Download Citation on ResearchGate | On Jan 1, , Lc Reese and others published Single Piles and Pile Groups Under Lateral Loading. Single Piles and Pile Groups. Under Lateral Loading. 2nd Edition. Lymon C. Reese. Academic Chair Emeritus. Department of Civil Engineering. The University. Single Piles and Pile Groups under Lateral Loading by Lymon C. Reese and William F. Van Impe. , Balkema, div. of Taylor & Francis Publishers, p.
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Reese, Lymon C._ Van Impe, William-Single Piles and Pile Groups Under Lateral Loading (2nd Edition)-Taylor _ Francis () - Ebook download as PDF File. Single Piles and Pile Groups Under Lateral Loading - Ebook download as PDF File .pdf) or read book online. Single Piles and Pile Groups Under Lateral. Single Piles and Pile Groups Under Lateral Loading. FULL ACCESS. Full Access : DownloadPDF MB Read online. The complexities of.
The piles were instrumented for measurement of bending moment at close spacing along the length and were tested in overconsolidated clay. Because the computed bending moment is affected only slightly by variations in the value of EpJp. Brief discussions are presented below about loadings from machinery and from earthquakes. Models f o r r e s p o n s e of soil and w e a k r o c k 75 coefficients up to the point where the computed soil resistance was equal to about one-half of the ultimate bearing stress. The problems of characterizing the soil at a test site. Soil mechanics and structural mechanics were used to develop methods of predicting p-y curves for various soils that yielded excellent agreement with the response of the piles. In obtaining a value of of.
The gapping around a pile is not as prominent in soft clay. As seen in Fig. In the full-scale experiments with stiff clay that have been performed. The clouds of suspension were not observed while testing piles in soft to medium clays. The cyclic loading of laterally loaded piles occurs with offshore structures.
For stiff clays above the water table and for sands. No failure of the soil has occurred because the resistance is transferred to. 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. Experiments have shown that stiff clay remains pushed away near the ground surface when a pile deflects. The re-application of a load causes water to be forced from the opening at a velocity related to the frequency of loading.
It is important to know that liquefaction can occur in loose granular soil below the water table. A load of 22 kN. Pile-supported structures can be subjected to dynamic loads from machines. Not only are the stress-strain characteristics necessary for formulating p-y curves for dynamic loading. Use of the finite element method appears promising.
As noted earlier. At the Pyramid Building site. There will be an increase in the bending moment in the pile. Brief discussions are presented below about loadings from machinery and from earthquakes. The influence of sustained loading. The frequency of loading from traffic and waves is usually low enough so that p-y curves for static or cyclic loading can be used.
Sustained loading of a pile in soft clay would likely result in a significant amount of time-related deflection. The generalization of such a procedure is not yet available in the literature. At the site of the Pyramid Building in Memphis. Analytical solutions could be made using the three-dimensional theory of consolidation.
Some errors in the data occurred because the load was maintained by manual adjustment of the hydraulic pressure rather than by a servo-mechanism. The decreasing value of p implies the shifting of resistance to lower elements of soil. Analytical techniques for solving for the response of a pile-supported structure have been presented by a number of writers.
Such an assumption. Not much experimental data is available on which to base a method of computation. The response of the piles. If the loading is a result of a seismic event. A standard earthquake may be used with an unknown degree of approximation.
If the site of construction is near. If the soil movement is constant with depth. T e c h n i q u e s f o r design II If the loading is due to rotating machinery. In the absence of comprehensive information on the response with depth of pilesupported structures that either have failed or have withstood an earthquake and taking into account the enormous amount of computations that are needed.
The distributed masses of the superstructure must be employed in solving for the motion of the piles and the motion of the superstructure. A similar model has been widely used. Terzaghi suggested values of the so-called subgrade modulus that. If the pile driving is some distance away. The free-field motion of the near surface soils at the site must be computed. Various simplifying assumptions are being used: Of course.
