Interference of the footings
The Interference of the footings is a phenomenon that is observed when two footings are closely spaced. The buildings when are to be constructed nearby to each other, the architectural requirements or the less availability of space for the construction forces the engineers to place the foundation footings close to each other, and when foundations are placed close to each other with similar soil conditions, the Ultimate Bearing Capacity of each foundation may change due to the interference effect of the failure surface in the soil.
Introduction
Foundations or group of foundations are important components of the structure through which the superficial structural loads are transmitted to the underlying foundation soil or bed on which the foundations are laid. The structural loads are transmitted to the foundation soil safely such that neither the foundation fail nor the foundation soil fails either in shear or in excessive settlement. The foundations are basically designed based on two criterion namely Bearing Capacity and Settlement criterion. Many classical theories have been postulated for the isolated foundations by many pioneers like Terzhagi (1943), Meyerhoff (1963), Hansen (1970) and Vesic (1973). In general as per the Terzaghi (1943), when an isolated shallow foundation is loaded, the stress or the failure zone in the foundation soil extends in horizontal direction on either side of the footing to about twice the width of the footing and in vertical downward direction to about three times the width of the footing. Unless until the stress or failure zone of individual footings do not interfere, the individual footings behave as an isolated footing. However, in many a situations such as lack of construction space, structural restrictions, rapid urbanization, architecture of the building, structures close to each other etc. In such situations the foundations or group of foundations may be placed close to each other. In such cases the stress isobars or the failure zone of closely spaced isolated footings may interfere with each other leading to the phenomenon called Interference. Owing to the phenomenon of footing interference, the failure mechanism, load-settlement, bearing capacity, settlement, rotational characteristics etc. of an isolated footing may be altered and therefore the classical theories as postulated in the literature for isolated footings cannot be applied. Due to interference the stress isobars of individual interacting footings coalesce to form a single isobar of larger dimensions altering the characteristic behavior of an isolated footing. Therefore, the study of interference of closely spaced footings is one of the significant practical importances.
Previous studies
Stuart^{[1]} was the first pioneer to study the interference phenomenon of closely spaced surface strip footing. He examined the effect of footing interference on ultimate bearing capacity of strip footings by theoretical analysis using limit equilibrium method, assuming a non-linear failure surface wherein the cross-section composed of logarithmic spiral and straight line portion tangent to the curvilinear portion. Further Stuart (1962) carried out few small-scale laboratory experiments and compared the results of theoretical analysis with that of the experimental results and concluded that the ultimate bearing capacity of two interfering footings increase with decrease in spacing between the footings and attains a peak magnitude at some spacing termed as critical spacing. The study of Stuart (1962) was further extended by West and Stuart (1965) by performing a series of small-scale laboratory tests to examine the effect of interference on bearing capacity of strip footings resting on the surface of cohesion-less soil bed. Moreover, West and Stuart^{[2]} (1965) carried out few theoretical analyses using method of stress characteristics to observe the eccentricity of load and reactions at the base of footing resulting from interference effect for footings resting on the surface of sand. The results obtained from this theory were smaller than those observed by Stuart (1962) using limit equilibrium method; however the trend was similar to the variation as observed by Stuart (1962) and the results obtained by experiments reasonably matched with those of the theoretical analysis. The researchers carried out the study by theoretical or numerical techniques for interfering footings by making use of the following methods : Method of stress characteristics, Analytical method, Probabilistic approach, Upper bound limits analysis, Lower bound limits analysis, Finite element method, Finite difference method.^{[3]}^{[4]}^{[5]}^{[6]}^{[7]}^{[8]}
Observed results
It is observed by the researchers that the characteristic behaviours of an isolated footing are affected if there exist other footing or group of footings close to each other and their individual zone of influence interfere with each other leading to interference phenomenon. The ultimate bearing capacity increases with decrease in the clear spacing between the footings and attains a peak magnitude at some critical spacing and thereafter with further decrease in clear spacing, the ultimate bearing capacity decreases and at spacing equal to zero the two footings act as an isolated footing of twice the width when width of two interfering footings are similar and loaded symmetrically. Moreover, the settlement at failure of interfering footing is observed to be greater than that of isolated footing at failure and the same decreases with increase in clear spacing between the footings. The variation of ultimate bearing capacity and settlement at failure of interfering footings were observed with respect to clearing spacing ratio by introducing efficiency factors which are defined as the ratio of magnitude of ultimate bearing capacity/settlement of interfering footings to that of the magnitude of ultimate bearing capacity/settlement of an isolated footing. The bearing capacity and the settlement of footings are the basic criterion which influence in the design of the footings and these are affected by the presence of one or more of the footings close to each other; however the interference phenomenon is not considered in the design of shallow footing. In the present scenario the structures may be forced to come close to each other or due to rapid urbanization, the buildings may be constructed in an irregular manner or due to lack of construction space or architecture of the building; the foundations or group of foundation may be laid close to each other which may lead to interference phenomenon and thereby influence the characteristic behaviour of an isolated footing which governs the design criterion and therefore make the motivation in the present study of interference of footings. So far the interference of footings is concerned all most all the study dealt with the interference phenomenon on ultimate bearing capacity and the settlement of interfering footings at failure for two or more closely spaced surface footings resting on either unreinforced or reinforced foundation soil beds. In the literature the foundation soil was considered to be cohesion-less, homogeneous, layered (each layer being homogeneous), Young's modulus linearly varying with depth etc. and the interfering footings were strip, square, rectangular, circular in shapes resting on the surface of foundation soil medium. Most of the literature dealt with interfering footings of symmetrical geometry and loading conditions except Nainegali et al. Though the interference phenomenon has been observed and studied since Stuart, the effect of interference on the group of footings is not being considered in the design.
References
- ^ "Interference between foundations, with special reference to surface footings in sand.", Geotechnique, 1962
- ^ "Oblique loading resulting from interference between surface footings on sand.", Soil Mech & Fdn Eng Conf Proc, Canada, 1965
- ^ Lohitkumar Nainegali, Prabir Kumar Basudhar, and Priyanka Ghosh. (2013), "Interference of Two Asymmetric Closely Spaced Strip Footings Resting on Nonhomogeneous and Linearly Elastic Soil Bed.", International Journal of Geomechanics, 13 (6): 840–851CS1 maint: Uses authors parameter (link)
- ^ Ghosh Priyanka. (2012), "FLAC based numerical studies on dynamic interference of two nearby embedded machine foundations.", Geotechnical and Geological Engineering, 30 (5): 1161–1181CS1 maint: Uses authors parameter (link)
- ^ Das Braja M., and Said Larbi-Cherif (1983), Bearing capacity of two closely-spaced shallow foundations on sand.CS1 maint: Uses authors parameter (link)
- ^ Nainegali L. S., P. Ghosh, and P. K. Basudhar. (2011), Interaction of Nearby Strip Footings Under Inclined Loading.CS1 maint: Uses authors parameter (link)
- ^ Kumar Jyant and Manas Kumar Bhoi. " (2009), "Interference of two closely spaced strip footings on sand using model tests.", Journal of Geotechnical and Geoenvironmental Engineering, 135 (4): 595–604CS1 maint: Uses authors parameter (link)
- ^ Amir Hossein Javid, Ahmad Fahimifar and Meysam Imani. " (2015), "Numerical investigation on the bearing capacity of two interfering strip footings resting on a rock mass.", Computers and Geotechnics, 69: 514–528CS1 maint: Uses authors parameter (link)