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4th Year Civil                   FOUNDATION ENGINEERING                   BEARING CAPACITY                      OF SHALLOW...
DEFINITION OF SOIL Soil is a mixture of irregularly shaped mineral particles of various sizes containing voids between par...
BEARING CAPACITY OF SOILS Bearing capacity is the ability of soil to safely carry the pressure placed on the soil from any...
Bearing Capacity of Shallow                       Foundations   s    Soil Bearing Capacity is Controlled by:         – Bea...
Types of Foundations                                               Shallow                                               F...
Failure Modes for Shallow Foundations                                          General Shear                              ...
Failure Modes, Continued                 Punching Failure, Zone I Only,                 Loose Sand and Soft ClayApril 5, 2...
Terzaghi’s Assumptions                Zone I, Active.                 Zones II, Transition.                Zones III, Pass...
Terzaghi B/C AssumptionsThree zones do exist:     1- Active zone, just below the foundation.     2- Transition zone, betwe...
Terzaghi Bearing Equation for                        Strip Footing            qu net = c Nc + γ 1 D (Nq - 1) + 0.5 B γ 2 N...
Terzaghi Bearing Equation   qult =   qult = c Nc          Cohesion Termqult = c Nc + γ 1 D Nq                      Above F...
Terzaghi Bearing Equation Nc, Nq, Nγ are Terzaghi B/C Coefficients, f(φ )C, φ            are the soil shear strength param...
Bearing Capacity Factors            qult = c Nc + γ 1 D Nq + 0.5 B γ 2 N γ                                     Nc         ...
Terzaghi Bearing Equation                                                B                   L                        PApr...
Foundation Shape Factorsqult = c.Nc λ c + γ 1 D Nq λ q + 0.5B γ 2 Nγ λ γ For Rectangular or Square Footing λ c = 1.0 + 0.3...
Terzaghi’s Equation for Different                 Foundation Shapes     Continuous (Strip) Footing:       qu = c Nc + γ 1 ...
Footings with inclined loads                                              β                                              P...
Inclined Loads                      λ ci = λ qi = (1.0 - β / 90) 2                                 λ γ i = (1.0 - β / φ )2...
Inclined Load Factorsqult = c Nc λ c λ ci + γ 1 D Nq λ q λ qi + 0.5B γ 2 Nγ λ γ λ γ iInclined Load Factors:λ ci = λ qi = (...
Bearing Capacity of Clay, φ = 0    qult = c Nc + γ 1 D Nq + 0.50 B γ 2 N γ      For Clay:      Nc = 5.70, Nq = 1.0, Nγ = 0...
Bearing Capacity of Sand, cu = 0    qult = c Nc + γ 1 D Nq + 0.50 B γ 2 N γ For Sand: Nc, Nq, Nγ are determined from curve...
Gross and Net Bearing Capacity                qult         qall =          Gross allowable bearing capacity               ...
Effect of Water Table on B/CApril 5, 2012              Bearing Capacity    23
Effect of Water Table on B/Cqult = c Nc + γ 1 D Nq + 0.5B γ 2 Nγ   Case (a):                                           Cas...
Settlement AnalysisAllowable bearing capacity, as calculated from thesettlement analysis, usually controls the soilbearing...
Bearing Capacity in Stratified Deposits                             P                       P = q1 A1 = q1 B1 L1          ...
Settlement Analysis  Total Settlement =  Immediate Settlement +  Primary Consolidation Settlement +   Secondary Consolidat...
Settlement Analysis     In Soft Clays, Silts and Organic Soils:     Total Settlement = Immediate Settlement +     Primary ...
Example   A footing 1.8 m x 2.5 m is located at a depth of   1.5 m below the ground surface, in an over-   consolidated cl...
Solutionqult = c Nc λ c + γ 1 D Nq λ q + 0.5B γ 2 Nγ λ γ  For Clay: Nc = 5.7, Nq = 1.0, Nγ = 0.0 For Rectangular Footing: ...
qult net = 60 x 5.7 x 1.22 = 417.20                  qult net 417.2     qall net   =         =      = 139.08 kN/m 2       ...
