Impacts of inclusion of folded geogrid on load-settlement behavior of a strip footing overlaid on fine sands

doi:10.21203/rs.3.rs-658387/v1

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Impacts of inclusion of folded geogrid on load-settlement behavior of a strip footing overlaid on fine sands

https://doi.org/10.21203/rs.3.rs-658387/v1

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This paper describes experimental studies on a strip footing overlaid an unreinforced, planar geogrid-reinforced, and folded geogrid layers of fine sand subjected to static loading. The footing settlement was determined for plate loading of over 25 kN. The variables are assessed in the testing program including the number of planar geogrid layers, the position of the folded geogrid within the soil, the thickness of the geogrid folded layer, wraparound lap and overlap lengths of a folded geogrid, the spacing within geogrid folded layers, and several geogrid layers. The results indicated the superiority of footing performance as a result of static loading for geogrid folded reinforced sand than for planar geogrid reinforced sand. Besides, a critical region was found at a certain depth under the footing, where a geogrid folded results in increased footing settlement. This critical area affects the behaviour of the sandy soils with low footing width. As a result of static loading, the soil compacts within depth, and sand particles penetrate between the geogrid apertures. Then they accumulate in a specific area inside the geogrid folded, therefore it causes small gaps that leads to the rotation of the strip footing in the soil at the foundation surface. In total, based on the results, the reinforced soil-footing systems with adequate folding geogrid layers behave much stiffer, thus, they can handle higher loads with the lower settlement than those in planar reinforced soil. Also, the results show that the values of embedment depth and thickness of geogrid folded are 0.41 and 0.2 of the footing width, respectively. Consequently, the settlement rate is significantly reduced by increasing the amount of folded geogrid layers. The findings revealed that the wraparound technique solution for reinforced cases considerably improves the bearing capacity, reduces settlement, and uses in tight bed spaces.

strip footing

geogrid folded

geogrid planar

fine sand

bearing capacity

settlement

The construction of expensive deep foundations can be avoided by utilizing geosynthetic layers within the soil bed as a very cost-effective method. There are numerous studies on the effects of various parameters and variables involving the enhanced performance of reinforced soil via experimental and numerical methods for various ground types. Binquet and Lee (1975) performed a systematic study for the first time to enhance the strip footing’s bearing capacity utilizing metallic strip. Then, several papers were published on improving the load-carrying capacity of shallow foundations overlaid a reinforced soil, with different arrangements of reinforcing materials for some samples geogrids (Akinmusuru and Akinbolade 1981; Khing et al. 1993; Guido et al. 1986; Das and Omar 1994; Shin et al. 1993; Omar et al. 1993a; Yetimoglu et al. 1994; Das et al. 1994; Adams and Collin 1997; Sitharam and Sireesh 2004; Patra et al. 2005; Shin et al. 2002; Ghosh and Bera 2005; Basudhar et al. 2007; Chung and Cascante 2007; Latha and Somwanshi 2009; Abu-Farsakh et al. 2013; Kumar and Sahoo 2013; Chen and Abu-Farsakh 2014; Badakhshan and Noorzad 2015; Chen et al. 2021). According to the consequences of these studies in the literature, the settlement characteristics and final bearing capacity of the ground can be enhanced by introducing reinforcements in the soil within a definite depth beyond which no substantial enhancement occurs. Moreover, to improve the geosynthetic reinforcement’s effectiveness, innovative methods were presented within literature such as installation of reinforcement multi-layers, presenting a granular soil layer above the reinforcement, utilizing a geocell mattress reinforcement system, and utilizing folded geosynthetic methods (Dash et al. 2001; Avesani Neto et al., 2013; Aria et al. 2019a; Hegde and Sitharam, 2015; Kazi et al., 2015a; Biswas et al., 2016; Wang et al., 2018; Raja and Shukla 2020; Ahmad and Mahboubi, 2021).

All the previous works are finally associated with an enhancement in the soil’s bearing capacity utilizing reinforcing substances. It is deduced that various factors changed the soil’s bearing capacity such as the kind of reinforcing substances, soil density, texture, and ratios of various parameters of geosynthetic materials including reinforcement layers, the position of the geosynthetic first layer, the vertical spacing between consecutive reinforcement layers, the geogrid layer’s width and the footing depth. In the above-mentioned studies, it was revealed that reinforcing the sand increases the footing’s ultimate bearing capacity. Normally, this increment is determined in a non-dimensional form, BCR, known as the bearing capacity ratio and determined by the ratio between the unreinforced and reinforced footings’ ultimate bearing capacity.

