Highway Pavement Design
Highway Pavement Design CE 755
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This 14 page Class Notes was uploaded by Jermain Lindgren on Thursday October 15, 2015. The Class Notes belongs to CE 755 at North Carolina State University taught by Staff in Fall. Since its upload, it has received 11 views. For similar materials see /class/223743/ce-755-north-carolina-state-university in Civil Engineering at North Carolina State University.
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Date Created: 10/15/15
ENGHNEERJING ONMNJE 406 Mann Lecture Notes Course Number CE 755 Instructor Dr Kim Date 9 1608 Lecture Number 8 if 2008 North Carmina Slate University All Rights Reserved Flexible Pavement Response Models T mac OLm ACExh LQL sg Basel E3 h Subgrade E3 I O effecuve minor elTect X negatit e effect The stress solutions use the following parameters Kl ElEg K EzEg A ahzt and H hrhz Vemcal Stress Minimizing the vertical stress at the top of the subgrade is very important to reduce the permanent derbrmau39on under the wheel paths Figure 21 handout Nielsen J P7quotRartonal Pavement Evaluattun Rene of Present Technologyquot Technical Report No AFW39IeTR 699l Arr Force Weapons Laboratory NM October 196 l39trt Air Force Bas LA 3 f Pt u C 531 amp 3 53 h of multilayer system 0 Veruc stress decreasest he straness of the surface layer Increases Lhe effect ts 1 6 e Howet39e erucal stress at the top of the base layer decreases dramaticall Figures 22 a and b handout al stress decreases as the stiffness and hckness el tlte base layer ll39lCl39CllSL S x Figure 23 handout Vertical stress at the top of the snbgrade a and b As we Increase the thickness ofbase layer the vertical stress at the top ofthe subgrade decreases signi cantly The stress level can be reduced to a lesser extent by increasing H For a constartt base course thickness this is done by increasing the surface thickness From Figures 2 l 21 one can determine that the most efficient ways to reduce the vertical stress at the top of the subgrade are to a increase the b increase the f the base andor surface layer and ofthe base layer This can be practically achieved Increasing the stiffness of the surface layer thus increasing K1 reduces the vertical stress at the top of the subgrade but not nearly as ef ciently as steps a andor b listed above An increase in K1 does however dramatically lower the vertical stress at the top of the base De ection Most ofthe pavement de ection is caused by elastic compression with the subgrade usually about 70 to 95 of total de ection Since de ection is merely the ma ematical integration of vertical strain with depth and since strain is a direct function of the triaxial stress state at a pornt in the pavement structure the same general factors which in uence the subgrade compressive stress directly influence de ection Shear Stresses From Figure 2 l we have seen the effect of decrease tn modulus of surface layer ie decrease in K on the vertical stress distribution Now let39s consider the effects on shear stresse From the quilibnum equation ofthe theory of linear elasticity we get the following relationship between the vertical stress and the shear stress 5a 32 Or By increasing Er the gradient of vertical stress along the depth decreases because the vemcal stress gradient is negatii c Also we know that the shear stress at the centerline ofload is zero and the maximum shear stress occurs directly at the edge of the loaded plate If we consider the above equation at the edge of the plate we can easily see that the maximum shear stress must increase by increasing Er due to decrease in the gradient of the vertical stress As astutimary we cannot achieve something for nothing quot The upper stiffer pavement layers prowde increased load spreading capability which Is made possible at the expenses ofan increase in shear stress Within the stifflayer K quot4 the top of quot quot 39 permanent defamation by USng stiffer surface layer but the stiffer la er will result in more cracking potential due to greater shear stress Figure 24 handout In uence of K1 39r39r stress within surface layer L TR in the MI vii chw m nhmii K I e E1 increases the shear stress iwmns permanent deformation vs cracking Figure 25 handout In