1 Introduction

Soil injection technology, which stabilizes the soil by employing an expanding polyurethane resin, is one treatment for building settling problems. The research [14] reports on the large-scale in-situ experiment that was conducted to investigate the effects of soil injection technology on the lifting of a concrete foundation and the soil stabilization (improving of the soil beneath the foundation) at different soil depths. The effects of adding polyurethane-resin for soil shear strength, settlement, deformation modulus, and unconfined compressive strength was investigated by Hassona and Abdelnaeem [6]. Polyurethane reduces settlement; whenever the void ratio is high, the polyurethane fills and expands inside; as a result, the drop in the settlement is high and requires a low injection ratio. The pressure needed to inject polyurethane into soil voids varies depending on how low or high they are, and how big they are. Polyurethane is injected horizontally in larger soil voids.

Bai et al. [2] studied the effect of polyurethane (PU) to protect and improve the soil slope. The results show that the addition of polymers to natural soil may greatly increase its resilience to rainfall and overland flow because treated specimens showed a marked decrease in soil erosion.

Lat et al. [9] examined the applicability and effectiveness of PU as a substitute technique for ground improvement projects. As closed-cell foam, PU is impervious to water, which prevents water from penetrating the soil below it and softens it and lowering its shear strength. To further reduce further settling, Polyurethane foam is a lightweight material. Sufficient overburden on the PU foam, anchorage, or an appropriate drainage system to counter the rising ground water table can all be used to manage the foam's uplift behavior.

Kumar et al. [7] studied the stabilizing effects of polyurethane foam on weak soil. They concluded that, strength of black cotton soil with liquid of polyurethane foam increases its strength. In addition, foam had been applied on and filled the soil gaps. Prior to any building, the (P.U.) foam injection techniques were intended to minimize differential settling in foundations.

Abdulrasool and Al-Wakel [1] studied the behavior of gypseous soil treated with polyurethane foam (PF). Next, using a CBR test, the effects of PF on the strength of this soil under the effect of static loading were assessed. Additionally, a theoretical method for the design and analysis was provided by a physical laboratory model of footings on both treated and untreated of collapsible soil.

Hassona and Abdelnaeem [5] conducted extensive experimental effort to examine the physical properties of polyurethane foam (P.U.). The behavior of polyurethane foam-impregnated sand in three different sites using a plate load test was examined. Also, an unconfined compression test on sand samples mixed with different proportions of polyurethane foam was studied. Each study's findings indicate that the addition of such material, when the sand is impregnated, significantly improves strength and reduces settlement.

An expanding polyurethane resin is used in the soil injection process, providing a unique opportunity to strengthen, improve and compensate for settlement in the foundations of already-existing buildings. According to Sabri et al. [15] the foundations and infrastructures, such as roads or aerodromes built on a particular soil are affected by the advent of such soil problems.

Polyurethane was employed by Tan et al. [16] to treat sand and clay slopes. Through rainfall modelling, unconfined compression, and direct shear testing, the treated slope's strength and erosion resistance were significantly improved.

Polyntsev and Kvitko [13] introduced a research to study the effect of using polyurethane binders in road construction is mainly aimed at strengthening slopes, recesses, bulk structures, cones of bridges and overpasses, the surface of which is strengthened by rubble or gravel, in order to protect them from external environmental factors.

According to Liu et al. [10] a large number of efforts have been focused on restoring inter-particle cohesiveness in order to increase topsoil stability, without sufficient consideration for ecological and environmental factors. Therefore, to prevent erosion and strengthen the top soil of a sandy slope, water-based polyurethane (PU) soil stabilizer is injected. An efficient and environmentally friendly substitute for topsoil stabilization on sandy slopes is PU treatment. The results indicated that within the approximate range of 30–40% is the most cost-effective and efficient PU concentration for soil strengthening.

In slope engineering, traditional reinforced concrete piles are strong and cheap, but their long maintenance period and slow forming make it hard to meet requirements of emergency work, including landslides brought on by rainfall. Wang et al. [17] examine the effect of a novel polymer anti-slide pile type on slope stability during rainfall. The results illustrated that when the intensity of the rainfall increases, the slope stability deteriorates.

