Various load experiments were performed on strip-model footing over geogrid-reinforced dense (Dr=90%) fine sand beds. As stated earlier, the load tests principally contributed to determining the outcome of the geogrid wraparound on the settlement performance of the strip footing overlying a fine sand bed. The investigated parameters were the load-bearing capacity for each test arrangement and the settlement (s) of the strip-model footing normalized by its width (B). The load-carrying pressure against the settlement plot was attained from the load test data that are discussed in the following. The strip footing performance on the utilized soil in the plane strain circumstances was assessed by employing 37 experimental tests on the mentioned physical model in Fig. 5. Here, the load is applied continuously to reach the failure with the final settlement magnitude once establishing the failure. The vertical settlement of the footing is stated in mm, and the results curves are plotted by both the applied stress and relative settlement (s/B%). Utilizing a nondimensional factor (BCR), the effect of enhancement was measured through reinforcement layers on incrementing the bearing capacity ratio of the strip footing overlaying a reinforced soil. The parameter BCR denotes the ratio of a reinforced soil bearing capacity to the final bearing capacity of an unreinforced soil (Eq. (1)), by (Badakhshan and Noorzad, 2015; Xu et al. 2019).
In the current work, a novel parameter called the increased bearing capacity ratio (BCRI) is inserted. Eq. (2) represents the ratio of the final load in the geogrid folded reinforced system to that in the system without folding (i.e.,). planar) reinforced system at a certain settlement.
Based on Eq. (1), the parameter BCRf is utilized to measure the bearing capacity ratio of a strip footing overlaying soil with the inclusion of a folded geogrid, as given in Eq. (3):
where qu denotes the ultimate bearing capacity.
3.1 The optimum length of the reinforcement layers
The current work explains the final bearing capacity utilizing the breakpoint technique. Previous surveys revealed the elastic performance of loose sand owing to the applied load allocation technique; a relative settlement of (s/B)=1% was achieved, equivalent to a 100 kPa limit applied pressure (Fig. 7). Regarding a wedge split in total settlement owing to the increased applied stress and applicable load, a nonlinear elastic model is established by passing a relative settlement of (s/B)=10%, for which the breakpoint is similar to the final failure load. The settlement continues at the breakpoint until the resistance is suddenly reduced, revealing the plastic performance of loose soil. Fig. 7a represents the results for analyzing the determination of the reinforcement length. Their performance utilizing other parameters was characterized through various tests with one geogrid reinforcement layer. Over the tests, the profoundness of the first support layer under the loading plate was also kept constant at u=0.3B. The parameters above were optimal based on the literature review. The applied pressure-based settlement curves obtained from the above four tests behaved approximately differently. The reason is that the plate footing gradually loaded until reaching a definite settlement. Loading continued upon this settlement, and by obtaining identical settlement values, the tests were stopped (an ultimate settlement that causes failure in soil mass). Fig. 7a represents the applied pressure-relative settlement curves for L= 3B, 5B, and 7B for the geogrid planar arrangement. It can be concluded that the applied pressure-relative settlement curves are affected by even a geogrid planar length equal to three times the footing width. For these L/B ratios, at the break point, even a bearing pressure takes place where the slope of the applied pressure-relative settlement curves is changed. An increase is observed at each percentage relative settlement ratio (s/B%) in the strip footing bearing capacity ratio (BCR) for s/B=10 and 11%. According to Table 4, the BCR increases by increasing the geogrid layer length. BCR nonlinearly increases with geogrid planar length until L=5B, after which the geogrid length is not further influenced by the BCR values. L=5B is the geogrid reinforcement optimal length at every relative settlement ratio (Figure 7b). Based on the results of Fig. 7 and Table 4, utilizing a geogrid planar length of 5B can lead to a greater resistance within the reinforced soil system, mostly affecting the geogrid reinforcement. Similar behavior is presented in the next figure (Fig. 7b) for a footing width of B=7.5 cm.
