Wang - Analysis of Large Group of Piles Under Axial and Lateral Loading
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Analys is of Large Group of Pile s Under Axial And Lateral Loading Shin-Tower Wang, M., ASCE, Luis Gonzalo Vasquez, and Lymon C. Reese, H. Mem., ASCE Ensoft, Inc., 3003 West Howard Lane, Austin, Texas 78728, PH (512) 244-6464; FAX: (512) 244-6067; email: [email protected]Abstract Analytical solutions have recently been developed for analyzing the behavior of piles in a group subjected to loading in three-dimensional space. The piles may be installed vertically or on a batter and their heads may be fixed, pinned, or elastically restrained by a rig id pile cap. The several components of the analytical method have been coded an d iteration is used to accommodate the nonlinear re sponse of the soil aroun d each pile in a group. With availability ofa rational and convenient tool, the engineer may consider several alternatives in a design, including pile spacing, batter angle, and type of pile. This paper presents an example of use of the analytical tool to study the behavior of a large group of piles. Introduction The ability to analyze a pile group under gener alized loading has advanced significantly in recent year s. Computer codes are available that allow the problem to be modeled with considerable precision. The individual piles may be analyzed for axial loading by the t-zmethod and under lateral loading by thep-ymethod, used internationally and long rec ognize d as ef fec tive met hods. All owance can be ma de for clos e spa cing of the individual pil es. Compatibility can be achieved between movement of the heads of the individual piles and the movement of the pile cap. Iteration is required to accommodate the nonlinear nature of the s oil and the pile material. The complex mecha nic s is pre sented for the problem of a gro up of pile s subjec ted to gen era lized three- dimens ional loa ding that inclu des the response of a pile when subje cte d to tor que . The equa tion s are far too compl ex for hand computatio ns, but the importanc e of variables , such as soil stren gth, can easily be investigate d. Comparisons are presented where the analytical results from use of computer codes are compared with results from experiments, where some of the piles are installed on a batter. Analytical solution using the personal computer was developed to compute the distribution of loads (vertical, latera l, and overtur ning moment) fr om the pile cap to indiv idual piles in the group. The piles may be installe d vertically or on a batter and their heads may be fixed, pinned, or elastically restrained by the pile cap. The cap may settle, translate, and rotate and is assumed to act as a rigid body. The software will generate internally the nonlinear response of the soil, in the form oft-zand q-wcurves for axial loading, t-rcurves for torsional loading, and p-ycurves for lateral loading. A solution requires iteration to accommodate the nonlinear respons e of each of the piles. The equations of equilibrium are satisfied, and compatibility is achieved between pile movement and soil response, and between the movement of the cap and the pile-head movement. Software, based on the technology noted above, is capable of analyzing a group of 500 or more piles where the response of each pile is unique. A pushover analy sis can be perfo rmed, considering the nonlinear response of the soil, where the failure of one or more of the piles is reflected in excessive movement or excessive bending moment. The program allows the engineer to investigate in a timely manner the comparative responses of groups with diff ering condit ions, such as the effect of the use of batter piles and the effe ct of varying the spacing. The code provides the engineering community an analytical tool that deals with the solution of a practical problem, frequently encountered in practice. Methods of Analysis of Three-Dimensional Group of Piles Figure 1 shows a pile cap su pported by three piles each battered in three directions. The global coordinate system is shown by X, Y, and Z, where X and Z def ine the plane of the top of the cap (Rees e and O’Neill 1967). The loadings at the origin of global coordinate system are shown by three components of force and three components of moment. Assumed movements at the origin of the global coordinate system in the X, Y, and Z directions, along with a set of
Wang - Analysis of Large Group of Piles Under Axial and Lateral Loading
