1. Introduction
Mining engineering and geotechnical engineering are intrinsically linked disciplines that collectively address the challenges of soil and rock behavior in mining environments. Mining engineering focuses on the extraction of minerals from the earth, necessitating robust infrastructure and stable ground conditions [1]. Geotechnical engineering complements this by analyzing and enhancing the mechanical properties of soils and rocks to ensure the safety and stability of mining operations [2,3,4,5]. Within the field of mining engineering, the stability and load-bearing capacity of soils are important for ensuring the safety and effectiveness of mining operations and tailing dams [6,7]. Weak soils, often encountered in mining sites, present significant challenges due to their insufficient strength and stability, which can lead to ground subsidence, equipment malfunctions, and hazardous working conditions [8]. Enhancing the load-bearing capacity of these soils is therefore essential to ensuring the structural integrity of mining infrastructures such as haul roads, embankments, and foundations, and especially tailing dams [7,9]. Soil has a significant impact on the ecosystem and environment from a geotechnical perspective. The environment formed through the gradual breakdown of plants, rocks, animals, and other substances is a valuable reservoir of mineral and metallic components. Considering that this material is a product of the erosion of more durable substances like rocks and gravel, it does not exhibit significant resilience to external forces. Conversely, each soil region possesses distinct and unique characteristics. According to [10], there are soils with a compact grain size that are capable of enduring high pressures, as well as some soils that have a fine-grained texture and possess a high thermal capacity. Throughout history, numerous tests and research studies have been conducted to examine the properties of soil and explore methods for enhancing it.
As mentioned, soils do not have the ability to transfer shear forces to lower layers, so they will be overstressed if the applied load exceeds the limit. Additionally, if the applied shear force enters the soil, which may be due to the weight of the structure and the resulting settlement, the soil will be overstressed and will create many problems. The solution to geotechnical problems can be done through one of the methods of resistance to structure, relocation of design and materials, or replacement, but due to the high cost of these methods, soil improvement using geosynthetics as one of the fastest, most economical, and most reliable methods for increasing soil shear resistance is used [11,12,13,14]. Questions raised about the use of geosynthetics for soil improvement are as follows:
Which model of geosynthetics will be effective for soil improvement?
In what classification of soils will the use of geosynthetics have better effects?
What depth is optimal for burying geosynthetics in order to have the highest soil bearing capacity?
What effect will the changes in the length of geosynthetics have on the soil bearing capacity?
These are the questions that have been investigated in this research, and the results have been stated.
One innovative solution to this problem is the use of geosynthetics. Geosynthetics are synthetic materials used in geotechnical engineering to reinforce, separate, filter, protect, or drain soils. They encompass a variety of products, including geotextiles, geomembranes, geogrids, and geocells, each serving distinct functions to improve soil properties. The application of geosynthetics in mining operations has gained prominence due to their ability to enhance the mechanical properties of weak soils [15], thereby improving their load-bearing capacity and overall stability. Additionally, geosynthetic products are available to engineers almost all over the world. It seems that it is practical and necessary to use these products in areas with loose soil [16].
The adoption of geosynthetics in mining is not only driven by their technical benefits, but also by economic and environmental considerations. Geosynthetics offer a cost-effective alternative to traditional soil improvement techniques such as deep excavation and replacement, chemical stabilization, or the use of expensive aggregates [17]. Moreover, their installation is relatively quick and less disruptive, which is particularly advantageous in the dynamic and often remote environments of mining sites. Geotextiles are the largest group of geosynthetic materials in terms of type and application. In this material, instead of using natural fibers such as yarn, silk, or wool, artificial polycarbonate fibers are used. Geotextiles have more than 80 different uses in construction projects, the most important of which are separation of materials, reinforcement or strengthening of soil layers, and filtration or drainage in soil layers [18]. Therefore, in this research, geotextiles have been used to reinforce the desired soils and increase their bearing capacity. Many scientists have studied and researched the behavior of reinforced soil under strip foundations, as well as the mechanism of soil rupture in such conditions. The single result that these scientists have reached is a dramatic increase in the bearing capacity of soils by placing geotextiles at a certain depth of the soil under the foundation. Environmentally, geosynthetics contribute to sustainable mining practices. Their use can minimize the need for extensive soil excavation and transportation, reducing the overall environmental footprint of mining operations. Additionally, geosynthetics are often made from durable, recyclable materials, aligning with the increasing emphasis on sustainability and resource conservation in the mining industry.
A considerable amount of literature has been published on geosynthetics. For instance, [19] provided an informative and detailed overview of soil stabilization designs using geosynthetics. The authors provide a comprehensive review of the various types of geosynthetics and their applications in soil stabilization projects. The paper also includes case studies from successful projects and provides a detailed analysis of the benefits of using geosynthetics in soil stabilization. The authors of Ref. [20] presented a numerical model for the analysis of geosynthetic-reinforced soil segmental walls under working stress conditions. The model is developed using a finite element approach based on the Mohr–Coulomb model for soil, and is verified against field data from two case studies. Wang et al. [21] investigated centrifuge model tests of geotextile-reinforced soil embankments during an earthquake. The research team used a centrifuge testing apparatus to study the dynamic behavior of a geotextile-reinforced soil embankment under earthquake loading. Rashidian et al. [22] reviewed several laboratory tests and numerical modeling techniques that were used to investigate the bearing capacity of reinforced soil. Panigrahi and Pradhan [23] provided a comprehensive overview of how natural geotextiles can be used to improve the bearing capacity of soil by discussing the different types of geotextiles and how they can be used to increase soil strength. Ouria et al. [24] provided an in-depth analysis of the effect of geotextile arrangement on the bearing capacity of a strip footing, a detailed description of the test setup, and a numerical analysis used to calculate the bearing capacity of the footing. Sinha et al. [25] reviewed the mechanical behavior of geotextiles and geogrids on soil stabilization and provided a provided a comprehensive overview of the various types of them and the different mechanisms by which they interact with soil. Abid et al. [26] provided a thorough review of the bearing capacity of annulus stone columns double-encapsulated with geotextiles. The authors evaluated the various parameters that affect the bearing capacity of these columns, including soil strength, stone size, and geotextile properties. Aliasgharzadeh et al. [27] presented an experimental study of the pullout capacity of horizontal plate anchors embedded in granular soil and reinforced with geocells and geotextiles. The authors conducted experiments to investigate the influence of reinforcement on the pullout capacity of the anchors.
After reviewing the existing above-mentioned literature, it is evident that significant advancements have been made in the application of geosynthetics for soil stabilization. However, gaps remain, particularly in understanding how the embedding depth and length of geotextiles affect the load-bearing capacity of strip foundations across different soil types. Most studies have focused on generalized applications, with limited emphasis on the complex interplay between these variables, especially in the context of varying soil conditions and specific challenges in mining geotechnics. This research seeks to address these flaws by exploring the following aspects:
Numerical Modeling of Geotextiles: this research utilizes advanced finite element analysis (FEA) through Abaqus to simulate the interaction between geotextiles and soil, providing a high-fidelity model that accounts for complex stress distributions.
