Pile Slenderness Research Articles

Piles for offshore wind turbines: a state-of-the-art review

The paper considers the current state of the art for estimating the pull-out capacity of driven open-ended piles used to support wind turbine foundations founded on sand. The latest edition of the American Petroleum Institute guidelines for pile design includes a conventional earth pressure approach and four alternative cone penetration test (CPT) methods for estimating pile shaft resistance in sand. A database of open-ended pile tests was used to assess the predictive reliability of the design approaches. While the earth pressure approach was unreliable, exhibiting bias with pile slenderness and sand relative density, the CPT methods were shown to provide improved and relatively consistent estimates of pile capacity. However, the tension loads experienced by wind turbine foundations are significantly higher than those applied to piles in the database. When the CPT methods were used to estimate the pile length required to support a 5 MW turbine installed in typical offshore soil conditions, the CPT methods provided a wide range of predicted pile lengths. The reasons for this divergence are discussed and an alternative framework for considering driven pile shaft resistance is put forward.

Numerical Investigation of the Scouring Effect on the Lateral Response of Piles in Sand

Scouring around a bridge foundation is a problem of much concern to civil engineers. The main purpose of this paper is to gain more understanding of the effect of scouring around the pile on the lateral capacity of the piles embedded in sandy soil. Factors such as soil stiffness, pile head fixity, and pile slenderness ratio (L/B) were studied to show their effects on the variation of the percentage decrease of lateral load capacity (PDC) due to scouring near an isolated pile. The results indicate that the PDC value reaches almost 50% when the scour depth reaches 1.3 to 2.4 times the pile diameter, and that piles with a fixed head are more capable of resisting lateral load loss. Furthermore, the PDC values remain almost constant after the pile slenderness ratio is greater than 10. Hence, the decrease in lateral load due to scouring of the soil will be more serious for short piles.

Design charts for elastic pile shortening in the equivalent top–down load–settlement curve from a bidirectional load test

With a rigid pile assumption, the equivalent top–down load–settlement curve constructed from the results of a bidirectional or bottom–up pile load test does not fully consider the total elastic shortening when all the load components from skin-friction and end-bearing are applied downward at the pile head. In effect, the equivalent curve constructed by the original method suggested from the Osterberg test showed a much stiffer curve compared to the top–down curve. Design charts are provided in this paper from the results of a parametric study on bored piles in order to approximately evaluate the λ-factor that is used to estimate the top–down pile shortening from the bottom–up shortening due to the skin-friction component of the load. It has been shown that the λ-factor varies with the distribution of the undrained shear strength profile, pile slenderness ratio, and mobilization of the skin-friction resistance. In addition, the pile shortening due to the end-bearing load component is added to the top settlements by treating the pile as an elastic column. A modified method for the construction of the equivalent top–down load–settlement curve is presented that considers the elastic pile shortening and validated with the measured top–down load–settlement curve from pile load tests.

Current Use of Prestressed Concrete Pipe Piles Founded in Silty Geomaterials

Prestressed concrete pipe piles have been increasingly used as deep foundation structures for decades. Despite the availability of a limited number of well-instrumented load test results, pile designers would like to know the general performance of such piles in case of lacking adequate experience. An attempt is made in this study to establish a database composed of more than one thousand of pile tests. All piles are founded in silty soil that is one of the competent bearing geomaterials. Short and medium-length piles with slenderness ratios ranging from 20 to 80 are most widely used. The capacity of pile increases with increasing the pile slenderness ratio until a limiting value is achieved. Use of very long piles to reduce settlement is unfavorable and the rebound rates for piles with various lengths are similar. An independent case study is also conducted to witness the success of employing the empiricism-based analyses in the preliminary design of concrete pipe piles.