3.2. Effect of multilayers of planar geogrid
Various tests were carried out with these depth ratios (h=0.4B and u=0.3B), the same length ratio (L=5B), and at the same relative density (Dr=90%) to account for the effects of the multilayers of planar geogrid on the bearing capacity for two different strip footing widths B=10 cm and B=7.5 cm. It is assumed that the multilayers of the planar geogrid (N) are within 1 to 3. The applied pressure against the settlement ratio is displayed in Fig. 8 and Fig. 9 for B=10 cm and 7.5 cm, respectively. Not only was their behavior dissimilar, but the slope of the applied pressure–settlement ratio plot also altered with the number of planar geogrid layers for both strip footing widths. For both strip footings, according to the results from Table 5, it was indicated that at the final load, the bearing capacity ratio was the highest when the number of geogrid planar layers was N=three. Therefore, the BCR has been incremented by the enhancement in the number of geogrid planar layers. Figures 8 and 9 and Table 5 confirm the considerable increment in the bearing capacity of the footings with multiple layers of planar geogrid. Incrementing multiple layers of planar geogrids increases the interaction area and their interlocking with sand particles. Thus, shear stresses and larger displacements were created in the soil bed underneath the footing and conveyed by geogrid planar layers to a larger contact mass of the soil bed. Thus, the failure wedge increases, and the frictional resistance on the failure planes becomes larger. Regarding the applied pressure-settlement ratio curves for the reinforced and unreinforced tests, it is indicated that local shear failure is the failure mode for a small strip footing (B=7.5 cm). In the large strip footing (B=10 cm), the unreinforced and reinforced tests contain different failure mechanisms. In the tests with no planar geogrid layers, incrementing the applied pressure, the failure mode remains constant (local shear failure); however, for the tests with planar geogrid layers, the failure mode alters by incrementing the applied pressure to general shear failure. In other words, for a large strip footing (B=10 cm), planar reinforcement layers are more pronounced than for a small strip footing (B=7.5 cm). According to the experimental results, the main cause for the largest increment in final bearing capacity in the large strip footing compared to the small strip footing under the same test conditions may be ascribed to the reinforcement mechanism limiting the lateral and spreading deformations of the soil. A larger mobilized tension is caused by the large strip footing in planar reinforcement layers supporting the reinforcement for resisting the imposed horizontal shear stresses created in the mass under the loaded area by transmitting the footing load to deeper soil layers. Thus, the failure wedge and consequently the frictional resistance on failure planes become greater. The discussion in this section will be utilized to compare with the other results of the strip footing resting on folded geogrid layers. Table 5 presents the results of the strip footing test for two footing widths (B=10 cm and B=7.5 cm) in both unreinforced and planar reinforced soils.
3.3. Effect of one geogrid folded layer
Currently, geogrid folded methods (GFMs) have become widely used as reinforcing elements in many geotechnical installations, including dams, embankments, slopes, roads, bridges, beneath shallow footings, stone columns, and others, by Shukla and Yin (2006). Geogrid wraparound methods have rarely been applied to soil reinforcement underneath shallow foundations. Nevertheless, there are advantages to using a quality-controlled geogrid folded as a reinforced soil bed. The advantages of folding a quality-controlled geogrid may be investigated as follows:
3.3.1. Optimum lap length
A series of bearing capacity tests were conducted on a fine sand bed to develop a new reinforcement method that is dissimilar from traditional reinforcement methods. Traditional methods usually place reinforcing materials (geogrids, geotextiles, geonets, etc.) horizontally into foundations (Binquest and Lee, 1975; Omar et al., 1993b; Huang and Tatsuoka, 1990; Adams and Collin, 1997; Das et al., 1994; Lee et al. 1999; Shin et al. 2002; Chen et al., 2013; Ahmad and Mahboubi, 2021). Part of the geogrid was folded around the end with the lab length (l/L=0.25 and 0.5) and embedded at different depths in the soil bed. The second technique is geogrid full folded with a lap length (l/L=0.75 and 1.0). However, the result of the trial in the traditional planar way (L/B=5) has been used to compare it with the new technique results. The mechanism of the reinforcement was investigated through the observation of the applied pressure-settlement