Influence on Soil Failure Mechanisms: this study investigates how geotextile placement alters soil rupture mechanisms, particularly in weak soils commonly found in mining applications.
Impact of Geotextile Embedment Depth: by varying the depth at which geotextiles are embedded, this research quantifies the effect on load-bearing capacity, offering precise recommendations for optimal depth in different soil types.
Effect of Geotextile Length on Bearing Capacity: this study systematically examines how changes in geotextile length influence bearing capacity, identifying critical lengths that maximize soil stabilization.
Variation in Soil Types: a comparative analysis of different soil types (ML, SM, SW) is conducted to determine how soil composition affects the performance of geotextiles.
Determination of Optimal Geotextile Placement: this research provides specific guidelines for the optimal burial depth and length of geotextiles tailored to different soil conditions, contributing to safer and more efficient geotechnical practices in mining.
The novel contribution of this research lies in its detailed examination of these factors through validated numerical models and its focus on practical applications within mining geotechnics. Unlike previous studies, which often generalize the benefits of geosynthetics, this research provides quantifiable insights into how specific variables can be optimized to enhance soil stability in mining environments. This contributes to the existing body of knowledge by offering data-driven recommendations for the effective use of geosynthetics in mining infrastructure, aiming to improve the safety, sustainability, and cost-effectiveness of mining operations.
In this study, we employ numerical modeling using Abaqus (R2016X) [28], a leading FEA software in geotechnical engineering. Abaqus is selected for its precision in handling complex stress analyses, particularly in models where stress concentrations at various soil depths are critical. The software’s ability to generate highly detailed elements in areas of stress concentration ensures accurate results that can be confidently applied to real-world scenarios. Following model validation through laboratory testing, this research proceeds with parametric studies to explore the effects of varying geotextile lengths and embedment depths. These findings are expected to provide actionable insights that enhance the structural integrity of mining operations, ultimately supporting the development of stronger, more resilient mining infrastructure.
The structure of this paper is as follows: Section 2 outlines the materials and methods, including the properties of the selected soils, foundation and geotextile specifications, model geometry, and processing stages. Section 3 discusses the validation of the numerical models comparing with laboratory results. Section 4 presents the findings, focusing on the effects of soil particle size and geotextile placement on bearing capacity. This paper concludes with a summary of key findings and recommendations in Section 5.
2. Materials and Methods
2.1. Material Specifications
To comprehensively investigate the effects of soil types, this research has selected three soil models, ranging from fine-grained to coarse-grained. Fine-grained soils have high cohesion and a low internal friction angle, while coarse-grained soils have very low cohesion but a high internal friction angle. The characteristics of the soils for numerical modeling are in Table 1.
This research assumes a rigid foundation that maintains its shape during settlement and directly transfers the stresses to the underlying soil. The Mashhad Pol Borj Company (Mashhad, Iran), a company that produces a variety of geosynthetics, provided the geotextile specifications used for modeling (Table 2 and Table 3).
2.2. Creating Model Geometry
To draw the model, due to the two-dimensional nature of the modeling, it has been drawn as a plane strain. Figure 1 displays the specifications and the model.
Next, we enter the property module to enter the material specifications. The parameters that need to be defined for the software are density, elasticity properties, and plasticity properties. After defining the characteristics of the materials (Table 4), the plane strain model of the soil, foundation, and geotextile is defined (Table 5), and finally, in the section of assigning materials to the sections, the defined characteristics are assigned to the desired geometry.
2.3. Assembly of Parts
In this stage (the assembly module), the geometry parts of the model are assembled together. We define the parts of soil geometry and foundation as dependent on each other, and the geotextile as non-dependent. Then, we use the tool to move the parts and place them in their proper positions by providing specific coordinates.
The analysis (step module) is divided into two steps. The first step is to apply geostatic stresses caused by the soil’s own weight; the second step is to apply controlled settlement over a longer period of time to apply it to the soil at an almost constant speed. For analysis, both steps are dynamically defined (Table 6).
In this module (Interaction module), once the parts have been assembled, we first define the surfaces that are in contact with each other (Figure 2), and then we define suitable physical characteristics for them. In this model, a contact surface is defined for the foundation and soil, and the geotextile is defined as being buried at the desired depth. In order to deploy geotextiles at the prescribed depths, a constraint called embedded region is used; additionally, to solidify the foundation, it is necessary to define a constraint called rigid body, which is shown in Table 7.
2.4. Loading, Boundary Conditions, and Meshing
In this step (Load module), the desired boundary conditions are first applied to the floor level and around the soil geometry.
First, by defining a reference point on the foundation surface, we block the horizontal movement of this point. Because the analysis of this model and the type of loading is displacement control, the value of 40 cm of displacement in the vertical direction (sitting) is defined for all models. For both sides of the soil geometry, we close the displacement in the horizontal direction, and for the bottom of the soil geometry, we close the displacement in both horizontal and vertical directions. Next, we define the loads applied to the soil during the model analysis in the load application section (Figure 3). We enter the soil’s weight during the analysis period as geostatic stress, and define the applied load on the foundation as displacement control in the foundation’s boundary conditions. Finally, the initial geostatic stress is defined for the stress distribution in the depth of the soil using the soil density. Additionally, in this module, for the gradual application of the amount of foundation leakage, a function is defined that gradually increases the amount of settlement in the given period of time until it reaches the final value (Table 8).
Given that the Abaqus software utilizes a finite element solver for programming, it is essential to initially segment the continuous environment of the model geometry into smaller components. The meshing (mesh module) of the model geometry is done in the form of more and finer elements in the areas of stress concentration, according to the conditions of the foundation on the soil and also the stresses applied to the soil (Figure 4). Using the continuity condition, the software will estimate the solutions for the continuous domain. The approximate number of geometry elements in the model is shown in Table 9.
After the modeling conditions are completed, by defining the job and naming it, the software first checks all the steps and modeling conditions, and then the model processing begins. The model undergoes processing in accordance with the previously mentioned analytical steps. In this step, one has the ability to observe and control the model’s progress stages, the duration of each stage, and the progression of both kinetic energy and total internal energy.
The post-processing module, also known as the Visualization module, allows users to view and extract the desired outputs for analysis (Figure 5). In this module, it is possible to observe and check the deformation of the geometry of the model, the amount of stress, the amount of soil and foundation settlement, the displacement vectors, and the areas of soil rupture.
3. Numerical Model
3.1. Validation of the Base Numerical Model
In this section, to ensure the accuracy of the numerical model, the results of the laboratory model [29] were compared with the results of the numerical model. In this model, the loading system, as shown in Figure 6, is implemented almost rigidly, with a strip foundation and two columns, and in the same way, beam and column connections are also installed. We utilized metal plates for the test box to ensure its rigidity. In front of the test box, a Plexiglas plastic plate is placed to observe the changes in the calibration points.
3.2. Numerical Material Specifications in the Base Model
The specifications of the laboratory model based on the research of [29] and its dimensions (Figure 7) are shown in Table 10 and Table 11. Another experimental study outlined in [30] was also studied and confirmed the procedure.
