Effects of including fully wraparound geogrid layers on the load-bearing capacity and settlement of a strip footing resting on sandy soil

Abstract

In this study, a series of small-scale physical model tests were conducted to investigate the effects of fully wrapped geogrid sheets on the load‒settlement response of medium-dense sandy soil beneath a single-strip foundation. Recent research has provided evidence of how different parameters affect the behavior of dense sandy soil when reinforced with fully wraparound geogrid sheets. Additionally, a parametric analysis was conducted to investigate the influence of various factors on the system. These factors include the presence of a folded geogrid sheet, the depth and length of an embedded wraparound geogrid sheet, the thickness of the fully wrapped geogrid layer, the impact of tensile strains along the geogrid sheet, and the effect of additional confinement pressure. The inclusion of a single sheet of full wraparound geogrid sheets has been found to significantly affect the pressure-bearing capacity of medium-dense sandy soil and settlement beneath the strip footing. The carrying capacity increases by 280%, and the settlement ratios decrease by 50% when using one layer of full wraparound geogrid. Moreover, when using one fully folded geogrid sheet, the strain induced beneath the center of the footing decreases significantly by approximately 45.5% and the applied pressure by approximately 15.5% in comparison with two inclusions of planar geogrid layers. In addition, the stress distributions are spread over a larger region within the soil mass. One significant finding is that the presence of two overlap** parts prevents the rupture of the geogrid sheet, as opposed to the planar geogrid sheet.

Highlights

• The fully folded geogrid layers are designed to improve the bearing capacity and significantly reduce settlement values.

• Using fully folded geogrid sheets greatly affects the distribution of stresses within the soil mass and allows for dissipation at greater depths.

• The inclusion of a fully wraparound geogrid has a significant effect on reducing the strain induced underneath the central area of a strip footing compared to using planar forms.

1 Introduction

Geosynthetic materials can play a significant role in improving the pressure-bearing capacity of weak soils and strengthening many structures of various geotechnical engineering applications. In many cases, however, real project boundary requirements, such as property line disputes and limited ground area, make achieving the ideal width of reinforcement impossible. Wraparound-strengthening technology can be used to strengthen the soil surrounding the structure in the event that a new building is planned near existing structures in the future.

Numerous studies have investigated the enhancement of improving bearings in reinforced soil by using physical experiments. Using laboratory model experiments, Abu-Farsakh [1] examined the effect of including geosynthetic reinforcement sheets on the behavior and performance of sandy soil beds that were reinforced. Ahirwar and Mandal [2] investigated the effect of bamboo grids on the behavior of reinforced sandy soil beds.

The impact of a novel kind of inclusion of geogrid sheets on the carrying capacity of a rigid strip foundation constructed on a sandy slope was discussed by Alamshahi and Hataf [3]. Bazne et al. [4] conducted a study on the impact of geonet reinforcement on the carrying capacity of low-compaction soft clay. Badakhshan et al. [5] studied the effect of eccentrical load on the behavior of square and circular footings resting on geogrid-reinforced sand. Buragadda and Thyagaraj [6] evaluated the optimal geometrical parameters for incorporating a jute geotextile sheet to enhance the load-bearing capacity of the soil.

Cicek et al. [7] demonstrated the influence of the width of reinforcement on the bearing pressure-settlement response of a strip footing placed on sandy soil using different geosynthetic reinforcements. Durga Prasad et al. [8] studied the pressure-settlement behavior of a square footing overlying layered granular foundations with the inclusion of geogrid sheets. The optimal depth of the geogrid sheets for the aggregate layer, which rests on the sand layer, was found to be 0.30 times the width of the footing. Chen et al. [9] carried out a series of plate loading tests on a reduced-scale strip foundation placed on transparent soils, both with and without a geotextile sheet. They found that each peak of deformation was related to the rupture of one reinforcement sheet, demonstrating a failure mode in which the geotextile developed into deeper sheets. Chang et al. [10] conducted a series of physical modeling tests to assess the influence of the bottom boundary conditions of a model box on the load‒settlement behavior of a circular footing placed on sandy soil with limited thickness, which included geogrid sheets. In a small-scale physical model, Dastpak et al. [11] investigated the behavior of a circular footing model subjected to an eccentric load on sandy soil reinforced with geonets.

By conducting experimental and numerical analyses, El Sawwaf [12] evaluated the response of an eccentrically loaded strip footing placed on geogrid-reinforced sand. They reported that by incorporating layers of geogrid, the performance of the footing can be significantly improved, leading to a more cost-effective footing design. In addition, they concluded that the sandy soil-geogrid interaction system is effective depending on the ratio of the load eccentricity and the geogrid reinforcement parameters. Kargar and Hosseini [13] conducted a series of experimental tests on a scaled-down physical model to examine methods for enhancing the behavior and performance of a strip footing supported on a geocell-reinforced sand foundation.

Lal et al. [14] studied the behavior of coir geotextile-reinforced sand beds. They stated that coir geocell reinforcement performs better than planar forms for the same quantity of reinforcement material. According to Kolathayar et al. [15], the bearing capacity and settlements of footings on clay beds can be improved by incorporating coir cell networks. They illustrate that coir cells have strengthened the clayey soil bed by increasing the lateral resistance impact and enhancing the vertical load dispersion factor.

Tafreshi and Dawson [16] present comprehensive results for strip footings resting on sand foundations reinforced with geotextiles and geocells. Based on the findings, it appears that the geocell-sand system exhibits greater strength and load-bearing capacity compared to the equivalent planar geotextile system using the same number of geotextile sheets.

During repeated loads, Mehrjardi and Khazaei [17, 18] demonstrated the significance of the scale effect on the behavior of geogrid-reinforced soil. The optimal nominal aperture size for geogrids is typically considered to be approximately four times the medium soil grain size and 0.2 times the width of the footing. The load-carrying capacity of square footings on sand reinforced with dissimilar geogrid layers has been reported by Rowshanzamir and Karimian [19]. The improvement ratio of the bearing capacity ranges from 1.8 to 5.35, depending on the placement of the reinforcement and the density of the sand bed.

Using a laboratory and numerical analysis, Ouria and Mahmoudi [20] studied the impact of cement processing on the interaction between geotextiles and sand. The study focuses on the load-carrying capacity of a footing constructed on sandy soil reinforced with geotextile inclusion. Experimental testing was conducted on the geosynthetic-reinforced soil beneath a strip footing, following a series of physical modeling experiments conducted by Xu et al. [21]. The testing setup was designed to observe the behavior of the soil. Geosynthetic reinforcement is optimally embedded at 0.4 times the width of the structure (0.4B). Stress-controlled settlement is found to exhibit a stepwise increase phenomenon. The significant results of the previous small physical modeling tests on horizontal planar geosynthetic-reinforced soil foundations are summarized in Table 1.

