地工格網應用於無鋪面道路之加勁效果，已有許多學者利用物理試驗及現地實驗等不同方式進行加州貫入比(CBR)之評估，但其產製方式與幾何性質對於加勁效果的相關研究，仍屬少數。
本研究分別以物理實驗與數值模型進行分析與探討，在物理實驗部分以CBR試驗進行分析，並以高嶺土作為軟弱路基黏土層的材料，基底層材料為單一尺寸的人造三角柱研磨石，由不同變數包含基底層厚度、地工格網開口幾何形狀、產製方式(市售PET材料與3D列印材料)等條件下探討加勁機制與效益。研究結果顯示，地工格網於軟弱黏土之加勁效果顯而易見，並以三角形孔徑地工格網加勁效果較佳。
在數值模型部分，本研究依據物理實驗模型，運用有限差分分析軟體(FLAC3D)以連體力學建立路基層架構，由離散元素分析軟體(PFC3D)以顆粒力學建立基底層與地工格網架構，並將FLAC3D與PFC3D藉由等效力系統轉換概念進行耦合運算，以探討無鋪面道路加載過程，路基層、基底層及地工格網加勁機制與微觀行為，並由實驗結果進行參數校正與模型驗證。研究結果顯示，地工格網提供張力作用，減少路基層與基底層界面之垂直應力；此外，由基底材顆粒位移、接觸力發展、路基層剪應力及累積剪應變等分析結果顯示，地工格網之加勁機制使基底層發揮顆粒互鎖機制，並與其產生圍束效應，使應力分布較寬廣，進而導致路基層頂部的接觸壓力相對較低，此一現象及加勁機制為相關課題首次以數值耦合分析證實。
綜合以上所述，運用3D列印之地工格網，具有與市售加勁格網之類似效果，因此可在後續研究中客製化不同類型地工格網，並藉由連續體耦合非連續體數值模型，調整路基層、基底層與地工格網相關參數，可進一步先行模擬各參數於設計路基剖面所產生之等值加勁效果，提供給工程設計使用。

The reinforcing effect of geogrid has been studied through physical tests, numerical modeling, and in-situ testing for the past decades. The effect is usually expressed in terms of California Bearing Ratio (CBR) or the equivalent shear strength. The reinforcing mechanisms of geogrid applied in soft subgrade have been studied by many researchers while producing customized geogrid using 3D printing technology and evaluating the reinforcing effect is uncommon yet necessary to study different configurations of geogrids. This study aims at evaluating the geogrid reinforcing effects among geogrids with various configurations using CBR tests. Afterward, the reinforcing mechanisms are evaluated through a novel numerical coupling analysis. Stress and deformation variations of the discrete base aggregate material and the subgrade represented by continuum medium during CBR simulation were investigated.
In physical tests, Kaolin powders were mixed with the specified water content as the soft subgrade material, while the aggregate base material was represented by artificial triangular-prism-type grindstone. Various design parameters such as base thickness, geogrid aperture shape, manufacturing method (commercial and 3D printed products) were considered to evaluate the effect of reinforcement. Results have shown that the geogrid improves the overall performance of the simulated soil layers, and triangular aperture geogrid performs better than square ones.
After the numerical models were verified using the physical test results, the aggregate layer simulated by discrete elements and the subgrade layer simulated by finite-difference models were coupled to investigate the reinforcing mechanisms of the unpaved roadway foundations. It was observed that due to the high stiffness of the geogrid, the vertical stress transferred to the subgrade layer was significantly reduced. Based on the displacement vectors, contact forces between aggregate particles, and subgrade shear strains, it could be seen that the geogrid provides an effective approach to limit the displacement of the aggregate particles close to the interface of two layers. The above response results in the effective interlocking between aggregate particles and the confinement of the aggregate layers.
Based on the above discussions and findings, the 3D-printed geogrid can perform equally as the commercial products. Hence the effect of different geogrid configurations could be customized during the research phase. Employing the numerical coupling analysis in this study is suitable for both aggregate and subgrade layers and interpreting the reinforcing mechanisms is straightforward. Therefore, the design of geogrid-reinforced roadways could be analyzed first using the proposed numerical approach and an optimized design cross-section could be provided to practitioners for further applications.

