresis effect for the peak frictions on the two interfaces to mobilize. Meanwhile, plastic shear zones in soil and DCM pile may sequentially arise with increasing load.

Simplified calculation methods for earthquake-induced hydrodynamic added mass of immersed pile caps with different cross-sections

Assessment of the earthquake-induced hydrodynamic added mass of pile caps is important in predicting the seismic resilience of deep-water bridges with an elevated pile group foundation. Simplified formulas for the hydrodynamic added mass of immersed pile caps with different cross-sections were derived in this paper. The added mass values of circular pile caps with various dimensions and submerged depths were estimated based on the numerical fluid-structure coupled model, and the corresponding added mass calculation formula was obtained through the curve fitting method. The formulas to determine the added mass for rectangular pile caps and rectangular pile caps with fillet or chamfer corners were further developed by incorporating the corresponding shape coefficients for the pile cap in the formula. A total of 200 pile caps with different cross-sections and physical parameters were selected using Latin hypercube sampling to assess the performance of the proposed formulas. Next, the consistency between these formulas and the numerical model for added mass results was observed. The proposed formulas are concise and enable efficient calculation of the hydrodynamic added mass of pile caps submerged in water.

Shaking Table Test for Seismic Response of Nuclear Power Plant on Non-Rock Site

In order to compare and analyze the seismic response characteristics of a safety-related nuclear structure on a non-rock site in the condition of raft and pile group foundations under unidirectional and multidirectional seismic motion input, a large-scale shaking table test of the soil-nuclear structure system was carried out in this paper. In the test, the soil was uniform silted clay, and the shear wave velocity was 213 m/s. Considering the similarity of the superstructure natural frenquency, the actual nuclear power structure was simplified to a three-story frame shear wall structure model. The annular laminated shear model box was used to take the boundary effect of soil into consideration; the seismic motions = were input in only one horizontal direction or three directions at the same time for the shaking table test, and the results were analyzed. The results of the test show that the acceleration response of the safety-related nuclear plant is affected by the directions of input seismic motion and the forms of the foundation. When the seismic motion is input simultaneously in three directions, the acceleration responses of the horizontal motion and vertical rocking of the safety-related plant are larger than those of the single-direction input. The acceleration response of the horizontal motion and vertical rocking of the safety-related structure with the pile group foundation is smaller than that with the raft foundation. The values of most frequency bands in the horizontal acceleration Fourier amplitude spectrum at the top of the pile-foundation structure are smaller than that at the top of the raft-foundation structure, while the displacement is basically the same as that of the raft-foundation structure. This is related to the relation between the frequency component of input seismic motion and the natural frequency of the structure system. Therefore, it is more reasonable to use three-dimensional seismic input in the seismic response analysis of nuclear power plants. The seismic performance of nuclear power plants can be enhanced by using pile group foundations.

Evaluasi Daya Dukung Pondasi Tiang Pancang Pada Gedung Universitas Muhammadiyah Lamongan

The pile foundation is a deep foundation that is often used in the construction of high-rise buildings and small-scale buildings. The foundation is required to have a greater bearing capacity than the load on it. This study aims to determine the maximum bearing capacity of the foundation against the work load including the additional load from the 15-story Lamongan Muhammadiyah University building which was found to be cracked. Calculation of the bearing capacity of a single pile is carried out to determine the bearing capacity of a single pile using the Mayerhoff, Reese O'neil, and Reese and Wright method. Calculation of the bearing capacity of group piles is carried out to determine the bearing capacity of piles in one group using the Converse-Labarre, Los Angle Group, and Seiler-Keeney methods. Controlling the bearing capacity of single and group pile foundations, whether they are able to withstand the load on them using the axial loads and moments obtained. The results of the calculation of the bearing capacity of a single pile foundation at a depth of 30 m using the Meyerhoff calculation method obtained the carrying capacity of a single pile permit (Q_a) at point DB-1 of 916,80 tons and DB-2 of 916,80 tons, Reese and O' neil obtained Power single pile permit bearing (Q_a) at point DB-1 of 668,67 tons and DB-2 of 668,67 tons, Reese and Wright obtained single pile permit bearing capacity (Q_a) at point DB-1 of 1.070,08 tons and a DB-2 of 1.070,08 tons, while the shamanic strength of the largest pile group foundation was obtained using the Converse-Labarre method with ultimate bearing capacity using the Reese anad Wright method, bearing configuration from the pile group capacity (Q_g) (2 x 2) obtained at point DB -1 of 9.733,45 tons and DB-2 of 9.733,45 tons, configuration (2 x 3) at point DB-1 of 13.810,45 tons and DB-2 of 13.810,45 tons, configuration (3 x 2 ) at point DB-1 of 13.810,45 tons and DB-2 of 13.810,45 tons. The results of controlling the bearing capacity of the foundation by looking at the value of the allowable bearing capacity is greater than the value of the axial load (P ≤ Q_g). From the calculation of the bearing capacity of the piles it can be concluded that the pile foundations at points DB-1 and DB-2 are safe.

