BEHAVIOUR OF SHALLOW FOUNDATIONS ADJACENT TO SLOPES

Abstract

Foundations are sometimes placed on slopes, near the top edge of a slope or near a proposed excavation. In such situations, the problem becomes of obtaining the maximum value of bearing capacity (i) from foundation failure and (ii) from the overall stability of slopes. In case of sandy soil, the bearing capacity will always be governed by the foundation failure, while in cohesive material, the bearing capacity of foundation may be limited by the stability of the whole slope. Several theories are available to compute the ultimate bearing capacity of foundations on slopes. However, the best estimation of both bearing capacity and settlement is possible only if the pressure settlement characteristics of the foundation soil are known. * The investigation deals with the behaviour of shallow footings near the soil slope. Review of literature indicated that many theories are available to find the ultimate bearing capacity, (Meyerhof, 1957), (Mizuno et al. 1960), (Sokolovski, 1960), (Siva Reddy, Mogaliah 1975), (Kusakabe et al. 1981). However, no method is reported, to find the settlement of footings, on or near the slopes except of course, finite element method. So far, in the 11 theories that are available for finding the ultimate bearing capacity, the methods used for level ground have been exten ded to the footings on slopes. So the need was felt to evolve amethod to find the ultimate bearing capacity which takes the effect of slope rationally and also to find a simple procedure to estimate the settlements. The ultimate bearing capacity has been found by two ' methods (i) uai-t equilibrium analysis and (ii) iimit analysis - upper bound. In limit equilibrium analysis it has been assumed that rupture surface is alog spiral and failure occurs on the side of the slope. The resistance mobilized on this side is full passive and that on the other is partial, bearing capacity factors Ny, Nq, Nc have been obtained considering three cases separately i.e. (i) c «q*0 (ii) c=Y=o and (iii) q =Y= o. 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 theorem of perfect plastic bodies. Same failure mechanism was adopted as in limit equilibrium approach. on the side of the slope, the uncontained plastic flow has been ' Ill considered and on the other side nominal plastic flow has been taken. The results obtained by the above two methods have been compared and it was found that values so obtained for the same rupture surface tally with each other closely. The results have been presented in the form of nondimensional, parameters N , N and Ny for different values of 0, slope angle and distance of footing from the slope edge. Pressure settlement relationship is essentially a function of non-linear constitutive laws of soil. In this investigation, an analytical analysis has been developed to predict the pressure settlement characteristics of actual foot ings resting on a slope using non-linear constitutive laws of soil. The analysis has been developed for rigid strip footings. It is assumed that the load on the footing gets distributed in the form of column of soil of width equal to that of the footing. The mobilization of the resistance of soil was considered to be maximum at the top of the soil column i.e. at the base of the footing and minimum at the base oi the column. In between linear variation of strength was considered. This was taken because the movement of the soil IV will be maximum at the top of the soil column and zero at the base of soil column. The pressures on the two sides of the column were taken as passive earth pressures computed on the basis of mobilized value of shear strength. The soil column was then divided into n-linear strips. Analysis has been developed for getting the passive earth pressure on the sides of each strip. The equilibrium of individual strip was then considered It gave the vertical and horizontal stresses on different strips along with the shear stresses. Using these stresses, principal stresses and their directions were evaluated. Vertical strains of each strip was then obtained using the non-linear constitutive laws of soil which in turn gave the settlement of the strip on multiplying with its thickness. Summation of the settlement of all the n-strips gave the settlement of the footing. This is repeated for different footing loads and complete pressure settlement characteristics of the footing were obtained. For verification of analytical solutions, model tests were conducted on footings of size 12 cm x 60 cm in a tank 300 cm x 60 cm x 90 cm high containing sand; The tests were conducted on Ranipur sand at two densities i.e. DR = 84 percent and DR = 72 percent. The footings were tested at three slope angles and at seven different edge distances. m each case footing was loaded upto failure and its pressure settlement, characteristics were observed. The test results agree reasonably well with analy tical solutions of ultimate bearing capacity and pressure settlement characteristics of the footings. A non-dimensional correlation has been established between the settlement of a footing resting on level ground (SQ) and the settlement (sB) of a footing adjacent to slope from model tests. It was found that there exists a unique relationship between Sg/SQ and De/B for different slope angles. The relationship is found to be independent of relative density and factor of safety. The value of S o may be estimated using the conventional plate load data. The correlation is useful for the proportioning of founda tion in conventional way i.e. estimating the ultimate bearing capacity and settlement by different approaches. The pressure-settlement characteristic approach gi the design of actual footings by estimating settlement and ultimate bearing capacity directly. In this case extrapola tion is not required.