End-bearing Pile Research Articles

Seismic response of end-bearing piles in saturated soil to P-waves

Seismic response of end-bearing piles in saturated soil to P-waves

Load-Bearing Characteristics of PHC Piles Constructed by the Inner Digging Method Based on Ultimate Load Testing and Numerical Simulation

This paper studies the load-bearing characteristics of two prestressed high-strength concrete (PHC) pipe piles constructed by the medium mid-digging and hammering methods. The ultimate load tests and numerical simulations of the pipe piles constructed by both methods were carried out to analyze the ultimate lateral resistance, and ultimate resistance performance characteristics of the two pipe piles and the influence of the wall thickness of the pipe piles on the bearing performance. The test results show that the pipe pile constructed by the middle inner digging method has a higher pile quality. The single pile bearing capacity of the pipe pile constructed by the middle inner digging method is 50% higher than that of the common hammering method. The enlarged part of the pile end has an obvious effect on improving the bearing capacity. The settlement of the pipe pile constructed by the middle inner digging method is smaller than that of the hammering method. The large diameter pipe pile constructed by the middle inner digging method usually shows characteristics of the end-bearing pile. The resistance of the pile end accounts for 40–50% of the top load. The numerical simulation results agree with the field test and are compared and discussed. The simulation results show that when the bearing capacity of the pile is provided by the pile side frictional resistance, the influence of the pile wall thickness on the bearing capacity is insignificant. When the top pile load is close to the bearing capacity of the pipe pile, the influence of the pipe pile wall thickness on the bearing capacity is greater.

Two-dimensional Analysis of the Group Interaction Effects Between End-bearing Piles Embedded in a Rock Mass

This research is a two-dimensional analysis of the interaction effect in a group of piles socketed in a rock mass when studying the end-bearing capacity of the group. This problem was extensively studied for deep foundations in soils, but very little is published about foundations in rock. The study was conducted in 2D to establish the basis and criteria to analyze the problem, as well as understand the main factors and failure mechanisms involved when several piles work together in a foundation. The factors included in the analysis are, among others: the parameters of the rock mass, the pile embedment, and the pile separation. The research highlights shaft resistance as one of the key factors in the interaction. It proves that neglecting shaft resistance changes the interaction influence and the failure mechanism which may not be on the safe side. The research includes an analysis of the failure modes of different pile configurations using the discontinuity layout optimization (DLO) method, by taking advantage of the method’s ability to show the wedge configuration at the failure. The minimum and maximum efficiencies are characterized in terms of the pile separation values, thereby proposing a procedure to obtain the absolute minimum efficiency of the group. A second procedure is also presented for the approximate prediction of the bearing capacity of the pile tip, for a group with a particular number of piles and properties, by considering the contribution of the corner piles and the intermediate piles.

Investigation of the dynamic vertical behaviour of a floating pile embedded in unsaturated poroelastic half-space

This paper proposes an analytical solution for investigating the dynamic vertical behaviour of a floating pile in unsaturated poroelastic half-space by considering the dynamic properties of the soil below the pile base. The pile shaft resistance is derived by applying Hankel integral transformation to the governing equations, and the pile base resistance is derived by introducing the potential function and operator decomposition methods. The dynamic interaction between the soil and the pile is considered by virtue of the impedance function. To account for the mixed boundary conditions of the pile-soil interface, an analytical solution for the vertical dynamic response of a floating pile is derived in the frequency domain. Additionally, by utilizing the inverse Fourier transform and convolution theorem, a quasi-analytical solution for the velocity response of the floating pile is derived in the time domain. Furthermore, the derived solution is verified through comparisons with existing solutions available in the literature. Finally, a parametric study is performed to investigate the influence of saturation and intrinsic permeability on the dynamic flexibility coefficient of porous unsaturated half-space, the influence of saturation on the dynamic impedance of the soil layer, and slenderness ratio on the vertical behaviour of floating pile and end-bearing pile.

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.

