NON-LINEAR SOIL-STRUCTURE INTERACTION IN FRAMED STRUCTURES

Abstract

INTRODUCTION The interaction between structures, their foundations and the subsoil covers a broad and a complex area of research in structural and geotechnical engineering. The term 'soi1-structure-interaction' has been largely used for the mechanics of interaction between the foundation, the soil and the superstructure. The conventional design procedure involves the assumption of the fixity at the base of the foundation and therefore neglects the flexibility of the foundation and the compressibility of the subsoil. In order to account for both these aspects, it is essential to consider the structure, foundation and the soil as one integral compatible unit. If this entire system is analysed, it yields a different behaviour of the structure as the shear forces and bending moments are significantly altered due to the resulting differential settlements and angular distortion of the foundation, which in turn depend upon the constitutive relationship of the soil mass. LITERATURE REVIEW In the present study, interaction of plane and space frame structures supported respectively by soi1-combined footing or soil-raft systems are considered for analysis. Grasshoff (1957), Soulier (1965), Lee (1970), Seetharamulu and Kumar (1973) have represented combined footing as a beam on Winkler medium. Brown (1975) used the elastic half space approach for the physical representation of subsoil. Jain et.al.(1977) proposed an economical iterative procedure for space frames and thereby found significant reduction in differential settlements iv and consequent additional moments. Haddadin (1971) suggested substructure approach for taking into account the relative stiffness between soil and the founda tion and that between foundation and the superstructure.This approach was also adopted by Lee and Brown (1972). Hain and Lee (1974)in the interactive analysis of frame structure-combined footing-soil system idealised soil as a Winkler and a half space models. It was found that the stiffness of the structure has a profound influence on the distribution of the loads and moments in the raft.King and Chandrasekaran (1974), King (1977), King and Yao (1983) and Sankaran and Srinivasaraghavan (1979, 1983) were among the few researchers who made use of the finite element method to consider superstructure-raft/co • bined footing-soil as a single compatible unit. The soil was represented as a linear elastic half space. Nayak et.a 1.(1985) and Brown and Yu (1986), carried out interactive analysis of both plane and space frames-considering the effect of sequence of construction as a loading pattern . The Winkler model was used to represent the deformation characteris tics of the soil. PROBLEM IDENTIFICATION On the basis of the above brief review of the literature, it is found that : I) Soil mass has been idealised as a Winkler medium In the discrete model and as a linear elastic half space in the continuum model. Eitherway, the constitutive relationship Is linear and was assumed to be in the elastic range. The Winkler model assumes that the foundation deforms only at the point of application of the load whereas in reality, the foundation deforms in a continuous manner. The assumption of soil as a linear elastic half space limits the scope of the analysis. ii) The other aspect of modelling includes the physical modelling. The earlier models proposed are the ones with all the finite elements. This increases the actual number of elements and therefore the computational time and effort. There is a scope for using infinite elements and improve upon the earlier models. In view of the above two major aspects -it was decided to study the interaction of plane and space frames subjected to static loading with the following objectives : a) To improve upon the physical modelling of the problem by suitably developing elements for structural members, founda tion and the soil mass and also those for taking into account interface characteristics between soil and the foundation. b) To improve upon the constitutive modelling by taking into account - * the nonlinear elastic behaviour of soil * the elasto - plastic behaviour of soil and c) The parametric study for considering the effect of varying slab and raft stiffnesses on the redistribution of forces and moments. vi PRESENT WORK I. Physical Modelling (a) Plane Frame-combined Footing-soil System A three noded isoparametric beam bending element with three degrees of freedom per node,which accounts for the effect of transverse shear deformations and axial-f1exural interaction has been formulated to represent the members of super structure and the foundation beam. The interface characteristics between the soil and the foundation are considered by using a specially developed three noded interface element which is compatible with the beam element, with 3 D.O.F./node of the foundation and the soil element, with 