Geogrids are widely used to enhance the performance of roadways, especially to improve the conditions associated with soft subgrade. However, the results in the literature do not always show the contribution of the geogrid to improve the elastic modulus of the base course layers consistently. This study demonstrates the use of an existing methodology to overcome such inconsistency. The method used in this study is based on sequentially loading the base course surface with three side-by-side lightweight deflectometers (LWD). The findings of this study showed that such an approach enables us to demonstrate the deterioration of the base course when no geogrid is present and the improved behavior with geogrid placed in between the base course and soft subgrade. The study demonstrates the effective use of KenPave analyses and the results from LWD testing to determine modulus improvement factor (MIF) when geogrids are used. Four different geogrids with different characteristics were evaluated and the determined MIF values ranged between 1.39 and 1.64. The findings were used to develop a relationship between the base course thickness and the allowed maximum stress on the base course for different geogrids, where the applied load is limited to keep the base course elastic.
NOTATION
- Basic SI units are given in parentheses.
- CBR
California bearing ratio (dimensionless)
- EBase
elastic modulus of base course (Pa)
- ESubgrade
elastic modulus of subgrade (Pa)
- MIF
modulus improvement factor (dimensionless)
- Pmax
maximum applied load (Pa)
- PSubgrade
stress at the interface of the base course/subgrade (Pa)
- tBase
base course thickness (m)
- δ
surface deflection (m)
- δKenPave
KenPave calculated surface deflection (m)
- δLWD
LWD recorded deflection (m)
ABBREVIATIONS
- AASHTO
American Association of State Highway and Transportation Officials
- APLT
automated plate load test
- APT
accelerated pavement testing
- ASTM
American Society for Testing and Materials
- DCP
dynamic cone penetrometer
- FWD
falling weight deflectometer
- LWD
light weight deflectometer
- MEPDG
mechanistic-empirical pavement design guide
- PET
polyester
- PP
polypropylene
- VDOT
Virginia Department of Transportation
1. INTRODUCTION
In geotechnical engineering practice, the majority of the laboratory and field tests involve applying load to a single location and determining modulus. Previous studies have shown that tests conducted on single point locations do not necessarily represent the same conditions that occur when the traffic load passes over the pavement layers (Kim and Tutumluer 2005; Yoshitsugu et al. 2005; Tatsuya et al. 2011; Dareeju et al. 2015). This is because when the load is applied at the same location, the magnitude of the load may vary but the principal stress directions remain constant. However, when the ground is exposed to the traffic loads, as the wheel rolls over the surface, the principal stress axes also rotate. Such conditions create a destabilizing effect in the ground (Dareeju et al. 2015). The best testing method that simulates these conditions accurately is the accelerated pavement testing (APT), however this test method does not provide modulus values (Brown 2004). Recently, Akmaz et al. (2025) proposed a new methodology using three side-by-side LWD equipment to determine the modulus of base course that simulates the conditions anticipated by the rolling wheel of a vehicle. The research outcomes demonstrated the difference between determining modulus by applying load to a single location versus multiple locations sequentially.
Modulus is an important parameter in the design of pavement layers (IRCSP59 2019; AASHTO 2013; and MEPDG 2015). Determining the modulus that has relevancy to the actual field conditions plays an even more important role if the design involves the use of materials such as geogrids to improve soft ground conditions (Giroud and Han 2013). The effectiveness of the use of geogrids has been investigated in detail by many researchers (Haas et al. 1988; Berg et al. 2000; Al-Qadi et al. 2008; Zornberg and Gupta 2010; Flutcher and Jonathan 2013; Abu-Farsakh et al. 2016; Oliver et al. 2016; Tamrakar et al. 2019; Vennapusa et al. 2020; Saride et al. 2022; Baadiga et al. 2022a and Baadiga et al. 2022b). Although it is widely accepted that the use of a geogrid improves the rutting performance of the ground, when it comes to demonstrating the improvement of the modulus values, the previous literature has not been able to consistently demonstrate this. The discrepancies in being able to show an improved modulus value with geogrids exists within the laboratory tests (Abu-Farsakh et al. 2007; Wayne et al. 2011; Han 2015; and Kang et al. 2020), large-scale tests (Leng and Gabr 2002; Abu-Farsakh et al. 2016; Suku et al. 2017; Sharbaf and Ghafoori 2021), and field in-situ tests (Webster 1993; Zornberg 2011; Aurimas et al. 2017; Tamrakar et al. 2019; Vennapusa et al. 2020; Alimohammdi et al. 2021), where in all of these tests, the load has been applied to a single location. The summary of the studies provided in the literature shows that the elastic modulus values obtained with geogrid reinforcement has been observed to be greater, equivalent to, or less than those without reinforcement. Similarly, Zornberg and Gupta (2010) also point out such discrepancy in their reported case field study, where in one geogrid reinforced section, the modulus measured with FWD was greater than the modulus of the unreinforced section and within the same site, at another section (also reinforced with geogrid), the measured modulus with FWD was lower than the unreinforced section. Zornberg and Gupta (2010) explain the discrepancies as an illustration of the inadequacy of the FWD evaluation technique to be used to quantify the benefits of geogrid reinforcement. The automated plate load test (APLT) system that has been developed more recently also applies load to a single location but the load application is dynamic (White and Vennapusa 2017). The results of the tests appear to provide more consistent outcomes, but the modulus values appear to increase within the first 100 to 250 load cycles for both geogrid and unreinforced base course layers (Tamrakar et al. 2019). This behavior is interpreted as the nature of the load compacting the soil and therefore the benefit observed is not solely due to the presence of the geogrid.