Study of the unified strength theory for seismic response of frame building on loess considering soil‐structure interaction

SummaryTo investigate the effect of soil‐structure interaction (SSI) on the seismic response of frame buildings on collapsible loess, the secondary development of Abaqus was used to realize the embedding of the unified strength theory constitutive model. Meanwhile, a new nonlinear elastic model generated by the unified strength theory (b, the failure criterion parameter in the unified strength theory, equals 0.5) was developed. Seven‐ and nine‐story frame buildings were selected as engineering examples in this study. The outcomes indicate that the nonlinear behavior of the loess–pile has a significant effect on the dynamic interaction of both group pile foundations and the superstructure under strong earthquakes. This results in an amplification of the displacement response and a reduction in inter‐story shear force. As the foundation soil becomes softer, the K‐type distribution of both peak accelerations and inter‐story displacements along height becomes more obvious in general.

Numerical Simulation of a Barge Impact on Bridges with Different Configurations of Pile Group Foundations

Three-dimensional finite element dynamic analyses were conducted to evaluate the effect of barge impact of different speeds on the lateral performance of three pile group (PG) configurations (vertical, battered, mixed) in terms of peak lateral displacement, peak shear force, lateral stiffness of PGs, and contribution of piles and pier columns to the total resisting force. The concrete material was modeled using the Concrete Damaged Plasticity model. The clay behavior was described using the Modified Cam Clay model; while the sand was modeled using the Drucker Prager model. The results showed that the vertical PG had the lowest lateral stiffness; while the battered and mixed PGs had closely larger stiffness, which allowed the development of larger impact force and pile cap displacement in vertical PG as compared to other PGs. The results of shear force showed that the foundation contributed up to 82% of the total lateral force in battered and mixed PGs. The results also showed that in vertical PG, the first row had slightly higher percentage of lateral force compared to other rows; while in battered PG, the load percentage was evenly distributed between rows. A contrast performance was observed for mixed PG. The results of bending moment (BM) showed that the piles in vertical PG had notably higher BM than the piles in other PGs due to larger pile cap displacement. In all PGs, the piles in the edge column had higher BM ratio, with the leading row (L) had the highest BM ratio (69–72%) in all PGs.

Parametric analysis and multi-objective optimization of the coupling beam pile structure foundation

To optimize the structure of a new coupling beam pile foundation, a finite element model that is verified by an indoor model test was established and compared with a pile group foundation to improve the uneven settlement phenomenon. The effects of different structural parameters on settlement and coupled beam axial forces were analysed. The corresponding mathematical model is created using the response surface method, and the NSGAII genetic algorithm is utilized to carry out multi-objective optimization while taking cost into account. The best structural parameters are then determined through the analysis of various weighting factors. The findings show that using the response surface method instead of finite element modelling can significantly shorten the optimization time while maintaining a high accuracy; that the cost weight factor should not be regarded too seriously; and that a value of 0.5 is recommended. When the optimum parameters were chosen, the coupling beam's axial force increased by 2.8%, the project cost of the structure was cut by 57.99%, and the settlement was lowered by 34.87%. The study offers a new concept for structural optimization and foundation treatment.