3.3. Comparison of Experimental and Numerical Model Results
In this section, the results of the experimental and numerical models are shown in the form of a soil element settlement diagram based on the foundation settlement. The results of comparing the experimental and numerical models for two models of loose and dense sandy soil are shown in Figure 8, Figure 9, Figure 10 and Figure 11. The comparison of the results reveals a slight agreement between the two models’ results, indicating that the current research’s numerical model is suitable for use in a parametric study.
The difference in settlement behavior around 2 m depth between experimental and numerical results in Figure 9 can be attributed to factors such as oversimplified assumptions, variations in soil properties, boundary conditions, and complex transfer of load through soil layers. The numerical model may not fully capture the geotextile’s behavior under load, such as deformation or slippage, which can significantly affect settlement, particularly at critical depths. Inaccurate installation of the geotextile in the laboratory can also cause differences.
3.4. Model Planning
In this section, we will categorize research parameters and data to investigate the effect of different variables on the model response. Geotextile burial depth, geotextile length, and soil type are the parameters that have been analyzed and compared with their changes in different models with different conditions. In experiments 1 to 3, the effect of a 1 m long geotextile at a depth of H/B = 0.125 on the bearing capacity of three soil models was investigated. In experiments 4 to 6, the effect of a geotextile 1.5 m long at a depth of H/B = 0.125 on the bearing capacity of three soil models was investigated. From test number 7 to the last test, the depth of geotextile installation was increased, as shown in Table A1.
4. Results and Discussion
In this section, data analysis and modeling results regarding the impact of burial depth, geotextile length, and soil type on bearing capacity and the mechanisms of soil types are presented. Then, according to the changes in different parameters, the load capacity diagrams of the models were drawn and compared with each other. At the end, by analyzing the results and data, a general summary is presented.
4.1. Mechanism of Soil Rupture
Soil rupture means reaching the ultimate limit of the soil’s bearing capacity, which makes it impossible for the soil to bear more stress and, so to speak, the soil breaks. According to Terzaghi’s theory, the ruptures that occur in soils are of three types: general shear, local shear, and punching shear. We know that soil, like concrete, has a very low tensile strength, which reinforcement methods have strengthened. This research partially compensates this soil deficiency with geotextiles. In the following, some examples of these breaks in the current research models are shown in Figure 12, Figure 13 and Figure 14.
4.2. Qualitative Investigation of the Effect of Geotextile Burial Depth on Bearing Capacity
In this section, the graphs of the bearing capacity for three types of soil reinforced [31] with a one-meter-long geotextile buried at different depths are drawn in one graph. All models report the bearing capacity and its corresponding settlement for the soil element located at the center of the foundation’s bottom surface. Then, by analyzing the graph and the amount of bearing capacity for three soil types (ML, SM, and SW) against the increase in settlement, the effects of geotextile depth have been explained. Observing the general trend of the diagram in Figure 15 and Figure 16, it shows that the effect of the presence of geotextile occurs mostly in the range of high settlements. This effect is observed for ML soil in settlements above 30 cm, SM soil in settlements above 20 cm, and SW soil in settlements in the range of 5 cm. Considering the elastic structure of geotextile, when it is placed in the tensile range, it shows its effects, which is evident in the graphs. It can be concluded that geotextiles have better performance at lower depths and in areas that are exposed to more strain.
Figure 15 shows the bearing capacity of ML-type soil (fine grain) against settlement at different depths of geotextile burial. By comparing the bearing capacities from the depth of H/B = 0.125 m to the depth of H/B = 2, we can see that with the increase of the depth to H/B = 0.250, the bearing capacity suddenly decreases. As the depth continues to reach H/B = 0.500, the bearing capacity gradually increases until we reach H/B = 0.750. At the depth of H/B = 0.750, the bearing capacity almost reaches its first value at the depth of H/B = 0.125, and from then on, with the increase of the depth up to H/B = 2, this value remains constant. Figure 16 provides a more detailed view of these fluctuations. Therefore, the trend of changes in bearing capacity from the depth H/B = 1.8 to H/B = 0.250 is decreasing, from the depth H/B = 0.250 to H/B = 0.750 it is increasing, and from the depth H/B = 0.750 to H/B = 2 it remains constant. The sudden decrease in bearing capacity at the depth of H/B = 0.125 to H/B = 0.250 may be due to the pull-out phenomenon [32]. It can be concluded that the presence of geotextile in fine-grained soils increases the bearing capacity, but at the depth of H/B = 0.125, it does not have much effect on improving the bearing capacity of the soil. SM soil exhibits both the characteristics of fine-grained soil and sandy granular soil, leading to a sinusoidal fluctuation trend in the bearing capacity. At shallow depths, the bearing capacity increases with the increase in settlement, and near the same depths, the bearing capacity suddenly decreases. Examining the diagram in Figure 16 reveals a decrease in the range of sudden changes in settlement, in contrast to the diagram in Figure 15. This reduction can be attributed to the incorporation of geotextile into the tensile spectrum, which effectively addresses the increase in settlement. This could be due to the larger size of SM soil particles compared to ML soil, which has a higher compaction and settlement speed and brings the geotextile into the tensile stress limit faster. Therefore, it can be concluded that by increasing the burial depth of the geotextile up to H/B = 2, confirming the progress of the bearing capacity and taking the average of the increases, the bearing capacity of the soil has increased.
Figure 16 shows the bearing capacity of SM-type soil (sandy soil with fine particles). By comparing the bearing capacity of this soil at different depths of geotextile burial, we come across a fluctuating trend in the amount of bearing capacity. By increasing the burial depth of the geotextile from H/B = 0.125 to H/B = 0.250, the highest increase in bearing capacity occurs. Further, with the increase in depth up to H/B = 0.500, the bearing capacity decreases. The cause of the cyclical increase and decrease in soil bearing capacity may be attributed to the performance of the geotextile, which initially settles the geotextile a little, which caused an increase in soil bearing capacity. Due to the fact that SM soil particles are coarser than ML, compaction occurs faster and as a result, we face a sudden increase in bearing capacity. Then, as the settlement continues, the curved part of the geotextile will act like a membrane for the soil and will not affect the amount of settlement or bearing capacity until it reaches its tensile capacity. Therefore, the bearing capacity has decreased. Then, from the burial depth of H/B = 0.500 to H/B = 0.750, the bearing capacity increases again, and with the continuation of the subsidence process, the bearing capacity decreases again until the depth of H/B = 1. After that, up to the depth of H/B = 2, the bearing capacity remains almost constant.
By analyzing the graphs in this section, we find that at the depths where the bearing capacity decreased, the reducing changes in the bearing capacity of the soil were low compared to different depths. In the depths where the bearing capacity increased, the incremental changes of the soil bearing capacity with respect to different depths remained almost constant and did not exceed the maximum value. Thus, the bearing capacity exhibits a sinusoidal pattern, with a gradual decrease as the settlement process progresses, as shown in Figure 17. The arrows in the figure indicate the amplitude of these sinusoidal fluctuations, illustrating their diminishing magnitude with respect to geotextile burial depth.
