Case 2 of the boundary conditions at the top of the pile is illustrated graphically in Fig. The prediction equations take on the general form of that used for clay, shown in Eq. The results of the comparisons in Chapter 7 show that bending moment with length along a pile can generally be computed more accurately than deflection. Of course, that assumption is seldom true. Introduction Derivation of the differential equation 2.
The nature of the loading, plus the kind of soil around the pile, are of major importance in predicting the response of a single pile or a group of piles. With respect to active loadings at the pile head, four types can be identified: short term or static, cyclic, sustained, and dynamic.
In single piles and pile groups under lateral loading pdf, passive loadings can occur along the length of a pile from moving soil, such as when a pile is used as an anchor. Another problem to be addressed is when existing piles are in single piles and pile groups under lateral loading pdf vicinity of pile driving or earth work.
Brief, general discussions are presented below of the pile response to the various loadings. Analyses are presented in later chapters to illustrate the influence of some of the kinds of loading. This case, called static loading for convenience, will seldom, if ever, be encountered in practice.
However, static curves are useful because 1 analytical procedures can be used to develop expressions to correlate. The curves in Fig. Several items are of interest: 1 the initial stiffness of the curves increases with depth; 2 the ultimate resis tance increases with depth; and 3 the scatter in the curves illustrates errors inherent in the process of analyzing numerical results from measurements of bending moment with depth. Points 1 and 2 demonstrate that analyses employing soil properties can be correlated with the experimental results, emphasizing the need to do static loading when performing tests of piles.
The shaded portion of Fig. For the case shown, the static and cyclic curves are identical through the initial straight-line portion to Point a and to a small distance into the nonlinear portion at Point c. With deflections larger than those for Point c, the values of p decrease sharply due to cyclic loading to a value at Point d. In some experiments, the value of p remained constant beyond Point d.
The loss of resistance shown by the shaded area is, for a given soil, plainly a function of the number of cycles of loading. As may be seen, for a constant value of deflection, the value ofEpy is lowered significantly even at relatively low strain levels, due to cyclic loading. A comparison of the curves in Figs.
As might be expected, at low magnitudes of deflection, the initial stiffnesses are only moderately affected. However, at large magnitudes of deflection, the p-values show considerable decreases. While the results of static loading of a pile may be correlated with soil properties, it is clear the results of cyclic loading will not easily yield to analysis.
Discussions in the following paragraphs will indicate the direction of some research. Of most importance are the. Formulations for taking cyclic loading into account will be presented in a later chapter where the methods are based on the available results of testing full-scale, fully instrumented piles. The cyclic loading of laterally loaded piles occurs with offshore structures, bridges, overhead signs, breasting and mooring dolphins, and other structures.
For stiff clays above the water table and for sands, the effect of cyclic loading is important, but for saturated clays below water, which includes soft clays, the loss of resistance in comparison to that from static loading can be considerable.
Experiments have shown that stiff clay remains pushed away near the ground surface when a pile deflects, online dating website builder as shown in Fig.
The re-application of a load causes water to be forced from the opening at a velocity related to the frequency of loading. Typically, as a result, scour of the clay occurs with an additional loss of lateral resistance.Mod-01 Lec-20 Tension and Lateral Loaded Piles
In the full-scale experiments with stiff clay that have been performed, the scour of the soil during cyclic loading is readily observed by clouds of suspension near the front and back faces of the pile Reese, et al.
The gapping around a pile is not as prominent in soft clay, probably because the clay is so weak to collapse when the loading is cycled. The clouds of suspension were not observed while testing piles in soft to medium clays, but single piles and pile groups under lateral loading pdf cycling caused a substantial loss in lateral resistance Matlock, As seen in Fig.
No failure of the soil has occurred because the resistance is transferred to. There will be an increase in the bending moment in the pile, of course, for a given value of lateral loading. The decreasing value of p implies the shifting of resistance to lower elements of soil.
The effect of sus tained loading is likely to be negligible for overconsolidated clays and for granular soils. Sustained loading of a pile in soft clay would likely result in a significant amount of time-related deflection.
Analytical solutions could be made using the three-dimensional theory of consolidation, but the formulation of the equations depends on a large num ber of parameters not clearly defined physically. The generalization of such a procedure is not yet available in the literature.