Modelling Study of Pile Group Foundation by Including Lateral Load in Clay Soil

Indonesia’s geographical condition causes earthquakes to occur more frequently. This study aims to investigate pile group response under earthquake loading by performing pushover analysis. Since clay soil is dominant and widespread in Indonesia, the study focused on pile group embedded in single layer of clay. The undrained shear strength (Su) parameters of the clay are varied from 20 kPa, to 100 kPa with 20 kPa intervals. The pile and soil were modelled by Beam-on-Nonlinear-Winkler-Foundation (BNWF), and the soil was presented as a series of Winkler springs using the nonlinear p-y method. The analysis was conducted with a finite element method (FEM) software, OpenSees. The pile was modelled as a fiber section, where the transversal and longitudinal reinforcement can be considered. The research found that the soil’s Su affects the ductility and formation of plastic hinge. Greater Su resulted in higher ductility and occurrence of plastic hinge. Higher Su was also found to increase the internal force experienced in the pile, as well as lead to higher group efficiency factor. There was no shear failure detected in the results, but bending failure happened at the lead pile in Su 100 kPa. The overturning moment phenomenon occurred on the pile group in Su 20 kPa and 100 kPa. For Su = 20 kPa, this phenomenon is caused by the middle pile and rear pile, which did not have optimal performance. Bending failure at the lead pile led to the phenomenonin Su 100 kPa.

Closed-form dynamic stiffness formulation for modal and dynamic response analysis of pile group foundations

A closed-form dynamic stiffness (DS) formulation is proposed for pile group foundations. This model consists of a rigid cap and an arbitrary number of flexible piles. The rigid cap, connecting to all piles, is modeled as a rigid body resting on an elastic foundation. For each pile, a longitudinal soil–pile model and a preloaded Timoshenko beam on viscoelastic Pasternak foundation are adopted to describe the longitudinal and transverse vibration, respectively. The piles can be either friction piles or end-bearing piles, and pile sections surrounded by different soil layers can be easily modeled by the assembly of pile elements with different parameters. The proposed DS formulations essentially use very few degrees of freedom to, nevertheless, describe the broadband dynamic behaviors of complex pile group foundations in a highly accurate manner. The DS formulation is then used for modal and dynamic response analysis. For modal analysis, the Wittrick–Williams algorithm is applied, with the key issue J0 count problems resolved. The proposed method is verified against some existing results. This research provides an exact and highly efficient modal and response analysis tool for pile group foundations, which can be used for the dynamic analysis of pile foundations subjected to earthquake or traffic excitations.

Study on Horizontal Bearing Capacity of Pile Group Foundation Composed of Inclined and Straight Piles

In all types of new arch bridge structures, the requirements of the foundation are becoming more and more strict. Under the action of horizontal thrust, the distribution of the internal forces of the pile group in which inclined piles participate in an arch foundation is complicated. In this regard, the horizontal forces of each pile in a pile group and the horizontal bearing performance of each pile in a pile group under the action of total thrust are investigated by establishing a pile group foundation model and a p-y curve difference equation. After an in-depth analysis of the simulation results, it is found that the load distribution calculated by the finite element method is very close to that calculated by the p-y curve method, both in terms of curve shape and numerical value, indicating that the pile top load distribution is close to the actual situation. In addition, the maximum shear force of each pile body occurs at the top of the pile, and the maximum bending moment occurs at the point 1/5 away from the top of the pile. Finally, the nonlinear analysis of the p-y curve method can be well applied to the calculation of bridge pile foundations.