Figure 18, a graph depicting the bearing capacity of fine-grained sand (SW) soil, clearly demonstrates that geotextile enhances the soil’s bearing capacity at certain depths, while it has minimal impact on other depths. By increasing the depth of the geotextile from H/B = 0.125 to H/B = 0.250, the bearing capacity in this area reaches its lowest value. However, by increasing the trend to H/B = 0.500, the bearing capacity increases to its maximum level. Then, from the depth of H/B = 0.500 to H/B = 1, the bearing capacity decreases, but it is higher than the bearing capacity at the depth of H/B = 0.250. Finally, from the depth of H/B = 1 to H/B = 2, the bearing capacity increases, but it has reached almost half of the incremental changes up to the depth of H/B = 0.500. Therefore, it can be said that the change in bearing capacity is much greater at lower depths because the size of the soil particles in this model is larger and the tendency for compaction is much greater in the upper layers. Secondly, with the increase in the burial depth of geotextile in SW soil, the tensile effects due to the compaction caused by the weight of the soil decreased, and for this reason, the effects of geotextile on the bearing capacity were observed less. By comparing Figure 19 with Figure 16 and Figure 17, we come to the point that with the increase in the size of soil particles at lower settlement values, the soil has entered the breaking stage. As a result, the geotextile enters its tensile performance stage. The cause of this problem is the reduction of the soil cohesion parameter and the increase of the internal friction angle by more than 36 degrees, which breaks in the lower strains of the soil. Therefore, it can be concluded that in the SW soil type, the increase in the bearing capacity of the soil is more visible at lower depths. At greater depths, due to the high settlement caused by the weight of the soil, the density of the soil has increased, and as a result, the effects of the geotextile are not very significant.
In the following, we compare the effects of geotextile at different depths by examining the distribution of stresses applied to the soil, as shown in Figure 19, Figure 20 and Figure 21.
Figure 19, Figure 20 and Figure 21 show the visualization of stresses generated in ML soil reinforced with a one-meter-long geotextile at different depths. As we can see, at the depth of H/B = 0.250, the stress under the foundation has decreased compared to other depths, the reason for which is explained below.
4.3. Quantitative Study of the Effect of Geotextile Burial Depth on Bearing Capacity
The previous section qualitatively investigated the effects of geotextile by drawing diagrams and analyzing the stress distribution in the soil model. In this section, the value of each model’s bearing capacity, derived from the outputs of the numerical model and diagrams, are available in Table A2. In fact, the bearing capacity diagram of each model indicates that the soil enters the rupture zone at any interval where the diagram suddenly drops. Therefore, we have selected the bearing capacity values prior to the soil rupture areas.
In this part, for three different types of soil reinforced with a geotextile model, the bearing capacities at different depths are compared with each other, and then it is checked that for each soil model, the depths for burying the geotextile are effective in improving the soil bearing capacity.
After comparing the bearing capacities of soils, Figure 22, Figure 23 and Figure 24 have been drawn to compare the numerical value and growth rate of the bearing capacity.
According to Figure 22 for fine-grained soil (ML), it can be seen that at the depths of H/B = 0.125 and H/B = 1, the soil has the highest bearing capacity value. At the depth of H/B = 0.250, the lowest value of bearing capacity is observed. As the burial depth increases, the average value of the bearing capacity shows an upward trend, but after passing through the depth of H/B = 1, the bearing capacity again finds a downward trend. Therefore, it can be concluded that the appropriate depth for burying geotextiles in fine-grained soils such as SM is about H/B = 0.125. In general, in fine-grained soils, increasing the depth of geotextile burial will increase the bearing capacity of the soil, although its effect will be less compared to the upper depths of the soil.
According to Figure 23, for sandy soil with fine particles (SM), it can be seen that the highest value of the bearing capacity corresponds to the depth of H/B = 0.250, and the lowest value corresponds to the depth of H/B = 0.125. With the process of increasing the depth of burial from H/B = 0.250, no significant change in the bearing capacity value is observed, and it has a constant average up to the depth of H/B = 2. Therefore, it can be concluded that in this type of soil, the depths near the soil surface will not be a suitable depth for burying geotextiles. In this type of soil, the depth of H/B = 0.250 is considered the optimal depth for burying geotextiles.
According to Figure 24, it can be seen that the depths of H/B = 0.500 and H/B = 0.125 show the highest soil bearing capacity. The graph shows a fluctuating trend in the rate of change of bearing capacity. From the depth of H/B = 0.125 to H/B = 0.250, there is a sharp decrease in bearing capacity and from the depth of H/B = 0.250 to H/B = 0.500, there is a great increase. It appears that this significant increase was due to the geotextile membrane’s performance. In the following, we observe a reduction in the bearing capacity, with the rate of change remaining nearly constant. Therefore, we can conclude that generally, in coarser-grained sandy soils, reinforcing the soil with geotextile will not significantly enhance the soil’s bearing capacity. As we have seen in Figure 22 and Figure 23, with the increase in the size of soil particles, the effects of geotextile gradually decreased. Therefore, in this soil model, the optimal depth for geotextile burial is estimated as H/B = 0.500.
4.4. Qualitative Investigation of the Effect of Geotextile Length on Bearing Capacity
This section scrutinizes the effect parameter of geotextile length by examining the graphs drawn for the soil models. The model program indicates the use of two geotextile models with lengths of one and one-and-a-half meters.
According to Figure 25, increasing the length of the geotextile significantly improves the bearing capacity of the ML soil. This is evident in the lower depths of the geotextile, where the bearing capacity has significantly decreased. However, when the length of the geotextile is increased to one-and-a-half meters, the bearing capacity increases significantly at the same depth. In the length of one-and-a-half meters of geotextile, there were more regular changes in increasing the bearing capacity, but for burial depths greater than H/B = 1, the effects of geotextiles decreased. By increasing the length of the reinforcement, the depth of H/B = 0.250 is the optimal depth for geotextile installation. Therefore, it can be concluded that in fine-grained soils, the use of geotextiles with lengths greater than the width of the foundation has more favorable effects on increasing the bearing capacity.
Further, according to Figure 26, increasing the length of the geotextile in SM soil generally did not have much effect, but in some depths, it also caused a decrease in the bearing capacity. Overall, like the length of one meter, it has gone through relatively constant changes with increasing depth. In some depths, increasing the length of the geotextile reduced the bearing capacity, but at the depth of H/B = 1, the maximum reduction of the bearing capacity can be observed. Only at the depth of H/B = 2 do we see a slight increase in the bearing capacity, which may be due to the function of the geotextile membrane. Therefore, we can conclude that extending the geotextile’s length will not enhance the soil’s bearing capacity in sandy soils containing fine particles (SM).
According to Figure 27, increasing the length of geotextiles in SM soil has not had a significant effect, except at some depths. It can be seen that the fluctuations of the bearing capacity have decreased and progressed at an almost constant rate. The greatest effect of the geotextile length can be seen at the depth of H/B = 0.250, which shows a significant increase in the bearing capacity compared to the one-meter length of the geotextile. In the rest of the depths, the bearing capacity has not changed or has decreased slightly. Therefore, we can conclude that first, extending the geotextile length in sandy soils (SW) at lower depths enhances the soil’s bearing capacity. Secondly, the use of reinforcement in these soils will have favorable effects on the bearing capacity, subject to the increase in the range of the soil tensile zone and the placement of the soil in the tensile zone.