Evaluating the strength increases of the polyurethane-treated sand-root composite and, consequently, examining the interactions between the polymer, the root, and the soil was examined by Liu et al. [11]. The strengthening effect is more effective with a higher polymer concentration, according to the results. The results showed that low root content had an unfavourable weakening influence on the treated soil's strength through variable vegetation root contents. Also, due to the special network structure of polymers, soil stability is significantly increased. This is because the roots' tensile strength may be fully mobilized due to the improved shear resistance at the root-soil interface.

Lightweight polyurethane (PU) foam is an effective ground improvement technique for addressing differential soil foundation settling, primarily for infrastructure such as roads, highways, and parking lots. The goal of the research is to investigate how soil uplift and settling interact using the technique of finite elements, overburden load change, and PU foam thickness [8].

Polyurethane columns can be used to increase the bearing capacity of marine clay, according to Yong et al. [19]. The results demonstrated that as the PU columns' length increased, increasing the marine clay's ultimate bearing capacity. At the end, bearing PU columns, a maximum improvement ratio of 220% was achieved.

In recent years, polyurethane polymer has become a popular material for emergency and disaster relief engineering because of its superior tensile qualities. For slope reinforcement, 3D multi-row polyurethane polymer micro anti-slide piles model which takes into account variations in embedded depth and pile placement has been developed. To investigate the viability and strengthening effect of employing small anti-slide piles made of polyurethane polymer to reinforce slopes [18].

In this paper, the effectiveness of medium-density sand and medium-clay slopes that was filled with polyurethane foam (P.U.) as soil piles was studied, the effect of employing various polyurethane foam pile dimensions on these slopes’ safety factor was investigated. In addition, the effect of the spacing between the (P.U.) foam piles used on improving slopes made of medium sand and medium clay soil was studied. Finally, authors have been considering the advantages of using this light material to improve slopes while taking into account a number of significant factors, including the length and diameter of polyurethane foam piles and the effect of the spacing between them on slopes composed of medium-density sand and medium-clay soil. The authors used numerical model (Geostudio program) which considered an important program in soil calculations, to simulate and analyse these cases as discussed in the current study. The constraints of this study: Boundary condition of the numerical program, this study focused on the pile, the pile subjected to axial force only, no bending moment allowed, and the stiffness and type of the support system.

2 Verification of GeoStudio finite element model using [12], and validation of soil model using the Alzey Bridge (after Engin et al. [4])

2.1 Model setup [12]

The problem is symmetric, so only one half is modelled (in this case the right half is chosen). The wide of embankment is 16.0 m high is 4.0 m. The slopes have an inclination of 1:3. The soil formation as shown in Fig. 1. The phreatic level is located 1 m below the original ground surface. Under the soft soil layers there is a dense sand layer of which 4.0 m are considered in the model as shown in Fig. 1, geotechnical properties of the soil layer are listed in Table 1.

Fig. 1
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Cross section of a road embankment (after PLAXIS 2D-Tutorial Manual [12])

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Table 1 Geotechnical properties of the sand and clay soil were used in this verification
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2.2 Comparing theoretical and experimental results

Figure 2 shows the computed and measured compressive strength versus deformation. Both measured and numerical results were found to be in very good agreement. In general, there is high agreement between the computed and measured results as shown in Fig. 2. Hence, It can be employed this finite element program (GeoStudio) that follows in this investigation.

Fig. 2
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Comparison of tutorial manual and GeoStudio software induced strength versus deformation

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2.3 Validation of soil model using the Alzey Bridge (after Engin et al. [4])

Authors using the results of field model (Near Frankfurt, pile loading test of Alzey Bridge) to check the validity of using this program. Also, when examining new soil models. The Alzey Bridge pile load test is commonly used by researchers as an axially loaded validation. The soil formation and groundwater table as shown in Fig. 3. The pile length is 9.5 m and 1.3 m in diameter. The loads were added gradually and kept there until the rate of settling was negligible. Measurements were taken of the applied loads and the resulting displacements at the tested pile head. The soil and pile properties data are presented in Tables 2 and 3, which are taken from the study of Engin et al. [4].