When it comes to incorporating the improved modulus values of the ground into the pavement design when geogrid is used, the most common approaches involve the calculation of the modulus improvement factor (MIF). This approach has been developed by Giroud and Han (2013) and involves determining the ratio between the reinforced and unreinforced base course modulus. The range of MIF for reinforced granular base course has been given by different researchers as 1 to 2 (Han 2015) and up to 5 (Baadiga and Balunaini 2023). Saride et al. (2022) have conducted a comprehensive study comparing the MIF values for the polypropylene (PP) and polyester (PET) geogrids placed within the aggregate that was underlain by a subbase and soft subgrade with a CBR of 1 resulting in deformation modulus of 4.12 MPa and resilient modulus of 10 MPa. The MIF values were presented as 3.88 and 1.88 for PET and PP geogrids, respectively. The modulus values in Saride et al. (2022) were determined from tests where the load is applied to a single point location at a rate of 0.5 mm/min. Even though the results clearly show the improvement in modulus due to the presence of geogrids, the testing methodology used does not represent the effects of a wheel that rolls over the surface. The previous literature does not provide the evidence for what happens if the MIF was determined from conditions that simulated the rolling of a wheel as opposed to from tests that are applied to a single location.
The focus of this study was to use the same approach as Akmaz et al. (2025) but in conditions when a geogrid is used in pavement applications. The goal was to evaluate whether or not the proposed methodology is able to capture the improved modulus when geogrids are used and that different types of geogrids result in different MIF values.
2. MATERIALS AND METHODOLOGY
2.1. Large scale model experiment: Configuration and materials
A test pit located at the George Mason University’s Sustainable Geo Infrastructure Laboratory, 80 cm wide, 120 cm long, and 90 cm high, was utilized as the testing platform. Figure 1 shows the layout of the test pit that consisted of 40 cm thick, soft subgrade and up to 20 cm thick aggregate base course. The dimensions of the test pit were intentionally selected to minimize boundary effects. As demonstrated in the prior study by Akmaz et al. (2020), conducting LWD tests at the center of this specific test pit ensures that the results are not affected by the surrounding boundaries.
The image illustrates a cross sectional view of a structural foundation with and without a geogrid. The left side features a concrete wall, while the bottom shows a concrete foundation. The vertical distance between the concrete wall and the ground is marked, indicating measurements of 5, 10, 15 and 20 centimetres. A layer of virgin aggregate is displayed above the subgrade, which has a thickness of 40 centimetres. The diagram includes labels for each of these components, clearly indicating their arrangement and dimensions, which aids in understanding the foundation structure.Setup of the test pit used for tests
The image illustrates a cross sectional view of a structural foundation with and without a geogrid. The left side features a concrete wall, while the bottom shows a concrete foundation. The vertical distance between the concrete wall and the ground is marked, indicating measurements of 5, 10, 15 and 20 centimetres. A layer of virgin aggregate is displayed above the subgrade, which has a thickness of 40 centimetres. The diagram includes labels for each of these components, clearly indicating their arrangement and dimensions, which aids in understanding the foundation structure.Setup of the test pit used for tests
Low plastic silt with sand (classified as ML according to ASTM D2487-17) was used as the subgrade material. As shown in Table 1, the soil contained 67% fine particles (ASTM D7928-21e1), had a liquid limit of 43, plastic limit of 31, and a plasticity index of 12 (ASTM D4318-17e1). The subgrade was placed to create a very soft layer that reflects the conditions observed in soils with a California Bearing Ratio (CBR) value of 1% (ASTM D1883-21). Considerable effort was devoted to constructing a consistent subgrade for each test section. The soft subgrade condition was achieved by adjusting the soil’s moisture content to 30% and compacting it to a dry unit weight of 15.6 kN/m³. A moisture barrier was installed along the base and sidewalls of the test pit to prevent moisture loss and maintain the desired water content throughout the testing period. The subgrade was placed in 5 cm lifts to a total thickness of 40 cm. For each lift the volumes corresponding to the target lift thickness were pre-marked on the test pit walls. Based on these volumes, corresponding predetermined mass to meet the target dry density was placed in the test pit. Compaction with a plate hammer was conducted until the top of the placed soil reached the pre-marked level in the test pit. Moisture content and dry density were checked frequently in every lift, and at least ten Dynamic Cone Penetrometer (DCP) tests per lift were performed. DCP data were converted to CBR, with known limitations for fine-grained soils at high moisture addressed by enforcing an acceptance envelope and reworking outliers. Further methodological details can be found in the study by Akmaz et al. (2025).
Properties of geogrids used in this study
| Geogrid | Material | Ultimate tensile strength (kN/m) | Junction efficiency (%) | Aperture shape | |
|---|---|---|---|---|---|
| MD | XMD | ||||
| Geogrid 1 | Polyester (knitted) | 30 | 30 | N/A* | Biaxial |
| Geogrid 2 | Polypropylene (knitted) | 20 | 20 | N/A* | Biaxial |
| Geogrid 3 | Polypropylene (extruded) | N/A** | N/A** | 93 | Triaxial |
| Geogrid 4 | Polypropylene (extruded) | 12.4 | 19 | 93 | Biaxial |
N/A: Not available, *not reported by the manufacturer, **tensile strength of the multiaxial geogrids cannot be tested
The aggregate used in this study satisfied the gradation of typical base course material classified as 21 A aggregate with 12% fines as defined by Virginia Department of Transportation (VDOT) agency (VDOT 2016). The aggregate was compacted to satisfy the relative compaction of 100% as determined from the vibratory hammer method based on ASTM D7382-20. The base course was constructed following a standardized, repeatable sequence. For each test, aggregate was placed in the test pit in 5 cm lifts following the same placement procedures as conducted for subgrade. In reinforced sections, the geogrid was placed directly on the finished subgrade surface and immediately covered with a 5 cm loose aggregate lift. Care was given to confirm that the final surface of aggregate was horizontal before any LWD tests started. Additional details regarding the methodology and material specifications can be found in the published work of Akmaz et al. (2025).
Four different geogrids were placed in between the subgrade and base course. Table 1 shows the properties of geogrids used in this study as reported by the manufacturers. The geogrids were selected to represent both knitted and extruded production types as well as biaxial and triaxial aperture shapes and polyester and polypropylene materials. The actual names of these products used in the market are not shared to prevent any referrals to a specific brand. Figure 2 shows the photos of the geogrids selected for this study and the naming assigned to each geogrid type.
