BEHAVIOUR OF SHALLOW FOUNDATIONS SUBJECTED TO ECCENTRIC-INCLINED LOADS

Abstract

A foundation engineer frequently comes across the problem of foundations subjected to eccentric-inclined loads e.g. in the case of foundations of retaining walls, abutments columns, etc. The criteria for satisfactory action of such founda tion are its ultimate bearing capacity, permissible settlement, tilt and horizontal displacement. Several theories are available to compute the ultimate bearing capacity of shallow foundations subjected to (i) central vertical loads (Terzaghi,1943; Meyerhof, 1951; Balia,1962; Vesic,1973), (ii) eccentric vertical loads (Meyerhof, 1953; Eastwood, 1955; 3umiksi,1961, Dhillon, 1961; Prakash and Saran,1971; Purkayasth and Char, 1977) and (iii) central oblique loads (Meyerhof,1953; Janbu,1957; Kezdi,1961; Hansen,1961; Sokolovski,1965; Muhs and Weiss,1969; Saran and Murthy,1971; Kameshwar Rao and Murthy,1972; Muhs and Weiss,1973; Hanna and Meyerhof,1981). No investigator so far has developed analysis for footings subjected to eccentric inclined loads. Further no method is reported to find the settlement, tilt and hori zontal displacement of such footings except of course finite element method. Very few investigators have studied the behaviour of footing subjected to eccentricinclined load experimentally (Meyerhof, 1953; Saran and Niyogi,1970). So need was felt to evolve a method to find ultimate bearing capacity of foundations subjected to eccentric-inclined loads and also to find a simple procedure to estimate settlement, tilt and horizontal displacement. In the present investigation ultimate bearing capacity has been found by the two methods (i) limit equilibrium analysis and (ii) limit analysis-upper bound. In the limit equilibriumanalysis it has been assumed that the rupture surface is a log-spiral and the failure occurs on one side of the footing i.e. on the side of the eccentricity or towards the direction of horizontal component of the inclined load. The resistance mobilised on this side is full passive and on the other side partial. Bearing capacity factors Ny , N, Nq have been obtained considering the three cases separetely i.e. (i) c = q = 0, (ii) c =Y= 0 and (iii) q =Y= 0. The total bearing capacity is then obtained by superposing the limit stresses obtained by the above three cases. The ultimate bearing capacity has also been found by the upper bound the of prefect plastic bodies. Same failure mechanism was adopted as in limit equili brium approach. On the side of eccentricity or towards the direction of horizontal component of the inclined load, the uncontained plastic flow has been considered and on the other side nominal plastic flow has been taken. The results obtained by the above two methods have been compared and found in very close agreement. The results have been presented in the form of non-dimensional charts of bearing capacity factors Ny , Nq and Nc for different values of angle of internal friction (0), eccentricity width ratio (e/B) and load inclination (i). Pressure-settlement relationship is essentially a function of non-linear consti tutive laws of soil. In this investigation an analysis has been developed to predict the pressure-settlement and pressure-horizontal displacement characteristics of rigid strip footing subjected to eccentric-inclined load using non-linear constitutive laws of soil. To predict the pressure-settlement characteristics a suitable contact pressure defined by a pressure coefficient has been assumed. The soil below the footing upto the significant depth has been divided into thin strips. For the assumed contact pressure, the vertical stresses, horizontal stresses and shear stresses have been obtained at the centre of different strips along various vertical sections. The principal stresses and their directions were then evaluated. Principal strains orem Ill have been obtained using non-linear constitutive laws. Using these strains, strain in the vertical direction was obtained, which in turn gave the vertical settlement of the strip by multiplying with the thickness of the strip. Summation of the settlement of all the strips gave the vertical settlement of the footing along a vertical section. The above process was repeated for other values of contact pressure coefficient till the settlement of footing along various vertical sections came out same. This is repeated for different footing loads and complete pressuresettlement characteristics of the footing were obtained. Similar procedure was adopted for obtaining pressure-horizontal displacement characteristics in which the principal strains were resolved in the horizontal direction and integration of displacement is done in the horizontal domain. The solutions of pressure-settlement and pressure-displacement characteristics have been obtained for (i) Buckshot clay and (ii) Ranipur sand. Non-linear consti tutive laws of these two soils in the form of Kondner's hyperbola were adopted for computations. To verify the analytical solutions model tests were conducted on different size of footings with Square (20x20 cm), rectangular (20x40 cm) and strip footing (10x60 cm) in a tank size 1.50 m x 1.50 m x 1.0 m high, containing sand. The tests were conducted on Ranipur sand at relative density 84 percent. Footings were tested at four eccentricity width ratio (e/B = 0.0, 0.1, 0.2 and 0.3) with five combination of load inclination with the vertical (0°, 5°, 10°, 15° and 20°). Strip footing was also tested at depth-width ratio equal to 0.5. Each footing was loaded upto failure and its pressure-settlement, pressure-tilt and pressurehorizontal displacement have been obtained. The test results agree well with the analytical solutions of ultimate bearing capacity and pressure-settlement and pressure-horizonral displacement characte ristics of footings. IV Using model test data non-dimensional correlations have been developed to predict the values of settlement, tilt and horizontal displacement of eccentrically obliquely loaded footing. These correlations have been found independent of size, shape of the footing and stress levels and dependent on eccentricity and inclination of load. To use these correlations the data of conventional plate load test is required. Thus settlement, tilt and horizontal displacement of footing subjected to eccentric-inclined load can be predicted from plate load test under central load. The ultimate bearing capacity can be determined by using bearing capacity factors developed in this investigation. An approach for prediction of pressuresettlement characteristic of footing using non-linear constitutive laws of soils facilitates in providing complete parameters required for the design. In this manner a complete rational solution of footing subjected to eccentric-inclined load have been obtained for the first time.