ENCE 4610 Foundation Analysis and Design Shallow Foundations: Overview Terzaghi s Method of Bearing Capacity Estimation

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1 ENCE 4610 Foundation Analysis and Design Shallow Foundations: Overview Terzaghi s Method of Bearing Capacity Estimation

2 Types of Shallow Foundations Shallow foundations are usually placed within a depth D beneath the ground surface less than the minimum width B of the foundation Shallow foundations consist of: Spread and continuous footings Square, Rectangular or Circular Footings Continuous footings Ring Foundations Strap Footings Wall footings Mats or Rafts

3 Footings A spread footing distributes column or other loads from the structure to the soil, where B < W < 10B A continuous footing is a spread footing where W > 10B. A wall footing is a long load bearing footing

4 Dimension and Rubble Stone Footings Before 1800, most all footings were unreinforced masonry, as shown Dimension stone footings Rubble stone footings Satisfactory for lighter structures, they were too heavy for the larger structures of the 19 th century

5 Steel Grillage Footings Used first with the Montauk Block Building in Chicago (1882). First foundation type specifically designed for flexure.

6 Typical Concrete Footing

7 Methods of Construction of Concrete Footings Once form is made, before concrete is poured either anchor bolts or dowels are placed to enable connection of the foundation with the building. Formed footing

8 This image cannot currently be displayed. Mat Foundations A mat is continuous in two directions capable of supporting multiple columns, wall or floor loads. It has dimensions from 20 to 80 ft or more for houses and hundreds of feet for large structures such as multi-story hospitals and some warehouses Ribbed mats, consisting of stiffening beams placed below a flat slab are useful in unstable soils such as expansive, collapsible or soft materials where differential movements can be significant (exceeding 0.5 inch).

9 Conditions for Mat Foundations Structural loads require large area to spread the load Soil is erratic and prone to differential settlements Structural loads are erratic Unevenly distributed lateral loads Uplift loads are larger than spread footings can accommodate; weight of the mat is a factor here Mat foundations are easier to waterproof Example: Chase Tower, Houston, TX Mat foundation is 3 metres thick and bottomed at 19.2 m below street level

10 Distribution of Bearing Pressure Distribution of bearing pressure depends on Eccentricity, if any, of applied load Magnitude of the applied moment, if any Structural rigidity of the foundation Stress-strain properties of the soil Roughness of the bottom of the foundation Spread footings are nearly rigid; effects of foundation/soil flexibility usually ignored Mat foundations are more flexible; flexibility an important factor

11 Bearing Pressure Distribution Concentric Loads Flexible foundation on clay Flexible Foundation on Sand Rigid foundation on clay Rigid Foundation on Sand Simplified Distribution

12 Terms Used in Shallow Foundations Total Overburden Pressure q o 0 Intensity of total overburden pressure due to the weight of both soil and water, at the base level of the foundation Effective Overburden Pressure q o = 1 γ D + γ D w sat w Effective overburden pressure at the base of the foundation 0 1 = γ D + γ D w sub w Ultimate Bearing Capacity o Maximum bearing capacity of the soil at which shear failure takes place Net Bearing Capacity o Bearing capacity in excess of the overburden pressure q = q q nu Gross and Net Allowable Bearing Pressure u q a = o qu F

13 Bearing Capacity Failure General Shear Failure o Most common type of shear failure; occurs in strong soils and rocks Local Shear Failure o Intermediate between general and punching shear failure Punching Shear Failure o Occurs in very loose sands and weak clays

14 Soil Conditions and Bearing Capacity Failure (after Vesić (1973)

15 Comments on Shear Failure Usually only necessary to analyse 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 analysed, but in practical terms is usually secondary to settlement analysis

16 Development of Bearing Capacity Theory Application of limit equilibrium methods first done by Prandtl on the punching of thick masses of metal Prandtl's methods adapted by Terzaghi to bearing capacity failure of shallow foundations Vesić and others (Meyerhof, Brinch Hansen, etc.) improved on Terzaghi's original theory and added other factors for a more complete analysis

17 Assumptions for Bearing Capacity Methods Foundation-Soil Interface Assumptions Foundation is very rigid relative to the soil No sliding occurs between foundation and soil (rough foundation) Loading Assumptions Applied load is compressive and applied vertically to the centroid of the foundation* No applied moments present Geometric assumption Depth of foundation is less than or equal to its width Geotechnical Assumptions Soil beneath foundation is homogeneous semi-infinite mass* Mohr-Coulomb model for soil General shear failure mode is the governing mode (but not the only mode) No soil consolidation occurs Soil above bottom of foundation has no shear strength; is only a surcharge load against the overturning load* * We will discuss workarounds to these assumptions

18 Limit Equilibrium Method (Circular Failure Surface, Cohesive Soil) M B 2 A = q ult Bb πcbb B p 0 Bb = B 2 0 q N q ult c ult = = = 2 πc + p 0 2 π 6.28 N c c + p 0 Assume: No soil strength due to internal friction (cohesive soil,) shear strength above foundation base neglected

19 Skempton Bearing Capacity (Undrained Cohesive Soils) Uses circular and other slip surface forms Only for undrained, uniform cohesive soils (non-uniform with modification) Equation for unit gross ultimate capacity: q ult = N c + p 0 Bearing capacity factor for rectangular foundations: ( Nc ) = R c ( N ) B c S L 100

20 Failure Geometry for General Bearing Capacity Methods

21 Terzaghi Equations and Factors

22 Terzaghi Bearing Capacity Equation Eccentricity will be explained later

23 Terzaghi Bearing Capacity Factors

24 Terzaghi Bearing Capacity Factor Table

25 Example of Terzaghiʹs Method Use Terzaghi's Method Given Square Foundation as Shown Grounwater table is 50' below surface Ignore slab-on-grade flooring Find Ultimate bearing capacity and column load to produce same

26 Example of Terzaghiʹs Method q = 1.3 c' N + q N ult c o q γ' BN γ ( Square ) Solve for q ult Obtain Bearing Capacity Factors

27 q ult Example of Terzaghiʹs Method = q ult = 1.3 c' ( 1.3 )( 150 )( ) + ( 121 )( 2 )( ) + ( 0.4 )( 121 )( 3.25 )( 19.7 ) q Compute ultimate capacity ult P ult = q ult * A P ult = (15,780)( ) P ult = kips N ult c + σ' zd Keep in mind that the design load supported by the foundation includes the weight of the footing, which is part of the dead load N q = q = 15,780 psf γ' BN γ

28 Notes on Terzaghiʹs Method Since soil cohesion can be difficult to quantify, conservative values of c (cohesion) should be used Frictional strength is more reliable and does not need to be as conservative as cohesion Terzaghi's 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 It is primarily presented for historical reasons

29 Other Variations of Terzaghi s Method Presented in Textbook Formulation for Rectangular Foundations o o o Rectangular foundations not part of original Terzaghi theory of bearing capacity Equations given in the book an extrapolation Rectangular foundations (all shallow foundations, really) better analyzed using methods such as Vesić, Meyerhof, Brinch-Hansen, etc.) Bearing Capacity for Local Shear Failure o o o Equations for local shear failure have different coefficients but same bearing capacity factors Unless otherwise stated, assume general shear failure (but see Vesić chart presented earlier) Make sure you don t use these for general shear failure and vice versa Equations for special cases of c = 0 or φ = 0

30 Questions?

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