STRESSES FROM LOADING ON RIGID PAVEMENT COURSES

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1 bartosova.qxd :34 StrÆnka 3 003/1 PAGES 3 37 RECEIVED ACCEPTED ¼. BARTOŠOVÁ STRESSES FROM LOADING ON RIGID PAVEMENT COURSES ¼udmila Bartošová, Ing., PD. Assistant lcturr at t Dpartmnt of Transport construction and Traffic nginring Rsarc fild: Traffic load in pavmnt, Pavmnt loading, Strss in concrt slab loadd Addrss: Slovak Univrsity of Tcnology, Faculty of Civil Enginring, Dpartmnt of Transport construction and Traffic nginring Radlinskéo 11, bratislava, Slovak Rpublic Tl , -mail: bartosova@svf.stuba.sk ABSTRACT KEY WORDS In tis papr strsss ar prsntd wic ar dducd from a traffic load prformd on t middl, dg and t cornr of a slab. T strsss wr calculatd using svral mtods. T pavmnt structur modl and traffic load wr dtrmind for t calculations. T strsss wr analysd according to a strss scal for various load positions and for t statd modulus of t sub-bas raction. Pavmnt structur Traffic load Pavmnt loading Strss in concrt slab INTRODUCTION Pavmnt structur as a wol is dsignd so tat for its wol construction lif, t pavmnt is capabl of transfrring a traffic load. Havily loadd vicls wit various wigts ar takn into considration for traffic loads and undrcarriag alignmnts. Multilayr pavmnt structur was loadd in caractristic points. T ffct of t traffic load on a strss scal on non-rinforcd; on layr concrt slab was dtrmind by slctd calculating mtods. THE TRAFFIC LOAD OF PAVEMENTS Traffic load in pavmnt valuation is considrd to b a load from avily loadd vicls (trucks, lorris). Load can affct t pavmnt itr as a static or dynamic load. Load in calculations is considrd to b simpl or rpatd. Havy vicls, wic av rcntly bn usd on roads, ar considrd. T ffct of ts vicls is transfrrd into t pavmnt troug t contact ara wit considration of t tyrs inflation and t constructional solution of t undrcarriag. According to t calculation mtodology, substitut or ral contact aras ar usd, wic rspond to tyr inflation and undrcarriag dimnsions. PARAMETRIC CALCULATIONS Paramtric calculations of t strsss on a concrt slab wr mad by a traffic load on modls of t pavmnt structurs by slctd mtods. Various qualitis of t sub-bas and diffrnt load locations ar considrd in t calculations SLOVAK UNIVERSITY OF TECHNOLOGY

2 bartosova.qxd :34 StrÆnka /1 PAGES 3 37 Pavmnt loading Simpl static loading of t pavmnts was simulatd by axls wit t following caractristics: a dsign axl wit a wigt of 10.0 tons, loading of P = 100 kn, avrag contact prssur p= 0.60 MPa, an axl wit maximum allowd wigt of 11.5 tons, loading of P = 115 kn, avrag contact prssur p = 0.65 MPa, a non-standard axl wit a wigt of 4,0 tons, loading of 3P = 40 kn, avrag contact prssur p = 0,70 MPa, Pavmnt structur modl For calculating t strsss, t pavmnt structur was substitutd for by a calculation modl. T uppr layr was a concrt slab 3,75 m wid, 5,00 m long and 0,4 m tick. T modulus of lasticity for t calculations was MPa. T sub-bas layrs ar caractrisd by a modul of t sub-bas raction. T quality of t sub-bas layrs was cratd for a modul of t sub-bas raction from MN/m 3, wit stps of 0 MN/m 3. Calculation mtods For t strss calculations in t concrt slabs, t following mtods wr usd: Wstrgaard mtod - Wstrgaard assumd a pavmnt slab to b a tin plat rsting on a spcial subgrad, wic is considrd lastic in a vrtical dirction only. Assssmnt of t inputs of rlation () is valid undr t condition (1) a < 1.74 (1) b = 1.6 a Strss in t middl of t slab σ m [ MPa ]; otrwis [N/mm ] P E σ m = () 1+ µ lg k b Strss at t dg of slab σ [MPa]; otrwis [N/mm ] P E 0.1 b σ () = µ lg + lg k b 1 µ Strss in t cornr of slab σ c [MPa]; otrwis [N/mm ] () (3) (4) ticknss of t slab [m], E modulus of lasticity of t concrt [MPa], a, b smi axis substitut contact aras [m], µ - Poisson s ratio of t concrt, k modulus of sub-bas raction [MN.m 3 ] Picktt-Ray mtod tat is t grapic dimnsions. T objctiv is to plac t wls on t cart so tat t maximum numbr of blocks is incorporatd witin t tir imprint aras. Bnding momnt in t middl of t nigbouring dg slab M m, [MN.m] M m, p l N = m, Strss in t middl of t nigbouring dg slab σ m, [MPa] 6 M, σ m m, = wr, p contact prssur [MPa], l radius of rlativ stiffnss of t slab [m], N m, - numbr of blocks nclosd, ticknss of t slab [m], calculations of finit lmnts - tis mtod uss a modl of a slab on an lastic smi-spac. T NEXIS softwar programm modl of t load by contact aras is usd. T load can b placd in any position on t slab. T sub-bas is modlld using layrs in ral spac wit t layrs of t following caractristics: E modulus of lasticity of t concrt [MPa], ticknss of t slab [m], µ - Poisson s ratio of t concrt, ρ - bulk wigt [kg.m 3 ]. Calculation of t momntums and strsss for a dfinit numbr of lmnts is prformd for an arbitrary loading combination. Location of t load T rsulting strss from simpl loading was calculatd for tr load positions: t gomtric middl, dg (transvrs and longitudinal) of t slab and t cornr of t slab. (6) (7) () 0,3 1 µ k 1, () 4 3 P 1 10 σ c = a E wr, P load on on contact ara [ kn ], (5) STRESSES IN THE UPPER PAVEMENT LAYER Strss analysis from dsign axl loading T initial strss analysis was focusd on assssing t impact of t STRESSES FROM LOADING ON RIGID PAVEMENT COURSES 33

