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1、1Bearing Capacity FailureGeneral shear failureLocal shear failurePunching shear failure第1頁/共58頁2Soil Conditions and BearingCapacity Failure第2頁/共58頁3 Load Displacement Curves (after Vesic (1973)a) General Shear Failureb) Local Shear Failurec) Punching Shear Failure第3頁/共58頁4Comments on Shear Failure U

2、sually only necessary to analyze general shear failure. Local and punching shear failure can usually be anticipated by settlement analysis. Failure in shallow foundations is generally settlement failure; bearing capacity failure must be analyzed, but in practical terms is usually secondary to settle

3、ment analysis.第4頁/共58頁5Development of Bearing Capacity Theory Application of limit equilibrium methods first done by Prandtl on the punching of thick masses of metal. Prandtls methods adapted by Terzaghi to bearing capacity failure of shallow foundations. Vesic and others improved on Terzaghis origi

4、nal theory and added other factors for a more complete analysis第5頁/共58頁6Assumptions for Terzaghis Method Depth of foundation is less than or equal to its width No sliding occurs between foundation and soil (rough foundation) Soil beneath foundation is homogeneous semi infinite mass Mohr-Coulomb mode

5、l for soil General shear failure mode is the governing mode (but not the only mode)第6頁/共58頁7Assumptions for Terzaghis Method No soil consolidation occurs Foundation is very rigid relative to the soil Soil above bottom of foundation has no shear strength; is only a surcharge load against the overturn

6、ing load Applied load is compressive and applied vertically to the centroid of the foundation No applied moments present第7頁/共58頁8Failure Geometry for Terzaghis Method第8頁/共58頁9Notes on Terzaghis Method Since soil cohesion can be difficult to quantify, conservative values of c (cohesion) should be use

7、d. Frictional strength is more reliable and does not need to be as conservative as cohesion. Terzaghis method is simple and familiar to many geotechnical engineers; however, it does not take into account many factors, nor does it consider cases such as rectangular foundations.第9頁/共58頁10The General B

8、earing Capacity Equation.第10頁/共58頁11The General Bearing Capacity Equation.第11頁/共58頁12The General Bearing Capacity Equation.第12頁/共58頁13Other Factors第13頁/共58頁14Other Factors For continuous footing, s = 1 For perpendicular load, i = 1 For level foundation, b =1 For level ground, g =1 Need to compute fa

9、ctors - Bearing Capacity Factor N, - Depth Factor d第14頁/共58頁15Groundwater Effects第15頁/共58頁16Groundwater EffectsShallow groundwater affects shear strength in two ways: Reduces apparent cohesion that takes place when soils are not saturated; may necessitate reducing the cohesion measured in the labora

10、tory Pore water pressure increases; reduces both effective stress and shear strength in the soil (same problem as is experienced with unsupported slopes)第16頁/共58頁17Groundwater Effects第17頁/共58頁18FOOTINGS WITH ECCENTRICOR INCLINED LOADINGSEccentricityInclination第18頁/共58頁19FOOTINGS WITH One Way Eccentr

11、icity In most instances, foundations are subjected to moments in addition to the vertical load as shown below. In such cases the distribution of pressure by the foundation upon the soil is not uniform.第19頁/共58頁20第20頁/共58頁21第21頁/共58頁22FOOTINGS WITH One Way Eccentricity Note that in these equations, w

12、hen the eccentricity e becomes B/6, qmin is zero. For e B/6, qmin will be negative, which means that tension will develop. Because soils can sustain very little tension, there will be a separation between the footing and the soil under it. Also note that the eccentricity tends to decrease the load b

13、earing capacity of a foundation. In such cases, placing foundation column off-center, as shown in Figure is probably advantageous. Doing so in effect, produces a centrally loaded foundation with a uniformly distributed pressure.第22頁/共58頁23FOOTINGS WITH One Way Eccentricity第23頁/共58頁24Footing with Two

14、-way Eccentricities Consider a footing subject to a vertical ultimate load Qult and a moment M as shown in Figures a and b. For this case, the components of the moment M about the x and y axis are Mx and My respectively. This condition is equivalent to a load Q placed eccentrically on the footing wi

15、th x = eB and y = eL as shown in Figure d.第24頁/共58頁25Footing with Two-way Eccentricities第25頁/共58頁26Example 1第26頁/共58頁27Example 1第27頁/共58頁28Example 2第28頁/共58頁29Example 2第29頁/共58頁30Footings with Inclined Loads第30頁/共58頁31Footings with Inclined Loads1. Compute the inclination factors using the equations

16、 given below: inclination of load with respect to vertical2. Use the inclination factors just computed to compute Hansen shape factors as 第31頁/共58頁32Footings with Inclined Loads3. These are used in the following modifications of the edited“ Hansen bearing capacity equation:Use the smaller value of q

17、ut computed by either of Equations. 第32頁/共58頁33The Bearing Capacity of Multi-Layered Soils第33頁/共58頁34The Bearing Capacity of Layered Soils第34頁/共58頁35The Bearing Capacity of Layered Soils In layered soil profiles, the unit weight of the soil, the angle of friction and the cohesion are not constant th

18、roughout the depth. The ultimate surface failure may extend through two or more of the soil layers. Consider the case when the stronger soil is underlain by a weaker soil. If H, the thickness of the layer of soil below the footing, is relatively large then the failure surface will be completely loca

19、ted in the top soil layer, which is the upper limit for the ultimate bearing capacity. If the thickness H is small compared to the foundation width B, a punching shear failure will occur at the top soil stratum, followed by a general shear failure in the bottom soil layer. If H is relatively deep, t

20、hen the shear failure will occur only on the top soil layer.第35頁/共58頁36The Bearing Capacity of Layered Soils Meyerhof and Hanna (1978) and Meyerhof(1974)第36頁/共58頁37第37頁/共58頁38第38頁/共58頁39第39頁/共58頁40第40頁/共58頁41第41頁/共58頁42The Bearing Capacity of Layered Soils Meyerhof and Hannas punching shear coeffici

21、ent Ks第42頁/共58頁43The Bearing Capacity of Layered SoilsVariation of ca/c1 with q2/q1based on the theory of Meyerhof and Hanna (1978)第43頁/共58頁44Example on layered soils第44頁/共58頁45Example on layered soils第45頁/共58頁46Example on layered soils第46頁/共58頁47Ground Factors第47頁/共58頁48Base Factor For footings with angled foundation bases When footing is level, b = 1第48頁/共58頁49RigidityFactors第49頁/共58頁50Bearing Capac