As mentioned, the geosynthetic material was utilized as a multilayer or single laid horizontally within the soil bed. Practically, by the site circumstances, it is not occasionally allowed to use a larger width of the geosynthetic element within the soil layer. To overcome this issue, a modern method is proposed by the authors in this work including a fully or semi folding reinforcing layer to conform to the architectural and engineering dimensions of the foundation. This new method also provides high soil tolerance, reduces settlement, and its rotation resistance compared to the normal horizontal reinforcement behaviour. The above literature (Kazi et al., 2015a and Aria et al. 2019a) indicate a big lack of complete studies on the performance of footings overlaid a reinforced soil for two different footing widths and another type of geosynthetic. Ahmad and Mahboubi, 2021 has been studied the concept of folded geogrid as semi- or full folded shapes according to strain analysis. This new technology assists to confine the soil under the shallow footing with an opposite (as bound sand material) length where the settlements and strains become very small while achieving the ideal increase in the bearing capacity of the soil. Hence, to build up a more serious comprehension of this performance, in this research, a series of experimental study tests were conducted to assess the behaviour of two strip footing widths in the reinforced dense sand with geogrid reinforcement.

To demonstrate the capability of the proposed method, it is essential to provide laboratory tests for this innovative procedure. and the characteristics of the experimental studies present:

2.1. Description of Soil material

Firozkoh sandy soil with fine grains (No.151) was utilized in the laboratory tests (Ahmad et al. (2020) and Ahmad and Mahboubi, 2021). A sampling of the soil was performed from the Tehran mountainous area, in the northeast of Iran. The soil classification ASTM D422 standard was used to analyze the grain size utilizing various mesh sizes sieves. The obtained laboratory results are Cu = 1.90, C_C=1.11, d₅₀ = 0.34 mm, d₁₀ = 0.20 mm, d_min=0.01 mm, and d_max=0.60 mm. Through the Unified Soil Classification System (USCS) and based on Table 1 and Fig. 1, this soil is classified as poor-graded sandy soil (SP). Determining the soil’s dry unit weight was oriented by the standard ASTM D2049 utilizing a 0.5′′ funnel along with the standard Proctor test where the mould height and diameter are 107.0 mm and 151.6 mm, respectively, and the minimum dry density (γ_dmin) of the soil was 14.09 kN/m³. Through the vibrator table test, the maximum dry density (γ_dmax) was determined in the same size of mould while obtaining the γ_dmax of 16.61 kN/m³ taking into account the specific gravity as G_s=2.68. Figure 2 represents the SEM analysis of particle size. Through six direct shear tests, the mechanical features of fine sand and geogrid-sand interaction coefficient were determined. The direct shear test is carried out using a 60 × 60 mm mould based on ASTM D5321 at relative densities of 90%. The obtained C, ϕ_risdual, and ϕ_peak values were 12 kPa, 32.3°, and 37.5°, respectively (Fig. 6). The test oedometric modulus has been acquired from the 1-dimensional experiment within a dry state as an elasticity value of E_oed=30 MPa.

2.2. Reinforcement element

Ahmad et al. (2020) used one type of geogrid named CE161 made by an Iranian company. It has a unit weight of 0.70 kg/m², a thickness of 3.3 mm, and an opening geometric of 10 mm × 10 mm. The ultimate tensile strength was evaluated at about 6.1 kN/m. In all directions, the geogrid possessed the same tensile strength. The specifications of the reinforcement substance presented by the manufacturer are summarized in Table 2. Figure 4 demonstrates the tensile strength of this kind of geogrid. The geogrid’s physical properties are defined in terms of isolation test conditions (ASTM D 4595, 2011).

2.3. Model footing

Here, physical modelling of the footings was performed using two-strip footings constructed of steel plate. The foundations’ thickness was 20 mm; hence, it is considered as a solid plate not subjected to the scale effect. These two footings have widths of 100 and 75 mm. The direction length of strip footing (390 mm) is the same as the laboratory model box. Through an adhesive coarse sand layer, the foundation bottom surface becomes rough utilizing epoxy glue for ensuring uniform roughness in all the tests. At the centre of the steel plate, the loading is carried out.

