Flexible Piles Research Articles

Safety factors and limit states analysis in geotechnical engineering: Discussion

The paper is a further valuable contribution by Dr. Meyerhof on the subject of safety factors and limit states design in geotechnical engineering. It is understood that the paper also represents the basic approach that will be adopted with respect to limit states design in the second edition of the Canadiaiz foundation engineering manual. The load and resistance factors given in Table 2 of the paper are indicated to agree with those specified in the National Building Code of Canada (1985) and in the Ontario Highway Bridge Design Code (1983), respectively. They also agree very closely with those given in the Danish Code of Practice for Foundation Engineering (1978). The author indicates that the total and partial safety factors for geotechnical analyses 'are interrelated, and that the partial factors suggested for use in limit states design have been obtained by calibration with conventional geotechnical analyses. It is apparent from the paper that a constant value for the overall factor of safety is obtained only if the partial factor, f+ for example, varies with the value of the friction angle, 4'. ~ l t e r n a t i v e l ~ , if fm is held constant, then the overall factor of safety will not remain constant. The writer has examined the variation of the overall factor of safety for simple slopes, cantilevered rigid retaining walls, flexible sheet pile walls, and shallow foundations, designed to satisfy the ultimate limit states criterion using the author's recommended partial factors and the results are bgeflv outlined herein. The design of simple slopes using shear strength parameters in terms of total stress may be carried out using Taylor's stability charts (d, = 0 analysis). For this particular case the author recommends a partial factor, f, = 0.65, which is equivalent to an overall factor of safety, F, of 1.54 on cohesion or height, which compares closely to the overall factor of safety of 1.5 employed for the design of such slopes in conventional practice. The design of simple slopes with uniform soil and ground water conditions using an effective stress approach may be carried out using the Bishop and Morgenstern (1960) stability coefficients. The slope inclinations obtained using the limit states analyses show increasing overall factors of safety with increasing pore water presswes, from 1.25 with r, = 0 to about 1.8 for ru = 1.5. It is customary in conventional practice to select an overall factor of safety, F, which is dependent upon the loading conditions and the consequences of having a slope failure-occur. Highway, railway, cut, and embankment slopes tend to be designed using a lower overall factor of safety than would be employed for a slope where a structure is to be constructed near the top or base. The recommended limit states

Pile capacity for eccentric inclined load in clay

In connection with the design of offshore structures and bridge foundations, the ultimate bearing capacity of rigid piles and pile groups in clay has been determined under various combinations of eccentricity and inclination of the load varying from the vertical to horizontal directions. The results of load tests on single rigid model piles and freestanding groups are compared with theoretical estimates. The influence of eccentricity and inclination of the load on the ultimate bearing capacity can be represented by simple interaction relationships between the ultimate loads and moments and between the axial and normal components of the ultimate load. The effect of a pile cap resting on the soil in piled foundations and the influence of pile flexibility on the ultimate load are examined briefly. Key words: bearing capacity, clay, eccentric load, inclined load, pile groups, pile–soil interaction, rigid piles, ultimate load, ultimate moment.

Horizontal Response of Piles in Layered Soils

An inexpensive and realistic procedure is developed for estimating the lateral dynamic stiffness and damping of flexible piles embedded in arbitrarily layered soil deposits. Starting point is the determination of the pile deflection profile for a static force at the top using any reasonable method—beam‐on‐Winkler foundation, finite elements, well‐instrumented pile load tests in the field, etc. Material as well as radiation damping due to waves emanating at different depths from the pile‐soil interface are rationally taken into account; the overall equivalent damping at the top of the pile is then obtained as a function of frequency by means of a suitable energy relationship. The method is applied to study the dynamic behavior of three different piles embedded in two idealized and one actual layered soil deposit; the results of the method, obtained by hand computations, compare favorably with the results of three dimensional dynamic finite element analyses.