Engineers are aware that the installation of piles near a pile-supported structure could lead to movements of the existing structure. If the assumption is made that the lateral soil movement during an earthquake is constant with depth. 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 problem.
The differential equation presented by Terzaghi required the use of values of moduli with a different format than used herein. The solutions have gained considerable attention but cannot readily be used to compute the larger deformation or collapse of the pile in nonlinear soil.
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. The standard beam equation was employed in a manner that had been suggested earlier by such writers as Hetenyi Terzaghi said that he had not been enthusiastic about writing.
Solutions have been presented for a variety of cases of loading of single piles and for the interaction of piles with close spacings. In view of computational power that is available.
Thompson used a plane-stress model and obtained soilresponse curves that agreed well with results from full scale experiments near the ground surface. The method cannot be employed without some modification to solve for the loading at which yielding will develop in a pile.
The soil resistance shown hatched in the figure is for cohesive soil. No attempt is made in the sketch to indicate an appropriate size of the map. The elements can be fully three-dimensional and nonlinear. After the ultimate loading is computed for a pile of particular dimensions. The pile is assumed to be rigid. Research is continuing with three-dimensional.
The method illustrated by Fig. Techniques for design 13 the paper and only did so in response to numerous requests. All of these problems currently have no satisfactory solution.
Kooijman and Brown. Broms suggests that the deflection for the working load may be computed by using the model shown in Fig. 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 soil may be either a clay or a sand. Dimensionless variables were employed in the prediction equations. The prediction equations take on the general form of that used for clay.
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. For a given problem of applied lateral load P t. Further benefits from the Broms method are: It is of interest to note that the computer code for the p-y method of analysis. The pile can then be employed at the starting point for the p-y method of analysis.
An equation similar to Eq. Solution of the equations will yield the size and length of the pile for the expected loading. 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. The authors state that the method can be used to solve for: 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.
A summary of the Broms equations with examples is presented in Appendix A for the convenience of the user. Rutledge About the same time offshore structures were built in the United States for military defense. Palmer and Thompson presented a numerical solution to the nonlinear differential equation. The limitations in the method with respect to applications were noted by the authors.
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. Endley et al. The relevant differential equations were stated by Timoshenko and by other writers. Hetenyi presented solutions for beams on a foundation with linear response. In 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 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. Terzaghi wrote "If the horizontal loading tests are made on flexible tubes or piles. Terzaghi visited the test site while participating in the Eighth Texas Conference on Soil Mechanics and Foundation Engineering in and.
The difference-equation method presented in detail in Chapter 2. Matlock and his associates devised an extremely accurate method of measuring the bending moments and formal procedures for interpreting the data. As shown in Fig. For many solutions it is unnecessary to vary the bending stiffness. As shown later. 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.
The horizontal lines across the pile are meant to show that it is made up of different sections. The result was the first set of comprehensive recommendations for predicting the response of a pile to lateral loading. The strain-gauge readings determine the intensity and distribution of the bending moments over the deflected portion of the tube or the pile. The mechanisms. Two integrations of the bendingmoment data yielded accurate values of deflection. As a matter of historical interest.
The p-y method is versatile and provides a practical means for design. The models that are used for the group of piles must address two problems: July A model for the solution of the problem in mechanics is shown in Fig. Two developments during the 's made the method possible: The method has been used with success for the design of piles.
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.
At the Foundation Engineering Congress. Techniques for design 17 corresponding curves that represent their behavior. Methods for finding the efficiency. Baguelin et al. 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 procedure is being cited broadly.
As may be seen in. Because of the variability of soil and the complex nature of constitutive models. 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.
In contrast. While the proposed solutions are limited to the foundation system response to axial loading. Also shown in Fig.
The model for the pile under lateral loading. With these movements. Each of the layers was characterized by a shear modulus G and a Poisson's ratio v. The forces generated at the pile heads serve to put the structure into equilibrium.