2.4. The experimental process and test arrangement

The model experiments were conducted in a big cubic box made of steel with its height, width, and length, which is 800, 400 mm, and 1400 mm, respectively. Selecting the box’s horizontal plane was based on the plane strain problem conditions. The length of the model to the footing width ratio of 16 is considered adequate to prevent interference with the failure surfaces with the model side dimensions. Likewise, the soil bed height in the steel box was chosen as 800 mm. The width of the box and footing was equal. Moreover, the footing length decreased by 5 mm from each side to prevent contact footing with the sandbox wall. Air pressure of almost 10 bars was provided using a pneumatic cylinder armed with an air compressor as a loading system. By employing the pressure circumstances to the soil sample, the system can secure a steady periodic load. Through a 5-ton capacity jack, the soil load is employed to acquire the soil marginal tolerance in all tests. To calculate the applied force, a load cell is used and two linear variable differential transformers (LVDT) was utilized for measuring the footing settlement. The test technique was conducted based on ASTM D 1196 (2016), where the load measurements were run and held continuously for 3 min until the settling rate was less than 0.03 mm/min. To prepare the sample, the rain sandy soil technique (Kolbsuzewski, 1948; Kazi et al., 2015a; Ahmad and Mahboubi, 2021) was utilized to attain the soil regular placement in the steel box proportional to the needed relative density. The preferred relative density values were gained by calibration of the sand particles’ fall speed and fall height through several trials in a particular aluminium cup. Using a tamper, the appropriate soil unit weight was acquired. The unit weight and relative density of fine sand are 16.46 kN/m³ and 90%, respectively. The former studies were concentrated on the dense sandy soil behaviour. Since there is no information and laboratory data regarding the dense sandy soil, it is essential to perform this study on a high compaction ratio to represent the soil performance. Figure 5 schematically illustrates this system. Table 3 and Fig. 6a summarize the explanations of the model experiments utilized in the results for geogrid planar. Table 3 and Fig. 6b represent all tests of this study schematically for a folded geogrid.

Table 3 Experimental setup

B (cm)	L/B or l/L	h/B	Placement of the first layer	N	Form of reinforcement	Tests No.
10	-	-	-	0	Unreinforced*	1
7.5	-	-	-	0	Unreinforced*	2
10	L=3B	-	0.3B	1	Planar	3
10	L=5B	-	0.3B	1	Planar*	4
10	L=7B	-	0.3B	1	Planar	5
10	L=5B	0.4B	u = 0.3B	2	Planar	6
10	L=5B	0.4B	u = 0.3B	3	Planar	7
7.5	L=5B	-	u = 0.3B	1	Planar*	8
7.5	L=5B	0.4B	u = 0.3B	2	Planar	9
7.5	L=5B	0.4B	u = 0.3B	3	Planar	10
10	l=0.25L	-	d=0.2B, D=0.3B	1	Semi-folded*	11
10	l=0.5L	-	d=0.2B, D=0.3B	1	Semi-folded	12
10	l=0.75L	-	d=0.2B, D=0.3B	1	Semi-folded	13
10	l=1.0L	-	d=0.2B, D=0.3B	1	Full-folded*	14
10	l=0.5L	-	d=0.1B, D=0.3B, x₁=0.2B	1	Semi-folded	15
10	l=0.5L	-	d=0.2B, D=0.4B, x₁=0.2B	1	Semi-folded	16
10	l=0.5L	-	d=0.3B, D=0.5B, x₁=0.2B	1	Semi-folded	17
10	l=0.5L	-	d=0.4B, D=0.6B, x₁=0.2B	1	Semi-folded	18
10	l=0.5L	-	d=0.5B, D=0.7B, x₁=0.2B	1	Semi-folded	19
10	l=0.5L	0.0B	d=0.2B, D=0.8B, x₁=0.2B	2	Semi-folded	20
10	l=0.5L	0.2B	d=0.2B, D=1.2B, x₁=0.2B	2	Semi-folded	21
10	l=0.5L	0.4B	d=dopt, D=Dopt, x₁=0.2B	2	Semi-folded	22
10	l=0.5L	0.6B	d=dopt, D=Dopt, x₁=0.2B	2	Semi-folded	23
10	l=0.5L	0.2B	d=0.2B, D=1.2B, x₁=0.2B	3	Semi-folded	24
7.5	l=0.25L	-	d/B=0.3, D/B=0.6, x₁=0.3B	1	Semi-folded	25
7.5	l=0.5L	-	d=0.3B, D=0.6B, x₁=0.3B	1	Semi-folded	26
7.5	l=0.75L	-	d=0.3B, D=0.6B, x₁=0.3B	1	Semi-folded	27
7.5	l=1.0L	-	d=0.3B, D=0.6B, x₁=0.3B	1	Full-folded	28
7.5	l=0.75L	-	d=0.2B, D=0.4B, x₁=0.2B	1	Semi-folded	29
7.5	l=0.75L	-	d=0.3B, D=0.6B, x₁=0.3B	1	Semi-folded	30
7.5	l=0.75L	-	d=0.4B, D=0.8B, x₁=0.4B	1	Semi-folded	31
7.5	l=0.75L	-	d=0.5B, D=1.0B, x₁=0.5B	1	Semi-folded	32
7.5	l=0.5L	0.0B	d=0.2B, D=0.8B, x₁=0.2B	2	Semi-folded	33
7.5	l=0.5L	0.2B	d=0.2B, D=0.8B, x₁=0.2B	2	Semi-folded	34
7.5	l=0.5L	0.4B	d=0.2B, D=1.0B, x₁=0.2B	2	Semi-folded	35
7.5	l=0.5L	0.6B	d=0.2B, D=1.2B, x₁=0.2B	2	Semi-folded	36
7.5	l=0.5L	0.2B	d=0.2B, D=1.2B, x₁=0.2B	3	Semi-folded	37