Table 1 Summary of the results of previous researchers using physical modeling tests on reinforced soil foundations with planar geosynthetics

The parameters in Tables 1 and 2 are described as follows:

Table 2 Summary of physical model tests on wrap-around geosynthetic reinforced soil foundations

For geosynthetic sheets, u, h, L, and N represent the embedment depth of the uppermost geosynthetic sheet, the vertical distance between the geosynthetic sheets, geosynthetic length, and number of geosynthetic sheets, respectively. BCR denotes the ratio of the final carrying capacity of reinforced soil to that of nonreinforced soil under the effect of optimum reinforcement parameters. For footing types, both B and D are the width of the strip/square footing and the diameter of the circular footing.

In previous studies, researchers have shown that reinforcement layers are placed horizontally under shallow foundations. Due to architectural conditions and limited ground level, a new building is constructed near the old building, and to improve the bearing capacity, the shallow footing can solve this problem by wrap** the reinforcement ends. The use of wraparound geogrid technology not only eliminates the limitations of improved area dimensions but also provides the opportunity to improve and increase the bearing capacity of granular soil. In this study, the mechanism of the subsurface behavior of a soil layer reinforced with geogrid sheets based on medium-fine sandy soils was investigated using physical modeling.

In previous studies, Shukla [22] developed and successfully demonstrated the wraparound reinforcement method for shallow foundations. The first experiment was conducted by Kazi et al. [23, 24] to determine the effectiveness of the technique in reinforcing foundation soils. Above the reinforcement, the horizontal and vertical components can be easily visualized to prevent lateral and vertical movements of the soil. In the study by Kazi et al. [24], the bearing capacity of a strip foundation resting on sand and reinforced with a geotextile membrane wrapped around the ends was evaluated. When the model of the soil reinforced with geotextile layers was compared to those sheets without wrapped ends, they found a significant improvement in ultimate bearing capacity (approximately 25 to 75 percent more). Hataf and Sayadi [25] investigated the improvement of soil bearing capacity using geobags. The research results show that the installation of geobags under foundations significantly improves the bearing capacity of the foundation. It was also found that the number and placement of the bags are most important for increasing the bearing capacity and reducing the settlement of the foundation. Noorbakhsh et al. [26] used tubular geotextiles with a braided structure as novel geosynthetics for soil improvement. A comparison of the performance of reinforcement with tubular and planar shapes showed that the use of tubular geotextile components resulted in higher bearing capacity (optimal increase of 68 percent), higher bedding stiffness (optimal increase of 48 percent), and lower foundation settlement (optimal decrease of 140 percent).

The wrap-around geotextile reinforcement approach was studied in detail experimentally by Aria et al. [27]. An investigation of the load–settlement behavior of reinforced sand was conducted using laboratory tests on a model in which the effect of overlap length coverage of folded ends was studied. Wraparound ends are explained as anchors that provide additional confinement to the lateral resistance of the soil, resulting in approximately 50% higher load capacity for foundations resting on soil reinforced with a folded geotextile layer.

Previous studies have identified certain limitations in their research, including the omission of certain factors such as the use of geogrid as a geosynthetic material, the impact of different overlap lengths, the influence of the thickness of the fully wrapped geogrid, the effects of length and embedment depths of fully wrapped geogrid sheets, the mode of failure and development stresses, induced strains, and vertical displacements within the soil bed, and the strains induced along with folded geogrid sheets. The summaries of the main results of the previous reduced physical model tests on folded geosynthetic reinforced soil beds are carefully listed in Table 2.

In light of these knowledge gaps, this study aims to investigate the behavior of a strip footing placed on fine sandy soil reinforced with a fully wrapped geogrid layer, without any additional layers of reinforcement, under a centrally applied load. Furthermore, the study aims to determine the placement of an internally fully wrapped geogrid sheet that contributes to enhancing the carrying capacity.

2 Basic concept of the geogrid wraparound technique

An analysis of strain fields indicates that the ideal reinforcing pattern should be placed horizontally below a shallow footing as indicated by Shukla [22]. The reinforcement should therefore be applied in the direction of the principal strain. In other words, tensile reinforcement is most effective if placed in the direction of the minor principal stress. A minor principal strain or tensile major strain occurs almost in the direction of the minor principal stress according to elastic theory, as shown in Fig. 1. The major and minor principal stresses induced within the soil mass at each point were calculated based on elastic theory as follows Das et al. [28]:

Fig. 1

Distributions of minor and major stresses in the soil mass based on elasticity theory

The total increase in the vertical principal stress (σ₁) at each point due to the strip loaded can be estimated by Eq. (1):

$$\sigma_{1} = \frac{q}{\pi }\left[ {\tan^{ - 1} \frac{z}{y - b} - \tan^{ - 1} \frac{z}{y + b} - \frac{{2bz\left( {y^{2} - z^{2} - b^{2} } \right)}}{{\left( {y^{2} + z^{2} - b^{2} } \right)^{2} + 4b^{2} z^{2} }}} \right] .$$

(1)

Similarly, Eq. (2) is used to determine the minor principal stress (σ₃):

$$\sigma_{3} = \frac{q}{\pi }\left[ {\tan^{ - 1} \frac{z}{y - b} - \tan^{ - 1} \frac{z}{y + b} + \frac{{2bz\left( {x^{2} - z^{2} - b^{2} } \right)}}{{\left( {y^{2} + z^{2} - b^{2} } \right)^{2} + 4b^{2} z^{2} }}} \right] ,$$

(2)

where b = 0.5B (B is the footing width) and y and z denote the coordinates of each point in the soil mass. The strip loading value that was transferred into the soil mass amounted to 400 kPa.

The most efficient way to reinforce foundations would be to place geogrids reinforced along the minor principal axis. Geogrid reinforcement should therefore be positioned in the direction where it can develop maximum tensile deformation. Consequently, a layer of geogrid is positioned along the semifolded direction of minor strain in the soil bed.

