Development of a technique to predict permanent deformation characterisation in asphalt mixtures

Development of a technique to predict permanent deformation characterisation in asphalt mixtures | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Development of a technique to predict permanent deformation characterisation in asphalt mixtures Van Bich Nguyen, Nick Thom This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4800961/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Permanent deformation (rutting) is a common type of distress in asphalt pavements. It is widely accepted that the problem occurs due to the heavy load applications and slow movement of traffic. It is clear that permanent deformation or rutting needs to be predicted to avoid major deformation to the flexible pavement. In this study, based on using the strain-dependent properties of the asphalt mixture in a multi-layer linear viscous analysis, a technique has been developed to predict asphalt mixture rut depth. Also, three different types of asphalt mixture were selected to apply the technique at various temperatures. The material properties of asphalt mixtures were derived from the repeated load axial test and they are represented by a strain-dependent axial viscosity. The predicted outcomes were then verified by comparison with measured results obtained from the wheel tracking tests. The research results have indicated that the technique is really practical and should be considered to predict a field rut depth. Moreover, based on the use of technique, the rutting prediction results applied for all mixtures at 45 o C was fairly good while they presented poorer performances at 60 o C. Finally, the study has found a quick adjusted method to achive more accurate prediction results when a mixture reaches the tertiary stage of creep. permanent deformation rutting asphalt mixtures viscosity multi-layer linear viscous Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 1. Introduction Rutting is well known as the main form of permanent deformation in asphalt mixtures. A number of studies, therefore, have investigated the mechanism of rutting formation and tried to find the best ways to avoid it [ 1 , 4 , 5 , 14 , 16 , 17 , 21 , 23 , 28 , 37 , 41 ]. In fact, permanent deformation is a crucial issue in the asphalt pavement design field, especially in places with high temperatures, and it can be determined by using laboratory tests [ 2 , 6 , 13 , 15 , 18 , 22 , 25 , 27 , 32 , 34 , 35 , 39 ]. In order to avoid deformation to the pavement, permanent deformation or rutting needs to be predicted. It is noted that the response of an asphalt mixture depends on loading time and temperature. Asphalt mixtures also behave as linear viscoelastic materials under low temperature (or under short loading time), while they work as non-linear elasto-viscoplastic materials under high temperature or under long loading time [ 3 , 18 , 19 , 20 , 26 , 29 , 33 , 38 , 40 , 42 ]. In this paper, a simple practical technique using a multi-layer viscous analysis will be developed and applied to predict the rut depth of the selected asphalt mixtures at different temperatures generated from the repeated load axial test (RLAT). The model is then verified by comparison with measured results obtained from the wheel tracking tests. 2. Permanent deformation prediction models 2.1 Review of permanent deformation prediction As described by previous studies [ 2 , 4 , 20 , 24 , 30 ], the layer-strain method and viscoelastic theory are the two most common methodologies used to predict asphalt mixture rutting in the flexible pavements. The method based on the layer-strain approach can predict rutting in all asphalt pavement layers by assuming a linear or non-linear relationship between the elastic stress field and vertical permanent deformation in each selected layer. This method is only dependent on the elastic material characteristics and is not dependant on the material viscosity properties. In addition, the method cannot model the characteristic longitudinal ridge created adjacent to the wheel path. Rutting models based directly on viscoelastic approaches use a time-dependent response and moving wheel loads. Assumptions of these models are that ruts form primarily by shear flow within flexible pavement materials and they can therefore account for the characteristic ridge formed adjacent to the wheel path. For this approach, permanent deformation is assumed to be dependent on the viscous properties of the asphalt mixtures and independent of the elastic properties. In general, confined or unconfined creep tests can be used to indicate the viscoelastic properties of the asphalt mixtures. A Collop et al. [ 12 ] used the viscoelastic approach and showed several beneficial features including the distribution of permanent deformation through the layers, effects of vehicle speed (loading time) and dynamic loads, and the effect of the pavement temperature on rut generation. The accuracy of this approach mainly depends on the estimation of the viscous properties of the asphalt mixtures. This is supported by S Khanzada [ 20 ] who reports that the success of this type of model relies on the ability to determine the viscous material properties (the viscous equivalents to a Young’s Modulus, E and Poisson’s ratio, ν) which need to be provided to the elastic model. Based on an elastic layered model, S Khanzada [ 20 ] developed a linearised approach to predict non-linear deformation behaviour of bituminous mixtures. For a linear viscous material, it was mentioned that the rutting rate would be expected to increase in proportion to the applied stress level. Moreover, it was assumed that a power law creep model describes viscous flow in the material. It can be shown that the rutting rate probably increases as a function of the applied stress raised to a power n (creep exponent). The study concluded that the predicted and measured rutting rates from the wheel tracking test for both idealised and realistic mixtures presented good agreement over a number of stress levels and temperatures. It was found that the predicted rutting rates were characterised by an effective creep exponent of n = 2.2 to 2.4 for both the idealised and realistic mixtures, and were realised to be similar to the effective creep exponent calculated from the measured rutting rates. Also, it was highlighted that the predicted creep exponent n = 2.2 to 2.4 indicated that the approach has the ability to predict non-linear deformation behaviour of bituminous mixtures. H Al-Mosawe [ 2 ] showed a method used to predict asphalt concrete wheel track rut depths. This method is based on using the strain-dependent properties of the asphalt mixture in a multi-layer linear viscous analysis. In this methodology, an important plot of mixture viscosity versus strain needs to be produced and it is used to establish the viscous material properties for rutting prediction. In the study carried out by H Al-Mosawe [ 2 ], six slabs were manufactured for six different gradations. The slabs were then tested in a wheel tracking test before four cores from each slab were taken to carry out RLAT tests at the same loading stress, loading time, and testing temperature. The author showed the results of the prediction process and compared these predictions to the wheel tracking rut depths. In order to verify the applicability of the approach, three temperatures of 30, 40 and 50 o C were selected. The results revealed that the approach showed a good ability to predict the wheel tracking rut depth at 30 and 40 o C for all mixtures. At 50 o C, although only one dense sample was manufactured, the approach gave a poorer prediction than at lower temperatures as expected due to the uncertainty inherent in the tertiary stage of deformation. In addition, the approach was applied to real road rut depths to check its validity further. The result indicated that the prediction of field rut depth was relatively poor and the main reason for this was suggested to be insufficient RLAT data to determine the non-linear properties. 