01 Fundamental of surveying

Earth shape : oblate spheroid of revolution

i) Geodatic Survey 

⇒Σangle < 540°

⇒By triangulation

ii) Plane Survey

⇒dam, highway, railway

⇒area < 260 km² 

⇒195km² 

iii) Topographical syr : natural features valley,lake,river

iv) Hydrographic syr : large water bodies

v) Engineering syr : design & construction of new routes ,roads & railway

vi) Geological syr : diff strata of earth surface

vii)Cadastral syr :plans of property boundaries for legal purpose. Revenue chain used 

viii) Astronomic syr : azimuths , latitude, longitude, absolute location of a point on earth

ix) Longitudinal land syr : linear bars used

★SOI : toposhot 1:50000.

⇒Archeological syr : old & nelic str info.

★traffic(topographic)→Reconnaissance→Preliminary →Detail/location/final survey.

PRINCIPLE OF SURVEYING:

a) work from whole to part : localise error & prevent their accumulation

b) Locate a point by atleast two measurement

⇒two side

⇒one side one angle

⇒two angle

⇒one side one right angle

SCALE:

⇒engineer scale : 1cm = 30m , RF = 1/3000

⇒Repersentative fraction (RF) = map distance/ground distance.

Types of scale :

i) Plain scale : two dimensions, units & tenth

ii) diagonal : three dimensions ,units, tenth & hundreds :m dm cm

iii) Shrunk scale = Original scale x shrinkage factor (SF)

⇒SF or SR = shrunk/original length = shrunk RF/original = Shrunk scale/original.

⇒Graphical scale not affected due to shrinkage of map ∴ better than Numerical scales.

⇒1/100 is larger than 1/1000

⇒ correct L & A = Lm / S.R. & Am / (SR)².

★correct = ( std ± δ ) x L,A,V. (+ longer than std & -ve shorter than std.)

iv) Vernier : (DRE 10 = 9 11 19)

a) Direct vernier 

⇒shorter than div. main scale

⇒reading /graduatⁿ in directⁿ of main scale

⇒n div of direct = ( n - 1 ) div. of main scale.

b) Retrograde Vernier.

⇒longer than div. of main scale

⇒opp direction of main scale

⇒n div = (n + 1) div of main scale

c) Extended Vernier.

⇒ n div = ( 2n - 1 ) div of main scale.

⇒Least count of main scale = s/n, 

s = value of one smallest div. of main scale

n = no. of div. on the Vernier.

Building = 1 : 1000

Town planing = 1 : 5000

Route (Rd & rail) = 1 : 10000

Topogrphical syr = 1 : 25000

Error = measured - true.

Correction = True - measured.

i). Cumulative/systematic errors : 

⇒ ∝ L ,(+ve or -ve )

⇒may increase or decrease with increase in measurement

⇒ occur in same direction & tend to accumulate

ii). Compensating/Random errors

⇒ ∝ √L , (

⇒occur in both direction & tend to compensate.

★permissible error hilly/rough region = 1 in 250.

Instruments:

⇒Horizontal distance = tape ,chain, tachometer & EDM

⇒Vertical distance = Tacheometer & Level

⇒H. Angle = compass, theodolite, total station & sextant.

⇒V.Angle = sextant, clinometer, theodolite.

⇒Paralex bar: parallex diff, use with mirror stereoscope.

⇒Substance bar: horizontal distance only.

⇒minidraft = T square + set square.

Soil origin & type

⇒father →Dr. Karl Terzaghi

⇒Pedogenesis: process of soil formation

⇒geological cycle : Weathering → transportation →deposition →upheavel →wheathering & repeat.

 ⇒Residual soil : bentonite

 ⇒Glacial soil : till, drift ,glacier deposit

 ⇒ colluvial /talus : Gravity deposit ,found in valley

 ⇒muck or peat : swamp & march deposit

TYPES OF SOIL :

⇒Alluvial : river deposit, dark in colour

⇒black cotton soil : low shearing strength , more swelling & shrinkage due to montmorillonite.

⇒Loess : wind blown, collapsible, (0.1mm - 0.05mm), yellowish or pallor colour.

⇒Loam : mix of sand silt & clay; best for plant growth & garden.