Because of nonlinearity. 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. As noted in the description presented above. A more detailed description of the method of solving for the distribution of loading to piles in a group is presented in Chapter 5. Using these parameters. Those authors employed a two-layer system for the soil.
Excellent agreement was found between computed and observed settlement. Upper-bound and lower-bound solutions can be done with relative ease. 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.
For piles in closely-spaced groups. 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. 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. Results from the extended method were compared with experimental results from tests of an instrumented.
In spite of these limitations. Guidance can be obtained in most cases with respect to the desirability of performing additional tests of the soil or performing a full-scale. 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. 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.
Techniques for design 21 cyclic case is great. The two tests represented by the figures were performed in identical soils. 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. An abbreviated version of the equation is shown and can be solved by a closed-form method for some purposes.
An example problem is worked to show the relevance of this case to practical applications. If an infinitely small unloaded element. Both of these kinds of solution are presented.
Differentiating Eq. And making the indicated substitutions. The shearing force in the plane normal to the deflection line can be obtained as 2. The sign conventions are presented graphically in Fig. Assumption 8 can be addressed by including more terms in the differential equation.
The pile material is homogeneous and isotropic. The pile has a longitudinal plane of symmetry. 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 numerical. The modulus of elasticity of the pile material is the same in tension and compression. Transverse deflections of the pile are small. The differential equation then is given by Eq. A solution of the differential equation yields a set of curves such as shown in Fig. 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 practical problems.
Other beam formulas that are needed in analyzing piles under lateral loads are: Except for the axial load P x. The pile is not subjected to dynamic loading. The axial load Px does not normally appear in the equations for beams. The proportional limit of the pile material is not exceeded. The pile is straight and has a uniform cross section.
The first two assumptions can be satisfied in many practical cases. All of the responses of the pile and soil are shown in the positive sense: The solution shown in this section is presented for two important reasons: An examination of Eq. The boundary conditions at the top of the long pile that are selected for the first case are illustrated in Fig.
A more complete discussion of boundary conditions is presented in the next section. If the assumptions shown above and the identity shown in 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. If one considers a long pile. For a long pile whose head is fixed against rotation.
These boundary conditions are given in Eqs. Table 2. V is zero at pile tip 2. New values of the parameters Ai. Referring to Eq. The solution for any length of pile L can be obtained by using the following boundary conditions at the tip of the pile: The solutions are not shown here. For convenience in writing. In order to demonstrate the effect of length on the response of a pile to lateral loading. The deflection of the piles below those lengths would oscillate between positive and negative values.
By comparing the values in Appendix B with those in Table 2. Only selected values in the table were printed to conserve space. Computations are made with constant loading and constant pile cross section. The reduced form of the differential equation will not normally be used for the solution of problems encountered in design. The figure shows that the groundline deflection is unaffected until the critical length is approached.
The computations proceed with the length being reduced in increments. The accuracy of the solution will depend. The influence of the length of a pile on the groundline deflection is illustrated in Fig.
There will be a significant increase in the groundline deflection as the length in the solution is made less than the critical. The formulation of the differential equation in numerical terms and a solution. At this length. The engineer can select a length that will give an appropriate factor of safety against excessive groundline deflection.
The value of P x. And perhaps of more importance. If two equations giving boundary conditions are written at the bottom. If the pile is divided into n increments. If the pile is subdivided in increments of length h. The concept of the soil reaction will be discussed fully in a later section. The assumption is implicit in Eq. The bending stiffness EpIp of the pile can be varied along the length of the pile. The resulting equations form the basis for a computer program that is essential in practice.
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. Equations have been derived for four sets of boundary conditions. As presented earlier. The second boundary condition at the bottom of the pile involves the shear. The engineer can select the set that best fits the physical problem. 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 case where there is a moment at the pile tip is unusual and is not treated by the procedure presented herein. The axial load Px is not shown in the sketches. The set of algebraic equations can be solved by matrix methods in any convenient way. The assumption is made that soil resistance due to shearing stress can develop at the bottom of a short pile as deflection occurs.