Fig. 3
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Geometry of the pile load test of Alzey Bridge (after Engin et al. [4])

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Table 2 Physical properties of soil used in this verification
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Table 3 Pile Properties used in this verification
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The pile load displacement behavior discovered using the GeoStudio software is contrasted with that derived from experimental results in Fig. 4. The load–displacement behavior of piles may be comparable between the findings of theoretical and field stress tests. As a result, the validity of the soil and pile GeoStudio modeling has been established.

Fig. 4
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Comparison between the experimental and numerical results

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3 Numerical simulation

3.1 Construction procedure of the slopes

Building well-built roads is not only economical but also safe and reduces environmental effects. A stable road's construction is, implicitly, a key element in achieving these objectives. Therefore, a well-built road must have stabilized cuts and fills. This covers the continuous stability of slopes with cut batter, constructed fill, and slopes close to river margins, culverts, bridge abutments, and waterways. The cut banks, ditches, road carriageway, berms, and fill slope are all part of the road structure that must be stable water control is an essential part of road stability. Slopes are typically less expensive to build than walls; therefore they are used to build stockpiles, highways, dams, levees, canals, and other structures. The following steps are used in the construction of the slopes and the polyurethane foam pile technique:

  1. 1.

    Remove unsatisfactory material, using construction drawings as a guide, dig and compact appropriate bedding material to the appropriate heights in steps based on the elevation of separate soil lifts.

  2. 2.

    Establish the reinforcement in accordance with construction drawings to ensure that it matches the design engineer's chosen orientation, elevation, and embedment. Polyurethane foam stacks, for example.

3.2 Using the GeoStudio 2018 program to establish the geometry of the 2D problem

In general, there is high agreement between the computed and measured results as shown in Fig. 3. Hence, It can be employed this finite element program (GeoStudio) that follows in this investigation. Also, the findings of theoretical and field stress tests as shown in Fig. 4. As a result, the validity of the soil and pile GeoStudio modeling has been established.

In the current study, GeoStudio (2D) program was employed to investigate the performance of medium dense sand and medium clay slopes when inclusions of polyurethane foam piles in slopes. The geometry of the numerical 2D model as shown in Figs. 5, 6, 7 and 8.

Fig. 5
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Geometry setup of model slope tests (slope angle = 30°)

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Fig. 6
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Model Slope tests geometry setup (slope angle = 35°)

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Fig. 7
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Model Slope tests geometry setup (slope angle = 25°)

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Fig. 8
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Numerical model Slope tests using GeoStudio 2D Software

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3.3 Boundary conditions and mesh generation

The program's structures mode is used to generate the structural elements. In this case, the modelled structures are (P.U.) foam piles with different diameters, different lengths, and different pile spacing's were adopted in medium dense sand and medium clay slopes. Boundary conditions were assigned as slip surface entry (left side) and exit range (right side) as shown in Fig. 7. When the geometry model using GeoStudio (SLOPE/W) finite element 2D program is completed, the finite element model can be generated. There are five mesh sizes available: medium, fine, very fine, coarse, and very coarse. In this study, to increase accuracy, a fine mesh size was used. The choice of mesh dimension depends on what accuracy of the results is required.

3.4 Material models parameters

The parameters taken in the present study are the density γ in kN/m3, cohesion c in kN/m2, and angle of internal friction Ø. The physical properties of the soil (medium dense sand and medium clay) as indicated in Table 4, these values are extracted from Bowles [3] and modelled in this study using Mohr–Coulomb Model. The characteristics listed in Table 5 were also used to model polyurethane foam piles. In the current study, the physical and mechanical properties of the polyurethane foam used in this investigation are given in Table 6 (after Hassona and Abdelnaeem [5]).

Table 4 Properties of sand and clay used in this investigation
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Table 5 Input data for pile’s material
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Table 6 Physical and mechanical properties of (P.U.) foam (after Hassona and Abdelnaeem [5])
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3.5 Model test series

One hundred sixty-two (162) numbers of test runs are conducted as indicated in Table 7 for slope angle 30°. In addition, eighty-four (84) cases were carried out on piles diameter = 0.5 m, piles length = 1.0–10 m, pile spacing = 0.5 m and sheet piles, using slope angle 25° and 35° to study the effect of slope angle for medium dense sand and medium clay on the value of factor of safety.

