Basic formulas for geotechnical engineering

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A handy reference formula for use in geotechnical analysis and design FieldΒ  Given Below :

  1. 𝐼𝑓=π‘Š1βˆ’π‘€2log10𝑁2/𝑁1
  2. 𝐼𝑑=𝐼𝑝𝐼𝑓
  3. 𝐢𝑒=𝐷60𝐷10
  4. 𝐢𝑐=𝐷302𝐷60𝐷10
  5. 𝐼𝑃=0.73 (π‘€πΏβˆ’20)
  6. 𝐼𝑃=π‘€πΏβˆ’π‘€π‘ƒ
  7. 𝐼𝑠=π‘€π‘ƒβˆ’π‘€π‘†
  8. 𝐼𝐿=π‘€βˆ’π‘€π‘ƒπΌπ‘ƒ
  9. 𝐼𝑐=π‘€πΏβˆ’π‘€πΌπ‘ƒ
  10. 𝐴=𝐼𝑝𝐹where 𝐹 is clay fraction (Activity)
  11. 𝑅𝐷=π‘’π‘šπ‘Žπ‘₯βˆ’π‘’π‘’π‘šaπ‘₯βˆ’π‘’π‘šπ‘–π‘›=1/𝛾𝑑,π‘šπ‘–π‘›βˆ’1/𝛾𝑑1/𝛾𝑑,π‘šπ‘–π‘›βˆ’1/𝛾𝑑,π‘šπ‘Žπ‘₯
  12. π‘˜1π‘˜2=tan𝛼1tan𝛼2 (non homogeneous)
  13. π‘˜=πΆπ›Ύπ‘€πœ‡π‘’31+𝑒𝑑2
  14. 𝐾=π‘˜πœ‡π›Ύπ‘€(absolute permeability)
  15. π‘˜=π‘žπœ‹ln(π‘Ÿ2/π‘Ÿ1)𝑧22βˆ’π‘§12 (Permeability in unconfined aquifer)
  16. π‘˜=π‘ž2πœ‹π‘ln(π‘Ÿ2/π‘Ÿ1)𝑧2βˆ’π‘§1 (Permeability in confined aquifer)
  17. π‘˜β„Ž=π‘˜1𝐻1+π‘˜2𝐻2𝐻1+𝐻2 (effective horizontal permeability in stratified soils)
  18. π‘˜π‘£=𝐻1+𝐻2𝐻1π‘˜1+𝐻2π‘˜2 (effective vertical permeability in stratified soils)
  19. π‘˜π‘’=βˆšπ‘˜β„Žπ‘˜π‘£(effective permeability)
  20. π‘˜=π‘ŽπΏπ΄π‘‘lnβ„Ž1β„Ž2 (falling head permeability test)
  21. π‘˜=π‘žπΏπ΄β„Ž(constant head permeability test)
  22. π‘ž=π‘˜π‘’β„Žπ‘π‘“π‘π‘‘Β (seepage discharge)
  23. πœŽπ‘§=3𝑄2πœ‹1𝑧2 (11+(π‘Ÿπ‘§)2 )52 (Boussinesq’s formula)
  24. πœŽπ‘§=𝑐𝑄2πœ‹1𝑧2 (1𝑐2+(π‘Ÿπ‘§)2 )32 where 𝑐=√1βˆ’2πœ‡2βˆ’2πœ‡(Wesrwegaard’s formula)
  25. πœŽπ‘§=2π‘žπœ‹π‘§(11+(π‘₯𝑧)2)2 (line load)
  26. πœŽπ‘§=π‘žπœ‹(2πœƒ+sin2πœƒ) whereΒ πœƒ=tanβˆ’1𝑏𝑧(stress under centre of strip load of width 2𝑏 )