Vertical kinematic response of an end-bearing pipe pile in fractional viscoelastic unsaturated soil under vertically-incident P-waves

This work investigates the kinematic response of a pipe pile embedded in a fractional-order viscoelastic unsaturated soil stratum over a rigid base subjected to vertically-propagating seismic P-waves based on a continuum model. The fractional standard line solid model is introduced to the governing equation of unsaturated soil to refine the frequency-dependent viscoelastic behavior of the soil skeleton. The Rayleigh-Love rod theory is utilized to characterize the vertical motion of the pipe pile. A rigorous series form solution for the vertical kinematic response of the end-bearing pipe pile under vertically incident P-waves is yielded theoretically with boundary conditions of pile-soil system. The proposed solution is then verified by comparing with the numerical result of the reported solution. Based on the given rigorous analyzed solution, the effects of physical parameters in pile-soil system on the vertical kinematic response of the end-bearing pipe pile under harmonic P-waves are studied in both the frequency and time domains through calculation example and parametric analysis. Finally, relevant meaningful conclusions are included and indicate that soil parameters and pipe pile dimensions have significant effect on the vertical kinematic response of the pipe pile.

Scattered wave effects on the vertical dynamic response of pile groups embedded in layered soil

This paper presents an analytical solution that provides the response to vertical dynamic loads of pile groups with arbitrary numbers of end-bearing piles. The solution allows accounting for pile–pile interaction effects on pile group response in a robust manner, as both wave diffraction and scattering are explicitly considered. The effects of soil layering are introduced by using the plane strain model to mathematically describe wave propagation in the subsoil. In addition to accounting for realistic soil conditions, the adopted plane strain formulation eliminates the need to calibrate the Winkler spring and dashpot parameters to obtain the impedance of pile groups. The presentation of the solution is accompanied by an arithmetic study focused on exploring the effects of scattered waves on the response of pile groups in layered soil.

Kinematic response of end-bearing piles in saturated soil to seismic SH-waves

This paper presents a mathematical model for the seismic analysis of end-bearing piles founded in a homogeneous saturated soil of finite thickness. Seismic loading is modelled as harmonic horizontal strong motion of the rigid bedrock, that generates vertically-propagating shear SH-waves. The transfer function of the soil layer is first established, considering soil as uniform isotropic poroelastic medium that obeys Biot’s governing equations. Accordingly, free-field and scattered soil displacements are co-evaluated, to establish a series-form expression that provides the dynamic lateral force acting on an Euler-Bernoulli elastic beam representing the pile. We employ the model to show that energy dissipation due to relative movement between the pore fluid and the solid matrix may have a noteworthy effect on the amplitude of high-frequency components of the strong motion in high permeability soils, and this in turn affects the kinematic response of piles. Finally, we use arithmetic examples to identify the soil permeability threshold, beyond which simpler single-phase soil models will produce reliable results for piles embedded in saturated two-phase soil.

Analytical solution of horizontal SV wave response considering pile shear deformation and soil free-field shear stress

An analytical solution is developed to investigate the horizontal SV wave responses of end-bearing pile considering shear deformation of Timoshenko beam and soil free-field shear stress. Firstly, the beam used is a Timoshenko beam that is more in line with the actual engineering project, in which taken into account the additional deflection caused by the bending and shear deformation of the pile. Meanwhile, the conditional transformation method is used to transform the coupled equation controlled by the two independent variables of displacement and rotation angle in the beam model into the decoupled governing equation. Then, the impedance of the soil to the pile under horizontal SV wave is obtained based on the fixed bottom and free top boundaries of the soil, and the continuous boundary conditions of the pile-soil interface. Furthermore, the closed solution of the problem is obtained according to the relationship of the governing equation of Timoshenko beam, the interaction between pile and soil, and the fixed bottom and free top boundaries of the end-bearing pile. In addition, the free vibration and forced vibration of the present solution are compared with the commercial finite element software ABAQUS and the existing analytical solutions of Euler beam to verify the rationality of the present analytical solution. Finally, the influence of soil free-field shear stress and pile shear deformation are emphatically analyzed. The results have certain guiding significance for engineering structure design.