Table 7 Details of testing programme for slope angle 30°
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4 Results and discussion

4.1 Introduction

Polyurethane foam piles having diameters of D = 0.5 m and 0.8 m were modelled in medium dense sand and medium clay soil, respectively. The piles length was changed from 1.0 to 10 m. Also, the spacing between these piles was changed between half, one, two meter, and sheet piles. There are many slip surface diagram for each case as shown in Fig. 9. The critical slip surface diagram generated in Geostudio software as shown in Fig. 10 for case of medium clay (pile diameter = 0.8 m, pile spacing = 2.0 m, and pile length = 10 m as an example). The values of factor of safety (F.O.S.) for each case were calculated and the percentage increases in each value were discussed for all cases as indicated in the following sections.

Fig. 9
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Slip surfaces for medium clay (pile diameter = 0.8 m, pile spacing = 2.0 m, and pile length = 10 m as an example)

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Fig. 10
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Critical Slip surfaces for medium clay (pile diameter = 0.8 m, pile spacing = 2.0 m, and pile length = 10 m as an example)

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4.2 Effect of polyurethane foam piles

4.2.1 Medium-stiff cay having 30° slope angle

Figure 11 illustrate the relationship between factor of safety and piles length for medium-stiff clay slope having 30° slope angle, having pile spacing 2.0 m, 1.0 m, 0.5 m, and sheet piles, respectively. The factor of safety increases with the increasing of length and diameter of polyurethane foam piles. The results show that the value of the factor of safety is constant without change until the length of the pile is about 8 m, after which there is an increase in the factor of safety because the critical slip surface does not pass through the pile until 8 m, and after that the critical slip surface cuts the pile, causing an increase in the factor of safety as shown in Figs. 12 and 13.

Fig. 11
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Variation in factor of safety with pile length embedded in the medium-stiff clay for different piles spacing: a s = 2.0 m, b s = 1.0 m, c s = 0.5 m, and d sheet pile

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Fig. 12
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Critical slip surface piles having 0.5 m diameter embedded in the medium- stiff clay, piles spacing = 2.0 m, up to 8.0 m in length

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Fig. 13
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Critical slip surface piles having 0.5 m diameter embedded in the medium-stiff clay, piles spacing = 2.0 m, 9.0 m in length

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4.3 Effect of polyurethane foam piles length

4.3.1 Medium dense sand having 30° slope angle

Using Polyurethane foam piles increases the F.O.S. for medium dense sand having 30° slope angle. Figure 14 shows the relation between factor of safety and piles length for medium dense sand having 30° slope angle, with pile spacing 2.0  m, 1.0 m, 0.5 m, and sheet piles, respectively. The findings indicate that the factor of safety keeps constant up to a length of approximately 3 m. Above that point, an increase in the F.O.S. occurs as a result of the critical slip surface cutting through the pile; as shown in Figs. 15 and 16.

Fig. 14
figure 14

Variation in factor of safety with pile length embedded in the medium dense sand for different piles spacing: a s = 2.0 m, b s = 1.0 m, c s = 0.5 m, and d sheet pile

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Fig. 15
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Critical slip surface piles having 0.5 m diameter embedded in the medium-dense sand, piles spacing = 2.0 m, 3.0 m in length

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Fig. 16
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Critical slip surface piles having 0.5 m diameter embedded in the medium-dense sand, piles spacing = 2.0 m, up to 8.0 m in length

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4.4 Effect of polyurethane foam piles spacing's

4.4.1 Medium-stiff cay having 30° slope angle

Figures 17 and 18 show the relationship between Polyurethane foam piles spacing's and factor of safety (F.O.S) for medium clay having 30° slope angle. The result indicated that factor of safety increased as the piles spacing's decreased. Based on the results, it can be noted that the factor of safety remains constant up to a length of approximately 8 m. Above that point, an increase in the factor of safety occurs as a result of the critical slip surface cutting through the pile, which raises the factor of safety. Also, the percentage increase in F.O.S. and (L/D) ratio as shown in Figs. 19 and 20.

