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Optimizing Non-Linear Granular Layer Coefficients of a Flexible Pavement for Mechanistic-Empirical Method

Yıl 2021, Cilt: 32 Sayı: 6, 11315 - 11336, 01.11.2021
https://doi.org/10.18400/tekderg.637166

Öz

In recent years, mechanistic-empirical (M-E) design methods are preferred in the design of flexible pavements instead of empirical methods using equations based on the road performance tests. However, the calibration of transfer equations that convert mechanical responses to pavement life and the definition of layer materials used in M-E methods have great importance for M-E methods.
In this study, mechanical analyzes of a cross-section designed with the AASHTO-93 method were performed, and service life values were calculated with different empirical transfer equations. The obtained M-E design results were compared with the results calculated with the AASHTO-93 method, and transfer equations compatible with the AASHTO-93 method were determined. Among the transfer equations examined, it was found that the rutting equation of the Asphalt Institute gave the most consistent results with the AASHTO-93 method. In the mechanical analysis of the selected cross-section, granular base and sub-base layers were defined as non-linear elastic reflecting the actual in-situ conditions. K-Ɵ model was preferred for non-linear elastic layer definition, and K1 and K2 parameters of this model were optimized.

Destekleyen Kurum

Sivas Cumhuriyet Üniversitesi

Proje Numarası

M-753

Kaynakça

  • [1] Huang, Y. H.,Pavement analysis and design. 2nd ed. Upper Saddle River, NJ: Pearson Prentice Hall, 1993.
  • [2] Mashayekhi, M., Amini, A.A., Behbahani, H., Nobakht, S., Comparison of mechanistic-empirical and empirical flexible pavement design procedures of AASHTO: A Case Study, 5th International Conference Bituminous Mixtures and Pavements, Thessaloniki, 2011.
  • [3] Alhasan, A., Ali, A., Offenbacker, D., Smadi, O., Lewis-Beck, C., Incorporating spatial variability of pavement foundation layers stiffness in reliability-based mechanistic-empirical pavement performance prediction, Transportation Geotechnics, 17, 1-13, 2018.
  • [4] Carvalho, R. L.,Schwartz, C. W., Comparisons of flexible pavement designs: AASHTO empirical versus NCHRP project 1–37A mechanistic–empirical, Transportation Research Record, 1947(1), 167-174, 2006.
  • [5] Sağlık, A.,Güngör, A.G., Highways flexible pavement design guide, Ankara, 2008.
  • [6] Çelik, O. N.,Eyada, S. O., Assessment of flexible pavement fatigue life of Turkish typical sections using mechanistic empirical pavement design approach for coastal region, Ain Shams Engineering Journal, 10(1), 33-43, 2019.
  • [7] Muniandy, R., Aburkaba, E., Thamer, N., Comparison of flexible pavement performance using Kenlayer and Chev PC software program, Australian Journal of Basic and Applied Sciences, 7(9), 112-119, 2013.
  • [8] Behiry, A. E. A. E. M., Fatigue and rutting lives in flexible pavement, Ain Shams Engineering Journal, 3(4), 367-374, 2012.
  • [9] Mousa, M. R., Abo-Hashema, M.A., Gadallah, A.A., Mousa, R.M., Evaluation of pavement performance prediction models under different traffic and climatic conditions, The Proceedings of International Conference on Asphalt Pavement Engineering and Infrastructure, London, 2015.
  • [10] Singh, A. K.,Sahoo, J. P., Analysis and design of two layered flexible pavement systems: A new mechanistic approach, Computers and Geotechnics, 117, 103238, 2020.
  • [11] Abd Alla, E. M., The rational use of finite element method in the analysis of flexible pavements, Journal of Engineering Sciences, Assiut University, 34(4), 1185-1211, 2006.
  • [12] Titi, H. H., Matar, M. G., Estimating resilient modulus of base aggregates for mechanistic-empirical pavement design and performance evaluation, Transportation Geotechnics, 17, 141-153, 2018.
  • [13] Ng, K., Henrichs, Z.R., Ksaibati, K., Wulff, S.S., Resilient modulus of subgrade materials for mechanistic-empirical pavement design guide, Road Materials and Pavement Design, 19(7), 1523-1545, 2018.
  • [14] Shahji, S. Sensitivity analysis of AASHTO’S 2002 flexible and rigid pavement design methods, Thesis (MSc), University of Central Florida, 2006.
  • [15] Masad, S.A., Little, D.N., Sensitivity analysis of flexible pavement response and AASHTO 2002 design guide to properties of unbound layers. Research report ICAR 504-1, International Center for Aggregates Research, 2004.
  • [16] Cerni, G., Cardone, F., Virgili, A., Camilli, S., Characterisation of permanent deformation behaviour of unbound granular materials under repeated triaxial loading, Construction and Building Materials, 28(1), 79-87, 2012.
  • [17] Sahin, H., Gu, F., Tong, Y., Luo, R., Lytton, R. L., Unsaturated soil mechanics in the design and performance of pavements, Advances in Unsaturated Soils, 105-118, 2013.
  • [18] Ahirwar, S. K., Mandal, J. N., Finite element analysis of flexible pavement with geogrids, Procedia Engineering, 189, 411-416, 2017.
  • [19] Seed, H. B., Mitry, F.G., Monismith, C.L., Chan, C.K., Prediction of flexible pavement deflections from laboratory repeated-load tests, Report No: 35, NCHRP, 1967.
  • [20] May, R. W., Witczak, M. W., Effective granular modulus to model pavement responses, Transportation Research Record, 810, 1-9, 1981.
  • [21] Uzan, J., Characterization of granular material, Transportation Research Record, 1022(1), 52-59, 1985.
  • [22] Ni, B., Hopkins, T.C., Sun, L., Beckham, T.L., Modeling the resilient modulus of soils, Proceedings of the 6th International Conference on the Bearing Capacity of Roads and Airfields, Lisbon, 2002.