Static and dynamic lateral deflexion of piles in non-homogeneous soil stratum

The Paper presents the results of a systematic parametric investigation of the static and dynamic response of single free-head piles embedded in a soil stratum, the modulus of which increases linearly with depth. The study is conducted by means of a dynamic finite-element formulation which accounts for the three-dimensionality of soil deformation while properly reproducing the radiation damping characteristics of the system. The soil is modelled as a linear hysteretic continuum and the excitation consists of a sinusoidally time-varying horizontal force or moment, applied at the pile head. Comprehensive plots of the results are presented in non-dimensional form, for a wide range of the most significant dimension-less groups of problem parameters. For the response of flexible piles, in particular, simple algebraic expressions are developed in terms of the ratio Ep/Es, of the pile and soil moduli. These expressions, being valid for several values of Poisson's ratios of the soil, compare favourably with results from previous studies and are expected to be useful in practical design calculations. Cet article donne les résultats de recherches paramétriques systématiques sur la réponse statique et dynamique des pieux libres en tête encastrés dans une couche de sol dont le module s'accroît linéairement avec la profondeur. L'étude est basée sur une formulation d'éléments finis dynamiques qui tient compte de la nature tridimensionelle de la déformation du sol, en même temps qu'elle reproduit de façon correcte les caractéristiques d'amortissement du systéme. Le sol est modehsé comme un continuum avec hystérśsise linéaire et l'excitation consiste en une force horizontale qui varie de façon sinusoidale dans le temps appliquée en tête du pieu. Les résultats sont tracés de maniére compréhensive sous une forme non-dimensionnelle pour une grande variété des groupes les plus importants des paramétres sans dimensions caractérisant le probléme. Plus particuliérement pour la réponse des pieux flexibles des expressions simples algébriques sont présentées en fonction du rapport Ep/Es des modules du pieu et du sol. Ces expressions, qui sont valables pour plusieurs valeurs du coefficient de Poisson pour le sol sont supérieures à celles fournies par les etudes précédentes, et on s'attend à ce qu'elles soient utiles pour els calculs pratiques des projects de fondations.

Lateral Dynamic Response of Constrained‐Head Piles

This paper utilizes an efficient finite‐element formulation to study the dynamic response characteristics of single constrained‐head piles embed ded in a soil stratum whose modulus is proportional to depth from the surface. The excitation consists of a harmonic horizontal force or moment applied at the pile head, and the soil is modeled as a linear hysteretic medium. The results of a comprehensive parametric study are presented in the form of non‐dimensional graphs from which one can readily estimate static and dynamic stiff nesses and effective damping ratios of piles in many practical situations. For flexible piles, in particular, simple, yet sufficiently accurate, algebraic formulas are derived, valid for a wide range of problem parameters. Finally, the concept of an effective soil modulus is introduced to elucidate the importance of soil nonhomogeneity and to gain valuable insight to the mechanics of the problem.

Response of flexible piles to lateral loading : Randolph, M F Geotechnique, V31, N2, June 1981, P247–259

Response of flexible piles to lateral loading : Randolph, M F Geotechnique, V31, N2, June 1981, P247–259

Dynamic characteristics of lateral load-deflection relationships of flexible piles : Kagawa, T; Kraft, L M Earthq Engng Struct Dynam, V9, N1, Jan–Feb 1981, P53–68

Dynamic characteristics of lateral load-deflection relationships of flexible piles : Kagawa, T; Kraft, L M Earthq Engng Struct Dynam, V9, N1, Jan–Feb 1981, P53–68

The response of flexible piles to lateral loading

The majority of piles encountered in practice may be regarded as ‘flexible’ under lateral loading. That is, the induced deformations and bending moments are confined to the upper part of the pile and the overall length of the pile does not significantly affect the response of the pile. The results of a parametric study, conducted using the finite element method and treating the soil as an elastic continuum with a linearly varying soil modulus, are presented as simple algebraic expressions. These expressions are similar in form to those which arise from a Winkler idealization of the soil, enabling immediate estimates to be made of: the active length of the pile; the ground level deformations; and the maximum bending moment down the pile. In addition, expressions are presented quantifying the effect of interaction between neighbouring piles. from which the behaviour of groups of piles subjected to lateral loading may be deduced. Application of the solutions is demonstrated by the analysis of lateral loading tests on single piles and on groups of piles. On peut considérer la majorité des pieux rencontrés dans la pratique comme ‘flexibles’ dans des conditions de charge latérale. Les déformations induites et les moments de flexion sont restreints à la partie supérieure du pieu et la longueur globale du pieu n'a pas d'effet significatif sur la réponse de celui-ci. Les résultats d'une étude paramétrique faisant appelàla méthode des éléments finis et dans laquelle le sol est représenté par un continuum élastique dont le module est à variation linéaire, sont préentés sous forme d'expressions algébriques simples. Lcs expressions sont semblables du point de vue de la forme à celles obtenues à partir d'une idéalisation Winkler du sol, et permettent l'estimation immédiate: de la longueur active du pieu; des déformations au niveau du sol;et du moment de flexion maximum en bas du pieu. En outre, I'article présente des expressions permettant de quantifier l'effet de l'interaction entre pieux adjacents, et de déduire le comportement de groupes de pieux soumis à une charge latérale. L'application des solutions est démontrée par l'analyse d'essais de charge 1atérale sur des pieux uniques et sur des groupes de pieux.