⇒Bentonite : a clay ,formed from volcanic ash by chemical action,used as lubricant.

⇒Peat : organic soil ,wind blown

★soil containing organic matters are of spongy nature.

 

Human eye light phenomenon

Humen Eye :

⇒basically a convex lens

⇒least distance of distinct vision = 25cm

⇒iris : ctrl size of pupil ←focus light

⇒Retina : real & inverted image of obj.

Defects

i) Myopia/short sightedness :

⇒can see near obj but not far

⇒diverging (concave lens)

ii) Hyperopia / hypermetropia/longshightedness :

⇒can see far but not near

⇒Converging (convex lens)

iii) Presbyopia : 

⇒elderly person : nearby obj can't seen

⇒Bifocal lens or two separate lens.

iv) Astigmatism:

⇒cylindrical lens.

v) Cataract : 

⇒crystalline lens become milky & cloudy at old age

⇒surgery.

Consolidation of soil

CONSOLIDATION SETTLEMENT:= immidiate + primary(1°) + secondary (2°)

★consolidation is fⁿ of eff stress but not total stress

i) initial → expulsion of air

Si = qB(1 - μ²)/Es ∝ If

ii) primary →excess pore water due to ↑ total stress. , time dependent

⇒ ∆H/H = ∆e/1+eo

⇒∆H = mv ∆ ⁻σHo = {CcHo/1+eo}log(

iii) secondary → plastic readjustment (due to creep) , constant eff stress.

⇒significant only for Highly plastic soil.

★Temp ↑ : rate of consolidation ↑

★Oedometer test / consolidation test : 

1D consolidation (zero lateral strain )

max pore water pressure will at centre

★odometer : distance in vehicle.

⇒Routine consolidation test (lab) : specimen t = 20mm , dia = 60mm

⇒general settlement formula {∆H/H = ∆V/V = ∆e/1+eo}

⇒e = wG(S=1) ,∆H = Hi - Hf , ∆e = eo-ef

1.} compression index (Cc)(coeff of compression) : a constant value

Cc ∝ LL

Cc = 0.009 (LL-10)← undisturbed & medium sensitivity.

Cc = 0.007(LL-10)←Remoulded & low to medium sensitivity.

Cc = ∆e/log(σ2/σ1) ∝ ∆H

Cc = 0.115Wn

2}Coeff of compressibility (Av) : variable not constant

Av = strain/stress = ∆e/∆σ ←m²/kn

1D & ∆σ = small then Av = constant.

3} coeff of vol compressibility (mv)

mv = Av/1+eo

★eo ↑ : ultimate settlement ↓

TERZAGHI 1-D CONSOLIDATION TEST.

→ only for 1-D

→analysis to behaviour of spring piston model

→homogeneous & isotropic soil

→fully saturated , laminar flow ( Darcy law valid)

→speciman t = 60mm

→e vs σ relation is linear

→rate of change of pore water with time

δu/δt = Cv x δ²u/δz² (u=γwh)

⇒Coeff of consolidation : 

 {Cv = K/mvγw = k(1+eo)/Avγw } ←cm²/s

→determination of Cv:

a} casagrande method ( logarithm of time fitting method)

Cv ∝ 1/LL ∝ 1/plasticity & Cc ∝ LL ∝ plasticity.

b} Taylor's m (square root time fitting )

Taylor curve much suitable as compared to casagrande m.

 TIME FACTOR

 Tv = Cvt/d². d = H (1 way drainage) & d= H/2 (2 way drainage)

 Tv = πu²/4 (u ≤ 60%)

{ T50 = 0.196 , T90 = 0.848 , T60 = 0.287 , To =0 }

 u = ∆h/∆H = (eo - e )/(eo - ef)

SHEAR strength of soil

⇒Shear strength bparameters (C , ϕ ) are not inherent properties ,they are related to type of test & condition under measured

⇒penitration test → field test ( τ ) 

★failure on soil occurs by shearing never by crushing

★τ ∝ eff stress ( not total stress)

⇒Coulomb eqn : {τ = C + σ tanϕ}

⇒ Terzaghi modification :{τ = C' + ⁻σ tanϕ'}

⇒{ ⁻σ = σ - u } , u ← pore water pressure 

  ★cohesionless soil (C=0) → τ ∝ σ ∝ rate of loading

⇒angle of failure {Ø= 45 + ϕ/2} ← with major principal plane.

