BEHAVIOUR OF RING FOUNDATIONS ON REINFORCED SOIL

Abstract

Foundations for tower-like structures and self-supporting vertical cantilevers (such as; Water tanks, Recreational towers, Chimney stacks, Storage tanks, Silos, T.V. Towers, Mosque minerates, ...etc.) are usually subjected to a eccentric-inclined loads, due to moments and horizontal thrusts in conjunction with the vertical loads. Ring foundations, besides being more economical they are, however, in some circumstances the only feasible solution for such structures. The main criteria for a satisfactory design of such foundations are; the ultimate bearing capacity, permissible settlements and tilt coupled with economic considerations. Few subjects, in recent years, have raised the general interest and imagination of the CIVILENGINEERING profession as the concept of the "Reinforced Earth", as tenned by its inventor Vidal (1966). In comparison with other applications of reinforced soil, such as reinforced soil embankments or retaining walls, less emphasis, however, has been given to reinforced soil for foundations. Binquet and Lee (1975) are among the first to report a systematic study on the bearing capacity of reinforced soil beds. Among the basic attributes of reinforced earth, which are of particular advantage in the CIVILENGINEERING, are; reductions in cost and time, ease of construction, improvement in the bearing capacity and reduction in the differential and total settlements, coupled with a relatively simple technique to use. An extensive review of literature revealed that very meagre information is available on the behaviour of ring footings subjected to eccentric-inclined load, resting on iinreinforced and reinforced soils. Keeping this in view, thus, the topic has been selected for investigation. The study has been conducted in the following steps : 1. Analytical procedure for ring footing subjected to eccentric-inclined load on unreinforced soil Pressure-settlement and pressure-tilt are essentially functions of the non linear stress-strain relationships of soils. Constitutive laws defining such a behaviour ofsoils have been adopted, in this study, to predict these relationships. The procedure has been evolved for two types of soils, namely; cohesive soil (i.e. <|)=0) and cohesionless soil (i.e. c=0). The whole footing area has been divided into a large number of small elementary areas, so that the total load in each area may be considered as a point load. The contact pressure distribution has been assumed as linear. While, the soil mass supporting the footing has been divided into numerous thin horizontal strips, upto a depth beyond which, the stresses become negligible. Various stress components due to each small area, at the middle of each strip along a vertical section, have been evaluated using Boussinesq's (1885) and Cerruti's (1888) equations. Normal and shear stresses, however, have been obtained by superimposing same stress components due to all elementary areas. Then the principal stresses and their directions have been determined. The principal strains in the direction of the principal stresses have been obtained using the non-linear constitutive laws, then 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 as the summation of the vertical settlements of all strips. The procedure has then, been repeated to obtain settlements along various vertical sections. The maximum settlement (Sm), li settlement of 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 flexible footing with 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 (a), eccentricity ratio (e/B), annular ratio (n) and footing size (B), for obtaining complete sets of pressuresettlement and pressure-tilt curves. Complete solutions in the form of pressure versus settlement and pressure versus tilt curves have been obtained for two soils, namely; (i) Buckshot Clay (<|> = 0), and (ii) Amanatgarh Sand (c = 0) The non-linear constitutive laws of these soils in the form of Kondner's hyperbolae have been used for performing the computations. 2. Analytical procedure for ring footing subjected to eccentric-inclined load on reinforced sand The analysis proposed by Binquet and Lee (1975) for computing the pressure intensity of a strip footing resting on reinforced soil has been modified, based on more realistic assumptions, and further extended for ring footing subjected to eccentric-inclined load on reinforced soil. Various normal and shear stresses due to the eccentric-inclined load, at a desired depth level, which are required for the calculation ofthe normal forces on the plan area ofthe reinforcing layers, inside and outside the assumed plane separating the downward moving and the outward moving zones have been obtained as described in the analysis for ring footings on umeinforced soil. The results obtained have been expressed in terms of J^, Jy,, IK, Iy,, M„, M^, Am and A^ and presented in non-dimensional charts for different depth ratio Z/B, e/B, a, n and size of reinforcing layer ratio Lr /B. in These charts are independent of type of soils and size of footings. The method enables the estimation ofthe pressure ratio pr (where pr is the ratio ofthe average contact pressure of footing on reinforced sand "q" to the average contact pressure of footing on umeinforced sand "q0", at the same settlement "S"). Therefore, the method requires the pressure-settlement curves for ring footing subjected to eccentric-inclined load, resting on umeinforced soil, which have been established, using the non-linear constitutive laws of soils. Further the pressure-settlement characteristics of ring footings resting on reinforced sand could be obtained upto the failure pressure of the same footing on umeinforced soil. 3. Experimental investigation of ring footing subjected to eccentricinclined load on reinforced sand A total of ninety eight model tests have been conducted on model ring footings of size (external diameter) B=200 mm, resting on umeinforced and reinforced Amanatgarh sand at a relative density of 70%. Details of the test programme are as follows; Sixty three tests on solid circular footings subjected to eccentric-inclined load having eccentricity ratio e/B=0.0, 0.1, 0.2 and load inclinations, a =0°, 10°, 20°. Fourteen tests on ring footings (n=0.4, 0.6) subjected to central vertical load and twenty one tests on ring footings (n=0.4) subjected to eccentric-inclined load, i.e. e/B=0.3 and a = 0°, 10°, 20°. Tensar SS20 Geogrid, square in shape, has been used throughout the study. The length of the reinforcing layer (Lr) has been kept as 2B and 3B, while the number of the reinforcing layers (N) has been provided in two, three or four layers. 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 ring footings on umeinforced and reinforced sand. Comparison of IV predicted values of settlement and tilt, for ring footing on umeinforced sand, has shown good agreement with model test settlements and tills. On the oilier, comparison of the predicted values of settlement, for ring footing on reinforced sand has, also, shown good tally with the model test settlements. 5. Since the ultimate bearing capacity cannot be obtained by the proposed analysis for ring footing resting on reinforced soil, an empirical approach, based on the model test data has, however, been suggested in the study. 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. 6. Some practical solved examples have been included in the studyto illustrate the use of the proposed non-dimensional correlations and charts, as well as, to demonstrate the application of various procedures developed throughout this investigation. 7. Based on analytical and experimental results, the following important conclusions have been drawn; i. Non-dimensional correlations have been developed, for predicting values of vertical settlement (Sm, Se) and tilt of ring foundation subjected to eccentric inclined load on umeinforced soil. These correlations are independent of size of footing, type of soil and factor of safety, however, they are dependent on the eccentricity ratio, load inclination and the annular ratio of footings. Use of these correlations simply requires the data of a conventional plate load test, ii. Values of the ultimate bearing capacity and tilt of ring footings on clay have been found to be independent of the size of footings, having the same n, e/B and a. While, the vertical settlement, for equal pressure intensity, has been found to increase in direct proportion with the increase in the size of ring footing. iii. Values of the ultimate bearing capacity of ring footing on unreinforced and reinforced soils, are drastically reduced with the increase of e/B and/or a. iv. Unlike the behaviour of ring footings on umeinforced soil, the ultimate bearing capacity of ring footings on reinforced soil, has been found to decrease with the increase in the annular ratio, v. An empirical approach to predict the ultimate bearing capacity of ring footing 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 an economical and safe design of ring foundations, subjected to eccentric-inclined load resting on reinforced or unreinforced soils. vi