Stresses in Soil around Vertical Compressible Piles

A method of analysing vertical stress by obtaining the side shear distribution using linear elastic theory. The influence of a pile's compressibility and L/d ratio on its stress distribution when mu equals 0.5 have been studied the difference between rigid and very flexible piles. The side shear distribution thus obtained for a given ratio is divided into uniform and linear variations and is finally summed up to get the net stresses. The double integration of the Mindlin's equation involved in this step-by-step procedure is solved partly analytically and partly numerically by computer, using Gauss Quadrature formulas. Although analysis is here confined to vertical stresses, other stresses could be evaluated with this method. Stress coefficient tables covering a wide range of stiffness factors from very flexible to very rigid are presented for selected ratios of pile length to pile depth and of radial distance to pile length.

Dynamic characteristics of lateral load‐deflection relationships of flexible piles

AbstractMost offshore platforms are supported on long and large‐diameter piles with variable wall‐thickness along the length, and soil properties varying with depth. The design and analyses of these piles are made by modelling the soil‐pile system with a beam‐on‐Winkler foundation. Therefore, evaluation of appropriate soil‐pile springs for use in such analyses is a matter of concern. Fundamental characteristics of dynamic lateral load‐deflection relationships for piles were studied analytically considering the soil‐pile‐structure interaction under seismic loading conditions. The soil layer was assumed homogeneous, linearly elastic with hysteretic type material damping, and overlying a rigid base. A superstructure with multi‐degrees of freedom was supported by a single vertical pile hinged at the rigid base.Parametric studies were carried out to identify the influence of the system parameters on the behaviour of the dynamic lateral load‐deflection relationships of piles. The lateral load‐deflection relationships vary considerably with depth and are influenced not only by the dynamic properties of soil but also by the structural properties of a pile and loading conditions. These lateral load‐deflection relationships can be used to define the soil‐pile springs for the seismic response analysis of a soil‐pile‐structure system, and the results can be extended to problems with soil profiles with layering and non‐linearity.

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.

The stability of slender piles during driving

It is known that slender driven or jacked piles, especially in soft soils, tend to wander away from their assumed lines of action during installation. Since the forces acting on a flexible pile are mainly of a non-conservative nature a dynamic analysis of directional stability of the pile during installation is performed. Two different types of instability are possible with different load configurations, the more important being the wholly non-conservative type known as flutter. Very simple assumptions are made about the loadings on the pile in this initial study, but the treatment is capable of extension to more realistic assumptions. Several examples of the stability limits for steel pile sections in cohesive soil are presented, and it is shown that, even allowing for the simplifying assumptions, directional instability can be a problem within the working ranges of many practical piles. On sait que les pieux battus légèrement ou les pieux enfoncés avec un vérin, spécialement dans des sols tendres, ont tendance à s'écarter de leurs lignes d'action présumées pendant l'installation. Puisque les forces agissant sur un pieu fléxible sont d'une nature principalement non-conservative, une analyse dynamique de la stabilité de direction du pieu pendant l'installation est réalisée. Deux genres différents d'instabilité sont possibles avec des conditions de chargement différentes, le plus important étant le genre entièrement non-conservatif connu comme agitation. Des hypothèses très simples sont faites au sujet des chargements sur le pieu, dans cette étude initiale, mais le traitement peut être étendu à des hypothèses plus réalistes. Plusieurs exemples des limites de stabilité pour des sections de pieu d'acier dans des sols cohérents sont présentés, et il est montré que, même avec les hypothèses simplificatrices, l'instabilité de direction peut être un probléme dans la gamme d'utilisation de nombreux pieux courants.

Three-dimensional analysis of flexible pile grillages

Three-dimensional analysis of flexible pile grillages

Model Pile Group Subjected to Cyclic Lateral Load

A 4-pile group of vertical, flexible piles embedded in dense sand was subjected to cyclic lateral load, with and without vertical load acting on cap. Conditions of free rotation and no rotation of the cap were imposed. A single pile was also tested. Effect of cyclic load on horizontal deflection, rotation of cap and moments induced in the piles has been investigated. The deflection, rotation and moment were observed to increase at a decreasing rate with cyclic loading. Cap restraint reduced the corresponding changes. Effect of vertical load was not of significance.

Behavior of Laterally Loaded Piles: I-Single Piles

An analysis is presented for the horizontal displacement and rotation of a vertical pile subjected to lateral loading and moment, and situated in an ideal elastic mass. Influence factors are presented for a wide range of pile flexibilities and length-to-diameter ratios, for both free-head and fixed-head piles. Comparisons between the elastic solutions and the corresponding solutions obtained from the subgrade reaction theory show that the latter considerably overestimates the displacement and rotation of the pile, but gives a reasonable estimate of the moments in the pile. The elastic analysis is extended to include the effect of local yield between the soil and the pile; the load-displacement relationship for relatively flexible piles is found to be markedly influenced by local yield. The characteristics of behavior indicated by the theoretical solutions agree reasonably well with those reported from measurements on full-scale piles.