Study on Mechanical Properties of Composite Foundation with Rigid Pile Based on the Cushion and Strength Adjustor Control

Settlement of the pile ends in end-bearing rigid pile composite foundations is generally minimal, so only relying on the cushion to coordinate the pile soil deformation may result in insufficient deformation adjustment capacity. Using a deformation adjustor with a specific stiffness on the top of the pile is a method to coordinate pile–soil deformation, and the stiffness value of the deformation adjustor depends on the accurate calculation of soil deformation; however, the calculation of soil deformation is not mature at present. A new deformation adjustor based on strengths used in composite foundations is proposed, in which foam slabs with different yield strengths are placed on the top of the pile to coordinate the pile–soil deformation. Five tests are used to study the mechanical and deformation properties of a composite foundation with a foam slab. The test results show that when the stress at the top of the pile is less than the yield strength of the foam slab, the coordination of the pile–soil deformation mainly depends on the cushion. When the stress of a rigid pile exceeds the yield strength of foam concrete, the foam slab begins to yield and coordinate the deformation of pile and soil, and the settlement coordination ability of a rigid pile composite foundation with a foam slab is significantly improved. Finally, an engineering case is used to simulate the pile–soil stress sharing when the actual settlement is greater than the calculated settlement. The case analysis shows that the pile-top stress can be well controlled by the successive yielding of foam concrete slabs of different strengths, which reduces the influence of settlement error on the pile–soil stress sharing, and further promotes the engineering application of end-bearing rigid pile composite foundations.

Model Test Study on the Load-bearing Behaviour of Multi-tooth Piles under Different Bearing Layers

In soft soil or karst areas, several problems exist, such as the poor properties of the pile tip bearing layer or difficulties in cutting the rock. Using multi-tooth piles, end-bearing piles can be turned into friction piles to solve these problems. Through the scale model device, three variables: the bearing layer, tooth length, and tooth number, are designed to experimentally explore the load-bearing behaviour of multi-tooth piles under different bearing layer conditions. The test results show that the model pile has better anti-settlement performance in the sand bearing layer than in the red clay bearing layer. Compared with smooth piles, multi-tooth piles can greatly improve the bearing capacity of pile foundations in bearing layers with poor stiffness. The tooth length and tooth number greatly impact the compressive bearing capacity and the pile-side resistance of the multi-tooth pile, respectively. The concept of roughness is innovatively introduced to quantify the roughness of pile surfaces, which provides an effective method for the subsequent experimental and theoretical research of multi-tooth piles and other similar piles with small cross-section modifications. This study can enrich the research field of small, modified cross-section piles and provide a reference for innovative research on pile foundations.

Semi-Analytical Solution for the Vertical Vibration of a Single Pile Embedded in a Frozen Poroelastic Half-Space

The theory of vertical pile vibration is the essential basis for pile integrity determination and dynamic analysis. The pile vibration characteristics are inevitably affected when the surrounding soil is frozen due to the low environmental temperature. Therefore, the investigation of pile vibration considering the surrounding soil as a saturated frozen porous medium is of great importance. In this paper, an analytical model for vertical pile vibration was established by employing the theory of composite saturated porous media, that is, by simplifying the upper frozen soil layer as a homogeneous isotropic saturated frozen porous medium and the foundation soil beneath the pile as an elastic half-space subjected to the motion of a rigid disk. By employing the integral transform and variable separation method, analytical solutions for the proposed model were derived under the three-dimensional axisymmetric condition. The analytical model and its solutions were verified by comparing them with the existing solutions for an end-bearing pile embedded in a homogeneously frozen soil layer as well as for a saturated half-space. A parametric study was conducted by utilizing the proposed solutions, and the results indicated that the pile bottom stiffness, the freezing temperature, the shear modulus of the unfrozen soil, etc., had a significant influence on the dynamic responses of the vertical pile vibration in both the frequency and the time domains.