2.2 Theoretic predictive models As presented in the previous section, there are two most common approaches, namely the layer-strain and viscoelastic approaches, used to predict permanent deformation (rutting) in asphalt mixtures. Methods using the layer-strain approach for permanent deformation prediction in all pavement layers assume either a linear or non-linear relationship between the elastic stress field and the vertical permanent deformation in each layer. These methods usually use the triaxial test to determine the permanent deformation characteristics of the various pavement materials. In addition, in this approach permanent deformation is assumed to be dependent on the elastic properties of pavement materials and does not directly use the viscous properties of the materials. Therefore, although the layer-strain approach can be used to predict rutting in each pavement layer, it cannot account for the characteristic ridge formed adjacent to the wheel path [ 20 ]. Rutting models using the viscoelastic approach directly incorporate time-dependent response and moving wheel loads. These predictive models assume that ruts form mainly by shear flow of the pavement materials. Unlike the layer-strain approach, this type of approach assumes that permanent deformation is dependent on the viscous properties of the asphalt materials and independent of the elastic properties. Commonly, the viscoelastic properties of the asphalt materials using the approach are illustrated from confined or unconfined creep tests [ 2 , 19 , 20 , 34 , 38 ]. Models using the linear viscoelastic approach to predict rutting in asphalt mixtures have been applied by some previous studies [ 12 , 30 , 31 , 36 ]. In these models, asphalt materials are assumed to behave with linear viscoelastic properties, and this is considered as the main disadvantage of the approach. In fact, the viscous behaviour of asphalt mixtures is, in general, non-linear at high temperatures or at high stress levels. However, using a non-linear constitutive law to predict permanent deformation probably requires a more advanced tool to be utilised. One of the important aims of this study is to develop a practical technique to predict the wheel rut depth by modifying a multi-layer linear viscous analysis. In the modified approach, the non-linear viscous properties of asphalt mixtures are incorporated into the technique. The principle of this method was introduced by N Thom [ 35 ]. After that, it was developed and relatively successfully applied by H Al-Mosawe [ 2 ]. The principle is that just as the multi-layer linear elastic analysis can be used to calculate elastic strains within a pavement, viscous strains can be calculated with the multi-layer linear viscous approach. In fact, using the same programs, the elastic modulus is replaced by a viscosity, then computed strain is replaced by strain rate and deformation by deformation rate. The accuracy of this technique is mainly dependent on the estimate of the viscosity values of the asphalt mixtures. 3. Materials and testing programme 3.1 Materials In this research, three asphalt mixture types including a 20mm Dense Bitumen Macadam (DBM50), a 14mm Enrobé à Module Élevé 2 (EME2) and a 10mm Stone Mastic Asphalt (SMA), were chosen to develop a permanent deformation prediction technique of asphalt mixtures. The DBM50 mixture, which used a 40/60 pen bitumen, was selected as it is typical of those used for base or binder course layers in the UK. The EME2 mixture, using a hard Styrene-Butadiene-Styrene (SBS) polymer modified binder (21 pen), is also a base or binder course material. Finally, the SMA mixture used a much softer SBS modified binder (65 pen) and is designed as a surface course layer. The reason for this broad selection is because the authors needed a wide range of materials to investigate the fundamentals of permanent deformation behaviour, aiming at more confident use of the prediction technique. 3.1.1 20mm Dense Bitumen Macadam With the DBM50 mixture, a standard continuously graded 20mm was chosen. The binder grade used was 40/60 bitumen, which is commonly used in the pavement field. The binder content was 4.7% by mass following BS-EN 4987 [ 10 ]. The aggregate of the mixture selected was limestone sourced from Buxton, UK, with a nominal maximum particle size of 20mm. 3.1.2 14mm Enrobé à Module Élevé 2 For the second mixture, a standard French 14mm EME2 was selected for this research. The gradation is fairly similar to the DBM50 as it is also designed for the same structural layer. The mixture used a hard SBS polymer modified binder at a binder content of 5.5% by mass as suggested by BS-EN 13108 [ 9 ]. The aggregate was also limestone sourced from Buxton, UK, with a nominal maximum particle size of 14mm. 3.1.3 10mm Stone Mastic Asphalt For the third mixture, a standard 10mm SMA surface course was selected. A soft SBS polymer modified binder was used at a content of 6.5% and granite aggregate with a design particle size distribution following BS-EN 13108 [ 7 ]. The design particle size distribution used for all DBM50, EME2 and SMA mixtures is shown in Fig. 1 . 3.2 Testing programme 3.2.1 Wheel tracking rutting test In this study, six slabs of DBM50, EME2 and SMA mixtures were manufactured for permanent deformation prediction purpose with a couple of slabs for each mixture type intending to be tested in the wheel tracking test at different high temperatures of 45 and 60 o C (Fig. 2 ). Each slab was tested in the wheel tracking machine at the temperatures according to Bsi [ 8 ]. The wheel load applied was 690N. The test duration was 10,000 cycles (20,000 passes). 3.2.2 Repeated load axial test (RLAT) The RLAT consists of a vertical stress repeatedly applied to the four cores taken from the outer region of each slab that had been tested in the wheel tracking test at the same temperatures (Fig. 3 ). The test applies a stress for one second to the specimen followed by a rest period of one second according to Bsi [ 11 ]. The core dimensions were 100mm in diameter and 50mm in height (after cutting 10mm from the top). The stress level for this study was 300kPa. The test temperatures were the same as for the wheel tracking rutting test, 45 and 60 o C. The test duration was 5,000 cycles (10,000 seconds). 4. Prediction technique methodology The methodology of this technique used to predict asphalt mixture rut depth is based on using the strain-dependent properties of the asphalt mixture in a multi-layer linear viscous analysis. In this technique, it is necessary to find a mathematical function of mixture viscosity that fits the viscosities generated from the RLAT. In this study, the modified viscosity is named as quasiviscosity. The relevant solution for quasiviscosity depending on strain, strain at peak viscosity and a power law is given by the following expression: η q = \(\:A{e}^{\left[\frac{B\epsilon\:}{1+{\left(\epsilon\:/{\epsilon\:}_{peak}\right)}^{C}}\right]}\) (1) where η q is the quasiviscosity; A, B, C are constants; ε and ε peak are the strain and strain at peak viscosity, respectively; In order to be easy, the methodology of the technique is summarised as follows: Step 1. Carry out the wheel tracking rutting test for a slab specimen. Step 2. Take four cores from the wheel tracking slab (outside the rut line as shown in Fig. 4 ) and then conduct the RLAT. Step 3. For each RLAT cycle calculate the strain rate ( \(\:ἐ\) ) by using the following equation: \(\:ἐ=\frac{{\epsilon\:}_{2}-{\epsilon\:}_{1}}{{t}_{2}-{t}_{1}}\) (2) where ε 2 and ε 1 are the strains corresponding to the time t 2 and t 1 (for the RLAT, in seconds = the number of cycles). Step 4. Determine the RLAT viscosity of the mixture (η) by dividing the stress (σ) in MPa by the strain rate ( \(\:ἐ\) ) as follows: η = σ / \(\:\:ἐ\) (3) A graph of the RLAT viscosity versus strain is then plotted, and the RLAT viscosity vs strain points in the graph are used to fit the quasiviscosity curve shown in the next step. A typical graph of an asphalt mixture showing a full three-stage creep behaviour (primary, secondary and tertiary) [ 40 ] is presented in Fig. 5 . Step 5. Derive quasiviscosity (η q ) as a function of strain, strain at peak viscosity and a power law (see Eq. (1)). Plot η q vs strain on the same graph so that the curve of η q is fitted against RLAT viscosity points as an illustrated in Fig. 5 . Step 6. Initial values of viscosity are determined from the quasiviscosity-strain curve by assigning zero to strain. These values are used in the first deformation increment. Step 7. KENLAYER is then used to model the wheel tracking asphalt slab (thickness of 60mm) as three layers with thickness of 20mm for each layer as shown in Fig. 6 . In KENLAYER, the vertical stress of wheel load is 300kPa. This stress corresponds to the stress in the wheel tracking test [ 3 ]. The radius value used in the software is 25mm as the tire width used in the wheel tracking test was 50mm. A final very stiff bottom layer is assigned (∞ viscosity). All the four layers are assumed to be incompressible (Poisson’s ratio of 0.5) to ensure that the deformation causes viscous shear flow, not densification. All layers are bonded (full friction between layers). Although the stress distribution in the wheel tracking test is complex and the assumption in KENLAYER that the model has an infinite width is incorrect, these influences are negligible to this practical technique. Step 8. Surface deformation and strain rates in the middle of each layer determined from KENLAYER (Positions 1, 2 and 3 in Fig. 6 ) are used to calculate the number of applications (N f ) and layer strains in the next increment. In this study, the surface deformation increment values were various (0.1, 0.2 or 0.5mm) depending on the rut depth of mixtures predicted. This is to save time running KENLAYER by reducing the number of increments for each separate prediction case. Step 9. Continue this loop until a specified deformation or N f is reached. It should be noted that this predictive technique requires no adjustment for the loading time due to the similarity in loading rate for the RLAT and wheel tracking tests. In order to summarise and clarify the above steps of the predictive technique, a methodology flow chart is shown in Fig. 7 . 