3 Experimental model and materials used

The soil utilized in this investigation is characterized as fine sand soil. The analysis of the grain size test was performed following the ASTM D422 [29] standard for soil classification. It involved using seven sieves with different mesh sizes, starting from N200 at the bottom and progressing to N100, N70, N50, N40, N30, and N20 at the top. The test results show that the values of the curvature coefficient and uniformity coefficient of the soil used are denoted as (C_C) = 1.18 and (Cu) = 1.90. In addition, the values for the particle size effect, medium particle size, minimum particle size, and maximum particle size are as follows: d₁₀ = 0.20 mm, d₅₀ = 0.34 mm, dmin = 0.01 mm, and dmax = 0.60 mm, respectively. According to the Unified Soil Classification System (USCS), the soil used can be classified as poorly-graded sandy soil (SP). Please refer to Table 3 and Fig. 2 for more information. The minimum dry unit weight of the sandy soil was determined by the standard ASTM D2049 [30] and determined to be 14.09 kN/m³. Using the test of the vibrator table, the maximum dry unit weight is defined as 16.61 kN/m³ by taking in the specific gravity value (Gs) of 2.68. By conducting nine direct shear tests, the basic mechanical properties of medium-dense sandy soil with and without geogrid sheets were evaluated. The direct shear test is performed following ASTM D5321 [31] using a 100 mm × 100 mm mold. The test is conducted on medium-dense sand with a medium relative density of 75%. The values of the mechanical properties of the medium sandy soil, namely, cohesion (C), residual friction angle (ϕ_residual), and peak friction angle (ϕ_peak), are determined to be 8 kPa, 30.5°, and 36°, respectively, as indicated in Table 3.

Table 3 Soil used features

Fig. 2

Analysis of the grain size test

One kind of geogrid called CE141 built by the Mesh Iranian company was used [32]. The peak tensile strength was determined to be approximately 6.25 kN/m. In the two directions, the properties of the geogrid sheet are the same. The mechanical and physical features of the geogrid are taken based on the standard test ASTM D 4595 [33] and are displayed in Table 4.

Table 4 Properties of the geogrid sheet

In this research, the strip footing was made of a steel plate. The thickness and width of the solid plate are denoted as 20 mm and 100 mm, respectively. The strip footing length (390 mm) is put in the same direction as the width of the physical modeling sandbox. The bottom surface of the footing is prepared by applying a layer of coarse sand as an adhesive coating. Epoxy glue is then used to ensure a consistent roughness for all testing. The loading is performed at the center of the steel plate footing.

4 Laboratory process and test arrangement

The physical modeling was carried out in a solid steel sandbox with the following dimensions: length (L = 1.6 m), height (H = 1.0 m), and width (B = 0.4 m). The test tank consists of three steel faces and a side open as a side for sample preparation and discharge, as well as plexiglass placement in front to observe deformations in the soil. The plane strain conditions show that the strain in the direction of the longitudinal axis of the foundation is very small compared to the deformation of the cross-section. Therefore, in these conditions, the strain along the width of the tank is assumed to be zero. As a result, the rectangular plane area of the sandbox was designed according to the condition of plane strain.

For the determination of the length of the test tank, two main aspects must be taken into consideration: the effect of the solid boundary on the soil shear failure mechanisms and the effect of the surface roughness of the solid boundary on the carrying capacity values of reinforced soil, the first factor being most crucial. The rupture length of mode failure (R_o), the log spiral (R), and the horizontal distance from the footing edge (b) are determined by considering a soil friction angle of 36° according to the rigid boundary effect of the sandbox as follows R_o = $\frac{B}{{2 \times \cos \left( {45 + \frac{\emptyset }{2}} \right)}}$ = 1.1B, R = $R_{o} e^{0.5\pi tan\emptyset }$ = 3.45B, and b = $R\cos \left( {45 - \frac{\emptyset }{2}} \right)$ = 3.07B, respectively, as demonstrated in Fig. 3a.

Fig. 3

a Schematic of the physical modeling used, b views of the horizontal planar geogrid arrangement, c views of the fully wraparound geogrid arrangement, and d picture of the preparation of the fully wraparound geogrid in the test

The total length of the sandbox is B_tot = 2 × (0.5B + 2b) = 13.28B. According to the assumption made in this study, when the width of the strip footing is 10 cm, the estimated rupture width is approximately 133 cm. Therefore, the sandbox length to width footing ratio of 16 (i.e., L_sandbox = 16B = 1600 mm) is sufficient to avoid an interruption between the wedges of failure and the vertical steel sides of the sandbox model. The interior surfaces of the sandbox were sufficiently smooth and polished to remove lateral frictional interactions between the soil used and the steel plates and given sufficient stiffness to create plate stress in the model. For this purpose, a thin layer of grease is glued to the interior surfaces. Then, the sand sample is poured by the sedimentation method, and the front surface of the clear glass is fixed in place. Therefore, the frictional contact between the inner surfaces and the soil grains does not rise and moves away.

It is possible to determine the variation in the vertical stress to the applied load (Δσ_z/q_o) at various points below a strip load of width B, as indicated by Das et al. [28]. The results can be used to plot stress isobars (i.e., contours of Δσ_z/q_o). The vertical stress can be reached at Δσ_z = 0.1qo at a depth of z = 3.8B. Therefore, if the bottom boundary of the tank test is approximately four times the footing width, then the impact of stresses on the load–settlement response of a strip footing is negligible. Similarly, the height of the soil foundation within the steel sandbox was determined to be 8B = 80 cm. The sandbox width and length of the footing were equal concerning the plane strain state for this problem.

Additionally, to prevent contact between a strip footing and a sandbox vertical sidewall, the length of the footing was reduced by 5 mm in all directions. In this study, a loading system consisting of a pneumatic cylinder and compressor was utilized to apply an air pressure of approximately 10 bars. This system enables the application of consistent periodic loads to the soil mass by controlling the pressure conditions. The carrying bearing pressure of sandy soil was determined in all tests by using a jack with a capacity of 5 tons to apply the central loading. Three linear variable differential transformers (LVDTs) and an S-shaped load cell were used to measure the footing settlement and determine the applied force. The experiments were carried out per the ASTM D 1196 [34] standard. Multiple strain gauges were attached to the ribs of the geogrid sheet at various spaces from the center of the footing (x*/B = 0, 0.5, 1.5, and 2) to evaluate the distribution of strain along with the length of the geogrid sheet. It is linked with the LVDTs at the surface of the geogrid and connected to the datalogger through electric wires. The vertical pressure stresses were quantified by employing 10 pressure cells positioned beneath the center of the footing. The space ratios from the footing center were designated as follows (z*/B = 0.5, 1, 1.5, and 2). To monitor data readings, a twenty-channel electronic data logger was connected to a PC. Various sensors, such as a load cell, pressure cells, strain gauges, and LVDTs, were connected to the data logger. The soil sample was prepared utilizing the method of rainfall sandy soil [35], ensuring that the soil attained the desired relative density within the steel sandbox. The selected relative density values were determined by calibrating the fall speed and height of the sand particles in a specific metal cup over several trials. The correct soil unit weight was measured utilizing a tamper. The medium fine sand has a dry unit weight of 15.9 kN/m³ and a relative density of 75%. This setup is shown schematically in Fig. 3. Under the effect of a strip foundation in this study, horizontal and wraparound reinforcements are positioned directly under the strip foundation (that is, the reinforcement is positioned longitudinally along the strip foundation). The nature of the problem indicates that strip foundations with reinforcement in the soil behave as plane strain conditions, as illustrated in Fig. 3. Table 5 describes the setup of the physical model test process.