The image contains four close up photographs of various grid like structures arranged in a two by two formation. The images are labelled a, b, c and d, with each grid featuring distinct patterns. The top row shows two grids with a square mesh design, while the bottom row presents a more complex pattern in c resembling a diamond formation and a simpler grid in d. Each grid is outlined with a blue border and set against a light background that enhances the visibility of the patterns. The grids may represent different materials or designs used in various applications.Geogrids used in this study (a) Geogrid 1, (b) Geogrid 2, (c) Geogrid 3, and (d) Geogrid 4
The image contains four close up photographs of various grid like structures arranged in a two by two formation. The images are labelled a, b, c and d, with each grid featuring distinct patterns. The top row shows two grids with a square mesh design, while the bottom row presents a more complex pattern in c resembling a diamond formation and a simpler grid in d. Each grid is outlined with a blue border and set against a light background that enhances the visibility of the patterns. The grids may represent different materials or designs used in various applications.Geogrids used in this study (a) Geogrid 1, (b) Geogrid 2, (c) Geogrid 3, and (d) Geogrid 4
2.2. Large scale model experiment: Applied load conditions
The load application was achieved by using a single LWD (as in traditional testing approaches) and three LWDs that are placed side by side and loaded sequentially. Dynatest LWD, model no. 3032 was used for these tests. The layout of the three LWDs is shown in Figure 3.
The image depicts two models, a field moving vehicle model on the left and a laboratory testing model on the right. The field model shows three vehicle wheels positioned over a surface labelled First, Second and Third, with annotations indicating the vehicle approaching point A, on point A and leaving from point A, represented with arrows. The laboratory model features three vertical structures also labelled First, Second and Third, above which are annotations explaining the drop of weight to represent vehicles coming to and leaving point A. Both models are arranged on a grey surface featuring a marked point A at the centre. The layout emphasises the functional relationship of vehicle movements in both scenarios.Comparison of LWD setup in the test pit with actual movement of rolling wheel from a moving vehicle
The image depicts two models, a field moving vehicle model on the left and a laboratory testing model on the right. The field model shows three vehicle wheels positioned over a surface labelled First, Second and Third, with annotations indicating the vehicle approaching point A, on point A and leaving from point A, represented with arrows. The laboratory model features three vertical structures also labelled First, Second and Third, above which are annotations explaining the drop of weight to represent vehicles coming to and leaving point A. Both models are arranged on a grey surface featuring a marked point A at the centre. The layout emphasises the functional relationship of vehicle movements in both scenarios.Comparison of LWD setup in the test pit with actual movement of rolling wheel from a moving vehicle
The LWD equipment used in this study was capable of applying 200 kPa maximum stress with depth of influence of 30 cm when the equipment is used with a 30 cm plate (Dynatest 2010). LWD equipment is designed to provide elastic modulus, which requires the equipment to operate within the elastic range (Khosravifar 2015; Kumar et al. 2017; Marecos et al. 2017, and Tamrakar and Nazarian 2018). The LWD equipment that was used in this study was configured by the manufacturer to record deformations that occur right underneath the surface of the equipment from a single drop. The elastic modulus was only provided by the equipment if the recorded deformations do not exceed 3 mm. This condition limits the maximum load that can be applied during testing. This keeps the stress-strain behavior primarily within the elastic range (Dynatest 2010). The dead weight used for all LWD tests in this study was 20 kg; however, the applied load magnitude could be adjusted by dropping the weight of the LWD from a lower height in order to ensure the deformations do not exceed 3 mm. The thickness of the soft subgrade was selected to be greater than 30 cm so that the measured parameters by the LWD are not affected by the presence of the concrete floor. The thicknesses of the base course were kept less than 30 cm to allow the parameters measured by the LWD to be affected by the presence of geogrids and the soft subgrade.
In all tests, the measurements were only recorded from one LWD device. In the multi-point LWD tests, the devices were arranged in close proximity without allowing the loading plates to touch each other. The tests were performed sequentially, by manually operating the equipment to drop weights beginning with the second LWD, followed by the third and first, and then repeated in the same sequence. This testing pattern was designed to simulate the rolling action of a vehicle wheel over the ground surface. Data was only recorded from the LWD located in the middle of the three LWDs (shown as second LWD in Figure 3). Further details of the test configuration and methodology are documented in Akmaz et al. (2025). All tests were conducted with dropping weight from all LWD equipment 100 times. Tests were conducted with 5, 10, 15, and 20 cm thick base course layers to understand the effects of the base course thickness on modulus. For the geogrid reinforced tests, the same base course thicknesses were used. It is important to note that, for each test, the test pit was completely emptied and re-built so that each loading condition was applied to virgin ground (with and without geogrid).
2.3. Large scale model experiment: Data analysis
LWD equipment used in this study was capable of internally storing the “stress vs. time” and “elastic deformation vs. time” values within 60 ms data collection time. The equation used to calculate modulus is provided in Dynatest (2010). Additionally, a damping ratio can also be calculated from the LWD data for each test, and it was seen that the results differ if the ground is tested with a single LWD versus three LWDs. This study was conducted to observe whether this behavior also holds true in the presence of geogrids. Therefore, in this study, a comparison of the damping ratio values with and without geogrid and with single and three LWDs were also evaluated.
Based on the selected base course thicknesses in this study (less than 30 cm), the modulus obtained from LWD tests conducted on the surface of the base course indicates the overall modulus of the system (which includes both the subgrade and the base course with and without the geogrid). Although such data is useful, in most pavement design applications, the user is required to know the modulus of each layer (not the combined modulus). Therefore, in order to compare the modulus of the base course with and without the presence of geogrid, the effects of the subgrade from the combined modulus have to be extracted out. This is achieved by using a software known as KenPave, which allows the users to create models with subgrade and base course with different thicknesses and compute stresses, strains, and elastic deformations at any location within the modeled profile (Huang 2004). Figure 4 presents the method used to conduct the KenPave analysis in this study to back-calculate the modulus of the base course (with and without the geogrid). It is important to note that KenPave requires the subgrade layer to be modeled as semi-infinite. This means no stress or strain reflects from a boundary below the modeled subgrade and the stresses are absorbed within the layer without reflecting. As shown in Figure 1, the thickness of the subgrade in the test pit was 40 cm and the maximum depth of influence from the LWD equipment is 30 cm. Therefore, the constructed subgrade thickness satisfied the semi-infinite condition. KenPave assumes all modeled layers to be linear elastic, isotropic, and homogenous. This assumption may not be valid to evaluate conditions when plastic deformations are expected. The premise of the in-situ tests such as LWD and FWD is to provide elastic modulus, which can only be achieved if the testing conditions result in elastic response. Therefore, it is important to note that the outcomes of the KenPave analyses presented apply to purely elastic conditions that were evaluated in this study.
