国际课件2土质学与土力学soil mechanics lecture8lyh

SoilInstructor:LiuYanhua SchoolofHighway,Chang’anLectureLectureStressesinBoussinesq’ssolution Stressincreasesduetosurfaceload3.6Stressincreasesinthe (附加应力)Howdoesstressincreasechangewithdepth(附加应力与深度关系)?WestartwiththeThree-dimensionalproblems(三维问题).3.6Stressincreasesinthe(i)Stressincreasesduetoverticalpointload竖向集中力作用下附加应力Considerahomogeneous均质),elastic弹性)andisotropic各向同性)semi-infinitehalfspace(半无限空间体)ryryqxRzyMzxr=x2+yR=r2+3.6Stressincreasesinthe(i)Stressincreasesduetoverticalpointload竖向集中力作用下附加应力Boussinesq’ssolution( 克解答fornormalstressincreasesatpointMduetothepointloadFare

3Fx2

Rz

z

R5+

RRz

-R3 3Fy2 2R+zy2 z -R3p Rz) wheremisPoisson’sratio泊松比3.6Stressincreasesinthe(i)Stressincreasesduetoverticalpointload竖向集中力作用下附加应力Boussinesq’ssolutionforshearstressincreasesatpointAduetothepointloadFaredtdt==3Fxyz-1-2mR+xy3R+=3FxR5=3F R5wheremisPoisson’sratio泊松比3.6Stressincreasesinthe(i)Stressincreasesduetoverticalpointload竖向集中力作用下附加应力Boussinesq’ssolutionforstressincreasesinverticaldirectioncanbere-arrangedasfollows:3F 2pz z=2pz15FK35zr22p1+ r21+z3.6Stressincreasesinthe(i-a)Asquarefoundation2mx2mcarriesapointloadof1500kNatitscentre.Determinetheverticalstressatapoint5mbelowthecentreofthefoundation.dsdsz=0.4781500=29dsz=KK35m52K32p r252z5 2p1+0F=1500kN,z=5m&r=0Stressincreasesduetoverticalpointload竖向集中力作用下附加应力.

K 5 5

r2

2p1+ 00.51.01.52.02.5

zPOntheconcentratedloadr=0,K=3/(2π）,z=0,Ona neatacertaindepthr=0,K um，r↑，K↓，σz↓Atacertaindistancerawayfromtheconcentratedloadline3.6StressincreasesintheStressincreasesduetoseveralverticalpoint xxrzyM3.6Stressincreasesinthe(ii)StressincreasesduetoseveralverticalpointBytheprincipleofsuperposition叠加原理),stressincreasesinverticaldirection(dsz)atpointMduetoseveralpointloadsFi(i=1,2,…n)canbepresentedbythefollowingexpression:szsz=nKi=ii3.6StressincreasesintheVerticalstressincreasesbeneaththecenterofaverticalanduniformlyloaded(竖直均布荷载)circularfoundationpOzpOzMz3.6StressincreasesintheVerticalstressincreasesbeneaththecenterofaverticalanduniformlyloaded(竖直均布荷载)circularfoundation = 3 2 +z2/r2 0wherer0istheradiusofthecircularfoundation,zisdepthofpointMfromthecenterofthefoundationandpisnetpressureonthefoundation.ValuesofKrcanbefoundin4-6(p.68)3.6StressincreasesintheVerticalstressincreasesofaverticalanduniformlyloaded(竖直均布荷载)rectangularfoundationxxpBLzyz3.6Stressincreasesinthe(1)Verticalstressincreasesbeneaththecenterofaverticalanduniformlyloaded(竖直均布荷载)rectangularfoundationxxpBLzyMz3.6StressincreasesintheVerticalstressincreasesbeneaththecenterofaverticalanduniformlyloaded(竖直均布荷载)rectangularfoundation2pp1+m2+4n2(1+4n2)(m2+4n22mn(1+m2+8n2m 1+m+22wherem=L/Bandn=z/B,Lislengthoftherectangle,Bisbreadthoftherectangle,zisdepthofpointMfromthebottomofthefoundationandpisnetpressureonthefoundation.Valuesofa0canbefoundin4-8(p.570)a0=F(B,L,z)

F

3.6StressincreasesintheVerticalstressincreasesbeneaththecornerofaverticalanduniformlyloaded(竖直均布荷载)rectangularfoundationxxpBLzyMz3.6Stressincreasesinthez=pmz=pm1+m+p221m+22+11+2mn1+m+22thefoundationandpisnetpressureonthefoundation.Valuesofaccanbefoundin4-9(p.71)wherem=L/Bandn=z/B,Lislengthoftherectangle,Bisbreadthoftherectan zisdepthofpointMthefoundationandpisnetpressureonthefoundation.Valuesofaccanbefoundin4-9(p.71)3.6Stressincreasesinthe(iv-a)Arectangularfoundation6mx3mcarriesauniformpressure300kN/m2 nearthesurfaceofasoilmass.Determinetheverticalstressatadepthof3mbelowcornerAoftheAdszdsz=0.2300=60kN/dsz=Ks ac=p=300m=L/B=6/3=n=z/B=3/3=3.6StressincreasesintheVerticalstressincreasesbeneaththeanypointofaverticalanduniformlyloaded(竖直均布荷载)rectangularxxpBLzyMz3.6StressincreasesintheVerticalstressincreasesbeneaththeanypointofaverticalanduniformlyloaded竖直均布荷载)rectangularsz =szsz =sz,oedh-sz,ofch-sz,oeag+sz,ofbgaebgfoIInIsz

+szII+s +s c cOtofrect3.6Stressincreasesintheact=F(B,L,z)ac

Verticalstressincreasesbeneaththe Verticalstressincreasesbeneaththecorneray (sBLz=L zz(p,m,tbxMs=atz z

3.6StressincreasesinthepxRzR1 thelengthLthelengthLtowidthB(基础底面长宽比)l/l/z3.6StressincreasesinthezpxyxRz1bMy3.6StressincreasesintheItis nestrainproblem,..yy

e=

m

+sz

M

=0xyzzyxyyx3.6Stressincreasesintheszszp(x2+z2sxpsxp(x2+z2ttzxp(x2+z23.6Stressincreasesinthe

pxBRzR1MxMz=3.6Stressincreasesinthe= uniformlystriploadedb2 sz=2p-z2+2 zspKz 1+2n 4m(4n2-4m2- sp -(4n2+4m2-1)2+16m2 wherem=z/Bandn=x/B,Bisbreadthofthestripfoundationandpisnetpressureonthefoundation.ValuesofKzscanbefoundin4-14(p.76)3.6StressincreasesintheVerticalstressincreasesbeneathaverticaltriangularstripmm=z/Bandn=x/B,Bpfoundation.Valuesofcanbefoundin4-15s =Ktzp

StressesinIn-situstresses原位应力—stressesduetoself—weight（自重应力Pressuresatthebottomoffoundation基底压力—Pressuredistributionduetoverticalandeccentricloads(竖向与偏心荷载下的基底压力)StressesinBoussinesq’ssolution Stressincreasesduetosurfaceloadstressduetoself-weightata,b,c.DrawthestressThestratum’sconditionsandtherelatedphysicalcharacteristicsparametersofstressduetoself-weightata,