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. It is further assumed that information can be developed that will allow Vo. The value of Vo should be set equal to zero for long piles with two or more points of zero deflection. The second of the two equations reflects the condition that the slope St at the top of the pile is known.
In many cases. The pile is assumed to be embedded in a concrete foundation for which the rotation is known. For the condition where the moment at the top of the pile is equal to M i5 the following difference equation is employed. If the embedment is small. One or two iterations should be sufficient in most instances.
The two equations needed at the pile head for Case 4 are Eqs. A moment is applied to the frame at that joint. An initial solution may be necessary in order to obtain an estimate of the moment at the bottom joint of the superstructure.
The solution for the problem can proceed by cutting a free body at the bottom joint of the frame. The boundary condition has proved to be very useful in some designs. The pile is assumed to continue into the superstructure and become a member of a frame. The moment divided by the rotation.
The pile is assumed to be embedded in a bridge abutment that moves laterally for a given amount. The pile. The Case 4 equations can be employed with a few values of Mt being selected along with the given value of yt. Figure 2. This analysis cannot be treated as an eigenvalue problem.
The computer output will yield values of Pt. A simple plot will yield the required value of Mt that will produce the given boundary condition Pt. The factor of safety against buckling is found by holding Pt constant and incrementing Px.
The application of the finite-difference-equation technique to the solution of the axial load at which a pile will buckle is illustrated in Fig.
For example. As shown in Fig 2. The application of the solution will be presented in later chapters. The bending stiffness Epip. The discussion will deal with the number of significant figures to be used in the internal computations and with the selection of increment length h.
The formulation shown in Appendix C has not been incorporated into a computer program for distribution. Another approximation is related to the variation in the bending stiffness. Iteration is required to achieve a solution to reflect the nonlinear response of the soil with pile deflection. Because of the obvious approximations that are inherent in the difference-equation method.
The remainder of this chapter will 1 The reaction modulus for the soil is referenced to the ground surface by the symbol z. The computer program to solve the finite-difference equations for the response of a pile to lateral loading will be demonstrated in a subsequent chapter. The equations become unstable at axial loads beyond the critical. The solutions of a number of example problems will be presented. The coding for the equations shown above is implemented in the computer program presented in Appendix D that solves the different equations.
The errors that are involved in using the approximation where there is a change in the bending stiffness along the length of a pile are thought to be small.
A derivation has been made for the case where there is an abrupt change in flexural stiffness and is shown in Appendix C. The origin for the case discussed here must be the same for the top of the pile and the ground surface. It is convenient to introduce some characteristic length as a substitute. D e r i v a t i o n of e q u a t i o n s and m e t h o d s of s o l u t i o n 39 show the use of the finite-difference-equation technique to produce nondimensional tables or curves that facilitate hand computations.
The principles of dimensional analysis may be used to establish the form of nondimensional relations for the laterally loaded pile. A linear dimension T is therefore included in the quantities to be considered.
For very long piles. With the use of model theory. The specific definition of T will vary with the form of the function for soil reaction versus depth.
T expresses a relation between the stiffness of the soil and the flexural stiffness of the pile and is called the "relative stiffness factor. Nondimensional tables were presented that show with relevance the nature of the pile problem and that allow for checking finite-difference-equation solutions.
A solution of the reduced form of the differential equation was presented earlier for the case where Epy is constant piles in heavily overconsolidated soils. Dimensional analysis.
Cohesionless soil and normally consolidated clay are two cases where the stiffness is zero at the groundline and increases rather linearly with depth.
The derivatives yield values of slope. The arrangements chosen are. If the assumption of linear behavior is introduced for the pile. If yA represents the deflection caused by the lateral load Pt and if ys is the deflection caused by the moment M i5 the total deflection is 2.
There are therefore four independent nondimensional groups which can be formed. In each case there are six terms and two dimensions force and length. The solutions may be expressed for Case A as 2. Zn Soil reaction function. These are shown below. Depth coefficient. From beam theory. The parameter T is still an undefined. The selected form of the soil reaction with depth should be kept as simple as possible so that a minimum number of constants needs to be adjusted.
