ECGD 4122 – Foundation Engineering Faculty of Applied Engineering and Urban Planning Civil Engineering Department 2nd Semester 2008/2009 ECGD 4122 – Foundation Engineering Lecture 5

Content Bearing Capacity Concepts Analysis for Shallow Foundations

Bearing Capacity Failures Modes of Soil Failure: General shear failure Local shear failure Punching shear failure

Terzaghi Bearing Capacity Formulas

General Shear Failure

Local Shear Failure

Punching Shear Failure

Model Tests - Vesic (1973)

General Guidelines Footings on clays - general shear Footings on dense sands (> 70%) - general shear Footings on loose to medium dense - local shear Footings on very loose sand (< 35%) - punching shear

Terzaghi’s Basic Assumptions D  B No sliding between footing and soil Soil is a homogeneous semi-infinite mass General shear failure Footing is very rigid compared to soil

Terzaghi Bearing Capacity Formulas General Shear Failure For Continuous foundations: For Square foundations: For Circular foundations:

Terzaghi Bearing Capacity Factors General Shear Failure

Terzaghi Bearing Capacity Formulas Local Shear Failure

Modified General Ultimate Bearing Capacity Formula

Modified General Ultimate Bearing Capacity Formula

Modified General Ultimate Bearing Capacity Formula

Modified General Ultimate Bearing Capacity Formula

Modified General Ultimate Bearing Capacity Formula

Effect of GWT Level

Effect of GWT Level Case I: 0 ≤ D1 ≤ Df

Effect of GWT Level Case II: 0 ≤ d ≤ B

Effect of GWT Level Case III: d > B

Selection of Soil Strength Parameters Use saturated strength parameters Use undrained strength in clays (cu) Use drained strength in sands For intermediate soils with partially drained conditions, undrained shear strength can be used but it will be conservative

Other Approaching Methods Skempton (1951) Meyerhof (1953, 1963) De Beer and Ladanyi (1961) Brinch Hanson (1961, 1970) Vesic (1973, 1975) Others

Factor of Safety Depends on: Type of soil Level of uncertainty in soil strength Importance of structure Consequences of failure Likelihood of design load occurrence

Factor of Safety Gross Allowable Bearing Capacity Net Allowable Bearing Capacity

Factor of Safety

Design Factor of Safety

Example 1 Use Terzaghi’s formula to determine the gross allowable load for the square footing shown below at a general shear failure condition with no GWT effect. Take Nc = 17.69, Nq = 7.44, N = 3.64, and FS = 3.0.

Example 1 - Solution

Example 2 Redo the previuos example under a local shear failure condition with no GWT effect. Use Terzaghi’s formula. Take Nc = 11.85, Nq = 3.88, N = 1.12, and FS = 3.0.

Example 2 - Solution

Example 3 Refer to the previous example to determine the net allowable load. Use Terzaghi’s formula. Take FS = 3.0.

Example 3 - Solution

Example 4 Determine the breadth of the square footing shown below using Terzaghi’s formula to withstand a gross mass of 30 tons with no GWT level effects. Nc = 57.75, Nq = 41.44, N = 45.41, and FS = 3.0.

Example 4 - Solution

Example 5 Determine the required breadth of a square footing using the general bearing capacity formula to withstand a gross load of 150 kN at a depth of 0.7 m with no GWT level effects. The applied load is inclined at angle of 20º to the vertical. c’ = 0, ’ = 30º,  = 18 kN/m3, Nq = 18.40, N = 22.40, and FS = 3.0.

Example 5 - Solution

Example 5 - Solution

Example 5 - Solution

Example 5 - Solution

Example 6 Determine the safe gross vertical loading for the square footing shown below using Terzaghi’s formula. Take Nq = 23.18, N = 22.02, and FS = 3.0.

Example 6 - Solution