BEHAVIOUR OF ECCENTRICALLY-OBLIQUELY LOADED FOOTING ON REINFORCED EARTH SLAB

Abstract

The foundations of retaining walls, abutments and tower-like structures such as columns, portal frames, chimneystacks, storage tanks, silos, etc., are subjected to eccentric-inclined loads, due to moments and horizontal thrusts along with the vertical loads. In general for such type of structures strip, rectangular, square and circular foundations are adopted. The main criteria for a satisfactory design of such foundation are; the ultimate bearing capacity, permissible settlement and tilt. The earth reinforcement technique is in use for a long in the earth embankments and retaining walls. However, less emphasis has been given to the use of this technique for shallow foundations on poor ground conditions. Binquet and Lee (1975a) are among the first to report a systematic study on the bearing capacity of strip footing resting on reinforced soil beds subjected to central vertical load. Significant improvement in the bearing capacity and reduction in the settlement was observed due to the inclusion of reinforcement in the soil beneath the footing. This technique of reinforcing the soil is becoming popular day by day in improving the poor grounds. An extensive review of literature revealed that very meagre information is available on the behaviour of shallow footings subjected to eccentric-inclined load, resting on reinforced soil. Keeping this in view, this topic has been selected for investigation. The complete study has been broadly divided in to three parts. 1. Analytical analysis for studying the behaviour of square footing on unreinforced sand 2. Analytical analysis for studying the behaviour of strip, square and rectangular footings on reinforced sand 3. Experimental study for studying the behaviour of strip and square footings on reinforced sand 1 Analytical procedure for studying the behaviour of square footing subjected to eccentric-inclined load on unreinforced sand Behaviour of shallow footings in terms of pressure - settlement and pressure - tilt are essential functions of the non - linear stress - strain relationships of soils. In this study constitutive laws of soils have been considered, to predict these relationships. The procedure has been developed for non-cohesive soil (c = 0) for square footing subjected to eccentric-inclined loading. Agarwal (1986) has already developed a procedure for strip footing subjected to eccentric-inclined load. In order to calculate the stresses below the square footing the whole area has been divided into a large number of small elementary areas. The total load in each small area has been considered as equivalent point load acting at the centre of each element. The soil mass supporting the square footing has been divided in to number of thin horizontal layers, up to a depth beyond which, the stresses become negligible. Various stress components due to each small area, at the middle of each layer, along a vertical section, have been evaluated using Boussinesq's (1885) and Cerruti's (1888) equations. Concept of effective width of footing has been made use of in working out the stresses in soil medium when the eccentricity of the applied load on the footing exceeds 1/6 times the width of footing. Normal and shear stresses have been obtained by superimposing stress components due to each small element. Then the principal stresses and their directions are obtained using the non-linear constitutive laws. The strain in the vertical direction has been determined. Thus, the vertical settlement of each strip has been evaluated by multiplying the vertical strain by its thickness. The total settlement, along a vertical section, due to an eccentric - inclined load has been obtained by the summation of the vertical settlements of all layers. The procedure has been repeated to obtain settlements along various vertical sections. The maximum settlement (Sm), settlement at the point of load application (Se) and tilt of the rigid footing have been computed by equating both the area and distance of the centre of the settlement diagram of the rigid footing. The whole procedure is then repeated, for other values of loads, load inclination (i), eccentricity ratio (e/B) and footing size (B), for obtaining complete sets of pressure-settlement and pressure-tilt curves. Complete solutions in the form of pressure versus settlement and pressure versus tilt curves for square footing have been obtained for Amanatgarh sand. 2. Analytical procedure for footings subjected to eccentric-inclined load on reinforced sand For analysis of strip footings resting on reinforced earth slab, the method proposed by Binquet and Lee (1975b) was modified based on the more realistic assumptions and extended for eccentric - inclined loading conditions. The analysis has also been extended for rectangular and square footings subject to eccentric-inclined load on reinforced earth slab. Complete analysis requires the normal and shear stresses in the soil under the footing, at various desired depths under eccentric-inclined loading. The procedure adopted for calculation of these stresses is the same as has already been explained in the case of footing on unreinforced sand subjected to eccentric - inclined load. The stresses are required for determination of normal forces on the plan area of reinforcement, inside and outside of the assumed plane separating the downward and outward in flow of soil. The results obtained have been presented in terms of nondimensional charts for different depth ratio (Z/B), eccentricity ratio (e/B), load inclination (i) and size of reinforcing layer (U/B). This method requires the pressure - settlement curve for the same footing subjected to eccentricinclined load resting on unreinforced soil. Hence the pressure - settlement characteristic of the footing on reinforced sand could be obtained up to the load intensity of same footing on unreinforced sand under the similar loading conditions. 3. Experimental investigation of footings subjected to eccentricinclined load on reinforced sand . A total of one hundred and seventeen model tests have been conducted on model strip (105 x 480 mm) and square (200 x 200 mm) footings resting on unreinforced and reinforced Amanatgarh sand at a relative density of 65%. Of these forty five model tests on strip footing and seventy two model tests on square footing subjected to eccentric - inclined load having eccentricity ratio e/B = 0.0, 0.1, 0.2 and load inclinations i = 0°, 10°, 20° were carried out. Tensar SS20 Geogrid, rectangular and/or square in shape, as per the requirement, has been used throughout the study. The length of the reinforcement (U) has been provided as B, 2B and 3B. Whereas the number of the reinforcing layers (N) has been kept as one, two, three or four. The pressure-settlement, pressure-horizontal displacement and the pressure-tilt curves have been obtained for each model test. 4. The model test results have been utilised to verify each case of the proposed analyses for square footing on unreinforced sand whereas strip and square footings on reinforced sand. Comparison of predicted values of settlement and tilt, for footings on unreinforced and reinforced sand, has shown good agreement with their respective values of model test. IV 5. Soil-reinforcement contact area gets reduced due to eccentricity and inclination of applied load on the footing resting on reinforced earth. This phenomenon would yield reduced values of pressure intensity in actual field application/model tests when compared to their corresponding predicted value. This has been taken care of by introducing the concept of reduction factors both due to inclination and eccentricity of applied load. Predicted values for such cases have been obtained by multiplying the frictional force component with the respective reduction factor. 6. To evaluate the ultimate bearing capacity of the footings on reinforced sand, an empirical approach has been proposed, based on the model test data. The predicted values of ultimate bearing capacity, obtained by this approach, compared reasonably well with values of ultimate bearing capacity obtained from the model tests and from previous investigations. 7. Few practical examples have been solved to illustrate the use of the proposed non-dimensional charts and to demonstrate the application of various procedures developed throughout this investigation. 8. Based on analytical and experimental results, the following important conclusions have been drawn: i. Values of the ultimate bearing capacity and tilt of square footing have been found to be dependent on the size of footings, having the same e/B and i. While, the vertical settlement, for equal pressure intensity, has been found to increase in direct proportion with the increase in the size of the footing. ii. Values of the ultimate bearing capacity of footings on unreinforced and reinforced soils are drastically reduced with the increase of e/B and / or i. iii. An empirical approach to predict the ultimate bearing capacity of strip and square footings subjected to eccentric-inclined load, resting on reinforced soil has been suggested. It is anticipated that, the analyses proposed herein, would facilitate in providing the complete parameters, required for economical and safe design of square foundation on unreinforced sand and strip, square and rectangular foundations on reinforced sand, subjected to eccentric - inclined load. VI