Analysis of Settlement of Group Pile Foundation in Linear Viscoelastic Soil

The settlement of a group pile foundation is the result of elastic-plastic settlement of the pile and rheological settlement of the soil. Unfortunately, most research only considers elasto-plasticity settlement of piles or rheological settlement of soils. Classical theories like the Poynting-Thompson model only provide some prediction for the elasto-plasticity behavior of pile groups, which cannot satisfactorily reflect the total settlement characteristics of pile group foundation. In the current paper, we presented a method to study settlement behaviors of pile group foundation in linear viscoelastic soil based on the pile-pile interaction factors, the calculated equation of settlement of single piles and pile groups under vertical loads that are derived, the influence law of pile end resistance, pile spacing, slenderness ratio, elastic modulus ratio, and Poisson ratio on pile end load ratio, and the interaction factors that have been presented. Finally, some typical predictive examples have been presented for a 2 × 2, 3 × 3 group pile showing settlement from a field test. It is found that the pile-pile interaction factors increase with the increase of the pile-soil elastic modulus ratio and length-to-diameter ratio but decrease with the increase of the ratio of distance to diameter, and the ratio of distance to diameter has little effect on the interaction factor when pile spacing is more than 10 d (d is the diameter of the pile). The error between the field test results and computed data is 14.9%, the settlement calculated by the present method shows good agreement with the reported results, and the correlativity coefficients R2 are greater than 0.9223, which signifies that the present method is suitable for the theoretical calculation and prediction of the composite foundation settlement of linear viscoelastic soil when piles are used to strengthen the foundation. The method would provide a unique view to quantitative prediction of the settlement characteristic of group pile foundation.

Optimization of beam parameters for coupling beam pile structure foundations under vertical loading

SummaryThe coupling beam pile structure is a new type of foundation for high‐rise buildings that can be easily constructed. The vertical load‐bearing characteristics of the coupling beam pile structure are examined using indoor model tests and numerical calculations to optimize the beam structure's parameters. The validity of the finite element model is then confirmed, and the beam structure's width, length, and stiffness are changed to examine their effects on the load‐bearing capacity. The results show that the load–settlement curve of the structure varies slightly, with a 45.10% increase in load‐carrying capacity compared to a pile group foundation for the same load, and that the coupling beam can support heavier loads while also distributing the tension of the loads. The width and length of the coupling beam are proportional to the load‐carrying capacity of the structure. The width of the coupling beam should be kept at 3.5 times the pile diameter since any wider width results in the “wall group effect,” which reduces the foundation's ability to support the weight. The coupling beam's short length, which should be kept above 4.5 times the pile diameter, can aid in reducing the “pile group effect.” The coupling beam stiffness can be changed according to the scenario in practice; there is no upper limit. The coupling beam stiffness is 5 times the reference value when it has the strongest force transmission capacity but has essentially little impact on the structure's load‐carrying capacity.

Optimized Design of a Squeezed-Branch Pile Group Based on an Improved Particle Swarm Algorithm

To reduce the differential settlement of pile group foundations, a squeezed-branch pile group optimization method based on an improved particle swarm algorithm is proposed in this paper. This method translates the problems of optimization design in the squeezed-branch pile group into the pile-bearing-plate distribution using the theory of variable-stiffness leveling. In the optimization process, the pile group is divided into groups according to the top axial force of the pile. The finite element analysis software is used to solve the pile group under the control of the particle swarm optimization algorithm, with the objective functions of bearing-plate number, vertical bearing capacity, settlement value and settlement difference as the constraint conditions. An engineering example is used to verify this method. The results show that the optimized design can reduce the settlement difference by 39%, while the number of the bearing plate is reduced by 56%, which makes the deformation and force of the pile group more uniform and is conducive to the normal use of the structure.

A probabilistic study on impedances and kinematic response factors of square pile groups in homogeneous soils

The complexity of the Soil-Structure Interaction (SSI) problem is mainly due to difficulties related to the modelling of the soil-foundation behaviour, which is not only frequency-dependent, but is also largely influenced by uncertainties related to soil properties and stratigraphic conditions. According to a sub-structuring scheme for the analysis of SSI problems, a deterministic approach is usually adopted for the analysis of the soil-foundation system assuming properties and geotechnical models based on the expert judgment, despite the fact that uncertainties related to the intrinsic variability of soil parameters are widely recognised and confirmed by experimental campaigns and laboratory tests.This paper presents a probabilistic study on the dynamic behaviour of square pile group foundations in homogeneous soils, focusing on the effects of the uncertainties related to (i) the frequency-dependent impedance functions and (ii) the kinematic response factors. Above quantities are required to define compliant restraints for the modelling of the soil-foundation system in performing inertial soil-structure interaction analysis, and for the definition of the foundation input motion starting from the free-field motion. Square pile groups are considered, and uncertainties are described through probabilistic distributions of parameters governing the soil-foundation dynamic response. The probabilistic analyses are performed through a numerical model developed by the Authors and some results are presented to show and discuss the variability of the results. In addition, a sensitivity analysis is performed to assess the influence of each variable uncertainty on the system response. Overall, response quantities are found to be very sensitive to shear wave velocity, although soil density and pile elastic modulus may often play a significant role.