5. Results and analysis 5.1 Viscosity-strain curves Table 1 shows parameters used in the quasiviscosity equation for DBM50, EME2 and SMA mixtures at 45 and 60 o C. Figures 8 - 9 - 10 present the viscosity-strain curves for all mixtures at 45 and 60 o C, respectively. In the figures, the quasiviscosity curves are displayed with the viscosity points calculated from the RLAT. This therefore helps to check the relevant level of the quasiviscosity curve used with the viscosities of RLAT data. In all RLAT tests conducted, only the DBM50 mixture at 60 o C reached a full three-stage of creep as shown in Fig. 8 b. This result allows a full quasiviscosity curve to be established, and its values of power (C) and strain at peak viscosity have been used for other mixtures (Table 1 ) which just experienced in the primary and secondary stages. Table 1 Parameters used for quasiviscosity curves of all mixtures at 45 and 60 o C Mixture Type Test Temperature A B C (Power) Strain at Peak Viscosity DBM50 45 o C 60 261 1.92 6.5% 60 o C 0.018 426 1.92 6.5% EME2 45 o C 12 430 1.92 6.5% 60 o C 0.7 470 1.92 6.5% SMA 45 o C 0.008 830 1.92 6.5% 60 o C 0.1 670 1.92 6.5% 5.2 Results of permanent deformation prediction based on RLAT 5.2.1 Prediction at 45 o C The results of permanent deformation prediction at 45 o C for DBM50, EME2 and SMA are shown in Fig. 11 . As can be seen from the figures, at a test temperature of 45 o C in general the prediction of the mixtures was fairly good. Among the three types of asphalt mixture tested at 45 o C, prediction results for EME2 were the nearest to the rut depth given by the wheel tracking test, followed by the SMA prediction results with an overestimate of the real wheel track curve by about 0.15mm. However, in the first 5000 passes, the prediction curves of the PMA mixtures gave higher permanent deformation than that observed from the wheel tracking test. Although the DBM50 prediction was the quite poor compared to the PMA mixtures at 45 o C with an average estimate of 0.7mm under the wheel tracking curve, it provided a reasonably similar curve in shape and slope in comparison with the wheel tracking curve. 5.2.2 Prediction at 60 o C Figure 12 presents the results of permanent deformation prediction at 60 o C for DBM50, EME2 and SMA mixtures. In comparison with the DBM50, EME2 and SMA mixtures tested at 45 o C, in general the results of rutting depth prediction of these mixtures at 60 o C were poorer. Although the DBM50 is the only mixture to have reached the tertiary stage of creep when tested at 60 o C, the prediction of this mixture only resulted in about 3500 passes as after that the predictive curve tended to failure as shown in Fig. 12 a. The reason is that the RLAT tests for the DBM50 mixture performed under a stress of 300kPa and a duration of 3600 load applications failed totally during the test. This can be seen from Fig. 8 b where the DBM50 viscosity values decreased noticeably after reaching a peak at 6.5% strain, leading a large increase in rutting depth after viscosity had reached its peak (at around 3500 loading applications). The prediction results for the PMA mixtures at 60 o C as presented in Fig. 12 b and Fig. 12 c indicate an underestimate of the real wheel track curve by about 0.7-1.1mm, and the prediction curves of PMA mixtures end in a very flat trend. This flat trend causes very high viscosity values of the PMA mixtures derived from the RLAT at 60 o C as shown in Fig. 9 b and Fig. 10 b. 6. Discussion As indicated above, the prediction of the DBM50 mixture at 60 o C showed an unexpected result as the predictive curve tended to failure after 3,500 cycles presented in Fig. 12 a. The reason for this is due to the total failure of the RLAT specimens after a duration of 3600 load applications. To gain a deeper understanding of the problem, one trial prediction for the mixture was conducted with an adjusted quasiviscosity curve. It can be seen from the viscosity-curve and the prediction result that the problem occurred after the mixture reached the tertiary stage of creep (the viscosity curve went down significantly after reaching a peak). Therefore, an adjusted quasiviscosity curve was constructed with an absolute flat trend after it reached a peak as shown in Fig. 13 a. A similar predictive process was applied to the mixture with the new viscosity-strain curve. The new result of the prediction is shown in Fig. 13 b. As can be seen from the figure, the predictive curve is quite close to the real wheel track rut depth. However, the curve becomes linear after the viscosity reaches its peak (about 3,500 cycles). The result also shows an overestimating of rut depth by 0.6 and 1.6mm at 15,000 and 20,000 passes, respectively compared to the real wheel track curve. Therefore, it is recommended that in practice in order to obtain closer prediction results to the real wheel track rut depth, adjusted viscosity-strain curves should experience a slight increase trend after reaching a peak as lower predictive rut depths need higher viscosity values. 7. Conclusions A detailed method of predicting asphalt mixture wheel rut depth based on using the strain-dependent properties of the asphalt mixture in a multi-layer linear viscous analysis has been developed in this research. It has been applied to predict rut depths for the DBM50, EME2 and SMA mixtures at 45 and 60 o C based on the RLAT results. The prediction outcomes thereafter have been verified by the wheel tracking rutting test results. The following conclusions can be drawn from this study: The predictive technique is practical and can be considered as a good method to predict permanent deformation of asphalt mixtures as well as a field rut depth. The technique was based on using a multi-layer linear viscous analysis with inputting viscous parameters replacing the elastic modulus, and strain rate and deformation rate outputs. The computation was conducted by a computer program known as KENLAYER. The viscosity (quasiviscosity) of the asphalt mixtures, a nonlinear function of strain, is derived from the RLAT data. The results of the rut depth prediction applied for DBM50, EME2 and SMA mixtures at 45 and 60 o C have indicated that the prediction of all mixtures at 45 o C was fairly good. The prediction performance of the EME2 mixture was the best compared to the rut depth given by the wheel tracking rutting test, followed by the SMA mixture at the test temperature. In contrast, the prediction results for these mixtures showed poorer performances when the test temperature increased to 60 o C. Especially, the prediction for the DBM50 mixture at 60 o C revealed a significant limitation of the technique when mixtures reach the tertiary stage of creep. This study has found that for an asphalt mixture that reaches the third stage of creep it is recommended that in order to obtain more accurate prediction results, an adjusted viscosity-strain curve should be taken with a slight increasing trend after reaching its peak. Declarations Acknowledgements The authors would like to acknowledge the facilities support provided by the Nottingham Transportation Engineering Centre (NTEC) – the University of Nottingham, United Kingdom. Conflict of interest The authors declare no conflict of interest. References Abdelfattah HFH, Baaj H, Kadhim HJ (2022) Calibration of MEPDG permanent deformation models using Hamburg Wheel Rut Tester and field data. 