→Clay ϕ= 5°-20°

A} DIRECT SHEAR TEST :

→ sand & gravel not for clay

→eff σ = total σ ( bcz U = 0)

→{τ = C' + ⁻σ tanϕ'}

→quick, inexpensive & simple

→shear & vertical deflection are measured (dial gauge)

Disadvantages: 

 a) drainage condition uncontrolled & pore water pressure can't measured

 b) failure plane predetermined & always horizontal

 c) non-uniform stress distⁿ

 

B} VANE SHEAR TEST : 

⇒soft clay , sensitive soil , cohesive soil , plastic clay soil

⇒lab test : silty sand shear parameters

⇒used to find sensitivity also {sensitivity = Cu undisturbed / Cu remoulded }

{Cu = qu/2}

{shear strength→ τf = Cu ←undrained cohesion}

⇒τ f = T /πd²(½h +⅙d) ← 2way shear top & bottom & if nothing is give..

 τ f = T /πd²(½h +¹/12d) ←one end shear from bottom

 

C}TRIAXIAL TEST:

→all type of soil 

→ Lenght / dia = 2-2.5

→pore water pressure & vol. Change can be measured

→drainage condtⁿ best controlled

→Axial strain & deviator stress are determined

→{ σ1 = σ3 tan²(45+ϕ/2) + 2C tan(45+ϕ/2) } & ϕ=0←undrain 

Stage 01 : cell pressure or consolidatⁿ test

Stage 02 : shear stage or deviater stage

{(σ 1)f = σ 3 +(σ d)f} & {σ 3= σ c}

{Sin ϕ = (σ 1 - σ 3)/(σ 1 + σ 3)}

⇒confined compressive strength = σ d at failure = P/Af

Type of TT

UU - clay ,quick test(15min)

CD - sand ,slow test 

CU - dam embankment

UD - physically impossible 

Representation of TT

⇒pure clay ϕ = 0 ←undrain test on sat clay

⇒CD test on NC clay then clay behave like sand (C=0)

⇒for C-ϕ soil →CD test on OC clay behave like silt

D} UNCONFINED COMPRESSⁿ TEST: 

⇒a undrained test

⇒cohesive soil ( saturated clay & silt) not for coarse grain soil

⇒special case of TT σ 3 = σ c = 0

⇒no moisture loss

⇒qu = 2Ctan (45 + ϕ/2) for clay ϕ = 0

⇒

PORE PRESSURE coeff : 

⇒B = ∆Uc/∆σc = 0 - 1 dry =0, fully saturated soil = 1

⇒A = -0.5 for OC soil & = 3 for loose soil

soil classification, MINERALOGY & structure

CLASSIFICATION (IS 498:1978):
1} The Unified Soil Classification System (USCS):
⇒4 major group: coarse,fine,organic & peat(Pt)
⇒general engg purpose
⇒coarse grain : based on size(sand,gravel)
⇒fine grain : based on plasticity chart.(fine sand, silt, clay)
2} American Association of state Highway & Transportation Official (AASHTO):
⇒into 8 groups
⇒GI = 0.2a + 0.005ac + 0.01bd  (range 0 - 20) if -ve it is reported as 0.
GI=0 ←good subgrade material, GI = 20 ←very poor subgrade material.
3} Indian standard soil classification system.
⇒coarse grain : based on size,fineness,Cc & Cu.
⇒fine grain : basis of PI,LL & compressibility.
★BIS classified soil in 18 groups.
⇒Highway research → 7 types of soil (based on particle size & plasticity)
★clay : aquiclude

Boulder > 300mm
Cobble : 300 - 80mm
Gravel : 80 - 4.75mm
Sand : 4.75 - 0.075mm(75μ)
Silt : 0.075mm - 0.002mm(2μ)
Clay < 0.002mm(2μ)
★partical size ↓ : surface area ↑ : permeability↓ : compressibility↑.
⇒sand particle are madeup of Quartz (rock mineral)

FINE GRAIND SOIL CLASSIFICATION:
⇒A-line : Ip = 0.73(LL- 20)  –(i)
⇒Ip = LL - PL  –(ii)
⇒(ii)>(i) : clay (C) & (ii)<(i) : silt(M) or organic soil
⇒ Ip or PI = 4 - 7 ←CL-ML soil.
⇒LL<35 : low plastic (L) , 35<LL<50: intermediate plastic (I) , LL>50: Highly plastic (H)
★CH→highly plastic clay.