Single Piles and Pile Groups Under Lateral Loading (2nd ed.)
The influence of sustained loading, in some cases, can be solved with reasonable accuracy by experiment. At the site of the Pyramid Building in Memphis, Tennessee, a lateral-load was applied to a CFA pile with a diameter of mm in a silty clay with an average value of undrained shear strength over the top several diameters of the pile of 35 kPa Reuss, et al.
A load of 22 kN, corresponding approximately to the working load, was held for a period of 10 days, and deflection was measured. Some errors in the data occurred because the load was maintained by manual adjustment of the hydraulic pressure rather than by a servo-mechanism. At the Pyramid Building site, some thin strata of silt in the near-surface soils are believed to have promoted the dissipation of excess pore water pressure. With respect to dynamic loading, the greatest concern is that some event will cause liquefaction to brown and keri dating in the soil at the pile-supported structure.
It is important to know that liquefaction can occur in loose granular soil below the water table, although the presentation of liquefaction in this text will remain brief. Pile-supported structures can be subjected to dynamic loads from machines, traffic, ocean waves, and earthquakes Hadjian, et al. The frequency of loading from man finds of covenant and waves is usually low enough so that p-y curves for static or cyclic loading can be used.
Brief discussions are presented below about loadings from machinery and from earthquakes. In addition, some discussion is given to vibrations and perhaps permanent soil movement, as a result of the vibrations, due to installing piles in the vicinity of an existing pile-supported structure.
As noted earlier, soil resistance for static loadings can be related to the stress-strain characteristics of the soil; however, if the loading is dynamic, an inertia effect must be considered.
Not only are the stress-strain characteristics necessary for formulating p-y curves for dynamic loading, but the mass of the soil must be taken into account.
Use of the finite element method appears promising, but if the FEM has not proven completely successful for static loading, the application to the dynamic problem appears to be doubly complex.
Thus, unproven assumptions must be made if the p-y method is applied directly to solving dynamic problems. If the loading is due to rotating machinery, the deflection is usually small, and a value of soil modulus may be used for analysis.
Analytical techniques for solving for the response of a pile-supported structure have been presented by a number of writers. The free-field motion of the near surface soils at the site must be computed, or selected, taking micro zonation into account. A standard earthquake may be used with an unknown degree of approximation.
The response of the piles, neglecting the superstructure, must be considered. If the soil movement is constant with depth, the piles will move with the soil without bending. Such an assumption, if valid, simplified the computations. The distributed masses of the superstructure must be employed in solving for the motion of the piles and the motion of the superstructure. Of course, p-y curves must be available with appropriate modification of the inertia effects.
Not much experimental data is available on which to base a method of computation. In the absence of comprehensive information on the response with depth of pilesupported structures that either have failed or have withstood an earthquake single piles and pile groups under lateral loading pdf taking into account the enormous amount of computations that are needed, fully rational analyses are currently unavailable. Various simplifying assumptions are being used: 1 pseudo horizontal load and available p-y curves are sometimes employed as a means of simulating the effects of an earthquake.
If the assumption is made that the lateral soil movement during an earthquake is constant with depth, and if existing p-y curves or curves perhaps modified empirically for inertia effects are used, the movements single piles and pile groups under lateral loading pdf elements of the superstructure can be computed by equations of mechanics. Engineers are aware that the installation of piles near a pile-supported structure could lead to movements of the existing structure.WHAT IS THE EFFECTIVE RANGE OF RADIOCARBON DATING
If the site of construction is near, the loss of ground from installing bored piles or the heave from installing driven piles can be detrimental. If the pile driving is some distance away, information from the technical literature can be helpful Ramshaw et al. Prudent engi neers can establish measurement points on existing structures and have observations made as pile installation proceeds. In cases of sensitive machinery near new construc tion, the installation of transducers for measurement of time-related movements can be helpful.
A number of models have been used for the design of piles under lateral loading, and some of them can be used as supplements to the principal method proposed herein. The model shown in Fig. A similar model has been widely used.
