1 Introduction

Soil stabilization is an increasingly common method for stabilizing soft soils in to meet the necessary engineering specifications and characteristics. This allows for the safe installation of buildings without experiencing significant settlements. Among various ground improvement methods, grouting stands out as an effective solution for stabilizing soft soil. The treated soil has lower compressibility, decreased hydraulic conductivity, and enhanced strength than the original soil (Kazemain & Barghchi, 2012).

In tunnel construction, challenges like water gushing and collapses are common occurrences. Grouting reinforcement emerges as a crucial technology utilized to such issues. Ding et al. (2020) introduced research to develop a model for grouting diffusion under continuous pressure control. As roughness increased, there was a decrease in both the maximum diffusion distance and grouting diffusion velocity.

In soft soils, grouting treatment is a common and efficient way to reduce excessive cross section deformation of tunnel lining rings. A field experiment investigating the application of grouting treatment in an operating shield metro tunnel was conducted. The wide range of monitoring techniques and diverse geometric arrangements utilized in the experiment enable thorough comparisons between the theoretical results and the field monitoring records. The results indicate that increasing the grouting’s effect on the tunnel’s convergence recovery can be achieved by increasing both its height and volume. The grouting efficiency is also influenced by the grout’s relative position in relation to the tunnel (Zhao et al., 2021).

To simulate the settling of flexible footings on loose sand, soils using GeoStudio 2018 (Hakeem, 2022) employed the PLAXIS finite element 2D program. The analysis discovered that in every situation examined, the numerical model outperforms the laboratory model in providing satisfactory results.

Jet grouting is a widely adopted technique for the construction of soil–cement columns, serving as an effective method for soil improvement. Recently, a study by Bilal et al. (2023) delved into the effectiveness of jet grouting columns in stabilizing excavation walls and improving soil stability. The findings underscored the remarkable ability of this method in ensuring the structural integrity of excavation walls.

Elwakil and Azzam (2016) performed research to evaluate and investigate the process of constructing vertical grouting diaphragm walls on each side of an already-existing footing or a loaded strip footing in order to control horizontal movement beneath the footing soil system, reduce settling, and improve bearing capacity. By using this technique, the structure’s capacity to deal with its present loads as well as those resulting from the anticipated addition of one or more stories—stories that are challenging to remove or justify—can be improved.

Karkush et al. (2018) studied the effect of penetrating grouting between soil particles and cementation gel on the value of unconfined compressive strength of soft-density clay. According to the test results, with an increase in the amount of grouting gel, the axial strain decreased while the unconfined compression strength improved.

Additionally, Tipsunavee et al. (2023) proposed a method to alleviate the stresses exerted on foundations by mitigating the soil-pile-structure interaction. Due to the improved soil caused by the cement wall, the shear forces and bending moment in the piles dramatically reduced.

The optimal alternative is to use cement injection as an alternative grouting method to achieve a higher strength suitable for construction purposes. In a study by Salimian et al. (2017), dental plaster was used to create artificial joints, which were then subjected to grouting with various water/cement ratios and tested through direct shear experiments. The results revealed that in both natural and grouted joints, residual and maximum strength increased with joint roughness.

Fracture grouting is a commonly employed technique for reinforcing construction foundations. According to Cheng et al. (2021), a model comprising soil and grouting veins was created to investigate the reinforcing mechanism based on numerical data from a single-hole fracture grouting procedure. The results of the study demonstrated that the compressive modulus of the composite soil increases gradually as grouting increases the pressure.

In the field of geotechnical engineering, the utilization of Portland cement for soil modification is widely practiced. One strategy for variation in soil treatment, grouting, and soil cement mixtures involves investigating the performance of micro-fine cement with different blains. A study conducted by Ahmadpour (2019) demonstrated that as the fineness of the cement increased, the compressive strength of the treated soil improved significantly, while permeability reduced considerably.

In a separate experimental investigation, Tian et al. (2020) carried out an experimental study to understand the characteristics of grouts and grouted specimens. The mechanical and structural properties of grouted specimens were compared, and the impacts on their mechanical behavior were examined using a uniaxial compression test.

