4.2 Boussinesq s Theory. Contents

Transcription

1 00477 Pvement Stuctue 4. Stesses in Flexible vement Contents 4. Intoductions to concet of stess nd stin in continuum mechnics 4. Boussinesq s Theoy 4. Bumiste s Theoy 4.4 Thee Lye System Weekset Sung Chte 4. Intoduction to stesses in flexible vement Vehicul wheel lods => induce stesses in vement stuctue. The stesses => cete stins => ccumulte esulting excessive lstic stin Ccking, utting nd oughness vement dmges which educe vement iding qulity nd e the mjo cuses of vement functionl filue. The knowledge of stesses nd stins nlysis is thus imotnt fo the design of vement stuctues. 4. Intoductions to concet of stess nd stin in continuum mechnics Continuum mechnics is the theoy fo the nlysis of stesses nd stin in defomble body solid nd liquid. =>It is lied only to continuous medi continuum in the mcoscoic mening. Mteils e discontinuous in molecul scle. => The incil ssumtion of Continuum mechnics equies tht fo given cos unde couse of defomtion, two oints initilly neighboing would emin neighboing fte defomtions Boussinesq s Theoy Idel Msses => nlysis soil ection unde lod by using Mthemticl Theoy of Elsticity Assumtion Soil is in elsticity mteil, Homogeneouse, Isotoic, Semi-infinite Medium Soil oseities following by Hook s lw 4. Boussinesq s Theoy-con t Unit weight of soil is eo γ = 0, conside only lod ction ove the soil sufce 4 No stess bon befoe lod cting. 5 Poisson sretio μ is constnt due to lod tnsfe ; nomlly using μ =0.5 6 Line Stess function distibution 7 Veticl stess is Symmety 5 6

2 7 5 ] [ P P K 5 ] [ K Veticl stess t oint due to Point Lod 8 A d d 5 Veticl stess t oint due to contct e Equl dii 9 0 Hoiontl stess Reltion between σ Z nd Deflection Deflection due to wheel lod by lying flexible lte, the mximum deflection t the cente of lods deflection E

3 Deflection behvio due to igid lte lod Minimum deflection t edge of igid lte Mximum deflection t cente of igid lte Stess in hoiontl distnce deflection P E Elstic Defomtion unde cicul e lod Consideing the smll volume of soil unde cicul e lod t ny deth fom the sufce then Elstic Stin Elstic Stin E E given μ = 0.5 E 4 Deflection unde cicul e lod Exmle -E =.8E, = 0.5 When = distnce fom cente of cicul e lod = dius in dii unit = vege stess Bumiste s Theoy Two lye systems wee esented by Bumiste, the solutions of stesses nd deflections unde the cente of cicul lod of the two-lye system by using ssumtion.soil is homogenous, Isotoic nd Elstic.Definite in deth nd Infinite in the ltel diection.this theoy cn be used Boussinesq s Theoy ly in ech lyes. 4. NO she stess between ech contct lyes Deflection Two-lye systems Flexible Plte Δ =.5F E Rigid Plte Δ =.8F E flexible vement concete vement given = stess essue on cicul e = dius of cicul lod E = modulus of elsticity of lst lye of soil F = fcto deended on E E nd see figue.4 7 8

4 Deflection Two-lye systems F is the deflection fcto, function of lye modulus tio, E E nd the lye deth in multile of contct dius is shown in figue.4, in this figue, the vlues of E E e shown on the cuve nd E eesents the modulus of the ue lye whee E s the modulus of hlf sce. Deflection Two-lye systems Method to clcultion F - F deended on E,E tht cn be detemine fom Plte Bing times fist test on subgde, the esult cn be detemine Δ - And cn be clculte E fom bove, second Plte Bing test on vement stuctue, the esult cn be detemine F nd E 9 0 4

5 Notice In two-lye system could be ly Boussinesq s theoy to detemine the stess nd deflection, but the soil is moe diffeent fom ssumtion of idel mss mteil, non-isotoic nd inelsticity then elsticity is not constnt ove deth, howeve Boussinesq s theoy could be use estimte the stesses fo designing method Thee Lye System The solution fo veticl stess ws given by Pettie. The hoiontl stess solution ws obtined fom John. The oblem teted is the xi-symetic tye so the stess tensos educe to only 4- comonents; the veticl noml stess, the hoiontl dil noml stess, the cicumfeentil noml nd the sheing stess. Thee Lye System Imotnt ssumtions mde in the nlysis e s follow: The mteils e weightless The sufce of to lye is fee of she stess The lyes e welded contct The Poisson tio is Whee i,i-rri e ed fom chts nd tble,figue.8 nd Tble.. The coesonding stins cn be comuted fom constitutive lw eqution. It is imotnt to be noted hee tht t the intefces the quntities which e continuous coss e the noml stess, the sheing stess nd the dislcements, u,v,w but not the dil stess., The hoiontl dislcements e equl, the dil stesses e detemined by the elevnt elstic modulus of ech lye 9 0

6 Exmle of Thee Lye Systems 4 5 6

7 Tble 4. thee-lye stess fctos Afte Jones 7 8 Refeence: จ รพ ฒน โชต กไกร, การออกแบบทาง, ภาคว ชาว ศวกรรมโยธา คณะ ว ศวกรรมศาสตร มหาว ทยาล ยเกษตรศาสตร,550 Question? 9 40