Behavior of Laterally Loaded Piles: II-Pile Groups

An elastic analysis is presented for the horizontal displacement and rotation of a laterally loaded pile group and the distribution of horizontal forces within the group. The interaction between two identical equally loaded piles is analyzed first, and the increases in displacement and rotation of the piles, in relation to the single pile values, are expressed in terms of interaction factors. Using these interaction factors, a method for calculating the displacement and rotation of a general pile group, based on the principle of superposition, is described. An examination of the behavior of square groups of piles reveals that the displacement, rotation, and load distribution in the group is largely influenced by the length-to-diameter ratio of the piles and the relative pile flexibility. It is also found that the displacement depends on the breadth of the group rather than the number of piles in the group. A reasonable measure of agreement is found between a limited number of reported measurements and theoretical predictions of group displacements.

Analysis of the Settlement of Pile Groups

Synopsis An analysis is made of the settlement interaction between two identical piles in an elastic mass and the increase in settlement of each pile due to interaction is expressed in terms of an interaction factor α. It is then shown that, for symmetrical pile groups (those in which the piles settle equally and are also equally loaded), the increase in settlement due to interaction may be obtained by superposition of the values of α for the individual piles in the group. On the assumption that superposition also holds for any general free standing pile group, the behaviour of pile groups is analysed for the case of a rigid pile cap (equal settlement of all piles) and a flexible pile cap (equal load in all piles). For the case of a rigid pile cap, values are obtained for the ratio of the settlement of the group to the settlement of a single pile carrying the same total load (the group reduction factor R G ), and the load distribution within the group. For the case of a flexible pile cap, values of the maximum settlement and maximum differential settlement are given. The influence of pile spacing, pile length, type of group, depth of layer and Poisson's ratio of the layer on the settlement behaviour of pile groups is examined. For a pile group in an ideal elastic twophase soil, it is shown that, as with a single pile, the major proportion of the total final settlement generally occurs as immediate settlement. Comparisons are made between reported observations on the behaviour of pile groups from model and field tests and the behaviour predicted by the theory. It is found that, as well as predicting the correct trends, the theory gives quantitative values which are in reasonable agreement with the observed values. On fait d'abord une analyse de l'interaction de tassement entre deux pieux identiques dans une masse élastique et l'accroissement du tassement de chaque pieu dû à l'interaction est exprimé en fonc-tion d'un facteur d'interaction α. On montre en-suite que pour des groupes de pieux symetriques (ceux dans lesquels les pieux se tassent d'une facon egale et supportent aussi des charges égales), l'accroissement de tassement dû à l'interaction peut etre obtenu par une superposition des valeurs de α pour les pieux individuels du groupe. En supposant que la superposition vaut aussi pour n'importe quel groupe general de pieux se tenant librement, le comportement des groupes de pieux est analysé dans le cas d'une longrine rigide (tassement 6gal de tous les pieux) et d'une longrine flexible (charge égale supporté par tous les pieux). Dans le cas d'une longrine rigide, des valeurs sont obtenues pour le rapport du tassement du groupe au tassement d'un seul pieu supportant la meme charge totale (le facteur de reduction du groupe RG), et la repartition de la charge a l'interieur du groupe. Dans le cas d'une longrine flexible, on donne des valeurs du tassement maximum et du tassement différentiel maximum. L'influence de l'espacement des pieux, de la longueur des pieux, le type du groupe, la profon-deur de la couche et le coefficient de Poisson pour la couche sur le comportement de tassement des groupes de pieux est examiné. Pour un groupe de pieux dans un sol idéal élastique à deux stades, on montre que, comme dans le cas d'un seul pieu, la plus grande proportion du tassement final total a lieu généalement sous forme d'un tassement im-médiat. Des comparaisons sont faites entre les observations ayant fait l'objet de rapports sur le comportement de groupes de pieux é partir d'essais sur maquette et sur les lieux et le comportement prévu par la théorie. On s'aperçoit que, outre une prevision des tendances exactes, la the'orie donne des valeurs quantitatives qui s'accordent de façon raisonnable avec les valeurs observéers.

Molecular biophysics lectures

A selection of generalized impulse response functions is presented for a variety of rigid and flexible marine structures (i.e. mono-hull, SWATH, floating drydock and twin dock, fixed flexible pile). These functions are determined from calculated and experimental frequency-dependent hydrodynamic data, and the characteristics of these data depend on the type of structure considered. This information is reflected in the shape and duration of the generalized impulse response functions which are pre-requisites for a generalized integro-differential mathematical model describing the dynamic behaviour of the structures to seaway excitation.