In tunnel and foundation treatments, loose sand-poor soils pose a common challenge. To address this issue, grouting with superfine cement slurry is necessary to fill the micro cracks in the soil. In order to study the effect of injecting superfine cement slurry, three sets of experiments were conducted. The results of these experiments, as highlighted in a study by Yao et al. (2018), reveal that the injection of superfine cement slurry into sand significantly enhances the mechanical and physical properties of the treated medium.

A circular foundation was situated on loose sand soil, surrounded by grout diaphragm walls constructed on both sides of it. This study involved extensive experimental work on twenty-one (21) soil models, both reinforced and unreinforced. The bearing capacity of the granular soil was investigated in relation to the width (b) and depth (L) of the grouted walls. The experimental models in this study were also evaluated and simulated using the PLAXIS (3D) tool, and GeoStudio (2D) program. A comparative analysis was carried out between the results obtained from the laboratory model tests and the numerical models to validate the effectiveness of these software applications in the realm of soil enhancement techniques.

2 Research objectives

A number of techniques have been developed to enhance the strength and stability of the ground, such as incorporating vertical reinforcing elements into the subgrade layer. Among these techniques, vertical grouting techniques has proven to be highly effective as a reinforcing element.

In this project, the grout was injected around an existing footing to create a diaphragm wall on one side of the footing. This diaphragm wall is used to provide lateral soil confinement beneath the footing, effectively controlling vertical and horizontal movements of the subgrade.

The primary objectives of the present paper were to study the effects of the grouted walls depth (L) and width (b) on the bearing capacity of granular soil. Additionally, the study aimed to investigate the load settlement characteristics and control horizontal movement underneath the footing soil. Furthermore, the research sought to validate the chosen numerical modelling by comparing findings from physical laboratory model tests with results generated through GeoStudio 2018 and PLAXIS (3D) software. Notably, the utilization of grouted walls in enhancing the properties of loose soils was a key focus of this investigation. This research is novel since it simulates the laboratory model and examines the degree to which the FEM methods predict laboratory results.

3 Experimental program

The Geotechnical Engineering Laboratory at the Higher Institute of Engineering, Minia, used a thorough experimental methodology to assess the effectiveness of grouting diaphragm walls on both sides of a loaded circular footing. A total of twenty-one (21) soil models were subjected to comprehensive analyses. This investigation examined the impact of grouted wall width (b) and depth (L) on the bearing capacity of granular soil.

3.1 Research materials

SikaGrout 214 and loose sand were employed in the course of the experiments. A steel circular foundation, a hydraulic jack, a proving ring, and dial gauges were the tools used in this investigation.

3.1.1 SikaGrout 214

SikaGrout 214 is a cost-effective, cementitious grout that boasts excellent flowability and high early as well as ultimate strength, making it ideal for applications in tropical and hot climates. This versatile grout, only requiring the addition of water, is user-friendly and convenient to work with.

In this study, SikaGrout 214 was used to reinforce and improve the properties of the loose sand soil in the experimental models. Figure 1 shows its application in the 2nd industrial zone, block 28 in Borg El Arab City, Egypt (SikaGrout 214). The physical properties provided by the manufacturer for this grout are indicated in Table 1.

Fig. 1
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SikaGrout 214 used in current study

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Table 1 Physical Properties of SikaGrout 214
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3.1.2 Description and uses

Sikagrout® -214 is a premium-grade, shrinkage-compensating grouting mortar that is pre-mixed for immediate use. It contains carefully selected quartz aggregates, a mixture of cement and fillers, as well as special additives. Upon hydration with water, the product transforms into a fluid paste of gray hue that closely resembles conventional concrete grout.

Uses for Sikagrout® -214 include anchoring bolts or iron bars in concrete, grouting railway rails or travelling crane tracks precisely, securing industrial equipment subject to shocks and vibrations, and grouting in various critical machinery such as turbines, alternators, compressors, generators, machine tools, and beam keying or bridge springier support construction.