This diagram presents a test pit methodology for analysing pavement structures in the context of the K E N P A V E model. On the left it describes parameters such as P max, t Base and E Subgrade, which are established through direct measurements or known values. The left section includes a graphical representation of the surface deflection d L W D as influenced by depth and displacement, emphasising the depth of influence. On the right the K E N P A V E methodology is outlined, indicating how E Base can be iteratively adjusted until the condition d K E N P A V E equals d L W D is met. The layout showcases relationships between various parameters, with equations and directional indicators guiding the reader through the calculation process. Elements such as arrows and boxed text visually clarify the flow of information and relationships among the variables.Method used in KenPave analysis to determine the modulus of the base course (EBase)
This diagram presents a test pit methodology for analysing pavement structures in the context of the K E N P A V E model. On the left it describes parameters such as P max, t Base and E Subgrade, which are established through direct measurements or known values. The left section includes a graphical representation of the surface deflection d L W D as influenced by depth and displacement, emphasising the depth of influence. On the right the K E N P A V E methodology is outlined, indicating how E Base can be iteratively adjusted until the condition d K E N P A V E equals d L W D is met. The layout showcases relationships between various parameters, with equations and directional indicators guiding the reader through the calculation process. Elements such as arrows and boxed text visually clarify the flow of information and relationships among the variables.Method used in KenPave analysis to determine the modulus of the base course (EBase)
The input data for the KenPave analyses included the LWD modulus of the soft subgrade (Esubgrade), base course thickness (tBase), maximum applied load from the LWD test on the base course surface (Pmax) that corresponded to the particular base course thickness, and the recorded elastic deflection from the LWD test (δLWD). The modulus of the base course layer in KenPave was iteratively changed until the computed elastic deformation at the surface of the base course layer matched δLWD. The resulting modulus is determined as the base course with and without the geogrid depending on the input parameters used from different LWD tests conducted in the test pit (with and without geogrid).
3. RESULTS
3.1. Suitability of simulated rolling wheel load applications to evaluate the inclusion of geogrids
Damping ratio values provide guidance to explain the reasons of the differences in elastic modulus with increased number of load repetitions. Therefore, in order to evaluate the suitability of the testing method, it is important to first look at the damping ratio results with and without geogrids. Figure 5 presents an example result of damping ratio values obtained from geogrid reinforced and unreinforced tests with single LWD. It is known that lower damping ratio values indicate stiffer ground conditions. Figure 5 shows that the presence of geogrid provides stiffness to the ground, which is reflected in the lower damping ratio values compared to the condition with no geogrid. Results in both conditions (reinforced and unreinforced) as presented in Figure 5 show reductions in the damping ratio with the increase in load repetitions. This observation indicates that the ground is getting stiffer with increased number of load applications whether or not geogrid reinforcement is used. The observation that the stiffness increases with the increase in number of load applications is consistent with what is observed from APLT results, where the increased number of load cycles for both geogrid reinforced and unreinforced conditions show improvement (Tamrakar et al. 2019).
The image shows a graph with the vertical axis labelled as Damping ratio ranging from 0.05 to 0.25, while the horizontal axis is labelled L W D drops ranging from 0 to 100. There are two sets of triangular data points, one in black and one in white, representing different conditions labelled as Geogrid and No geogrid. The data points exhibit a downward trend for both conditions as L W D drops increase. The black data points represent values under geogrid conditions and the white data points represent values without geogrid. Two annotations indicate the two conditions where data points are labelled accordingly. Some of the points show visible clustering around certain values.Comparison of the damping ratio values from tests with and without geogrid based on single location LWD testing
The image shows a graph with the vertical axis labelled as Damping ratio ranging from 0.05 to 0.25, while the horizontal axis is labelled L W D drops ranging from 0 to 100. There are two sets of triangular data points, one in black and one in white, representing different conditions labelled as Geogrid and No geogrid. The data points exhibit a downward trend for both conditions as L W D drops increase. The black data points represent values under geogrid conditions and the white data points represent values without geogrid. Two annotations indicate the two conditions where data points are labelled accordingly. Some of the points show visible clustering around certain values.Comparison of the damping ratio values from tests with and without geogrid based on single location LWD testing
Figure 6 presents the results obtained from the same large scale model configuration as in Figure 5 but the load was applied with three LWDs sequentially. The results shown in Figure 6 from the unreinforced case show that with the initial load, the damping ratio decreases, indicating that the ground initially shows a behavior similar to compaction. However, as the number of load cycles continues to increase, the damping ratio starts to increase, which indicates that the ground is destabilizing. This destabilizing behavior is an expected condition under rolling wheel as described by Dareeju et al. (2015). After a certain number of load cycles, the behavior stabilizes. When a geogrid is present, the damping ratio values remain almost the same regardless of the number of load repetitions. At the end of 100 load cycles, it was observed that the geogrid reinforced base course has a lower damping ratio compared to the unreinforced ground. This is because the geogrid successfully stabilizes the base course and prevents the destabilization with the number of load repetitions. When the damping ratio values are compared, the results show that the presence of geogrid provides stiffness to the ground. However, when the results from Figures 5 and 6 are compared, the damping ratio of the geogrid reinforced ground is larger with the three LWD tests. This result also shows the effects of compaction of the ground by the single point LWD load applications. Hence, the method suggested by Akmaz et al. (2025) also holds true for the conditions where there is geogrid present in the ground. Based on these observations, the remainder of the tests were conducted with three LWDs loaded sequentially, simulating the effects of the rolling wheel.