[1] 黃文昭，「地工格網於無鋪面道路加勁設計之回顧與展望」，地工技術，第134期，第47-58頁，2012年。
[2] 林士誠，「標準貫入試驗N值應用之彙整（一)」，台灣省土木技師公會技師報，2017年。
[3] 段瀚瀛、陳柏瑋、陳祐旻、吳睿恆，「地工格網於無鋪面道路加勁設計之回顧與展望」，工程永續與土木防災研討會論文集，第155-160頁，高雄，2016年。
[4] 黃忠皓，「以離散元素法探討加勁砂土層在淺基礎受載重下之力學」，國立中央大學，碩士論文，第1-139頁，2015年。
[5] 江明軒，「FLAC 耦合 PFC2D 應用於雙楔刀貫切破壞之初探」，臺北科技大學，碩士論文，第1-91頁，2008年。
[6] 李宏輝，「砂岩力學行為之微觀機制-以個別元素法探討」，國立臺灣大學，博士論文，第1-159頁，2008年。
[7] 盟鑫工業股份有限公司，「PET地工格網(90kNx30kN)抗拉測試報告」， 2019年。
[8] AASHTO. AASHTO Guide for Design of Pavements Structures. Washington,DC: American Association of State Highway and Transportation Officials. (1993).
[9] Ashmawy, A.K., and Bourdeau, P.L., ‘‘Geosynthetic-Reinforced Soils under Repeated Loading: A Review and Comparative Design Study,’’ Geosynthetics International, Vol. 2, No. 4, pp. 643-678 (1995).
[10] Al-Qadi, I.L., and Hughes, J.J., ‘‘Field Evaluation of Geocell Use in Flexible Pavement,’’ Transportation Research Record, Vol. 1313, pp. 26-35 (2000).
[11] Aboelwafa, M.M., Roodi, G.H., and Zornberg, J.G., “In-isolation Properties of Biaxial and Triangular Geogrids along Various Directions,” Industrial Fabrics Association International, Houston, TX, U.S.A., pp. 918-928. (2019).
[12] ASTM-6637-15, ’’ Standard Test Method for Determining Tensile Properties of Geogrids by the Single or Multi-Rib Tensile Method,’’ ASTM International, West Conshohocken, PA, U.S.A. (2015).
[13] ASTM-1883-16, ’’ Standard Test Method for California Bearing Ratio (CBR) of Laboratory-Compacted Soils,’’ ASTM International, West Conshohocken, PA, U.S.A. (2016).
[14] ASTM-D2166/ D2166M-16, ’’ Standard Test Method for Unconfined Compressive Strength of Cohesive Soil,’’ ASTM International, West Conshohocken, Pennsylvania, U.S.A. (2016).
[15] Bourdeau, P.L., ‘‘Modelling of membrane action in a two-layer reinforced soil,’’ Computers and Geotechnics, Vol.7, No. 1-2, pp.19-36 (1989).
[16] Barksdale, R.D., Brown, S.F., and Chan, F., “Potential Benefits of Geosynthetics In Flexible Pavement Systems, ” Highway Research Progress Report, National Cooperative, Washington DC, U.S.A. (1989).
[17] Buss, S. R. "Accurate and Efficient Simulation of Rigid-Body Rotations," J. Comp. Phys., 164, pp. 377-406 (2000).
[18] Boussinesq, M.J., Applications des potentials, a l’etude de l’equilibre et du movement des solides elastique. Gauthier-Villars, Paris (1885).
[19] Cundall, P. and Hart, R., "Numerical modeling of discontinuation," in Proceedings of the First US Conference on Discrete Element Methods, vol. 19: Golden Colorado: CSM Press. (1989).
[20] Cundall, P. A., and Strack, O. D. L.. "A Discrete Numerical Model for Granular Assemblies," Geotechnique, Vol.29, NO.1, 47-65 (1979).
[21] Cundall, P. A. "Distinct Element Models of Rock and Soil Structure," in Analytical and Computational Methods in Engineering Rock Mechanics, London, pp. 129-163 (1987).
