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# Geotechnical Engineering-II [Lec #19: General Bearing Capacity Equation]

Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.

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### Geotechnical Engineering-II [Lec #19: General Bearing Capacity Equation]

1. 1. 1 Geotechnical Engineering–II [CE-321] BSc Civil Engineering – 5th Semester by Dr. Muhammad Irfan Assistant Professor Civil Engg. Dept. – UET Lahore Email: mirfan1@msn.com Lecture Handouts: https://groups.google.com/d/forum/geotech-ii_2015session Lecture # 19 15-Nov-2017
2. 2. 2 Terzaghi (1943) developed the theory for continuous/strip foundations (simplest, 2D problem).  BNNDNcq qfcult '5.0''  Contribution of: Shear strength Surcharge Soil self- weight  sBNNDsNcq qfccult '5.0''  General form of Terzaghi’s Bearing Capacity Theory sc and sγ → shape factors TERZAGHI’S BEARING CAPACITY THEORY
3. 3. 3  BNNDNcq qfcult '5.0''  TERZAGHI’S BEARING CAPACITY THEORY
4. 4. 4 GENERAL BEARING CAPACITY EQUATION  After Terzaghi, several researchers worked in this area.  Bearing capacity factors Nc and Nq do not change much.  Nγ varies, mainly because of the assumption of the wedge shape of soil immediately below the foundation. Meyerhof (1963) presented a general form of bearing capacity equation as follows;  idsBNidsNDidsNcq qqqqfccccult '5.0''  sc, sq and sγ → shape factors dc, dq and dγ → depth factors ic, iq and iγ → inclination factors
5. 5. 5 MEYERHOF’S BEARING CAPACITY EQUATION To be used with Vesic’s equation as well
6. 6. 6 GENERAL BEARING CAPACITY EQUATION Hensen’s (1970) general bearing capacity equation;  bgidsBNbgidsNDbgidsNcq qqqqqqfccccccult '5.0''  sc, sq and sγ → shape factors dc, dq and dγ → depth factors ic, iq and iγ → inclination factors gc, gq and gγ → ground factors (based on ground slope) bc, bq and bγ → base factors (tilted base) Vesic (1975) general bearing capacity equation is identical, but with slightly different factors.
7. 7. 7 GENERAL BEARING CAPACITY EQUATION
8. 8. 8 GENERAL BEARING CAPACITY EQUATION
9. 9. 9 Practice Problem #3 A square column foundation is to be designed for a gross allowable load of 250 kN. If the load is inclined at an angle of 15° to the vertical, determine the width of the foundation. Take a factor of safety of 3.0.  = 19 kN/m3, f’ =35°, and c’ = 5 kN/m2 the depth of foundation is 1.0 m.
10. 10. 11 Practice Problem #4
11. 11. 14 EFFECT OF GROUNDWATER TABLE ON BEARING CAPACITY Shallow groundwater affects soil shear strength in two ways: 1. Reduces apparent cohesion which is present in soil in unsaturated state → may necessitate reducing the cohesion measured through UCCT 2. Pore water pressure increases → reduces both effective stress and shear strength in the soil
12. 12. 15 Case-III EFFECT OF GROUNDWATER TABLE ON BEARING CAPACITY Case-I Case-II
13. 13. 16 Case I Groundwater table is located at a distance D above the bottom of the foundation. Case-I  BNNDcNq qfcult 5.0 1. Modify γDf term as γ(Df – D) + γsub.D 2. Modify 0.5γBNγ term as 0.5γsubBNγ Where, γsub = γsat - γw EFFECT OF GROUNDWATER TABLE ON BEARING CAPACITY
14. 14. 17 Case II Groundwater table is located at the foundation base.  BNNDcNq qfcult 5.0 1. No change to γDf term. 2. Modify 0.5γBNγ term as 0.5γsubBNγ Where, γsub = γsat - γw Case-II EFFECT OF GROUNDWATER TABLE ON BEARING CAPACITY
15. 15. 18 Case III Groundwater table is located at a depth D below the foundation base.  BNNDcNq qfcult 5.0 1. No change to γDf term. 2. Use γav in the third term; γav = γ (for D > B) γav = 1/B [γD + γsub (B – D)] (for D ≤ B) γsub = γsat - γw Case-III EFFECT OF GROUNDWATER TABLE ON BEARING CAPACITY
16. 16. 19 CONCLUDED REFERENCE MATERIAL Foundation Analysis and Design (5th Edition) Joseph E. Bowles Chapter #4 Principles of Geotechnical Engineering (7th Edition) Braja M. Das Chapter #16