The image depicts a scatter plot graph with the vertical axis representing damping ratio, ranging from 0.05 to 0.25, and the horizontal axis indicating L W D drops, spanning from 0 to 100. The data points feature two types distinguished by their shape, solid black circles signify the Geogrid group, while open circles denote the No geogrid group. Two annotations indicate the points associated with each condition, showing a slight distinction in trends between the two datasets across the range of L W D drops. The data flows left to right along the horizontal axis, providing a comparison of the damping ratios as the number of L W D drops increases.Comparison of damping ratio values with and without geogrid based on three LWD equipments loaded sequentially
The image depicts a scatter plot graph with the vertical axis representing damping ratio, ranging from 0.05 to 0.25, and the horizontal axis indicating L W D drops, spanning from 0 to 100. The data points feature two types distinguished by their shape, solid black circles signify the Geogrid group, while open circles denote the No geogrid group. Two annotations indicate the points associated with each condition, showing a slight distinction in trends between the two datasets across the range of L W D drops. The data flows left to right along the horizontal axis, providing a comparison of the damping ratios as the number of L W D drops increases.Comparison of damping ratio values with and without geogrid based on three LWD equipments loaded sequentially
3.2. Modulus values recorded from LWD tests in this study
Prior to any base/geogrid testing, the subgrade was completely rebuilt five times and repeat LWD tests using a multi-point protocol were conducted in the test pit directly on the surface of the freshly constructed 40 cm-thick subgrades. In all tests, the maximum applied load (resulting in deformations not exceeding 3 mm) was almost exactly the same resulting in very similar modulus values. Based on the results, the representative average modulus of the subgrade is determined as 5.7 MPa. This subgrade modulus value is within the expected range of modulus values cited in the literature for very soft subgrade (VanTil et al. 1972; AASHTO 1993; and Huang 2004).
For the geogrid/aggregate experiments, the same mass-controlled placement and DCP-based acceptance were repeated to replicate the verified subgrade state; however, LWD tests directly on the subgrade surface were avoided to prevent disturbing the soft conditions created for subgrade layer.
Table 2 displays the maximum load that could be applied to each base course layer that was constructed over the soft subgrade with no geogrid and four different geogrids. These maximum loads were determined to keep the behavior elastic, meaning the maximum corresponding LWD deformations does not exceed 3 mm in all tests. The results show that for each geogrid (regardless of the type), as the thickness of the base course increases, the magnitude of the maximum applied load that would keep the test in elastic range increases. This is an expected behavior because the effects of the applied load onto the soft subgrade decreases with increasing base course thickness. However, for each thickness, depending on the type of the geogrid, the maximum allowable applied load is slightly different from each other but in all cases is greater than the no geogrid condition.
Maximum allowable applied load on base course with LWD tests in this study
| Test section | Base course thickness (cm) | |||
|---|---|---|---|---|
| 5 | 10 | 15 | 20 | |
| Maximum applied load (kPa) | ||||
| No Geogrid | 80 | 100 | 122 | 138 |
| Geogrid 1 | 91 | 126 | 148 | 172 |
| Geogrid 2 | 89 | 120 | 142 | 165 |
| Geogrid 3 | 88 | 118 | 138 | 162 |
| Geogrid 4 | 87 | 113 | 136 | 160 |
Figure 7 shows the elastic modulus values obtained from the LWD equipment after the 100 weight drops for each base course thickness. The figure consistently shows the improvement of elastic modulus with geogrid. This indicates that in all tests, the applied load conditions and the thicknesses of the base course were appropriately selected to engage the geogrid reinforcement over the soft subgrade created in this study.
The image features a bar chart illustrating the performance of various geogrids under four different base courses, 20 centimetres, 15 centimetres, 10 centimetres and 5 centimetres. Each base course is represented in a separate section of the chart, with the vertical axis indicating the measured values, ranging from 0 to 20. Bars labelled No geogrid, Geogrid 1, Geogrid 2, Geogrid 3 and Geogrid 4 show the comparative data across each base course. The data flows from left to right, with each section having a consistent layout for easier comparison of the different geogrid types.Elastic modulus values from LWD tests in this study with the influence of the underlying soft subgrade below the base course with and without geogrid
The image features a bar chart illustrating the performance of various geogrids under four different base courses, 20 centimetres, 15 centimetres, 10 centimetres and 5 centimetres. Each base course is represented in a separate section of the chart, with the vertical axis indicating the measured values, ranging from 0 to 20. Bars labelled No geogrid, Geogrid 1, Geogrid 2, Geogrid 3 and Geogrid 4 show the comparative data across each base course. The data flows from left to right, with each section having a consistent layout for easier comparison of the different geogrid types.Elastic modulus values from LWD tests in this study with the influence of the underlying soft subgrade below the base course with and without geogrid
The modulus values shown in Figure 7 also show that with increase in thickness of the base course the modulus values also increase. This is because these modulus values represent the conditions that combine the presence of both the soft subgrade and base course. Therefore, these modulus values do not represent the modulus of the base course without the effects of the soft subgrade.
3.3. Back calculated elastic modulus for base course with and without geogrid
Table 3 was created to demonstrate how the test results obtained from the multi-point tests in this study may be used as an input to KenPave analyses, which may then be used to estimate an elastic modulus value of the base course that disassociates the effects of the soft subgrade. These elastic modulus values are referred to herein as back calculated elastic modulus (EBase). Table 3 shows that the EBase results were slightly different from each other for each base course thickness for a given condition but overall, the values are very close. This is an expected outcome because in this study, in all cases, the maximum applied load that corresponds to a specific base course thickness was limited to keep an elastic behavior (conditions that would result in nonlinear stress dependent behavior were not investigated). Furthermore, all layers in the test pit were constructed with the same material and under similar compaction and moisture. Therefore, based on the test results in this study and the assumptions of the KenPave analyses, the results in Table 3 show that changing the thickness alone does not inherently change the EBase, when the base course shows purely elastic behavior. This finding is consistent with the outcomes of the previous studies conducted by Schwartz (2007), and Huang (2004).
