# Manual 21366537

Various mathematical and tested these using and physical the models are divided non-linear models, used. both cases In Sciences (Nie et and non-linear the prepared regression set logarithmic as the The values from the is of Figures A.2 and evaluation, The reason with it for the are stored. basin scale, like slightly and analysis the Social the choice computer of system Each of the models results are plotted on a in Figure A.1, some guiding of models can be used. curved. line, althouih Based on these obser- models as shown in Table A.1, were used. related parameters regression 1975) for a typical Linear of regression a tendency towards a straight still the linear The results deflection following of namely; of 1984) was used to do linear can be made as to what types it The discussion in terms of the results. linear in general shown, vations. of versus observations There is basin data sets were selected Package for compatibility discussed a typical Robinson, analyses. SPSS package was the If procedures SPSS Statistical 1975; where the deflection sets. two subgroups based on the al., used are briefly RSD data into the models available, are also given as derived model in the SPSS package (Nie et al., data set. these models for A.3. Before can be seen typical even that data sets considering there are are the shown in statistical some shortcominis in some of these models. Figure A.2 illustrates that A.1) are only applicable models 1 and 2 (as to the area of positive 2 is however able to be accurate Figure A.3 shows that that if lead to an ill in Table curvature. curvature fit. Model over a wider area (10 to 300 mm). model 1 is used over a wider area covered by the positive can easily defined of the deflection For that reason than basin, it models 1 and 2 ~~ 101 z 0 ~ u W ...J lL. W 0 ~----.. ..... ~ ••• E E x~ x • FITTED MODEL MEASURED POINTS __ . ~ •• I~ .~ 16 . .~. ... . .. .. ,..:~~ FIGURE A.I TYPICAL LOG VERSUS LINEAR PLOT OF RSD DEFLECTION BASIN MEASUREMENTS 200 HORIZONTAL DISTANCE (mm) FIGURE A.2 TYPICAL PLOTS OF LINEAR REGRESSION MODELS FITTED TO THE POSITIVE CURVATURE D 5 .... a a 0,200 u W --J tt o 0,150 FIGURE TYPICAL A.3 PLOTS OF LINEAR REGRESSION MODELS FITTED TO THE WHOLE DEFLECTION BASIN Parameters for a typical data set l. Y ••• A exp (A 1 0 or y •••A A x2) o 10(A1x2) •••0,2959 A 0 o -6 •••0,991 x 10 or log y •••log Ao + A1x2 2. y •••A x2 3. y •••exp (a x2 2 A 0 ••• a 1 x + a ) 0 2 or y •••10(a2x +a'1x+ao) a 0 0 ••• 0,4578 ••• -0,4990 a1 ••• -0,4513 x 10-3 a2 ••• -0,1330 x 106 a 0 a1 •• 0,4467 •• 0,7818 x 10 -3 a2 ••• 6 0,2309 x 10- a3 ••• -0,1021 x 10 were only applied to the first 200 rom. wider than the normal width of positive 0,98 -9 This is covering an area curvature (Dehlen 1962) but it does not lead to ill fits of model 1 (see Figure A.2). A distinctive feature of the deflection basin curves as shown in Figure A.3, is the peakedness of the area of the area of positive curvature. than 10 This area of positive per cent deflection basin. of the curvature horizontal is on average distance of the less whole The R-square values of model 1 and 2 are an acceptable 0,99. The goodness of fit was also calculated as follows: n i=l T - Y )2 (y - E i i * 100 % n -E (y i=l where A - A)2 i = Average of measured values Y. = Measured data values Yi = Values from model fitted ~ The goodness of fit for a typical data set for models 1 and 2 is 95 per cent. Both therefore have acceptable values of R-square and goodness of fit for the positive curvature region. Models 3 and 4 are polynomial functions of the order 2 and 3. There is no real advantage gained in accuracy when the order of the polynomial is increased above the third order. tion takes longer and becomes costlier too. of the second order polynomial measurements is 99 per cent. The computa- The goodness of fit (model 3) for a typical set of It can be seen in Table A.1 that the R-square values for models 3 and 4 are also an acceptably high 0,98. This is very good, but visually it can be seen in Figure A.3 that the deviance from the observed values in the very small area near the origin (positive curvature) does lead to some concern as to the applicability deflection basin. This tendency thereof for the whole to give equal weight to all data points along the linear horizontal distance (x) is typical of this linear regression model used in the SPSS package. For that reason re- it was decided to investigate the non-linear gression analysis with available models that would tend to give a better description of the whole deflection basin. Another point of interest in the vicinity of maximum deflection (x-a) is the gradient of the tangent at x-a. In Table A.2 the gradient of the curve described by any of the 4 models is given as first order differentials. First order differentials ~ = A dx 2. y" A o x2 » (Exp (Alx2 0 2Alx ~ - 2A x 0 ~ = .a 1.- 2'2x) exp (a xl2+a dx dx ~ dx X o + a ) - At the point of maximum deflection (x-O) only models land 2 have a horizontal gradient as the first order differentials are equal to dependent zero. The gradient on the values given by Models 3 and of the constants when x-O. 4 This are is another indication of ill fit of models 3 and 4 at the point of maximum deflection. As indicated earlier, the non-linear model of regression analysis used in the SPSS packaie (Robinson, 1984) tends to give equal weight to each measurement on the deflection basin. In using this non-linear is regression analysis package the aim then to minimize the sum of squares. It is the sum squares of the model difference measured points. between the fitted and the observed For this reason it is therefore important that the unnatural "spikes should be smoothed out before curve fitting is done. There are two options in the non-linear regression analysis package of SPSS (Robinson, 1984) namely using the Gauss method or the Marquardt method. The latter was selected as superior due to its shorter computing time required. two models tested by the two options In Table A.3 the are shown with the calculated constants and sum of squares values. Sum of squares 8,914 x 10 -1 3,768*10-3 Parameters for a typical data set A ••3,321*10-1 A~ •• -9,991*10-1 a •• -1,066 3 o a1 "" -1,134*10_7 a •• -2,796*10 2 As can be seen both models had been tested for curve fitting by the linear regression analysis facility of SPSS before. was again tested here on an area wider than the Model 1 positive curvature by selecting the first 350 mm for curve fitting. As could be expected it did lead to a poor fit as reflected in the rather high value of sum of squares. The residuals (difference between prediction and observation) are also plotted. goodness of Apart from giving a visual impression of the fit, it also serves as a monitor patterns which indicate poor fitting models. specific In Figure A.4 the residual plot of the model 1 fitting is shown. pattern confirms the ill fit. for It re-emphasises The definite the fact that model 1 can only be applied to the area of positive curvature « 150 rom). Model 2 (Table A.3) proved to be better suited for the fitting of the whole deflection basin and particularly the large area of 0 0 0 15 0 en en L&J 0 <t 0 u 0 ~ 0 a: UJ 0 lD ~ 0 ::l 0 Z 0 5 0 0 0 0 0 10 RESIDUALS 20 (X 30 16~ FIGURE" AA RESIDUAL PLOT OF AN ILL FITTING MODEL the reverse curvature of the deflection basin. The good fit thereof is reflected by the low value of the sum of squares in table A.3. The plot of residuals in Figure A.S also reflects no specific patterns indicating a good fit. the area of deflection positive still regression curvature persists analysis too. as The lack in fitting in the was vicinity indicated in of the maximum linear It would be possible though to use these two models of table A.3 and limit the curve fitting of the positive curvature to that by model 1 and the curve fitting of the larger reverse curvature to that of model 2 and achieve satisfactory results. The non-linear relatively package complex of models SPSS makes it possible in the regression to analysis. use This gives the opportunity to look at physical models which can be adapted to the observed deflection basin. that of beams of unlimited concentrated by Het~nyi loading. length on elastic foundations with This model is described and Fryba (1967). (1971) A promising model is give a detailed description in great detail The intention is not to of this theory here, but rather concentrate on the use and manipulation of the derived solutions in the curve fitting exercise. In the analysis of bending of beams on an elastic foundation H~tenyi (1971) assumption is proportional that reaction forces of states that the the foundation are at every point to the deflection of the beam at that point based on the Winkler theory. that deformation This theory also states exists only along the portion--d±·ree-t.ly--··under loading and was verified in experiments for a variety of soils. Het~nyi (1971) is quoted as follows; II that the Winkler theory, in spite of its simplicity may often more represent the actual conditions existing accurately in soil foundations than do some of the more complicated analysis •••11 A short description of the model is as follows; Consider an infinite beam subjected to a single concentrated force P at the a point 0, which is the origin of the axis system as shown in figure A.6. The general solution for the deflection curve of a • •• • .100 • • • • •• • • • • • • • • • • 70 • • • • • • • •• • • • • en o;t I ~ 0 .;r en -10 i::: ••••• G:: •• ~ 10 « • • •• • • C C ~ w 0:: ::> e" IJ.. ~ ••••• C -5 ~ <t) • • • lA,J ~ •• • • •• • • •• • • •• • • • • -15 <: • • • • m -20 ~ ~ • • • • (f) ID ID C § • • ~ -..J •• • .