The distribution of stresses applied to each soil model in Figure 28, Figure 29 and Figure 30 allows us to observe how the length of the geotextile affects the soil’s bearing capacity. Additionally, each shape corresponds to the ideal burial depth for extending the geotextile’s length.
4.5. Effect of Soil Type on Bearing Capacity
This section compares the bearing capacities of soils. First, the bearing capacity of the three soil models investigated in this thesis has been calculated using the modified Meyerhof Equation (1). Therefore, we have compared the theoretical and modeled bearing capacity values, which are close to the real dimensions, in this section. Generally, three scenarios arise during soil rupture. In this section, after observing the graph of plastic strains created in each soil model, the failure mechanism of each soil has been investigated.
qu = cNc + γDfNq + 0.5γBNγ(1)
where:qu = ultimate bearing capacity of the soil
c = cohesion of the soil
γ = unit weight of the soil
Df = depth of the foundation
B = width of the foundation
Nc, Nq, Nγ = bearing capacity factors, which are dimensionless and depend on the angle of internal friction (ϕ) of the soil.
Using Equation (1), the bearing capacity for the three soil models (ML, SM, and SW) in Table 12 has been calculated.
According to Table 12, the bearing capacity of SW soil is higher than that of other soils. Therefore, we can conclude that as the size of soil particles increases, so will the soil’s bearing capacity. Keep in mind that Table 12 calculates the bearing capacity values for unreinforced soils.
According to Table A3, the value of bearing capacity for three soil models in reinforced soil states has been compared with each other. Additionally, the Meyerhof bearing capacity and the reinforced soil bearing capacity will be compared.
According to Figure 31, Figure 32 and Figure 33, the significant effect of geotextile on ML soil’s bearing capacity is clear. The bearing capacity of three soil models has increased with increasing particle size. We can also conclude that Meyerhof’s relation calculates a higher bearing capacity in SM and SW soils than the software displays. It is possible that the bearing capacity has decreased due to the local and general shear ruptures that occur for SM and SW soils, respectively, as shown in Figure 13 and Figure 14. Therefore, the reason for the significant reduction in the bearing capacity of the SW soil is the complete shear failure that has occurred for the soil.
After the quantitative and qualitative analyses of the previous sections, the results are summarized in Table A4 in Appendix A.
5. Conclusions
This study examined the effects of geosynthetics on the load-bearing capacity of three different soil types, clay loam, sand, and well-graded sand, using numerical modeling with Abaqus software. Based on the results of the current research, it was determined generally that ML and SM soil types exhibit local shear failure, and SW soil type demonstrates general shear failure. As soil particle size increases from fine to coarse, the bearing resistance of the soil also increases due to the rise in Meyerhof bearing capacity parameters, which can lead to soil failure at lower settlements. The optimal depths of geotextile placement for each soil type were determined as follows: for ML soil, H/B = 0.125; for SM soil, H/B = 0.250; and for SW soil, H/B = 0.5. It was also found that the effects of increasing the length of the geotextile on the bearing capacity of ML soil are more significant, indicating that geotextile usage is more effective in fine-grained soils. The appropriate depths for extending the geotextile were identified as follows: for ML soil, H/B = 0.250; for SM soil, H/B = 2.0; and for SW soil, H/B = 0.250. Furthermore, the suitable lengths of geotextile for installation were found to be approximately 1.5 times the width for ML soil, 1.0 times for SM soil, and 1.0 times for SW soil. Moreover, it was concluded that SW soil typically fails at lower settlements compared to the other two soil types. Therefore, the use of geotextiles at shallower depths, where the soil is subjected to higher tension and pressure, is most appropriate for SW soil. To further enhance the understanding of geosynthetics in soil stabilization, future studies can explore the impact of varying the shape and size of geotextiles on load-bearing capacity, as well as detailed analyses of ground deformation and failure mechanisms related to geotextile-reinforced soils.
Conceptualization: H.T.R. and R.Y.K.; methodology: M.G. and R.Y.K.; software: F.M.J. and M.G.; writing—original draft preparation: H.T.R., F.M.J. and R.M; validation: R.M. and A.A.; formal analysis: M.G. and A.A.; writing—review and editing: R.M. and A.A.; visualization: R.Y.K.; and H.T.R.; supervision, R.Y.K. and A.A. All authors have read and agreed to the published version of the manuscript.
Not applicable.
Not applicable.
The data that support the findings of this study are available in
The authors declare no conflicts of interest.
Footnotes
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Enlarge this image.Figure 3. Soil geometry after applying boundary conditions and loading. (yellow arrows show the loading force direction and orange pins show the boundary condition).
Enlarge this image.Figure 4. The geometry of the model after meshing and the concentration of elements in the high-tension areas.
Enlarge this image.Figure 8. Comparison of the settlement diagrams of loose sandy soil in the (A) numerical model with the base (B) laboratory model.
Enlarge this image.Figure 9. Comparison of the settlement diagrams of dense sandy soil reinforced with geotextile in the (A) numerical model with the base (B) laboratory model.
Enlarge this image.Figure 10. Comparison and matching of loose sandy soil settlement diagrams of two numerical and laboratory models at different depths.
Enlarge this image.Figure 11. Comparison of settlement diagrams of dense sandy soil reinforced with geotextile in two numerical and laboratory models at different depths.
Enlarge this image.Figure 15. Comparison diagram of the bearing capacity of ML soil reinforced with one-meter-long geotextile at different depths.
Enlarge this image.Figure 16. Comparison chart of bearing capacity of SM soil reinforced with one-meter-long geotextile at different depths.
Enlarge this image.Figure 18. Comparison diagram of the bearing capacity of SW soil reinforced with one-meter-long geotextile at different depths.
Enlarge this image.Figure 19. Stress distribution in ML soil reinforced with geotextile at two depths H/B = 0.125 and H/B = 0.250.
Enlarge this image.Figure 20. Stress distribution in ML soil reinforced with geotextile at two depths H/B = 0.500 and H/B = 0.750.
Enlarge this image.Figure 21. Stress distribution in ML soil reinforced with geotextile at two depths H/B = 1 and H/B = 2.
Enlarge this image.Figure 22. Comparison of the bearing capacity of ML soil at different geotextile burial depths.
Enlarge this image.Figure 23. Comparison of bearing capacity of SM soil at different depths of geotextile burial.
Enlarge this image.Figure 24. Comparison of the bearing capacity of SW soil at different geotextile burial depths.
Enlarge this image.Figure 25. Comparison diagram of the effect of changing the geotextile length on the bearing capacity of ML soil at different depths.
Enlarge this image.Figure 26. Comparison diagram of the effect of changing the geotextile length on the bearing capacity of SM soil at different depths.
Enlarge this image.Figure 27. Comparison diagram of the effect of changing the geotextile length on the bearing capacity of SW soil at different depths.
Enlarge this image.Figure 28. Stress distribution related to the optimal depth (H/B = 0.250) of geotextile extension in ML soil.