3.1.3 Sand samples and tests in this study

Sand from an area of EL-Minya’s New Minia was obtained for the purpose of the work. For the model investigations, the base sand was cohesive-free, clean, and dry. In a direct shear test box, it was discovered that sand with an internal friction angle of 30° had a relative density of 33%. The sand used in this experiment was of loose density. Table 2 and Fig. 2 show the properties of sand soil that was found during the laboratory study (ECP 202-2001).

Table 2 Geotechnical parameters of the sand used in this investigation
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Fig. 2
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Grain size distribution of test sand used in the current study

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3.2 Model test setup

The tank size selection criteria were based on prior studies (Elsaied et al., 2014). The minimum height and diameter of the tank must be at least six times the width of the footing. For the purpose of conducting the experiments, a custom test tank was fabricated with a diameter of 60 cm and a depth of 60 cm, as shown in Figs. 3 and 4. The construction material of the tank consisted of steel with a thickness of 2 mm to ensure structural integrity. Reinforcements were added to all sides of the tank to keep it from bulging during testing. To reduce side friction, the internal walls of the tank were smoothed.

Fig. 3
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Photo of test setup

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Fig. 4
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Geometry of model footing tests

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3.2.1 The model’s foundation

For experimentation, a steel model footing with dimensions of 10 cm in diameter and 10 cm in thickness is employed. A narrow groove slicing through the footing’s center, as depicted in Fig. 5, aids with load support.

Fig. 5
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Circular footing model

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3.2.2 Dial gauge

Two dial gauges, each with a minimum count of 0.025 mm, are provided—one on each footing, as shown in Fig. 6—to calculate the average settlement of the footing. The settlement of the footings was measured by carefully positioning two dial gauges on the flanges and on the footing. A stand was used to support the dial gauge on the footing; as depicted in Figs. 3 and 7.

Fig. 6
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Dial gauge used

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Fig. 7
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The dial gauge on the footing is supported by a stand

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3.3 Test setup and testing methodology

3.3.1 General

A laboratory test was conducted using a circular foundation placed on loose sand as the model. To enhance the stability and strength of the foundation, vertical grouted diaphragm walls were employed as reinforcement on both sides of the footing. The primary purpose of employing these walls was to provide lateral confinement for the underlying subgrade layer. In multiple testing, twenty-one soil models with a density of 18.0 kN/m3 were employed. The test results, analysis, and experiment observations are presented in this paper.

3.3.2 Model test methodology

A test tank with dimensions of 60 cm in diameter and 60 cm in depth was filled with granular sand that had been sieved using IS standard. The steel tank was filled to the specified height following the same procedure as described in Hakeem's study (2018) after the approximate height was marked. As shown in Fig. 8, a large hand compaction hammer was utilized to complete the task. After thorough analysis, it was decided to ensure that, when hammer drops were released from a predetermined height, they would land uniformly and evenly on all compacted layers. In order to ensure equal ground compaction and the required distribution of unity weight, this type of compaction was used. More compacted soil layers were added in order to achieve an overall soil layer thickness of 0.6 m. The top surface was then levelled, as shown in Fig. 9. To provide lateral confinement for the subgrade layer, grout vertical diaphragm walls were placed along the sides of the footing. A strong piece of reinforcement can be noticed in the grouting diaphragm. Table 1 provides an overview of the physical characteristics of the test cement.

Fig. 8
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The hammer used in soil compaction

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Fig. 9
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Levelled soil surface after completing compaction process

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During the preparation of water-grout mixtures, it is essential to adhere to the recommended weight ratio of 1:2 between the injected sand and cement as suggested by Hakeem (2018). For the present experiment, dry mixing was chosen. The following steps were carried out in order to prepare the grout mix for use:

  1. 1-

    The most accurate way to calculate the weight of the sand that needs to be injected is to measure its volume. This means that the weight of sand needed is equal to ((π × d2 / 4) × L) × γsand), where d is the sand’s diameter and L is its depth.