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Nguyen","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAvklEQVRIiWNgGAWjYBACA2YGNiBlkwDhshGvJY0ULRBlh0nQYs7O/OxxYdv5PIPjhw8wfCg7zGBwuwG/FstmNnPjmW23iw3OpCUwzjgH1HLnAAGHHeZhk+Y5cztxww0eA2betsMMkjMSiNJyDqiF/wPzX+K1VBwA2cLAzAjUwi9BQAvQL2ZALcmJM8+kGRzsOZfOQ1CLOf/hZ9I8BnaJfccPP3zwo8xajo2QFhRwAIh5SFA/CkbBKBgFowAXAABRhD7OEIUOOQAAAABJRU5ErkJggg==","orcid":"","institution":"Ha Noi University of Civil Engineering: National University of Civil Engineering","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Van","middleName":"Bich","lastName":"Nguyen","suffix":""},{"id":336648339,"identity":"b871a878-4d34-4659-abf4-7558c40ef760","order_by":1,"name":"Nick Thom","email":"","orcid":"","institution":"University of Nottingham","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Nick","middleName":"","lastName":"Thom","suffix":""}],"badges":[],"createdAt":"2024-07-25 10:10:11","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4800961/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4800961/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":63795165,"identity":"14c12182-ebd8-445b-a030-c2d3c53e404b","added_by":"auto","created_at":"2024-09-02 12:20:40","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":41715,"visible":true,"origin":"","legend":"\u003cp\u003eDesign particle size distribution for the DBM50, EME2 and SMA mixture\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-4800961/v1/a766c04a5f88b8d348a01ff3.png"},{"id":63793858,"identity":"0816324d-5026-4005-a0c2-e632aa1a82bc","added_by":"auto","created_at":"2024-09-02 12:04:40","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":1041581,"visible":true,"origin":"","legend":"\u003cp\u003eWheel tracking rutting test\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-4800961/v1/62eb5430fe921d6ec0e57608.png"},{"id":63793856,"identity":"6d60a690-a0b7-428d-9fc2-1af6f624bce9","added_by":"auto","created_at":"2024-09-02 12:04:40","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":988231,"visible":true,"origin":"","legend":"\u003cp\u003eRLAT configuration\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-4800961/v1/07df94faedd366ccbccfdd24.png"},{"id":63794519,"identity":"da1aabd6-425d-480e-be89-e6976ce42211","added_by":"auto","created_at":"2024-09-02 12:12:40","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":264651,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic diagram of coring specimens from a wheel tracking slab\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-4800961/v1/0db048a2556deff9b0590c27.png"},{"id":63793855,"identity":"8b714709-c4ce-4cee-9edd-4e3c22233be8","added_by":"auto","created_at":"2024-09-02 12:04:40","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":103797,"visible":true,"origin":"","legend":"\u003cp\u003eTypical graph of viscosity versus strain for an asphalt mixture\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-4800961/v1/e995b9206a4bdb54b116282c.png"},{"id":63794518,"identity":"82a315c6-53d9-4e5e-9327-4a6d7554ec24","added_by":"auto","created_at":"2024-09-02 12:12:40","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":34231,"visible":true,"origin":"","legend":"\u003cp\u003eSlab layers modelled in KENLAYER\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-4800961/v1/1d694c86229b131e11023b2c.png"},{"id":63793866,"identity":"52d44e19-35c9-4c4d-83a2-d2b0cb5b4f56","added_by":"auto","created_at":"2024-09-02 12:04:41","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":150109,"visible":true,"origin":"","legend":"\u003cp\u003eMethodology flow chart of predictive technique based on RLAT\u003c/p\u003e","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-4800961/v1/f5beecdf8903c1f3b04ba2e9.png"},{"id":63793864,"identity":"74999443-20e3-4572-9ab3-51831194d045","added_by":"auto","created_at":"2024-09-02 12:04:41","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":244340,"visible":true,"origin":"","legend":"\u003cp\u003eViscosity-Strain curve for DBM50 mixture at 45\u003csup\u003e \u003c/sup\u003eand 60\u003csup\u003eo\u003c/sup\u003eC\u003c/p\u003e","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-4800961/v1/51b194201e8aaa9d417ac1f3.png"},{"id":63793867,"identity":"c0dc34f6-2372-4fdd-ad93-9d31e7713f30","added_by":"auto","created_at":"2024-09-02 12:04:41","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":212992,"visible":true,"origin":"","legend":"\u003cp\u003eViscosity-Strain curve for EME2 mixture at 45 and 60\u003csup\u003eo\u003c/sup\u003eC\u003c/p\u003e","description":"","filename":"floatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-4800961/v1/9f6f3eed2588e12b80685b8a.png"},{"id":63793863,"identity":"25d9e19a-9f27-45e0-959f-640642fe784a","added_by":"auto","created_at":"2024-09-02 12:04:41","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":235763,"visible":true,"origin":"","legend":"\u003cp\u003eViscosity-Strain curve for SMA mixture at 45 and 60\u003csup\u003eo\u003c/sup\u003eC\u003c/p\u003e","description":"","filename":"floatimage10.png","url":"https://assets-eu.researchsquare.com/files/rs-4800961/v1/95f9816e441cd6b2f9b73aff.png"},{"id":63793862,"identity":"19b1bd5e-9beb-40fe-8288-b77333388fc1","added_by":"auto","created_at":"2024-09-02 12:04:41","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":155714,"visible":true,"origin":"","legend":"\u003cp\u003ePermanent deformation prediction results for all mixtures at 45\u003csup\u003eo\u003c/sup\u003eC\u003c/p\u003e","description":"","filename":"floatimage11.png","url":"https://assets-eu.researchsquare.com/files/rs-4800961/v1/1c522c3c8c736eae44792c85.png"},{"id":63794521,"identity":"57278e31-adbb-4654-96db-3dfeba96d8c8","added_by":"auto","created_at":"2024-09-02 12:12:41","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":404006,"visible":true,"origin":"","legend":"\u003cp\u003ePermanent deformation prediction results for all mixtures at 60\u003csup\u003eo\u003c/sup\u003eC\u003c/p\u003e","description":"","filename":"floatimage12.png","url":"https://assets-eu.researchsquare.com/files/rs-4800961/v1/8615faa1de652456a0c844a8.png"},{"id":63793861,"identity":"37fc379c-2bc4-4e22-8d98-c664902710c4","added_by":"auto","created_at":"2024-09-02 12:04:41","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":162174,"visible":true,"origin":"","legend":"\u003cp\u003eAdjusted prediction for DBM50 mixture at 60\u003csup\u003eo\u003c/sup\u003eC\u003c/p\u003e","description":"","filename":"floatimage13.png","url":"https://assets-eu.researchsquare.com/files/rs-4800961/v1/c868128fbd6562ba71447b29.png"},{"id":65641554,"identity":"8c1f2b27-39b6-415a-9d8a-f0ead395c2db","added_by":"auto","created_at":"2024-09-30 20:07:23","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":5598365,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4800961/v1/c8733208-73ce-4712-aa8e-c094a4016764.pdf"}],"financialInterests":"","formattedTitle":"Development of a technique to predict permanent deformation characterisation in asphalt mixtures","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eRutting is well known as the main form of permanent deformation in asphalt mixtures. A number of studies, therefore, have investigated the mechanism of rutting formation and tried to find the best ways to avoid it [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e, \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e]. In fact, permanent deformation is a crucial issue in the asphalt pavement design field, especially in places with high temperatures, and it can be determined by using laboratory tests [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e, \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e, \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e, \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn order to avoid deformation to the pavement, permanent deformation or rutting needs to be predicted. It is noted that the response of an asphalt mixture depends on loading time and temperature. Asphalt mixtures also behave as linear viscoelastic materials under low temperature (or under short loading time), while they work as non-linear elasto-viscoplastic materials under high temperature or under long loading time [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e, \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn this paper, a simple practical technique using a multi-layer viscous analysis will be developed and applied to predict the rut depth of the selected asphalt mixtures at different temperatures generated from the repeated load axial test (RLAT). The model is then verified by comparison with measured results obtained from the wheel tracking tests.\u003c/p\u003e"},{"header":"2. Permanent deformation prediction models","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Review of permanent deformation prediction\u003c/h2\u003e \u003cp\u003eAs described by previous studies [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e], the layer-strain method and viscoelastic theory are the two most common methodologies used to predict asphalt mixture rutting in the flexible pavements. The method based on the layer-strain approach can predict rutting in all asphalt pavement layers by assuming a linear or non-linear relationship between the elastic stress field and vertical permanent deformation in each selected layer. This method is only dependent on the elastic material characteristics and is not dependant on the material viscosity properties. In addition, the method cannot model the characteristic longitudinal ridge created adjacent to the wheel path. Rutting models based directly on viscoelastic approaches use a time-dependent response and moving wheel loads. Assumptions of these models are that ruts form primarily by shear flow within flexible pavement materials and they can therefore account for the characteristic ridge formed adjacent to the wheel path. For this approach, permanent deformation is assumed to be dependent on the viscous properties of the asphalt mixtures and independent of the elastic properties. In general, confined or unconfined creep tests can be used to indicate the viscoelastic properties of the asphalt mixtures.