N= number of reinforcing layers, x₁= thickness of the folded geogrid reinforcing layer, d=depth of lap element, D= total embedment of geogrid layers, h= vertical spacing between geogrid folded layers, l= length of lap and overlap elements, L=length of a geogrid layer in planar or folded, u=embedment of the first layer, B= footing width, and signs (*) mean to repeated each test two following times.

Various load experiments were performed on strip-model footing over the 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’s performance on the utilized soil in the plane strain circumstances was assessed by employing 37 experimental tests on a 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 footing is stated in mm and the results curves are plotted by both applied stress and relative settlement (s/B%). Utilizing a non-dimensional 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).

$$BCR= \frac{{q}_{u \left(reinforced\right)}}{{q}_{u \left(unreinforced\right)}} \left(1\right)$$

In the current work, a novel parameter called increased bearing capacity ratio (BCR_I) is inserted. Eq. (2) represents a ratio of the final load in the geogrid folded reinforced system to that in the without folded (i.e. planar) reinforced system at a certain settlement.

$${BCR}_{I}= \frac{{q}_{u (reinforced-folded)}}{{q}_{u (reinforced-unfolded)}} \left(2\right)$$

Based on Eq. (1), the parameter BCR_f is utilized to measure the bearing capacity ratio of a strip footing overlaying soil with the inclusion of geogrid folded as given in Eq. (3):

$${BCR}_{f}= \frac{{q}_{u (reinforced-folded)}}{{q}_{u \left(unreinforced\right)}} \left(3\right)$$

where q_u 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. Former surveys revealed the elastic performance of loose sand owing to the applied load allocation technique, to a relative settlement of (s/B) = 1% is 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 non-linear 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 reducing the resistance suddenly, revealing the plastic performance of loose soil. Figure 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 different. The reason is 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). Figure 7a represents the applied pressure-relative settlement curves for L = 3B, 5B, and 7B for 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, on break point as 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’s bearing capacity ratio (BCR) for s/B = 10 and 11%. According to Table 4, the BCR increments by increasing the geogrid layer length. BCR non-linearly raises by geogrid planar length until L = 5B, after which, the geogrid length is not further influenced by the (BCR) values. It is observed that L = 5B is the geogrid reinforcement optimal length at every relative settlement ratio (Fig. 7b). Based on the results of Fig. 7 and Table 4, utilizing a geogrid planar length of 5B can leads to a greater resistance within the reinforced soil system mostly affecting the geogrid reinforcement. Similar behaviour was presented in the next figure (Fig. 7b) for footing width of B = 7.5 cm.

Table 4

Results of strip footing test for footing width (B = 10 cm and B = 7.5 cm) in both unreinforced and planar reinforced soils.
B (cm)	L/B	Number of tests	N	u/B	q_u (kPa)	BCR
10	0	1	0	-	330	1.00
10	3	2	1	0.3	440	1.33
10	5	3	1	0.3	487	1.48
10	7	4	1	0.3	425	1.29
7.5	0	5	0	-	280	1.00
7.5	3	6	1	0.3	310	1.11
7.5	5	7	1	0.3	365	1.30
7.5	7	8	1	0.3	308	1.10