  • [23] Luo, X., Gu, F., Zhang, Y., Lytton, R. L., Zollinger, D., Mechanistic-empirical models for better consideration of subgrade and unbound layers influence on pavement performance, Transportation Geotechnics, 13, 52-68, 2017.
  • [24] Masad, S., Little, D., Masad, E., Analysis of flexible pavement response and performance using isotropic and anisotropic material properties, Journal of Transportation Engineering, 132(4), 342-349, 2006.
  • [25] Adu-Osei, A., Little, D. N., Lytton, R. L., Cross-anisotropic characterization of unbound granular materials, Transportation Research Record, 1757(1), 82-91, 2001. [26] Tutumluer, E., Thompson, M. R., Anisotropic modeling of granular bases in flexible pavements, Transportation Research Record, 1577(1), 18-26, 1997.
  • [27] Yang, S. R., Huang, W. H., Tai, Y. T. Variation of resilient modulus with soil suction for compacted subgrade soils, Transportation Research Record, 1913(1), 99-106, 2005.
  • [28] Butalia, T.S., Huang, J., Kim, D.G., Croft, F., Effect of moisture content and pore water pressure buildup on resilient modulus of cohesive soils in Ohio, ASTM Special Technical Publication, 1437, 70–84, 2003.
  • [29] Wolfe, W., Butalia, T., Continued monitoring of SHRP pavement instrumentation including soil suction and relationship with resilient modulus, Report No: FHWA/OH-2004/007, Department of Transportation, Federal Highway Administration, 2004.
  • [30] Gupta, S., Ranaivoson, A., Edil, T., Benson, C., Sawangsuriya, A., Pavement design using unsaturated soil technology, Report No: MN/RC-2007-11, University of Minnesota, 2007.
  • [31] Cary, C. E., Zapata, C. E., Resilient modulus for unsaturated unbound materials. Road Materials and Pavement Design, 12(3), 615-638, 2011.
  • [32] Ghadimi, B., Nikraz, H., A comparison of implementation of linear and nonlinear constitutive models in numerical analysis of layered flexible pavement, Road Materials and Pavement Design, 18(3), 550-572, 2017.
  • [33] Ghanizadeh, A. R., Ziaie, A., NonPAS: a program for nonlinear analysis of flexible pavements, International Journal of Integrated Engineering, 7(1), 2015.
  • [34] Karagöz, C.,Analysis of Flexible pavements incorporating nonlinear resilient behavior of unbound granular layers, Thesis (PhD), Middle East Technical University, 2004.
  • [35] Hicks, R. G.,Factors influencing the resilient properties of granular materials, Thesis (PhD), University of California, Berkeley, 1970.
  • [36] Hicks, R. G., Finn, F. N., Analysis of results from the dynamic measurements program on the San Diego test road, Proceedings, Association of Asphalt Paving Technologists, 39, 153-185, 1970.
  • [37] Allen, J. J.,The effects of non-constant lateral pressure on the resilient response of granular materials, Thesis (PhD), University of Illinois at Urbana-Champaign, 1973.
  • [38] Kalcheff, I. V., Hicks, R. G., A test procedure for determining the resilient properties of granular materials, Journal of Testing and Evaluation, 1(6), 472-479, 1973.
  • [39] Boyce, J. R., Brown, S. F., Pell, P. S., The resilient behaviour of a granular material under repeated loading,Australian Road Research Board Conference Proceedings, 8, 1-12, 1976.
  • [40] Monismith, C. L.,Witczak, M. W., Moderator's report, paper in session I, Pavement Design, Proceedings Fifth International Conference on the Structural Design of Asphalt Pavements, Netherlands, 2, 2-58, 1982.
  • [41] Pan, E., Chen, E., Alkasawneh, W., An exploratory study on functionally graded materials with applications to multilayered pavement design, Report No: FHWA/OH-2007/12, Department of Civil Engineering the University of Akron, 2007.
  • [42] Hafeez, I., Shan, A., Ali, A., Ahmed, I., Flexible pavement design evaluation using mechanistic-empirical approaches. Technical Journal, University of Engineering and Technology, 22, 27-33, 2017.
  • [43] Beskou, N. D., Tsinopoulos, S. V., Theodorakopoulos, D. D., Dynamic elastic analysis of 3-D flexible pavements under moving vehicles: A unified FEM treatment, Soil Dynamics and Earthquake Engineering, 82, 63-72, 2016.
  • [44] Al-Azzawi, A. A., Finite Element Analysis of Flexible Pavements Strengthed with Geogrid, ARPN Journal of Engineering and Applied Sciences, 7(10), 1295-1299, 2012.
  • [45] Ekwulo, E. O.,Eme, D. B., Fatigue and rutting strain analysis of flexible pavements designed using CBR methods, African Journal of Environmental Science and Technology, 3(12), 2009.
  • [46] Perraton, D., Di Benedetto, H., Carter, A., Proteau, M., Link between different bottom-up fatigue’s law coefficients of mechanical-empirical pavement design software, Construction and Building Materials, 216, 552-563, 2019.
  • [47] Priest, A.,Calibration of fatigue fransfer functions for mechanistic-empirical flexible pavement design,Thesis (PhD), Auburn University, 2005.
  • [48] Ziari, H., Khabiri, M. M., Interface condition influence on prediction of flexible pavement life, Journal of Civil Engineering and Management, 13(1), 71-76, 2007.
  • [49] Chegenizadeh, A., Keramatikerman, M., Nikraz, H., Flexible pavement modelling using Kenlayer, The Electronic Journal of Geotechnical Engineering, 21, 2467-2479, 2016.
  • [50] Hadi, M. N.,Bodhinayake, B. C., Non-linear finite element analysis of flexible pavements, Advances in Engineering Software, 34(11-12), 657-662, 2003.
  • [51] Samad, E., Sensitivity analysis in flexible pavement performance using mechanistic empirical method (Case study: Cirebon–Losari road segment, West Java), Journal of the Civil Engineering Forum, 20(1), 1163-1174, 2011.
  • [52] Turkey General Directorate of Highways, Highways technical specification, Ankara, Turkey, 2013.