Table 5 Configuration program details

The steps for conducting a small-scale physical model of laboratory test studies using the mentioned system are (1) position a sandbox under the sedimentation system and carry out sand deposition operations, (2) process leveling of all shallow surfaces for the installation of the footing model and the installation of the instruments under the loading system, (3) install the foundation model and place it on the soil surface, (4) apply the needed load (in the form of force control) employing the written program, and (5) read and record information by the data logger. To create compacted soil with a wrapped geogrid, follow these steps. First, the soil bed was prepared, and the total embedment depth was determined. Next, the soil was compacted to a relative density of 75%. Then, folded geogrid layers were placed in the designated area. After that, sandy soil with the appropriate box volume was placed and compacted to a relative density of 75%. The surface was leveled by compacting it and adding another layer. These steps are repeated until the desired depth is achieved. The summary and details of the series tests of the small-scale physical model are demonstrated in Table 5.

5 Results and discussions

Experimental model testing has been the mainstay of research to date on the effectiveness of folded and planar geogrid-reinforced soil beds and the numerous contributing elements.

The impact of various parameters on the bearing-pressure capacity and settlement ratio of reinforced soil was carefully examined based on small-scale model testing. These influencing aspects mostly consist of the reinforcement layout parameters and attributes, the footing size and shape, the type of load, and the soil bed characteristics. Recently, researchers [20, 21, 36] have compared the bearing pressure–settlement ratio response curves of reinforced and unreinforced foundations to examine the effect of various parameters on the bearing properties of foundations.

The bearing capacity ratio (BCR) is frequently utilized as a dimensionless metric to assess the reinforcement effect of the geogrid sheet. The following Eq. (3) defines the bearing capacity ratio (BCR):

$$BCR = \frac{{q_{{ur \left( {reinforced} \right)}} }}{{q_{{u \left( {unreinforced} \right)}} }},$$

(3)

where q_ur denotes the reinforced foundation bearing capacity as the footing settles to a particular level and q_u depicts the nonreinforced soil carrying capacity at the same level.

5.1 Applied pressure–settlement response

In geotechnical engineering, it is crucial to determine the bearing-pressure capacity and settlement ratio of a strip footing that is situated on both unreinforced and reinforced soils. By conducting 29 experimental tests on a small-scale physical model, the response of a single-strip foundation resting on medium-density sandy soil under plane strain conditions was investigated. The final settlement value is applied once the stress is continuously applied to achieve failure. To display the results graphically, the results of the vertical settlement of the footing are measured in millimeters by utilizing the settlement ratio (s/B%) and applied pressures (kPa). The final load-carrying capacity was defined using the breakpoint approach in this study. The behavior of the medium-dense sandy soil is initially in an elastic state when the settlement ratio reaches s/B = 2%, in which the pressure limit is 150 kPa, as indicated in Fig. 4, according to previous research [7, 21]. The assumption is made based on the method employed to assign the relevant load. The settlement ratio (s/B) follows a nonlinear elastic state until it reaches this value of 10%. At this point, the breaking point is the same as the final load, which results in total failure within the soil mass. This occurs after the total settlement increases, corresponding to an increase in the applied stress. Once the settlement ratio reaches its breaking point, a sudden decrease in the carrying-pressure capacity occurs, and the behavior of the medium-density fine soil transitions to a plastic mode. Figure 4 displays the variety of applied pressures with increasing settlement ratio of the strip footing regarding four experimental tests (unreinforced, single geogrid sheet, two geogrid sheets, and three geogrid sheets), where the kind and form of planar geogrid sheets are the same for all four-test series. The curve of the response of the bearing pressure-settlement ratio of the nonreinforced sand foundation is plotted in Fig. 4 for comparison with other tests. The embedded depth of the uppermost sheet of the planar geogrid was considered from the bottom surface of a strip footing (u/B = 0.3), but the vertical space between planar geogrid sheets (h/B = 0.4) was kept constant. This distinctly indicates that the load-carrying capacity of the ground is greatly increased with the inclusion of planar geogrid sheets. A comparison with a multilayer geogrid shows that the performance improvement is better for different instances. It can be debated that the case with three planar geogrid sheets N = 3 gives the highest improvement at all settlement values compared with one (N = 1) and two (N = 2) inclusions of planar geogrid sheets.

Fig. 4

Impact of planar geogrid inclusion on the response of medium-dense sandy soil

5.2 Effect of different reinforcement arrangements

Figure 5 demonstrates a series of three planar geogrid forms (soil with the inclusion of a single geogrid planar sheet, with the inclusion of two geogrid planar sheets, and with the inclusion of three geogrid planar sheets), in which one type of geogrid sheet is used in each test, to evaluate the impact of various lengths of planar geogrid sheets on the bearing capacity ratio. The bearing capacity ratios of medium-dense soil with various lengths of planar geogrid sheets were compared with the multilayer geogrid-reinforced statuses. It was found that with increasing length and number of planar geogrid sheets, the bearing capacity ratios increase. Until the length ratio of the planar geogrid is five times greater than the width of the footing, there is no improvement in the bearing capacity ratios when the length ratio is L/B = 7. The findings of [37, 38], which indicate a limited increase in ultimate bearing capacity for a specific length of the planar geogrid sheet (L > 5B), were comparable. According to prior studies by [1, 7, 23, 39], the best vertical spacing and the uppermost geogrid embedment depth are 0.3 and 0.4 of the footing widths, respectively. During each test of this study, the length aspect ratio (L/B) for each geogrid sheet was set at 5. The ratios h/B = 0.40 and u/B = 0.30 represent the vertical distance between the geogrid planar sheets and the uppermost geogrid planar sheet, respectively. These ratios were kept constant throughout the study. Nevertheless, the uppermost fully lap geogrid and fully embedded depth of the fully folded geogrid sheet are 0.2B and 0.4B, respectively. The addition of folded geogrid sheets demonstrates a significant improvement in the soil-bearing capacity. To investigate the load‒settlement response of the strip footing on fine sand, multiple test series were compared, including a single geogrid sheet, two geogrid sheets, and one fully wrapped geogrid sheet. Figure 6 indicates that including two geogrid planar sheets gives the greatest improvement in the settlement ratio when compared to incorporating one geogrid planar sheet. Incorporating one fully folded geogrid layer enhances the load-carrying capacity while also reducing settlement and deformation beneath the strip footing. Figure 6 further shows that the addition of one completely folded geogrid layer improves the soil load-carrying capacity by 70% for a settlement ratio of s/B = 10%. Furthermore, with a settlement ratio of s/B = 10%, the bearing capacity ratios increase to 40% and 55% for one and two inclusions of planar geogrid sheets, respectively, compared to soil without a reinforced layer. The completely folded geogrid outperforms the one- and two-planar geogrid layers in terms of load‒settlement behavior. Aria et al. [40] discovered that a single fully wrapped geotextile outperforms two flat geotextile sheets. However, with a settlement ratio of s/B = 10% in our study, the ultimate carrying capacity of sandy soil with a single fully wrapped geogrid surpassed 510 kPa, whereas Aria et al. [40] found a final load-bearing capacity of 210 kPa for sandy soil with a single fully wrapped geotextile layer. Because of the substantial frictional mobilized strength between the soil grains and the soil-geogrid contact surface, geogrid inclusions have a greater mobilized tensile strength than geotextile inclusions. As a result, under strip stress, the full-wraparound geogrid approach increases the load‒settlement response of reinforced fine sand. In addition, Fig. 6 demonstrates the case of adding two wraparound geogrid sheets, which improves the load‒settlement behavior of reinforced soil and strengthens it. The load‒settlement response is comparable to that of reinforcing soil behavior with a multiplanar and single fully-folded geogrid sheet at a low settlement ratio of up to 2%. After adjusting the settlement ratio from 2 to 8%, the bearing pressure increases significantly compared to another geogrid sheet configuration. When the settlement ratio reaches 10%, the bearing capacity of reinforced medium-dense sand exceeds that of a single fully-folded geogrid layer, resulting in an increased bearing capacity ratio of approximately 1.18 and 1.28 when compared to the inclusion of two and three-planar geogrid sheets, respectively.