•.••. l;j • • • •• ~ • •.... • • • • • • • • 0 RESIDUALS • • 5 3 ( x 10 ) • • • 10 Y PA -AX = 2k e (cos AX . to S In A X ) DOWNWARD DEFLECTION M= :A BENDING MOMENT e-AX (cos AX - sin AX) PAx' Q =-2' e- cos AX SHEARING FORCE FIGURE A.6 POINT LOAD ON AN INFINITE BEAM ON AN ELASnC FOUNDATION beam subjected to transverse loading is derived by Hetenyi (1971) as; where y is the deflection taken as positive downwards x is the horizontal distance from the origin C1, CZ' C3, C4 are constants ~ is the damping factor, and k is the modulus of the foundation expressed in kg/m2/m E is the modulus of elasticity in kg/mn I is the second moment of area of the beam Without even going into further detail of the simplification this model between of it can be seen in Figure A.6 what the similarities the deflection modelled basin deflection curves are. curve When the and the symmetry measured of the deflection curve and the equilibrium of the reaction forces are considered this general equation reduces to; Y = p Zk e -).x (cOSAX + sin~x), which gives the deflection curve for the right side (x>o) of the beam. the data preparations preceding sections. case of no dampening curve analyzed. This correlates well with of the deflection basin described in the The form of the curve suggests that the can be considered for this part of the Fryba (1967) gives the solution as follows for such a situation; e -blxl (a cosax + bsina Ixl) This form is obviously similar to that derived by Hetenyi (1971. In order to simplify the determination process of the constants in these equations, fitting model; it was decided to use the following curve In figure A.7 a plot of a typical data set and the curve fitting is shown. Visually it can be seen that this model succeeds in describing the observed deflection basin accurately. The sum of squares value is low (4.15 x 10-3 for this typical data set) and the plot of the residuals does not indicate any ill fit. The goodness of fit for such a typical data set is above 98 per cent. range It was found that this mode is applicable of variances in load. condition of pavements. load repetitions over a wide and structural It is obvious though that although this model gives the best fit of all models tested it still tends to give an ill fit in the positive curvature area. Although this area is very small and very peaked in relation to the rest of the deflection basin. it was decided to use the parabola of the linear models in this area of possible curvature in order to arrive at a true representation of the whole deflection basin. E 0.2 E Y = B 1e 82 X (COS B 3X + si n B 3X ) z Q U LOAD 60 kN NO REPETITIONS LL W x - PREDICTED I- w ...J o • - OBSERVED FIGURE A.7 TYPICAL CURVE FITTING OF PHYSICAL MODEL SUHHARY ON CONDITION DEFLECTION SURVEYS ENHANCING BASIN ANALYSIS A condition survey is an important input in the non-destructive testing of an analysis procedure. In Figure B.1 it is shown how this kind of visual survey greatly enhance the understanding of the material characterization in a typical analysis procedure for overlay design. Condition surveys are non-destuctive testing procedures enhancing the other non-destuctive testing procedures such as deflection basin analysis. In Figure 4.1 it was explained how in the South African mechanistic rehabilitation design procedure (Freeme, 1983) it is important to identify the pavement layer state. The discussion on condition survey will therefore focus on crack and rut classification related to the deflection basin survey (see Figure B.1). Ullidtz (1982) defines a functional and structural condition in his model on pavement rehabilitation. He states that; "The structural condition is of no immediate interest to the road user but is is extremely important to the highway agency because the future functional condition. " condition depends on the present structural A visual condition survey can be seen as an aid to a proper structural evaluation. The standard procedure outlined Draft in for conducting TRH12 (NITRR. a 1983), condition should be survey, as followed. Normally the visual assessment precede the deflection basin survey but it is suggested that the deflection basin survey and visual assessment may be done simultaneously on smaller scale projects. The results of both surveys should be plotted on the same scale. By this means the obvious weak spots can be identified when other relevant information such as drainage, cut or fill transition and soil changes is taken into consideration. Pavement Evaluation and Overlay Design Inputs Destr u ct iv e Testi ng raff ic Data In-situ Material Sampling 1esting Lab. Testing Deflection Survey Analysis Sections Pavement Class Identification Compute Deflection Basin Parameter Function Compute Distress Determi nants Fatigue Cracking Overlay Criteria Overlay Thickness and System Selection FIGURE 8.1 Mechanistic overlay design flow diagram B.3 Cracks in the existing asphalt concrete layer have a major inNormally pavements are fluence on the overlay design procedure. However, the majority of pavements fall somewhere between these extremes. The classified as either cracked or not cracked. aim of this section is therefore to establish quantitive procedures to classify cracked pavements in order to improve the rehabilitation design procedure. Grant and Curtayne (1982) point out that fatigue is not necessarily the cause of cracking in asphaltic concrete layers in South Africa. Other factors, not necessarily traffic-related, should also be considered as being possible causes of premature cracking (Grant, et al (1979). with full depth Pronk asphalt and Buiter pavements, even (1982) indicate that in the Netherlands, cracking does not necessarily begin at the bottom of the asphalt layer. Grant and Curtayne (1982) therefore stress that a study of the past behaviour of the pavements can provide good clues in this respect. complexity of The preceding crack mechanisms statements are of asphalt to indicate concrete the layers. Different reasons for cracking are therefore discussed in order to arrive at a classification for cracked pavements. The aim of this is purely to simplify the analysis of such a pavement by using the deflection basin parameters in the mechanistic approach. First it is suggested that the difference in basic crack mechanism, due to the difference in pavement structure be considered. For the South African condition it is suggested that on the grounds of as-built plans or matericiTsam-pting--procedure (Figure B.1), a flexible pavement under survey be classified according to the basic TRH4 (NITRR, 1985a) catalogue, i.e. (a) granular base pavements (b) bitumen base pavements (tar as an alternative) (c) cemented base pavements. This basic classification is taken a step further by Freeme (1983) by relating the time-dependent behaviour of different pavement types to the concept of equivalent material state Figure B.2. It is explained in Chapter 3 illustrated in how the measured deflection basin parameters can be used to accurately identify any such pavement behaviour state. Next, the degree of cracking should be defined. In the light of work done by Kilareski et al. (1982) and Treybig et al. (1978), it is suggested that the AASHO definition of cracking could be applied. Jordaan and Servas (1983) give a very clear description of three types of cracking and how it should be calculated. types are crocodile or map or block cracking, These longitudinal cracking and other crack patterns or combinations of the preceding types. For these types each 100 m of road length is classified as being in a sound, warning or severe condition. This depends on the percentage of 100 m being cracked and the road category. Crack conditions can be improved by crack filling and repair of the low percentage of severe cracking of the defined categories or crack types. The decision to repair cracks should be based on economic comparisons, improve possible but it is obvious that crack repair will crack attenuation behaviour in general. Koole (1979) suggests though that an overlay design based on the severe condition of cracking might in some cases be the most economical in the final analysis owing to the expensive nature of procedures to upgrade the pavement in regard to the crack condition outlined above. In the final level of crack classification methods should be considered. more sophisticated This normally consists of analysis procedures associated with the overlay design analyses. researchers, such as Molenaar Various (1983) and Coetzee and Monismith (1979) suggest the use of fracture mechanics principles and finite element computer programs in the analysis stage. In order to use these procedures though, the previous crack classification would have to be elaborated crack width too. in order to establish average values of Molenaar (1983) states the following: I 1940-4 -4760/9 B.D. STATE .