curves. One geogrid layer of length L=5B=50 cm is placed horizontally in the soil bed at a depth of u=0.3B=3 cm below the ground. The test only proves a substantial increment in bearing capacity, which is due to mobilized tensile stress at the soil-geogrid interaction, distributed vertical stress at a wider width, and transferred it to deeper depths in the soil mass. However, the settlement of the strip footing increases with increasing applied load. Agreeing with the theory of elasticity, the minor principal strain ε3 or the major tensile strain takes place almost along the direction of the minor principal stress σ3. It is expected that placing geogrid-reinforced materials along the direction of the minor principal strain ε3 would be the most efficient means to reinforce foundations. This is because the geogrid reinforced material should be placed in the most extendable direction where the material may develop maximum tensile deformation. Therefore, it is placed at embedment depth (d=0.2B=2 cm and uf=0.3B=3 cm) by closing a part of the geogrid around the end with lap length l=0.25 L=12.5 cm. As anticipated, the bearing capacity of the reinforced soil is incremented owing to the frictional resistance between the upright element of the folded geogrid and the soil particles. Nevertheless, the increase is not enough because the soil particles move upwards from the two positions of the footing, and failure occurs as local punching shear. To overcome this problem, both sides of the geogrid folded underside of the footing with lap length l=0.5 L=25 cm and placed at embedment depth (d=0.2B=2 cm and u=0.3B=3 cm) can be offered. As a consequence, the holding capacity increases dramatically, and the settlement ratio decreases. When the lap length is extended to (l=0.75 L=37.5 cm and l=1.0 L=50 cm) and shares two sides of the lap length with them, the bearing capacity is more significantly improved, and the settlement is much smaller than that measured in geogrid planar layers. Because two sides of the lap length are shared and fixed with them, an additional tensile force induced in the geogrid folded, and additional lateral resistance affected the behavior of the strip footing on the reinforced sand. The mechanism of support is experimentally investigated in the following images. It can be understood that a large slip line is generated under the geogrid folded layer. This is because when the external load is applied on the strip footing, the wrapped material behaves as part of the footing. To explain the largest bearing capacity in a full geogrid folded state, a close look at the geogrid wrapped embedment in fine sand underneath the footing subjected to strip loads is needed. The width of a geogrid folded rectangular shape is increased up to several centimeters due to lateral expansion. Moreover, the soil inside the wrapped geogrid seems to have been more densified and solidified, as if it was integrated with the footing. The external force applied on the footing induces a tensile force along with the geogrid layer as a result of the reinforcement extension. The soil particles within the folded geogrid are restrained, leading to an increment in the vertical effective stress. Later, the shear strength of the soil particles increases. As part of the footing, the solidified system (soil-geogrid folded) thus greatly increases the bearing capacity of the foundation. This theory is analogous to the increase in normal strength (N) leading to an increase in friction force F=μN. It is concerned that the hypothesis implies a “reversal idea” of applying an external force to reinforce foundations, which was ordinarily the “enemy” of institutions. Figure 10 presents the observational study results of the plate load test (PLT), in which it describes the settlement ratio (%) of the strip footing relative to the applied force per unit area. According to Figure 11 and Table 6, the ultimate settlement ratio and BCRf of the footing for a geogrid planar layer (L=5B) are 12% and 1.47, for folded geogrid (l=0.5 L) are 6% and 1.55, for folded geogrid (l=0.75 L) are 4% and 1.56, and for folded geogrid (l=1.0 L) are 5% and 1.58. Therefore, the new technique has a large effect on asperity settlements of the footing and deformation of the soil layer. Therefore, the soil particles inside the geogrid folded element do not have a relative motion to the footing. Likewise, a wedge failure sandwich-shaped zone is made beneath the geogrid wrapped system. It seems that this new system has integrated with the strip footing to form a wider and deeper footing. This observation explains the effect of additional confinement strength by the inclusion of folded geogrids. Table 6 denotes the results of the strip footing test for footing width (B=10 cm) in both unreinforced and geogrid folded reinforced soils.