uence ofhl As you increase he thickness ofthe surface layer in the maxrmum shear stress in the surface layer As hi Increases the location ofthe maximum value of shear stress shifts upward from about middepth to about the third point upper of the layer The in uence ofhz on the magnitude of shear stress is best illustrated in the follomng table Depth below M 125 05081 3 75 03998 5 0 00682 Also it was found that increasing K2 while holding K1 constant causes hz 10quot l hg 20 04961 05125 03855 00628 n Reduction 237 308 358 792 a slight decrease in shear stress Thus the trend is that K and 11 have strong in uences on the shear stress while K1 and h hm e only a minor in uence on shear stress distribution Tensile Stresses and Strains Horizontal stressstrain at the bottom of the surface layer or at the bottom of the stiffest layer which 15 normally the surface layer 15 a critical problem in pavement deSignanalysis Larger tensi e stressesstrains result in cracking usually due to fatigue Figure 26 handout Horizontal tensile strain at the bottom of surface layer v De nition of SF gt SF 21 x Eip 51 horizontal tensile strain at the bottom of the surface layer II n m m 0 2 3 a line SF increases exponentially as h1h1 decreases and ahg anreases SF reaches an optimum value along the ahg or hihz contours Spectl39ically at ahg 16 the contour proceeds from right to left through a 11121lele and falls off rapidly as shown by the dotted Maximum SF values occur at high Values Ufah and at low values of llihz When we design a pavement for given critical SF value there exist two thickness ratios corresponding to a xed value of ihg The thinner of the two pavements would not be satisfactory because a nomral stresses on the subgrade Ill be too high and b shear suesses in the surface will be too high Figure Zt4 handout Horiyontal tensile stress at the bottom of surface layer Very large tensile stress develops at small hi value especrally when Hlt2 As K1 therefore Er increases the tensrle stress in the bottom of the surface layer increases However horizontal tensile strain may not be in uenced very much because strain is a ftmction ofstress and modulus as follows sr LaHllfog 0 El One should remember that ilelt1 J due to say base course stabilization the critical tensile stress Will occur in the base course ui lieu of the surface and surface layer will be in compression Effect of39l iro Pressure and Total Load Figure 25 handout The e ect of tire pressure and wheel load on the Boussinesq distribution of vertical stress in onelayered system o A pronounced effect of are pressure in the upper layers LllllL or no effect oftire pressure in deeper layers I An increase in vertical strss at all depths With an increase in wheel load Summary Miiltilayered elastic solutions are approximate but provide a power tool for a pavement engineer to predict the effects of different combinations of thicknesses and moduli of layers 2 If we increase the su f fness of surface layers in order to reduce the vertical stress in the system large tenstle stress usually develops in the Whyer FIGURE 2 l PAVEMENI DEPIHS OI IHICKNESS IN 39EIMS OF hz A o n III pc u y j 2 KzID IOLSSINESQ VBIICAL SI IESS RATIO 1 PAVEMENI DEFIHS 0R IHICKNESS IN IERMS OF Ii EA r Kz as VETICAL STRESS RATIO 0 p O 0 2 0 4 0 6 08 LG quotI u K2 2 J In 6 ch v6 IQ a R 10 h NESQ k HR 0 g n FIGURE 2 2 a PAVEMENI DEPIHS OR THICKNESS IN TERMS OF h2 VRTICAL STRESS RATIO 0 4 0 6 O Z 05 5 13 A aoussmso DISTRIBUTION FOR uhz J KlZO KzIO FIGURE 2 3 a m 3 0 at 2 FIGURE 22 b Vac wag 5B CLowu ra H a Keg PM CNSkGKj 3 39Iwmse m 44 5 73 5 Oiy megsm I613 Kcaf k1 cams kw 2r Ihc agt9 M Aft wxe E 39f 407 Theda93 7w at 11 m u a m lt E a u gt AVERAGE UNIT smsss p DEPIN BELOW PAVEMENI SURFACE UN 0 m HGIZONI AL sum STRESS Juno 1 p 02 39 04 0N WHICH VALUES OF 739 FIGURE 2 4 IMICKNESS h INJ HUIZONTAL SHEAR STRESS RATIO Trp 02 0 FIGURE 2 5 HORIZONIAL UNII IENSILE STRAIN FAC39IG SF ININ a Hj Yb 3 2333 0 1V W4in4g FH P T W p 39 wHiO film um Thur 1tmMm Juanno WHnGwh N m 6 H Illll Kennil sues nlio at Lhz bottom of the n hyn ol Ihruhyued d H Vertical sues w 30 120 l u napmmcms s a s m 313 40 Jim 1amp1 L 39 hm I ly w z I ltnu 2mm ariuian n Vania men wllh depth Bauxinaq problm
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