Terzaghi suggested values of the so-called subgrade modulus that. The standard beam equation was employed in a manner that had been suggested earlier by such writers as Hetenyi Terzaghi stated that the tabulated values of subgrade modulus could not be used for lateral loads larger than the one that resulted in a soil resistance of one-half of the bearing capacity of the soil.
However, no recommendation was included in regard to the computation of the bearing capacity under lateral load, nor were any comparisons given between the results of computations and experiments. Solutions have been presented for a variety of cases of loading of single piles and for the interaction of piles with close spacings.
The solutions have gained considerable attention but cannot readily be used to compute the larger deformation or collapse of the pile in nonlinear soil. The differential equation presented by Terzaghi required the use of values of moduli with a different format than used herein, but conversion is easily made.
Values in terms of the format used in this text are presented in Chapter 3 for the benefit of the reader. The recommendations of Terzaghi have proved useful and provide evidence that Terzaghi had excellent insight into the single piles and pile groups under lateral loading pdf. However, in a private conversation with the senior writer, Terzaghi said that he had not been enthusiastic about writing.
The method illustrated by Fig. The method cannot be employed without some modification to solve for the loading at which yielding will develop in a pile. The case shown in Fig. No attempt is made in the sketch to indicate an appropriate size of the map, boundary constraints, special interface elements, favored shape and size of elements, or other details. The finite elements may be axially symmet ric with non-symmetric loading, or fully three dimensional. Additionally, the elements single piles and pile groups under lateral loading pdf be selected as linear or nonlinear.
In view of computational power that is available, the model shown in Fig. The elements can be fully three-dimensional and nonlinear, and nonlinear geometry can be employed. However, in addition to the problem of selecting the basic nonlinear element for the soils, some other challenges are coding to disregarding tensile stresses, modeling layered soils, accounting for the separation between pile and soil during repeated loading, coding for the collapse of sand against the back of a pile, and accounting for the changes in soil characteristics associated with the various types of loading.
All of these problems currently have no satisfactory solution. Thompson used a plane-stress model and obtained soilresponse curves that agreed well with results from full scale experiments near the ground surface. Womens singles final and Brown, et al. However, a finiteelement model likely will be developed that will lead to results that can be used in practice.
Broms a, b, employed the model shown in Fig. The pile is assumed to be rigid, and a solution that puts the pile in equilibrium is found by using the equations of statics for the distribution of ultimate resistance korean men online the soil that puts the pile in equilibrium.
The soil resistance shown hatched in the figure is for cohesive soil, and a solution was developed for cohesionless soil as well. After the ultimate loading is computed for a pile of particular dimensions, Broms suggests that the deflection for the working load may be computed by using the model shown in Fig.
The Broms method obviously makes use of several simplifying assumptions but can be useful for the initial selection of a pile. A summary of the Broms equations with examples is presented in Appendix A for the convenience of the user. The engineer may wish to implement the Broms equations at the start of a design if the pile has constant dimensions and if uniform characteristics can reasonably be selected for the soil.
Solution of the equations will yield the size and length of the pile for the expected loading. The pile can then be employed at the starting point for the p-y method of analysis. Further benefits from the Broms method are: 1 the mechanics of the problem of lateral loading is clarified, and 2 the method may be used as a check for some of the results from the p-y method of analysis.
It is of interest to note that the computer code for the p-y method of analysis, implemented in Appendix D, is so efficient that many trial solutions can how meet people with interests made in a short period of time.
An experienced engineer can use the computer model to "hone in" rapidly on a correct solution for a particular application without the limitations imposed by the Broms equations. Duncan et al.
A series of solutions were made with nonlinear p-y curves for a range of soils and for a range of pile-head conditions. The results were analyzed with the view of obtaining simple equations that could be used for rapid prediction of the response of piles under lateral loading. Dimensionless variables were employed in the prediction equations.
The authors state that the method can be used to solve for: 1 ground-line deflections due to lateral load for free-head conditions, fixed-head conditions, and the "flagpole" condition; 2 ground-line deflections due to moments applied at the ground line; 3 maximum moments for the three conditions in 1 ; and 4 the location of the point of maximum moment along the pile.