Fig. 5

Variable between the bearing capacity ratio and the length ratios of planar geogrid sheets

Fig. 6

Effects of adding full-wrapped and planar geogrid sheets on the medium-dense sand load–settlement response

5.3 Effect of the length of the fully wrapped geogrid

In Fig. 7, the effect of fully wrapped geogrid layers of varying lengths is shown to illustrate the load‒settlement response of reinforced soil. Based on these findings, an optimal length ratio for full-wrapped geogrid inclusions was determined. To investigate this behavior, a series of 5 laboratory tests were carried out using 2 geogrid planar layers and a single fully wrapped geogrid sheet. Based on earlier research [7, 41] the same ratios of u/B = 0.3 and h/B = 0.4 were used. The ratios d/B, u/B, and x/B for the fully folded geogrid sheet, on the other hand, were 0.2, 0.4, and 0.2, respectively, while the length ratios L/B varied. Figure 7 depicts the load‒settlement behaviors of the strip footing derived from experimental testing with these varied length ratios (L/B = 1, 3, 5, and 7). The applied load on the strip footing surface was gradually raised until a settlement ratio of 10% was attained. The applied load dropped after this settlement ratio until it was stopped at the same settlement ratio. Figure 7 indicates that a geogrid length ratio of 5 times the footing width has a significant influence on the load‒settlement behavior. The ultimate settlement ratio (SR) showed a reduction in settlement of 17%, 9%, 7.5%, and 7% (S/B) for L/B = 1, 3, 5, and 7, respectively. Based on Fig. 7, the optimal geogrid length is denoted as 5B, where B represents the width of the footing. This length ratio resulted in a substantial reduction in both the settlement ratio and induced deformation, leading to a significant increase in the soil carrying capacity. Aria et al. [27] indicated that the full-folded geotextile sheet length should be more than six times the width of the footing. By comparing the results with those of Aria et al. [27], it can be concluded that the fully folded geogrid layer offers a better solution than geotextile sheets for reinforcing sandy soil foundations. Therefore, the use of a geogrid layer is recommended in such applications.

Fig. 7

Effect of various lengths of full wraparound geogrid sheets on the bearing pressure–settlement ratio response

5.4 Impact of the depth of the wrap around the geogrid box

Figure 8 shows the load-carrying capacity ratio at the final footing settlement utilizing a fully wrapped geogrid layer with an equal length (5B) and embedding the overlap element at a depth ratio of d = 0.2B with different reinforcing layers (1 and 2). Based on the results, the multilayer inclusion of full-wrapped geogrid layers significantly influences the soil bed final carrying capacity. The final carrying capacity of the soil bed increases as more fully folded geogrid sheets are added. It is worth noting that an optimal thickness for full-wrapped geogrid layers, in terms of the maximum bearing capacity ratio, has been identified within the values of the thickness ratio of 0.35B–0.45B, for N = 1 and 2, where B is the footing width. The values of bearing capacity ratios exhibit a nonlinear increase with the thickness of the full-folded geogrid layers when using a geogrid sheet with an average thickness ratio of x/B = 0.4. Beyond this point, no further improvement was observed.

Fig. 8

Effect of multilayers on the bearing capacity ratio (BCR) and thickness ratio (x/B)

The fully wrapped geogrid sheet can be considered as reinforcement for geogrid boxes, which helps improve the soil-bearing capacity. The geogrid box exhibits similar mechanical behavior to the geocell but differs from it in terms of dimensional structure. It creates a three-dimensional confinement effect, which enhances lateral sand resistance and improves reinforcing effectiveness. Researchers have described this three-dimensional confinement effect as resembling a centrally compressed beam or slab when compared to the frictional resistance along a geogrid in fully wrapped models. Due to the complete wrap** of the reinforcement, it acts as a cohesive body and deforms as a slab or beam under tension in the axial direction, rather than as a flat sheet. Similar findings have been reported regarding geocell-reinforced foundation soil by [42,43,44,45].

5.5 Impact of the full wraparound geogrid on the strain–stress distribution

In this study, the behavior of the geogrid sheets varies for the various configurations of the geogrid-reinforced soil, such as planar and wraparound sheets. There is a significant discrepancy between the geogrid-reinforced soil displacement distribution and the geogrid damage pattern. To study the stresses, strains, and displacements of various forms of geogrid-reinforced soil beds in addition to the damage deformation pattern of planar and folded geogrid sheets, this work uses single-planar, two-planar, and single-folded geogrid sheets as examples.