April 5, 2012   Bearing Capacity   32
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Transcript of "Bearing capacity"

  1. 1. 4th Year Civil FOUNDATION ENGINEERING BEARING CAPACITY OF SHALLOW FOUNDATIONS Dr. Tarek Nageeb Salem Associate ProfessorApril 5, 2012 Bearing Capacity 1
  2. 2. DEFINITION OF SOIL Soil is a mixture of irregularly shaped mineral particles of various sizes containing voids between particles. The particles are a by-product of mechanical and chemical weathering of rock and described as gravels, sands, silts, and clays.. Any manmade structure should, one way or another, rest and/or transmit its load to the underlying soilApril 5, 2012 Bearing Capacity 2
  3. 3. BEARING CAPACITY OF SOILS Bearing capacity is the ability of soil to safely carry the pressure placed on the soil from any engineered structure without undergoing a shear failure with accompanying large settlements.Therefore, settlement analysis should generally beperformed since most structures are sensitive toexcessive settlement.April 5, 2012 Bearing Capacity 3
  4. 4. Bearing Capacity of Shallow Foundations s Soil Bearing Capacity is Controlled by: – Bearing Capacity Analysis: » Terzaghi’s Theory (1943), based on Prandtl theory (1920). » General B.C. Equation. – Settlement Analysis: » Immediate Settlement » Consolidation SettlementApril 5, 2012 Bearing Capacity 4
  5. 5. Types of Foundations Shallow Foundations Spread Mat or Raft Deep Foundations Belled Pier Friction PilesApril 5, 2012 Bearing Capacity 5
  6. 6. Failure Modes for Shallow Foundations General Shear Failure, Zones I, II, III, Dense Sand Local Shear Failure, Zones I, II, Medium Dense SandApril 5, 2012 Bearing Capacity 6
  7. 7. Failure Modes, Continued Punching Failure, Zone I Only, Loose Sand and Soft ClayApril 5, 2012 Bearing Capacity 7
  8. 8. Terzaghi’s Assumptions Zone I, Active. Zones II, Transition. Zones III, Passive.April 5, 2012 Bearing Capacity 8
  9. 9. Terzaghi B/C AssumptionsThree zones do exist: 1- Active zone, just below the foundation. 2- Transition zone, between the active and passive zones. 3- Passive zone, near the ground surface, just beside the foundation. passive active TransitionApril 5, 2012 Bearing Capacity 9
  10. 10. Terzaghi Bearing Equation for Strip Footing qu net = c Nc + γ 1 D (Nq - 1) + 0.5 B γ 2 Nγ Overburden γ1 D B Failure Zone (depth ≈ 2B)Generalized soil strength : c, φ Soil unit weight : γ 2 (total or(drainage as applicable) effective as applicable)April 5, 2012 Bearing Capacity 10
  11. 11. Terzaghi Bearing Equation qult = qult = c Nc Cohesion Termqult = c Nc + γ 1 D Nq Above F.L.qult = c Nc + γ 1 D Nq + 0.5B γ 2 Nγ Below F.L.April 5, 2012 Bearing Capacity 11
  12. 12. Terzaghi Bearing Equation Nc, Nq, Nγ are Terzaghi B/C Coefficients, f(φ )C, φ are the soil shear strength parametersApril 5, 2012 Bearing Capacity 12
  13. 13. Bearing Capacity Factors qult = c Nc + γ 1 D Nq + 0.5 B γ 2 N γ Nc Nq Nγ 40 Ø – in Degrees 30 20 10 0 70 60 50 40 30 20 10 0 10 20 40 60 80 Nc and Nq 5.7 1.0 NγApril 5, 2012 Bearing Capacity 13
  14. 14. Terzaghi Bearing Equation B L PApril 5, 2012 Bearing Capacity 14
  15. 15. Foundation Shape Factorsqult = c.Nc λ c + γ 1 D Nq λ q + 0.5B γ 2 Nγ λ γ For Rectangular or Square Footing λ c = 1.0 + 0.30 B/L λ q = 1.0 Egyptian Code of Practice λ γ = 1.0 – 0.30 B/L For Circular Footing λ c = 1.30 λ q = 1.00 Egyptian Code of Practice λ γ = 0.70April 5, 2012 Bearing Capacity 15
  16. 16. Terzaghi’s Equation for Different Foundation Shapes Continuous (Strip) Footing: qu = c Nc + γ 1 D Nq + 0.5 B γ 2 Nγ qu-net = c Nc + γ 1 D (Nq - 1) + 0.5 B γ 2 Nγ Square Footing: qu-net = 1.3 c Nc + γ 1 D (Nq - 1) + 0.35 B γ 2 Nγ Circular Footing: qu-net = 1.3 c Nc + γ 1 D (Nq - 1) + 0.35 B γ 2 Nγ N , Nq, Nγ = B.C. Factors cApril 5, 2012 Bearing Capacity 16
  17. 17. Footings with inclined loads β P PInclined Load Factors λ ci, λ qi, λ giApril 5, 2012 Bearing Capacity 17