\u003c/p\u003e \u003cp\u003eA Collop et al. [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e] used the viscoelastic approach and showed several beneficial features including the distribution of permanent deformation through the layers, effects of vehicle speed (loading time) and dynamic loads, and the effect of the pavement temperature on rut generation. The accuracy of this approach mainly depends on the estimation of the viscous properties of the asphalt mixtures. This is supported by S Khanzada [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e] who reports that the success of this type of model relies on the ability to determine the viscous material properties (the viscous equivalents to a Young\u0026rsquo;s Modulus, E and Poisson\u0026rsquo;s ratio, ν) which need to be provided to the elastic model.\u003c/p\u003e \u003cp\u003eBased on an elastic layered model, S Khanzada [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e] developed a linearised approach to predict non-linear deformation behaviour of bituminous mixtures. For a linear viscous material, it was mentioned that the rutting rate would be expected to increase in proportion to the applied stress level. Moreover, it was assumed that a power law creep model describes viscous flow in the material. It can be shown that the rutting rate probably increases as a function of the applied stress raised to a power n (creep exponent). The study concluded that the predicted and measured rutting rates from the wheel tracking test for both idealised and realistic mixtures presented good agreement over a number of stress levels and temperatures. It was found that the predicted rutting rates were characterised by an effective creep exponent of n\u0026thinsp;=\u0026thinsp;2.2 to 2.4 for both the idealised and realistic mixtures, and were realised to be similar to the effective creep exponent calculated from the measured rutting rates. Also, it was highlighted that the predicted creep exponent n\u0026thinsp;=\u0026thinsp;2.2 to 2.4 indicated that the approach has the ability to predict non-linear deformation behaviour of bituminous mixtures.\u003c/p\u003e \u003cp\u003eH Al-Mosawe [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e] showed a method used to predict asphalt concrete wheel track rut depths. This method is based on using the strain-dependent properties of the asphalt mixture in a multi-layer linear viscous analysis. In this methodology, an important plot of mixture viscosity versus strain needs to be produced and it is used to establish the viscous material properties for rutting prediction.\u003c/p\u003e \u003cp\u003eIn the study carried out by H Al-Mosawe [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e], six slabs were manufactured for six different gradations. The slabs were then tested in a wheel tracking test before four cores from each slab were taken to carry out RLAT tests at the same loading stress, loading time, and testing temperature. The author showed the results of the prediction process and compared these predictions to the wheel tracking rut depths. In order to verify the applicability of the approach, three temperatures of 30, 40 and 50\u003csup\u003eo\u003c/sup\u003eC were selected. The results revealed that the approach showed a good ability to predict the wheel tracking rut depth at 30 and 40\u003csup\u003eo\u003c/sup\u003eC for all mixtures. At 50\u003csup\u003eo\u003c/sup\u003eC, although only one dense sample was manufactured, the approach gave a poorer prediction than at lower temperatures as expected due to the uncertainty inherent in the tertiary stage of deformation. In addition, the approach was applied to real road rut depths to check its validity further. The result indicated that the prediction of field rut depth was relatively poor and the main reason for this was suggested to be insufficient RLAT data to determine the non-linear properties.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Theoretic predictive models\u003c/h2\u003e \u003cp\u003eAs presented in the previous section, there are two most common approaches, namely the layer-strain and viscoelastic approaches, used to predict permanent deformation (rutting) in asphalt mixtures.\u003c/p\u003e \u003cp\u003eMethods using the layer-strain approach for permanent deformation prediction in all pavement layers assume either a linear or non-linear relationship between the elastic stress field and the vertical permanent deformation in each layer. These methods usually use the triaxial test to determine the permanent deformation characteristics of the various pavement materials. In addition, in this approach permanent deformation is assumed to be dependent on the elastic properties of pavement materials and does not directly use the viscous properties of the materials. Therefore, although the layer-strain approach can be used to predict rutting in each pavement layer, it cannot account for the characteristic ridge formed adjacent to the wheel path [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eRutting models using the viscoelastic approach directly incorporate time-dependent response and moving wheel loads. These predictive models assume that ruts form mainly by shear flow of the pavement materials. Unlike the layer-strain approach, this type of approach assumes that permanent deformation is dependent on the viscous properties of the asphalt materials and independent of the elastic properties. Commonly, the viscoelastic properties of the asphalt materials using the approach are illustrated from confined or unconfined creep tests [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e, \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eModels using the linear viscoelastic approach to predict rutting in asphalt mixtures have been applied by some previous studies [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e, \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]. In these models, asphalt materials are assumed to behave with linear viscoelastic properties, and this is considered as the main disadvantage of the approach. In fact, the viscous behaviour of asphalt mixtures is, in general, non-linear at high temperatures or at high stress levels. However, using a non-linear constitutive law to predict permanent deformation probably requires a more advanced tool to be utilised.\u003c/p\u003e \u003cp\u003eOne of the important aims of this study is to develop a practical technique to predict the wheel rut depth by modifying a multi-layer linear viscous analysis. In the modified approach, the non-linear viscous properties of asphalt mixtures are incorporated into the technique. The principle of this method was introduced by N Thom [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]. After that, it was developed and relatively successfully applied by H Al-Mosawe [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. The principle is that just as the multi-layer linear elastic analysis can be used to calculate elastic strains within a pavement, viscous strains can be calculated with the multi-layer linear viscous approach. In fact, using the same programs, the elastic modulus is replaced by a viscosity, then computed strain is replaced by strain rate and deformation by deformation rate. The accuracy of this technique is mainly dependent on the estimate of the viscosity values of the asphalt mixtures.\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Materials and testing programme","content":"\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Materials\u003c/h2\u003e \u003cp\u003eIn this research, three asphalt mixture types including a 20mm Dense Bitumen Macadam (DBM50), a 14mm Enrob\u0026eacute; \u0026agrave; Module \u0026Eacute;lev\u0026eacute; 2 (EME2) and a 10mm Stone Mastic Asphalt (SMA), were chosen to develop a permanent deformation prediction technique of asphalt mixtures. The DBM50 mixture, which used a 40/60 pen bitumen, was selected as it is typical of those used for base or binder course layers in the UK. The EME2 mixture, using a hard Styrene-Butadiene-Styrene (SBS) polymer modified binder (21 pen), is also a base or binder course material. Finally, the SMA mixture used a much softer SBS modified binder (65 pen) and is designed as a surface course layer. The reason for this broad selection is because the authors needed a wide range of materials to investigate the fundamentals of permanent deformation behaviour, aiming at more confident use of the prediction technique.