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Formula Sheet
Chapter 2: Soil Origin & Grain Size
Uniform Coefficient 𝑪
𝑼
Gradation Coefficient 𝑪
𝑪
(𝐷 30 )^2
Chapter 3 : Soil - Phase relations Water (moisture)
content 𝒘^
Void Ratio 𝒆
Porosity 𝒏
Degree of Saturation 𝑺
Volume of water 𝑽𝑾 𝑆 𝑥 𝑛 𝑥 𝑉𝑡
Moist density
𝑥 𝜌𝑤 = 𝑘𝑔/𝑚^3
𝑥 𝛾𝑤 = 𝑘𝑁/𝑚^3
Dry density
3
= 𝑘𝑁/𝑚^3
Saturated Density 𝝆𝒔𝒂𝒕
𝑥 𝜌𝑤 = 𝑘𝑔/𝑚^3
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Saturated Unit
Weight 𝜸𝒔𝒂𝒕
𝑥 𝛾𝑤 = 𝑘𝑁/𝑚^3
Chapter 4 : Plasticity of Soil (Atterberg limits) Water (moisture)
content 𝒘^
Plasticity index 𝑷𝑰 𝐿𝐿 − 𝑃𝐿
Liquidity Index 𝑳𝑰
Shrinkage Limit 𝑺𝑳 (
Effective density when Submerged
● Sieve sizes: Sieve Number Opening Size ( mm ) Sieve Number Opening Size ( mm ) 4 4.750 50 0. 6 3.350 60 0. 8 2.360 80 0. 12 1.680 100 0. 16 1.180 140 0. 20 0.850 200 0. 30 0.600 270 0. 40 0.
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Table 3.1: Typical Values of Drained Angles of Friction for Sands and Silts
Soil Type 𝝓 (deg) μ = tan𝝓
Sands: Rounded Grains
Loose 27 - 30 0.51 - 0.
Medium 30 - 35 0.58 - 0.
Dense 35 - 38 0.70 - 0.
Sands: Angular grains
Loose 30 - 35 0.58 -.
Medium 35 - 40 0.70 - 0.
Dense 40 - 45 0.84 - 1.
Gravel with some Sand 34 - 48 0.67 - 1.
Silts 26 - 35 0.49 - 0.
Chapter 7: Shear Strength of Soils
Shear Strength 𝝉f = c + 𝝈ntan𝝓
Normal Stress 𝝈n = 𝛾. Z = Load \ Area
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Chapter 8: Bearing Capacity Ultimate Bearing Capacity for Isolated Foundations
Strip qu = c Nc + q Nq + 0.5 𝛾 BN𝜸 = kPa
Square qu = 1.3 c Nc + q Nq + 0.4 𝛾 BN𝜸 = kPa q = 𝛾 Df
Circular qu =1.3 c Nc + q Nq + 0.3 𝛾 BN𝜸 = kPa
Ultimate Bearing Capacity for Foundations near Slope
qu = c Ncq + 0.5 𝛾 BN𝜸q
For granular soils (c = 0) qu = 0.5 𝛾 BN𝜸q
For cohesive soils ( 𝝓 = 0) qu = c Ncq
Stability Number Ns =
𝛾 𝑥 𝐻 𝒄 Foundations subjected to Eccentric Loads
qmax =
𝑄 𝐵 𝑥 𝐿
6 𝑀 𝐵^2 𝑥 𝐿
≤ qallow. qmin =
𝑄 𝐵 𝑥 𝐿
6 𝑀 𝐵^2 𝑥 𝐿
Eccentricity "𝒆" =
𝑻𝒐𝒕𝒂𝒍 𝒗𝒆𝒓𝒕𝒊𝒄𝒂𝒍 𝒍𝒐𝒂𝒅 𝑴𝒐𝒎𝒆𝒏𝒕 𝒐𝒏 𝒕𝒉𝒆 𝒇𝒐𝒖𝒏𝒅𝒂𝒕𝒊𝒐𝒏
𝑴 𝑸
qmax (eccentric) =
𝑄 𝐵𝑥𝐿
6 𝑒 𝐵
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Settlement Settlement = instantaneous settlement 𝜹𝒊 + consolidation settlement 𝜹𝒄 𝛥 = 𝜹𝒊 + 𝜹𝒄
𝟐
P2 = P1 + 𝚫P 𝚫P =
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Chapter 13: Soil Seepage Flow Rate Equation
K = permeability H = Hight diff. of water bodies Nf = Num. of Flow Lines Nh = Num. of Equip. Lines
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I 3 Tables
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● Conversion table: 𝟏 𝒄𝒎 = 0. 393 𝑖𝑛𝑐ℎ𝑒𝑠 𝟏 𝑲𝑷𝒂 = 0. 1450 𝑃𝑠𝑖 (^) 𝟏 𝒎𝟑^ = 35. 314 𝑓𝑡^3 𝟏 𝒎 = 3. 280 𝑓𝑡 𝟏 𝑴𝑷𝒂 = 145. 038 𝑃𝑠𝑖 𝟏 𝒚𝒅𝟑^ = 27 𝑓𝑡^3 𝟏 𝒚𝒅 = 3 𝑓𝑡 𝟏 𝑲𝑵 = 224. 8 𝑙𝑏𝑓 𝟏 𝒌𝒈/𝒄𝒎𝟑^ = 62 , 428 𝑙𝑏/𝑓𝑡^3 𝟏 𝒌𝒈 = 2. 204 𝑙𝑏 𝟏 𝑷𝒔𝒊 = 0. 00689 𝑀𝑃𝑎 𝝆𝑪𝒐𝒏𝒄. = 145 𝑙𝑏/𝑓𝑡^3 𝑺𝑮 𝒓𝒂𝒏𝒈𝒆 𝒐𝒇 𝒘𝒐𝒐𝒅 < 𝟏 (^) 𝝆𝑾 = 62. 4 𝑃𝑐𝑓 𝝆𝑪𝒐𝒏𝒄. = 0. 002323 𝑘𝑔/𝑐𝑚^3 𝑺𝑮 𝒐𝒇 𝒄𝒆𝒎𝒆𝒏𝒕 = 3. 15 𝑙𝑏/ 𝑓𝑡^3 𝝆𝑪𝒐𝒏𝒄. = 145 𝑃𝑐𝑓 𝝆 = 𝑚 / 𝑣 = 𝑆𝐺 𝑥 𝜌𝑊 𝑲𝒊𝒍𝒐 = 1 𝑥 10 3 , 𝑴𝒆𝒈𝒂 = 1 𝑥 10 6 , 𝑮𝒊𝒈𝒂 = 1 𝑥 10 9 𝝆𝒘 = 1000 𝐾𝑔/𝑚^3 • 𝝆𝒘 = 1 𝑔/𝑐𝑚^3 • 𝜸𝒘 = 𝟏 0 𝐾𝑁/𝑚^3 • 𝜸 = 𝝆 𝒙 𝒈
I 4 Table
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