UKSSSC- Soil Mechanics

 

INTRODUCTION

Soil Mechanics- The detailed studies about the physical,chemical and geological structure of a soil called soil mechanics. The formation of soil classified in broad categories but here I will discussed on few which are important in the favors of exam only.

Soil Transported by the various medium

THREE PHASE SOIL

Soil Observation by three phase

Description from three phase diagram-

1- void ratio = volume of void / vol. of solid

                  e = Vv/Vs

2- porosity = vol. of void / total volume

                 n = Vv/V

3- degree of saturation = vol. of water / vol. of void

s = Vw/Vv

4- water content = weight of water / weight of solid

w = Ww/Ws

5- unit weight of solid = total weight / total volume

 Y = W/V

 6- dry unit weight = weight of solid / total volume

 Yd = Ws/V

 7- saturated unit weight = weight of solid / volume of solid

 Ysat = Ws/Vs

 8- submerged or bouyent unit weight (Ysub) = Ysat-Yw

 Here Yw = unit weight of water = 9.81 Kn/m2

9- specific gravity = density of solid / density of water

G= ρs/ρw

Specific gravity or water content measured by pycnometer

10- percentage air void = vol.of void / total vol multiple by 100

av = (Vv/V)×100

11- air content = vol. of air / vol. of void

ac = Va/Vv

12- Density = total mass /  total volume

ρ = M/V

13- dry density = mass of solid / total volume

ρd = Ms/V

14- saturated density = mass of solid / volume of solid

ρsat = Ms/Vs

15- submerged or bouyent density (ρsub)= 

 ρsat-ρw 

 Here ρw = density of water = 1000kg/m3

◆ if soil is fully saturated- 

s=1 and Vw=Vv

◆ if soil is fully drya-

s=0 and Vv=0

👉 Important relationship between all above terms are- 

1- relationship b/w void ratio (e) and porosity (n) are-

I)-  e = 1/1-n

II)- n = 1/1+e

2- relationship b/w void ratio (e),porosity (n), degree of saturation (s) and specific gravity (G) - 

wG=es

3- relationship b/w dry unit weight (Yd), unit weight (Y) and water content (w)-

Yd = Y/1+w

4- relationship b/w dry unit weight (Yd),specific gravity (G) and porosity (n)-

Yd = G.Yw(1+n) or Yd = GYw/1+e

5- relationship b/w saturated unit weight(Ysat), dry unit weight (Yd), specific gravity (G) and porosity (n)-

Ysat = G.Yw(1+n)+n.Yw

6- relationship b/w  bouyent unit weight(Ysub), specific gravity (G) and void ratio (e)-

Ysub = (Yw/1+e)×(G-1)

We know that hydraulic critical gradient

 ic = G-1/1+e

Therefore Ysub = Yw×ic

7- relationship b/w air content (ac) and degree of saturation (s)-

ac = 1- s

📝  CHAPTER -2: PERMEABILITY

Permeability or hydraulic conduct measures by permeameter.

"The flow of water through soil mass was first studies by Darcy, who demonstrated experimentely that for Laminar flow of saturated soil mass."

Theory of Discharge (Q) - the rate of flow or the discharge per unit area is proportional to hydraulic gradient (i)

Q ∝ i , remove the proportional 

Q =ki , where k= coefficient of permeability

Hydraulic gradient= head  loss / seepage length

¡ = h1 - h2/ L

Keep in mind 👇

◆ permeability is proportional to square of particles size

◆ permeability inversely proportional to viscosity

◆ permeability proportional to seepage length

◆ permeability depends upon the direction of water through soil mass

Or

Critical hydraulic gradient- ic = G-1/1+e

Exit or downstream gradient -

● minimum = head loss / seepage length

● maximum = ic / factor of safety

Seepage velocity (Vs) = v/n , v= m3/s and n=porosity

Percolation coefficient (kp) = k/n 

k = permeability , n= porosity

Allen Hazen equation for permeability-

I)- particle size b/w 0.1 mm to 3 mm

k = CD¡^2 here i = 10

C = 100 to 150

D¡ = particle size

Particle size measured by Hydrometer

II)- particles size greater than 3mm

k = Cv.Mv.Yw

Mv = coefficient of volume compressibility

Cv = coefficient of consolidation

Yw = unit weight of water

Clay size - 0.0002mm to 0.002mm

Silt size - 0.002mm to 0.06 or 0.075mm

📝  CHAPTER -3: COMPRESSIBILITY

Compressibility of soil measured by Oedometer.

◆Coefficient of compressibility- in a small soil sample phenomena, if the total void in soil mass is e., Increase the pressure at small amount as ∆p, then the coefficient of compressibility expressed by- 

Av = e.-e/∆p

◆Coefficient of volume compressibility -

Mv = Av/1+e

◆Consolidation - situation of consolidation occurs due to effective stress only.

Effective stress = total stress - pore water pressure

◆Coefficient of consolidation-

Cv= k(1-e.)/Av×Yw

◆Coefficient of uniformity-

Cu = D60/D10

Cu=1 that mean a uniform soil mass

Cu>4 well graded soil

Cu<4 poor soil

◆Coefficient of curvature-

Cc = D30 square / D60×D10

Cc= 1 uniform soil mass

Cc= 1 to 3 well graded soil

Cc> 3 poor soil 

Proctor test performing for the measurements of soil compaction.

📝  CHAPTER -4: SHEAR STRENGTH OF SOIL

Shear strength of soil measured by the vane test method.

◆ Angle of internal fraction - the shearing resistance of the soil particles along the plane called angle of internal fraction.

Angular grained > round grained > clay

Dense grained > loose grained > clay

Value of internal angle fraction for various-

Dense soil - 32° to 37°

Loose soil - 25° to 30°

Clay  - 5° to 20°

Shearing strength of soil - soil are classified into two categories.

1- cohesive soil 

2- non cohesive soil

Cohesion = 1/2 unconfined compressive strength of soil

●- for non cohesive soil strength- τ = σtanΦ

●- for cohesive soil strength- τ = c + σtanΦ

Earth pressure = σh/σv (horizontal stress/vertical stress)

Active earth pressure (ka) = 1-sinΦ/1+sinΦ

Ka ∝ cot^2(45°+Φ/2)

Passive earth pressure (kp) = 1+sinΦ/1-sinΦ

Kp ∝ tan^2 (45°+Φ/2)

Kp>Ka always

Earth pressure at rest (Ko) = μ/1-μ

Rankine's earth pressure P- wh^2/2 (1-sinΦ/1+sinΦ)

In terms of depth of foundation H - p/w(1-sinΦ/1+sinΦ)^2

📝  CHAPTER -5: PLASTIC/LIQUID THEORY

◆ The minimum water content at which the soil will just begin to crumble rolled into a tread approximately 3mm in diameter, called plastic limit.

◆ The minimum water content at which the soil is sufficient fluid to flow a special amount when jarred 25 times in a standard apparatus, called liquid limit.

● plastic index = liquid limit - plastic limit

Ip = WL-Wp

● liquid index = W- Wp/WL-Wp

Where W = Moisture Content

● Toughness index IT = Ip/If

Here If = flow index

● Liquid limit = w×(N/25)^0.121

Where w= moisture content

N= Number of blows

● Density index ID = Emax-E / Emax -Emin