3.3.2. Optimum depth for geogrid semifolded
Among the vital parameters for reinforced soil with semifolded geogrids is the reinforcement layer embedment depth from the soil surface. Various results have been reported (u) in planar geogrid reinforcement under strip loading conditions. Researchers have highlighted the critical values for (u) beyond which further increment has no effects on bearing capacity, as stated in the previous section. For the geogrid folded system, five different depths (d=0.1B- 0.2B- 0.3B- 0.4B, and 0.5B) from the footing bottom are considered for the lap length (upper part l/L=0.5) of a single geogrid folded layer (in which the total embedment depths in dimension condition u/B=3, 4, 5, 6 and 7 cm are considered). The thickness of the geogrid folded layer (x=0.2B=2 cm) is proposed. With a relative density of 90% and B=10 cm. The results of the applied pressure versus settlement ratios of one layer of folded geogrid are represented in Fig. 12. It is found that the depth ratio of u=0.4B gives the highest final bearing capacity and lower settlement amount.
Hence, it can be expressed that semifolded geogrids are more effective in reinforcement based on an increase in the final load-bearing capacity when installed in dense sand beds at D=0.4B. Figure 13 represents the changes in the subgrade reaction modulus (ks) with an embedment depth ratio (u/B) for geogrid semifolded sand beds with Dr=90%. According to Fig. 11, the load-bearing pressures equivalent to settlements of 1.25 mm and 2.00 mm and the ultimate settlement at failure are determined for reinforcement with geogrid wraparound end conditions. It is found that by increasing u/B, ks continues to increase until u/B=0.41; then, it decreases by increasing u/B for the reinforced case with the geogrid semifolded at all relative settlements. Moreover, for u/B=0.41, the geogrid semifolded increases ks by approximately 13800, 11000, and 11685 kN/m3 for settlement ratios s/B%=1.25, 2.00, and final settlement (su%), respectively. Therefore, semifolded geogrids are more advantageous based on increasing the subgrade reaction modulus when installed in very dense sand beds at u=0.41B. It was indicated that a lower footing settlement is significantly obtained by any applied load-bearing pressure and the semifolded ends in comparison to the planar reinforcement case. The improvement is mainly caused by the confinement effect resulting from the folded method, Shukla (2004) and Shukla (2016). Thus, the geogrid reinforcement should always be installed in dense to very dense sand appropriately possessing geogrid semifolded ends to reach the highest effectiveness based on increasing the modulus of the subgrade reaction and final load-bearing capacity. Moreover, it is worth noting that a relatively lower land width is required for this installation technique to construct the reinforced soil foundation bed.
Figure 14 illustrates the impact factor (IF) variation with the embedment depth ratio (u/B) for reinforced soil with a relative density of 90% for a one-layer reinforcement located at various depths with a semifolded geogrid. It is worth noting that IFu does not denote the same as IF1.25 and IF2, in which the subgrade reaction modulus is defined as (IFu=Ksu/Kun, IF1.25=Ks1.25/Kun and IF2=Ks2/Kun) for folded geogrid layers (where kun, ksu, Ks1.25 and Ks2 denote the subgrade modulus amounts of the unreinforced soil, the folded-reinforced bed at an ultimate settlement ratio, the folded-reinforced bed at a 1.25% settlement ratio and the folded-reinforced bed at a 2% settlement ratio, respectively). The IFu is an enhancement factor utilized by Latha and Somwanshi (2009). They found that the IF increments by increasing the embedment depth of the case with a geogrid semifolded for all three relative settlement ratios. It is worth noting that for any settlement ratio, IFu is always greater in the case of reinforcement with geogrid semifolded at u/B=0.41. For instance, for s/B=1.25%, the wraparound increments IF by approximately 1.73 in comparison to the case with no reinforced layer for Dr=90%. For s/B=2%, the corresponding value is 1.57. Therefore, the results dictate that the semifolded method is highly effective in the case of very dense conditions.
