Visco-elastic Layers

Transcription

1 Visc-elasic Layers

2 Visc-elasic Sluins Sluins are bained by elasic viscelasic crrespndence principle by applying laplace ransfrm remve he ime variable Tw mehds f characerising viscelasic maerials: Mechanical mdel Creep cmpliance curve

3 Spring - lasic lasic: Sress α Srain

4 Dashp - Viscus λ 0 0 λ λ λ Viscus: Sress α ime rae f srain λ λ Under cnsan sress, i.e.,

5 Maxwell Mdel λ + λ + λ + T λ Where, T relaxain ime

6 Kelvin Mdel + λ λ 0 0 λ λ ( ) 0 0 ln λ ln λ T e e λ exp T if a cnsan Sress is applied, T is reardain ime. When, 0, 0; when, / When, T, / Therefre, T is he ime reach 63.2% f al rearded srain.

7 Burgers Mdel + + exp T T T T Three cmpnens f srain:. lasic srain 2. Viscus srain 3. Rearded elasic srain

8 Three Cmpnens f Srain exp T T /

9 Generalised Mdel T Under a cnsan sress, he srain in a generalised mdel is given by T + n + T i exp Ti i 2 n T 2 T n Creep cmpliance: D() ()/ () ime dependen srain under cnsan sress D( ) + T + n i i exp Ti

10 xample n Creep Cmpliance 2 T 5 Deermine he creep cmpliance a varius imes and pl he creep cmpliance. 0 T 0 Time D() Time D() T T is in kn/m 2 T is in secnd D() is in m 2 /kn

11 Cllcain Mehd The creep cmpliance f visc-elasic maerials are deermined frm creep ess. Cmpued and acual respnses are clleced a predeermined ime respnses. A 000 s creep es wih cmpliances measured a differen ime durains f 0.00, 0.003, 0.0, 0.03, 0., 0.3,, 3, 0, 30 and 00 s is recmmended. Insead f deermining bh T i s and i s, several arbirary values f T i s are assumed and crrespnding i s are fund by slving simulaneus equains. Reardain imes Ti f 0.0, 0.03, 0.,, 0, 30 and secnds are specified.

12 lasic Sluins Given he creep cmpliance f each viscelasic maerial a a given ime, he viscelasic sluin a ha ime can be easily bained frm he elasic sluins:

13 Visc-elasic sluins frm elasic sluins Given he creep cmpliance f each visc-elasic maerial a a given ime, bain he visc-elasic sluins a ha ime frm he elasic sluins using Burmiser s w-layer hery. µ 0.5, h 254 mm a 254 mm p 690 kpa µ 2 0.5, h 2 Creep Cmpliance Values f he Layers Time, s D() f Layer, 0-6 /kpa) D() f Layer 2, 0-6 /kpa)

14 Time Temperaure Superpsiin Time emperaure shif facr is defined as a T T T Where, T ime bain creep cmpliance a emperaure T T ime bain creep cmpliance a emperaure T

15 Time Temperaure Superpsiin Labrary ess n asphal mixes have shwn ha a pl f lg a T varies linearly wih emperaure. β β T lg 0 T T T 0 lg a T Temperaure r lg T T β ( T T T β ( T T ) T T r 0 exp[ β ( T T )] T ) [ ( T T )] r T T exp β (A) By subsiuing equain (A) fr in he creep cmpliance equain, creep cmpliance a emperaure T can be bained.

16 Analysis f Mving Lads 6a A Lad has pracically n effec a A when i is a a disance f 6a. A The inensiy f lad a A reaches a maximum value f p (cnac pressure) when he wheel is exacly abve he pin. A 6a The inensiy f lad a A reaches zer again when he wheel is beynd a disance f 6a.

17 Analysis f Mving Lads L() p L( ) p sin π π + 2 d 2 +d/2 0 d +d/2 When 0, L() p ±d/2, L() 0 By aking he speed f vehicle, v, as 7.7 m/s (64 km/hr) and he radius f cnac, a, as 53 mm, he durain f lad, d, can be cmpued as d (2 a)/v (2 0.53)/ s

18 Nn-linear Layers Mdulus f elasiciy () f nn-linear layers depends n he sress level The relain beween and he sress level depends n he ype f maerial Fr granular maerials he fllwing relain is used: K θ Where, K 2 K and K 2 are he parameers f he maerial be calibraed θ sum f nrmal sresses and weigh f layered sysems i.e., θ x + y + z +γz(+2k ) K cefficien f earh pressure a res 0.6

19 Nn-linear Layers Fr fine grained sils he fllwing relain is used: K + K 3 (K 2 - d ) when d <K 2 K K 4 ( d - K 2 ) when d >K 2 The parameers, K, K 2, K 3 and K 4 are deermined in a ri-axial resilien mdulus es by pling resilien mdulus (M R ) versus deviar sress ( d ) as shwn in he figure d - 3 and 2 3 n a ri-axial specimen. K 3 In layered sysems, M R K 2 K 4 d 0.5( ) + γz(-k ) K 0.8 K d

20 Apprximae Mehd fr Nn-linear lasic Sluins Divide he nn-linear layer in sub layers f 50 mm hick r less and use he sress a mid heigh f each layer fr cmpuing value As furher apprximain, he sress a mid heigh f a nn-linear layer culd be used fr cmpuing

21 Demnsrain f KNLAYR