1) Shallow foundation D/B ≤ 1, D = depth of foundation, B = breadth

Deep foundation D/B > 1

2) SHEAR FAILURES

General shear failure

Density index > 70

Penetration number > 30

Angle of internal friction > 36°

Void ratio < 0.5

Ultimate bearing capacity > 200 kN/ m2

Local shear failure

Density index < 20

Penetration number < 10

Angle of internal friction < 28°

Void ratio > 0.75

Ultimate bearing capacity < 100 kN/ m2

Punching shear failure

Ultimate bearing capacity < 30 kN/ m2

3) Mohr coloumb equation S = C + Ω tanФ

4) Flow ratio = tan2(45+(Ф/2))

5) Effective stress = total stress – pore water pressure

6) Relative density = ((emax - e)/( emax - emin))

7) Void ratio = (water content x specific gravity) / degree of saturation

8) Relation between poisons ratio (µ) and earth pressure (k) is

K = µ / (1-µ)

9) Average permeability in horizontal direction

Kh = (K1H1+K2H2+………..KnHn) / (H1+H2+……Hn)

K – permeability, H – thickness

10)Average permeability in vertical direction

Kv = (H1+H2+………..Hn) / ((H1 /K1)+ (H2/K2)+…… (Hn /Kn))

K – permeability, H – thickness

11)Relation between coefficient of permeability and effective size

K = C x D102 where C = 100

12)Seepage velocity = V / N = Ki / porosity

13)Constant head permeability K = QL / ATH

14)Total settlement = depth x coefficient of compressibility x pressure increment

Coefficient of compression = decrease in void ratio / increase in pressure

15)Residual factor = (peak - residual) / (peak - insitu)

16)Compatiability = (emax - emin) / emin

17)Air voids = porosity x air content

Air content = 1 – degree of saturation

18)Plasticity index = liquid limit – plastic limit = (Wl - Wp)

19)Liquidity index = (water content – plastic limit) / plasticity index

20)Consistency index = (liquid limit – water content) / plasticity index

21)Shrinkage index = plastic limit – shrinkage limit

22)Toughness index = plasticity index / flow index

23)Sensitivity = undisturbed sample / remoulded sample

24)Ultimate point resistance capacity of pile is = 14.7C , where C is cohesion

25)Influence factor = 1 / number of elements of chart

26)Degree of saturation = volume of water in soil / volume of voids

27)For silty sand, (emax/ emin )= 3

28)Activity (A) = plasticity index / percentages finer than 2µ

A < 0.75 inactive

A = 0.75 to 1.25 normal

A > 1.25 active