  2. 2-

    Taking into account the sand injection zone, the weight of grout is computed using a 1:2 ratio.

  3. 3-

    The optimal weight-to-cement ratio is established. (typically assumed to be 0.55, aligning with prior studies (Elwakil & Azzam, 2016)).

  4. 4-

    To make the grout mix, the designated amount of water was added to the cement.

Table 3 shows the physical parameters of the tested grout-cement mix for grout. For the injection method, a small piece of hand equipment, such as a syringe, was used to place the grout on the subgrade layer. The problem explanation and the parameters being researched are shown in Fig. 10. Various influences on the bearing capacity of the reinforced subgrade layer were analyzed by modifying the test parameters, including:

  1. 1.

    The breadth of the footing divided by the width of the reinforcing portion. (d/B)

  2. 2.

    The reinforcing member depth divided by the footing width. (L/B)

Table 3 Geotechnical properties of the grout-sand mix
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Fig. 10
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Studied parameters for the problem being investigated

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3.3.3 Test program model

A total of twenty-one (21) tests with circular footing were carried out under both unreinforced and reinforced situations, as indicated in Table 4.

Table 4 Testing program
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4 Results of experimental work

4.1 General

For load testing, a model of circular footing with a diameter of 10 cm was placed on both reinforced and unreinforced sand substrates. The test result and the settlement of each load increment are displayed on a load-settlement curve.

4.2 Effect of the (L/B) ratio on the circular footing’s bearing capacity during experimental investigations

Figures 11, 12, 13, 14, 15 illustrate the relationship between applied pressure and settlement behaviors in experimental models. Table 5 indicates the percentage increase in bearing capacity values for different soils with variable (L/B) and (b/B). The footing load capacity rises as the relative depth (L/B) of grouted inclusions increases, as discerned from the graphical representations in the aforementioned figures. In addition, an improvement in the load settling curves with an increase in the width ratio (b/B) was noticed. In addition, the interlocking mechanism between the grouted wall and the surrounding soil generates interface friction that reinforces the soil beneath the footing.

Fig. 11
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Load–settlement curve for sand reinforced with grout (b/B = 0.25)

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Fig. 12
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Load–settlement curve for sand reinforced with grout (b/B = 0.50)

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Fig. 13
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Load–settlement curve for sand reinforced with grout (b/B = 0.75)

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Fig. 14
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Load–settlement curve for sand reinforced with grout (b/B = 1.0)

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Fig. 15
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Load–settlement curve for sand reinforced with grout (b/B = 1.25)

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Table 5 The % increase in estimated bearing capacity values for experimental models
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4.3 Effect of (b/B) ratio on the bearing capacity of circular footings during experimental investigations

Table 5 and Figs. 16, 17, 18 show how the bearing capacity of loose sand under a footing increases with the enlargement of the ratio (b/B). To maximize the benefits of soil confinement, the grouted diaphragm should be extended to a reasonable depth below the failure surface of the footing soil system. Results from various loading experiments indicate that extending the diaphragm wall to a certain depth offers significant lateral confinement, thereby preventing soil displacement beneath the footing. At L/B > 1.0, the bearing capacity ratio values are found to be nearly constant. In addition, the stiffness and rigidity of grouted walls serve as a constraint to keep the subgrade layer contained. Additionally, the results demonstrate that using the grouted diaphragm is not cost-effective over the range (b/B > 1 and L/B > 1.0). As evidenced by successful experimental investigations. b/B = 1 and L/B = 1.0 are the most practical and economical ratios for optimal results.