3.3.3. Effect of multilayers of geogrid semifolded
Here, the effects of vertical spacing between geogrid folded layers (h) on the load-bearing capacity of footings were assessed utilizing the optimal u/B, d1/B, l/L1, and Dr values of 0.40, 0.2, 0.5, and 90%, respectively. The total embedment depth for each layer is computed as (D=u+ (h+x) ×N, in which u=d1+x and d2=u+h). where d1 and d2 are the embedment depths of the lap folded element for the first and second geogrid folded layers, respectively. The details of the layout are shown in Fig. 6b. The variation in BCR, as h/B, is constant for the second and third layers (Fig. 16). It was found that by the bearing capacity of the reinforced footing, the optimal value of vertical spacing is obtained between geogrid folded layers at h/B = 0 for a relative density of 90% and gives a greater bearing capacity ratio of BCRf=2.22 for both and three reinforcement layers. Fig. 15 shows the change in compressive stress with their equivalent displacement at a relative density of 90%. The curves reveal a peak point for h/B=0 at the second and third reinforcement layers since geogrid layers have induced tensile strengths leading to failure. This means that deformation at the tensile strength of the geogrid is much less than the deformation at the final load-bearing capacity. Moreover, the results revealed no significant difference between the curves at the steps of the first loading (displacement ratio lower than 2%) for geogrid layers with h/B=0.2 and 0.4 values; however, the difference between curves was more obvious at a higher displacement. When h/B=0.0 (no space between geogrid layers), the settlement ratio, confining pressure, and bearing capacity are at their lowest highest and greatest values, respectively. Furthermore, it was found that incrementing the vertical depth increased the confining pressure; however, no considerable difference was found for h/B>0.
For two geogrid folded layers that are embedded at depths D/B=1.2 and 1.8, sudden failure occurs at a certain point at settlement ratios of 6% and 6.6%, respectively. Inclusion strengthens the geogrid folded layer, leading to passive vertical pressure and rearrangement of the stresses between reinforcement layers. Geogrid folding helps with densifying soil, expanding the volume of soil, and remobilizing sand particles around the lap length. This behavior of soil takes place by increasing the bearing capacity and settlement to reach the final failure point, and the failure surface of the soil will lengthen to the ground surface. This failure refers to the occurrence of general shear failure in reinforced soil with two geogrid folded layers. The settlement is lower for a considered applied pressure, with the inclusion of part or full folded layer of the geogrid reinforcement, and is lower again by increasing the number of reinforcement layers. Figure 16 displays that, in general, for constant vertical spaces between the geogrid folded layers (h/B=0.0), more reinforcement layers result in a stiffer foundation. The inclusion of more than two geogrid folded layers had no considerable effect on the increasing load-bearing capacity of footings and reducing settlement. It also did not change the failure mechanism of the soil foundations. Therefore, in this research, the optimum number of geogrid folded layers was achieved as two layers.