Improved Evaluation of Equivalent Top-Down Load-Displacement Curve from a Bottom-Up Pile Load Test

A modified procedure is presented in this study to evaluate the equivalent top-down load-displacement curve in a bottom-up pile load test considering elastic shortening. On the basis of the results of a parametric study on a bored pile in normally consolidated cohesive soils under undrained conditions, varying shear strength distribution and pile slenderness ratio, it was concluded that the pile shortening caused by the skin-friction component of the load in a top-down test can be related to the measured elastic shortening in a bottom-up test. A λ-factor is used to define this relationship, that is, the ratio of the top-down to bottom-up pile shortening. The factor λ=1.0 is used for the case of a pile in soil with uniform shear strength profile, λ=2.0 for linear profiles, 1.0<λ<2.0 for nonlinear profiles varying above linear, and λ>2.0 for nonlinear profiles varying below linear. In addition, the method suggests taking the corresponding readings of the skin-friction load component from the upward displacement curve of the top of the pile, which is a closer approximation to rigid pile displacement than the bottom when corrections for elastic pile shortening are to be applied. Assuming a fully mobilized skin-friction, a logarithmic relation for the factor λ to the normalized area under the shear strength profile was generally formulated and is limited to the assumptions on which they were derived. The suggested procedure in this study has produced the equivalent top-down load-displacement curves that are in close agreement with the measured top-down curve, as validated in the case studies.

Seismic analysis of coupled soil-pile-structure systems leading to the definition of a pseudo-natural SSI frequency

The elastodynamic response of coupled soil-pile-structure systems to seismic loading is studied using rigorous three-dimentional (3D) finite element models. The system under investigation comprises of a single pile supporting a single degree of freedom (SDOF) structure founded on a homogeneous viscoelastic soil layer over rigid rock. Parametric analyses are carried out in the frequency domain, focusing on the dynamic characteristics of the structure, as affected by typical foundation properties such as pile slenderness and soil-pile relative stiffness. Numerical results demonstrate the strong influence on effective natural SSI period of the foundation properties and the crucial importance of cross swaying-rocking stiffness of the pile. Furthermore, the notion of a pseudo-natural SSI frequency is introduced, as the frequency where pile-head motion is minimized with respect to free field surface motion. Dynamic pile bending is examined and the relative contributions of kinematic and inertial interaction, as affected by the frequency content of input motion, are elucidated.

Note on the Interaction Factor for Two Laterally Loaded Piles

This technical note revisits the interaction factors for two piles under lateral loading by means of a rigorous analytical method. The basic idea of the approach presented is to decompose the problem into an extended elastic soil and two fictitious piles having Young's modulus equal to the difference between the modulus of the real pile and the surrounding soil. By considering the displacement compatibility condition, the pile-soil interaction problem is found to be governed by a Fredholm equation of the second kind. The displacement and bending moment distribution along the fictitious piles, and consequently, the desired interaction factor at the pile head are obtained. Comparison with existing solutions validates the accuracy of the present formulation and confirms that the conventional interaction factor approach would exaggerate the interaction effect for long flexible piles. Some numerical examples are presented to illustrate the influences of the pile spacing, pile-soil stiffness ratio, pile slenderness ratio, and departure angle of the loading direction on the calculated results. A set of interaction factor charts is also provided.

Termination Criteria for Jacked Pile Construction and Load Transfer in Weathered Soils

Pile jacking is a piling technique that provides a noise- and vibration-free environment in the construction site. To improve termination criteria for pile jacking and to better understand the behavior of jacked piles, two steel H piles were instrumented, installed at a weathered soil site, and load tested. A set of termination criteria was applied to the test piles, which includes a minimum blow count from the standard penetration test, a specified final jacking force, a minimum of four loading cycles at the final jack force, and a specified maximum rate of pile settlement at the final jacking force. The two test piles passed all required acceptance criteria. Punching shear failure occurred at the failure load for both piles and the shaft resistance consisted of approximately 80% of the pile capacity. Based on the results of field tests in Hong Kong and Guangdong and several centrifuge tests, a relation between the ratio of the pile capacity Pult to the final jacking force PJ and the pile slenderness ratio is established. The Pult∕PJ ratio is larger than 1.0 for long piles but may be smaller than 1.0 for short piles. A regression equation is established to determine the final jacking force, which is suggested as a termination criterion for jacked piles. The final jacking force can be smaller than 2.5 times the design load for very long piles, but should be larger than 2.5 times the design load for piles shorter than 37 times the pile diameter.

