1、2 Experimental Equipment3 Deflection and Settlement3.1 Induced Stresses beneath Shallow FoundationsThe bearing pressure from shallow foundations induces a vertical compressive stress in the underlying soils. We call this stress, because it is the change in stress that is superimposed on the initial
2、vertical stress: Where: = induced vertical stress due to load from foundation;= stress influence factor= bearing pressure along bottom of foundation= vertical effective stress at a depth of D below the ground surface3.2 Boussinesqs MethodBoussinesq (1885)developed the classic solution for induced st
3、ress in an elastic material due to applied point load. Newmark(1935)then integrated the Boussinesq equation to produce a solution for at a depth beneath the corner of a rectangular foundation of width B and length L. This solution produces the following two eqations: Square footingContinuous footing
4、4 Bearing Capacity of nature ground4.1 Bearing Capacity FailuresGeneral shear failure is the most common modeIt occurs in soils that are relatively incompressible and reasonably strong,in rock, and in saturated,normally consolidated clays that are loaded rapidly enough that the undrained condition p
5、revails. The failure surface is well defined and failure occurs quite suddenly. A clearly formed bulge appears on the ground surface adjacent to the foundation. Although bulges may appears on both side of the foundation, ultimate failure occurs on one side only, and it is often accompanied by rotati
6、on of the foundation. The opposite extreme is the punching shear failure. It occurs in very loose sand, in a thin crust of strong soil underlain by a very weak soil, or in weak clays loaded under slow, drained condition. The compressibility of such soil profiles causes large settlement and poorly de
7、fined vertical shear surface. Little or no bulging occurs at the ground surface and failure develops gradually. Local shear failure is an intermediate case. The shear surfaces are well defined under the foundation, and then became vague near the ground surface. A bulge may occurs, but considerable s
8、ettlement ,perhaps on the order of half the foundation width, is necessary before a clear shear surface forms near the ground. Even then, a sudden failure does not occur, as perhaps in the general shear case. The foundation just continues to sink into the ground.Ves (1973) investigated these three m
9、odes of failure by conducting load tests on model circular foundations in sand. These tests include both deep foundations and shallow foundations. The results indicate shallow foundations (D/B less than about 2) can fail in any of the three modes, depending on the relative density. However, deep fou
10、ndations (D/B greater than about 4) are always governed by punching failure. Although these test results apply only to circular foundations in Vess sand and cannot necessarily generalized to other soils, it dose give a general relationship between the mode of failure, relative density, and the D/B r
11、atio. Complete quantitative criteria have yet to be developed to determine which of these three modes of failure will govern in any given circumstance, but the following guidelines are helpful: .Shallow foundations in rock and undrained clays are governed by general shear failure. .Shallow foundatio
12、ns in dense sands are governed by the general shear case. In this context, a dense sand is one with a relative density, Dr, greater than about 67%. Shallow foundations in loose to medium dense sands (30 % Dr67%) are probably governed by local shear failure. Shallow foundations on very loose sand (Dr
13、30%) are probably governed by punching shear failure.4.2 Methods of Analyzing Bearing Capacity Full-scale load tests, which constructing real spread footings and loading them to failure, are the most precise way to evaluate bearing capacity. However such tests are very expensive, and thus are rarely
14、, if ever, performed as a part of routine design. A few such tests have been performed for research purpose. Model footing tests have been used quite extensively, mostly because the cost of these tests is far below that for full-scale tests. Unfortunately , model tests have their limitations, especi
15、ally when conducted in sands, because of uncertainties in applying proper scaling factors. However, the advent of centrifuge model tests has partially overcome this problem.Limit equilibrium analyses are the dominant way to assess bearing capacity of shallow foundations. These analyses define the shape of the failure surface, then evaluate the stress and strengths along this surface. These methods of analysis have their roots in Prandtls studies of the punching resistance of metals (Prandtl, 1920). He considered of very thick masses of metal (i.e., not sheet metal
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