In solving problems of laterally loaded piles by using nondimensional methods. It is convenient to select a definition that will simplify the corresponding nondimensional functions. The resulting A and B coefficients may then be used. A general form of Epy with depth is a power form. From the theory given above. The relative stiffness factor T can be defined for any particular form of the soil reaction-depth relationship.
The common equations are: The nondimensional coefficients. The coefficients are shown as a function of the nondimensional depth Z and the nondimensional length of the pile Zmax. The soil resistance p is equal to Epy times y. The following equation shows the rotational restraint that is used in the example that follows.
The slope rotation at the top of the pile can be found from the following equation. In the example solution. With these values of the nondimensional coefficients for slope. The equation for deflection is: If the pile head is fixed against rotation in one case and free to rotate in another case. Article 5. If the engineer could achieve a particular pile-head restraint.
For the case where there is a rotational restraint kg at the top of the pile. The distance below the mudline to each of the curves is shown. A jacket or template. One of the legs of the jacket is shown in Fig. The curves are typical of those for sand or normally-consolidated clay. Loading may be considered to arise from wave action during a storm.
The portion of the pile above the mudline and within the jacket is shown in the upper sketch in Fig. A pile is driven after spacers are welded inside the jacket leg to ensure contacts between the pile and the jacket. While the curves are for no particular soil. The p-y curves to be used are shown in Fig. At this stage of the analysis. The assumption is made that no restriction exists on the deflection of the pile. Examination of the relevant equations show that there are two unknowns that must be solved by iteration.
With the pile passing beyond the upper panel point in the sketch. The EpIp is The steel has a yield strength of A more comprehensive approach to achieving a given factor of safety will be discussed in Chapter 9.
The ultimate load can then be factored to achieve a safe load.
The pile is a steel pipe with an outside diameter of mm. After selecting the value of T. The computations for this case. The second trial could have been done with a T of 3. A value of Mt of —1. The referenced equations. The computations with this expression are shown in the Table 2. The value of Pt selected for the initial computations is kN. A value of T equal to about 5 pile diameters 4 m is selected for the first trial. The values of Epy are plotted in Fig. Using that value.
The value of T is related to the loading. In using the curves in the appendix. As shown for Trial 1. The dashed line in the figure passes through 6. A straight line can be used to connect the plotted points. It is unlikely that the line connecting the two plotted points is straight but the assumption is satisfactory for this method. The relative stiffness factor T was computed to be 6.
The maximum bending moment occurred at the pile head and was — m-kN. The point for the second trial plots across the equality line.
The Zmax for this value of T is 8. With values of P i5 M i5 and T. The computed values of deflection and bending moment can now be found by following the procedure indicated for the Pt of kN computed for the relevant equations. The plots are shown in Fig. These trials. With the value of T of 3. In continuing with the assigned problem. The nonlinear response of the pile to lateral load can be surmised by examining the p-y curves.
Using the nondimensional curves for Zmax of The computed negative moment at that point is more than twice the maximum positive moment that occurs at depths of about 8 m for the Pt of kN and about 12 m for the Pt of kN. A convenient rule-of-thumb is that a "long" pile is one where there are at least two points of zero deflection along its length. The point is made. A soil failure is not possible except for a short pile under lateral loading where the value of T would be 2 or less.
An increase in the lateral load from to kN. For one thing. For another. In this particular case. The limitations in the solutions shown above are: The recommendations for the prediction of p-y curves for use in the analysis of piles. For the long pile shown in the example computations.
The nondimensional length of the pile in the example decreased from Another interesting point is that the plastic hinge will develop at the top of the pile. An examination of the curves in Fig. These restrictions are removed with the computer code. Thus a larger lateral load could have been sustained had the distance between the spacers in the jacket been increased above 6.
