1. SEMBODAI RUKMANI VARATHARAJAN ENGINEERING COLLEGE DEPARTMENT OF CIVIL ENGINEERING SHALLOW FOUNDATION BY KARTHIVELU

2. Basic Definitions  Footing: Part of foundation that transmit the load directly to soil.  Foundation : Part of structure which is in direct contact with & transmit load to ground.  Foundation soil: Upper part of earth mass that carrying the load of the structure.

3. Basic Definitions Foundation Footing Foundation soil

4. Bearing capacity Pressure intensityUltimate BCSafe BC GrossTotal 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 (q f ) Maximum pressure, soil can carry without risk of shear failure q s = q ns + Y D Netpressure at base of footing due to wt of super strct, self wt of foundation q n = q - Y D The minimum q n at which soil fails by shear (q nf ) = q f - Y D q ns = q nf / F

5.  Allowable bearing capacity q a : The net loading intensity at which the soil fails neither by shear nor by settlement

6. 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

7. Modes Of Shear Failure

8. General shear failure Local shear failure Punching shear failure FAILURE SURFACE Well defined, reaching upto ground surface Clearly defined only immediately below the footing No failure pattern is observed. Vertical & follows the pattern of base BULGINGmoreslightnil FAILURESudden & accomplished with tilting of footing Not sudden & no tilting. Only large settlement Only very large settlement ULTIMATE BEARING CAPACITY Well definedNot well defined RELATIVE DENSITY OF SOIL high35% to 75 %< 35% EXIn Very dense sand in shallow footing In High compressible soil In soft clay

9. Terzaghi’s Bearing Capacity Analysis Terzaghi (1943) analysed a shallow continuous footing by making some assumptions.

10. Plastic Zones Of Failure

11.  The failure zones do not extend above the horizontal plane passing through base of footing  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.  Downward forces are due to the load (=qu× B) & the weight of soil wedge (1/4 γB 2 tanØ)  Upward forces are the vertical components of resultant passive pressure (Pp) & the cohesion (c’) acting along the inclined surfaces.

13. q u B= 2[ (Pp) r +(Pp) c +(Pp) q ]+ BCtanø-¼ γ B 2 tanø Substituting; 2 (Pp) r - ¼rB 2 tanø = B × ½ γ BN r 2 (Pp) q = B × γ D N q & 2 (Pp) c + BC tanø = B × C N c ; We get, q u =CN c + γ D N q + 0.5 γ B N γ This is Terzaghi’s Bearing capacity equation for determining ultimate bearing capacity of strip footing. Where N c, N q & N r are Terzaghi’s bearing capacity factors & depends on angle of shearing resistance (ø)

15. 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

16. LIMITATIONS  As soil compresses, Ø changes  Slight downward movement of footing does not develop fully plastic zones  Error due to assumption 4 is small  Error due to assumption 5 increases with depth of foundation. Hence suitable for shallow foundation.

17. 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 C m = 2/3 C Mobilised angle of ø m = tan –1 (⅔tanø) Thus, N c ’,N q ’ & N r ’ are B.C. factors for local shear failure q u = C m N c ’+ γ D N q ’ + 0.5 γ B N r ’