Bearing Capacity of Shallow Foundations PDF

Geotechnical Engineering (Part 4) Bearing Capacity of Shallow Foundations Professor Hadi Khabbaz Email: [email protected] C...

Geotechnical Engineering (Part 4) Bearing Capacity of Shallow Foundations Professor Hadi Khabbaz Email: [email protected] CB11.11.244 1 OUTLINE Types of foundations Types of shallow foundations Design criteria Allowable bearing capacity Failure of shallow foundations Failure mechanisms Bearing capacity equation Types of failure Selection of parameters Examples Karl Terzaghi (1883-1963) 2 1  Types of Foundations Deep Deep Foundation Shallow foundation foundation (Piles with (mat or raft foundation) (piles) a pile cap) Shallow Shallow foundation foundation (pat footing) 3 3 Shallow Foundations B ⚫ Condition: D DB Soil ⚫ Types of shallow foundations: Strip footings: Circular, square, rectangular footings: 5 2  Shallow Foundations B ⚫ Condition: D qo = goD DB Soil ⚫ Types of shallow foundations: Strip footings: Unit length Circular, square, rectangular footings: 6 Definition of Shallow Foundations The ratio of the embedment (Df) to the minimum plan dimension (B = width) is: D f  2.5B 7 7 3  Geotechnical Design Criteria ⚫ Design criteria: Strength criterion: ❖ Applied load < Strength of soil Serviceability criterion: ❖ Deformation < Acceptable value 8 Failure of Shallow Foundations ⚫ Methods of analysis: Lower bound approach: ❖ The state of stresses at failure is assumed; ❖ Failure load is obtained based on stress compatibility; ❖ Failure load is less than or equal to the true ultimate capacity. Upper bound approach ❖ Failure mechanism is assumed; ❖ Failure load is obtained based on deformation compatibility; ❖ Failure load is greater than or equal to true ultimate capacity. ⚫ Exact solution exists if the two methods give the same result. 9 4  Transcona Grain Silos The Canadian Pacific Railway Company built the Transcona grain elevator near Winnipeg, Canada in 1913. https://www.geotech.hr/en/case-of-foundation-soil-failure-transcona-grain-elevator/ 10 10 The Foundations of Transcona Grain Silos Failed The failure of the foundation soil occurred due to insufficient bearing capacity of the soil under the foundation structure. https://www.geotech.hr/en/case-of-foundation-soil-failure-transcona-grain-elevator/ 11 11 5  Grain Silos After Remediation After the accident, remediation was carried out by the Foundation Company Limited. Works consisted of building supporting structures, gradually excavating the foundation slabs and building the piles in order to return the building to its original condition. The Transcona grain elevator was purchased by the Parrish & Heimbecker company in 1970 and still exists today. https://www.geotech.hr/en/case-of-foundation-soil-failure-transcona-grain-elevator/ 12 12 What Type of Failure can be observed here? a. Structural Failure b. Sliding Failure QUIZ c. Overturning Failure d. Bearing Capacity Failure 13 6  Failure Mechanism 14 Failure Mechanism O 15 7  Failure Mechanism 16 Bearing Capacity Equation The first general bearing capacity equation for shallow strip footings was proposed by Terzaghi in 1943. qu = cNc + qo Nq + 0.5 gBNg Failure mechanism used by Terzaghi qu qo qo f f 45-f/2 45-f/2 Wedge Passive Zone B Zone Active Zone B 18 8  Bearing Capacity Equation The first general bearing capacity equation for shallow strip footings was proposed by Terzaghi in 1943. qu = cNc + qo Nq + 0.5 gBNg The terms Nq, Ng and Nc are known as the bearing capacity factors. f (o) Nc Nq Ng 0 5.7 1.0 0.0 5 7.3 1.6 0.5 10 9.6 2.7 1.2 15 12.9 4.4 2.5 20 17.7 7.4 5.0 25 25.1 12.7 9.7 30 37.2 22.5 19.7 35 58 41 42 40 96 81 100 45 172 173 298 19 400 1000 Ng Nq Ng 350 Nq 300 100 250 200 150 Nc 10 100 50 Nc 0 1 0 10 20 30 40 50 0 10 20 30 40 50 Friction Angle (o) Friction Angle (o) 20 9  Terzaghi’s Bearing Capacity Factors Alternative Equation An empirical equation for Kpg from the given values of Ng: K pγ = 8ϕ′2 − 4ϕ′ + 3.8 tan2 (60 + ϕ′ Τ2) 21 Bearing Capacity Equation ⚫ The first general bearing capacity equation for shallow strip footings was proposed by Terzaghi in 1943. qu = cNc + qo Nq + 0.5 gBNg The terms Nc,Nq and Ng are known as the bearing capacity factors. ⚫ Bearing capacity equations for other foundation shapes: Square footings: qu = 1.3cNc + qoNq + 0.4 gBNg Circular footings: qu = 1.3cNc + qoNq + 0.3 gBNg Rectangular footings: qu = cNc [1 + 0.3 B / L] + qoNq + 0.5 gBNg [1 − 0.2 B / L] 22 10  Types of Failure ⚫ General shear failure: q qu Sudden failure. Surface heave Settlement Dense or stiff soils 23 23 Types of Failure ⚫ General shear failure: q qu Sudden failure. ⚫ Local shear failure: Medium soil compaction. Minor surface heave Settlement Medium dense or firm soils24 24 11  Types of Failure ⚫ General shear failure: q Sudden failure. ⚫ Local shear failure: qu Medium soil compaction. ⚫ Punching shear failure: Compaction under foundation. Settlement No heave Loose or soft soils 25 25 Types of Failure ⚫ General shear failure: Sudden failure. ⚫ Local shear failure: Medium soil compaction. ⚫ Punching shear failure: Compaction under foundation. ⚫ The failure mechanism corresponds to general shear failure. For local or punching shear failure corrections need to be applied: 2  2 f design = tan −1  tan f  c design = c 3  3 26 12  qu = cNc + qo Nq + 0.5 gBNg For what type of soils? 2  f design = tan −1  tan f  3  2 c design = c 3 27 Selection of Parameters ⚫ Drained: Clays: long time after loading, sands: always. ❖ Soil has high coefficient of permeability or loads are applied at low rate compare with the permeability of soil, no excess pore pressure will be generated. Use effective strength parameters in an effective stress analysis: ❖ Effective cohesion, c; ❖ Effective friction angle, f. ⚫ Undrained: Clays, immediately after loading. ❖ Loading increases pore pressure in soil which may take months to dissipate; Use undrained strength parameters in a total stress analysis: ❖ Undrained cohesion, cu; ❖ Undrained friction angle, fu, (zero for saturated N.C. clay). 28 13  Selection of Parameters Unit weight of soil, g, and water table location: qu = cNc + qo Nq + 0.5 gBNg B qu go qo= go Df Df g g g 29 Selection of Parameters ⚫ Unit weight of soil, g, and water table location: Undrained analysis: ❖ Water table has no effect in a total stress analysis. Drained analysis: ❖ Always use the effective overburden pressure, qo. ❖ Use submerged unit weight g = gt - gw if water table is at or above the base of the foundation. ❖ If water table is at depth d below the foundation base: If d>B, water can be assumed to have no effect. If d