Evaluation of the Bearing Capacity of the Board Pile in Collapsible Soil using A Laboratory Model

The pile’s ultimate capacity or failure load must be computed by some criteria using load-settlement curve data gathered during the pile load test. Many scholars have proposed several approaches for evaluating the pile’s ultimate capacity in the past. This study compared different failure criteria to predict the ultimate load capacity for piles with two different lengths-to-diameter ratios embedded in gypseous soil with gypsum content of 60% under soaked and unsoaked conditions. Two types of piles were used. Floating pile and end-bearing pile. Davisson, Brinch Hansen’s 80 percent, Chin-Kondner, Mazurkiewicz’s, and Brinch Hansen’s 90 methods that were used in this study predict a higher value of the ultimate pile capacity, whereas the Decourt Extrapolation method gave fluctuated value. Fuller and Hoy’s, Butler and Hoy’s methods give far away value from realistic. On the other hand, Shen’s, ASTM, Terzaghi, and DeBeer’s methods predicted an acceptable and realistic value. The failure criterion of (15%D) where (D) is pile diameter according to(ASTM D-1143) was adopted in this type of soil.

Model Experiment Study on Vertical Bearing Characteristics of Large-Diameter Ring Piles

The hollow structure of large-diameter ring piles (LDRPs) reduces the amount of concrete used, is economically efficient, and reduces the weight of the pile. However, its bearing characteristics and safety performance are still not fully known. In this study, to determine the properties of the LDRP structure, a combination of the indoor scale model test and numerical simulations was used, and a new parameter, K, which is the thickness-to-diameter ratio, was introduced. A comparative study of LDRPs with different hollow ranges was conducted. The results show that for a value of K in the range of 0.2–1, the ultimate bearing capacity of LDRPs is not significantly different from that of large-diameter solid piles (LDSPs), and they can ensure sufficient safety reserves. Under ultimate bearing capacity, the strain on an LDRP is large, but it does not exceed its own material strength, and the strain variation law is similar to that of a solid pile. LDRPs show the characteristics of end-bearing piles, and concrete savings can reach up to 50% for K in the range of 0.2–1.

Analytical solution for horizontal vibration of end-bearing single pile in radially heterogeneous saturated soil

Employing Biot's dynamic equations and Novak's thin-layer theory, an analytical model for the horizontal vibration of a single pile embedded in the radially heterogeneous saturated soil is established. Firstly, the frequency-domain response of surrounding soil is derived by means of the potential function, Laplace transformation and variable separation methods. Secondly, the analytical solution for the horizontal impedance of pile head is deduced by combining the conditions of the displacement continuity and stress equilibrium on the soil-pile interface. Finally, the obtained solution is degenerated to validate its accuracy via independent comparisons with different existing solutions. On this basis, the effect of soil radial heterogeneity on the horizontal vibration of an end bearing pile is further discussed by conducting an extensive parametric analysis.

An elasto-plastic numerical analysis of THM responses of floating energy pile foundations subjected to asymmetrical thermal cycles

Although end-bearing energy pile foundations subjected to symmetrical thermal cycles have been extensively studied in the laboratory and in the field, the mechanisms underlying the thermo-hydro-mechanical (THM) interactions in floating energy pile groups and rafts, especially when subjected to asymmetrical thermal loads, are not well understood. In this study, an advanced thermo-mechanical bounding surface model was implemented in finite-element (FE) code to investigate the THM interactions of a two-by-two floating energy pile group and pile raft, focusing on asymmetrical thermal cycles. Computed results are compared with published centrifuge model test results in soft clay. It is revealed that the irreversible volumetric contraction of the soil adjacent to the energy piles accumulates with each thermal cycle, resulting in a decrease in the horizontal stress and hence shaft resistance of the floating piles. During thermal cycles, the stress states of the soil around the energy pile shaft and the soil beneath the pile toe approach the critical state line along different paths. The induced temperature in the soil adjacent to the non-energy pile (NEP) is 5°C lower than that in the soil at the energy pile EP1, which is flanked by the other two energy piles EP2 and EP3. Consequently, the induced excess pore pressure in the soil at the NEP is approximately 20% smaller than that in the soil at EP1. The irreversible volumetric soil contraction at the NEP is about half that at EP1, resulting in approximately 45% less toe settlement. The thermally induced ratcheting settlements of the head and toe of the NEP are less than those of the energy piles, resulting in unacceptable ratcheting tilting of the floating energy pile group. However, the excessive tilting can be reduced by the use of a pile raft.