2 D.O.F./node. The supporting soil medium has been modelled by coupled finite-infinite elements having 1/r and 1/-/F decay patterns. The applicability of such a multi-element model has been proved by analysing a plane frame-combined footing-soil system (Viladkar,Godbole, Noorzaei,1990, 1991). (b) Space Frame-Raft-Soil System The three noded beam bending element which was formulated to represent the members of the plane frame was further extended to represent beams and columns of the space frame with six degrees of freedom per node. The raft and structural slabs have been modelled via eight noded isoparametric plate bending element with five degrees of freedom per node. vii Various types of new three dimensional isoparametric infinite elements have been developed to account for the far field behaviour of the soil (Viladkar, Godbo1e,Noorzaei,1990) with both 1/r and 1/Vr decay patterns. These infinite elements have been coupled to conventional three dimensional isoparametric brick elements to represent the soil media. All the above elements are used to model space frame-raftsoil system. (Godbole, Viladkar,Noorzaei, 1991 and Noorzaei, Viladkar, Godbole, 1991). II. Constitutive Modelling The constitutive law of the material plays a major role in deciding the entire behaviour of the structure-foundation-soil system. In the present work, the structural material whose strength/stiffness is usually much higher than that of the soil,is assumed to be linear elastic while the constitutive law for the soil has been considered as - (a) Nonlinear elastic and (b) Elasto-plastic with and without strain hardening. Based on the review of various nonlinear-elastic models, the hyperbolic model (Kondner and Zelasko,1963, Duncan and Chang, 1970) was found to be more attractive to fit the stress-strain response of the soil. This is due to its simplicity in : i) the implementation in any finite element program, ii) due to ease in the determination of the hyperbolic constants and iii) wide range of its applicability. viii Furthermore, It is also essentia I to ensure th e realistic stress-strain behaviour of soil upto its failure (collapse). Therefore, an attempt has been made in this study to employ the various el asto-plastic models of soil. Nayak, and Zienkiewicz, (1972) introduced a generalized procedure for the elasto-plastic analysis alongwith an approach for the calculation of elasto-plastic CD] matrix by converting ep some conventional yield criteria into convenient forms. Based on this approach, various isotropic yield criteria of soils have been converted in the present study,into convenient forms. These include : i) Mohr-Coulomb criterion ii) Drucker-Prager- I iii) Drucker-Prager -II iv) Drucker-Prager- III v) Compromise cone model vi) Axial Extension model vii) Extended Von-Mises model viii) Eekelen 3-D model ix) Critical state Model 1 x) Critical state Model -II xi) Lade and Duncan Single parameter model xii) Lade Double Parameter model xi ii)Cap Model xiv) Desai's Modified Cap Model xv) Desai's Generalised model ix Depending upon the types of soils under consideration, any of the above yield criteria can be employed for the elasto-plastic analysis. Here, the elasto-plastic interactive analysis of a plane frame-combined footing-soil system (two-dimensional problem) has been carried out using the yield criteria i) to vii) above. III. A Modified Frontal Solver with Multi-element and Multidegrees of Freedom Features The physical modelling of both the plane and the space frames alongwith their soi1-foundation system consists of a variety of elements with varying degrees of freedom for different elements . There was therefore a dire need for a solver to deal with the system of the linear simultaneous equations arising from the multi-element pattern of discretization. In the present work, the frontal solver presented by Hinton and Owen (1977) has therefore been further modified into multi-element and variable degrees of freedom features (Godbole, Viladkar, Noorzaei, 1991) and has successfully been used for the interactive analysis of both plane and the space frames. IV. Finite Element Packages With the tremendous advancement in the finite element software as a commercial item, It is possible to purchase any standard finite element package and use it as a black box. However, this would not serve the objective of the research investigator as for e.g. in the present study, new elements have been developed, new yield criteria for soils have been employed and a totally new solver has been developed. Three types of finite element packages have been developed during the course of this study : (i) Two dimensional nonlinear finite element program I2DFEA] (II) Three dimensional nonlinear finite element program C3DFEAJ (iii)Two-dimensional elasto-plastic finite element program CELPLAI All these packages are having multi-element,and multidegrees of freedom features. This software has been