Enlarge this image.Figure 29. Stress distribution related to the optimal depth (H/B = 2) of geotextile extension in SM soil.
Enlarge this image.Figure 30. Stress distribution related to the optimal depth (H/B = 0.250) of geotextile extension in SW soil.
Enlarge this image.Figure 32. Comparison of Meyerhof’s bearing capacity and the bearing capacity of modeled soil reinforced with one-and-a-half-meter long geotextile at a depth of H/B = 0.250.
Enlarge this image.Figure 33. Comparison of Meyerhof’s bearing capacity and the bearing capacity of modeled soil reinforced with one-and-a-half-meter long geotextile at a depth of H/B = 1.
Characteristics of numerical modeling soils.
| Soil Type | Class | Φ (°) | C (KPa) | γ (kg/m3) | E (KPa) | μ | Dr (%) |
|---|---|---|---|---|---|---|---|
| Fine-grain | ML | 15 | 40 | 1400 | 10 × 104 | 0.1 | 15 |
| Granular | SM | 30 | 25 | 1740 | 15 × 104 | 0.2 | 30 |
| Granular | SW | 40 | 0,10 | 1950 | 24 × 104 | 0.3 | 80 |
Specifications of the geotextile.
| Model | Maximum Strain (%) | Tensile Resistance Force (N) | Thickness (m) | Weight per m2 (Kg) |
|---|---|---|---|---|
| G-150 | 60 | 340 | 0.0016 | 0.150 |
Specifications used in numerical modeling.
| Plastic Strain | Modulus of Elasticity | Maximum Tensile Stress | Density |
|---|---|---|---|
| 60% | 354.17 | 212.50 | 93.75 |
Definition of ML soil characteristics in the Property module.
| Density (kg/m3) | 1400 | Dilation Angle | 0.01 |
|---|---|---|---|
| Modulus of elasticity (KPa) | 10 × 104 | Cohesion (KPa) | 40 |
| Poisson’s ratio | 0.1 | Plastic strain | 5% |
| Internal friction angle | 15 |
Defining geotextile specifications in the Property module.
| Density (kg/m3) | 93.75 | Maximum Tensile Stress | 212.50 |
|---|---|---|---|
| Modulus of elasticity | 354.17 | Plastic strain | 60% |
| Poisson’s ration | 0.02 |
Definition of analysis steps for numerical model processing and processing time in each step.
| Name of the Analysis | Type of Analysis | Duration (s) |
|---|---|---|
| Initial | (Initial) | 0 |
| Geostatic | Dynamic-explicit | 1 |
| Limit load | Dynamic-explicit | 8 |
Definition of interaction.
| Name | Type | Place of Effect |
|---|---|---|
| Geotextile installation in the prescribed depth | Embedded region | Geotextile surface with soil |
| Solidifying the foundation | Rigid body | Foundation |
Load type and values for modeling with ML soil.
| Type of Load and Settlement | Amount of Load and Settlement |
|---|---|
| Soil and foundation weight | 1400 (kg/m2) |
| Foundation settlement control | 40 cm |
| Initial geostatic stress at Z = 0 | 0 |
| Initial geostatic stress at Z = 10 | 14,000 (kg/m2) |
The number of elements for numerical modeling meshing.
| Meshing Area | Approximate Number of Elements |
|---|---|
| Upper and lower bar of soil geometry | 240 |
| Side strips of soil geometry | 200 |
| Foundation environment | 1 |
| Geotextile tape | 40 |
Characteristics of laboratory model soil in two forms, loose and dense.
| Soil Type | Classification | Φ (°) | C (Pa) | γ (kg/m3) | E (Pa) | μ | Dr (%) |
|---|---|---|---|---|---|---|---|
| Granular | SP | 30 | 9810 | 1478 | 1.3734 × 107 | 0.3 | 10% (loose) |
| Granular | SP | 28 | 981 | 1596 | 2.3544 × 107 | 0.3 | −70% (dense) |
Laboratory model geotextile specification.
| Unit weight (Kg/m2) | 0.3 |
| Thickness (m) | 0.0016 |
| Maximum tensile strength (N/m) | 12,959.6 |
| Elongation in the maximum stretch position (%) | 50 |
| Density (kg/m3) | 187.5 |
| Modulus of elasticity (Pa) | 1.617 × 107 |
| Yield stress (Pa) | 8.102 × 106 |
| Poisson’s ratio | 0.02 |
Calculated bearing capacity for three soil models.
| Soil Type | ML | SM | SW |
|---|---|---|---|
| Bearing capacity | 438.38 | 873.84 | 895.11 |
Appendix A
Model planning.
| Test | Geotextile Deployment Specifications | Soil Characteristics | |||||
|---|---|---|---|---|---|---|---|
| H/B | B (m) | H (cm) | C (KPa) | Φ | Υ (kg/m3) | E (KPa) | |
| 1 | - | - | - | 10 | 30 | 1478 | 1.40 × 104 |
| 1 | 0.125 | 1 | 12.5 | 40 | 15 | 1400 | 1.00 × 105 |
| 2 | 0.125 | 1 | 12.5 | 25 | 30 | 1740 | 1.50 × 104 |
| 3 | 0.125 | 1 | 12.5 | 0.10 | 40 | 1950 | 2.40 × 104 |
| 4 | 0.083 | 1.5 | 12.5 | 40 | 15 | 1400 | 1.40 × 104 |
| 5 | 0.083 | 1.5 | 12.5 | 25 | 30 | 1740 | 1.00 × 105 |
| 6 | 0.083 | 1.5 | 12.5 | 0.10 | 40 | 1950 | 2.40 × 104 |
| 7 | 0.250 | 1 | 25 | 40 | 15 | 1400 | 1.00 × 105 |
| 8 | 0.250 | 1 | 25 | 25 | 30 | 1740 | 1.50 × 104 |
| 9 | 0.250 | 1 | 25 | 0.10 | 40 | 1950 | 2.40 × 104 |
| 10 | 0.167 | 1.5 | 25 | 40 | 15 | 1400 | 1.00 × 105 |
| 11 | 0.167 | 1.5 | 25 | 25 | 30 | 1740 | 1.50 × 104 |
| 12 | 0.167 | 1.5 | 25 | 0.10 | 40 | 1950 | 2.40 × 104 |
| 13 | 0.500 | 1 | 50 | 40 | 15 | 1400 | 1.00 × 105 |
| 14 | 0.500 | 1 | 50 | 25 | 30 | 1740 | 1.50 × 104 |
| 15 | 0.500 | 1 | 50 | 0.10 | 40 | 1950 | 2.40 × 104 |
| 16 | 0.333 | 1.5 | 50 | 40 | 15 | 1400 | 1.00 × 105 |
| 17 | 0.333 | 1.5 | 50 | 25 | 30 | 1740 | 1.50 × 104 |
| 18 | 0.333 | 1.5 | 50 | 0.10 | 40 | 1950 | 2.40 × 104 |
| 19 | 0.750 | 1 | 75 | 40 | 15 | 1400 | 1.00 × 105 |
| 20 | 0.750 | 1 | 75 | 25 | 30 | 1740 | 1.50 × 104 |
| 21 | 0.750 | 1 | 75 | 0.10 | 40 | 1950 | 2.40 × 104 |
| 22 | 0.500 | 1.5 | 75 | 40 | 15 | 1400 | 1.00 × 105 |
| 23 | 0.500 | 1.5 | 75 | 25 | 30 | 1740 | 1.50 × 104 |
| 24 | 0.500 | 1.5 | 75 | 0.10 | 40 | 1950 | 2.40 × 104 |
| 25 | 1.000 | 1 | 100 | 40 | 15 | 1400 | 1.00 × 105 |
| 26 | 1.000 | 1 | 100 | 25 | 30 | 1740 | 1.50 × 104 |
| 27 | 1.000 | 1 | 100 | 0.10 | 40 | 1950 | 2.40 × 104 |
| 28 | 0.667 | 1.5 | 100 | 40 | 15 | 1400 | 1.00 × 105 |
| 29 | 0.667 | 1.5 | 100 | 25 | 30 | 1740 | 1.50 × 104 |
| 30 | 0.667 | 1.5 | 100 | 0.10 | 40 | 1950 | 2.40 × 104 |
| 31 | 2.000 | 1 | 200 | 40 | 15 | 1400 | 1.00 × 105 |
| 32 | 2.000 | 1 | 200 | 25 | 30 | 1740 | 1.50 × 104 |
| 33 | 2.000 | 1 | 200 | 0.10 | 40 | 1950 | 2.40 × 104 |
| 34 | 1.333 | 1.5 | 200 | 40 | 15 | 1400 | 1.00 × 105 |
| 35 | 1.333 | 1.5 | 200 | 25 | 30 | 1740 | 1.50 × 104 |
| 36 | 1.333 | 1.5 | 200 | 0.10 | 40 | 1950 | 2.40 × 104 |
Bearing capacity of numerical models.