Several comments can be given in response to the valid criticism of the method. Show the error in the solution you obtain. The methods of predicting p-y curves have been used in a number of case studies. Matlock performed some tests of a pile in soft clay where the pattern of pile deflection was varied along the length of the pile by restraining the pile head in one test and allowing it to rotate in another test.
Study the example p-y curves shown in Figure 2. The analytical solution that is presented herein can be readily modified to deal with the multi-valued p-y curves. How would the solution to the problem of the analysis of a pile as one leg of an offshore platform be changed if the space between the pile had been grouted instead of the use of spacers at the panel points?
Explain when you think the engineer might want to use the "hand-solution" presented in the example. Explain why a numerical solution to the problem of pile buckling. In such a case. The p-y curves that were derived from each of the loading conditions were essentially the same. Chapter 1 demonstrated the concept of the p-y method. The resulting curves are intended to reflect as well as possible the deflection and the bending moment as a function of pile depth under lateral loading.
A number of fundamental concepts are presented that are relevant to any method of analyzing piles. For a given soil profile. Case studies presented in Chapter 7 compare experimental and computational results for a range of soils and landing.
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. Among the concepts presented in Chapter 1 was the principle that the soil-reaction modulus is not a soil parameter. Chapter 3 Models for response of soil and w e a k rock 3. In spite of the complexities noted above. More than in any other deep foundation problem. This chapter will provide recommendations for selecting a family of p-y curves for various cases of soils and loadings.
In making some computation. Returning to a discussion of Fig. A series of such tests for each of the strata that are encountered will provide data on the strength of soil for use in design. Laboratory tests are usually complemented with in situ tests in the field. The specimen is initially subjected to an all-around stress as where as is selected to reflect properties at a particular point in the continuum.
The correspondence of. The next section of the chapter presents a detailed discussion of the relevance of soil parameters and shows that any solution of a problem requires a thorough discussion of the soil profile. An appropriate cylindrical specimen is presumed to have been obtained and tested to represent the properties of the soil at a particular point in the continuum where an analysis is to be performed.
The slope of the lines. Finding the applicable properties of soil in the laboratory to direct the solution of a particular problem requires attention to numerous details: Loading is assumed to continue in increments until the resulting curve of principal stress versus strain becomes asymptotic to a line parallel to the strain axis. In the general discussion that follows and in specific recommendations at the end of this chapter.
A more detailed discussion is presented here. Careful measurements of lateral strain must be made. While the values of the properties as shown in Fig. The parameters that. The values of E s m a x of sand and normally consolidated clay are zero at the ground line and increase in some fashion with depth. As will be demonstrated by examples and case studies in later chapters. The variation of the maximum tangent shear modulus with depth z and related to the zero deflection of the pile has been proposed as shown below.
The computation of the deflection under the working load would. In most designs. The deflection of the pile where the initial portion of the p-y curves would be effective would occur at a considerable distance below the ground line. These high values are for extremely small strains. Rock is frequently a brittle. Employing the concepts emphasized herein. Models f o r r e s p o n s e of soil and w e a k r o c k 57 govern the stiffness of near-surface soils have been investigated extensively during the past two decades.
Two cases can be identified: For cohesive soils.. Elementary solutions. Stokoe reported that values of 2. In these investigations. There are some cases. As may be seen in Fig. Observed values probably would have been reported as much higher had very careful attention been given to the early part of the laboratory curves.
Of particular significance are the works of C. As a means of establishing the parameters that must be evaluated in employing linear-elastic concepts in finding equations for the slope values of the initial portions of p-y curves. Analytical methods. Some serious mistakes were made during early years in the analysis of piles under lateral loading when engineers failed to heed Terzaghi's warning that the ultimate resistance against a pile could not exceed one-half the bearing capacity of soil.
Theoretical considerations. In the absence of more rational methods for computing a limiting value of the ultimate. The equation pertains to vertical loading. These data suggest that the value of z must reflect the location of the ground surface. The following equation is from the theory of elasticity Skempton. When the load was removed. The simplicity of the model is obvious.