---.. VERY I STIFF APPROXIMATE DEFLECTION (mm) LEVEL STIFF 0,2 I 0,4 CONCRETE EXAMPLES OF CHANGE OF STATE PAVEMENT OF DIFFERENT TYPES I . FLEXIBLE VERY FLEXIBLE 0,6 ~ CEMENT TREATED • BASE PAVEMENT CRUSHED- STONE OR BITUMEN CEMENT TREATED SUBBASE TREATED BASE OVER BITUMEN TREATED BASE OVER GRANULAR SUBBASE GRANULAR BASE IGRANULAR SUBBASE. LOW SUBGRADE CBR VALUE CONCRETE ROAD N2 HOORNSNEK (TVU TYPICAL IN EXAMPLES ; BRONKHORSTSPRUIT P67/1 (TVU; N3 SWINBURNE (OFS) P157/1 a PI57/2 JAN SMUTS AIRPORT nVU;PARADISE N3 MARIANNHILL (NTU PRACTICE P205/2 VALLEY (NTU GI LLOOL Y (TVU KOEBERG (CAPE) PI23 MAGALIESBURG nvu P6/1 BABSFONTEIN (TV L) FIGURE B.2 DIAGRAMMATIC REPRESENTATION OF THE TIME DEPENDENT BEHAVIOUR OF DIFFERENT PAVEMENT TYPES (Freeme, /983) "Although the fracture mechanic's approach has the potential to be an excellent tool in solving the reflection crack problem, it has not gained very much popularity. In fact it can be stated that it is still a research tool and that its practical application is limited to only a few cases." Recently the monitoring of crack movements, as described by Rust (1984), has become another viable method that may be associated with the classifications outlined above. (CAM) that was developed total crack movement. The Crack Activity Meter can measure amongst others the defined Crack activity or total crack movement normally has the typical peaking behaviour with axle repetitions as shown in Figure B.3. Rust (1985) was able to determine that for a flexible pavement with a cemented base and under specific conditions, there crack movement. size below between block size and The data indicated that there is a critical block which further decrease Figure B.4. is a good correlation the crack movement in block size. increases Typical results markedly with are shown in These concepts can be used effectively to enhance the crack classification as given above. In Appendix E the good correlation between the measured crackactivity and measured deflection basin parameters is illustrated by means of an example. As will be shown there this greatly enhances the rehabilitation analysis procedure. One of the major aims of a rut survey is to determine the amount of material needed for the levelling of the existing rut before an overlay is applied. This is all related to ride comfort (PSI values) and, in wet conditions The extent of rutting in particular, to rider safety. is generally used in overlay design as a major criterion of permanent deformation and the structural state of the pavement. The general procedure is to limit rutting in overlay designs by limiting the vertical subgrade strain (e: This approach was originally developed by Dorman and ). vs Metcalf • JOINT 132 -x- JOINT 131 WHEEL LOAD: 40 kN E -=IZ llJ 400 -x .•..•. ....•• ...•. ::E llJ > ••.•x 0 ....... ::E :l<:: ..•.. ..•.. ....•. U <t a: u ...J <t I- 0 ..•.. •.... ....•. ,•.... "X 200 I- o o 200 400 REPETITIONS (x 103) FIGURE B.3 CHANGE IN TOTAL CRACK MOVEMENT DURING HVS TESTING ON THE N2 CONCRETE ROAD-SECTION 258A2 (Rust o lD If) .... If) If) ~ I V I o ·v I 1984) BS 140-4-5097/2 400 .\ \ \ \ \ \ 300 \ E \ ~ J- .,, \ \ .•..• .', \ \ z • • \ \ • w :IE 200 w > 0 :IE \ ~ 0 « 0:: 0 100 o "- ,, ,, "'- . tJ:l ......... .......-. .....•.. -...- . • • •• . 00 ------ ---• • "........ ----- ---- ---• --a-_ . • --- -- ---.•• • • -------------~---- o 4 BLOCK SIZE (m) FIGURE 8.4 CORRELATION BETWEEN CRACK MOVEMENT AND BLOCK SIZE ON THE MR 27 (Rusf,1985J (1963) in their analysis of the behaviour of the test sections of the AASHO road test. It is should be noted that rutting is not only related to the subgrade but that contributions also come from the various layers in the pavement. For this reason Koole (1979) mentions that the rut in the asphalt concrete layer should be treated separately. The South African experience also indicates that such a direction should be followed. Freeme et ale (1982a) indicate that better characterization of the bitumen layer in terms of volumetric and shear properties is necessary to accommodate phenomenon in the bitumen layer. this deformation Maree et ale (1982) show that for granular base pavements tested with the Heavy Vehicle Simulator (HVS). most of the permanent deformation took place within the granular base and subbase. The subgrades never meaningfully contributed towards the total deformation and were always well protected. strong In the same report Maree et ale (1982) illustrate the correlation between cracking, excessive rain, moisture intrusion and deformation for typical granular base pavements; this is shown Figure B.S. The preceding statements make it obvious that a more qualitative classification of rutting is needed than just a report of the average rut. In line with the classification outlined in the previous section on cracking, it is suggested that the pavement structure classification as defined be used also. In fact it is re-emphasized that no indicator like rutting or deflection should be used Freeme in isolation. (1983) behaviour of A further The concept is clearly illustrated by in Figure B.6 where various indicators of the typical granular layers are shown. practical classification is needed to discriminate between various mechanisms of permanent deformation. Molenaar (1983) classifies two types of rutting (see Figure B.7). The first type is that without lateral displacement due to densification. The second type is that with lateral displacement due to Prandtl type of shear deformation. ious discussion This ties in with the prev- on the South African experience. Grant and z Q ti ~ 10 Q: ~ W o INGRESS OF WATER \ \ \HIGH QUALITY GI STANDARD FIGURE 8.5 SCHEMATIC DIAGRAM OF THE RELATIVE BEHAVIOUR GRANULAR MATERIAL OF DIFFERENT QUALITIES (Moree, of 01., 1982) OF PHASE 2 I DENSIFICATION E E STABLE 15 ~ 0:: OF WATER tv<1:- ~ RATE OF INCREASE OF DEFORMATION CAN REDUCE AGAIN IF WATER IS REMOVED ~'i" I e, 0'< <lot/; ~(j WATER AND WATER-I SUSCEPTIBLE MATERIAL I I 10 OF INGRESS I I I o ~ I EFFECT STATE I I Z ~ I PHASE 3 " 5 RATE OF INCREASE DEPENDENT ON QUALITY OF MATERIAL AND STA BLE MOISTURE· CONDITIONS 1LI o ESOs OR TRAFFIC (a) PERMANENT •• DEFORMATION IF WATER IS REMOVED DEFLECTIONS CAN BECAUSE OF REDUCE INCREASE IN RESILIENT MODULUS OF LAYER ~ ~ - - ---- I- Ua: ....•. lLIlL1 -I)- INGRESS WATER L&.<t 1LI-1 o Z 1-- zJ: DEFLECTION REMAINS LOW IF LAY ER NOT SUSCEPTIBLE TO WATER e.g. CRUSHED- STONE BASE OR WATERBOUND MACADAM 1LI!:: ::::;~ (f) lLI 0:: (b) ESOs BEHAVIOU R RESILIENT OR TRAFFIC •• 0500 0.. MATERIAL NOT SIGNIFICANTLY SUSCEPTIBLE TO THE INGRESS OF WATER ~ (f) / :3 :> I ~ 250 I o -- -~WATER I Z lLI ------ ,..,. I I- REMOVED I NGRESS OF WATER AND WATER-SUSCEPTIBLE MATERIAL -I (f) lLI 0:: 0 ESOs (c) CHANGE IN MODULUS OR TRAFFIC OF CEMENTED LAYER I INGRESS ~ I g I I m ........ z 2 0.. OF WATER AND WATERSUSCEPTIBLE MATERIAL I u~ 00:: lLI Z lLI o w (d) STRENGTt-l ESOs OR TRAFFIC BEHAVIOUR I •• FIGURE 8.6 ~ I o INDICATORS OF THE BEHAVIOUR OF GRANULAR LAYERS ~ lI'L -_ MATERIAL NOT SIGNIFICANTLY SUSCEPTIBLE TO THE INGRESS 0.. r-~ WATER~""" REMOVED I I- ....... .,.,....---... _ .. IE r eeme. / !lE31 r r LORIGINAL SURFAr PROFILE ~-~ · · 1 ~ ~ · · I ......•.....•.• Type I ~ A Rutting without lateral displacement of the material. This type of rutting is due to densification of the material . . _I t~~ I · ~-------.;I · I· r Type 8 Rutting with lateral displacement of the material. Rutting can be judged to be a Prandtl type of shear deformation. FIGURE 8.7 TYPES OF RUTTI NG WHICH CAN 8E DISCERNED ( Molenaar, 1983) Curtayne (1982) note that shear in the subgrade is characterized by wide rutting. Shear in the base layer is characterized narrow displaced ruts with material appearing like a by mound adjacent to the rut. From the visual survey therefore a classification of the type of rutting that exists may be made. which will strongly influence the overlay design analysis. The Draft TRH12 (NITRR. 