A Nonlinear Analysis of a Soil Supported Frame

Abstract

Abstract A discrete element method for the nonlinear analysis of plane frames has been developed which considers nonlinear supports, material properties, and geometric effects. The associated computer program can analyze frames supported by battered piles which have axial and lateral restraints. The solution of a plane frame in an offshore drilling platform is presented and the nonlinear effects of supports, material properties, and changes in geometry are demonstrated. Introduction The analysis of offshore structures for the effects of gravity, wind and wave forces is one of the most complex problems facing the structural engineer today. A three-dimensional space frame is supported on piles which are driven into a non-homogeneous and highly nonlinear soil medium. The material from which the frame is constructed is nonlinear or at best bilinear. The change in geometry of the structure during loading causes additional nonlinearities. The dynamic and cyclic nature of the loading makes inelastic unloading of the frame material and soil important. The development of a closed-form or "exact" analysis for such frames does not seem likely in the foreseeable future. However advances in computer technology and matrix methods of structural analysis make possible the numerical solution of the problem using finite and discrete element techniques. As a step in the development of a complete analysis package, a static analysis of plane frames supported on nonlinear Winkler-type springs was developed which considers both material and geometric nonlinearities. The discrete element solution allows the entire structure, including the piles, to be solved internally in the computer and requires no costly and time consuming external iterations. Sources of Nonlinear Behavior A plane frame on batter piles such as might occur in an offshore structure is shown in Fig. 1. The solution of a single pile as a member in a non-homogeneous and nonlinear half space is such a complex and costly problem (Ref. 16) that it does not appear feasible to solve a complete frame supported by a number of such members. However, it was shown in Ref. 12 that the soils' restraint on the pile could be modeled using distributed nonlinear Winkler type springs. That is to say, the soil is assumed to be composed of independent layers in providing lateral and axial resistance to the movement of the pile. The properties of the springs are described by curves of distributed force (q) versus displacement (w) as shown in Fig. 1. These curves are almost always highly nonlinear, particularly for soft clays. Criteria for determining the lateral q-w curves for clays subjected to static and cyclic loads are available (Ref. 12). Criteria are also available for determining static nonlinear q-w curves for the axial response of clayey soils (Ref. 2) and the axial and lateral response of sandy soils (Ref. 15). Axial end-bearing forces Q are developed which are a function of the pile end displacement was shown in Fig. 1. Criteria for the development of such curves are available (Ref. 18).