3.4. Comparison of the behavior of multilayered geogrid folded and multillayer geogrid planar arrangements
Fig. 17 represents the bearing pressure-settlement behavior of unreinforced soil, geogrid folded and planar geogrid reinforced foundations when the geogrid semifolded layers were placed in N=3, h/B=0, d2/B=1.0, D=1.2B; N=2, h/B=0, d2=0.6B, D=0.8B; N=2, h=0.2B, d2=1.0B, D=1.2B; N=2, h=0.4B, d2=1.6B, D=1.8B, and planar geogrids were rested at N=2, u=0.3B, h=0.4B and N=3, u=0.3B, h=0.4B, respectively, at a relative density Dr=90%. The lap length and upper depth of laps are kept constant for all geogrid semifolded layers as l/L=0.5 and d1/B=0.2, where L=5B and B=10 cm. It may be found that by incrementing the reinforcement layers (incremented mass of the geogrid folded and geogrid planar reinforcements and subsequent increment in the reinforced zone depth; D/B), both bearing pressure (bearing pressure at a specified settlement) and the stiffness considerably increase. For unreinforced soil (Fig. 17), the peak bearing pressure occurs at a footing settlement equivalent to approximately 9% of the footing width. In the case of planar geogrid layers, the failure points for two and three layers occur at footing settlements equal to 25% and 20%, respectively. On the other hand, for two and three geogrid folded layers, the peak failure point takes place at a settlement ratio of less than 7% of all multilayered geogrid semifolded layers. This explains the significant effect of inclusion geogrids semifolded in the soil mass bed. For the planar arrangement, over a footing settlement level of s/B=10–25%, a considerable reduction in the pressure-settlement curve slope is observed. In this range of settlement, the upper surface heave became observable by the naked eye with distinct gradient alterations. By ending the test, the obtained results indicated that the heave was attributed to the soil-reinforcement composite material locally rupturing near the footing owing to the larger footing displacement. Over this phase, the pressure–settlement curve slopes for the moderate and heavily reinforced cases remain almost constant although increasing the footing bearing pressure continuously and incrementally as more mobilization of reinforcement and anchorage is activated. In contrast, folded geogrid behaves differently. The settlements are relatively small in comparison with the case of planar reinforcement. The behavior of the folded lap section as an anchorage element helps reduce the deformations and displacements that are accumulated under the surface of the strip foundation and move them horizontally to spread it into the soil (increasing tensile strength and matching lap part with footing leads to get wider strip footing); thus, it leads to an increment in the resistance confining pressure and transferring a portion of the load to be distributed with the depths without an increase in the settlement, and the resistance continues to increase gradually to reach general shear failure.
The behavior of the geogrid folded and planar arrangement in incrementing the bearing capacity of a reinforced sand bed owing to the increased number of geogrid folded layers or in the number of planar geogrid reinforcement layers are given in Table 7. The unreinforced bed and the effect of the bearing capacity ratio variation (BCRI and BCRf) can be compared based on the reinforcement layer number. In all situations, the values of BCRI and BCRf are larger at failure for folded geogrids than for planar geogrid layers, with multilayered reinforcement as the footing penetrates further. This can be attributed to the tensile strain’s greater mobilization in the reinforcement layers and the additional confinement pressure provided between layers by the inclusion of the folded reinforcement. For multilayered reinforcement, no considerable enhancement in performance is attained when more than three (N>3) folded geogrids are used. Therefore, when three layers of folded geogrids are located in d1=0.2B, h/B=0.0, and u=0.4B, the highest zone of soil usefully reinforces lengthens to a depth of approximately 0.8B (D=0.8B, Table 7). However, Table 7 shows that the performance enhancement caused by the planar arrangement provision may continue beyond 3 layers (N=3 with a reinforcement zone depth of D=1.1B. Table 7 also shows that an enhancement in bearing capacity is greater for the geogrid folded arrangement than for the geogrid planar arrangement, regardless of the settlement ratio of the footing. For instance, for N=2 and a level of settlement ratio of s/B=7%, the geogrid folded installation enhances the bearing pressure for BCRI and BCRf by 1.5 and 2.22, respectively, more than the planar geogrid installation (BCRI =1.13 and BCRf =1.67). In total, the results demonstrate that the geogrid folded system presents better performance than the geogrid planar system.