\u003c/p\u003e \u003cdiv id=\"Sec7\" class=\"Section3\"\u003e \u003ch2\u003e3.1.1 20mm Dense Bitumen Macadam\u003c/h2\u003e \u003cp\u003eWith the DBM50 mixture, a standard continuously graded 20mm was chosen. The binder grade used was 40/60 bitumen, which is commonly used in the pavement field. The binder content was 4.7% by mass following BS-EN 4987 [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. The aggregate of the mixture selected was limestone sourced from Buxton, UK, with a nominal maximum particle size of 20mm.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section3\"\u003e \u003ch2\u003e3.1.2 14mm Enrob\u0026eacute; \u0026agrave; Module \u0026Eacute;lev\u0026eacute; 2\u003c/h2\u003e \u003cp\u003eFor the second mixture, a standard French 14mm EME2 was selected for this research. The gradation is fairly similar to the DBM50 as it is also designed for the same structural layer. The mixture used a hard SBS polymer modified binder at a binder content of 5.5% by mass as suggested by BS-EN 13108 [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. The aggregate was also limestone sourced from Buxton, UK, with a nominal maximum particle size of 14mm.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section3\"\u003e \u003ch2\u003e3.1.3 10mm Stone Mastic Asphalt\u003c/h2\u003e \u003cp\u003eFor the third mixture, a standard 10mm SMA surface course was selected. A soft SBS polymer modified binder was used at a content of 6.5% and granite aggregate with a design particle size distribution following BS-EN 13108 [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe design particle size distribution used for all DBM50, EME2 and SMA mixtures is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Testing programme\u003c/h2\u003e \u003cdiv id=\"Sec11\" class=\"Section3\"\u003e \u003ch2\u003e3.2.1 Wheel tracking rutting test\u003c/h2\u003e \u003cp\u003eIn this study, six slabs of DBM50, EME2 and SMA mixtures were manufactured for permanent deformation prediction purpose with a couple of slabs for each mixture type intending to be tested in the wheel tracking test at different high temperatures of 45 and 60\u003csup\u003eo\u003c/sup\u003eC (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). Each slab was tested in the wheel tracking machine at the temperatures according to Bsi [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. The wheel load applied was 690N. The test duration was 10,000 cycles (20,000 passes).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section3\"\u003e \u003ch2\u003e3.2.2 Repeated load axial test (RLAT)\u003c/h2\u003e \u003cp\u003eThe RLAT consists of a vertical stress repeatedly applied to the four cores taken from the outer region of each slab that had been tested in the wheel tracking test at the same temperatures (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). The test applies a stress for one second to the specimen followed by a rest period of one second according to Bsi [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. The core dimensions were 100mm in diameter and 50mm in height (after cutting 10mm from the top). The stress level for this study was 300kPa. The test temperatures were the same as for the wheel tracking rutting test, 45 and 60\u003csup\u003eo\u003c/sup\u003eC. The test duration was 5,000 cycles (10,000 seconds).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"4. Prediction technique methodology","content":"\u003cp\u003eThe methodology of this technique used to predict asphalt mixture rut depth is based on using the strain-dependent properties of the asphalt mixture in a multi-layer linear viscous analysis.\u003c/p\u003e \u003cp\u003eIn this technique, it is necessary to find a mathematical function of mixture viscosity that fits the viscosities generated from the RLAT. In this study, the modified viscosity is named as quasiviscosity. The relevant solution for quasiviscosity depending on strain, strain at peak viscosity and a power law is given by the following expression:\u003c/p\u003e \u003cp\u003eη\u003csub\u003eq\u003c/sub\u003e = \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:A{e}^{\\left[\\frac{B\\epsilon\\:}{1+{\\left(\\epsilon\\:/{\\epsilon\\:}_{peak}\\right)}^{C}}\\right]}\\)\u003c/span\u003e\u003c/span\u003e(1)\u003c/p\u003e \u003cp\u003ewhere η\u003csub\u003eq\u003c/sub\u003e is the quasiviscosity;\u003c/p\u003e \u003cp\u003eA, B, C are constants;\u003c/p\u003e \u003cp\u003eε and ε\u003csub\u003epeak\u003c/sub\u003e are the strain and strain at peak viscosity, respectively;\u003c/p\u003e \u003cp\u003eIn order to be easy, the methodology of the technique is summarised as follows:\u003c/p\u003e \u003cp\u003e \u003cb\u003eStep 1.\u003c/b\u003e Carry out the wheel tracking rutting test for a slab specimen.\u003c/p\u003e \u003cp\u003e \u003cb\u003eStep 2.\u003c/b\u003e Take four cores from the wheel tracking slab (outside the rut line as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e) and then conduct the RLAT.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eStep 3.\u003c/b\u003e For each RLAT cycle calculate the strain rate (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:ἐ\\)\u003c/span\u003e\u003c/span\u003e) by using the following equation:\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Taba\" border=\"1\"\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:ἐ=\\frac{{\\epsilon\\:}_{2}-{\\epsilon\\:}_{1}}{{t}_{2}-{t}_{1}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(2)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003ewhere ε\u003csub\u003e2\u003c/sub\u003e and ε\u003csub\u003e1\u003c/sub\u003e are the strains corresponding to the time t\u003csub\u003e2\u003c/sub\u003e and t\u003csub\u003e1\u003c/sub\u003e (for the RLAT, in seconds\u0026thinsp;=\u0026thinsp;the number of cycles).\u003c/p\u003e \u003cp\u003e \u003cb\u003eStep 4.\u003c/b\u003e Determine the RLAT viscosity of the mixture (η) by dividing the stress (σ) in MPa by the strain rate (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:ἐ\\)\u003c/span\u003e\u003c/span\u003e) as follows:\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabb\" border=\"1\"\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eη = σ /\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\:ἐ\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(3)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eA graph of the RLAT viscosity versus strain is then plotted, and the RLAT viscosity vs strain points in the graph are used to fit the quasiviscosity curve shown in the next step. A typical graph of an asphalt mixture showing a full three-stage creep behaviour (primary, secondary and tertiary) [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e] is presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cb\u003eStep 5.\u003c/b\u003e Derive quasiviscosity (η\u003csub\u003eq\u003c/sub\u003e) as a function of strain, strain at peak viscosity and a power law (see Eq.\u0026nbsp;(1)). Plot η\u003csub\u003eq\u003c/sub\u003e vs strain on the same graph so that the curve of η\u003csub\u003eq\u003c/sub\u003e is fitted against RLAT viscosity points as an illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eStep 6.\u003c/b\u003e Initial values of viscosity are determined from the quasiviscosity-strain curve by assigning zero to strain. These values are used in the first deformation increment.\u003c/p\u003e \u003cp\u003e \u003cb\u003eStep 7.\u003c/b\u003e KENLAYER is then used to model the wheel tracking asphalt slab (thickness of 60mm) as three layers with thickness of 20mm for each layer as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eIn KENLAYER, the vertical stress of wheel load is 300kPa. This stress corresponds to the stress in the wheel tracking test [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. The radius value used in the software is 25mm as the tire width used in the wheel tracking test was 50mm. A final very stiff bottom layer is assigned (\u0026infin;\u0026thinsp;viscosity). All the four layers are assumed to be incompressible (Poisson\u0026rsquo;s ratio of 0.5) to ensure that the deformation causes viscous shear flow, not densification. All layers are bonded (full friction between layers). Although the stress distribution in the wheel tracking test is complex and the assumption in KENLAYER that the model has an infinite width is incorrect, these influences are negligible to this practical technique.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eStep 8.