1983) give clear indications for rut criteria related to pavement class and pavement type. It is suggested that those criteria and those suggested by Jordaan and Servas(1983) be followed. At any specific moment, an existing pavement has a certain amount of accumulated damage done to it by repeated traffic loading. There is normally also a certain amount of remaining damage which the existing pavement can undergo before failure. The severity of the damage caused by each repeated traffic loading depends on the structural strength of the existing pavement. This is usually expressed in terms of the equivalent number of standard axles (E80s). If the magnitude of the critical strains is reduced, then the existing pavement can carry a larger number of standard axle loads (E80s). The function of an overlay is therefore to reduce the magnitude of these critical load-induced strains or stresses, depending on the distress determinants being used. Remaining life has two meanings. Without an overlay a pavement normally has remaining life and with an overlay a pavement has a remaining life, that is usually lengthened or prolonged. For this reason "remaining life" will refer to the remaining life of a pavement without an overlay. In the literature remaining life is usually analysed on the basis of the phenomenological theory of cumulative damage. Attempts to relate the structural condition, based on deflection basin measurements, in a different way to the life of the pavement, will also be discussed. The phenomenological theory of cumulative damage is also referred to as the linear summation of cycle ratios. This was advanced by Miner (1945) to predict the fatigue life of metals subjected to fluctuating stress amplitudes. Monismith et ale (1966, 1969) used it to estimate fatigue life of bituminous layers in pavement structures and established it as an acceptable and useful relationship. n. ••number of applications at stress or strain level Let 1 N. ••number of applications to failure at stress or strain 1 level D.1 ••damage due to N.1 number of applications at stress or strain level Then the damage, D , is defined as the stress or strain cycle i ratio, i.e. D . = n1· 1 N.1 Failure will occur when D. = 1. 1 Let r = number of different stress or strain levels involved D = cumulative damage due to number of applications at different stress or strain levels Then the cumulative damage, D, is stated as the linear summation of cycle ratios, i.e. r E i=l = D i r E i=l ni N. 1 r n. or E 2i=l N. = 1 1 Snaith et al. (1980) use the distress determinants vertical subgrade strain (€vs)' and maximum horizontal aspahlt strain (ERA)' as discussed in chapter 4 and 6 , to determine damage due to rutting deformation and fatigue cracking respectively. For both forms of damage the strain-life relationship is given by the general equation: It is therefore possible to apply the cumulative damage theory to both forms of damage. applications matically The accumulation of damage from repeated at various strain levels is illustrated diagram- in Figure C.1. In Figure C.1(a) the strain-life diagram is shown with a typical strain-life curve, l-k. On this curve a strain level E1, for example, corresponds to a life N1. Lines a-b, c-d, etc., represent n applications at strain level 1 E , and n applications at strain level E ' etc. These lines, l Z Z represented by arrows, are called damage paths. The dashed lines, b-c, d-e etc. are called iso-damage lines. of damage at band If the amounts c are the same, then This is represented more simply in a damage-life diagram (see Figure C.1(b». The damage scale ranges from 0 to 1. The damage paths can be plotted continuously as shown in Figure C.1(c). In this way, the cumulative damage arising from repeated applications is determined in diagrammatic form. In practice the number of repeated applications (n.) is expressed 1 in terms of the equivalent number of standard axles (E80s). This reduces the analysis to only one strain level to determine remaining life. In Figure C.1(a), therefore, at strain level E1 the damaged or consumed life is nl and total life is N . 1 Remaining life at this strain level is equal to: Alternatively, damage (D1) is often expressed as previously defined and remaining life (R ) is then: 1 E', a b , 'c -.. DAMAGE PATH --- ISO-DAMAGE LINE ., d '" "' ••.._e _ lll n I N4 N--" N4 N-.... n4 h ~ DAMAGE PATH - ISO-STRAIN (c) FIGURE LINE DAMAGE-PATH DIAGRAM C.I GRAPHICAL PRESENTATION OF CUMULATIVE DAMAGE THEORY (Snaith , et a I., 1980 ) R1 = 1-D = 1 - 1 n1 N1 Using the same distress criteria, vertical subgrade strain (evs ) and maximum horizontal asphalt strain and (eRA)' Anderson (1977) also used this theory to determine remaining life. though, that future environmental It is pointed out, or traffic changes cannot usually be foreseen and therefore such a procedure should be seen as a guide only. In considering the remaining life of a pavement with rutting due to permanent deformation, Anderson (1977) reasons that the damaged life or consumed life will be nullified when the surface deformation is removed by an overlay. Koole (1979) supports this view by Anderson (1977) in his description of the Shell overlay design method. The remaining life of a pavement with fatigue cracking is determined et ale in accordance with the description by Snaith (1980). Treybig et ale (1978) also use the theory of cumulative damage in order to determine remaining life for a pavement with fatigue cracking and rutting due to permanent deformation. As mentioned in Appendix B, however, the cracked state of the existing pavement is taken into consideration asphalt). in determining the material parameters (E Chapter 4 described how these material parameters are used to determine the distress determinants. In a pavement with fatigue cracking the maximum horizontal asphalt strain (ERA) is calculated and used to determine the remaining life in terms of standard axle (E80) repetitions, (1980). as described by Snaith et ale It was shown in Chapter 6, Treybig et ale (1978) consider the contribution of all the structural layers to rutting due to permanent deformation by determining the various stresses and strains of each layer. It is obvious that Kilareski et ale (1982) only considered fatigue cracking when determining not necessarily remaining life. be determined, The strain (eRA) need but as shown in Figure C.2 the deflection basin parameter. surface curvature index (SCI). is related to the number of equivalent single-axle loads (EAL). In this case the structural number has also been determined. based on the AASHO Design Procedure (for the various test sections). The 10 per cent fatigue cracking line is the same form as described above for the general relationship. N = A(l)b. e: The equation for Kilareski - n ). 1 1 et al. (1982) advance this one step further by relating remaining remaining life is as described above. namely (N life (in terms of equivalent axle loads) to the SCI for various structural numbers (pavement strengths). as shown in Figure C.3. Residual life determined from deflection measurements lead to satisfactory results. Koole (1979) states: alone does not "It is not possible to determine the residual life of a pavement solely from deflection measurements". The reasoq lies in the fact that the change in a structural parameter. for example elastic modulus (E). with an increase in load repetitions shows a sharp decrease in value initially but thereafter there is a long period during which virtually no change occurs and only at the end of the structural life is there a definite sharp decrease to distress. measurements also reflect this typical behaviour. Deflection However. it is possible to relate early life deflections empirically to the critical life of particular types of pavement structures. as shown in Figure C.4 using work done by Lister and Kennedy (1977). Koole (1979) also mentions that original design life can be determined from FWD deflections. FWD deflections measured A "crude" test on consumed life is to take between the wheel tracks. If the deflections in the wheel tracks. are significantly greater than those measured between the wheel tracks the pavement is approaching the end of its service life. Pronk and Buiter (1982) mention the procedure in which the decline in effective layer thickness is related to the structural strength. This forms the basis of the structural performance model developed by Molenaar (1983). This principle is shown schematically in Figure C.5 where equivalent layer thickness (H ) decreases in e c: 1000 10 I 0 ~ 700 Section No. • • C,) 500 )( Q) 400 c: 300 •... 200 Q) - ~ 10% Fatigue Crocking Line 8 (:3.14) 9(3.58 ) 14 (3.65) ~,..,... ::s ___ 1d (3.72 ) C Ic (3.94) __ > •... ::s 2 (4.38) C,) Q) (,) c •... ::s (J) No. H (2.70) (J) ~ Structural I ,........ .•, " " 7 (4.74)-- 100 .• .-#/1, ••.• 80 60 I x 10s 18-kip 2 3 (80-kN) 4 6 8 Ix 106 Equivalent Single-Axle 2 3 4 6 Loads FIGURE C.2 VARIATION OF SURFACE CURVATURE lNOEX-WITH EAL. (Kiloreski, et 01.,1982) STRUCTURAL NUMBER, --l 5.0' 4.5 ~ 3.0 ~ 2.0 4.0 3.5 SN 3.0 W lL. --l ~ z w 1.0 0.7 ~ w ~ (,!) z z 0.2 <t ~ w a:: O. I 0.07 0.05 50 SURFACE 100 150 CURVATURE 200 INDEX, 250 6 300 SCI<l6 IN.) FIGURE C.3 REMAINING PAVEMENT LIFE BASED ON FATIGUE CRACKING FOR BITUMINOUS CONCRETE PAVEMENTS WITH SUBBASE. (Kilareski, et aI., 1982) 140-4-4760/38 ROAD BASE Hot rolled asphalt & Dense bitumen macadam Dense tarmacadam Medium textured tarmacadam x Open textured tarmacadam Readings still sound AO • 200 • 150 I 0 )( E E " • N 100 • 80 .yAy Z 0 .