Influence of vertical load on the lateral response of piles in sand

Pile foundations are often subjected to both vertical and lateral loads. The current design practices assume that the effect of these two loads is independent of each other and hence the pile design is carried out separately for vertical and lateral loads. The conventional methods for analysis of piles based on sub-grade reaction methods also do not account for the interaction between the vertical and lateral loads. The influence of vertical loads on the lateral response of piles installed in sandy soils is brought out in this paper through 3-dimensional finite element analyses. In the numerical model, the pile was treated as a linear elastic material and the soil was idealized using the Drucker–Prager constitutive model with a non-associated flow rule. The results from the analysis of single piles under pure lateral loads and combined vertical and lateral loads are presented in this paper. The influence of related parameters, viz. sequence of load application, shear strength (angle of internal friction and dilation angle) of soil, pile head fixity and pile slenderness ( L/ B) ratio have also been studied in the paper.

Influence of reaction piles on the behaviour of a test pile in static load testing

This paper employs a simplified analytical method to investigate the influence of reaction piles on the load–displacement behaviour of a test pile in static load testing. A parametric study is conducted to examine the effects of factors such as pile spacing ratio, pile slenderness ratio, and pile soil stiffness ratio. Several soil profiles are considered in the study. The parametric study also includes the cases of static load testing in the lateral direction. The correction factors for the initial pile head stiffness obtained from static pile load tests with the use of reaction piles are given in charts. Furthermore, analyses of centrifuge modelling of axially loaded piles are carried out using the simplified analytical method. Good agreements between the test results and the analysis results are demonstrated, and the applicability of the correction factors is verified.Key words: reaction piles, interaction, initial pile head stiffness, static vertical load testing, static lateral load testing, simplified analytical method.

Rationality of load transfer approach for pile analysis

New closed form solutions accounting for non-homogeneous, elastic plastic or visco-elastic soil properties have been established for a single pile subjected to vertical loading, and for vertically loaded pile groups. The solutions are based on load transfer approach, with the pile–soil interaction being characterised by springs distributed down the pile shaft and at the pile base. As such, the accuracy of the solutions lie in the load transfer factors linking the gradient of the load transfer curves with elastic modulus values. This paper presents an extensive investigation into the load transfer approach, by comparing the new closed-form solutions for a pile embedded in an elastic medium with rigorous numerical analysis. By this means: 1. The rationality of the load transfer approach has been extensively explored; 2. Load transfer factors have been calibrated against the numerical solutions to account for a number of factors, such as the ratio of the depth to the underlying rigid layer and the pile length, the degree of soil non-homogeneity, Poisson’s ratio for the soil, and the pile slenderness ratio; 3. Expressions for estimating the load transfer factors have been provided. With the new load transfer factors, the closed form solutions may be applied with high accuracy over a very wide range of pile geometries and soil conditions.

ULTIMATE CAPACITY OF DRIVEN PILES IN SAND.

An earlier proposal for the ultimate capacity of driven piles in sand by Fleming et al, is modified to a closed-form procedure and extended to include explicitly the decreasing influence of vertical effective stress and pile slenderness ratio with progressive increase in the magnitude of these parameters. In formulating the proposal, the author has endeavoured to combine, in an appropriate way, fundamental theory, past research findings and the field measured results from a recently published extensive data set. A convenient procedure for interpretation of relative density from cone penetration test results is also presented. (A)

Torsional piles in non-homogeneous media

Abstract The torsional response of a pile exhibits features which are a mixture of those for axial and lateral response. At low load levels, the response is dominated by interaction with the upper soil layers and by the pile rigidity itself, similar to laterally loaded piles. However, failure will generally occur by the whole pile twisting, and so the latter part of the response incorporates the integrated effect of all soil penetrated by the pile, as is the case for axial loading. In view of the above, solutions for the torsional response of pile must endeavour to incorporate accurate modelling of the soil stiffness profile, and also pay appropriate attention to the gradual development of slip (relative twist) between pile and soil. The paper presents analytical and numerical solutions for the torsional response of piles embedded in non-homogeneous soil, where the stiffness profile follows a simple power law with depth. The solutions encompass: (1) vertical non-homogeneity of soil expressed as a power law; (2) non-linear soil response, modelled using a hyperbolic stressstrain law; (3) effect of relative slip between pile and soil for non-homogeneous stiffness and limiting shaft friction; (4) expressions for the critical pile slenderness ratio (or length) beyond which the pile head response becomes independent of the pile length. The solutions are developed using a load transfer approach, with each soil layer acting independently from neighbouring layers, and are expressed in terms of Bessel functions of non-integer order, and as simple non-dimensionalised charts. The solutions are applied to two well-documented case histories in the latter part of the paper.