Optimizing Non-Linear Granular Layer Coefficients of a Flexible Pavement for Mechanistic-Empirical Method

Yıl 2021, Cilt: 32 Sayı: 6, 11315 - 11336, 01.11.2021
https://doi.org/10.18400/tekderg.637166

Öz

In recent years, mechanistic-empirical (M-E) design methods are preferred in the design of flexible pavements instead of empirical methods using equations based on the road performance tests. However, the calibration of transfer equations that convert mechanical responses to pavement life and the definition of layer materials used in M-E methods have great importance for M-E methods.
In this study, mechanical analyzes of a cross-section designed with the AASHTO-93 method were performed, and service life values were calculated with different empirical transfer equations. The obtained M-E design results were compared with the results calculated with the AASHTO-93 method, and transfer equations compatible with the AASHTO-93 method were determined. Among the transfer equations examined, it was found that the rutting equation of the Asphalt Institute gave the most consistent results with the AASHTO-93 method. In the mechanical analysis of the selected cross-section, granular base and sub-base layers were defined as non-linear elastic reflecting the actual in-situ conditions. K-Ɵ model was preferred for non-linear elastic layer definition, and K1 and K2 parameters of this model were optimized.

Proje Numarası

M-753

Kaynakça

  • [1] Huang, Y. H.,Pavement analysis and design. 2nd ed. Upper Saddle River, NJ: Pearson Prentice Hall, 1993.
  • [2] Mashayekhi, M., Amini, A.A., Behbahani, H., Nobakht, S., Comparison of mechanistic-empirical and empirical flexible pavement design procedures of AASHTO: A Case Study, 5th International Conference Bituminous Mixtures and Pavements, Thessaloniki, 2011.
  • [3] Alhasan, A., Ali, A., Offenbacker, D., Smadi, O., Lewis-Beck, C., Incorporating spatial variability of pavement foundation layers stiffness in reliability-based mechanistic-empirical pavement performance prediction, Transportation Geotechnics, 17, 1-13, 2018.
  • [4] Carvalho, R. L.,Schwartz, C. W., Comparisons of flexible pavement designs: AASHTO empirical versus NCHRP project 1–37A mechanistic–empirical, Transportation Research Record, 1947(1), 167-174, 2006.
  • [5] Sağlık, A.,Güngör, A.G., Highways flexible pavement design guide, Ankara, 2008.
  • [6] Çelik, O. N.,Eyada, S. O., Assessment of flexible pavement fatigue life of Turkish typical sections using mechanistic empirical pavement design approach for coastal region, Ain Shams Engineering Journal, 10(1), 33-43, 2019.
  • [7] Muniandy, R., Aburkaba, E., Thamer, N., Comparison of flexible pavement performance using Kenlayer and Chev PC software program, Australian Journal of Basic and Applied Sciences, 7(9), 112-119, 2013.
  • [8] Behiry, A. E. A. E. M., Fatigue and rutting lives in flexible pavement, Ain Shams Engineering Journal, 3(4), 367-374, 2012.
  • [9] Mousa, M. R., Abo-Hashema, M.A., Gadallah, A.A., Mousa, R.M., Evaluation of pavement performance prediction models under different traffic and climatic conditions, The Proceedings of International Conference on Asphalt Pavement Engineering and Infrastructure, London, 2015.
  • [10] Singh, A. K.,Sahoo, J. P., Analysis and design of two layered flexible pavement systems: A new mechanistic approach, Computers and Geotechnics, 117, 103238, 2020.
  • [11] Abd Alla, E. M., The rational use of finite element method in the analysis of flexible pavements, Journal of Engineering Sciences, Assiut University, 34(4), 1185-1211, 2006.
  • [12] Titi, H. H., Matar, M. G., Estimating resilient modulus of base aggregates for mechanistic-empirical pavement design and performance evaluation, Transportation Geotechnics, 17, 141-153, 2018.