Fig. 17
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Piles length vs. factor of safety behavior for piles embedded in the medium clay, diameter = 0.5 m

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Fig. 18
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Piles length vs. factor of safety behavior for piles embedded in the medium clay, diameter = 0.8 m

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Fig. 19
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Relationship between % increase in F.O.S and (L/D) for piles having different lengths embedded in the medium clay (dia. = 0.5 m)

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Fig. 20
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Relationship between % increase in F.O.S and (L/D) for piles having different lengths embedded in the medium clay (dia. = 0.8 m)

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4.5 Effect of polyurethane foam piles spacing's

4.5.1 Medium dense sand having 30° slope angle

Again, the same results were obtained using Polyurethane foam piles with different lengths embedded in medium dense sand. Figures 21 and 22 show the relationship of Polyurethane foam piles spacing's and factor of safety (F.O.S) for medium dense sand having 30° slope angle. The results show that the value of the factor of safety is constant without change until the length of the pile is about 3 m, after which there is an increase in the F.O.S. because the critical slip surface does not pass through the pile until 3 m, and after that the critical slip surface cuts the pile, causing an increase in the F.O.S.

Fig. 21
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Piles length vs. factor of safety behavior for piles embedded in the medium dense sand, diameter = 0.5 m

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Fig. 22
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Piles length vs. factor of safety behavior for piles embedded in the medium clay, diameter = 0.8 m

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4.6 Effect of polyurethane foam piles spacing's on the percentage increase in factor of safety (F.O.S)

4.6.1 Medium dense sand having 30° slope angle

Also, the percentage increase in F.O.S. and (L/D) ratio as shown in Figs. 23 and 24. The critical slip surface cuts the pile, causing an increase in the factor of safety.

Fig. 23
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Relationship between % increase in F.O.S and (L/D) for piles having different lengths embedded in the medium dense sand (dia. = 0.5 m)

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Fig. 24
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Relationship between % increase in F.O.S and (L/D) for piles having different lengths embedded in the medium dense sand (dia. = 0.8 m)

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4.7 Effect of slope angle on medium clay slope factor of safety (F.O.S.)

As mentioned before, numerical models were built with different slope angles 25º and 35º, polyurethane foam piles having variables lengths embedded in the medium clay, and having the same pile diameter 0.5 m to study the effect of slope angle on factor of safety (F.O.S). Figures 25, 26, 27, and 28 illustrate that increasing the slope angles decreased the (F.O.S.).

Fig. 25
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Piles length vs. factor of safety behavior for piles embedded in the medium clay, slope angle = 35°

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Fig. 26
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Piles length vs. factor of safety behavior for piles embedded in the medium clay, slope angle = 25°

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Fig. 27
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Piles length vs. factor of safety behavior for piles embedded in the medium clay having piles spacing = 0.5 m

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Fig. 28
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Piles length vs. factor of safety behavior for piles embedded in the medium clay, sheet piles

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4.8 Influence of slope angle on medium clay slope factor of safety (F.O.S.) percentage

Figures 29, 30, 31, and 32 show the percentage increase in F.O.S. and (L/D) ratio. The critical slip surface cuts the pile, causing an increase in the factor of safety.

Fig. 29
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Relationship between % increase in F.O.S and (L/D) for piles injected in medium clay, slope angle = 35°

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Fig. 30
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Relationship between % increase in F.O.S and (L/D) for piles injected in medium clay, slope angle = 25°

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Fig. 31
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Relationship between % increase in F.O.S and (L/D) for piles injected in medium sand, piles spacing = 0.5 m

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Fig. 32
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Relationship between % increase in F.O.S and (L/D) for piles injected in medium sand, sheet piles

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4.9 Influence of slope angle on factor of safety (F.O.S) for medium dense sand slope

Also, numerical models were built with different slope angles 25º and 35º, polyurethane foam piles having variable lengths embedded in the medium dense sand, and having the same pile diameter 0.5 m to study the effect of slope angle on factor of safety (F.O.S). Figures 33, 34, 35, 36, 37, and 38 illustrate that increased the slope angles decreased the (F.O.S.). This is because increasing the angle of slope reduces the intersection of the critical slip surface with the piles and thus reduces the (F.O.S.) value for all cases.