Figure 9 illustrates the maximum strain of the geogrid sheets distributed at various depths of the reinforcement layers when the geogrid-reinforced sheet fails. This demonstrates that the strain distribution beneath the central strip footing is approximately similar for both the single and double planar forms of the geogrid layers. However, the strain distribution over the depths of the wraparound geogrid layers is smaller compared to other planar forms, as shown in Fig. 9. When compared to planar geogrid sheets, the inclusion of a single wraparound geogrid sheet increases the stiffness and mobilizes the tensile strength at the interface between the overlap** section and soil particles. In addition, when the soil grains move due to strip loading, the wraparound geogrid benefits from increased confinement-bearing capacity, higher stiffness, and mobilized tensile strength. These factors not only enable the geogrid to withstand more soil particle impact but also reduce the likelihood of deformation in the folded geogrid. Furthermore, the overlapped upper part will improve the interaction between the wraparound geogrid and the surrounding soil grains, thereby reducing settlement and displacement of the soil foundation. On the other hand, Fig. 9 demonstrates that as the burial depth of the reinforcement sheet increases, the strain induced in the geogrid sheet gradually decreases. This behavior indicates that the inclusion of geogrid sheets may have a negligible effect on performance, and it suggests that the strip footing is likely to fail due to general shear failure. Therefore, previous studies [23, 24, 27] have reported that the optimal burial depth of planar and wraparound geogrid sheets is approximately in the range of 0.30B and 0.40B.

Fig. 9

Distribution of strain induced at the geogrid center with burial depth

Figure 10 compares the tensile strain distribution of planar geogrid layers to that of folded geogrid sheets along with the distance from the footing center. Tensile strains caused by the inclusion of one or two layers of planar geogrid form are greater in the vertical direction than those induced by folded geogrid reinforcement, as shown in Fig. 10a. The maximum tensile strain values induced at the center of the footing are 0.55, 0.52, and 0.48 for the single planar geogrid inclusion, the first layer of two planar geogrid sheets, and the second layer of two geogrid sheets, respectively, as shown in Fig. 10a. These induced strains are larger than the maximum tensile strain of 0.408 obtained from Table 4. Therefore, the tensile forces induced under the central ribs of geogrids exceed the maximum tensile strength of the geogrid used. Consequently, this is attributed to the rupture of the longitudinal ribs of the geogrid sheet, concentrated loads on joints and junctions leading to cracks, and the limited effectiveness of the mobilized tensile force in the planar geogrid sheet. In addition, with the inclusion of the overlap geogrid restraint, the peak displacement of the fully folded geogrid-reinforced form is relatively small, and it provides more lateral additional resistance than the planar geogrid-reinforced form, as demonstrated in Fig. 10b. Therefore, the deformation and settlement of the strip footings decrease.

Fig. 10

Deformation mode and displacement of single full wraparound and planar geogrid sheets

Figure 10b depicts the displacement distributions of a single planar and a wraparound geogrid reinforcement sheet. The vertical axis (s/B) refers to the values of the displacement ratio not the thickness of the fully-folded geogrid. The aim of the added Fig. 10b is to observe the difference between planar and folded geogrid sheet behaviors. Figure 10 shows that while the planar geogrid sheet has a different distribution of maximum deformations and displacements than the folded geogrid sheet, the planar geogrid form does not have the same ability to reduce the horizontal movement of soil particles as the fully folded geogrid layer because the planar geogrid sheet lacks the interfacial frictional strength and mobilized tensile locking strength of the geogrid on the soil grains, and the displacement value of the soil grains when using the planar geogrid sheet is larger.

When the two types of geogrids in a single-layer reinforced soil bed are damaged, they are depicted in Fig. 11. The fully folded geogrid exhibits no damage, whereas the planar geogrid exhibits both nodal and rib damage. The folding structure of the fully folded geogrid form results in high structural stability and accelerates pressure transfer between high-strength nodes and the ribs when the geogrid is subjected to pressure from soil particles (horizontal and vertical) in all directions. Under pressure, this behavior will make the fully folded geogrid more capable of interlocking with soil particles. Additionally, this puts more stress on the geogrid nodes despite protecting the geogrid ribs from damage. The nodes are the first to break when stresses are applied to them that are larger than their strength. Because planar geogrids lack significant structural stability, which results in a limited load transfer capability of the ribs when subjected to loads, the ribs will be broken when the weight applied to them surpasses their ultimate strength. Furthermore, when the geogrid as a whole is subjected to high external stress, the nodes will experience damage even if there is inadequate external load transmission from the ribs to the nodes.

Fig. 11

Rapture and damage mode of both a single fully folded and b planar geogrid sheets

In Fig. 12, the distribution of pressures measured in the geogrid sheets underneath the footing center is shown according to different forms of reinforcement. The peak stress measured over the interaction soil-geogrid layer is induced underneath the strip footing center and decreases gradually with an increasing number of geogrid sheets. Nonreinforced soils experience greater pressures than reinforced soils under strip footings. Across the geogrid sheet underneath the footing center, the vertical pressures measured are 140 kPa, 135 kPa, 125 kPa, 120 kPa, 119 kPa, and 114 kPa for the unreinforced soil, single planar geogrid, two planar geogrids, three planar geogrids, one folded geogrid, and two folded geogrid sheets, respectively. As a result, the stress induced in the soil mass appears to be reduced by the geogrid sheet. Folded geogrid sheets explain this phenomenon by creating a lateral effect. By distributing the applied load over a larger area, this reinforced zone acts as a flat slab, which significantly reduces lateral displacement. However, as the footing settles, soil displacement in the reinforced zone increases significantly at the left and right corners. As a result, tensile strengths are mobilized within folded geogrid sheets. The geogrid reached its maximum tensile strength under these conditions. In addition, the geogrid layers exhibit similar results in terms of tensile strain.

Fig. 12

Stress measured for different cases of reinforced soil

5.6 Failure mechanism

The failure mechanism observed in reinforced systems with fully folded geogrid sheets is presented in Fig. 13. This figure illustrates that progressive shear failure in the dense fine sand of the geogrid-reinforced soil bed occurs at a deeper level compared to soil without geogrid layers. This failure also results in an increase in soil mass volume due to the inclusion of fully folded geogrid layers. The improved failure mode can be attributed to the interaction between the geogrid wraparound and soil particles. In addition, it can be attributed to the interaction between soil particles and the reinforcement tensile strength. This observation aligns with previous studies on deep-footing effects [46, 47]. Shear bands can spread far into the ground under the reinforcing layer when completely folded geogrid layers are present in a thick soil mass. Then, the induced shear stress is distributed along the wrapped geogrid sheet sides and dissipates within the soil mass. Consequently, the movement of the strip footing decreases, leading to a significant increase in the rigidity of the sandy soil reinforced with the wrapped geogrid sheet. The strip footing and the sandy soil reinforced with a wrapped geogrid sheet act together as a support system, resulting in mode failure as general shear failure. However, in terms of failure modes, there is a substantial difference when the planar geogrid and fully wrapped geogrid sheets are included.