  27. πœŽπ‘§=π‘žπœ‹(2πœƒ+sin2πœƒsin2βˆ…)Β where 2πœƒ=𝛽1βˆ’π›½2Β π‘Žn𝑑2βˆ…=𝛽1+𝛽2 ( strip eccentric point)
  28. πœŽπ‘§=π‘ž(1βˆ’cos3πœƒ) whereΒ πœƒ=tanβˆ’1𝑅𝑧(stress under centre of circular load)
  29. sinβˆ…=𝜎1βˆ’πœŽ3𝜎1+𝜎3 (for cohesion less soils)
  30. sinβˆ…=(𝜎1βˆ’πœŽ3)/2𝑐cotβˆ…+(𝜎1+𝜎3)/2 (for cohesive soils)
  31. 𝜎1=2𝑐tan𝛼+𝜎3tan2𝛼where 𝛼=45+βˆ…2
  32. tanβˆ…=𝜏𝜎(shear box test for cohesion less soils)
  33. 𝑇=π‘πœ‹π·2(𝐻2+𝐷6) (if both top and bottom surfaces contributes)
  34. 𝑇=π‘πœ‹π·2(𝐻2+𝐷12) (if only bottom surface contribute)
  35. 𝑆𝑖=π‘žπ΅Β 1βˆ’πœ‡2𝐸 𝐼𝑓 (immediate settlement )
  36. 𝑆𝑓=𝑆𝑝(𝐡𝑓𝐡𝑝𝐡𝑝+0.3𝐡𝑓+0.3)2 (settlement of footing based on plate settlement)
  37. Δ𝑒=𝐡(Ξ”πœŽπ‘)+𝐴𝐡(Ξ”πœŽπ‘‘) (Skempton’s pore pressure parameters)
  38. π‘ž=π‘šπ‘ƒ+π‘˜is stress path equation whereΒ βˆ…=tanβˆ’1π‘šΒ and 𝑐=π‘˜/cosβˆ…
  39. 𝐢𝑐=Δ𝑒log10𝜎0+Ξ”πœŽπœŽ0
  40. 𝐢𝑐=0.009 (π‘€πΏβˆ’10) (for normally consolidated soil)
  41. 𝐢𝑐=0.007 (π‘€πΏβˆ’10) (for over consolidated soil)
  42. Δ𝑒1+𝑒0=Δ𝐻𝐻
  43. π‘šπ‘£=Δ𝐻/π»Ξ”πœŽ0
  44. 𝑐𝑣=π‘˜π›Ύπ‘€π‘šπ‘£
  45. 𝑇𝑣=𝑐𝑣𝑑𝑑2
  46. 𝑇𝑣=πœ‹4π‘ˆ2 whenΒ π‘ˆβ‰€0.6
  47. 𝑇𝑣=βˆ’0.933 log10(1βˆ’π‘ˆ)βˆ’0.085 whenΒ π‘ˆ>0.6
  48. 𝑆𝑓=𝐢𝑐𝐻1+𝑒0 log10𝜎0+Ξ”πœŽπœŽ0
  49. 𝑆𝑓=πΆπ‘Ÿπ»1+𝑒0 log10πœŽπ‘πœŽ0+𝐢𝑐𝐻1+𝑒0 log10𝜎0+Ξ”πœŽπœŽπ‘
  50. π΄π‘Ÿ=𝐷02βˆ’π·π‘–2𝐷𝑖2
  51. 𝑆𝑛=𝑐𝑒𝐹𝛾𝐻
  52. π‘žπ‘’=𝑐𝑁𝑐+π‘žπ‘π‘ž+0.5 𝛾 𝐡 𝑁𝛾 (Terzaghi’s strip)
  53. π‘žπ‘’=1.3 𝑐𝑁𝑐+π‘žπ‘π‘ž+0.4 𝛾 𝐡 𝑁𝛾 (Terzaghi’s square)
  54. π‘žπ‘’=1.3 𝑐𝑁𝑐+π‘žπ‘π‘ž+0.3 𝛾 𝐡 𝑁𝛾 (Terzaghi’s circle)
  55. π‘žπ‘’=(1+0.3𝐡𝐿) 𝑐𝑁𝑐+π‘žπ‘π‘ž+(1βˆ’0.2𝐡𝐿)0.5 𝛾 𝐡 𝑁𝛾 (Terzaghi’s rectangle)
  56. π‘žπ‘’=𝑐𝑁𝑐𝑆𝑐𝑑𝑐𝑖𝑐+π‘žπ‘π‘žπ‘†π‘žπ‘‘π‘žπ‘–π‘ž+0.5 𝛾 𝐡′ 𝑁𝛾 𝑆𝛾𝑑𝛾𝑖𝛾 (Meyerhof)