[22] Department of the Army, ‘‘Use of Geogrids in Pavement Construction, ’’ U.S. Army Corps of Engineers, Technical Letter No. 1110-1-189, U.S.A.(2003).
[23] Das, B.M., and Shin, E.C., “Strip foundation on geogrid-reinforced clay: behavior under cyclic loading,” Geotextiles and Geomembranes, Vol.13, NO.10, pp. 657–666 (1994).
[24] Giroud, J.P., and Han, J., ‘‘Design method for geogrid-reinforced unpaved roads. I. Development of design method,’’ Journal of Geotechnical and Geoenvironmental Engineering, Vol.130, No. 8, pp. 775-786 (2004).
[25] Giroud, J.P., and Han, J., ‘‘Design method for geogrid-reinforced unpaved roads. II. Calibration and Applications,’’ Journal of Geotechnical and Geoenvironmental Engineering, Vol.130, No. 8, pp. 787-797 (2004).
[26] Giroud, J. P., Ah-Line, C., and Bonaparte, R., ‘‘Design of unpaved roads and trafficked areas with geogrids,’’ Polymer Grid Reinforcement, Thomas Telford Limited, London, pp. 116–127 (1985).
[27] Geosynthetic Materials Association, ‘‘Geosynthetic reinforcement of the aggregate base/subbase courses of pavement structures,’’ GMA White Paper II, United States Department of Transportation, U.S.A., pp. 1-190 (2000).
[28] Giroud, J.P., and Noiray, L., “Geotextile-reinforced unpaved road design,” Geotechnical Engineering, Vol.107, pp. 1233-1254. (1981).
[29] Huang, Wen-Chao, “Numerical Modeling and Probabilistic Analysis of Subgrade Improvement Using Geosynthetic Reinforcement, ” Ph.D. Dissertation, Purdue University, West Lafayette, Indiana, U.S.A. (2007).
[30] Heukelom, W., and Klomp, A. J. G. "Dynamic testing as a means of controlling pavements during and after construction. " Proc., 1st Int. Conf. on Structural Design of Asphalt Pavements, Univ. of Michigan, pp 667–679 (1962).
[31] Hegde, A. and Venkateswarlu, H., "FLAC3D modeling of geocell reinforced foundation beds," Department of Civil and Environmental Engineering, Monash University in Australia, pp. 1-6 (2020).
[32] Hegde, A. M. and Sitharam, T. G. Experimental and numerical studies on protection of buried pipelines and underground utilities using geocells. Geotextiles and Geomembranes, Vol. 5, No. 43 , pp. 372-381( 2015b)
[33] Hu, W., Zhang Q., and Potyondy, D. O., "FLAC3D-PFC3D Coupled Simulation of Triaxial Hopkinson Bar," Minneapolis, Vol. 9, No. 40, pp. 1-6 (2020).
[34] Itasca Consulting Group Inc., 2004. PFC2D (Particle Flow Code in 2 Dimensions), Version 4.0. Minneapolis, MN: ICG. (2004)
[35] Itasca Consulting Group Inc., 2017. PFC3D (Particle Flow Code in 3 Dimensions), Version 5.0. Minneapolis, MN: ICG. (2017)
[36] Itasca Consulting Group Inc. FLAC3D (Fast Lagrangian Analysis of Continua in 3 Dimensions), Version 7.0. Minneapolis, MN: ICG., (2019)
[37] Kumar Senthil and Ramasamy Rajkumar, “ Effect of Geotextile on CBR Strength of Unpaved Road with Soft Subgrade,” Electronic Journal of Geotechnical Engineering, Vol. 17, pp. 1355-1363 (2012).
[38] Miura, N., Sakai, A., Taesiri, Y., Yamanouchi, T., and Yasuhara, K., ‘‘Polymer Grid Reinforced Pavement on Soft Clay Grounds,’’ Geotextile and Geomembranes, Vol. 9, pp. 99-123 (1990).
[39] Marti, J., and Cundall, P.. "Mixed Discretization Procedure for Accurate Modelling of Plastic Collapse," Int. J. Num. & Analy. Methods in Geomech., pp. 129-139 (1982).