- u 60 50 w 40 0 30 -I LL W 0 0 ~ • A • A . n -0 y A 0,2 0,3 0,4 0,6 0,8 1,0 1,5 2 3 CUMULATIVE STANDARD AXLES 4 5 6 (x 106) 8 10 15 FIGURE C.4 RELATION BETWEEN DEFLECTION AND CRITICAL LIFE OF PAVEMENTS WITH BITUMINOUS AND TAR BOUND BASES (Lister and Kennedy, 1978 ) 20 (f) (f) w z :::c: u :c I-~ 0::- W Q) >-:c <X:...J I- Z W -J <X: > ~ o W LOAD REPETITIONS n FIGURE C.5 HYPOTHESIZED DECREASE OF THE EQUIVALENT LAYER THICKNESS (He) WITH RESPECT TO THE NUMBER OF LOAD APPLICATIONS (n). relation to the number of load applications(n). The structural condition of the pavement can be characterized by means of the structural condition index p. which is defined as: P = H ecn where H ecn /H eco = equivalent layer thickness after n load applications corrected for temperature and environmental H eco fluctuations = equivalent layer thickness just after construction corrected for temperature and environmental fluctuations In order to determine H • deflection values between the wheel eco paths are measured as described above. Molenaar (1983) defines Heco values determined in this way as "candidate" H values since they eco would have been subjected to some loading between the wheel paths. The amount of future deterioration depends on the expected number of load applications. the deterioration Values for Sl measurements. og the structural condition index P and the shape of function characterized by Sl N. N should also be determined by means of deflection Sl og N can be calculated as follows: 2 2 2 S2 = a1 b1 S log He + l.o.f(l where og N 1 ) og - oge: a1 = slope of fatigue relation b1 = slope of H S2 e versus log e:relation (=2) 1.o.f. = lack of fit of the equation used to describe the fatigue relation (=0,16) In Figure 4.10 the typical relationship between H e and surface curvature index (SeI) is shown from results of deflection basin - a.. - 1,0 x w 0 z z 0 I0 0,8 z 0 U ...J <r 0:: :::> f3 I- u :::> 0:: Ien 0,6 --- S\OgN 0,2 ° 0,4 REPETITION RAT\ n/ N FIGURE C.6 COMPARISON OF THE THEORETICALLY DERIVED STRUCTURAL PERFORMANCE MODEL AND THE EQUIVALENT LAYER THICKNESS DETERIORATION MODEL (Molenaar, 1983) plotted in relation to deterioration Sl og (n/N) and the influence of N can also be seen. Molenaar (1983) takes this even further by calculating directly from deflection curvature P P and SlogN basin parameter values such as surface index (SCI) as follows: = (SCI /SCI )d o S2 log N where SCI SCI o n = n d2 2 2 2 1 c1 S 10gSCI+ Sl.o.f (log N-log €) = SCI at time of construction = SCI after n load applications d1 = absolute value of the slope of the SCI versus He relation c (a reasonable value is 0,53) = slope of the 10g(SCI)-in relation to log N (=0,943) 1 All other variables have been defined before. However. Molenaar (1983) warns as follows: "Although the procedure to calculate P seems very simple, one should be aware of the fact that in a number of cases the ratios H and SCI /SCI o Remaining n ecn /H eco might be larger than one. life is determined by this procedure as illustrated in Figure C.7. Molenaar (1983) modified the work done by the Belgian Road Research Centre. He uses the following equation for permanent deformation model: where u· p permanent deformation (m) Z o I- o Z- o~ ~ [j 0.9 _1__ I _-_n I_N_.....•••. <:to a:Z ::>IU ::> a: Ien 0.8 0.75 0.5 REPETITION RATIO n/N FIGURE C.7 PROCEDURE TO ASSESS THE REMAINING LIFE (Molenaar,1983) -...... ¢ o CD ~ ¢ I ~ I o ~ ... u e = elastic deformation (m) By means of regression analyses of a typical three-layered pavement system Molenaar (1983) used the BISAR computer program to arrive at values of bo' b1 and n for the various interfaces between the layers. The elastic deformation at the pavement surface must be known in order to be able to determine the elastic deformation of the top layer. This deformation due to dual wheel loading can be estimated from the maximum deflection (6 ) value of the falling o weight deflectometer (FWD) by using the following equation: log Ue surface = 0,09+0,948 log 60FWD The elastic deformation of each layer can be calculated by subtracting the deformation at the lower interface from the deformation at the upper interface. The permanent deformation can then be calculated by means of the permanent deformation model with constants shown in Table C.1. A correction factor is applied to relate observed rut depth to these calculated values. applications By these means rut depth can be related to load (n), and consumed rut life can be determined by defining a terminal rut depth of for example 20 mm. In chapter 4 and 6 it was concluded that the current mechanistic design procedure in South Africa using distress determinants vertical subgrade strain (€ ) and horizontal asphalt strain (€h ) vs a is a sound one. Proper fatigue relationships have been established for these parameters. This makes the use of the linear summation of cycle ratios applicable to both distress criteria: fatigue cracking and deformation rutting. = (l)b), € The generalized relationship, described by Snaith et al. (1980) can thus be used to (N TABLE C.1. Values forob and b to be used in the calculation 1 of the permanent deformation (Molenaar. 1983) b = Bituminous layers U *b n 1 e 0 U *4.49nO.25 e U *2nO.3 if n<0.12 m e U *2nO.2 if n<0.12 m e Stone base Lean concrete base Granular subbase 500 1 500 U *2nO.3 e Subgrade 5 000 (summer) 200 5. 1O. 20. 40 U *(1+0.7 logn) e determine remaining life for both distress criteria. The more critical value can then be used in the selection of an overlay, as described in Appendix D. Although Freeme et al. (1982a) give a fundamental basis to rehabilitation the mechanistic design procedure. the case of establishing design in their description of it is felt that. particularly in criteria to determine consumed life due to rutting, some advances can be made. This would again be possible with the information available from HVS tests and observed field data. In this regard the approach by Treybig et al. (1978), where the deformation contributions of each layer is better rep~e$ented by~_ the computed stresses and strains of each layer, should be pursued with the available data. It is clear too that the approach to relate the remaining life of the pavement to other structural indicators such as the equivalent layer approach shows much promise. model suggested by Molenaar three-layered The structural performance (1983) was developed specifically for a pavement structure and therefore it is obvious that it would not be possible to use this approach in all cases. it is suggested that, with the previously mentioned available on pavement performance Instead information in South Africa, the performance model be established with values determined from regression analyses. This approach would then take into consideration factors such as the deflection basin measuring device, deflection basin parameter selected and pavement structure classification described previously. The model relating permanent deformation and elastic deformation to the number of load applications seems a sound approach. It would also be possible to establish these relationships with the regression analysis of the information available for the South African condition. This section is a logical continuation of the discussion in Appendix C. In general, the decision to overlay a pavement under analysis will be based on criteria related to the remaining life or consumed life. The distress criteria, fatigue cracking and permanent deformation rutting, are considered separately to determine the remaining life of the pavement. The decision to overlay the pavement is based on the more conservative of the two criteria, but both criteria are checked again to ensure that the prolonged life (remaining life after the overlay) would indeed be achieved. As in any situation where various possible alternatives are generated, sound engineering considerations. judgement is influenced by economic The latter type of decision strongly indicates the typical considerations of a maintenance or pavement management programme and should be viewed against that broader background although the focus here is on a project level based on deflection basin related criteria. Snaith et al. (1980) describe how on the basis of the theory of cumulative damage, the remaining life can be determined. general this remaining life, as described in Appendix C, = In would be or R1 = 1-n /N . Snaith et al. (1980) do 1 1 not mention any specific criteria related to this remaining life for expressed as: R1 N1-n 1 decisions to overlay or not. Anderson (1977) bases the decision to overlay or not on the length of the remaining life. If the anticipated or estimated future traffic is more than the remaining life, an overlay is needed. If the remaining life is more than the anticipated traffic over the functional no overlay is needed. life of the pavement, An overlay may be required for other functional reasons such as improving the skid resistance of the riding surface. It is in this regard that Anderson (1977) states that even a nominal thickness of asphalt concrete placed on an existing pavement gives the pavement a new "life" by removing the surface deformation. "There is no theoretical or practical evidence which suggests that the permanent deformation which existed before rehabilitation will affect the future performance of the pavement." In general Anderson (1977) does support the analysis procedure described by Snaith et al. (1980). For the generalized fatigue relationship (N_(l)b) the aim of an overlay would be to reduce the e: strain level (e: ) to the level where the anticipated traffic would vs meet the prolonged life or remaining life after overlay. This process is shown in Figure 0.1 and in a more general form in Figure 0.2. The formulation of the fatigue relationship considered by Treybig et al. (1978) (as discussed in chapter 6 and