3.5. Effects of footing width on geogrid folded system
The effect of another footing width (B=7.5 cm) on the behavior of very dense reinforced fine sand with the folded improvement method was carried out. The constant parameters in this series of tests for the folded system were D=0.6B, d=0.3B, L=5B, and N=1, assuming for planar system u=0.3B, L=5B, and N=1. The variable parameters are only lap length l/L=0.25, 0.5, 0.75 and 1.0 (these parameters are l=9.375, 18.75, 28.125 and 37.5 cm, respectively). Figure 18 shows the applied pressure–settlement ratio results for unreinforced geogrid layers, one planar geogrid layer and one folded geogrid layer with various lap lengths. The bearing capacity increases with increasing lap length, and this increment is more considerable for lap length increases for full lap lengths l/L=0.75 and 1.0 than for semifolded lab lengths l/L=0.25 and 0.5. In the case of full folding with a lap ratio l/L=1, the curve reached its maximum bearing capacity at a lower settlement than the other three lap lengths. In the three semifolded cases (Fig. 18), the applied pressure–settlement ratio curves first experienced a peak value qur(1)= 220, 175, and 438 kPa for l=0.25 L, 0.5 L, and 0.75 L, respectively, at settlement ratio s/B=4.85, 3.67 and 10.21%, respectively, then followed by a sudden decrease in their correspondent bearing pressures and a large increase in settlement ratio with this value s/B=35%, after this step the applied pressure increases with increase in settlement ratio to reach at the second peak pressure values qur(2)= 396, 414 and 560 kPa for l=0.25 L, 0.5 L and 0.75 L, respectively, at the largest settlement ratio s/B=42.69, 42.13 and 27.71%, a result of developing a failure surface.
The behavior of the small strip footing (B=7.5 cm) under consideration rests on the folded reinforced sand with dense compaction, and an increment in the applied pressure on the footing will also occur with increasing settlement. Nevertheless, in this case, the failure surface in the soil mass will extend gradually outward from the foundation. When the applied pressure on the foundation equals qur(1), the foundation movement will be along with sudden jerks (Das, 2019). The failure surface requires a significant movement of the foundation in the soil to prolong to the ground surface. This explains the mechanical effect of the upper part of the geogrid semifolded (lap effect) in which the rupture occurs in transverse and longitudinal ribs. Beyond that point, because of the inclusion of a semifolded geogrid, an increment in applied pressure will be accompanied by a larger increment in foundation settlement. This refers to the performance of the lower part of the geogrid semifolded. The load per unit area of the foundation, qur(1), is referred to as the first failure bearing pressure (Vesic, 1963). Note that the second peak pressure value, qur(2)=qur, is referred to as the local shear failure of geogrid semifolded reinforced soil, as shown in Fig. 19b. In contrast, at a larger lap length l/L=1 for the full-folded geogrid, the applied pressure–settlement ratio curve reached its peak value (qur=566 kPa) at a lower settlement ratio (s/B=8.81%) until the failure surface was generated. This behavior is similar to the behavior of the strip footing with a larger width (B=10 cm) at the same relative density Dr=90%.
To determine the optimum embedment depth for strip footing with width B=7.5, a series of experimental tests was performed. The constant parameters in this series of tests for the semifolded system were Dr=90%, L/B=5, and N=1. The variable parameters are only lap depth d/B=0.2, 0.3, 0.4 and 0.5 these parameters with numbers are d=1.5, 2.25, 3.0 and 3.75 cm, respectively, and the total depth are D/B=0.4, 0.6, 0.8 and 1.0 these parameters with numbers are d=3.0, 4.5, 6.0 and 7.5 cm, respectively. Figure 20a demonstrates applied pressure–settlement ratio results for folded geogrid layer system with various lap embedment depth, and it is observed that the bearing capacity increases with increasing the lap depth, with this increase more significant for a lap depth increase for embedment depth d=0.2B and D=0.4B, than for a semifolded lab length d/B=0.3, 0.4 and 0.5. As a result, the optimum depth for this type of technique is d/B=0.2 and D/B=0.4, in which B=7.5 cm, the footing width. Figure 20b represents the variation in applied stress with their equivalent displacement at a relative density of 90%. Note that when h/B=0.0 (no space between geogrid folded layers), the bearing capacity, confining pressure, and settlement ratio are at their maximum, highest and minimum values, respectively. Furthermore, it was found that incrementing the vertical depth increased the confining pressure; nevertheless, there were no significant differences for h/B>0.