The soil may be either a clay or a sand, both limited to uniform strength with depth. The prediction equations take on the general form of that used for clay, shown in Eq. For a given problem of applied lateral load P tfor a pile in clay with a constant shear strength, a value of Pc is computed by the equation above. An equation similar to Eq. Also, equations and nonlinear curves were developed for computing the value of the maximum bending moment and where it occurs along the pile.
Duncan and his co-workers were ingenious in developing equations and curves that give useful solutions to a number of problems where piles must sustain lateral loads. The limitations in the method with respect to applications were noted by the authors. Endley et al. The Endley equations were designed to deal with piles that penetrated only a short distance into the ground surface as well as with long piles. Interest in the model shown in Fig.
About the same time offshore structures were built in the United States for military defense. Rutledge The relevant differential equations were dating website filipina by Timoshenko and by other writers. Hetenyi presented solutions for beams on a foundation with linear response.
InPalmer and Thompson presented a numerical solution to the nonlinear differential equation. Inthe American Society for Testing and Materials sponsored a conference on the lateral loading of piles, and papers by Gleser, and McCammon and Asherman notably emphasized full-scale testing. The offshore industry embarked on a program of full-scale testing of fully instru mented piles in the 's. Fortuitously, the digital computer became widely available about the same time, and as a result, full-scale testing and the digital computer allowed the development of the method emphasized in this document; contributions continue from engineers in many countries.
As a matter of historical interest, Terzaghi wrote "If the horizontal loading tests are made on flexible tubes or piles - values of soil resistance - can be estimated for any depth, if the tube or pile is equipped with fairly closely spaced strain gauges and if, in addition, provisions are made single piles and pile groups under lateral loading pdf measuring the deflections by means of an accurate deflectometer.
The strain-gauge readings determine the intensity and distribution of the bending moments over the deflected portion of the tube or the pile, and on the basis of the moment diagram the intensity and distribution of the horizontal loads can be ascertained by an analytical or graphic procedure.
Matlock and his associates devised an extremely accurate method of measuring the bending moments and formal procedures for interpreting the data. Two integrations of the bendingmoment data yielded accurate values of deflection, but special techniques were required for the two differentiations to yield adequate values of soil resistance. The result was the first set of comprehensive recommendations for predicting the response of a pile to lateral loading.
Terzaghi visited the test site while participating in the Eighth Texas Conference on Soil Mechanics and Foundation Engineering in and, in comments to Matlock and the senior author, single piles and pile groups under lateral loading pdf, appeared to be interested in the direction of the research. As shown in Fig. The horizontal lines across the pile are meant to show that it is made up of different sections; for example, steel pipe could be used with the wall thickness varied along the length.
Furthermore, the method of solution allows EpIp to be nonlinear and a function of the computed values of bending moment. For many solutions it is unnecessary to vary the bending stiffness, even though the loading is carried to a point where a plastic hinge is expected to develop. An axial load is indicated and is considered in the solution with respect to its effect on bending and not in regard to computing the required length to support a given axial load.
As shown later, the computational procedure allows to determine the rare case of the axial load at which the pile will buckle.
Single Piles and Pile Groups Under Lateral Loading
The soil around the pile is replaced by a set of mechanisms that merely indicate that the soil resistance p is a nonlinear function of pile deflection y.
The mechanisms, and the. As may be seen, the p-y curves are fully variable with respect to distance x along the pile and pile deflection y. There is no reasonable limit to the variations that can be employed to represent the soil response to the lateral deflection of a pile.
The p-y method is versatile and provides a practical means for design. The p-y method evolved principally from research sponsored by the petroleum indus try when faced with the design of pile-supported platforms subjected to exceptionally large horizontal forces from waves and wind.
Rules and recommendations for using the p-y method for the design of such piles are presented by the American Petroleum Institute and Det Norske Veritas The use of the method has been extended to the design of onshore foundations, as exemplified by publications of the Federal Highway Administration USA Reese The procedure is being cited broadly, for example by Jamiolkowski,Baguelin et al.
The method has been used with success for the design of piles; however, research is continuing and improvements, particularly in the characterization of a variety of special soils, are expected. Piles are most often used in groups as illustrated in Fig. The models that are used for the group of piles must address two problems: the efficiency of closely-spaced piles under lateral loading and axial loading ; and the distribution of the loading to each of the piles in the group, a problem in single piles and pile groups under lateral loading pdf.