Appendix C) is obViously more complicated. Although no specific mention is made of any criteria for overlays related to remaining life the reasoning above was evidently followed. Molenaar (1983) does not use his permanent deformation model (see Appendix C) in his proposed overlay design. It is obvious though that this model, if properly calibrated to field performances, would also be able to provide the same criteria based on remaining life as described in Appendix C. If an overlay is needed, the aim would be to reduce the elastic deformation deformation (Ue ) and resulting permanent. (Up ) of each layer in order to meet the required . prolonged life. Remaining life (N1-n1) compared with the anticipated or future traffic is the general criterion for overlays, based on analysis using the cumulative damage (linear summation ratio) theory. This has already been briefly described on the basis of the discussion by Snaith et al. (1980) (see Appendix C and sections 2). In considering the previously defined rema1n1ng life, Anderson (1977) also considers the cracked state of the existing asphalt concrete layer and whether the pavement has an asphalt concrete layer when establishing criteria for considering an overlay. remaining life is automatically zero if the pavement is cracked The _0_ :tI~ _0_ "': :'4. -0- 0_ FIGURE 0.1 CHANGES IN STRAIN LEVELS 2 " DUE TO OVERLAY. , "" "", "' .••.., 4 r>- O· ISO-STRAIN LINE €2 (b) Damage- Life Diagram t DOl I.I (c) NOTE: B.O. - BEFORE OVERLAY Domage - Path Diagram A.O. - AFTER OVERLAY N ~ .••.. FIGURE 0.2 o U) DAMAGE ~. STRUCTURE •..... I ~ I o ~ PROCESS IN A PAVEMENT WITH A SINGLE ( Snaith, et 01., 1980) OVERLAY. and warrants consideration for an overlay, or if there is no asphalt concrete layer yet. the anticipated If the remaining life is less than traffic an overlay may be considered. If the remaining life is more than the anticipated traffic no overlay is needed. When an overlay is considered as was discussed in section 2 (referring to Figures D.1 and D.2), the aim would again be to reduce the strain level (ERA) to accommodate a prolonged life or remaining life after the overlay, which would meet the required anticipated in this way, Anderson traffic life. Analysing various pavements (1977) arrived at characteristic shown in Figure D.3. curves as In this figure remaining life is expressed as a percentage of the overlay thickness. The latter value of overlay thickness corresponds to the reduction in strain level (ERA)' Comparing these results with those of a fully cracked asphalt concrete layer with no remaining life, Anderson (1977) concludes that it will always be more economical to neglect any existing asphalt when the remaining life is below 75 per cent. In this overlay design procedure, a "critical" remaining life of 50 per cent was adopted, this being the point at which the existing life is disregarded in designing an overlay. fatigue relationships This approach, based on the described in chapter 6, was also followed by Monismith and Markevich (1983). The approach by Molenaar (1983), using the structural performance model, obviously differs from the one described above. Molenaar (1983) is quoted as follows: "Although Miner's law is applicable to the development of one crack, further extension of cracks is dependent on the redistribution of the stresses, and in this case Miner's law may not be fully applicable. Furthermore Miner's law defines a clear failure condition which occurs at e.g. the fracture of a test specimen. Such a failure point does not exist in the case of pavements. A 100 per cent cracked pavement surface can still be used as a reasonable driving surface unless large deformations pot-holes occur. Therefore a straightforward the estimation of overlay thicknesses and/or use of Miner's law in is not considered to be a proper approach, since this will result in an unrealistic overlay design especially in those cases where Miner's ratio comes close to 12 II 10 f/) Q) 9 .J:: 8 - 7 (,) C f/) f/) Q) t* t Case 3 C .¥. (,) .J::. I~ 0 6 5 ~ Q) > 0 * 4 ~ Case 2 3 * ~ Case 6 t~t Case 1 t ,t Case 5 2 t* t Case 4 25% 500/0 750/0 1000/0 Remaining Life EFFECT FIGURE 0.3 OF REMAINING LIFE ON OVERLAY THICKNESS(Anderson, 1977) This supports the reasoning of Anderson (1977), but also points to the possibility of the structural performance model being used to give a more realistic estimate of the structural life of a bitumen pavement. Molenaar (1983) does not give any specific indication of criteria for decisions on overlays. It is evident from the reasoning, however, that the remaining life determined in this way, would also be used, but with different preconditions. The two distress criteria, fatigue cracking and permanent deformation rutting have deliberately been considered separately. The reasoning behind this is explained by Koole (1979): "In determining the thickness required for an overlay, the subgrade-strain separately; and asphalt-strain criteria should be considered. it is quite possible that the design criterion that did not govern the original pavement design will become limiting for the overlay thickness." In this section an overlay thickness is thus decided upon by means of the limiting life of the two defined criteria described in section 2 and 3. The resulting lower distress criteria parameters (ERA and E ) are usually calculated for the possible thicknesses vs considered. Anderson (1977) calculates these relationships for the various thicknesses of overlays by means of the techniques described in chapter 4. This is shown in Figures D.4 and D.5 for reduction in subgrade strain (E ) and asphalt tensile strain (ERA)' In vs Figure D.3 only pavements with more than 50 mm of asphalt concrete prior to overlaying are considered. The reason was discussed in chapter 6 and in Figure 6.2 what the effect of relatively thin asphalt concrete layers (50 to 75 mm) on tensile strain in asphalt concrete was shown. From the quotation by Koole (1979) above it is obvious that an overlay of for example 25 mm on the existing 25 to 40 mm of asphalt for rut requirements, could in fact shorten the remaining life of the fatigue cracking requirements. The desired '"TV "".- "" , ""V', '"T "" I 8 - v Thickness of OVerIOY-f.. 5 7 I 0 )( c 6 ..•..•... c c - 5 0 ~ en Q) 4 . "0 t:l 0 ~ '-I en :J 3 .0 en c c 0 2 0 "0 :J Q) 0:: 2 4 6 8 Subgrade Strain Prior to Overlay (in lin x 10- 4 REDUCTION 10 ) FIGURE 0.4 IN SUBGRADE STRAIN DUE TO OVERLAY (Anderson, 1977) fO- 4-4 7 60/45 i V I o 2.5 )( Thickness of Overlay (inches) C "'- -.S 20. c: -•.. 0 en 1.5 .t:' 0 00 .s:::. Q. en 0 1.0 - 0.5 o ::J '0 4) 0:: 234 Asphalt strain prior to overlay (in/in x 104) FIGURE 0.5 REDUCTION IN ASPHALT TENSILE STRAIN DUE TO OVERLAY ( Pavements with more than 2" of asphalt concre~e prior to overlaying) ( Anderson 1 1977 ) reduction in strain level can also be expressed in terms of the selected deflection basin parameters, according to Anderson (1977). as shown in Figure D.6, Similarly the desired lower deflection basin parameter such as surface curvature index (SCl) can be related to a higher equivalent layer thickness (H ) (see e Figure 4.10) according to the analyses of Molenaar (1983). Treybig et al. (1978) established the most comprehensive procedure for considering the effect of fatigue cracking and rutting simultaneously. This is shown in Figure D.7 where the existing asphalt concrete layer is regarded as uncracked. The overlay thickness required, is determined by selecting the thicker of the two thicknesses related to the various criteria for the desired load repetitions. Koole (1979) also describes how three separate overlay thicknesses are determined. This includes the previously discussed criteria for fatigue cracking and rutting, and also a method of determining thickness based on the assumption that the existing pavement has deteriorated to such an extent that the asphalt concrete layer is treated as a granular layer and the overlay as a "new" asphalt concrete layer. The latter approach is also suggested by Thompson and Hoffman (1983) when the asphalt concrete layer displays interconnected Class 2 cracking. Remaining life in relation to the distress criteria, rutting and fatigue cracking, is the main criterion in the consideration overlays. of The remaining life determined by methods described in chapter 6 was determined for each of the distress criteria separately. For the rutting criterion the views on remaining life vary considerably. The view that remaining life is completely restored by an overlay removing the deformations overlay design. is Widely accepted in Using the various models discussed in Appendix C it is possible to determine the prolonged life by lowering the -u:c 120 z -><! ....J 0::: OVERLAY THICKNESS 110 100 W > 0 90 0 I- 80 w ::> 0 70 N 0 I 0 0 . t1 60 - 0 50 z z 40 0 - I- u ::> 30 0 w 20 0::: o 10 20 30 40·50 60 70 80 90 100 110 120 130 140 150 DO - 012 PRIOR TO OVERLAY (INCH) FIGURE 0.6 REDUCTION IN 00- 012 DUE TO OVERLAY (Anderson, 1977) --;;;8 Cl) .J::. o c: •.....