3 bartosova.qxd :34 StrÆnka /1 PAGES 3 37 Tabl 1. Strss on concrt slab loadd by dsign axl by slctd mtods Modulus of Position Strss in tnsion by curvatur σ [MPa] sub-bas of load According to t mtod raction on t slab Wstrgaard Picktt- finit [MN/m 3 ] Ray lmnts middl 0,878 0,836 1, dg,073 1,579,081 cornr,073-0,71 middl 0,854 0,88 1, dg,05 1,761,03 cornr,037-0,691 middl 0,835 0,97 1, dg 1,986 1,808 1,969 cornr,005-0,67 middl 0,819 0,973 1, dg 1,95 1,854 1,95 cornr 1,976-0,657 middl 0,805 1,00 1, dg 1,94 1,900 1,88 cornr 1,951-0,643 cangabl quality of t sub-bas by calculating t strss wit t mntiond mtods. T strss on t concrt slab was calculatd by dsign axl loading by t mntiond mtods. An ovrviw of t rsults acivd, is in Tabl 1. Similar valus of t strsss wr calculatd using t Wstrgaard mtod and t finit lmnt mtod. In bot cass t maximum strsss wr calculatd according to tnsion in t curvatur in t slabs by t minimum valu of t moduls of t sub-bas raction,.g., 80 MN/m 3. T diffrnc in t strsss in t concrt slabs according to t minimum and maximum valus of t raction modulus of t subbas is vry small. T suspnsion of t smallr strsss in t bttr sub-bas was confirmd by calculations using t Wstrgaard mtod and t finit lmnts mtod. T dclin of t strsss in prcntags using t Wstrgaard mtod is 8.31% for t middl, 7.19% for t dg and 5.88% for t cornr of t slab. Similar diffrncs wr also obsrvd using t finit lmnts mtod. T diffrnc in strss is 8.77% for t middl, 9.56% for t dg and 9.69% for t cornr. According to tis comparison, w dcidd to mak anotr calculation analysis only for pavmnts wit a modulus of a sub-bas raction of 80 MN/m 3. Paramtric calculations using t finit lmnts mtod wr calculatd for t dsign axl loading by on and two imprints. Pictur No s.1 and indicat t diffrnt dvlopmnt of strsss by on and two imprints. T ffct of t dsign axl is lss favourabl in t cas of load transmission by on imprint, t strss is about 3% igr. Higr strss is lss favourabl undr a total valuation,.g., strss undr on imprint of a doubl axl is dcisiv for furtr assssmnt. Pictur 1. Strss in tnsion by curvatur σ x - from loading and in t middl of slab dsign axl (P = 100kN) for on substitutiv contact ara sctions: 0,.5; 3.75,.5 Pictur. Strss in tnsion by curvatur σ x - from loading and in t middl of slab dsign axl (P = 100kN) for two substitutiv contact ara sctions: 0,.5; 3.75,.5 34 STRESSES FROM LOADING ON RIGID PAVEMENT COURSES