Fig. 13

The failure mechanism of the fully wraparound geogrid: a Photograph of the failure mode in the laboratory and b a detailed schematic of the failure mode

The general shear failure mode for strip footings may explain the behavior of the complete folded geogrid-soil system, as shown in Fig. 13. This model consists of a wedge-failure area I within the plastic equilibrium zone as well as two radial shear regions II immediately beneath the footing along the wedge-failure zone. In addition, within the full-folded geogrid layer, there is an extra confinement effect zone III that limits lateral stresses and horizontal displacements. Two passive Rankine regions IV extend over the full-folded geogrid layer to the zero-ground surface, giving increased shear strength surrounding the strip footing. This decreases footing settlement and heave deformations while also limiting horizontal movement surrounding the strip footing.

The higher bearing capacity in soil owing to full-folded geogrids is ascribed to numerous processes acting together, as with other geosynthetics employed as planar reinforcements. Unlike planar reinforcements, which produce membrane and confinement effects, geogrid folding produces a third mechanism known as the stress dispersion effect. This effect is only seen when more than one full-folded geogrid layer is present, and it results in greater confinement efficiency. Each mechanism has a distinct performance, although they are linked and impacted by the loading application. The stress dispersion effect is caused by two full-folded geogrid-reinforced inclusion layers working as an instantaneous acting platform, spreading the applied load per unit area across a greater surface area (Fig. 13). This impact is comparable to the confinement effect in that it does not require relocation for mobilization. This concept may be explained by the stress-spreading influence of the wrapped geogrid structure on the main layer and the relative density of the soil material. This produces a structure that, like a concrete slab (raft foundation), can withstand bending, tension, compression, and shear. The load is transmitted to the foundation soil as a result of this dispersion, operating on a broader surface area and resulting in lower stress levels. The 2:1 approach can be used in the soil bed without a reinforcing layer to distribute the surface tension produced. The full-folded geogrid is made up of a three-dimensional layer of soil materials, which causes lateral spreading and increases the shear strength of compacted soil-filled materials. The lower lateral strain is further increased by the interfacial resistances caused by the contact between the soil under and above the reinforcement and the geogrid folded reinforcement. This, in turn, enhances the soil layer’s elastic modulus and improves the vertical stress distribution on the bed, also known as the ‘vertical stress dispersion effect’. Consequently, the vertical pressure over the soil bed is reduced due to the dispersion effect [43].

Full-folded geogrids increase the soil bearing capacity due to multiple processes working together, unlike planar reinforcements. Geogrid folding creates a third mechanism called the stress dispersion effect, resulting in higher confinement efficiency. The stress dispersion effect comes from two full-folded geogrid-reinforced inclusion layers working as an instant acting platform, spreading the applied load per unit area across a greater surface area. The load is transmitted to the foundation soil, resulting in lower stress levels. The full-folded geogrid is made up of a three-dimensional layer of soil materials, causing lateral spreading, increasing shear strength, and enhancing the soil layer’s elastic modulus. This improves the vertical stress distribution on the bed, reducing the vertical pressure over the soil bed due to the dispersion effect.

6 Scale effect

It is essential to begin the physical modeling design by identifying the scope of the study objective and the major scientific issues. Among the important steps involved in building the model are the type of model, its dimensions, its scale factor, its analog components, and the measurement of the model. Through physical modeling, large and complex structures such as excavations, buildings, or buried structures can be reduced in size while maintaining similar physical features and interactions with the surrounding soil so that they behave as they should under a variety of loading conditions. An analytical expression is needed to link the prototype and model based on similarity laws, similitude laws, and/or scale factors. The following considerations need to be considered when designing the scaled physical model, as reported by [48]:

• (1) The design of physical modeling is determined by the study purpose and the prototype features;

• (2) The laboratory model test (m) must correspond to the real test (prototype) (p); and

• (3) The scale factor is the ratio between the real test (prototype) and physical modeling parameters.

Similarity theory states that the scale factors related between the real test (prototype) and physical modeling, are defined as “L* = L(m)/L(p)”, in which “L(m)” denotes the dimension of the physical modeling, and “L(p)” refers to the dimension of the real structure (prototype).

Three attractions are still present in the physical model of one gravity. The laboratory test of the physical model offers the validity of trustworthy data for simulating the numerical modeling and process of back-analysis because the boundary conditions are determined under control, as in another laboratory model. The linear scaled-model from usual real tests may be low because the models’ sizes can be fairly enormous. Small-scale physical models may also have other unwanted impacts that can be somewhat prevented, such as issues with particle size. Due to the size of the models, there will be more space for instruments and actuators, allowing for more nuanced loading, control, and observation. The restricted size of the instruments will result in correspondingly less soil disturbance, as reported by [48]. The scale factors for geometries, unit weights, and gravity affect the scale factors for effective stresses and their distribution within depths. Al Heib et al. [48] confirmed that the following parameters should be considered for the similarity of granular materials: the unit weight, elasticity parameters, and physical and mechanical parameters. The unit weight scaling in the 1 g physical model is set to 1. The scale of the elasticity modulus denotes the scale factor (n), and the scale of Poisson's ratio refers to one. To take into account potential scale factors in elastic properties, similar geomaterials are typically used. Granular material such as sand is frequently utilized to replicate soil due to the constrained number of characteristics [48, 49]. The behavior of sandy soil is primarily determined by the friction angle and density. The friction angle has a scale factor of one, making physical model construction easier. As mentioned by [48], different sands are used with internal friction angles ranging from 30° to 41°.

Previous studies [17, 18, 50, 51] have reported helpful insight into the critical variables affecting the scale effect in small-scale physical models of shallow footing loading tests and how to minimize it. The most frequent physical variables affecting the ultimate carrying capacity (q_ur) of reinforced sand with folded geogrid sheets are “B, u, h, l_i, L, D₅₀, a₀, g, Er, and Es”, where a₀ and E_r represent the aperture of the opening size and the elastic modulus of the geogrid sheet. The function (f) that regulates the wraparound geogrid-reinforced sand can be written as follows using the dimension analysis rules:

$$f\left( { B,u,h, a_{0} ,l_{i} ,D_{50} , L,x,E_{s} ,\gamma , E_{r} } \right) = q_{ur} .$$

(4)

The eleven parameters in Eq. (4) may be broken down into nine independent parameters, denoted as (1; 2; 3; … 9), as illustrated below, using lengths and forces as the primary dimensions:

$$\frac{{q_{ur} }}{\gamma B} = f\left[ {\left( {\frac{{q_{u} B}}{T}} \right),\left( \frac{L}{B} \right),\left( \frac{u}{B} \right),\left( \frac{h}{B} \right),\left( \frac{x}{B} \right),\left( {\frac{{a_{0} }}{B}} \right),\left( {\frac{{D_{50} }}{B}} \right),\left( {\frac{{l_{i} }}{B}} \right), \left( {\frac{{\gamma D_{50} }}{{E_{s} }}} \right), \left( {\frac{{E_{s} }}{{E_{r} }}} \right)} \right] .$$

(5)