  • [13] Ng, K., Henrichs, Z.R., Ksaibati, K., Wulff, S.S., Resilient modulus of subgrade materials for mechanistic-empirical pavement design guide, Road Materials and Pavement Design, 19(7), 1523-1545, 2018.
  • [14] Shahji, S. Sensitivity analysis of AASHTO’S 2002 flexible and rigid pavement design methods, Thesis (MSc), University of Central Florida, 2006.
  • [15] Masad, S.A., Little, D.N., Sensitivity analysis of flexible pavement response and AASHTO 2002 design guide to properties of unbound layers. Research report ICAR 504-1, International Center for Aggregates Research, 2004.
  • [16] Cerni, G., Cardone, F., Virgili, A., Camilli, S., Characterisation of permanent deformation behaviour of unbound granular materials under repeated triaxial loading, Construction and Building Materials, 28(1), 79-87, 2012.
  • [17] Sahin, H., Gu, F., Tong, Y., Luo, R., Lytton, R. L., Unsaturated soil mechanics in the design and performance of pavements, Advances in Unsaturated Soils, 105-118, 2013.
  • [18] Ahirwar, S. K., Mandal, J. N., Finite element analysis of flexible pavement with geogrids, Procedia Engineering, 189, 411-416, 2017.
  • [19] Seed, H. B., Mitry, F.G., Monismith, C.L., Chan, C.K., Prediction of flexible pavement deflections from laboratory repeated-load tests, Report No: 35, NCHRP, 1967.
  • [20] May, R. W., Witczak, M. W., Effective granular modulus to model pavement responses, Transportation Research Record, 810, 1-9, 1981.
  • [21] Uzan, J., Characterization of granular material, Transportation Research Record, 1022(1), 52-59, 1985.
  • [22] Ni, B., Hopkins, T.C., Sun, L., Beckham, T.L., Modeling the resilient modulus of soils, Proceedings of the 6th International Conference on the Bearing Capacity of Roads and Airfields, Lisbon, 2002.
  • [23] Luo, X., Gu, F., Zhang, Y., Lytton, R. L., Zollinger, D., Mechanistic-empirical models for better consideration of subgrade and unbound layers influence on pavement performance, Transportation Geotechnics, 13, 52-68, 2017.
  • [24] Masad, S., Little, D., Masad, E., Analysis of flexible pavement response and performance using isotropic and anisotropic material properties, Journal of Transportation Engineering, 132(4), 342-349, 2006.
  • [25] Adu-Osei, A., Little, D. N., Lytton, R. L., Cross-anisotropic characterization of unbound granular materials, Transportation Research Record, 1757(1), 82-91, 2001. [26] Tutumluer, E., Thompson, M. R., Anisotropic modeling of granular bases in flexible pavements, Transportation Research Record, 1577(1), 18-26, 1997.
  • [27] Yang, S. R., Huang, W. H., Tai, Y. T. Variation of resilient modulus with soil suction for compacted subgrade soils, Transportation Research Record, 1913(1), 99-106, 2005.
  • [28] Butalia, T.S., Huang, J., Kim, D.G., Croft, F., Effect of moisture content and pore water pressure buildup on resilient modulus of cohesive soils in Ohio, ASTM Special Technical Publication, 1437, 70–84, 2003.
  • [29] Wolfe, W., Butalia, T., Continued monitoring of SHRP pavement instrumentation including soil suction and relationship with resilient modulus, Report No: FHWA/OH-2004/007, Department of Transportation, Federal Highway Administration, 2004.
  • [30] Gupta, S., Ranaivoson, A., Edil, T., Benson, C., Sawangsuriya, A., Pavement design using unsaturated soil technology, Report No: MN/RC-2007-11, University of Minnesota, 2007.
  • [31] Cary, C. E., Zapata, C. E., Resilient modulus for unsaturated unbound materials. Road Materials and Pavement Design, 12(3), 615-638, 2011.
  • [32] Ghadimi, B., Nikraz, H., A comparison of implementation of linear and nonlinear constitutive models in numerical analysis of layered flexible pavement, Road Materials and Pavement Design, 18(3), 550-572, 2017.
