Nombor :3009023

Lecture 2 - Layeristic theory

- Can look at stress or strain under repeated loading.

r

cumulationp

t = r + p

Mr = d / r ;d = deviator stressr = recoverable strain

Wave Form

Square W by Mc Lean. (1974)

Sin (/2 + t/d)

Sinusoidal Wave by Barksdale (1971)

Sin2 (/2 + t/d)

t = thickness of specimend = diameter of specimen

Determine the load duration of the given layer setup

________________________________Bituminous 3" 10"________________________________Base ________________________________Sub base 16"________________________________Subgrade

Vehicle speed = 40 mph (64 kmh)

From Figure 7.3 (Barksdales) Haversine waveFrom Figure 7.4 (Mc Leans) Square wave

Table l

Vertical Stress Pulse Times (load duration)MaterialB. SurfaceBase C.SB Course

Depth (in)31020Haversine w0.028 s0.041 s0.064 sSquare w0.014 s0.020 s0.031 s

Asphalt Mixes

Mr, can use triaxial or IDT (repeated)

Triaxial IDT

Mr = P (v + 0.2734) t

Where P = dynamic loadv = poisons ratio = total recoverable deformation (inches)t = specimen thickness

Granular Material

Granular & Fine grained soil

Mr = K 3nor Mr = K1 K2Where 3 = Confining stress

K1, K2 = non Linear Coefficients (function of material property)

= stress invariant = 1 + 23 = d + 33K1 is the slope interceptK2 is the slope of curve

Exercise to model MR equation

Given:

LVDT distances = 4 in (100 mm)Average recoverable deformation after 200th repetitions of linear stress

(See table 7.2)

d of 1,2,3,4,8,10 (psi)

Solution Plot MR VS (stress invariant) Find K1 when = 1 K2 from eq : Slope (K2) = log (18.58/3.69) = 0.351 log (100/1) K1= 3690 psi

Therefore MR = 3690 x 610.351 = 15,619 psi

Subgrade Soil

R value using stabilometer (Hveem) California Highway Division

Measures internal friction of material.R = 100 100 __________ (2.5/D2)(Pv/Ph.1) + 1Pv = Applied Vertical Pressure (1.1 MPa = 160 psi)D2 = Displacement of fluid to increase pressure from 5 to 100 psi (35 to 690 kPa)

R value ranges from 0 10 if the sample is liquid (Ph = Pv) ; R = 0 If the sample is rigid no deformation . Therefore Ph = 0 ; R = 100 CBR Value

MR = 1500 (CBR) by Heukelom & Klomp (1962)If CBR 5 x 106 N/m2 < x 109 N/m2

log Sm = 4 + 3 (log Sb-8)+ 4 - 3 2 2 |log Sb-8| + 2

1 = 10.82 13.42 (100 - Vg)Vg + Vb2 = 8.0 + 0.00568 Vg + 0.0002135 Vg23 = 0.6 log (1.37 Vb2-1) 1.33 Vb-14 = 0.7582 (1-2)

for Sb > 109 N/m2 < 3 x 109 N/m2

log Sm = 2 + 4 + 2.0959 (1 - 2- 4) (log Sb-9)

The above equation are SI units.

The Asphalt institute Method.

By Hwang & Witczak (1979)

|E*| = 100,000 x 101 1 = 3 + 0.0000052 - 0.00189 2 f -1.1 2= 4 0.5 T5 3 = 0.553833 + 0.028829 ( P200 f-0.1703) 0.03476va + 0.070377 + 0.931757 f-0.02774 4 = 0.483Vb 5 = 1.3 + 0.49825 log f

1 & 2= temporary constants f = load frequency HzT = temperature (F) P200 = % by with of ass passing # 200 sieve. Va = Vol. of anivoids = Asphalt viscocity at 70F ( x 106 poise ) Vb= volume of bitumen (%) if viscocity at 70F not available = 29,508.2 (P77F) -2.193P77F = Pen at 77F

Comparison of A.I & Shell Method

1. A.I considers % of fines passing # 200

2. A.I uses pen. or Vis of original Asphalt but Shell uses pen. or Vis of recovered Asphalt (from mix).

3. A.I uses temperature and Vis of A.C Shell uses normalized temperature (which is above and below TR&B & P.I

Fatigue Equations

By Bonnaure (1980)- Shell

For constant stress test

t = [36.43 PI 1.82 PI (Vb) + 9.71 Vb 24.04] x 10-6 (Sm)-0.28 (Nf)-0.2 - metric (5x109) (106) t = tensile strainP.I = penetration indexVb = % bitumen vol.Sm = stiffness modulus (N/M2) from nomograph Nf = number of repetitions to failure

if Sm is in psi

then Nf = [0.0252 PI 0.00126 PI (Vb) + 0.00673 Vb 0.0167]5 t-5 Sm-1.4

For Constant Strain (less than 50 mm thick HMA)

t = [36.43 PI- 1.82 PI (Vb) + 9.71 Vb - ?4.04] x 10-6 (Sm)0.36 (Nf)-0.2 metric ( 5x1010 ) (106 )

Fatigue Testing

center point testing 3rd point testing cantilever beam indirect tensile testing (repeated)

Test Procedures

Constant Stress

NN

Constant Strain

NN

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