𝐡′=π΅βˆ’2𝑒π‘₯Β and 𝐿′=πΏβˆ’2 𝑒𝑦

  1. π‘žπ‘›π‘’=𝑐𝑁𝑐(Skempton

𝑁𝑐=5(1+0.2𝐷𝑓𝐡)(1+0.2𝐡𝐿)

Limiting value of 𝐷𝑓/𝐡 𝑖𝑠 2.5

  1. 𝑄𝑒=π‘Šβ„Žπœ‚β„Žπ‘†+𝐢 (ENR) where 𝐢=2.54Β π‘π‘šΒ π‘“π‘œπ‘ŸΒ π‘‘π‘Ÿπ‘œπ‘Β β„Žπ‘Žπ‘šπ‘šπ‘’π‘ŸΒ π‘Žn𝑑 0.254Β π‘π‘šΒ π‘“π‘œπ‘ŸΒ π‘ π‘‘π‘’π‘Žπ‘šΒ β„Žπ‘Žπ‘šπ‘šπ‘’π‘Ÿ
  2. 𝑄𝑒=π‘Šβ„Žπœ‚β„Žπœ‚π‘π‘†+𝐢2 (Hiley)

where 𝐢=𝐢1+𝐢2+𝐢3

𝐢1=9.05𝑅𝐴 with dolley and 𝐢1=1.77𝑅𝐴 without dolley and 𝐢2=0.657𝑅𝐿𝐴 𝐢3=3.55𝑅𝐴 𝐿=πΏπ‘’π‘›π‘”π‘‘β„ŽΒ π‘œπ‘“Β π‘ƒπ‘–π‘™π‘’Β π‘–π‘›Β π‘šΒ π‘…=π‘ƒπ‘–π‘™π‘’Β π‘π‘Žπ‘π‘Žπ‘π‘–tπ‘¦Β π‘–π‘›Β π‘‘π‘œπ‘›π‘›π‘’π‘ =0.1𝑄 𝐴=π‘π‘Ÿπ‘œπ‘ π‘ Β π‘ π‘’π‘π‘‘π‘–π‘œπ‘›Β π‘Žπ‘Ÿπ‘’π‘ŽΒ π‘œπ‘“Β π‘π‘–π‘™π‘’Β π‘–π‘›Β π‘π‘š2

πœ‚π‘=π‘Š+𝑒2π‘ƒπ‘Š+𝑃 whenΒ π‘Š>𝑃

πœ‚π‘=π‘Š+𝑒2π‘ƒπ‘Š+π‘ƒβˆ’(π‘Šβˆ’π‘’π‘ƒπΈ+𝑃)2 whenΒ π‘Š<𝑃𝑒

  1. 𝑄𝑒=π‘Šβ„Žπœ‚β„Žπ‘†+𝑆02 (Danish) 𝑆0=√2πœ‚β„Žπ‘Šβ„ŽπΏπ΄πΈ
  2. 𝑄𝑒=𝐴𝑝𝑐𝑁𝑐+𝐴𝑠𝛼𝑐 (clays)
  3. 𝑄𝑒=𝐴𝑝𝑐𝑁𝑐+π΄π‘ πœ†(πœŽΜ…+2𝑐) (clays)
  4. 𝑄𝑒=π΄π‘πœŽΜ…Β π‘π‘ž+π΄π‘ πœŽΜ…Β π‘˜tan𝛿(sands)Β πœŽΜ…Β π‘–π‘›π‘π‘Ÿπ‘’π‘Žπ‘ π‘’Β π‘’π‘π‘‘π‘œΒ 15Β π‘‘Β π‘‘π‘’π‘π‘‘β„Ž
  5. 𝑄𝑒=𝑁(𝐴𝑝𝑐𝑁𝑐+𝐴𝑠𝛼𝑐) or 𝑄𝑒=(𝐴𝑔𝑝𝑐𝑁𝑐+𝐴𝑔𝑠 𝑐) (Group)
  6. π‘π‘Ž=π‘˜π‘ŽπœŽΜ…βˆ’2π‘βˆšπ‘˜π‘Ž+𝑒
  7. 𝑝𝑝=π‘˜π‘πœŽΜ…+2π‘βˆšπ‘˜π‘+𝑒
  8. π‘˜π‘Ž=1βˆ’sinβˆ…1+sinβˆ…andΒ π‘˜π‘=1+sinβˆ…1βˆ’sinβˆ…
  9. 𝐻𝑐=2π‘π›ΎβˆšπΎπ‘ŽΒ and unsupported vertical cut =2𝐻𝑐
  10. π‘˜π‘Ž=sin2(𝛽+βˆ…)sin2𝛽sin(π›½βˆ’π›Ώ) (1+√sin(βˆ…+𝛿)sin(βˆ…βˆ’π‘–)sin(π›½βˆ’π›Ώ)sin(𝛽+𝑖))2 (Coulomb’s active )
  11. π‘˜π‘=sin2(π›½βˆ’βˆ…)sin2𝛽sin(𝛽+𝛿) (1βˆ’βˆšsin(βˆ…+𝛿)sin(βˆ…+𝑖)sin(𝛽+𝛿)sin(𝛽+𝑖))2 (Coulomb’s passive )
  12. π‘˜π‘Ž=cosπ›½βˆ’βˆšcos2π›½βˆ’cos2βˆ…cos𝛽+√cos2π›½βˆ’cos2βˆ…andΒ π‘ƒπ‘Ž=π‘˜π‘Žπ›Ύβ„Ž22cos𝛽 (Inclined backfill)
  13. π‘˜π‘=cos𝛽+√cos2π›½βˆ’cos2βˆ…cosπ›½βˆ’βˆšcos2π›½βˆ’cos2βˆ…and 𝑃𝑝=π‘˜π‘π›Ύβ„Ž22cos𝛽 (Inclined backfill)
  14. 𝑁𝑐=15+12(π‘βˆ’15)Β π‘€β„Žπ‘’π‘›π‘>15Β π‘Žπ‘›π‘‘Β π‘π‘=π‘Β π‘€β„Žπ‘’π‘›Β π‘β‰€15 (dilatancy)
  15. 𝑖𝑐=πΊβˆ’11+𝑒(Quick sand condition)
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Hello friends, my name is Bipin Kumar, I am the Writer and Founder of this blog and share all the information related to Civil Engineering, Civil practical Knowledge, Site Execution Knowledge, latest information about construction and more through this website.

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