  • [33] Ghanizadeh, A. R., Ziaie, A., NonPAS: a program for nonlinear analysis of flexible pavements, International Journal of Integrated Engineering, 7(1), 2015.
  • [34] Karagöz, C.,Analysis of Flexible pavements incorporating nonlinear resilient behavior of unbound granular layers, Thesis (PhD), Middle East Technical University, 2004.
  • [35] Hicks, R. G.,Factors influencing the resilient properties of granular materials, Thesis (PhD), University of California, Berkeley, 1970.
  • [36] Hicks, R. G., Finn, F. N., Analysis of results from the dynamic measurements program on the San Diego test road, Proceedings, Association of Asphalt Paving Technologists, 39, 153-185, 1970.
  • [37] Allen, J. J.,The effects of non-constant lateral pressure on the resilient response of granular materials, Thesis (PhD), University of Illinois at Urbana-Champaign, 1973.
  • [38] Kalcheff, I. V., Hicks, R. G., A test procedure for determining the resilient properties of granular materials, Journal of Testing and Evaluation, 1(6), 472-479, 1973.
  • [39] Boyce, J. R., Brown, S. F., Pell, P. S., The resilient behaviour of a granular material under repeated loading,Australian Road Research Board Conference Proceedings, 8, 1-12, 1976.
  • [40] Monismith, C. L.,Witczak, M. W., Moderator's report, paper in session I, Pavement Design, Proceedings Fifth International Conference on the Structural Design of Asphalt Pavements, Netherlands, 2, 2-58, 1982.
  • [41] Pan, E., Chen, E., Alkasawneh, W., An exploratory study on functionally graded materials with applications to multilayered pavement design, Report No: FHWA/OH-2007/12, Department of Civil Engineering the University of Akron, 2007.
  • [42] Hafeez, I., Shan, A., Ali, A., Ahmed, I., Flexible pavement design evaluation using mechanistic-empirical approaches. Technical Journal, University of Engineering and Technology, 22, 27-33, 2017.
  • [43] Beskou, N. D., Tsinopoulos, S. V., Theodorakopoulos, D. D., Dynamic elastic analysis of 3-D flexible pavements under moving vehicles: A unified FEM treatment, Soil Dynamics and Earthquake Engineering, 82, 63-72, 2016.
  • [44] Al-Azzawi, A. A., Finite Element Analysis of Flexible Pavements Strengthed with Geogrid, ARPN Journal of Engineering and Applied Sciences, 7(10), 1295-1299, 2012.
  • [45] Ekwulo, E. O.,Eme, D. B., Fatigue and rutting strain analysis of flexible pavements designed using CBR methods, African Journal of Environmental Science and Technology, 3(12), 2009.
  • [46] Perraton, D., Di Benedetto, H., Carter, A., Proteau, M., Link between different bottom-up fatigue’s law coefficients of mechanical-empirical pavement design software, Construction and Building Materials, 216, 552-563, 2019.
  • [47] Priest, A.,Calibration of fatigue fransfer functions for mechanistic-empirical flexible pavement design,Thesis (PhD), Auburn University, 2005.
  • [48] Ziari, H., Khabiri, M. M., Interface condition influence on prediction of flexible pavement life, Journal of Civil Engineering and Management, 13(1), 71-76, 2007.
  • [49] Chegenizadeh, A., Keramatikerman, M., Nikraz, H., Flexible pavement modelling using Kenlayer, The Electronic Journal of Geotechnical Engineering, 21, 2467-2479, 2016.
  • [50] Hadi, M. N.,Bodhinayake, B. C., Non-linear finite element analysis of flexible pavements, Advances in Engineering Software, 34(11-12), 657-662, 2003.
  • [51] Samad, E., Sensitivity analysis in flexible pavement performance using mechanistic empirical method (Case study: Cirebon–Losari road segment, West Java), Journal of the Civil Engineering Forum, 20(1), 1163-1174, 2011.
  • [52] Turkey General Directorate of Highways, Highways technical specification, Ankara, Turkey, 2013.
Toplam 51 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular İnşaat Mühendisliği
Bölüm Makale
Yazarlar

