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# Geotechnical Engineering-I [Lec #3: Phase Relationships]

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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-I [Lec #3: Phase Relationships]

1. 1. 1 Geotechnical Engineering–I [CE-221] BSc Civil Engineering – 4th Semester by Dr. Muhammad Irfan Assistant Professor Civil Engg. Dept. – UET Lahore Email: mirfan1@msn.com Lecture Handouts: https://groups.google.com/forum/#!forum/geotech-i Lecture # 3 31-Jan-2017
2. 2. 2 S: Solid Soil particle W: Liquid Water A: Air Air SOIL AS A THREE PHASE SYSTEM
3. 3. 3 SOIL AS A THREE PHASE SYSTEM V = Total volume of soil mass Vs = Volume of soil solids Vw = Volume of water Va = Volume of air Vv = Va+Vw = Volume of voids W = Total weight of soil Ws = Weight of soil solids Wa = Weight of air ≈ 0 Ww = Weight of water
4. 4. 4 1) Void ratio, e (0 < e < ∞) For sands, 0.5 ≤ e ≤ 0.9 For clays, 0.7 ≤ e ≤ 1.5 (or even higher) )V(solidsofVolume )V(voidsofVolume e s v  VOLUMETRIC RATIOS
5. 5. 5 2) Porosity, n (0 < n < 1) Typical range, 9-70% For sands, 25% ≤ n ≤ 50% 3) Air Porosity, na’ (0 < na’ < 1) 4) Percentage Air Voids, na (0 < na < 1) )V(samplesoilofvolumeTotal )V(voidsofVolume n t v  VOLUMETRIC RATIOS )( )( ' t a a VsamplesoilofvolumeTotal VairofVolume n  )( )( v a a VvoidsofVolume VairofVolume n 
6. 6. 6 5) Degree of Saturation/ Saturation Ratio, S (or Sr) (0 < Sr < 100%) 6) Volumetric Water Content, θv (0 < θv < 1) VOLUMETRIC RATIOS %100 )( )(  v w VvoidsofvolumeTotal VwatercontainingvoidsofVolume S )( )( t w v VsamplesoilofvolumeTotal VwatercontainingvoidsofVolume 
7. 7. 7 1) Moisture/Water Content/Gravimetric Water Content, w (0 < w < ∞) Typical value for Sands >> 10-30% For clays >> 10% or higher typically For some organic soils w>100%, even up to 500%. For quick clays w is typically > 100%. WEIGHT RELATIONSHIPS %100 )( )(  s w WsolidssoilofWeight WwaterofWeight w
8. 8. 8 2) Unit Weight, γ 3) Dry Unit Weight, γd 4) Bulk Unit Weight, γb 5) Unit Weight of Soil Solids, γs WEIGHT RELATIONSHIPS );;( 333 cmgftlbmkN V Mg Volume Weight  t s d V W VolumeTotal solidssoilofWeight  t b V W VolumeTotal WeightTotal  s s s V W soildssoilofVolume soildssoilofWeight 
9. 9. 9 6) Saturated Unit Weight, γsat 7) Submerged Unit Weight, γsub (or γbouyant) γw = 9.81 kN/m3 → 1 g/cm3 = 1000 kg/m3 = 62.4 lb/ft3 WEIGHT RELATIONSHIPS wsatsub   VolumeTotal soilsaturatedofWeight sat  Archimede’s principle: The buoyant force on a body immersed in a fluid is equal to the weight of the fluid displaced by that object.
10. 10. 10 SPECIFIC GRAVITY (Gs) w s s CatwaterofvolumeequalofweightUnit soildssoilofweightUnit G      4 Generally for soils 2.6 ≤ Gs ≤ 2.7
11. 11. 11 WEIGHT-VOLUME RELATIONSHIPS w b d   1   n n e   1 e e n   1 VG W n ws s 1 . 1   1 ..  s ws W GV e           e w G wsb 1 1 . e G ws d   1 .  S Gw e s.    e eG ws sat    1      e Gsw sub    1 1  rv Sn.
12. 12. 12 CONCLUDED REFERENCE MATERIAL An Introduction to Geotechnical Engineering (2nd Edition) By R. D. Holtz, W. D. Kovacs and T. C. Sheahan Chapter #2 Geotechnical Engineering – Principles and Practices - (2nd Edition) By Donald P. Coduto, M. R. Yeung and W. A. Kitch Chapter #4 Fundamentals of Soil Mechanics By M. S. Qureshi & Aziz Akbar Chapter #3