The efficiency of a particular pile is defined as the ratio of the load that it can sustain in close spacing to the load that could have been sustained if the pile had been isolated. Because of the variability of soil and the complex nature of constitutive dating rules, theoretical solutions are currently unavailable for computing the efficiency of a particular pile.
Methods for finding the efficiency, both under lateral and axial loading, are based single piles and pile groups under lateral loading pdf the results of experiments, most of which are from the laboratory. In contrast, if one can assume that the procedures are accurate for analyzing a single pile under lateral loading and under axial loadingthe problem of the distribution of the loading for each of the piles in a group can be solved exactly.
A model for the solution of the problem in mechanics is shown in Fig. As may be seen in. Then, a local coordinate system is utilized for each of the piles with axial and lateral coordinates. Also shown in Fig. With these movements, the lateral and vertical movements and the rotation can be found at each pile head. The forces generated at the pile heads how to meet people with similar interests to put the structure into equilibrium.
Because of nonlinearity, iteration is required to find the unique movements of the global coordinate system. The model for the pile under lateral loading, already described, is used for finding the pile forces as a function of a lateral deflection and a pile-head rotation. As may be seen, nonlinear mechanisms are used to represent the soil resistance in skin friction and in end bearing as a function of axial movement. Also, the spring representing the stiffness of the pile can be nonlinear if necessary and desirable.
A more detailed description of the method of solving for the distribution of loading to piles in a group is presented in Chapter 5.ONLINE VIDEO SPEED DATING
As noted in the description presented above, all of the loading on the superstructure is assumed to be taken by the piles and none by the cap or raft supported by the piles. The problem of finding the distribution of axial load to the cap or raft and to the piles has been addressed by a number of authors.
Single piles and pile groups under lateral loading pdf the proposed solutions are limited to the foundation system response to axial loading, a brief introduction to the technology is warranted because extensions will likely occur to the general problem, where lateral loading is an important parameter. Those authors employed a two-layer system for the soil. Each of the layers was characterized by a shear modulus G and a Poisson's ratio v.
Using these parameters, equations were developed. The equations were solved to find the identical settlements for the elements of the system in order to obtain the distribution of load to the piles and to the cap. An important analytical difficulty was to assume a fixed radius for influence of distribution of stresses or distribution influence of stresses in the continuum to limit the magnitude of the computed settlements.
Results from the extended method were compared with experimental results from tests of an instrumented, full-sized, pilesupported bridge pier. Excellent agreement was found between computed and observed settlement, and good agreement was found between computed and observed loads to the elements of the system after an assumption was made about the distribution of the load due to the placement of concrete.
The results from the case studies suggest that benefits can be derived in extending the general method to the case of both axial and lateral loading. As presented in Appendix D, computer programs are readily available for solving the different equations, describing the behavior of a single pile and a group of piles, efficiently and in a user-friendly fashion.
The use of computer codes will be demon strated in Chapters 6 and 7; however, it is useful here to write briefly about the current state-of-the-art. The computer codes single piles and pile groups under lateral loading pdf the engineer to make solutions rapidly in order to investi gate the influence of a variety of parameters. Upper-bound and lower-bound solutions can be done with relative ease. Guidance can be obtained in most cases with how to meet ukrainian women to the desirability of performing additional tests of the soil or performing a full-scale, lateral-load test at the site.
The principal advances in computational procedures in the future relate to p-y curves. Better information is needed for piles in rock of all kinds, in soils with both cohesion and a friction angle, and in silts. For piles in closely-spaced groups, relevant informa tion is needed on pile-soil-pile interaction. In spite of these limitations, the technology presented herein is believed to represent a signal advance in engineering practice with respect to previously available methods.
The two tests represented by the figures were performed in identical soils. Hint: You can assume a theory has been developed to predict the amount of scour of an overconsolidated clay as a function of time and the velocity of water flow. The equation for the beam-column must be solved for implementation of the p-y method, and a derivation is shown in this chapter. An abbreviated version of the equation is shown and can be solved by a closed-form method for some purposes, but a general solution can only be made by a numerical procedure.