Back calculated elastic modulus from KenPave analysis for each geogrid and no geogrid sections
| Type of geogrid | Base course thickness (cm) tBase | Subgrade elastic modulus (MPa) ESubgrade | Max applied load (kPa) Pmax | Max deflection recorded (micron) δ LWD | Max deflection predicted (micron) δ KENPAVE | Back calculated elastic modulus (MPa) EBase | Average back calculated elastic modulus (MPa) EBase |
|---|---|---|---|---|---|---|---|
| No Geogrid | 20 | 5.7 | 138 | 2917 | 3021 | 35.9 | 36 |
| 15 | — | 122 | 2987 | 3008 | 36.1 | — | |
| 10 | — | 100 | 2979 | 2998 | 35.8 | — | |
| 5 | — | 80 | 3029 | 2993 | 36.2 | — | |
| Geogrid 1 | 20 | 5.7 | 172 | 3079 | 3012 | 59.1 | 59 |
| 15 | — | 148 | 3049 | 3017 | 58.8 | — | |
| 10 | — | 126 | 2978 | 2997 | 59.3 | — | |
| 5 | — | 91 | 2939 | 2991 | 59.1 | — | |
| Geogrid 2 | 20 | 5.7 | 165 | 3012 | 3013 | 56.0 | 56 |
| 15 | — | 142 | 2934 | 3007 | 55.6 | — | |
| 10 | — | 120 | 2974 | 2996 | 56.2 | — | |
| 5 | — | 89 | 3007 | 3018 | 56.3 | — | |
| Geogrid 3 | 20 | 5.7 | 162 | 3098 | 2989 | 52.8 | 53 |
| 15 | — | 138 | 3018 | 2978 | 53.3 | — | |
| 10 | — | 118 | 2961 | 3018 | 53.0 | — | |
| 5 | — | 88 | 2917 | 3001 | 53.3 | — | |
| Geogrid 4 | 20 | 5.7 | 160 | 3102 | 2997 | 49.9 | 50 |
| 15 | — | 136 | 2925 | 3078 | 50.0 | — | |
| 10 | — | 113 | 2976 | 3037 | 50.3 | — | |
| 5 | — | 87 | 3039 | 3029 | 50.1 | — |
4. PRACTICAL IMPLICATIONS
Two different demonstrations are presented in this study to show practical implications that may be derived from the outcomes of the newly proposed test method to assess the contribution of the geogrid to base course performance.
4.1. Quantifying the difference in geogrid contribution to elastic modulus
Based on the values presented in Table 3, it is possible to characterize the modulus of each test condition with an average representative value for the purposes of this study. These values are listed as the average EBASE in the far-right column of Table 3. These average EBase values in Table 3 show that even though for all geogrid conditions the modulus values are higher than no geogrid condition; for each geogrid, average EBase is slightly different to the other. If the EBase values from geogrid and no geogrid conditions are compared to each other, an expression such as modulus improvement factor (MIF) may be developed to assess the contribution of each geogrid to improve elastic modulus.
Table 4 presents the calculated MIF values for each geogrid type tested in this study. Being able to develop MIF values allows the discussion of the potential reasons why differences in elastic modulus from one geogrid to another may possibly exist. For example, the difference between MIF from geogrid 1 and geogrid 2 (one is polyester and other is a polypropylene, both have the same aperture geometry, and both are considered relatively flexible) shows that the tensile strength of the material is potentially an effective parameter on the behavior. The comparison between geogrid 3 and geogrid 4 (both relatively rigid) shows the effects of the geometry of the geogrid, where the triaxial shape results in better MIF than the biaxial shape. However, when the results from geogrids 3 and 4 are compared against geogrids 1 and 2, the results show that the knitted geogrids appear to result in higher MIF than the extruded geogrids. A similar observation was also noted by Saride et al. (2022). One of the reasons for this difference could be that knitted geogrids tend to be more flexible and this results in more effective engagement with the granular material. This fact was also supported by the observations made in this study during the installation at the beginning and dismantling of the layers at the end of each test. Lackner (2012) also observed that flexible geogrids align well around the granular soil particles and thereby the geogrid provides a higher horizontal and vertical resistance.
Modulus improvement factor (MIF) for each type of geogrid tested in this study
| Geogrid vs No geogrid | Back calculated elastic modulus of base course (MPa) (EBase) | Modulus improvement factor (MIF) (EGeogrid/ENoGeogrid) | Improvement in modulus (%) |
|---|---|---|---|
| Geogrid 1 | 59 | 1.64 | 64 |
| No Geogrid | 36 | — | — |
| Geogrid 2 | 55 | 1.53 | 53 |
| No Geogrid | 36 | — | — |
| Geogrid 3 | 53 | 1.47 | 47 |
| No Geogrid | 36 | — | — |
| Geogrid 4 | 50 | 1.39 | 39 |
| No Geogrid | 36 | — | — |
EGeogrid represents the EBase for the model with geogrid and ENoGeogrid represents the EBase for the model with no geogrid
4.2. Quantifying the difference in geogrid contribution based on different base course thicknesses
It is a known fact that the geogrids contribute the most to improving the base course performance when the subgrade is very soft (Nazzal 2007; Tang et al. 2009). That is why the tests conducted in this study were based on very soft subgrade conditions. It is also commonly stated that as the thickness of the base course increases the contribution of the geogrid decreases (Haas et al. 1988; Al-Qadi et al. 1994; Perkins 1999). This statement is straightforward if the magnitude of the applied load is kept constant with each base course thickness. In this study, the magnitude of the applied load was increased with increased base course thickness. This creates a complex scenario because the MIF values shown in Table 4 indicate that the contribution of the geogrid to improve the base course modulus does not change based on the base course thickness as long as the system behaves purely elastically. However, it is also important to evaluate the changes that occur in stress distribution at the zone where the geogrid is placed. KenPave analyses may be used (based on the method described in Figure 4) to calculate the stress at the interface between the base course and subgrade (where the geogrid is placed). Table 5 shows an example dataset with no geogrid, where the far right two columns compare the magnitude of the actual applied test load in this study and the calculated load at the interface between the base course and the subgrade. This comparison shows that, for example, at 5 cm base course thickness, almost 94% of the applied load transfers to the top of the subgrade (i.e. the stress on the subgrade decreases from 80 to 75 kPa). As the base course thickness is increased to 20 cm, the magnitude of the load that transfers to the subgrade reduces to 26% of the applied load (i.e. decreases from 138 to 36 kPa). Based on this demonstration, it can be stated that as the thickness of the base course increases the stress distribution to the zone where the geogrid is placed decreases. However, Table 2 shows that the difference between the maximum applied loads in this study for geogrid and no geogrid conditions does not systematically decrease with increased base course thickness. Therefore, as long as the top of the subgrade experiences more than 0 stress, the geogrid still contributes to the improvement of the base course modulus. Therefore, to bluntly state that “as the thickness of the base course increases the contribution of the geogrid decreases” may not be appropriate for conditions where the applied load also increases with the increase in base course.