  18. 18. Inclined Loads λ ci = λ qi = (1.0 - β / 90) 2 λ γ i = (1.0 - β / φ )2 Correction Factors, λ ci, λ qi, and λ γ i are empirically determined from experimentsApril 5, 2012 Bearing Capacity 18
  19. 19. Inclined Load Factorsqult = c Nc λ c λ ci + γ 1 D Nq λ q λ qi + 0.5B γ 2 Nγ λ γ λ γ iInclined Load Factors:λ ci = λ qi = (1.0 – β /90)2λ γ i = (1.0 – β /φ )2April 5, 2012 Bearing Capacity 19
  20. 20. Bearing Capacity of Clay, φ = 0 qult = c Nc + γ 1 D Nq + 0.50 B γ 2 N γ For Clay: Nc = 5.70, Nq = 1.0, Nγ = 0.0 qult = 5.70 cu + γ 1 D qult net = 5.70 cu qall net = 1.90 cu cu = qu/2 qu Unconfined compressive strengthApril 5, 2012 Bearing Capacity 20
  21. 21. Bearing Capacity of Sand, cu = 0 qult = c Nc + γ 1 D Nq + 0.50 B γ 2 N γ For Sand: Nc, Nq, Nγ are determined from curve, and cu = 0, then: qult = γ 1 D Nq + 0.50 B γ 2 N γApril 5, 2012 Bearing Capacity 21
  22. 22. Gross and Net Bearing Capacity qult qall = Gross allowable bearing capacity F .S . qult = qult net + γ 1 D Gross ultimate B/C qult net qall = + γ1 D Gross allowable B/C F .S . qult net qall net = Net allowable B/C F .S . γ 1 D is the overburden pressureApril 5, 2012 Bearing Capacity 22
  23. 23. Effect of Water Table on B/CApril 5, 2012 Bearing Capacity 23
  24. 24. Effect of Water Table on B/Cqult = c Nc + γ 1 D Nq + 0.5B γ 2 Nγ Case (a): Case (b): γ 1 D = γ b (Df-d) + γ sub d, γ 1 D = γ b Df, γ 2 = γ sub γ 2 = γ subCase (c):γ 1 D = γ b Df, γ b = Bulk unit weightIf , d ≤ B, then γ 2 = γ sub γ sub = Submerged Unit weight,If , d > B, then γ 2 = γ b γ sub = γ sat - γ waterApril 5, 2012 Bearing Capacity 24
  25. 25. Settlement AnalysisAllowable bearing capacity, as calculated from thesettlement analysis, usually controls the soilbearing capacity, especially in clay and silt.The maximum allowable settlement is set first,then the stress (bearing pressure) that will inducethat settlement will be the allowable bearingcapacity.For stratified soils, 2:1 stress distribution is used todetermine the stresses at the top of each layer.April 5, 2012 Bearing Capacity 25
  26. 26. Bearing Capacity in Stratified Deposits P P = q1 A1 = q1 B1 L1 B1 soft clay P = q2 A2 = q2 B2 L2 q1 q1 is the allowable q2 bearing capacity for layer 1 2B q is the allowable B2 2 bearing capacity stiff clay or for layer 2, and dense sand so on The allowable bearing capacity as determined from either the shear strength parameters or the settlement analysis.April 5, 2012 Bearing Capacity 26
  27. 27. Settlement Analysis Total Settlement = Immediate Settlement + Primary Consolidation Settlement + Secondary Consolidation Settlement In Sand: Total Settlement ≈ Immediate settlement In Silts, Stiff and Medium Clays: Total Settlement ≈ Immediate Settlement + Primary Consolidation CapacityApril 5, 2012 Bearing Settlement 27
  28. 28. Settlement Analysis In Soft Clays, Silts and Organic Soils: Total Settlement = Immediate Settlement + Primary Consolidation Settlement + Secondary Consolidation SettlementApril 5, 2012 Bearing Capacity 28
  29. 29. Example A footing 1.8 m x 2.5 m is located at a depth of 1.5 m below the ground surface, in an over- consolidated clay layer. The groundwater level is 2 m below the ground surface. The unconfined compressive strength of that clay is 120 kPa, γ bulk = 18 kN/m3, and γ sat = 20 kN/m3. Determine the net allowable bearing capacity, assuming a factor of safety of 3.April 5, 2012 Bearing Capacity 29
  30. 30. Solutionqult = c Nc λ c + γ 1 D Nq λ q + 0.5B γ 2 Nγ λ γ For Clay: Nc = 5.7, Nq = 1.0, Nγ = 0.0 For Rectangular Footing: λ c = 1.0 + 0.30 B/L = 1.0 + 0.30 x 1.8/2.5 = 1.22 λ q = 1.0 qult net = c Nc λ c + γ 1 D (Nq -1) λ q qu = 120 kPa, cu = 60 kPaApril 5, 2012 Bearing Capacity 30
  31. 31. qult net = 60 x 5.7 x 1.22 = 417.20 qult net 417.2 qall net = = = 139.08 kN/m 2 F .S . 3 qall net = 13.91 t/m2 = 1.39 kg/cm2April 5, 2012 Bearing Capacity 31
  32. 32. April 5, 2012 Bearing Capacity 32
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