3.2. Effect of multi-layers 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 multi-layers of planar geogrid on a bearing capacity for two different strip footing widths B = 10 cm and B = 7.5 cm. It is assumed that the multi-layers of planar geogrid (N) is within 1 to 3. The applied pressure against settlement ratio is displayed in Fig. 8 and Fig. 9 for B = 10 cm and 7.5 cm, respectively. Not only their behaviour was dissimilar, but also the slope of the applied pressure–settlement ratio plot altered with the number of planar geogrid layers for both strip footings 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 the multi-layers of planar geogrid. Incrementing the multi-layers of planar geogrid increase 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 failure planes becomes larger. Regarding the applied pressure-settlement ratio curves for the reinforced and unreinforced tests, it is indicated that the local shear failure is the failure mode for small strip footing (B = 7.5 cm). In large strip footing (B = 10 cm), the unreinforced and reinforced tests contain different failure mechanism. 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 large strip footing (B = 10 cm), planar reinforcement layers contain more pronounced compared to the small strip footing (B = 7.5 cm). According to the experimental results, the main cause for the largest increment in final bearing capacity in large strip footing compared to the small strip footing in the same test condition may be ascribed to the reinforcement mechanism limiting the lateral and spreading deformations of soil. A bigger mobilized tension is caused by the large strip footing in planar reinforcement layers supporting the reinforcement for resisting against 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 present the results of the strip footing test for two footings width (B = 10 cm and B = 7.5 cm) in both unreinforced and the number of planar reinforced soils.

Table 5

Results of strip footing test for two footings width (B = 10 cm and B = 7.5 cm) in both unreinforced and number of planar reinforced soils.
B (cm)	L/B	N	u/B	h/B	q_u (kPa)	BCR
10	0	0	-	-	330	1.00
10	5	1	0.3	-	487	1.48
10	5	2	0.3	0.4	530	1.61
10	5	3	0.3	0.4	550	1.67
7.5	0	0	-	-	280	1.00
7.5	5	1	0.3	-	365	1.30
7.5	5	2	0.3	0.4	390	1.39
7.5	5	3	0.3	0.4	415	1.48

3.3. Effect of one geogrid folded layer

Nowadays, geogrid folded methods (GFM) become widely used as reinforcing elements in many geotechnical installations: dams, embankments, slopes, roads, and 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 quality-controlled geogrid folded as a reinforced soil bed. The advantages of the quality-controlled geogrid folded may be investigated as follows:

3.3.1. Optimum lap length

A series of bearing capacity tests were conducted on the fine sand bed to develop a new technique reinforcement method that is dissimilar from the traditional ones. The traditional methods usually place the reinforcing materials (geogrid, geotextile, geonet, etc…) horizontally into the foundation (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 just 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. But the settlement of strip footing increases with increase applied load. Agreeing to 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 put in the most extendable direction where the material may develop maximum tensile deformation. Therefore, it is placed at embedment depth (d = 0.2B = 2cm and u_f=0.3B = 3cm) by closing a part of geogrid around end with lap length l = 0.25L = 12.5 cm. As anticipated, the bearing capacity of the reinforced soil is incremented owing to the frictional resistance between the upright element of geogrid folded and the soil particles. Nevertheless, the increase is not enough because the soil particles move upwards from the two positions of the footing and the failure occurs as local punching shear. To overcome this problem, it can be offered both sides of the geogrid folded in the underside of the footing with lap length l = 0.5L = 25 cm and it is placed at embedment depth (d = 0.2B = 2 cm and u = 0.3B = 3 cm). As a consequence, the holding capacity increases dramatically and the settlement ratio decreases. When the lap length is extended to (l = 0.75L = 37.5 cm and l = 1.0L = 50 cm) and shared two sides of the lap length with them, the bearing capacity has more significantly improved and the settlement is very smaller than that measured in geogrid planar layers. Because two sides of lap length are shared and fixed with them, an additional tensile forced-induced in geogrid folded and additional lateral resistance affected the behaviour of the strip footing on reinforced sand. The mechanism of support is to be 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, it needs a close look at the geogrid wrapped embedment in fine sand underneath footing subjected to strip loads. The width of a geogrid folded rectangular shape is increased up to several centimetres due to lateral expansion. Moreover, the soil inside geogrid wrapped 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 increases greatly 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 Fig. 11 and Table 6, the ultimate settlement ratio and BCR_f of the footing for a geogrid planar layer (L = 5B) are 12% and 1.47, for folded geogrid (l = 0.5L) are 6% and 1.55, for folded geogrid (l = 0.75L) are 4% and 1.56, and for folded geogrid (l = 1.0L) are 5% and 1.58. Therefore the new technique holds 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 one. This observation explains the effect of additional confinement strength by the inclusion of geogrid folded. Table 6 denotes the results of the strip footing test for footing width (B = 10 cm) in both unreinforced and geogrid folded reinforced soils

Table 6

Results of strip footing test for footing width (B = 10 cm) in both unreinforced and geogrid folded reinforced soils
B (cm)	L/B	l/L	u/B	d/B	q_u (kPa)	BCR_I	BCR_f
10	5	-	0.3	-	487	1.00	1.47
10	5	0	0.3	0.2	490	1.01	1.48
10	5	0.25	0.3	0.2	500	1.03	1.52
10	5	0.5	0.3	0.2	510	1.05	1.55
10	5	0.75	0.3	0.2	511	1.05	1.56
10	5	1	0.3	0.2	520	1.07	1.58