The first of the models is shown in Fig.. The contours show the heave of the ground surface in front of a steel-pipe pile with a diameter of mm in over-consolidated clay Reese. If three-dimensional constitutive relationships become available for all soils and rocks.
With a lateral load of kN. Integration of Fp with respect to the depth z below the ground surface will yield an expression for the ultimate resistance along the pile. The force Fp may be computed by integrating the horizontal components of the resistances on the sliding surfaces. The p-y curves that were derived from the loading test are shown in Fig.
One can reason that. Soil movement will cause Block 4 to fail by shearing. The assumption is made that the movement of the pile will cause a failure of Block 5 by shearing. Block 3 to slide.
The second model. Figure 3.
Two assumptions are made: The introduction of drainage of clays into the analysis. Partially saturated clays can change in water content with time. Cohesive soil. The Mohr-Coulomb diagrams shown in Fig.
Four of the blocks are assumed to fail by shear and that resistance due to sliding is assumed to occur on both sides of Block 3. Equations for forces on the sliding surfaces in Fig.
His results are shown in Fig. The value. Plots are shown for the case where KC is assumed equal to zero or equal to 1. The value of KC can be set to zero with some logic for the case of cyclic loading because one can reason that the relative movement between pile and soil would be small under repeated loads.
With these assumptions. Cohesionless soil. For most granular soils. Hansen considered the roughness of the pile wall. The ultimate soil resistance near the ground surface per unit length of the pile is obtained by finding the total force against an upper portion of the pile and by differentiating the results with respect to z.
The two models presented earlier are employed by following a similar procedure to that used for clay. In practice. Thompson noted that Hansen a. The recommended methods of computing the p-y curves for clays are presented later in this chapter. Other work. He suggested that the influence of the unit weight be neglected. Full drainage is assumed in the analyses that follow. Equations 3. Solving for the intersection between Eqs. Soil-resistance curves for the depths shown in those figures have a dominant effect on the response of a pile to lateral loading.
At the outset in the discussion of subgrade modulus. If a concentrated vertical load is applied to the plate at the central point. As can be understood.
If increasingly larger loads are applied. If a plate with dimensions larger or smaller than given by m and n is employed in the same soil. If the states of stress shown in Fig. The assumption is based on two-dimensional behavior. The effect of the ground surface is revealed for all of the curves that were shown. A line is drawn in Fig. From the work of Baldi. The maximum value of the subgrade modulus would be obtained from a line drawn through the initial portion of the curve.
While the reasoning in the development of Eq. A simple equation can be developed to obtain a value of the modulus for the analaysis of displacement piles. More recent research on in situ testing has revealed the possibility of obtaining the subgrade modulus from Menard pressuremeter tests Y.
The tabulated values of subgrade modulus shown in some publications must refer to the maximum values or an average value. Resources to the following titles can be found at www.
What are VitalSource eBooks? For Instructors Request Inspection Copy. 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.
The loads on structures should be supported either horizontally or laterally or in both directions and most structures have in common that they are founded on piles. To create solid foundations, the pile designer is driven towards finding the critical load on a certain structure, either by causing overload or by causing too much lateral deflection.
It addresses the analysis of piles of varying stiffness installed into soils with a variety of characteristics, accounting for the axial load at the top of the pile and for the rotational restraint of the pile head. The presented method using load-transfer functions is currently applied in practice by thousands of engineering offices in the world.
Moreover, various experimental case design examples, including the design of an offshore platform pile foundation are given to complement theory. The rich list of relevant publications will serve the user into further reading.
We provide complimentary e-inspection copies of primary textbooks to instructors considering our books for course adoption. CPD consists of any educational activity which helps to maintain and develop knowledge, problem-solving, and technical skills with the aim to provide better health care through higher standards. It could be through conference attendance, group discussion or directed reading to name just a few examples. We provide a free online form to document your learning and a certificate for your records.
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