Fig. 33
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Piles length vs. factor of safety behavior for piles injected in the medium sand, slope angle = 35°

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Fig. 34
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Piles length vs. factor of safety behavior for piles injected in the medium sand, slope angle = 25°

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Fig. 35
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Piles length vs. factor of safety behavior for piles injected in the medium sand having piles spacing = 0.5 m, and sheet piles

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Fig. 36
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Relationship between % increase in F.O.S and (L/D) for piles injected in medium sand, slope angle = 35°

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Fig. 37
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Relationship between % increase in F.O.S and (L/D) for piles injected in medium sand, slope angle = 25°

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Fig. 38
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Relationship between % increase in F.O.S and (L/D) for piles injected in medium sand, piles spacing = 0.5 m, and sheet piles

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5 Conclusions

This research has presented, A Finite Element analysis employing the GeoStudio 2D software to examine the importance of using PU foams to soil stabilization. Also, this research studies the use of PU as a new type of materials (polyurethane foam piles) (with different diameters, lengths, and pile spacing) injected in clay and sandy soils. The results demonstrated that after the PU was injected, the medium dense sand and medium clay characteristics were significantly improved. Many factors affect the improvement, including the type of soil, the length of injected polyurethane piles, the diameter of the piles, the pile spacing, and the slope angles. It can be concluded that:

  1. 1.

    The PU foam has filled the soil voids, thereby enhancing the characteristics of the slope.

  2. 2.

    PU foam is a lightweight material that may improve soil slope safety factors.

  3. 3.

    The use of polyurethanes as a stabilizing medium for clay and sand soil is technically feasible, mostly because of how quickly they gel and harden. This makes them a good and rapid improvement approach, quick to create, and useful for rehabilitation projects.

  4. 4.

    Percentage increase in F.O.S. increased with the decrease in pile spacing's for both soft clay soil and medium dense sand soil.

  5. 5.

    Using polyurethane piles of diameter 0.5 m, 0.8 m, having spacing of 2.0 m, 1.0 m, 0.50 m, and sheet piles doesn't have any effect on the factor of safety for any pile length less than 9.0 m, but its effect appears from 9.0 m pile length for both types of soils (slope angle = 30°).

  6. 6.

    Also, percentage increase in the F.O.S. continues to increase when using polyurethane piles of diameter 0.8 m, having spacing of 2.0 m, 1.0 m, 0.50 m, and sheet piles), the results show that the value of the factor of safety is constant without change until the length of the pile is about 8 m, after which there is an increase in the factor of safety because the critical slip surface does not pass through the pile until 8 m, and after that the critical slip surface cuts the pile, causing an increase in the factor of safety (slope angle = 30°).

  7. 7.

    In addition, polyurethane piles having diameters of 0.5 m, and 0.8 m had the same increase in the factor of safety for medium sand soil until 8.0 m pile length (slope angle = 30°).

  8. 8.

    The results showed that the percentage increase in the F.O.S. decreased with the increase in slope angles for soft clay soil. But, the increase in the factor of safety was found to increase with the increase in slope angles in case of sand soil.

  9. 9.

    This study demonstrated that the use of polyurethane foam piles has a higher benefit when used in sandy soils than clay soils, because this soil contains a high percentage of voids, and when injected with polyurethane foam solidify the sand and the slope will be more resistant to failure.

  10. 10.

    Comparing these results with those obtained using other stabilization methods, polyurethane reduces settlement; whenever the void ratio is high, the polyurethane fills and expands inside; as a result, the drop in the settlement is high and requires a low injection ratio. It is easy to inject the soil with P.U. comparing with other materials, also cost savings compared to other chemicals materials.

6 Suggestions for future studies

The research can be carried out in the following cases:

  • The study can be done using PLAXIS 3D to study the effects of PU as a new type of materials (polyurethane foam piles) (with different diameters, lengths, and pile spacing) injected in clay and sandy soils.

  • In this study, GeoStudio program was used to improve the F.O.S. for clay and sand soil. In future studies, the author recommends using software such as ABAQUS, Midas, and Flac to simulate these cases.

  • Study the influence ground water table on the F.O.S. for clay and sand.

  • This study can be extended to the use of inclined and horizontal piles and compare them with the results reached from this study.