3.3.2. Optimum depth for geogrid semi-folded

Among the vital parameters for reinforced soil with geogrid semi-folded, is the reinforcement layers’ embedment depth from the soil surface. Various results 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 geogrid folded system, five different depths including (d = 0.1B- 0.2B- 0.3B- 0.4B, and 0.5B) from footing bottom are considered for the lap length (upper part l/L = 0.5) of 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 = 10cm. The results of applied pressure versus settlement ratios of the one-layer of geogrid folded 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 the geogrid semi-folded are more effective in a reinforcement based on an increment in final load-bearing capacity when installing in dense sand beds at D = 0.4B. Figure 13 represents the changes in subgrade reaction modulus (k_s) with an embedment depth ratio (u/B) for geogrid semi-folded sand beds with Dr = 90 %. According to Fig. 11, the load-bearing pressures equivalent to the settlement of 1.25 mm, 2.00 mm, and ultimate settlement at failure is determined for reinforced with geogrid wraparound end conditions. It is found that by increasing u/B, k_s continues to increment until u/B = 0.41, then, it reduces by increasing u/B for the reinforced case with geogrid semi-folded at all relative settlements. Moreover, for u/B = 0.41, the geogrid semi-folded increase k_s by about, 13800, 11000, and 11685 kN/m³ for settlement ratios s/B%=1.25, 2.00, and final settlement (s_u%), respectively. Therefore, it may be indicated that the geogrid semi-folded are more advantageous based on increasing the subgrade reaction modulus when installing 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 semi-folded ends in comparison to the planar reinforcement case. The improvement is mainly caused by the confinement effect resultant from the folded method, Shukla (2004) and Shukla (2016). Thus, the geogrid reinforcement should be always installed in a dense to very dense sand appropriately possessing geogrid semi-folded ends to reach the highest effectiveness based on increasing the modulus of 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 embedment depth ratio (u/B) for reinforced soil with a relative density of 90 % for a one-layer of reinforcement located at various depth with geogrid semi-folded. It is worth noting that IF_u does not denote the same as IF_1.25 and IF₂, which the subgrade reaction modulus is defined as (IF_u=K_su/K_un, IF_1.25=Ks_1.25/K_un and IF₂ = Ks₂/K_un) for folded geogrid layers (where k_un, k_su, K_s1.25 and K_s2 denote the subgrade modulus amounts of the unreinforced soil, the folded-reinforced bed at an ultimate settlement ratio, the folded-reinforced bed at 1.25% settlement ratio and the folded-reinforced bed at a 2% settlement ratio, respectively). The IF_u 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 geogrid semi-folded for all three relative settlement ratios. It is worthy to note that for any settlement ratio, IF_u is always greater in the case of reinforcement with geogrid semi-folded at u/B = 0.41. For instance, for s/B = 1.25%, the wraparound increments IF by about 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 semi-folded method are highly effective in the case of very dense conditions.

3.3.3. Effect of multi-layers of geogrid semi-folded

Here, the effects of vertical spacing between geogrid folded layers (h) on the load-bearing capacity of footings was assessed utilizing the optimal u/B, d₁/B, l/L_1, and Dr values as 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 the h/B is constant for the second and third layers (Fig. 16). It was found that by the reinforced footing’s bearing capacity, the optimal value of vertical spacing is obtained between geogrid folded layers at h/B = 0 for relative density 90% and gives the greater bearing capacity ratio as BCR_f=2.22 value for both two and three reinforcement layers. Figure 15 shows the change in compressive stress with their equivalent displacement at the relative density of 90%. The curves reveal a peak point for h/B = 0 at second and third reinforcement layers since geogrid layers have induced them some tensile strengths leading to failure. It means that deformation at the tensile strength of geogrid is much less than the deformation at 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; though, no considerable difference was found for h/B > 0.