\u003c/b\u003e Surface deformation and strain rates in the middle of each layer determined from KENLAYER (Positions 1, 2 and 3 in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e) are used to calculate the number of applications (N\u003csub\u003ef\u003c/sub\u003e) and layer strains in the next increment. In this study, the surface deformation increment values were various (0.1, 0.2 or 0.5mm) depending on the rut depth of mixtures predicted. This is to save time running KENLAYER by reducing the number of increments for each separate prediction case.\u003c/p\u003e \u003cp\u003e \u003cb\u003eStep 9.\u003c/b\u003e Continue this loop until a specified deformation or N\u003csub\u003ef\u003c/sub\u003e is reached.\u003c/p\u003e \u003cp\u003eIt should be noted that this predictive technique requires no adjustment for the loading time due to the similarity in loading rate for the RLAT and wheel tracking tests.\u003c/p\u003e \u003cp\u003eIn order to summarise and clarify the above steps of the predictive technique, a methodology flow chart is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"5. Results and analysis","content":"\u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003e5.1 Viscosity-strain curves\u003c/h2\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows parameters used in the quasiviscosity equation for DBM50, EME2 and SMA mixtures at 45 and 60\u003csup\u003eo\u003c/sup\u003eC.\u003c/p\u003e \u003cp\u003eFigures \u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e-\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e-\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e present the viscosity-strain curves for all mixtures at 45 and 60\u003csup\u003eo\u003c/sup\u003eC, respectively. In the figures, the quasiviscosity curves are displayed with the viscosity points calculated from the RLAT. This therefore helps to check the relevant level of the quasiviscosity curve used with the viscosities of RLAT data. In all RLAT tests conducted, only the DBM50 mixture at 60\u003csup\u003eo\u003c/sup\u003eC reached a full three-stage of creep as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003eb. This result allows a full quasiviscosity curve to be established, and its values of power (C) and strain at peak viscosity have been used for other mixtures (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) which just experienced in the primary and secondary stages.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eParameters used for quasiviscosity curves of all mixtures at 45 and 60\u003csup\u003eo\u003c/sup\u003eC\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMixture Type\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTest Temperature\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eB\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eC\u003c/p\u003e \u003cp\u003e(Power)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eStrain at Peak Viscosity\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eDBM50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e45\u003csup\u003eo\u003c/sup\u003eC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e261\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e6.5%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e60\u003csup\u003eo\u003c/sup\u003eC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.018\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e426\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e6.5%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eEME2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e45\u003csup\u003eo\u003c/sup\u003eC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e430\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e6.5%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e60\u003csup\u003eo\u003c/sup\u003eC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e470\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e6.5%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eSMA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e45\u003csup\u003eo\u003c/sup\u003eC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.008\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e830\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e6.5%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e60\u003csup\u003eo\u003c/sup\u003eC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e670\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e6.5%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003e5.2 Results of permanent deformation prediction based on RLAT\u003c/h2\u003e \u003cdiv id=\"Sec17\" class=\"Section3\"\u003e \u003ch2\u003e5.2.1 Prediction at 45\u003csup\u003eo\u003c/sup\u003eC\u003c/h2\u003e \u003cp\u003eThe results of permanent deformation prediction at 45\u003csup\u003eo\u003c/sup\u003eC for DBM50, EME2 and SMA are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eAs can be seen from the figures, at a test temperature of 45\u003csup\u003eo\u003c/sup\u003eC in general the prediction of the mixtures was fairly good. Among the three types of asphalt mixture tested at 45\u003csup\u003eo\u003c/sup\u003eC, prediction results for EME2 were the nearest to the rut depth given by the wheel tracking test, followed by the SMA prediction results with an overestimate of the real wheel track curve by about 0.15mm. However, in the first 5000 passes, the prediction curves of the PMA mixtures gave higher permanent deformation than that observed from the wheel tracking test. Although the DBM50 prediction was the quite poor compared to the PMA mixtures at 45\u003csup\u003eo\u003c/sup\u003eC with an average estimate of 0.7mm under the wheel tracking curve, it provided a reasonably similar curve in shape and slope in comparison with the wheel tracking curve.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section3\"\u003e \u003ch2\u003e5.2.2 Prediction at 60\u003csup\u003eo\u003c/sup\u003eC\u003c/h2\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e presents the results of permanent deformation prediction at 60\u003csup\u003eo\u003c/sup\u003eC for DBM50, EME2 and SMA mixtures. In comparison with the DBM50, EME2 and SMA mixtures tested at 45\u003csup\u003eo\u003c/sup\u003eC, in general the results of rutting depth prediction of these mixtures at 60\u003csup\u003eo\u003c/sup\u003eC were poorer.\u003c/p\u003e \u003cp\u003eAlthough the DBM50 is the only mixture to have reached the tertiary stage of creep when tested at 60\u003csup\u003eo\u003c/sup\u003eC, the prediction of this mixture only resulted in about 3500 passes as after that the predictive curve tended to failure as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003ea. The reason is that the RLAT tests for the DBM50 mixture performed under a stress of 300kPa and a duration of 3600 load applications failed totally during the test. This can be seen from Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003eb where the DBM50 viscosity values decreased noticeably after reaching a peak at 6.5% strain, leading a large increase in rutting depth after viscosity had reached its peak (at around 3500 loading applications).\u003c/p\u003e \u003cp\u003eThe prediction results for the PMA mixtures at 60\u003csup\u003eo\u003c/sup\u003eC as presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003eb and Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003ec indicate an underestimate of the real wheel track curve by about 0.7-1.1mm, and the prediction curves of PMA mixtures end in a very flat trend. This flat trend causes very high viscosity values of the PMA mixtures derived from the RLAT at 60\u003csup\u003eo\u003c/sup\u003eC as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003eb and Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003eb.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"6. Discussion","content":"\u003cp\u003eAs indicated above, the prediction of the DBM50 mixture at 60\u003csup\u003eo\u003c/sup\u003eC showed an unexpected result as the predictive curve tended to failure after 3,500 cycles presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003ea. The reason for this is due to the total failure of the RLAT specimens after a duration of 3600 load applications.\u003c/p\u003e \u003cp\u003eTo gain a deeper understanding of the problem, one trial prediction for the mixture was conducted with an adjusted quasiviscosity curve. It can be seen from the viscosity-curve and the prediction result that the problem occurred after the mixture reached the tertiary stage of creep (the viscosity curve went down significantly after reaching a peak). Therefore, an adjusted quasiviscosity curve was constructed with an absolute flat trend after it reached a peak as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003ea.