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Abstract: Cr iterion of differential settlement in subgrade is useful for keeping road in a good serving condition.The theory of traditional ma terials streng th and their technologic economy are applied to analyze the additionalbend stress of the pavement structure, the equiv alent beam of elastic foundatio n and influence on the pavementstructure of an uneven settlement.The allow able settling ratio of pavement index( Δi)is go t and is used toappraise the uneven settlement standard value in subgrade.The allow able settling ratio of pavement index isapplied in an certain widening expressway project and Δi 0. 36% is attained by the analyzing , calculatingand adding a certain safe coefficient.This v alue was put into practice and is effective dur ing the past tw oy ears.Key words: w idening and reconstruction project; differential settlement; allow able settling ratio: 35313
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The sett lement of subg rade especial for new sub-g rade af ter const ruction can exert additional stress inpavement , which could cause st ructural damage onc ethe sum of this stress and t raff ic load exceeds the al-lowable strength of pavement[ 1 ].It is the commonphenomenon that crack and rut will occur af ter a peri-od of serving , according to the ex pressw ay w ideningexamples f rom domestic and abroad . Therefore , it iss igni f icant to assure a low er set tlement of pavementthan a certain threshold for the purpose of normalserving. Unfo rtunately , complete and uniform desig nmethods for w idening road are scarcely used in hig h-w ay management department.Even thoug h someregulations[ 2]are stipulated concerning subg rade andpavement w idening des igning , but those regulationsare mainly discussed about the detai led design andconst ruction requirements in the interface of subgradeand pavement in existing subgrade and the o ne to bew idened , and nothing about the design and const ruc -tion co nt rol facto rs considering damages of pavementdue to the common differential set tlement was in-volved. Therefore , it has s igni f icant value for the ap-plication to ascertain the control criterio n of differen-tial set tlement in pavement during const ruction.
1 Theoretical Analysis on DifferertialSettlement of Subgrade Three reasons can be assumed for the dif ferent ialsett lement in existing subgrade and the one to bew idened as fol lows[ 3 ]:①Consolidation defo rmation in subgrade due toload of new embankment.② Compression defo rmation in new embank-ment due to self-gravity .③Accumulative plastic deformation in new em-bankment due to t raffic load.The differential set tlement has several influenceson pavement such as saltat ion and concent ration ofst ress in combination regions , cracks and dispos it ionin regions wi th high stress and combination st reng th and transverse displacement of slope co rner ofw idened subg rade due to self-g ravi ty. Further , basedon the last influence , transverse and vertical displace-ment of whole widened filling along wi th combinationregion w il l occur , w hich will shape lengthw ayscracks. It is sure that the quality of construction is acause of lo ngitudinal crack .But in sof t-soil area , main causes fo r cracks inpavement are as follow s , the set tlement and consol i-dation status of foundation soil in the bottom of sub-g rade , the performance of hydrolog y and strength ;the influence of addi tional force af ter w idening on set-tlement deformatio n.Generally , dif ferential settlement is unavoidablein the combinatio n region of existing subgrade and theone to be w idened.But the critical point is how tocont rol the magni tude and dif ferential degree in thedesign and construct ion process , so in order to avoidthe damage of pavement ow ning to the differentialset tlement exceeding a certain value during serving.Consequently , i t is crucial to study the influence dif-ferential set tlement on pavement based on economicand technological perspective for avoiding pavementdamage and const ruction qual ity .
2 Numerical Analysis on DifferentialSettlement Acco rding to t raditional material theo ry ofstrength[ 4], it is hard for cracks to propagate in thecombination region betw een old and new subgradew hen i ts maximum bending st ress is low er than al-lowable bending st rength.Two conditions should beunder considerations fo r choos ing al lowable bendingstrength , such as al lowable bending strength and in-terface streng th of surface course and base course inpavement. Both st reng ths should be checked in nor-mal situations.2. 1 Extra Bending -Strength Analysis on PavementStructureThe differential sett lement in the combinationregion of existing subgrade and the one to be w idenedw ill make a gap between pavement and fil ling ow ingto plane characteristics of pavement.Bending stressw i ll initialize in different positions of pavement ,w hich due to the fol lowed displacement and deforma -tion under traf fic load and gravity[ 5]. In order to cal -culate the bending st ress, some basic assumptions aremade for w idened subg rade model based on the fea -ture analy s is of load and deformation features of pave -ment[ 6-8]:①Pavement is assumed as elastic beams in foun-dation.②Embankment is regarded as Winkler elasticfoundation.③Contact interface of pavement and embank-ment is glazed.④The set tlement curve of exist ing subg rade andthe one to be w idened is assumed asu( x)=ax2+bx +c. (1)According to the analysis of the set tlementcurve , Eq. ( 1)can be revised as u(x)=u0(x/ L) 2,w here u(x)indicates dif ferential settlement at cer-tain point of surface subg rade;u0 is the maximumsett lement on the surface of embankment ;L is thefeature leng th , w hich is the distance betw een maxi -mum set tlement point of embankment and the combi -nation point of existing subg rade and the one to bew idened.It can be seen f rom Eq. (1)that thew idened point (x =0)of subgrade is the positivebending point , the maximum sett lement point (x =L)is the inverse f lex point of set tlement curve.With di f ferential set tlement in subgrade[ 14 ], theload-balance equation of elastic beams on foundat ionare stated asD d4ωd x4 +kω=q +k u(x), (2)w here k is the Winkler response facto r; D is the set-t lement curve of foundation value;ωis the deforma -tion of elastic beam ( pavement);u(x)is the differ-ential set tlement curve of surface of subg rade.The particular solut ion of Eq. ( 2)isω=u(x)+qk.A generalized solution isw =eβk( C1cos( βx)+C2s in( βx) )+e-βk( C3cos( βx)+C4s in( βx) ) +u( x)+qk, w here β= k/ D .Based on the boundary condi tion , w e haveC1=C3= u0Qβ2L2( e-2βL-e2βL-2sin( 2βL) ),C2=-C4= u0Pβ2L2( e-2βL+e2βL+2sin( 2βL) ),Q=eβL( cos( βl) -s in( βL) ) -eβL( cos( βL) +s in( βL) ),P = e-βL( cos( βL) -sin( βL) )- eβL( cos( βL)+s in( βL) ) .