Random wave action on pile group foundations with complex geometry for sea-crossing bridges

To explore the mechanical properties of pile group foundations (PGFs) with complex geometry in sea-crossing bridges under ocean wave action, this study develops a numerical model for predicting wave loads on PGFs under multidirectional random wave action. Furthermore, an experimental model of the PGF composed of a quasi-elliptical pile cap and 13 tilted piles is designed and made based on the gravity similarity criterion. By performing model experiments and numerical analysis, the mechanical characteristics of the PGF model under random wave action, the effect of principal wave direction angle and random wave directionality, and the influence of the pile cap on wave loads of tilted piles are systematically investigated. The results show that the calculated results of the presented numerical model match well with the experimental data. The frequency characteristics of wave loads on the PGF model are mainly determined by the wave spectrum. The increase of the significant period improves the contribution of the pile group to the horizontal wave loads on the PGF. The effect of the principal wave direction on the vertical wave loads on the PGF is not obvious under the experimental wave conditions. Neglecting the wave directionality will overestimate the wave loads in the principal wave direction and vertical direction on the PGF. Under the influence of diffraction waves from the pile cap, the wave loads on the pile group and the piles where the wave finally acts are easily amplified when the wave number is small, but in the large wave number case, the wave loads on the pile group and the piles below the middle of the pile cap may be weakened.

DESIGN OF MARTAPURA RIVER BRIDGE STRUCTURE, BANJAR REGENCY

The Martapura River Bridge is located on Jalan A. Yani KM 40 Martapura, Banjar Regency, South Kalimantan. Traffic processes that occur on Jalan A. Yani KM 40 Martapura often experience problems because congestion often occurs and the condition of the old IA bridge sometimes makes driving users feel restless when crossing the bridge located on the Martapura river. So that at the location of the Martapura river, it is deemed necessary to build a bridge next to the IA bridge so that the IB bridge to be built can be more sturdy and durable so that there is no anxiety for driving users and also to reduce congestion that occurs, where later the IB bridge will be used as a road with one way only towards Banjarmasin and the martapura IA bridge will be used as a one-way road towards the Hulu Sungai so that it will make it easier for traffic on Jalan A. Yani KM 40 Martapura.
 The methodology used in loading planning refers to SNI 1725-2016 concerning Loading Standards for Bridges. For the methodology in calculating the stress loss, refer to the NAASRA Bridge Design Specification on Chapter VI Bridge Design Specifications (Prestressed Concrete Design). For the methodology in calculating the moment of the vehicle floor using the Three Moment Equation method and for the method of subsidence of group pile foundations using the method of Schultze and Sheriff (1973), assuming that the pile group is the Equivalent Raft Foundation. The material used in the design of the upper structure is prestressed concrete, while the lower structure is planned to use reinforced concrete with a square pile.
 The results obtained are the T-Girder Prestressed type bridge with class A, 34 m span, 7 m traffic width, and 1 m wide sidewalk. Prestressed T-Girder is designed using fc' 40 MPa (K-482) Strands used are uncoated 7 wire super strands ASTM A-416 grade 270 with a diameter of 12.7 mm and an area of 100 mm2 with a tensile strength of 1860 MPa. As for the lower structure, the abutment uses concrete with a quality of fc' 25 MPa (K-300) with a height of 565 cm, a width of 480 cm and a length of 1050 cm.type piles Square Pile with a length of 15 m with a quality of 50 MPa (K-600) with a width of 60x60 cm with a configuration of 18 piles for each abutment. Estimated Budget Plan The cost of constructing the Martapura river bridge is IDR 8,129.511,475.00.-.