For two geogrid folded layers that are embedded at depth D/B = 1.2 and 1.8, a sudden failure occurs at a certain point at settlement ratio 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 folded helps with densifying soil, expanded volume of soil, and remobilized particles of sand around lap length. This behaviour of soil takes place by increasing 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 the general shear failure in the 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 the reinforcement layer. Figure 16 displays that, in general, for constant vertical spaces between the geogrid folded layers (h/B = 0.0), more reinforcement layer results 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 is also didn't 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 behaviour of multi-layered geogrid folded and multi-layers geogrid planar arrangements

Figure 17 represents the bearing pressure-settlement behavior of unreinforced soil, geogrid folded and planar geogrid reinforced foundations when the geogrid semi-folded 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 geogrid 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 semi-folded 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 an unreinforced soil (Fig. 17), the peak bearing pressure occurs at a footing settlement equivalent to about 9% of footing width. In the case of planar geogrid layers, the failure point for two and three layers are occurring at a footing settlement 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 multi-layered geogrid semi-folded. This explains the significant effect of inclusion geogrid semi-folded in 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. At this range of settlement, the upper surface heave became observable by the naked eye as the gradient distinct 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 curves slopes for the moderate and heavily reinforced cases remain almost constant though 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 behaviour of the folded lap section as an anchorage element helps in reducing the deformations and displacements which are accumulated under the surface of the strip foundation and moving 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 behaviour of the geogrid folded and planar arrangement in incrementing the bearing capacity of a reinforced sand bed owing to the increased number of the 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 ratios variation (BCR_I and BCR_f) can be compared based on the reinforcement layers number. In all situations, the values of BCR_I and BCR_f are larger at failure for geogrid folded compared with planar geogrid layers, with multi-layered 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 multi-layered reinforcement, no considerable enhancement in performances is attained when more than three (N > 3) geogrid folded are used. Therefore, when three layers of geogrid folded are located in d₁ = 0.2B, h/B = 0.0, and u = 0.4B, the highest zone of soil usefully reinforced lengthens to a depth of about 0.8B (D = 0.8B, Table 7). However, Table 7 represents 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 presents an enhancement in bearing capacity is greater for geogrid folded arrangement than for 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 BCR_I and BCR_f as 1.5 and 2.22, respectively more than the planar geogrid installation (BCR_I =1.13 and BCR_f =1.67). In total, the results demonstrate that the geogrid folded system presents better performance compared to the geogrid planar system.

Table 7

Results of strip footing test for footing width (B = 10 cm) in both planar and geogrid folded reinforced soils
B (cm)	Form of layer	No. of layers	l/B	h/B	d₂/B	q_u (kPa)	BCR_I	BCR_f
10	-	-	-	-	-	330	-	1.00
10	Planar	2	0.5	0.4	-	530	1.09	1.61
10	Planar	3	0.5	0.4	-	550	1.13	1.67
10	Folded	2	0.5	0.0	0.6	732	1.50	2.22
10	Folded	2	0.5	0.2	1	690	1.42	2.09
10	Folded	2	0.5	0.4	1.6	667	1.37	2.02
10	Folded	3	0.5	0.0	1	734	1.51	2.22

3.5. Effects of footing width on geogrid folded system

The effect of another footing width (B = 7.5 cm) on the behaviour 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 applied pressure–settlement ratio results for unreinforced, one planar geogrid layer and one folded geogrid layer with various lap lengths, and it is indicated that the bearing capacity increments by rising the lap lengths, with this increment more considerable for a lap length increase for full lap length l/L = 0.75 and 1.0, than for a semi-folded lab length l/L = 0.25 and 0.5. In the case of fully folded with 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 semi-folded cases (Fig. 18), the applied pressure–settlement ratio curves first experienced a peak value q_ur(1) = 220, 175, and 438 kPa for l = 0.25L, 0.5L, and 0.75L, 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 q_ur(2) = 396, 414 and 560 kPa for l = 0.25L, 0.5L and 0.75L, respectively at the largest settlement ratio s/B = 42.69, 42.13 and 27.71 %, a result of developing a failure surface.

The behaviour of small strip footing (B = 7.5 cm) under consideration rests on the folded reinforced sand of dense compaction, an increment in the applied pressure on the footing will also be along with increasing the 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 q_ur(1), the foundation movement will be along with the 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 semi-folded (lap effect) that the rupture occurs in transverse and longitudinal ribs. Beyond that point, because of the inclusion of semi-folded geogrid, an increment in applied pressure will be along with a larger increment in foundation settlement. This refers to the performance of the lower part of geogrid semi- folded. The load per unit area of the foundation, q_ur(1), is referred to as the first failure bearing pressure (Vesic, 1963). Note that the second peak pressure value, q_ur(2) = q_ur, is referred to as the local shear failure of geogrid semi-folded reinforced soil, as shown in Fig. 19b. In contrast, at larger lap length l/L = 1 for geogrid full-folded, the applied pressure–settlement ratio curve reached its peak value (q_ur=566 kPa) at a lower settlement ratio (s/B = 8.81%) and until the failure surface was generated. This behaviour is similar behaviour of the strip footing with 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 semi-folded 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 7.5cm, 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 semi-folded 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 the 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.