Example of computed stresses from KenPave analyses based on test results in this study (No geogrid)
| Base course thickness (tBase) (cm) | Base course elastic modulus (EBase) (MPa) | Subgrade elastic modulus (ESubgrade) (MPa) | Max. applied load on base course (pmax) (kPa) | Calculated load on subgrade (PSubgrade) (kPa) |
|---|---|---|---|---|
| 5 | 35.9 | 5.7 | 80 | 75 |
| 10 | 36.1 | — | 100 | 59 |
| 15 | 35.8 | — | 122 | 47 |
| 20 | 36.2 | — | 138 | 36 |
In practice, both the thickness of the base course and the load that is acting on the surface of the base course may be higher than what was achieved in the tests conducted in this study. For these conditions (e.g. increased base course and increased applied load), if the stress at the interface of the base course/subgrade is evaluated, a relationship may be developed to determine at what base course thickness the contribution of the geogrid should no longer be expected (where the applied load at the top of the base course dissipates to 0 by the time it reaches the top of the subgrade). KenPave may also be used to estimate the stress distributions for these scenarios, however these analyses cannot be conducted with the same method described in Figure 4. Figure 8 presents the steps to conduct such analyses with KenPave based on the following assumptions:
All layers behave in a linear elastic, homogenous, and isotropic way (nonlinear response is not considered).
Theoretical maximum load (Pmax) that may be applied to the surface of the base course will be limited to keep the behavior of the base course elastic.
Elastic behavior of the base course is achieved as long as the surface deflections (δ) stay within 3 mm (3,000 micron).
The geogrid will continue to interact with the base course as long as the stress on the geogrid surface (or at the interface of subgrade and base course) is greater than 0.
The modulus of the base course (EBase) (with and without geogrid) does not change as a function of base course thickness as demonstrated in Table 3.
The image presents a diagram of a test pit setup used in pavement engineering. At the top, the title T E S T P I T is displayed, accompanied by an arrow pointing to the variables. The diagram features a graphic of a layered structure where the top layer indicates stress distribution with an arrow labelled P max pointing downwards. The surface deflection is represented by the symbol d, indicating changes in the surface due to load. Below the top layer, constants for measured and back calculated elastic moduli, E Subgrade and E Base, are noted with their respective formulas citing Table 3. Additionally, variables are detailed, including t Base, which is selected for computations, and P max, which is modified iteratively until the computed surface d achieves a target of 3000 microns. The output values d K E N P A V E for calculated surface deflection and P Subgrade for computed load at the subgrade and base course interface are also highlighted, integrating information from the graph and text. The layout segments these concepts clearly, aiding in understanding complex relationships in the context provided.Steps followed in KenPave analysis to determine thickness of base course (tBase) required to result in zero stress on subgrade/base course interface
The image presents a diagram of a test pit setup used in pavement engineering. At the top, the title T E S T P I T is displayed, accompanied by an arrow pointing to the variables. The diagram features a graphic of a layered structure where the top layer indicates stress distribution with an arrow labelled P max pointing downwards. The surface deflection is represented by the symbol d, indicating changes in the surface due to load. Below the top layer, constants for measured and back calculated elastic moduli, E Subgrade and E Base, are noted with their respective formulas citing Table 3. Additionally, variables are detailed, including t Base, which is selected for computations, and P max, which is modified iteratively until the computed surface d achieves a target of 3000 microns. The output values d K E N P A V E for calculated surface deflection and P Subgrade for computed load at the subgrade and base course interface are also highlighted, integrating information from the graph and text. The layout segments these concepts clearly, aiding in understanding complex relationships in the context provided.Steps followed in KenPave analysis to determine thickness of base course (tBase) required to result in zero stress on subgrade/base course interface
Table 6 presents the results of the KenPave analyses to determine the changes in the calculated stresses at the interface of the base course/subgrade (PSubgrade) as a function of the base course thickness (tBase) and the magnitude of the applied load (Pmax). The average ESubgrade and EBase values used for these analyses are shown in Table 3. For a given tBase, Pmax has been iteratively increased until the calculated deflection at the ground surface is within the 3,000 micron range. Table 6 only shows the data for the no geogrid conditions. Similar calculations were also conducted for the different geogrids tested in this study based on the EBase values shown in Table 3.
Example of computed stresses from KenPave analyses to keep base course elastic (No geogrid)
| Input | Constants | Iterated input | Target | Computations | ||
|---|---|---|---|---|---|---|
| Base course thickness (tBase) (cm) | Base course elastic modulus (EBase) (MPa) | Subgrade elastic modulus (ESubgrade) (MPa) | Max. Applied load on base course (pmax) (kPa) | Surface deflection (δ) (micron) | Calculated surface deflection (δKenPave) (micron) | Calculated load on subgrade (PSubgrade) (kPa) |
| 25 | 36 | 5.7 | 160 | 3000 | 3018 | 30 |
| 30 | — | — | 175 | — | 3012 | 25 |
| 38 | — | — | 200 | — | 3083 | 19 |
| 45 | — | — | 215 | — | 2998 | 17 |
| 50 | — | — | 230 | — | 3007 | 14 |
| 55 | — | — | 240 | — | 3003 | 10 |
| 60 | — | — | 260 | — | 2988 | 8 |
| 65 | — | — | 280 | — | 2991 | 2 |
| 77 | — | — | 319 | — | 2986 | 0 |
Figure 9 presents the relationship developed between the maximum stress that can be applied on the base course surface (Pmax) and the thickness of the base course (tBase) required to engage the geogrid and keep the base course behaving elastically. The points in Figure 9 for the 5, 10, 15, and 20 cm are directly from the test results conducted from this study. The points for all other thicknesses come from KenPave analyses as shown in the example presented in Table 6. The linear relationships were developed based on all of the points shown for each condition.