Murat Bostancıoğlu 0000-0001-6820-2213

Proje Numarası M-753
Yayımlanma Tarihi 1 Kasım 2021
Gönderilme Tarihi 23 Ekim 2019
Yayımlandığı Sayı Yıl 2021 Cilt: 32 Sayı: 6

Kaynak Göster

APA Bostancıoğlu, M. (2021). Optimizing Non-Linear Granular Layer Coefficients of a Flexible Pavement for Mechanistic-Empirical Method. Teknik Dergi, 32(6), 11315-11336. https://doi.org/10.18400/tekderg.637166
AMA Bostancıoğlu M. Optimizing Non-Linear Granular Layer Coefficients of a Flexible Pavement for Mechanistic-Empirical Method. Teknik Dergi. Kasım 2021;32(6):11315-11336. doi:10.18400/tekderg.637166
Chicago Bostancıoğlu, Murat. “Optimizing Non-Linear Granular Layer Coefficients of a Flexible Pavement for Mechanistic-Empirical Method”. Teknik Dergi 32, sy. 6 (Kasım 2021): 11315-36. https://doi.org/10.18400/tekderg.637166.
EndNote Bostancıoğlu M (01 Kasım 2021) Optimizing Non-Linear Granular Layer Coefficients of a Flexible Pavement for Mechanistic-Empirical Method. Teknik Dergi 32 6 11315–11336.
IEEE M. Bostancıoğlu, “Optimizing Non-Linear Granular Layer Coefficients of a Flexible Pavement for Mechanistic-Empirical Method”, Teknik Dergi, c. 32, sy. 6, ss. 11315–11336, 2021, doi: 10.18400/tekderg.637166.
ISNAD Bostancıoğlu, Murat. “Optimizing Non-Linear Granular Layer Coefficients of a Flexible Pavement for Mechanistic-Empirical Method”. Teknik Dergi 32/6 (Kasım 2021), 11315-11336. https://doi.org/10.18400/tekderg.637166.
JAMA Bostancıoğlu M. Optimizing Non-Linear Granular Layer Coefficients of a Flexible Pavement for Mechanistic-Empirical Method. Teknik Dergi. 2021;32:11315–11336.
MLA Bostancıoğlu, Murat. “Optimizing Non-Linear Granular Layer Coefficients of a Flexible Pavement for Mechanistic-Empirical Method”. Teknik Dergi, c. 32, sy. 6, 2021, ss. 11315-36, doi:10.18400/tekderg.637166.
Vancouver Bostancıoğlu M. Optimizing Non-Linear Granular Layer Coefficients of a Flexible Pavement for Mechanistic-Empirical Method. Teknik Dergi. 2021;32(6):11315-36.