used in the following analysis - * Nonlinear analysis of strip footing using coupled finite - Infinite elements (Godbole, Viladkar, Noorzaei, 1990). * Linear and nonlinear interactive analysis of a single storey, two bay plane frame-combined footing- soil system (Viladkar, Godbole, Noorzaei, 1991) * Linear/nonlinear analysis of five storey, two bay planeframe- footing-soil system including parametric study (Viladkar, Godbole, Noorzaei, 1990, 1991) The parameters considered are - i) Variation of soil modulus with depth ii) Variation of foundation stiffnesses Three dimensional Interactive analysis of a space frameraft- soil system using coupled finite - infinite elements (Godbole,Viladkar, Noorzaei, 1991). * Three dimensional linear and nonlinear interactive analysis of a four storey space frame (5x3 bay) -raft-soil system with and without slab effect(Godbole,Vi1adkar,Noorzaei,1991). A parametric study on the variation of thickness of the raft xi and slabs of superstructure (Noorzaei, Viladkar, Godbole, 1991). * Elasto-plastic analysis of strip-footing resting on the soil media for verification of elasto-plastic software. » Elasto-plastic interactive analysis of a two storey,two bay plane frame-combined footing-soil system and comparison with linear elastic and nonlinear elastic behaviour. V. CONCLUSIONS On the basis of the investigation, as regards the soilstructure interaction of both plane and space frames, carried out using the improved physical and constitutive modelling, the following conclusions are drawn : i) In two dimensional problems, an infinite element with —— type of decay has been found to be stiffer compared to the following — decay. An infinite element with the latter r decay pattern has therefore been suggested for use in the coupled formulations. ii) For any boundary value plane strain problem, it is essential to locate the position of the transition boundary. This transition boundary has been found to lie at a depth of about four to six times the width of the foundation with a minimum of three to four layers of finite elements in this depth. iii) The use of the interface element between the foundation beam and soil is extremely essential for analysis of laterally loaded structures. Special attention should be paid in assigning the tangential and the normal stiffnesses, xii otherwise it may lead to i11-conditioning of the equation system. The use of interface element causes substantial alteration in the distribution of base shear along the foundation and an increase in the sway of the structure. iv) The mixed (Incremental- iterative) technique of nonlinear analysis, with the element stiffnesses recalculated for the first iteration of each load increment, has been found to be suitable for the interactive analysis of plane frames whereas in view of the constraint on computational time and effort, initial stiffness method has been found to be better suited for the interactive analysis of space frames. v) The effect of soil nonlinearity in general is to increase the total settlements and to redistribute the contact pressure, bending moments in structural members, foundation beams and the raft. vi) Consideration of the effect of stiffness of structural slabs in the interactive analysis suggests that the bending moments in the outer columns increase significantly. The increase of moments in beams is relatively lesser. The redistribution of the axial forces in the columns also takes place due to the consideration of the slab action. vii) Various yield criteria have been converted into the conven ient forms so as to consider the elasto-plastic behaviour of soil. Expressions were derived for the constants required in the determination of the flow vector, viii) The elasto - plastic analysis has been carried out in two xiii ways viz. a) Elastic-Rigid plastic analysis (H* = O) b) Elastic-plastic analysis with strain hardening (H' * O) It was observed that the ultimate load factor found for the case of strain hardening was much higher than that for the rigid-plastic case. ix) In the elasto-plastic interactive analysis, at lower load factors, the analysis gives results close to those due to linear interactive analysis. However, at higher load factors, there is a progressive yielding of the soil mass below the outer edge of the footing which advances in the downward direction as well as towards the centre of the structurefoundation- soil system. This phenomenon causes transfer of forces and moments to the inner beams and columns below which, the soil is still in the elastic state. This development has been observed at higher load increments and is a major deviation compared to other interactive analyses. x) The detailed study on use of infinite elements in elasto plastic analysis indicates that the elements extending to infinity in the direction of applied loading should be avoided as otherwise it leads to instability (illconditioning of the equation system).