The graph illustrates the relationship between stress on the base course measured in kilopascals and base course thickness measured in centimetres. The vertical axis shows stress values ranging from 50 to 400 kilopascals with increments of 25. The horizontal axis indicates base course thickness from 0 to 90 centimetres. Five distinct lines represent different data sets, Geogrid 1, Geogrid 2, Geogrid 3 and Geogrid 4, each accompanied by corresponding equations of the form y equals m times x plus b, where m denotes the slope and b the y intercept, along with R squared values indicating the fit of each line to the data. The No geogrid line is also included with its equation and R squared value. Each line has a distinct colour and visual style, indicating varying stress levels associated with base course thickness under different conditions.Relationship between base course thickness and maximum allowed stress on base course
The graph illustrates the relationship between stress on the base course measured in kilopascals and base course thickness measured in centimetres. The vertical axis shows stress values ranging from 50 to 400 kilopascals with increments of 25. The horizontal axis indicates base course thickness from 0 to 90 centimetres. Five distinct lines represent different data sets, Geogrid 1, Geogrid 2, Geogrid 3 and Geogrid 4, each accompanied by corresponding equations of the form y equals m times x plus b, where m denotes the slope and b the y intercept, along with R squared values indicating the fit of each line to the data. The No geogrid line is also included with its equation and R squared value. Each line has a distinct colour and visual style, indicating varying stress levels associated with base course thickness under different conditions.Relationship between base course thickness and maximum allowed stress on base course
The practical implication of developing a figure such as Figure 9 can be demonstrated in two different approaches:
For a given stress that is anticipated to act on the base course, the necessary base course thickness that would keep the base course elastic could be obtained for both geogrid reinforced and unreinforced cases. For example, if the load on the base course was anticipated as 300 kPa, the minimum thicknesses should be targeted to 52 cm, 55 cm, 57 cm, and 60 cm for geogrids 1, 2, 3, and 4, respectively. This thickness would be 71 cm if no geogrid was used between the interface of the subgrade and base course.
For a given base course thickness, the maximum stress that can be applied on the surface of the base course that would still keep the base course elastic can be estimated. For example, if the base course thickness was targeted to be 40 cm, the maximum stress on the base course that should be allowed would be 250, 241, 234, and 227 kPa for the geogrids 1, 2, 3, and 4, respectively. This stress magnitude should be limited to 200 kPa, if no geogrid was used between the interface of the subgrade and base course.
5. CONCLUSIONS
This study aimed to assess the validity of the testing methodology previously developed by Akmaz et al. (2025), with a focus on determining whether it is also suitable for evaluating the elastic modulus of a base course constructed over a soft subgrade and reinforced with geogrids. The primary conclusion of this study is that the new testing methodology based on multi-point LWD is applicable to evaluate the contributions of geogrid to improve the modulus of the base course, when the base course is constructed over soft subgrade. The data also shows that not only is this new method applicable to evaluate the contributions of the geogrid but a better approach than LWD tests can also be conducted by applying load at single point locations.
The results presented in this study show that utilizing damping ratio as a tool to evaluate the ground response with and without geogrid provides insights to interpret the modulus values obtained from LWD tests (both for single-point and multi-point tests). Based on damping ratio values, the results from this study show that tests conducted with single-point load application tends to compact the ground even in the presence of the geogrid and therefore the reinforcement effect of the geogrid may not be captured accurately and consistently. However, conducting tests based on the newly developed multi-point methodology appears to simulate the effects of rolling wheel from a moving vehicle. For the cases where there is no geogrid, the damping ratio trends show that even though there could be an initial stiffening response from the initial load, with the continuing repeat loading, overall, the multi-layer system (base course and the underlying soft subgrade) response indicates deterioration until reaching a stable condition. When a geogrid is installed at the interface between the base course and soft subgrade, damping ratio trends do not change significantly with number of applied load cycles. This indicates that the geogrid is successful in preventing the deterioration of the base course and the newly developed method accurately captures this response.
The test results have shown that the elastic modulus values measured were consistently higher when a geogrid is placed between the subgrade and the base course compared to a no geogrid condition. The consistency in results with four very different geogrids validates the applicability of the newly proposed methodology and provides new information to the literature. The results of this study also showed that different geogrids have different reinforcement abilities that are most likely due to the difference in their properties. Although not demonstrated in this study, the testing methodology used may also be implemented in the field after construction of the base course for verification.
This study also demonstrated that if coupled with KenPave analyses, the results of the multi-point tests could also be used towards engineering assessments. However, it is important to note that KenPave analyses assume the layers to be linear elastic, isotropic, and homogenous, which is a valid assumption for purely elastic systems. In the case where plastic deformations are expected, it may be more appropriate to incorporate the nonlinear stress-dependent behavior. Based on the demonstrations in this study, the following conclusions could be derived:
A modulus improvement factor (MIF) can be calculated to quantify the contribution of the different geogrids. The MIF values determined in this study for the tested geogrids ranged between 1.39 and 1.64.
A relationship between the base course thickness and the stresses that should be allowed on the surface of the base course that would keep the base course elastic can be developed. This relationship may then be used to determine a base course thickness for different geogrids that are intended to be used to reinforce soft subgrade.
6. LIMITATIONS OF THE STUDY
It is important to note that the findings and data presented in this study, as in all experimental and numerical studies, are based on the conditions tested and the assumptions made for the calculations. While the findings demonstrate the validity of the proposed testing approach, broader validation is encouraged. Loading conditions that would create plastic deformations are not accounted for in this study as the focus was to evaluate the elastic response of the materials. The values and figures shown in this study were presented to showcase approaches for practical applications that may be used to assess the test data. They are not intended to be used for design. Users are highly encouraged to develop their own relationships based on the relevant assumptions that relate to the conditions that are of interest.
ACKNOWLEDGEMENTS
The cost of the experiments and the materials used for the study were supported by Huesker. The authors greatly appreciate this support. The graduate researcher who worked on this study while at George Mason University was sponsored by the Republic of Türkiye Ministry of National Education.