Analysis Stability of Abutment on the Railway Bridge

Railway bridge Bangunan Hikmah (BH 39) Pariaman (Padang– Pariaman Route) is a new bridge. This new bridge was built because the old one could not accommodate the load of the additional locomotive. The railway bridge consists of two parts: the upper structure and the substructure. The substructure consists of abutments and foundations. When the abutment accepts considerable lateral ground pressure, so the stability of the abutment will be disturbed. To resolve the problem, the need exists to study abutment reinforcement with geotextile or additional foundation pile to raise the stability abutments on the Railway bridge Bangunan Hikmah (BH 39) Pariaman. The result of the loading on the upper structure is obtained. The total vertical force acting on the abutment is 6111,624 kN, and the horizontal load is 2849,689 kN. Abutment stability analysis is carried out in 3 stages (without reinforcement, with reinforcement geotextiles, and with existence foundation pile (bored pile). The results of the analysis show value safety factor minimum without Reinforcement (SF) is 1,29; this shows that the abutment is unstable because the safety factor obtained is < 1.5,  with reinforcement geotextile, the value of the safety factor minimum  (SF) is 1,66,  this indicates that the abutment is stable but still critical and the value of the safety factor (SF) minimum with bored pile foundations is 2,10.  Installation of a bored pile foundation (pile group) at a depth of 10m shows a significant increase in the value of the safety factor. In the BH 39 Kurai Taji Pariaman railway bridge project, it is recommended to use a pile group foundation with a depth of 10 m.

Seismic uplift behavior and energy dissipation mechanism of scoured bridge pile-group foundations: Quasi-static test and numerical analysis

Seismic-induced pile uplift is likely to happen in coastal bridges with scoured pile-group foundations. This study investigates the seismic performance of scoured pile-group foundations with pile uplift behavior. To this end, a quasi-static test was conducted on a reinforced concrete specimen comprising a rigid single-column pier and a 2 × 2 pile-group foundation partially embedded in homogeneous sand. Cyclic lateral loading was imposed near the top of pier to produce sufficient bending moments on the foundation for achieving the pile uplift behavior. After that, a finite element (FE) model for the quasi-static test is developed and validated using the experimental data. An in-depth comparative study is conducted on two FE models with and without pile uplift. Results show that bridge models with pile uplift show apparent self-centering behavior, while those without pile uplift do not. Pile uplift prevents the yielding of pile head sections and meanwhile delays the yielding of underground ones. Besides, bridges with or without pile uplift have quite close total energy dissipation capacity, but the contribution of soil-pile frictional interaction is greatly increased (from 24% to 76%) while the contribution of structural damage is significantly decreased (from 40% to 2%) due to pile uplift.

Study on pile cap effects of pile group foundations under linear wave action by a hybrid BEM and EEM method

For pile group foundations (PGFs) subjected to ocean wave action, diffraction waves from the large-scale pile cap can remarkably change wave loads on slender piles below the pile cap (i.e., pile cap effects). However, relevant influencing factors and the variation pattern of wave loads on piles are still unclear. To this end, this study develops a three-dimensional hybrid method for calculating wave loads on slender piles in PGFs under linear wave action. The presented method is implemented by combining the boundary element method (BEM) and the eigenfunction expansion method (EEM) and can consider the effect of diffracted waves from the pile cap. The proposed method is then applied to a truncated cylinder and a PGF with a square pile cap, and the calculated results are respectively compared with the analytical and numerical results. Excellent agreements verify the validity of the presented method. The effects of various factors, including cap shapes, cap dimensions, cap drafts, wave propagation directions, wave numbers, pile slopes, and pile tilt directions, on wave loads of piles are investigated using the presented method. The results show that wave numbers and cap horizontal dimensions have a very strong effect on wave forces on slender piles in PGFs, and wave forces on piles decrease substantially as they increase. However, the influence of cap drafts is weaker. The wave propagation direction determines the distribution pattern of wave load magnitudes at different pile locations, and this distribution pattern varies with different cap shapes. For tilted piles, the wave propagation direction and the pile tilt direction jointly affect (enhance or weaken) wave loads on piles, and the pile slope can amplify this effect. Wave loads on the external piles of the pile group are generally stronger and these external piles need to be reasonably strengthened. This research can assist with the design and optimization of PGFs for offshore bridges.