4 bartosova.qxd :34 StrÆnka /1 PAGES 3 37 Tabl. Strsss from loading by axl wit maximum allowd wigt using t finit lmnts mtod (NEXIS softwar programm) Modulus of Position of load Dformation in Strss on slab Strss at t Strss on slab Strss at t sub-bas raction plac of load work surfac bottom of slab surfac bottom of slab [MN/m 3 ] [mm] σ + x [MPa] σ x [MPa] σ + y [MPa] σ y [MPa] 80 middl -0,16-1,335 +1,335-1,358 +1,358 long. dg -0,490-0,80 +0,80 -,407 +,407 trans. dg -0,514 -,36 +,36-0,3 +0,3 cornr -1,16-0,858 +0,858-0,815 +0,815 Analysis of strss from loading of axl wit maximum allowd wigt Strsss from a traffic load by an axl wit a maximum allowd wigt (P = 115kN) wr calculatd by t finit lmnts mtod. T calculations wr don for a sub-bas wit a raction modulus of 80 MN/m 3 and for all t loading positions. T numrical valus for t dformation and strsss ar listd in Tabl No.. T maximum strsss wr obsrvd at t load position on t longitudinal and transvrs dgs. T strsss wr approximatly two tims igr tan by loading on t middl of t slab. T dvlopmnt of t strsss from loading by an axl wit a maximum allowd wigt (P = 115 kn) in t two sctions is in Pictur No s.3 and 4. T load is on t longitudinal dg situatd in t middl alongsid t slab. Analysis of strsss from a load by a non-standard axl T following calculations focus on t dvlopmnt of strss from a non-standard axl (3P = 40kN). T calculations wr don undr t sam modl conditions as for t axl wit t maximum allowd wigt. T strsss calculatd ar mntiond in Tabl No. 3. T strss calculatd wit t igst valu was also indicatd in tis cas by t load position on t transvrs and longitudinal dgs. T siz of t strsss in comparison wit t strsss from t load wit t maximum allowd wigt is 0.38% lowr on t transvrs dg and 6.7% on t longitudinal dg. Tis load inducs igr strss only in t middl of t slab, i..,11.3%. Strsss wr dtrmind for t ntir load positions of nonstandard axl (3P=40,0kN). T dvlopmnt of t strsss in t mntiond sctions by load position on t transvrs and longitudinal dgs is in Pictur No s.5 and 6. Pictur 3. Strss in tnsion by curvatur σ - x from load on t longitudinal dg of t slab dsign axl (P = 115kN) for on substitutiv contact ara sctions: 0,.5; 3.75,.5 Pictur 4. Strss in tnsion by curvatur σ - y from load on t longitudinal dg of slab dsign axl (P = 115kN) for on substitutiv contact ara sctions: ,0; ,5 STRESSES FROM LOADING ON RIGID PAVEMENT COURSES 35

5 bartosova.qxd :34 StrÆnka /1 PAGES 3 37 Tabl 3. Strsss from load by non-standard axl calculatd by finit lmnts mtod (NEXIS softwar programm) Modulus of Position of load Dformation in Strss on slab Strss at t Strss on slab Strss at t sub-bas raction plac of load work surfac bottom of slab surfac bottom of slab [MN/m 3 ] [mm] σ + x [MPa] σ x [MPa] σ + y [MPa] σ y [MPa] 80 middl -0,33-1,499 +1,499-1,057 +1,057 long. dg -0,831-0,150 +0,150-1,763 +1,763 trans. dg -0,544 -,353 +,353-0,747 +0,747 cornr -1,339-0,444 +0,444-1,445 +1,445 CONCLUSION T dvlopmnt and siz of strsss from traffic load was input for a total valuation of t strsss on t uppr layrs of rigid pavmnts. Total strss in concrt slab of rigid pavmnts, mainly strss in tnsion by curvatur, sall not xcd firm of matrial, otrwis t tnsion crack and dtrioration of matrial firm is occurrd. On t basis of t strss analysis from t load of t dsign axl, wic was calculatd by svral mtods, w can say tat by igr valu of raction modulus of sub-bas w didn t find out any significant dcras of strss. Strsss form load, calculatd by Wstrgaard mtod and by finit lmnts mtod wr not significant diffrnt. T strss for t dsignatd modl was valuatd using tr typs of modl loading. T igst strss occurs on t transvrs and longitudinal dgs of t slab using t dsign axl and an axl wit t maximum allowd wigt. T most unfavourabl ffct causd by strss in t middl of t slab was from t non-standard axl. T strss calculatd acivd a valu 3.3% igr tan t strsss from t dsign axl. W know tat for a complx valuation of rigid pavmnts, t rsultant strss is ndd. Strss from a load dtrmind by t mntiond mtods sall b supplmntd by strss from t diffrnc in tmpratur btwn t surfac and bottom of t slab furtr analysis. Tis articl was dvlopd witin t fram of rsarc projct VEGA No.1/713/0: Rsarc on t Factors and Conditions on t Quality and Srvic Lif of Pavmnt Structurs for Traffickd Aras wic is at t Dpartmnt of Transportation Enginring, Faculty of Civil Enginring, STU, Bratislava Pictur 5. Maximum strss in tnsion σ x - from non-standard axl (3P=40,0kN) on transvrs dg sctions: 0, ; 3.75, Pictur 6. Maximum strss in tnsion σ y - from non-standard axl (3P=40,0kN) on longitudinal dg sction: ,0; ,5 36 STRESSES FROM LOADING ON RIGID PAVEMENT COURSES

6 bartosova.qxd :34 StrÆnka /1 PAGES 3 37 REFERENCES GSCHWENDT, I.: Vozovky Konštrukci a ic dimnzovani, Jaga group, Bratislava1999 GRANÈIÈ, A. a kol.: Navrovani a výstavba vozovik z cmntovéo btónu, ALFA, Bratislava 1981 STN Vozovky pozmnýc komunikácií, Základné ustanovnia pr navrovani, SÚTN, Bratislava 1997 STN Stavba vozovik, Cmntobtónové kryty, SÚTN, Bratislava 1996 EISENMANN, J.: Btonfarbann, Ernst und Son, Brlin 1979 STRESSES FROM LOADING ON RIGID PAVEMENT COURSES 37