SOIL-STRUCTURE INTERACTION IN FRAMES

Abstract

INTRODUCTION Frame structures are commonly used in the construction of buildings and industrial structures. The conventional practice considers the isolated behaviour of structures during their analysis and design. In reality, however, supporting soil-foundation system alters the behaviour of super structure and hence the need for considering the mutual interaction. STATEMENT OF PROBLEM Review of literature indicated that considerable investigation has been carried out into interaction of frame structures with combined-footings, rafts and piles. However, investigation into the interaction of frames with individual column-footings and with raft pile system was very meagre. The problem of frame structure, supported by individual column footings and soil mass was, therefore, taken up for investigation. VI AIM The aim of this investigation was to propose suitable method/methods for interactive analysis of frame-footingsoil system so as to estimate the total and differential settlements and the extent to which the superstructure behaviour is altered by the supporting soil mass so that the frame and footings could be properly designed. ANALYSIS The method of analysis should be such as to - i) Consider frame-footings and soil mass as an integral compatible unit and ii) Consider the relative stiffness between structure and footings and that between footings and soil mass. With these two points in view, three different methods have been attempted and proposed for analysis. All the three methods consider thewhole system as behaving in a linear elastic fashion. 1. Spring-Analogy Method i) The method consists in replacing the soil footing system below an individual footing by equivalent elastic springs corresponding to every degree of free dom of the structure i.e. three for a plane frame and six for a space frame. Vll ii) The basic spring constants involved in case of plane frames are K, f, the horizontal spring constant (kg/cm), K -, the vertical spring constant (kg/cm) and Lf, the rotational spring constant(kg-cm/rad). An additional spring constant K f, the torsional spring constant (kg-cm/rad) comes into play in case • of space frames. iii) Methodology has been proposed and expressions derived for evaluating the four spring constants. The expre ssions take into account the effect of size of foo ting and the confining pressure. iv) Having evaluated these spring constants, it is possi ble to include them directly into the diagonal stiff nesses of columns corresponding to the degrees of freedom at base joint. v) The plane and the space frame could be analysed by releasing the individual column bases in every bay, in turn, and then using the method of superposition. 2. Iterative Method i) The method consists of analysing the plane/space frames by the matrix displacement method assuming the Vlll base fixity condition. This analysis yields the displacements and rotations of all the joints of the frame, its member end actions and reactions at the base. ii) These reactions, with their directions reversed, are considered as forces acting on footing resting on soil mass. Each individual column-footing is then analysed by three dimensional finite element method and the deformations (translations as well as rota tions) of the footing are computed. iii) The deformations of the footings are fed back as initial boundary displacements for the re-analysis of the superstructure. This re-analysis gives a new set of reactions at the column bases. iv) The re-analysis of footings and superstructure is carried out alternately till the difference in defor mations of the footings in two successive iterations is negligible. v) The net deformations and forces for both the frame and footings are computed by superposition. Carrying out such iterative analysis is an indirect way of accounting for the relative stiffness between IX structure and footings and that between footings and soil mass. 3. Three Dimensional Finite Element Analysis This is by far the most generalised formulation for the interactive analysis of frame-footing-soil system. The superstructure components i.e. beams and columns are discretised into twelve noded isoparametric brick elements with parabolic displacement variation in 5 direction (always along the axis of the member) and linear variation of displacements along n and % directions (in crosssectional plane of member). The column-footing, which due to the forces and moments acting on it, is subjected to biaxial bending, is descretised into group of eight, twelve and sixteen noded isoparametric brick elements. The sixteen noded brick element has parabolic variation of displacements in £ and C directions (in the plane of the footing) and linear variation in n direction. This element accounts for biaxial bending. The supporting soil mass is also discretised into a group of eight and sixteen noded elements. Such a combination of twelve, eight and sixteen noded elements gives a harmonious blending of elements and because the degree of freedom per node for any element is three(i.e. translations, in X, Y and Z directions), the whole system is compatible. In order to reduce the size of the mesh,the number of simultaneous equations involved, the concept of symmetry and antisymmetry of loading was used for all the cases of unsymmetrical loads. The elastic soil constants, namely E and v were experimentally determined on basis of s s triaxial tests performed on samples of soil at site. Solution of the equation system yields displacements, strains and stresses. The results of symmetrical and unsymmetrical load cases were superposed to get the net results. EXPERIMENTAL VERIFICATION In order to have experimental verification of theo retical results, interactive experimental testing was carried out on single storey, single bay plane and space frames, fabricated out of mild steel square bar sections. Square mild steel footing plates were welded to the columns of the frame. The frames along with their footings were installed on the ground with footings embedded below the ground surface. Variable point load was applied on the top beam of the frames through a loading assembly and the settle ments of the footings, sway of frame and strains at various points of the frame measured. Five tests on plane frame with five different load positions and four tests on space frame with four load positions, were conducted. XI RESULTS Results of analysis of plane and space frames are com pared with each other and with test results. It has been observed on basis of the study that - i. For the same load acting on the frame, the total and differential settlements for the frames increase with increase in value of eccentricity of load i.e. with the shift in the load position. This also means a corresponding increase in sway and joint rotations. ii. For the same load, increasing the eccentricity of load increases the settlement of the right footing and simultaneously reduces that of the left footing thereby aggravating the differential settlement. iii. The values of shear forces and bending moments obtai ned on basis of independent analysis are always higher than those obtained via interactive analysis. iv. The values of total and differential settlements observed in case of space frame are lesser compared to those for the plane frame. This is because all other conditions remaining the same, the stiffness of the space frame is always higher than that of plane frame. Xll v. Results obtained by Iterative Method are comparable to those obtained by spring analogy method with spring constants evaluated on basis of triaxial test data. VI. Three dimensional finite element approach gives the best possible physical representation of the problem. However, the efforts required in data pre paration and the computational time are large. Spring Analogy Method with spring constants evalua ted on basis of laboratory triaxial test data seems better suitable as the efforts required in data preparation and the computational time are both negligible.