| Test | Geotextile Deployment Specifications | Soil Characteristics | Bearing | |||||
|---|---|---|---|---|---|---|---|---|
| H/B | B (m) | H (cm) | C (KPa) | Φ | Υ (kg/m3) | E (KPa) | ||
| 1 | - | - | - | 10 | 30 | 1478 | 1.40 × 104 | 388.847 |
| 1 | 0.125 | 1 | 12.5 | 40 | 15 | 1400 | 1.00 × 105 | 508.9540 |
| 2 | 0.125 | 1 | 12.5 | 25 | 30 | 1740 | 1.50 × 104 | 908.0960 |
| 3 | 0.125 | 1 | 12.5 | 0.10 | 40 | 1950 | 2.40 × 104 | 706.1300 |
| 4 | 0.083 | 1.5 | 12.5 | 40 | 15 | 1400 | 1.40 × 104 | 502.3580 |
| 5 | 0.083 | 1.5 | 12.5 | 25 | 30 | 1740 | 1.00 × 105 | 910.1440 |
| 6 | 0.083 | 1.5 | 12.5 | 0.10 | 40 | 1950 | 2.40 × 104 | 704.3690 |
| 7 | 0.250 | 1 | 25 | 40 | 15 | 1400 | 1.00 × 105 | 490.8000 |
| 8 | 0.250 | 1 | 25 | 25 | 30 | 1740 | 1.50 × 104 | 941.1730 |
| 9 | 0.250 | 1 | 25 | 0.10 | 40 | 1950 | 2.40 × 104 | 632.1840 |
| 10 | 0.167 | 1.5 | 25 | 40 | 15 | 1400 | 1.00 × 105 | 504.6220 |
| 11 | 0.167 | 1.5 | 25 | 25 | 30 | 1740 | 1.50 × 104 | 873.8600 |
| 12 | 0.167 | 1.5 | 25 | 0.10 | 40 | 1950 | 2.40 × 104 | 677.0650 |
| 13 | 0.500 | 1 | 50 | 40 | 15 | 1400 | 1.00 × 105 | 496.5650 |
| 14 | 0.500 | 1 | 50 | 25 | 30 | 1740 | 1.50 × 104 | 920.9610 |
| 15 | 0.500 | 1 | 50 | 0.10 | 40 | 1950 | 2.40 × 104 | 733.3540 |
| 16 | 0.333 | 1.5 | 50 | 40 | 15 | 1400 | 1.00 × 105 | 507.5590 |
| 17 | 0.333 | 1.5 | 50 | 25 | 30 | 1740 | 1.50 × 104 | 909.8120 |
| 18 | 0.333 | 1.5 | 50 | 0.10 | 40 | 1950 | 2.40 × 104 | 646.2090 |
| 19 | 0.750 | 1 | 75 | 40 | 15 | 1400 | 1.00 × 105 | 506.5840 |
| 20 | 0.750 | 1 | 75 | 25 | 30 | 1740 | 1.50 × 104 | 929.6590 |
| 21 | 0.750 | 1 | 75 | 0.10 | 40 | 1950 | 2.40 × 104 | 656.7460 |
| 22 | 0.500 | 1.5 | 75 | 40 | 15 | 1400 | 1.00 × 105 | 507.7100 |
| 23 | 0.500 | 1.5 | 75 | 25 | 30 | 1740 | 1.50 × 104 | 911.2680 |
| 24 | 0.500 | 1.5 | 75 | 0.10 | 40 | 1950 | 2.40 × 104 | 660.8910 |
| 25 | 1.000 | 1 | 100 | 40 | 15 | 1400 | 1.00 × 105 | 508.0010 |
| 26 | 1.000 | 1 | 100 | 25 | 30 | 1740 | 1.50 × 104 | 924.8770 |
| 27 | 1.000 | 1 | 100 | 0.10 | 40 | 1950 | 2.40 × 104 | 665.3290 |
| 28 | 0.667 | 1.5 | 100 | 40 | 15 | 1400 | 1.00 × 105 | 508.9090 |
| 29 | 0.667 | 1.5 | 100 | 25 | 30 | 1740 | 1.50 × 104 | 772.7800 |
| 30 | 0.667 | 1.5 | 100 | 0.10 | 40 | 1950 | 2.40 × 104 | 601.3890 |
| 31 | 2.000 | 1 | 200 | 40 | 15 | 1400 | 1.00 × 105 | 503.2950 |
| 32 | 2.000 | 1 | 200 | 25 | 30 | 1740 | 1.50 × 104 | 919.0260 |
| 33 | 2.000 | 1 | 200 | 0.10 | 40 | 1950 | 2.40 × 104 | 657.1950 |
| 34 | 1.333 | 1.5 | 200 | 40 | 15 | 1400 | 1.00 × 105 | 492.3850 |
| 35 | 1.333 | 1.5 | 200 | 25 | 30 | 1740 | 1.50 × 104 | 931.7800 |
| 36 | 1.333 | 1.5 | 200 | 0.10 | 40 | 1950 | 2.40 × 104 | 692.0160 |
Comparison of Meyerhof’s bearing capacity with numerical model.