\u003c/p\u003e \u003cp\u003eA similar predictive process was applied to the mixture with the new viscosity-strain curve. The new result of the prediction is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003eb. As can be seen from the figure, the predictive curve is quite close to the real wheel track rut depth. However, the curve becomes linear after the viscosity reaches its peak (about 3,500 cycles). The result also shows an overestimating of rut depth by 0.6 and 1.6mm at 15,000 and 20,000 passes, respectively compared to the real wheel track curve. Therefore, it is recommended that in practice in order to obtain closer prediction results to the real wheel track rut depth, adjusted viscosity-strain curves should experience a slight increase trend after reaching a peak as lower predictive rut depths need higher viscosity values.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"7. Conclusions","content":"\u003cp\u003eA detailed method of predicting asphalt mixture wheel rut depth based on using the strain-dependent properties of the asphalt mixture in a multi-layer linear viscous analysis has been developed in this research. It has been applied to predict rut depths for the DBM50, EME2 and SMA mixtures at 45 and 60\u003csup\u003eo\u003c/sup\u003eC based on the RLAT results. The prediction outcomes thereafter have been verified by the wheel tracking rutting test results. The following conclusions can be drawn from this study:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eThe predictive technique is practical and can be considered as a good method to predict permanent deformation of asphalt mixtures as well as a field rut depth.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eThe technique was based on using a multi-layer linear viscous analysis with inputting viscous parameters replacing the elastic modulus, and strain rate and deformation rate outputs. The computation was conducted by a computer program known as KENLAYER. The viscosity (quasiviscosity) of the asphalt mixtures, a nonlinear function of strain, is derived from the RLAT data.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eThe results of the rut depth prediction applied for DBM50, EME2 and SMA mixtures at 45 and 60\u003csup\u003eo\u003c/sup\u003eC have indicated that the prediction of all mixtures at 45\u003csup\u003eo\u003c/sup\u003eC was fairly good.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eThe prediction performance of the EME2 mixture was the best compared to the rut depth given by the wheel tracking rutting test, followed by the SMA mixture at the test temperature.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eIn contrast, the prediction results for these mixtures showed poorer performances when the test temperature increased to 60\u003csup\u003eo\u003c/sup\u003eC. Especially, the prediction for the DBM50 mixture at 60\u003csup\u003eo\u003c/sup\u003eC revealed a significant limitation of the technique when mixtures reach the tertiary stage of creep.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eThis study has found that for an asphalt mixture that reaches the third stage of creep it is recommended that in order to obtain more accurate prediction results, an adjusted viscosity-strain curve should be taken with a slight increasing trend after reaching its peak.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAcknowledgements\u003c/h2\u003e \u003cp\u003eThe authors would like to acknowledge the facilities support provided by the Nottingham Transportation Engineering Centre (NTEC) \u0026ndash; the University of Nottingham, United Kingdom.\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eConflict of interest\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no conflict of interest.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAbdelfattah HFH, Baaj H, Kadhim HJ (2022) Calibration of MEPDG permanent deformation models using Hamburg Wheel Rut Tester and field data. Int J Pavement Eng 23:4174\u0026ndash;4189\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAl-Mosawe H (2016) Prediction of Permanent Deformation in Asphalt Mixtures. In:University of Nottingham\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAl-Mosawe H, Thom N, Airey G et al (2018) Linear viscous approach to predict rut depth in asphalt mixtures. Constr Build Mater 169:775\u0026ndash;793\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBabadopulos LFDL, Ferreira JLS, Soares JB (2016) An approach to couple aging to stiffness and permanent deformation modeling of asphalt mixtures. Mater Struct 49:4929\u0026ndash;4945\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBehbahani H, Najafi Moghaddam Gilani V, Salehfard R et al (2020) Evaluation of fatigue and rutting behaviour of hot mix asphalt containing rock wool. 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Int J Pavement Eng 10:19\u0026ndash;28\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHussan S, Kamal MA, Hafeez I et al (2019) Evaluation and modelling of permanent deformation behaviour of asphalt mixtures using dynamic creep test in uniaxial mode. Int J Pavement Eng 20:1026\u0026ndash;1043\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eInocente Domingos MD, Faxina AL, Bernucci LLB (2021) Modelling and permanent deformation analysis of low-density polyethylene (PE)-modified bitumens and asphalts. Road Mater Pavement Des 22:1860\u0026ndash;1880\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJaczewski M, Graziani A (2024) Strain-dependent behaviour of cold recycled material mixtures in cyclic compression tests. Mater Struct 57:92\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKhanzada S (2000) Permanent Deformation in Bituminous Mixtures. In:University of Nottingham\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKorkiala-Tanttu L, Dawson A (2007) Relating full-scale pavement rutting to laboratory permanent deformation testing. Int J Pavement Eng 8:19\u0026ndash;28\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLi N, Zhan H, Yu X et al (2021) Research on the high temperature performance of asphalt pavement based on field cores with different rutting development levels. Mater Struct 54:70\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLi P, Ding Z, Rao W (2016) Evaluation of deformation properties of asphalt mixture using aggregate slip test. Int J Pavement Eng 17:542\u0026ndash;549\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLing M, Lee SI, Ji J et al (2023) Assessing permanent deformation potential of asphalt mixtures based on viscoelastic characteristics. 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Mater Struct 55:248\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"permanent deformation, rutting, asphalt mixtures, viscosity, multi-layer linear viscous","lastPublishedDoi":"10.21203/rs.3.rs-4800961/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4800961/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003ePermanent deformation (rutting) is a common type of distress in asphalt pavements. It is widely accepted that the problem occurs due to the heavy load applications and slow movement of traffic. It is clear that permanent deformation or rutting needs to be predicted to avoid major deformation to the flexible pavement. In this study, based on using the strain-dependent properties of the asphalt mixture in a multi-layer linear viscous analysis, a technique has been developed to predict asphalt mixture rut depth. Also, three different types of asphalt mixture were selected to apply the technique at various temperatures. The material properties of asphalt mixtures were derived from the repeated load axial test and they are represented by a strain-dependent axial viscosity. The predicted outcomes were then verified by comparison with measured results obtained from the wheel tracking tests. The research results have indicated that the technique is really practical and should be considered to predict a field rut depth. Moreover, based on the use of technique, the rutting prediction results applied for all mixtures at 45\u003csup\u003eo\u003c/sup\u003eC was fairly good while they presented poorer performances at 60 \u003csup\u003eo\u003c/sup\u003eC. Finally, the study has found a quick adjusted method to achive more accurate prediction results when a mixture reaches the tertiary stage of creep.\u003c/p\u003e","manuscriptTitle":"Development of a technique to predict permanent deformation characterisation in asphalt mixtures","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-09-02 12:04:36","doi":"10.21203/rs.3.rs-4800961/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"0dda18d7-947b-4103-9b1a-4d456b6ddadc","owner":[],"postedDate":"September 2nd, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-09-30T19:59:10+00:00","versionOfRecord":[],"versionCreatedAt":"2024-09-02 12:04:36","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4800961","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4800961","identity":"rs-4800961","version":["v1"]},"buildId":"7rjqhiLT3MXkJMwkYKINL","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}