THREE DIMENSIONAL ANALYSIS OF FOUNDATIONS WITH DEFECTIVE PILES

Abstract

Pile foundations often consist of a group of vertical and batter piles and are subjected to a combination of vertical and lateral forces. The placement of piles in the group and the nature of loads make the foundation behaviour three dimensional. Further, it is a common experience that one or more piles in a group may get constructed with defects. Defects introduce structural weakness in the pile resulting in inferior support points and redistribution of loads among other piles in the group. This makes the behaviour ofeven symmetrically placed and loaded pile groups three dimensional. Literature reports various kinds of defects that may get formed in the construction of piles and foundation failures induced by defective piles. Presently, tools like low strain integrity testing are available for diagnosing defects in piles. The technology is now available to assess reliably well the location and extent of the defective portion in a pile. The integrity test is conducted after the piles have been constructed and before the cap is cast. Once the defect is identified, a rational approach would be to re-evaluate the possible performance of the foundation as it exists and design a remedial measure accordingly, if found necessary. However, the common prevailing practice is to install additional piles to take care of the function of the defective ones. This practice has obviously been prompted by the lack of analytical tools for a rational evaluation of the problem. Though some efforts towards analytical evaluation of the behaviour of groups with defective piles in some simple situations have been reported, an appropriate procedure which can account for the three dimensional nature of the problem and the most commonly occurring pile-soil situations is still lacking. The present work is an attempt to fill this gap. The response of a pile group is the sum total of the response of individual piles. As such, estimation of response of single pile is an essential pre-requisite for the analysis of a group. The piles in the group are subjected to axial compressive load, lateral load and moment, and axial uplift load. The piles may be of varying cross-section along the length like step-tapered piles and may traverse through layers of soil having different geotechnical properties. Further, one or more piles in the group may be defective. Considering these pile-soil situations (including that of defective piles), appropriate procedures to evaluate the single pile response under various kinds of loads have been first established. The single pile response obtained from these analyses are then incorporated in a three dimensional group analysis to obtain pile cap displacements, and forces and displacements of individual piles of the group. As the present work was prompted due to the problem of occurrence of defects in piles, the types of defects formed and their causes are described (Chapter 2). The principles of low strain integrity testing are discussed and the technique of obtaining information from such a test regarding the following aspects of a defect is outlined : (i) The type of defect and its location in the pile shaft. (ii) Quantitative estimate of the defect, i.e., its length, width/diameter, concrete quality etc. Results of integrity testing reported in the literature show that reliable information can be obtained on the defect. First, estimation of pile response (load-settlement behaviour) to axial compressive loading is considered (Chapter 3). The available methods can be grouped into three major categories, viz., elastic continuum method, finite element method and load transfer method. Ofthese, the load transfer approach is found to provide the requisite flexibility to account for the pile-soil situations considered in the present work. Accordingly, the load transfer approach has been adopted and appropriately modified for the purpose. The method works by dividing the pile into a number of segments, which may be assigned different geometrical and material properties. This enables modelling of piles of various shapes and of different materials. Also, variation in pile cross-section as in step-tapered pile or in the case ofdefective pile can be accommodated. The soil response along the pile shaft and at the pile base are described by load transfer curves, obtained analytically from a few pile-soil parameters that can be reliably estimated. A computer program LOADSET has been developed to carry out the analysis. Some numerical examples depicting typical pile-soil situations have been solved using the program and the results are presented in the form of load-settlement curves to : (1) bring out the capability of the procedure to handle situations like layered soil deposits, piles ofvarying cross-sections, free standing lengths, etc., and (ii) study the effect of defects like necking of pile shaft and debris at the pile base on the load-settlement behaviour. To obtain the pile response to lateral loads, subgrade reaction approach has been adopted (Chapter 4). The finite difference technique which allows discretization of pile-soil system into closely spaced nodal points is used. This enables assigning varying pile and soil stiffness properties along the length of the pile. The differential equation governing the deflection ofthe pile is written at every nodal point using the finite difference operators, and the resulting set of simultaneous equations are solved. The solution in the form of pile deflection at the nodal points are obtained, and value of slope, moment and shear force at the nodal points are determined using the relevant finite difference operators. The procedure has been implemented in a computer program LATPILE. Results obtained for typical pile-soil situations are presented to bring out: (i) the correctness of the formulation and program developed by comparing with the results obtained from some of the existing analytical solutions applicable to simple pile-soil situations, (ii) sensitivity of the pile response to the soil modulus values near the pile head, (iii) effect ofpossible changes in ground conditions on the pile response, and (iv) effect ofthe magnitude and location ofthe defect (in the pile) on pile head deflection and structural integrity of the pile. Piles in a group may experience uplift under the action of large lateral loads. A review of the literature reveals that the methods available for the evaluation ofpile response under uplift loads are only a few, and do not provide the flexibility required to account for the pile-soil situations considered in the present work. Hence, a procedure is suggested to obtain load-displacement response under uplift loading using the load transfer approach (Chapter 5). The resistance to uplift loading is only through shaft resistance. The literature suggests that the shaft resistance mobilized under uplift is less than that under compressive loading. The database on this aspect is appropriately incorporated in the procedure and a program ( LOADRISE ) developed. Using the program, numerical solutions have been obtained for some typical problems and the following points have been iv brought out: (i) The procedure is capable oftackling situations considered in the estimation ofpile response under compressive and lateral loading. (n) The elastic extension of the pile shaft could constitute a major portion of the total upward displacement. Therefore, neglecting this elastic extension in the estimation ofmobilized shaft resistance as in the case ofprocedures proposed by certain investigators could lead to significant deviation in the predicted pile response from the actual. The response ofindividual piles including that ofdefective piles estimated as described above are appropriately integrated in a group analysis procedure (Chapter 6). The procedure is based on principles of matrix analysis of structures and has been appropriately modified to solve the present problem. The method allows for three dimensional loading of the foundation, and can handle pile groups having non-regular geometry, e.g. unequal spacings of piles, piles with batter of varying degrees and in different directions, piles having unequal lengths and unsymmetrical cross-sections, one or more piles in the group being defective etc. The procedure has been implemented in a computer program PILEGROUP. The program has been used to solve a few typical problems ofpile foundations and the results show that: (i) Provision of batter piles in apile group is found to be effective in reducing large lateral displacements experienced by foundations under the action of lateral forces. However, if the batter piles are not located at appropriate positions in the group, it may lead to large variations in the forces experienced by the piles, with the possibility of some of them getting excessively loaded. (ii) Presence of a defective pile in a group leads to increase in foundation displacements and redistribution of forces among the piles in the group. The extent to which a defective pile affects the group response depends upon the position of the defective pile in the group. When the defective pile is centrally located, the increase in forces in the defect free piles is often only marginal and within the acceptable limits of design. In such cases, the foundation performance remains satisfactory, and no remedial measure need to be taken. If, however, the defective pile is located in a corner position, the load redistribution is such that some piles get excessively loaded, beyond the designed load carrying capacity. In such cases, additional piles may be required to make the performance of the foundation satisfactory. Thus, a three dimensional analysis of pile group which can account for some of the most commonly occurring pile-soil situations and the presence of defective piles has been developed. The modelling ofthe pile-soil system is simple and straightforward. The procedure models the soil response in terms of a few fundamental geotechnical parameters that can be reliably estimated from routine laboratory/field tests and/or suitably selected from available database. The analysis provides a rational procedure to evaluate the response of a foundation with defective piles so that appropriate remedial measures can be designed. VI