# Finite Element Analysis of Geogrid-Incorporated Flexible Pavement with Soft Subgrade
## 1 Introduction  
Flexible pavements, the most prevalent type of pavement, are found on 85-90% of roadways globally. However, excessive wheel loads, environmental impacts, etc., significantly impair pavements, so careful consideration must be given to their design and construction. The principal controlling elements are fatigue and rutting failures, which are mostly caused by tensile strain at the bituminous layer's bottom and vertical strain at the top of the subgrade. To lessen these tensile and vertical strains, researchers created a synthetic polymeric substance called geosynthetic that works to stabilize the subgrade soil. Among the many types of geosynthetics, geogrid is a popular type that can be employed as a filtration membrane, drainage system, separation layer, and soil reinforcement in various pavement layers [1, 2].  
Several types of geogrids exist depending upon their pattern, manufacturing process and materials. Uniaxial, biaxial, and triaxial geogrids can be found based on the pattern of geogrid, where uniaxial geogrid provides longitudinal tension, biaxial geogrid provides both longitudinal and horizontal tension and triaxial geogrid provides strength in three dimensions. Based on the manufacturing process, geogrid can be classified as extruded geogrid, woven geogrid and bonded geogrid. Fiberglass geogrid, PET geogrid and warp knitted fiberglass geogrid are also very common nowadays. Geogrids are mostly used in pavements for reinforcing the materials of different layers due to their higher rigidity and ability to distribute the wheel loads. However, geogrids can also be used in retaining walls, soil foundation, slope stabilization, etc. Numerous investigators have investigated the performance of geogrid-modified pavements and verified the efficacy ofgeogrid materials [3; 4; 5]. The results of these tests demonstrated that reinforcement could lessen the possibility of persistent deformation in reinforced parts while also extending and enhancing their service life. It was clear that the geogrid's strengthening and reinforcing properties improve tensile forces, boost stability, and contain persistent deformations [6]. The researchers noted that several variables, such as geogrid properties, interlocking with aggregate, pavement layer thickness, geogrid placement, and the condition of subgrade and base layers, impact how effectively geogrid reinforcement works in flexible pavements. However, the majority of research has focused on experimental studies at different scales, with limited attention given to numerical investigations [7]. In previous numerical investigations of geogrid-modified soil, the geogrid's performance was simulated using either one- or three-dimensional computer models, often incorporating one-dimensional tensile elements to represent its behaviour [8; 9] or a planar sheet-like structure [10; 11; 12]. Some researchers have recently introduced three-dimensional finite element numerical models for analysing geogrid reinforcement. These models can depict the performance of biaxial geogrids in both unconfined and soil-confined conditions [13; 14]. Because rutting failure is primarily caused by vertical strains on the subgrade's surface, understanding its strength and the impact of geogrid on the subgrade soil is crucial. This study focuses on conducting a three-dimensional numerical analysis of geogrid-reinforced pavements, considering various strengths of subgrade soil or California bearing ratio (CBR) values. The geogrid is predominantly positioned atop the subgrade, and different thicknesses of the aggregate base layer are examined to assess the reinforcement's effect on base thickness. The primary emphasis lies in understanding the strains developed in pavements and the geogrid.