Both of these kinds of solution are presented. An example problem is worked to show the relevance of this case to practical applications. The solution with the linearly increasing reaction is also help ful in demonstrating the nature of the nonlinear method of analysis, and the method can be used in checking computer solutions that are presented later.
In most instances, the axial load on a laterally loaded pile has relatively small or little influence on bending moment. However, there are occasions when it is desirable to find the buckling load for a pile; thus, the axial load is needed in the derivation. The derivation for the differential equation for the beam-column on a foundation was given byHetenyi The assumption is made that a bar on an elastic foundation is subjected to horizontal loading and a pair of compressive forces Px acting in the center of gravity of the end cross-sections of the bar.
If an infinitely small unloaded element, bounded by two horizontals a distance dx apart, is cut out of this bar see Fig. Differentiating Eq. And making the indicated substitutions, Eq. The shearing force in the plane normal to the deflection line can be obtained as 2. Thus, Eq. Vn will mostly be used in computations, but Vv can be computed from Eq. The ability to allow a distributed force W per unit of length along the upper portion of a pile is convenient in solving a number of older women prefer younger men problems.
The differential equation then is given by Eq. Other beam formulas that are needed in analyzing piles under lateral loads are: 2. Except for the axial load P xthe sign conventions are the same as those usually employed in the mechanics for beams, with the axis for the pile rotated 90 clockwise from the beam axis. The axial load Px does not normally appear in the equations for beams. The sign conventions are presented graphically in Fig, single piles and pile groups under lateral loading pdf.
A solution of the differential equation yields a set of curves such as shown in Fig. The mathematical relationships for the various curves that give the response of the pile are shown in the figure for the case where no axial load is applied. The assumptions that are made when deriving the differential equation are as follows.
The pile is straight and has a uniform cross section, The pile has a longitudinal plane of symmetry; loads and reactions lie in that plane, The pile material is homogeneous and isotropic, The proportional limit of the pile material is not exceeded, The modulus of elasticity of the pile material is the same in tension and compression, Transverse deflections of the pile are small, The pile is not subjected to dynamic loading, and Deflections due to shearing stresses are small.
Assumption 8 can be addressed by including more terms in the differential equation, but errors associated with the omission of these terms are usually small. The numerical. A simpler form of the differential equation results from Eq. The first two assumptions can be satisfied in many practical cases; however, the last of the three assumptions is seldom, if ever, satisfied in practice. The solution shown in this section is presented for two important reasons: 1 the resulting equations demonstrate several factors that are common to any solution; thus.
If the assumptions shown above and the identity shown in Eq. If one considers a long pile, a simple set of equations can be derived.
An examination of Eq. The boundary conditions for the top of the pile that are employed for the reduced form solution of the differential equation are shown by the simple sketches in Fig. A more complete discussion of boundary conditions is presented in the next section.
The boundary conditions at the top of the long pile that are selected for the first case are illustrated in Fig. It is convenient to define some functions for simplifying the written form of the above equations: 2.
For a long pile whose head is fixed against rotation, as shown in Fig. Table 2. Using the procedures as for the first set of boundary conditions, the results are as follows: 2. These boundary conditions are given in Eqs. The solution for any length of pile L can be obtained by using the following boundary conditions at the tip of the pile: at x.
When the above boundary conditions are fulfilled, along with a set for the top of the pile, the four coefficients ,2,3, and X4 can be evaluated.
The solutions are not shown here, but Appendix B includes a set of tables that were derived for the case shown in Fig. In order to demonstrate the effect of length on the response of a pile to lateral loading, Table 2. Referring to Eq. Only selected values in the table were printed to conserve space, and an expanded version of the table shows that points of zero deflection occur at nondimensional lengths close to 1.
The deflection of the piles below those lengths would oscillate between positive and negative values, with the deflections being extremely small. By comparing the values in Appendix B with those in Table 2. The influence of the length of a pile on the groundline deflection is illustrated in Fig. Computations are made with constant loading and constant pile cross section, as well as with an initial length that will be in the longpile range. The computations proceed with the length being reduced in increments; the groundline deflection is plotted as a function of the selected length, as shown in Fig.