•• en6 (J) Cl) c ~ o .J::. I- Fatigue--- 4 :>; o ~ Cl) > 2 o o 10 100 1,000 10,000 100,000 Allowable 18- Kip Equivalent Load Applications, N x 103 SAMPLE FIGURE 0.7 OVERLAY THICKNESS DESIGN CURVES vertical subgrade strain (€ vs ) for example. The more comprehensive model proposed by Treybig et al. (1978) warrants a closer look if it were to be related to the South African situation as were the other proposals and recommendations mentioned before. This may all be incorporated in a proposed catalogue of overlay designs, which would be similar to the existing TRH4 (NITRR, 1985a). In consideration of remaining life as a criterion for fatigue cracking, the consideration of cracking only leads to some uneconomical overlay proposals. Anderson (1977) indicates that a 50 per cent remaining life for fatigue cracking should be a critical value. The structural performance model by Molenaar (1983) attempts to be more economical by considering the structural value of the cracked asphalt layer. of the use It also offers better consideration of other new materials like bitumen-rubber. In the final selection of the thickness of the proposed overlay for the critical strain parameter, the emphasis is on checking the other parameter again in order to ensure that the overlay does not shorten remaining life after overlay for the previously non-critical parameter value. From Anderson's (1977) work it is obvious that this would be of particular importance with thin overlays on thin asphalt concrete layers. The approach by Treybig et al. (1978) to plot overlay thickness for both criteria simultaneously in relation to remaining life gives a good graphical indication of such trends. It has been stated that the selection of an overlay must be seen against the background of maintenance or rehabilitation management systems. The models discussed for analysis are not always applicable to the South African situation. suggested that the recommendations It is therefore in regard to pavement per- formance and structure were made in previous sections be extended . to this area of overlay design in order to make the whole design procedure mechanistically sound. This could easily be incor- porated in the suggested catalogue of overlay designs, mentioned above. In Appendix B it was mentioned that there exists a good correlation between the measurements deflection basin Deflectometer of the parameters (RSD). as Crack-Activity-Meter measured with (CAM) the Road and Surface The normal procedure of initial assessment according to the draft TRH12 (1983) guidelines are carried out on a typical cemented base pavement. In the detailed assessment stage the question whether the cracks recorded on specific sections are active or not must then be addressed with confidence. The new service of the NITRR where the CAM and the RSD are combined can then give the required information to make a sound decision in regards to . the rehabilitation option. Various cracks with related block sizes and degrees of severity are selected on such a section under investigation. At the same point (crack) the CAM and RSD are set up and measurements are taken with the Benkelmanbeam truck travelling over the crack following the WASHO procedure. The crack activity measurements are then ·correlated with various other parameters such as block size and deflection basin parameters (Rust, 1984). This appendix therefore describes how such an analysis on the N4/3 was used to verify the rehabilitation option selected in terms of its crack attenuation. The cemented base of N4/3 is cracked and urgently needs rehabilitation. 1986) . Crack movement measurements were taken in October (Rust, It was found that there exists sections of road where the crack movements are very high. relatively large. The block sizes were found to be This means that the crack movements are likely to increase as the block sizes break down to a smaller size. The rehabilitation option that was selected is to overlay the existing pavement with a 100 mm G1 crushed stone base and 40 mm asphalt surfacing. The analysis described in this technical note is to determine what the effectiveness of the overlay is to reduce crack movement. In the analysis use was made of measured deflection basins and the correlation thereof with crack movement measurements. This was followed with a mechanistic analysis of the rehabilitation option to calculate the deflection basin and predicted crack movements. On each of the measuring points of the CAM the deflection basin was also measured with the RSD. The measurement of the wnole deflection basin with the RSD makes it possible to determine various deflection basin parameters. The most common deflection basin parameters (Rust. 1986) that can be calculated from RSD measurements are listed in Table 1.1 with their respective formula. crack movements (VETOT) (HMAX) and the maximum in micro-meters basin parameters. were correlated The maximum horizontal vertical with crack movements various The results were as follows: 904,271* (MAX. DEFL)2,6 - 9,483E-6*(SCI )2,5 915 3,086E-3*(SCI )I,5 610 9,81*(SCI + - 2,538E-2*(Dl )l,3 1 4931.765*(MAX. DEFL)5.2 - l,813E-12*(SCI )5.1 915 4.312E-8*(SCI )3.6 + 1;65E-3*(Dl )1.9 - )1.9 + 49.713 610 1.887E-3*(SCI 305 = + + 71.765 )l,4 305 Where: SCI deflection + 1 Surface curvature index with the subscripts indicating the offset for deflection in mm. Dl1 = Deflection Index which is the difference in deflection at 127 mm and 305 mm. MAX. DEFL VETOT = = Maximum deflection in mm. Total vertical movement in micrometer. The regression analysis indicate that VETOT correlated better with the deflection basin parameters than HMAX. The reason for that can clearly be related to the relatively large block sizes (Rust, 1986). The pavement structures as shown in Figure E.1 for the existing pavement and the rehabilitated pavement were analysed mechanistically with the computer program ELSYM5. indicated in the figure. base was calculated overlay. The input values are as The stress directly on top of the cemented before and after the G1 crushed stone base The calculated vertical stress was 374 kPa and after the overlay it was reduced to 111 kPa. This is a drastic reduction in the calculated stress values and clearly indicates that the overlay did indirectly reduce the possible crack movements. During the mechanistic analysis the deflection basin was calculated for the two pavement flection basin structures. parameters are In Table E.1 the relevant indicated. The deflection de- basin parameters on top of the old cemented base (now sub-base) and on top of the overlayed pavement are shown. Deflection basin parameters (mm) MAX. DEFL SCI915 SCI610 SCI305 0,253 0,230 When comparing the deflection basin parameters calculated on the surface directly it is shown in Table E.1 that the overlay reduces the deflection basin parameters values drastically. This reduction in the respective deflection basin parameter values are even more when the values calculated on top of the cemented base are compared. i 2,4m EXISTING PAVEMENT I I 3,7 m 3,7m EXISTING EXISTING 150 CI <t. EXISTING PAVEMENT I 50 150 AC CI FIGURE E.! REHABILITATION OPTION ON N4 /3 3,7 m rI The regression analysis described earlier were also used to calculate the respective predicted crack movements. These results are shown in Table E.2. The results in Table E.2 show that there is a drastic reduction in the vertical and the horizontal crack movements. In the case of the vertical crack movements the reduction was more. This vertical movement was the more severe case for crack movement due to the relatively large block sizes. (a) The crack movements (HMAX and VETOT) were correlated with various deflection basin parameters as measured with the CAM and the RSD. (b) The vertical stress calculated on top of the cemented base show a drastic reduction in values when compared with the vertical stress values calculated on top of the sub-base of the overlayed pavement. cemented This reduction indicates that there should be a reduction in crack movements too. (c) The deflection basin parameters were calculated existing pavement and the overlayed pavement. for the These calcu- lated deflection basin parameters were used in the correlation relationships to determine the calculated crack movements. There is a drastic reduction in the crack movements on top of the cemented base due to the overlay. Odemark (1949) equivalent IS layer thickness concept is used as a simple method of approximation. multi-layered It enables the transformation of a system into a single layer with equivalent thickness. The principle is that the equivalent layer has the same stiffness as the original layer, so as to give the same pressure distribution underneath the layer. This concept of classifying a pavement with one number that represents more or less the bearing capacity of that pavement is clearly illustrated by Molenaar and Van Gurp (1980) and Molenaar (1983). The typical South African pavement structures that were analysed in chapter 7 were also converted to layer thickness. the equivalent The equivqlent layer thickness values calculated were then rlated to various distress determinants and fatigue life in order to evaluate this concept as a possible aid in the mechanistic rehabilitation design procedure. L-l = aE 2 E.