Torsional Dynamic Analysis Of Single Piles By Time-Domain BEM

The transient dynamic response of single piles in a layered half-space under a time-dependent torque is analyzed by a coupled FEM-BEM approach in which the pile is modelled by FEM and the half-space by a general cylindrical co-ordinates time-domain BEM. By virtue of the Fourier theory, only one-dimensional discretization is necessary for the boundaries of the three-dimensional layered half-space, while the pile shaft can be discretized as a one-dimensional elastic column member. The compatibility and equilibrium conditions between pile shaft and soil layers are employed to assemble the respective equations into one set. A comparison is carried out to demonstrate the accuracy of the approach. The influence of several parameters on the transient behavior of single piles is investigated through numerical examples. Of all the parameters, the shear modulus ratio Gp /Gs is found to be the most important governing factor. The other effective factors are the pile slenderness ratio l/r0 , the soil layering and so on.

Service Load of Short Large‐Diameter Bored Piles

Field loading tests of 10 short nondisplacement piles are analyzed using the writer's method of calculating the service load of long piles. The method is based on the analysis of over 200 field loading tests. A hyperbolic relation is assumed between the specific skin friction qs or toe pressure qt and the slenderness L/D (length/diameter) of piles. The assumption is affirmed statistically to be acceptable for long piles (since qt→0forL/D→0). Using the method, an expression is deduced relating the skin friction share of the total service load to the pile slenderness. This forms a simple and uniform basis of the calculation of service load of piles of different slenderness and of soils of different consistencies and densities. The calculated service load of short piles was overestimated. This was explained by the toe pressure having been reduced by the heavy disturbance of the soil experienced at the pile toe by boring.

Resistance of a soil layer to horizontal vibration of a pile

AbstractThe resistance of a soil to horizontal harmonic vibration of a vertical, end bearing pile with circular cross‐section is theoretically investigated. The soil is considered to be a continuum with material damping of the hysteretic type. The motions of the soil and pile are expressed as series, and a resistance coefficient on each term in the series of the pile motion is found. The resistance is found to depend on the excitation frequency, the pile slenderness and on the material properties of the soil. Finally a study of the influence of the parameters is carried out.

Lateral Load-Deflection Relationships of Piles Subjected to Dynamic Loadings

A simple representation of the dynamic lateral load-deflection relationship of a pile is presented for both pile-head and seismic excitation conditions. The lateral load-deflection relationship of a pile is represented by the soil reaction coefficient that is the ratio between a unit soil reaction on a pile and the product of soil modulus and pile displacement relative to the free field. As the soil reaction coefficient varies significantly along the pile even in a homogeneous soil, an averaging procedure is presented to determine an equivalent soil reaction coefficient that is constant with depth. The average soil reaction coefficients, δ˜, for homogeneous soil profiles are affected by the loading condition, pile flexibility factor, and pile slenderness ratio. The magnitudes of these influences are quantified. This averaging procedure can also be applied to heterogeneous layered soil profiles if a weighted soil modulus is used. The concept of the average soil reaction coefficient is extended to develop a procedure to compute the dynamic lateral load-deflection relations of piles when the stress-strain response of the soil is nonlinear and degrades due to pore pressure increases with cyclic loading.

Resistance of soil to a horizontally vibrating pile

AbstractThe resistance of a soil layer to steady horizontal vibration of an elastic pile is theoretically investigated. The pile is assumed to be vertical and of circular cross‐section. The soil is modelled as a linear viscoelastic layer with hysteretic material damping. A closed form solution is obtained for the resistance of the soil layer to the motion. This resistance depends on shear modulus of soil, frequency, pile slenderness, material damping and Poisson's ratio. A parametric study of the effect of these parameters is included. The soil layer resistance is expressed in a form which can be used directly in the solution of the soil‐pile interaction problem which is treated in a subsequent paper. The approach also applies for rigid deeply embedded footings.