Fig. 16
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Load–settlement curve for loose sand reinforced with grout cement (L/B = 0.50)

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Fig. 17
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Load–settlement curve for loose sand reinforced with grout cement (L/B = 0.75)

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Fig. 18
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Load–settlement curve for loose sand reinforced with grout cement (L/B = 1.0)

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5 Numerical modelling

5.1 Geometric analysis of the 3D problem using PLAXIS software

In this study, a laboratory model was employed to examine the behavior of a circular footing placed on a loose density sand base reinforced with steel. To validate the experimental models, 3D numerical analysis was conducted using the advanced finite element program PLAXIS. Figure 19 illustrates the geometric configuration of the numerical 3D model. All the testing parameters incorporated into the numerical models are presented in Tables 6 and 7. Subsequently, the results obtained from both the experiments and numerical simulations were carefully evaluated to gain comprehensive insights into the system.

Fig. 19
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An analytical representation of a loose, dense sand soil bed stabilized by a grout diaphragm wall

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Table 6 The geotechnical characteristics of sand soil used in the present study
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Table 7 Properties of grout-sand mix used for PLAXIS and GeoStudio models
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5.2 Material model parameters, boundary conditions and mesh generation using PLAXIS 3D

Tables 6 and 7 present the parameters that were derived following procedures similar to those employed in the development of experimental models. The Poisson’s ratio was sourced from the seminal work by Wojciech et al. (2015), the calculation of specific gravity conducted in accordance with the guidelines outlined in ECP 202-2001, and the value of modulus of elasticity was inferred as per the provisions in ECP 202-2001. Through the refinement of the model representing the correlation between applied loads and settlements, the researchers successfully ascertained the load-bearing capacity of the sand soil bed characterized by loose density. Subsequently, a comprehensive comparative analysis was undertaken between the measurements from the physical model and the numerical results. Boundary conditions were established by providing a vertical weight to the soil surface. It should be noted that the model’s deformation was restricted to vertical displacement or movement along the roller boundaries due to the fixed boundary conditions fully enforced at the model’s base. Following the finalization of the geometric model, the mesh or finite element model was developed, as elaborated in Fig. 20.

Fig. 20
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3D view of the used finite element mesh in the modelling of the experimental models

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5.3 Geometric evaluation of the 2D problem using GeoStudio 2018 software

As mentioned before, an actual laboratory model was built to evaluate the performance of a circular foundation resting on reinforced loose sand. The experimental models were then built and validated using 2D numerical analysis and the 2-D finite element tool GeoStudio 2018. Figure 21 shows the geometry of the numerical 2D model.

Fig. 21
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Numerical model of loose sand soil bed reinforced with grout diaphragm wall (GeoStudio Model)

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The soil surface was subjected to a vertical load in order to identify boundary conditions. The model was only allowed to deform along its vertical sides, or the roller edges, because it was completely fixed along the model foundation. As a result, the geometry model was completed, and the finite element model, also referred to as the mesh, could be generated. Subsequently, the results of the experiment and the numerical model were compared and evaluated.

5.4 Parameters of material models

A comprehensive compilation of the soil characteristics associated with the grout-sand mixture used in these models can be referenced in Tables 6 and 7. Additionally, an in-depth comparative analysis was conducted between the numerical results and the measurements obtained from the physical model.

6 Results of numerical modelling

6.1 Comparison between the numerical and experimental outcomes

Figures 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33 show the relation between applied pressure and settlement for loose sand soil. This relationship was evaluated through both physical laboratory models and numerical simulations (Plaxis & Geostudio, 2018). The outcomes obtained from these experimental investigations and computational calculations exhibit strong agreement.

Fig. 22
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Relation between pressure and settlement for unreinforced loose sand bed, and for reinforced loose sand bed in the case that L/B equals 0.5

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Fig. 23
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Relation between pressure and settlement for reinforced loose sand bed in the case that L/B equals 0.5 and b/B equals 0. 5, 0.75

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Fig. 24
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Relation between pressure and settlement for reinforced loose sand bed in the case that L/B equals 0.5 and b/B equals 1.0, 1.25

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Fig. 25
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Relation between pressure and settlement for unreinforced loose sand bed, and for reinforced loose sand bed in the case that L/B equals 0.75

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Fig. 26
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Relation between pressure and settlement for reinforced loose sand bed in the case that L/B equals 0.75 and b/B equals 0. 5, 0.75