(l-v) I]. ~I h. ]. E (I-v.) s ]. II 3 where = 0,9 for flexible pavements a = E. = ]. E = s v. = V = s h.]. ]. thickness of layer i in m elastic modulus of layer i in N/m2 2 elastic modulus of subgrade in Nlm Poisson ratio of layer i Poisson ratio of subgrade layer with value equal to 0,35 L = Number of layers Molenaar (1983) and Molenaar and Van Gurp (1980) analysed a typical three-layered pavement structure. The typical flexible pavement structures referred to in this Appendix differ from this three- layered system in the sense that the pavement structures are either four layered or five-layered systems with a different standard wheel load and tyre resemble these thickness of pressure. The three-layered the bitumen bitumen pavements bases. base most Most of pavements closely analysed in terms the typical of flexible pavement structures analysed. though, have thin asphalt surfacings (S 40 mm). In Figures F.l and F.2 typical relationships of H e versus deflection basin parameters, shape factor (Fl) and slope of deflection (SO) are shown as calculated for bituminous base pavements. The purpose is to show that some deflection basin parameters like SO, R. SCI, BCI and BOI can discern between the various subgrade while others, such as F 1, F2, S, A and Q cannot. elastic moduli In Figure F.3 surface curvature index (SCI) is shown for bituminous and granular bases versus H. In both cases SCI can discern between the various e subgrade effective elastic moduli. The gradients for these functions of the bitumen base pavements correlate well with bitumen base pavements with three layers (SCI with r Gurp, 1980). = 500 mm) (Molenaar and Van The gradients for the relationships of the granular base pavements though, are shallow and reflect a greater sensitivity to changes in H . e Flexible pavements in general were grouped together in Figure F.4 to show that H e correlates well with vertical subgrade strain (e: vs ). The various values of effective elastic moduli of the subgrade lead to different relationships as shown in Figure F.4. the other distress determinant, (e:HA) , at the bottom horizontal of the bituminous In Figure F.5 asphalt tensile strain base, is shown versus He' Here again, there is a clear discernment between the elastic moduli of the subgrade. It is however not possible to develop the same relationship between e:HA and He for the thin surfacings of granular base pavements. One of the reasons for the latter situation seems to be that the thickness, Poisson ratio and elastic modulus ratio of the thin surfacing, compared to that of the base and even subgrade, differ markedly from that of a bituminous base pavement. This is IJ.. a:: 0 I- U ~ 0,5 w a.. <t J: CJ) 0,2 0,1 0, I 0,2 0,5 t 2 5 EQUIVALENT LAYER THICKNESS (He) (m) 10 FIGURE F. I EQUIVALENT LAYER THICKNESS VERSUS SHAPE FACTOR F! 0 en Z 0 IU W ...l IJ.. W 0 IJ.. 0 W a.. 0 ...l CJ) CJ) CD •...•. 0 to 10 0,I 0,2 0,5 I 2 5 EQUIVALENT LAYER THICKNESS (He)(m) (\J 10 I .;t I 0 .;t en FIGURE F.2 EQUIVALENT LAYER THICKNESS VERSUS SLOPE OF DEFLECTION GRANULAR '" ~ "- - I- Es = 50 MPa ~ ""'lIl ~ ~ "' "'" ~ 10 0 ~ \ \ tj U') ,.\ , 1\\ \ \~. BASES Es=50MPa Es=70 , ~ ~ ~ BITUMEN ~,. ~ ~~ ~ ~ ~ 1\ \ E ::L Es = 150 MPa ~ II -- ~ \' , \ •.. Es = 70 MPa ....• .. 100 I'f) ~ lC""" '" E E I BASES--- ~ " MPa "\~\ Es= 150 MPa \ 10 0,3 EQUIVALENT I LAYER THICKNESS ,\ . 2 (Hel (ml F.3 Equivalent layer th i ckness versus surface curvature index FIGURE z ~ 500 ~ (J) I ::i.. 100 0,3 EQUIVALENT I LAYER THICKNESS 2 (HeJ (m) FIGURE F.4 VERTICAL SUBGRADE STRAIN VERSUS EQUIVALENT LAYER THICKNESS FOR FLEXI BLE .0 111 .•... .... ut o to I ~ I o 'f ~-- PAVEMENTS ~ 100 <t Q: I(/l I ::t Es = 50 MPo Es = 70 M Po Es =150 MPo 10 O,~____ EQUIVALENT I LAYER FIGURE THICKNESS 2 (HeHml F.5 EQUIVALENT LAYER THICKNESS VERSUS MAXIMUM ASPHALT STRAIN FOR BITUMEN BASE PAVEMENTS clear when one looks at the formula for the calculation of H • given e Equivalent layer thickness (H ) can be used to indicate whether a e pavement structure with cemented subbases or bases is in the flexible state, with the cemented layers in the cracked phase exhibiting equivalent granular behaviour according to the definition given by Freeme (1983). pavements with In Figure F.6, H e for the pre-cracked life of cemented subbases and bases is shown in terms of standard 80 kN axle repetitions (E80s) determined as prescribed by Freeme et al. (l982a). A distinction can be made based on the variance of the elastic modulus of the subgrade. however, that an H It can be seen, value of at least 1,1 m is required for a e subgrade modulus of 70 MPa to have any significant pre-cracked life of cemented layers. This is rather high and reaffirms that the major portion of the structural life of typical TRH4 (NITRR, 1985a) pavement structures with cemented layers is in the cracked phase or flexible behaviour state. The recommended vertical subgrade strain (e ) criteria for diffevs rent road categories (Freeme et al., 1982a) were used to calculate the standard 80 kN axle repetitions for all the flexible pavement structures for their respective values of H. e This relationship between He and E80s is shown in Figure F.7 for all flexible pavement structures. In this figure the fatigue life of bitumen base pavements was also calculated with respect to maximum asphalt strain (eRA) and correlated with the respective He value. The recommended fatigue life criteria for thick bitumen base pavements were used in The recommended shift the ca 1cu 1at·J.on (Freeme et al., 1982a). factors shown in Table F.1 were applied to the calculated fatigue lives. Ul 0 CD IJJ CJ) Z 0 !:: ~ IJJ Es Cl. IJJ a:: 105 50 MPo 70 MPo 150 MPo'" IJJ ...J X « z ..lie: 0 CD 0 a:: « 0 z « ~ CJ) ~ 104 u « a:: u IJJ a:: Cl. j 103 0,20 EQUIVALENT 1,0 LAYER THICKNESS 5,0 (He) (m) FIGURE F.G Initiation of cracking of cemented bases and su bbases in terms of equivalent layer thickness '0 m ~ "'- CD o II') I qI o 'f' -Q'I I _ - I E vs I FORI r FLEXIBLE PAVEMENTS I I I I I I TRH4 (NITRR 19850 TRAFFIC CLASSES I t en 0 - E4 CO W C/) 107 - z 0 I- I- E3 ~ W Cl. W 0:: - W ...J X « I- a E2 ,.,. 0:: « a z « I- "'s 106 = 70 MPo - C/) ~EI ~ J EO 105 - - E FOR HA BITUMEN BASE PAVEMENTS 0,1 1,0 EQUIVALENT LAYER FIGURE THICKNESS(He) (m) F.7 Pavement life for maximum asphalt strain and vertical subgrade strain criteria in terms of equivalent layer thickness - to I V I o V --"""--------- The equivalent layer thickness (H ) concept proved to be a concept e that more or less represents the structural capacity of flexible pavements. Deflection basin parameters correlate well with a value such as H e in general, as calculated for flexible pavements. however only such deflection basin parameters, It is that normally use points of deflection near each other in the calculation procedure (e.g. scr, R, BCI, BDI and SD), that can discern the effect of variance in subgrade elastic moduli. Such relationships however do not have much value except as for an interim step towards establishing relationships between the distress determinants (£RA and £VS) and H . e He correlates well with subgrade vertical strain (£VS) for flexible pavement structures and discerns the effect of variance of subgrade elastic moduli. Granular bases on the other hand do not give any clear relationships between maximum asphalt strain (£RA) and He as is the case with bitumen base pavements. The reason seems to be the ratios of the thickness, elastic modulus and Poisson ratio of the surfacing and the base as well as that of the subgrade, in the calculation of· H , which leads to this marked difference e between granular and bitumen bases. The value of H e can be used in a mechanistic design or analysis procedure to establish the structural life of a flexible pavement with regard to the distress determinants (£VS and £RA)' The pre- cracked life of a cemented base and subbase layer can be determined. 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WISEMAN, G, UZAN, J, HOFFMAN, M S, ISHAI. I and LIVNEH, M. (1977). Simple elastic models for pavement evaluation. Proc. of the 4th Int. Conf. on the Structural Design of Asphalt Pavements. Ann Arbor, Vol. 2. YODER, E J and WITCZAK. M W. (1975). Principles Second Edition. John Willey and Sons. Inc. of pavement design. Parameter . Formula I. Maximum deflection 2. Radius 3. of 80 curvature Spreadability 4. Area 5. Shape factors 6. Sur face curvature 7. Base curvature 8. Base damage 9. Deflection 10. Bending II. Slope index index index ratio index of deflection 12. Tangent 13. Radius slope of influence r2 R = S :: A = 6[1+ 2 (SI/80) F = (80- 82) I 81 SCI = 8o'-:8r BCI = 8610 -8915 BDI = 8305 -8610 Or = 8r/80 BI = 80/a SO = tan-1 (80-8r)/r ST = (8 o -8d/r RI = R'/80 280 ( 80/8 r - \) [( 80+81+82+ 83)/5] 80 r , , where ) = 127 mm 100 ,. F2 = =( 81""83 spaced 305mm 8, -83) 182 or 305 500 mm 8r ~ 80/2 where ,. r +2(82/801"83/80] ; , i a = deflection ; where where r = r shape of road ~Point surface Positive curvature 610 mm to poi nt R I is the distance from where 80 to whe re basin is tangent to hori zontal. P / = distance inflection a or R' Deflection basin length Deflected basin length of inflection

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