CLAY MINERALS:
i) montmorillonite:
⇒Vanderwall force ( weakest force)
⇒Black cotton soil & Bentonite
⇒activity 1 - 7
ii) illite :
⇒activity 0.5 - 1
⇒K+ve Bond (ionic bond)
⇒stiff clay & soft clay
iii)kaolinite:
⇒Activity 0.4-0.1
⇒china clay
Hydrogen bond (most stable bond)
★M>i>K>silica →Dry strength , PI , plasticity, swelling & shrinkage , Activity
Grain size : K>i>M

SOIL STRUCTURE:
i} Single Grained str : (>0.02mm)
⇒C-less soil , Gravel & Sand
ii} Honey combed str : (0.02mm - 0.002mm)
⇒gravity & surface electric force
⇒sand & silt
iii} flocculated str: (<0.002mm)
⇒edge of face orientation
⇒clay partical settle on sea bad
⇒low compressibility, High permeability & shear strength
iv} Dispersed str : (w of soil >omc)
⇒face to face configuration, ∥ to each other.

Permeability of soil

Darcy Law :

 ⇒1D flow & fully saturated soil

 ⇒Re ≤ 1

 ⇒ laminar flow

 ⇒fine grounded soil ,not for gravel

 ⇒{V = Ki} & {q = KiA} i = ∆h/L

 V→discharge velocity or superficial V or avg velocity

 ⇒Vs = V/n = Ki/n

 ★Vs > V

 ⇒ coeff of percolation Kp = K/n

 ⇒ coeff of Transmissibility T = KH ,H←thickness of aquifer

 ★coeff of absolute permeability / intrinsic permeability: Ko = Kμ / γw (cm² or m²)

Factor affecting K:

⇒K ∝ D10²

⇒K ∝ e³/ 1+e ∝ e²

⇒K ∝ γw/μ

⇒K ∝ 1/impurties

⇒K ∝ DOS

⇒K ∝ Temp ∝ 1/μ

⇒K ∝ 1/ρsoil

⇒K ∝ size ( less size → high compressibility)

⇒K ∝ 1/compressibility

⇒– σ↑ : e↓ : K↓

Determination of K:

A} laboratory methods

A.1) constant head method :

⇒coarse graind soil & pervious soil like sand & gravel 

⇒K = QL/thA ( Q=kia)

A.2) Falling/variable head m: 

⇒fine soil & impervious soil like clay 

⇒K= (aL/Ato) x (2.303log(h1/h2))

B} Field test:

B.1) Pumping out : 

⇒large Area

⇒homogeneous coarse grain soil

⇒radii of influence: R = 3000d √K (sichardts formula)

B.2) Pumping in:

⇒small Area

⇒economical bu less reliable

C} Indirect method :

i) from consolidation data

ii) from particle size & Specific surface area

⇒kozeny - Carman equation : 

K = (1/c) x (γ w/μ) x (e³/1+e) x D10²

⇒Allen Hazen's formula :

K = CD10² cm/s C=100,D10→cm

⇒Louden's formula :

⇒Tarzaghi's eqⁿ

K= 200e²D10²

⇒consolidation eqⁿ :

K = CvMvγw

★{K1/K2 = tanϕ1 / tanϕ2}

Gravel > 1cm/s →very pervious

Sand = 1 to 10⁻³ →Pervious

Silt = 10⁻³ to 10⁻⁶ →poorly pervious

Clay < 10⁻⁶ cm/s →Impervious

Kh = ΣKiHi / ΣHi

Kv = ΣHi / Σ(Hi/Ki)

★(Kh > Kv)

eff permeability k' = √(Kx.Kz)