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Fig. 27
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Relation between pressure and settlement for reinforced loose sand bed in the case that L/B equals 0.75 and b/B equals 1.0, 1.25

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Fig. 28
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Relation between pressure and settlement for unreinforced loose sand bed, and for reinforced loose sand bed in the case that L/B equals 1.0

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Fig. 29
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Relation between pressure and settlement for reinforced loose sand bed in the case that L/B equals 1.0 and b/B equals 0. 5, 0.75

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Fig. 30
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Relation between pressure and settlement for reinforced loose sand bed in the case that L/B equals 1.0 and b/B equals 1.0, 1.25

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Fig. 31
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Relation between pressure and settlement for unreinforced loose sand bed, and for reinforced loose sand bed in the case that L/B equals 1.25

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Fig. 32
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Relation between pressure and settlement for reinforced loose sand bed in the case that L/B equals 1.25 and b/B equals 0. 5, 0.75

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Fig. 33
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Relation between pressure and settlement for reinforced loose sand bed in the case that L/B equals 1.25 and b/B equals 1.0, 1.25

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The GeoStudio 2D and PLAXIS 3D models developed in this study demonstrated remarkable predictive capabilities in establishing the correlation between applied pressure and settlement, shown in Figs. 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33. Discrepancies observed in settlement values between laboratory experimental data and numerical simulation output may be attributed to several influential factors, including:

  • Potential inaccuracies inherent in settlement measurements obtained through laboratory monitoring procedures;

  • Friction between the tank walls and the sand;

  • The accuracy of the results impacted by the utilization of conventional calculation techniques;

  • Variability in sand distribution within the experimental setup may introduce uncertainties impacting the accuracy of the simulation results.

7 Relation between bearing capacity variations and grouted wall dimensions (depth L and width B)

Figure 34 describes the correlation between variations in bearing capacity and the dimensions of the grouted wall (depth L and width B). Through the use of a second-degree polynomial equation, a significant correlation between these factors was unveiled and is depicted in Table 8.

Fig. 34
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Bearing capacity as a function of (b/B) for all cases that L/B equals 0.5, 0.75, 1.00, and 1.25

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Table 8 Correlation equations between soils bearing capacity as a function of the grouted wall dimensions
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8 Conclusions

Physical laboratory model tests were conducted to evaluate the ultimate bearing capacity of a circular footing subjected to vertical centric load and supported by a grout diaphragm wall-reinforced sand base. The experimental results are documented in this research. The following conclusions can be drawn from the investigation:

  1. 1.

    Injecting grouted walls on both sides of the existing footing proves to be an excellent method for enhancing the subgrade layer’s bearing capacity by an average of 83%. This method may also be considered as a rigid component that creates actual confinement conditions.

  2. 2.

    For optimal cost-effectiveness, the grout wall’s width and depth should match the footing width (B).

  3. 3.

    The grouting procedures used in the reinforced loaded footing system reduce vertical settlement by an average of 38%.

  4. 4.

    The study employed the PLAXIS finite element 3D software to simulate footing settlements in loose sand, using GeoStudio 2018 for modeling. The analysis showed that in every situation examined, the numerical model outperformed the laboratory model in providing satisfactory results.

  5. 5.

    In order to illustrate the relationship between applied pressure and settlement, the suggested numerical model was evaluated by comparing the finite element results with laboratory results.

  6. 6.

    Utilizing finite element analysis facilitated a comprehensive understanding of subgrade layer failure patterns, both confined and unconfined. The insights garnered from this study align with the experimental findings, highlighting the profound impact of reinforcement on the footing’s bearing capacity and its ability to regulate both horizontal and vertical soil movement.

  7. 7.

    The proposed approach offers the potential to enhance the existing building’s load-bearing capacity, enabling it to withstand additional loads such as the inclusion of extra floors that were not originally specified or potentially removed.

  8. 8.

    Lastly, a new correlation equation was introduced to estimate soil bearing capacity as a function of grouted wall dimensions.