Analysis of floating and end-bearing pile foundations affected by deep-excavations

This paper investigates the response of pile foundations to deep-excavations. An elastoplastic two-stage model is used to study the response of pile groups (with free- or rigidly capped-heads) and of piled structures (grade beams or bearing walls), considering piles embedded in either uniform or layered ground. The model is validated using results of analytical solutions, as well as data from centrifuge tests and from real case histories. Then, a parametric study investigates excavation-induced displacements and internal forces of piles, and deformations of the superstructure. Soil–pile transfer mechanisms and pile–superstructure interactions are analysed for various foundations and ground conditions, with results showing that settlements and slopes between piles are larger for floating piles than for end-bearing piles. Results show that rigidly capped piles and semi-flexible piled structures cause bending moments at the foundation heads that increase with the excavation-induced slope between piles, whereas the risk for tensile failure of piles is low. Also, results indicate that the superstructure stiffness is more relevant to decrease the slope and deflection ratio of foundations when composed of floating piles, compared to end-bearing piles. Finally, modelling end-bearing piles embedded in a stiff base using hinged connections to such stiff base may not be appropriate.

Numerical Study of Bearing Capacity of the Pile-Supported Embankments for the Flexible Floating, Rigid Floating and End-Bearing Piles

Floating pile-supported embankment involves more complex load transfer mechanisms, and there are no clear uniform guidelines available for its design. The concepts of flexible floating, rigid floating and end-bearing pile-supported embankments were proposed in this paper. Based on three typical field cases, their pile-soil interactions and soil arching effect were examined using the three-dimensional finite element method. Due to symmetry, only a half-width embankment model was simulated here. It has been found that the flexible floating piles carry the load mainly relying on the skin friction, but end-bearing piles rely on the pile tip resistance. The rigid floating piles were somehow in between. The earth pressure coefficient (K) in the end-bearing pile-supported embankment reached a maximum of 3.28, greater than Rankine passive values of the earth pressure coefficient (KP), in which the soil arching was fully developed. The K in the embankment with rigid floating pile reached 2.21, where soil arching might be partially formed. At the bottom of the flexible floating pile-supported embankment, the K tended to equal the Rankine active values of the earth pressure coefficient (Ka), and thus soil arching was insignificant. It has also been found that using rigid floating piles might significantly improve the bearing capacity of the embankments and was cost-effective for deep soft soil areas.

Kinematic seismic response of end-bearing piles to S-waves

In this paper we revisit the problem of modelling analytically the kinematic interaction between a single pile and its surrounding soil under the action of seismic shear waves, by means of a Tajimi-type continuum elastodynamic model in three dimensions. The model provides the steady-state kinematic response of a cylindrical end-bearing pile embedded in a homogeneous viscoelastic soil layer, subjected to vertically propagating harmonic S-waves. Results of the model are first validated against the results of numerical simulations, and the results of an existing, approximate solution. Accordingly, we employ the model in a parametric study, where we investigate the sensitivity of the seismic response of piles to certain key problem parameters, including pile slenderness, soil-pile relative stiffness, excitation frequency and fixity conditions at the pile head. The solution yields closed-form expressions for pile deformations and for the soil resistance developing on the pile, that do not require introducing fitting coefficients.

A numerical model with high-accuracy and high-efficiency for the soil dynamic impedance of pile groups under vertical vibration

This paper develops a novel numerical model for the calculation of dynamic impedance of soil considering end-bearing pile groups under vertical vibration. The soil layer is treated as a linear viscoelastic material with hysteretic damping. The vertical displacement is assumed to be uniform in each individual pile in the groups at the same embedment depth. Using separation of variables and applying proper boundary conditions at the surface and rigid bedrock, the governing equation of soil layer in three-dimensional (3D) is first transformed into a two-dimensional (2D) Helmholtz equation in xy plane, where the solution in the vertical direction is obtained analytically. To solve this problem efficiently and accurately, the whole 2D unbounded soil is then divided into a finite interior domain and an infinite exterior domain. The finite domain is discretized using the finite element method (FEM) while an exact circular artificial boundary condition (ABC) is developed to model the infinite domain. Finally, the effect of pile group interaction on the dynamic impedance of soil is investigated considering various factors, e.g., dimensionless frequency, pile number, pile slenderness ratio and relative distance between piles.