[40] Nimmesgern, M., and Bush, D., ’’The Effect of Repeated Traffic Loading on Geosynthetic Reinforcement Anchorage Resistance,‘‘ Proceedding of the Conference on Geosynthetics, Atlanta, Georgia, U.S.A., pp. 665-672 (1991).
[41] Perkins, S.W. and Ismeik, M., ‘‘A Synthesis and Evaluation of Geosynthetic-Reinforced Base Layers in Flexible Pavements- Part II,’’ Geosynthetics International, Vol. 4, No. 6, pp. 605-621 (1997).
[42] Perkins, S.W., Geosynthetic Reinforcement of Flexible Pavements: Laboratory Based Pavement Test Sections, Rep. No. FHWA/MT-99/ 8106-1, Montana Dept. of Transportation, Helena, MT, pp. 140 (1999).
[43] Patra Souvik and Bera Ashis Kumar, “California Bearing Ratio of Fine Grained Soil and its Correlation,” International Journal of Earth Sciences and Engineering, Vol. 10, No. 3, pp. 666-672 (2017).
[44] Sepehri, S., Shirinabadi, R., Hosseini, Alaee N., Moosavi, E., and Bangian Tabrizi, A. H., "A 3D Discrete Element Analysis of Failure Mechanism of Shallow Foundations in Rocks," Journal of Mining and Environment, Vol. 11, No. 2, pp. 467-480, (2020).
[45] The Tensar Corporation, ‘‘Design guideline for flexible pavement with tensar geogrid reinforced base courses.’’ Tensar Technical Note (TTN:BR96), United Kingdom, pp. 1-77 (1996).
[46] The Tensar Corporation, ‘‘A review of geosynthetic functions and applications in paved and unpaved roads,’’ Tensar Technical Note (TTN:BR11), United Kingdom, pp. 1-45 (1998).
[47] The Tensar Corporation, ‘‘The Properties and Performance of Tansar Biaxial Geogrids,’’ Tensar information limited, No. 3, United Kingdom, pp.1-20 (2003).
[48] The Tensar Corporation, ‘‘Understanding Radial Stiffness,’’ Tensar information bulletin, United Kingdom, pp. 1-2 (2014).
[49] The Tensar Corporation, ‘‘Radial stiffness and its performance relationship,’’ Tensar information bulletin, United Kingdom, pp. 1-4 (2014).
[50] The Tensar Corporation, ‘‘Mechanically Stabilised Layers for Subgrade Stabilisation.’’ Tensar information bulletin, United Kingdom, pp. 1-79 (2019)
[51] Vesic, A. S., "Analysis of Ultimate Loads of Shallow Foundations," Journal of the Soil Mechanics and Foundations Division, New York, Vol. 99, No. 1, pp. 45-73, (1973)
[52] Venkateswarlu, H. and Hegde, A. Numerical Analysis of Machine Foundation Resting on the Geocell Reinforced Soil Beds. Geotechnical Engineering, Vol. 49, No. 4, pp. 55-62, ( 2018).
[53] Virginia Department of Transportation, ‘‘Soils and aggregate compaction, ’’ U.S. Virginia, pp. 1-420 (2019)
[54] Webster, S.L., ‘‘Geogrid Reinforced Base Courses for Flexible Pavement for Light Aircraft, Test Section Construction, Behavior Under Traffic, Laboratory Tests and Design Criteria,’’ Waterways Experiment, Vicksburg, Mississippi, U.S.A (1993).
[55] Zornberg, J.G., “Functions and Applications of Geosynthetics in Roadways: Part 1,” Geosynthetics, Industrial Fabrics Association International, U.S.A., pp. 34-40 (2017)
[56] Zheng, L., Roodi, G.H., and Zornberg, J.G., “Case History of a Geosynthetic-stabilized Base Roadway Founded over Expansive Clay Subgrade,” Geotechnical Special Publication, Geotechnical Materials, Modeling, and Testing, ASCE Geo-Congress 2019, Philadelphia, Pennsylvania, U.S.A., pp. 430-443 (2019)