Geotechnical Eng CH3

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3-1 3 Design of Shallow Foundations by Nagaratnam Sivakugan James Cook University, Townsville, Australia Marcus Pacheco Universidade do Estado do Rio de Janeiro, Brazil 3.1 Introduction .................................................................................. 3-2 3.2 Stresses beneath Loaded Areas .................................................... 3-2 Point and Line Loads ã Uniform Rectangular Loads ã Newmark’s Chart for Uniformly Loaded Irregular Areas 3.3 Bearing Capacity of Sha
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  3-1 3 Design ofShallow Foundations by  Nagaratnam Sivakugan James Cook University, Townsville, Australia Marcus Pacheco Universidade do Estado do Rio de Janeiro, Brazil 3.1Introduction..................................................................................3-23.2Stresses beneath Loaded Areas....................................................3-2 Point and Line Loads ã Uniform Rectangular Loads ã Newmark’sChart for Uniformly Loaded Irregular Areas 3.3Bearing Capacity of Shallow Foundations..................................3-6 Historical Developments ã Terzaghi’s Bearing Capacity Equation ãMeyerhof’s Bearing Capacity Equation ã Hansen’s Bearing Capacity Equation ã Vesic’s Bearing Capacity Equation ã Gross and NetPressures and Bearing Capacities ã Effects of the Water Table ãPresumptive Bearing Pressures 3.4Pressure Distribution beneath Eccentrically LoadedFootings.......................................................................................3-183.5Settlement of Shallow Foundations in Cohesive Soils.............3-19 Immediate Settlement ã Consolidation Settlement ã Secondary Compression Settlement 3.6Settlement of Shallow Foundations in Granular Soils.............3-24 Terzaghi and Peck Method ã Schmertmann et al. Method ãBurland and Burbidge Method ã Accuracy and Reliability of theSettlement Estimates and Allowable Pressures ã ProbabilisticApproach 3.7Raft Foundations........................................................................3-32 Structural Design Methods for Rafts ã Bearing Capacity andSettlement of Rafts 3.8Shallow Foundations under Tensile Loading...........................3-40 Tensile Loads and Failure Modes ã Tensile Capacity Equations inHomogeneous Soils: Grenoble Model Appendix A........................................................................................3-49Appendix B........................................................................................3-50  3-2 Geotechnical Engineering Handbook 3.1Introduction A foundation is a structural element that is expected to transfer a load from a structure to theground safely. The two major classes of foundations are shallow foundations  and deep founda-tions. A shallow foundation transfers the entire load at a relatively shallow depth. A commonunderstanding is that the depth of a shallow foundation ( D   f  ) must be less than the breadth ( B ).Breadth is the shorter of the two plan dimensions. Shallow foundations include pad footings,strip (or wall) footings, combined footings, and mat foundations, shown in Figure 3.1. Deepfoundations have a greater depth than breadth and include piles, pile groups, and piers, whichare discussed in Chapter 4. A typical building can apply 10 – 15 kPa per floor, depending on thecolumn spacing, type of structure, and number of floors.Shallow foundations generally are designed to satisfy two criteria: bearing capacity  and settlement. The bearing capacity criterion ensures that there is adequate safety against possiblebearing capacity failure within the underlying soil. This is done through provision of anadequate factor of safety of about 3. In other words, shallow foundations are designed to carry a working load of one-third of the failure load. For raft foundations, a safety factor of 1.7 – 2.5is recommended (Bowles 1996). The settlement criterion ensures that settlement is withinacceptable limits. For example, pad and strip footings in granular soils generally are designedto settle less than 25 mm. 3.2Stresses beneath Loaded Areas In particular for computing settlement of footings, it is necessary to be able to estimate thestress increase at a specific depth due to the foundation loading. The theories developed forcomputing settlement often assume the soil to be a homogeneous, isotropic, weightless elasticcontinuum. FIGURE 3.1 Types of shallow foundations. (a) Pad footing(b) Strip footing (c) Mat or raft foundation  Design of Shallow Foundations 3-3 3.2.1Point and Line Loads Boussinesq (1885) showed that in a homogeneous,isotropic elastic half-space, the vertical stress in-crease ( ∆σ v  ) at a point within the medium, dueto a point load ( Q  ) applied at the surface (seeFigure 3.2), is given by  ∆σπ v  Q z x z    =+ 3211 2252 ()   (3.1) where z  and x  are the vertical and horizontaldistance, respectively, to the point of interest fromthe applied load.Westergaard (1938) did similar research, assuming the soil to be reinforced by closely spaced rigid sheets of infinitesimal thicknesses, and proposed a slightly different equation: ∆σπ ν ν ν ν v  Q z x z    =−−−−     +      212221222 2232  (3.2) Westergaard ’ s equation models anisotropic sedimentary clays with several thin seams of sandlenses interbedded with the clays. The stresses computed from the Boussinesq equationgenerally are greater than those computed from the Westergaard equation. As it is conservativeand simpler, the Boussinesq equation is more popular and will be used throughout thissection.If the point load is replaced by an infinitely long line load in Figure 3.2, the vertical stressincrease ∆σ v  is given by: ∆σπ v  Q z x z    =+ 211 22 ()  (3.3) 3.2.2Uniform Rectangular Loads The vertical stress increase at a depth z  beneath the corner of a uniform rectangular load (seeFigure 3.3a) can be obtained by breaking the rectangular load into an infinite number of pointloads ( dq    =   Qdxdy  ) and integrating over the entire area. The vertical stress increase is givenby  x z Q  GL ∆ σ v  FIGURE 3.2 Stress increase beneath a pointor line load.
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