The prototype and model tests should be identical for the best response. However, maintaining complete similarity would be practically impossible. Some of the parameters that are especially vulnerable to the phenomenon known as the “scale effect” might thus be mentioned [39]. The footing width of the prototype (Bp) with dimensions (n) times the footing width of the model (Bm) may be used to formulate the following equation:

$$\frac{{B_{p} }}{{B_{m} }} = \frac{{a_{p} }}{{a_{m} }} = \frac{{L_{p} }}{{L_{m} }} = \frac{{u_{p} }}{{u_{m} }} = n.$$

(6)

The terms “model” and “prototype” should be used interchangeably to preserve consistency. For instance, the parameters u, l_i, h, L, D₅₀, and a_o should be taken into account ten times as much as those of the physical model if a strip footing width of 100 mm is being analyzed. The final carrying capacity of the prototype strip footing can be calculated by satisfying Eq. 7, with respect to the same soil used within the real test (prototype) and physical model:

$$\left( {\frac{{q_{ur} }}{{{\gamma B}}}} \right)_{{\text{m}}} = \left( {\frac{{q_{ur} }}{{{\gamma B}}}} \right)_{{\text{p}}} \mathop \Rightarrow \limits^{{{\text{yields}}}} { }\left( {{\text{q}}_{{{\text{ur}}}} } \right)_{{\text{p}}} = {\text{n}}.\left( {{\text{q}}_{{{\text{ur}}}} } \right)_{{\text{m}}} .$$

(7)

Fakher and Jones [52] noted that failing to take the scale effect into account in reinforced soils would result in undesirable results; as a result, the mechanism of reinforcement is not evaluated in real-world circumstances. The geogrid tensile strength and stiffness of reinforcement utilized in the small-scale physical model were confirmed to be n and n² times lower than those used in the prototype model, in which n denotes the scale factor used in the physical model. Viswanadhama and Koenig [53] established the scale effect rule for geogrid modeling by taking into account two fundamental requirements: (i) scaling down the interaction frictional behavior and (ii) scaling down the tensile stress‒strain behavior. Rib thickness and aperture size are idealized features of a geogrid reinforcement that will be reduced scale by (n) as a scale factor, as demonstrated in Eq. (6). They recommended using the small thickness of the geogrid rib in the small-scale physical model to mobilize the tensile strength at the soil-geogrid interface.

Figure 14 depicts a schematic illustration of the idealized tensile stress‒strain relationship. The scaling factor for the tensile strength of the model geogrid Tg, whether in the longitudinal or transverse direction, can be determined for ng modeling. This can be done by assuming that the tensile stresses in the geogrid are the same in both the model and prototype (σ_(m) = σ_(p) = σ) and that the constitutive law of the geogrid is based on Hook’s law as follows, σ_r = E_r·ε (in which Er is the modulus of elasticity of the geogrid reinforcement), and the geogrid strains in the model and prototype are also the same (ε_g(p) = ε_g(m) = ε). Figure 14 shows that the tensile strength of a prototype may be scaled by n⁻¹ times that of a model. In contrast, the strains in the model and prototype remain constant, and therefore, the strains are not affected by scale effect phenomena. As a result, the strain values in the model and prototype are equal.

Fig. 14

Comparison between the prototype and model for tensile strength–strain behavior Viswanadhama and Koenig [53]

7 Conclusions

This paper presents the findings of small-scale physical modeling studies conducted on single strip footing with a width of 10 cm that are layered over one or two sheets of geogrid-reinforced fine sand. The effect of the geogrid length, embedded depth of the uppermost sheet, spacing between sheets, stress–strain analysis inside the geogrid sheets, and increased load-carrying capacity with inclusions of wraparound geogrid sheets were all examined through a series of 29 experimental experiments. The following experimental analysis results are displayed:

• 1) The installation of a full-wraparound geogrid sheet in the supported strip footings resulted in a significant increase in the carrying capacity compared to the installation of a planar geogrid sheet. Conversely, the use of a single sheet of the wraparound geogrid layer proved effective in reducing settlement and deformation within the soil foundation. The average embedded depth and optimum thickness of the full-folded geogrid were found to be approximately 0.4 and 0.35, respectively.

• 2) The stress‒strain response of the geogrid sheet was examined following the ultimate failure loading. The findings indicate a notable distinction between the planar geogrid and fully folded geogrid sheets. The incorporation of a fully folded geogrid results in a more widespread distribution of stress at greater depths, thereby reducing the deformation mechanism associated with the overall shear failure mode for strip footing.

• 3) A comparative analysis was conducted to evaluate the outcomes of utilizing planar geogrids and fully folded geogrid forms. The findings indicate that the fully folded reinforced soil bed has a greater bearing capacity, smaller deformation and settlement of the strip footing, and smaller movements of the soil particles.

• 4) It was determined that the optimal effective overlap length of the geogrid occurs when the geogrid layer is fully wrapped over a width that is five times the width of the foundation. Additionally, the resulting improvement in strength is similar.

• 5) As a result, a novel approach is proposed that involves folding the ends of the reinforcement layer. This technique enhances efficiency and reduces settlement and deformation within the soil and geogrid sheet, respectively. The reinforced soil, in this practical method, exhibits behavior similar to that of a bonded material.

• 6) Experimental observations indicate a significant reduction in stress-induced under strip footing when one or two fully folded geogrid layers are included, compared to using multiple layers of planar geogrids. The same results were obtained for the deformation caused by the soil-geogrid interaction under applied pressure.

• 7) By comparison with prior research, this study has shown that the utilization of a single sheet of fully wrapped geogrid provides a significant improvement in the soil bearing capacity compared to the inclusion of multilayers of geotextiles. Additionally, the installation process for the fully folded geogrid is notably uncomplicated.

This work presents a detailed study toward understanding the behavior of reinforced soil foundations. However, the performance of reinforced soil foundations is influenced by numerous factors, but there are some limitations and future suggestions. This study only addresses some limitation factors, such as one type of footing, one type of geogrid, and one type of sandy soil. Future research in this field of study is recommended as follows:

• 1) Another type of reinforcement is used to determine the performance of this technique.

• 2) Studying the effect of the water table on the load‒settlement behavior of reinforced soil.

• 3) Inclusion of the tire-ship materials inside the wraparound reinforcement.

• 4) Effect of cyclic loading on the load‒settlement behavior of wraparound reinforced soil.

The present study used a small-sized footing in a 1 g environment. The footing size has an impact on the sand bed's load-carrying capacity. As a result, a large-scale field trial on large-sized footings should be conducted to better understand this problem. Future applications of particle chasing technology, image capture, and strain measurement devices will be utilized to explicitly establish the assumptions and considerations regarding the scale effect and to modify or update the proposed theoretical mechanism for wraparound reinforcement.