The figure shows that the groundline deflection is unaffected until the critical length is approached. At this single piles and pile groups under lateral loading pdf, only one point of zero deflection will occur in the computations. There will be a significant increase in the groundline deflection as the best paid dating websites in the solution is made less than the critical.
The engineer can select a length that will give an appropriate factor of safety against excessive groundline deflection. The accuracy of the solution will depend, of course, on how well the soil-response curves reflect the actual situation in the field. The reduced form of the differential equation will not normally be used for the solution of problems encountered in design; however, the influence of pile length, pile stiffness, and other parameters is illustrated with clarity.
The formulation of the differential equation in numerical terms and a solution. The resulting equations form the basis for a computer program that is essential in practice. The effect of the axial load on deflection and bending moment will be considered, and problems of pile buckling can be solved. The bending stiffness EpIp of the pile can be varied along the length of the pile. And perhaps of more importance, the soil reaction Epy can vary with pile deflection and with distance along the pile.
The concept of the soil reaction will be discussed fully in a later section, as the introduction here is presented in a generic sense. If the pile is subdivided in increments of length h, as shown in Fig. The assumption is implicit in Eq. Of course, that assumption is seldom true.
However, experience has shown that the maximum bending moment usually occurs a relatively short distance below the groundline at a point where the value of Px is virtually undiminished. The value of P xexcept in cases of buckling, has little influence on the magnitudes of deflection and bending moment, and leads to the conclusion that the assumption of a constant Px is generally valid.
If two equations giving boundary conditions are written at the bottom. The set of algebraic equations can be solved by single piles and pile groups under lateral loading pdf methods in any convenient way.
The two boundary conditions that are employed at the bottom of the pile are based on the moment and the shear. If the existence of an eccentric axial load that causes a moment at the bottom of the pile is discounted, the moment at the bottom of the pile is zero.
The assumption of a zero moment is believed to produce no error in all cases except for short rigid piles that carry their loads in end bearing. The case where there is a moment at the pile tip is unusual and is not treated by the procedure presented herein.
Thus, one of the boundary equations at the pile tip is 2. The second boundary condition at the bottom of the pile involves the shear. The assumption is made that soil resistance due to shearing stress can develop at the bottom of a short pile as deflection occurs. It is further assumed that information can be developed that will allow Vo, the shear at the bottom of the pile, to be known as a function of yo. Thus, the second equation for the boundary conditions at the bottom of the pile is.
The value of Vo should be set equal to zero for long piles with two or more points of zero single piles and pile groups under lateral loading pdf. As presented earlier, two boundary equations are needed at the top of the pile. Equations have been derived for four sets of boundary conditions, each with two equations.
The engineer can select the set that best fits the physical problem. Case 1 of the boundary conditions at the top of the pile is illustrated graphically in Fig. The axial load Px is not shown in the sketches, but Px is assumed to be acting for each of the four cases of boundary conditions at the top of the pile.
For the condition where the shear at the top of the pile is equal to P i5 and Rt is the bending stiffness at the top of the pile, the following difference equation is employed. For the condition where the moment at the top of the pile is equal to M i5 the following difference equation is employed. Case 2 of the boundary conditions at the top of the pile is illustrated graphically in Fig. Add to Wishlist Add to Wishlist. The complexities of best dating sites for polyamorous couples piles for lateral loads are manifold as there are many forces that are critical to the design of big structures such as bridges, offshore and waterfront structures and retaining walls.
The loads on structures should be supported either horizontally or laterally or in both directions and most structures have in common t. More Business.
Blueprint to a Billion David G. Exclusive web offer for individuals on all book. Preview this Book. Reese, William F. Add to Wish List.
Close Preview. Toggle navigation Additional Book Information. Summary The complexities of designing piles for lateral loads are manifold as there are many forces that are critical to the design of big structures such as bridges, offshore and waterfront structures and retaining walls.
Van Impe has been an emeritus professor since March but remains active as a consultant and as manager of AGE bvba. He has been also a full professor at the Catholic University of Louvain in Belgium.
His main field of experience is deep foundations, ground improvement and soil parameter analysis, currently dealing mostly with crushable soils. Request an e-inspection copy. Share this Title.