Some static loading tests were conducted on two shallow strip footings on geogrid-reinforced and unreinforced sand. A small-scale physical model was considered comprising 37 tests. Two tests were performed on the unreinforced sand foundation, and thirty-two tests were conducted on reinforced sand, with various reinforcing schemes (planar and semi-folded). One type of fine sand at relative density 90%, one type of geogrid, two footings width (B = 75mm and 100mm), three number of LVDT, ten pressure cells and steel box are used to carry out the experimental procedure and to comprehend the performance of reinforced soil with geogrid folded technique. The following concluding remarks are drawn:

1- The inclusion of one geogrid folded could leads to an increment in the ultimate bearing capacity of the footings compared with the installation of geogrid planar. The final bearing capacity ratio BCR_f (the ratio between the final bearing capacity of geogrid folded and unreinforced bed) and BCR_I (the ratio between the final bearing capacity of geogrid planar and geogrid folded bed) could be as high as 1.58 and 1.07, respectively. The maximum increment in final bearing capacity was found in the footing on soil with one layer of geogrid full-folded at the depth of lap 0.2B, lab length l = L, and total depth D/B = 0.41 for relative density 90%. Therefore, the mobilized shear strength at the lap part of the geogrid–soil interface affects the tension effect and performance anchorage of the geogrid folded system.

2- Inclusion of one layer of geogrid folded can highly decrease the settlement response and deformation in the soil bed. For soils with one layer of geogrid semi-folded (l = 0.75L), the settlement reduction was most effective in the case of sharing two sides of a lap with them. Inclusion of geogrid reinforcement folded was as effective as incorporating more layer of planar reinforcement based on settlement reduction and bearing capacity increment. By sharing two sides of overlaps with them, the lower lateral strain and lateral confinement are increased by interfacial resistances resultant from the interaction between the soils beneath above the reinforcement and the geogrid folded reinforcement. This increases the soil layer's elastic modulus and improves the vertical stress distribution on the bed, known as the “vertical stress dispersion effect”, which correspondingly reduces the vertical pressure over the soil bed.

3- The optimal embedment depth to achieve the highest load-bearing capacity and minimum settlement is approximately 0.41B (B is footing width), in which the optimum depth of lap length is 0.2B for fine sand with the largest relative density of 90%. As a result, this embedment depth transfers the stress in a deeper depth inside the soil mass and redistributes the footing load per unit area over a wider area, this is referred to herein as the “stress dispersion effect.”

4- Incorporating more layers of geogrid semi-folded highly increases the foundation soils stiffness, greatly improves bearing capacity and significantly reduces the foundation's settlement. The highest bearing capacity ratio has been obtained for optimum numbers of the two layers. The BCR ratios are in the very large limits for the vertical space between layers (h) is zero (i.e. geogrid folded layers are placed over them directly).

5- The footing width considerably affected the behaviour of the strip footing on reinforced soil. Strip static loading on smaller width changes the footings failure mechanism on geogrid folded reinforced sand: general failure occurred in soils with two layers of geogrid full-folded reinforcement, and local shear failure in the geogrid semi-folded cases. As a result, the optimum depth for this type of technique is d = 0.2B and D = 0.4B, in which B = 7.5cm, the footing width. Note that when h/B = 0.0 (no space between geogrid folded layers), the bearing capacity, confining pressure, and settlement ratio are at their greatest, highest and least values, respectively. Furthermore, it was found that incrementing the vertical depth increases the confining pressure; nevertheless, there was no significant difference for h/B > 0.

Conflict of interest

No conflicts of interest associated with this study and no financial support influencing the results are declared by the authors.

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Tables 1 and 2 are available in the Supplementary Files section

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Impacts of inclusion of folded geogrid on load-settlement behavior of a strip footing overlaid on fine sands

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Abstract

Figures

1. Introduction

2. Experimental Analysis

2.1. Description of Soil material

2.2. Reinforcement element

2.3. Model footing

2.4. The experimental process and test arrangement

3. Results And Discussion

3.1. The optimum length of the reinforcement layers

3.2. Effect of multi-layers of planar geogrid

3.3. Effect of one geogrid folded layer

3.3.1. Optimum lap length

3.3.2. Optimum depth for geogrid semi-folded

3.3.3. Effect of multi-layers of geogrid semi-folded

3.4. Comparison of the behaviour of multi-layered geogrid folded and multi-layers geogrid planar arrangements

3.5. Effects of footing width on geogrid folded system

4. Conclusion

Declarations

References

Tables

Supplementary Files

Status:

Version 1