SEMBODAI RUKMANI VARATHARAJAN ENGINEERING COLLEGE DEPARTMENT OF CIVIL ENGINEERING SHALLOW FOUNDATION BY KARTHIVELU Basic Definitions οFooting: Part of foundation that transmit the load directly to soil. οFoundation : Part of structure which is in direct contact with & transmit load to ground. οFoundation soil: Upper part of earth mass that carrying the load of the structure. Basic Definitions Foundation Footing Foundation soil Bearing Pressure intensity capacity Ultimate BC Safe BC Gross Total pressure at base of footing due to wt of super strct, self wt of foundation & earth fill (q) The minimum q at which soil fails by shear (qf) Maximum pressure, soil can carry without risk of shear failure qs= qns+ YD Net pressure at base of footing due to wt of super strct, self wt of foundation qn = q - YD The minimum qn at which soil fails by shear qns = qnf / F (qnf) = qf - YD * π = YD → ππππππ‘ππ£π π π’ππβπππππ ππ‘ π‘βπ πππ π πππ£ππ οAllowable bearing capacity qa: The net loading intensity at which the soil fails neither by shear nor by settlement Modes of shear Failure Vesic (1973) classified shear failure of soil under a foundation base into three categories depending on the type of soil & location of foundation. 1) General Shear failure. 2) Local Shear failure. 3) Punching Shear failure Modes Of Shear Failure General shear failure Local shear failure Punching shear failure FAILURE SURFACE Well defined, Clearly defined No failure pattern is reaching upto ground only immediately observed. Vertical & surface below the footing follows the pattern of base BULGING more slight FAILURE Sudden & accomplished with tilting of footing Not sudden & no Only very large tilting. Only large settlement settlement ULTIMATE BEARING CAPACITY Well defined Not well defined Not well defined RELATIVE DENSITY OF SOIL high 35% to 75 % < 35% EX In Very dense sand in In High In soft clay shallow footing compressible soil nil Terzaghi’s Bearing Capacity Analysis Terzaghi (1943) analysed a shallow continuous footing by making some assumptions. Plastic Zones Of Failure • Zone-I :Immediately beneath the footing. Does not undergo any lateral yield by friction & adhesion & hence act as part of foundation. Line db& da are straight &anggle isØ. • Zone-II : (zone of radial shear) One set of shear pattern radiates from outer edge of base of footing. Another set- lograthamic spiral with center at outer edge of base of footing • Zone-III : (zone of linear shear) The ∅ o boundaries rise at 45 2 ο The failure zones do not extend above the horizontal plane passing through base of footing ο The equilibrium occurs when the down ward pressure exerted by loads on the soil adjoining the inclined surfaces on soil wedge is equal to upward pressure. ο Downward forces are due to the load (=qu× B) & the weight of soil wedge (1/4 γB2 tanØ) ο Upward forces are the vertical components of resultant passive pressure (Pp) & the cohesion (c’) acting along the inclined surfaces. • For equilibrium: ΣFv = 0 π γ B2tan ø + quB= 2Pp +2CLi sinø π where Li = length of inclined surface CB ( = B/2 /cosø) quB= 2Pp + BCtanø- ¼ γ B2tanø –------ (1) The resultant passive pressure (Pp) on the surface CB & CA constitutes three components ie. (Pp)r, (Pp)c& (Pp) q, Thus, Pp = (Pp)r + (Pp)c + (Pp)q quB= 2[ (Pp)r +(Pp)c +(Pp)q ]+ BCtanø-¼ γ B2 tanø Substituting; 2 (Pp)r - ¼rB2tanø = B × ½ γ BNr 2 (Pp)q = B × γ D Nq & 2 (Pp)c + BC tanø = B × C Nc; We get, qu =CNc + γ D Nq + 0.5 γ B N γ This is Terzaghi’s Bearing capacity equation for determining ultimate bearing capacity of strip footing. Where Nc, Nq & Nr are Terzaghi’s bearing capacity factors & depends on angle of shearing resistance (ø) ø General Shear Failure Local Shear Failure Nc Nq Nr Nc’ Nq’ Nr’ 0 5.7 1.0 0.0 5.7 1.0 0.0 15 12.9 4.4 2.5 9.7 2.7 0.9 45 172.3 173.3 297.5 51.2 35.1 37.7 ASSUMPTIONS 1. soil is homogeneous, isotropic & its shear strength is represented by Coulomb’s equation. 2. Strip footing has a rough base, & the problem is two dimensional. 3. The elastic zone has straight boundaries inclined at ø to horizontal & plastic zone is fully developed. 4. Pp has 3 components which can be computed and added separately. 5. The failure zones do not extend above the horizontal plane passing through base of footing LIMITATIONS οAs soil compresses, Ø changes οSlight downward movement of footing does not develop fully plastic zones οError due to assumption 4 is small οError due to assumption 5 increases with depth of foundation. Hence suitable for shallow foundation. Important points : * Terzaghi’s Bearing Capacity equation is applicable for general shear failure. * Terzaghi has suggested following empirical reduction to actual c & ø in case of local shear failure Mobilised cohesion Cm = 2/3 C Mobilised angle of øm = tan –1 (β tanø) Thus, Nc’,Nq’ & Nr’ are B.C. factors for local shear failure qu = CmNc’+ γ D Nq’+ 0.5 γ B Nr’ Ultimate Bearing Capacity for square & Circular footing -Based on the experimental results, Terzaghi’s suggested following equations for UBC – ο Circular footing qu = 1.3 C Nc + γ D Nq + 0.3 γBNr ο Square footing qu = 1.3 C Nc + γ D Nq + 0.4 γ BNr ο Rectgrfootingqu = 1+ π© 0.3 π³ C Nc+ γ D Nq + 0.4 γ BNr