| Test | Geotextile Deployment Specifications | Soil Characteristics | Bearing | Meyerhof Bearing Capacity (KPa) | |||||
|---|---|---|---|---|---|---|---|---|---|
| H/B | B (m) | H (cm) | C (KPa) | Φ | Υ (kg/m3) | E (KPa) | |||
| 1 | - | - | - | 10 | 30 | 1478 | 1.40 × 104 | 388.847 | 306.03 |
| 1 | 0.125 | 1 | 12.5 | 40 | 15 | 1400 | 1.00 × 105 | 508.9540 | 447.1100 |
| 2 | 0.125 | 1 | 12.5 | 25 | 30 | 1740 | 1.50 × 104 | 908.0960 | 889.8300 |
| 3 | 0.125 | 1 | 12.5 | 0.10 | 40 | 1950 | 2.40 × 104 | 706.1300 | 913.4800 |
| 4 | 0.083 | 1.5 | 12.5 | 40 | 15 | 1400 | 1.40 × 104 | 502.3580 | 447.1100 |
| 5 | 0.083 | 1.5 | 12.5 | 25 | 30 | 1740 | 1.00 × 105 | 910.1440 | 889.8300 |
| 6 | 0.083 | 1.5 | 12.5 | 0.10 | 40 | 1950 | 2.40 × 104 | 704.3690 | 913.4800 |
| 7 | 0.250 | 1 | 25 | 40 | 15 | 1400 | 1.00 × 105 | 490.8000 | 447.1100 |
| 8 | 0.250 | 1 | 25 | 25 | 30 | 1740 | 1.50 × 104 | 941.1730 | 889.8300 |
| 9 | 0.250 | 1 | 25 | 0.10 | 40 | 1950 | 2.40 × 104 | 632.1840 | 913.4800 |
| 10 | 0.167 | 1.5 | 25 | 40 | 15 | 1400 | 1.00 × 105 | 504.6220 | 447.1100 |
| 11 | 0.167 | 1.5 | 25 | 25 | 30 | 1740 | 1.50 × 104 | 873.8600 | 889.8300 |
| 12 | 0.167 | 1.5 | 25 | 0.10 | 40 | 1950 | 2.40 × 104 | 677.0650 | 913.4800 |
| 13 | 0.500 | 1 | 50 | 40 | 15 | 1400 | 1.00 × 105 | 496.5650 | 447.1100 |
| 14 | 0.500 | 1 | 50 | 25 | 30 | 1740 | 1.50 × 104 | 920.9610 | 889.8300 |
| 15 | 0.500 | 1 | 50 | 0.10 | 40 | 1950 | 2.40 × 104 | 733.3540 | 913.4800 |
| 16 | 0.333 | 1.5 | 50 | 40 | 15 | 1400 | 1.00 × 105 | 507.5590 | 447.1100 |
| 17 | 0.333 | 1.5 | 50 | 25 | 30 | 1740 | 1.50 × 104 | 909.8120 | 889.8300 |
| 18 | 0.333 | 1.5 | 50 | 0.10 | 40 | 1950 | 2.40 × 104 | 646.2090 | 913.4800 |
| 19 | 0.750 | 1 | 75 | 40 | 15 | 1400 | 1.00 × 105 | 506.5840 | 447.1100 |
| 20 | 0.750 | 1 | 75 | 25 | 30 | 1740 | 1.50 × 104 | 929.6590 | 889.8300 |
| 21 | 0.750 | 1 | 75 | 0.10 | 40 | 1950 | 2.40 × 104 | 656.7460 | 913.4800 |
| 22 | 0.500 | 1.5 | 75 | 40 | 15 | 1400 | 1.00 × 105 | 507.7100 | 447.1100 |
| 23 | 0.500 | 1.5 | 75 | 25 | 30 | 1740 | 1.50 × 104 | 911.2680 | 889.8300 |
| 24 | 0.500 | 1.5 | 75 | 0.10 | 40 | 1950 | 2.40 × 104 | 660.8910 | 913.4800 |
| 25 | 1.000 | 1 | 100 | 40 | 15 | 1400 | 1.00 × 105 | 508.0010 | 447.1100 |
| 26 | 1.000 | 1 | 100 | 25 | 30 | 1740 | 1.50 × 104 | 924.8770 | 889.8300 |
| 27 | 1.000 | 1 | 100 | 0.10 | 40 | 1950 | 2.40 × 104 | 665.3290 | 913.4800 |
| 28 | 0.667 | 1.5 | 100 | 40 | 15 | 1400 | 1.00 × 105 | 508.9090 | 447.1100 |
| 29 | 0.667 | 1.5 | 100 | 25 | 30 | 1740 | 1.50 × 104 | 772.7800 | 889.8300 |
| 30 | 0.667 | 1.5 | 100 | 0.10 | 40 | 1950 | 2.40 × 104 | 601.3890 | 913.4800 |
| 31 | 2.000 | 1 | 200 | 40 | 15 | 1400 | 1.00 × 105 | 503.2950 | 447.1100 |
| 32 | 2.000 | 1 | 200 | 25 | 30 | 1740 | 1.50 × 104 | 919.0260 | 889.8300 |
| 33 | 2.000 | 1 | 200 | 0.10 | 40 | 1950 | 2.40 × 104 | 657.1950 | 913.4800 |
| 34 | 1.333 | 1.5 | 200 | 40 | 15 | 1400 | 1.00 × 105 | 492.3850 | 447.1100 |
| 35 | 1.333 | 1.5 | 200 | 25 | 30 | 1740 | 1.50 × 104 | 931.7800 | 889.8300 |
| 36 | 1.333 | 1.5 | 200 | 0.10 | 40 | 1950 | 2.40 × 104 | 692.0160 | 913.4800 |
Summary of modeling results.
| Test | Geotextile Deployment Specifications | Soil Characteristics | Bearing | Meyerhof Bearing Capacity (KPa) | Settlement | Possible Rupture Mechanism | |||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| H/B | B (m) | H (cm) | C (KPa) | Φ | Υ (kg/m3) | E (KPa) | |||||
| 1 | - | - | - | 10 | 30 | 1478 | 1.40 × 104 | 388.847 | 306.03 | 0.1177 | General shear |
| 1 | 0.125 | 1 | 12.5 | 40 | 15 | 1400 | 1.00 × 105 | 508.9540 | 447.1100 | 0.3994 | Local shear |
| 2 | 0.125 | 1 | 12.5 | 25 | 30 | 1740 | 1.50 × 104 | 908.0960 | 889.8300 | 0.3995 | Local shear |
| 3 | 0.125 | 1 | 12.5 | 0.10 | 40 | 1950 | 2.40 × 104 | 706.1300 | 913.4800 | 0.0698 | General shear |
| 4 | 0.083 | 1.5 | 12.5 | 40 | 15 | 1400 | 1.40 × 104 | 502.3580 | 447.1100 | 0.3959 | Local shear |
| 5 | 0.083 | 1.5 | 12.5 | 25 | 30 | 1740 | 1.00 × 105 | 910.1440 | 889.8300 | 0.3994 | Local shear |
| 6 | 0.083 | 1.5 | 12.5 | 0.10 | 40 | 1950 | 2.40 × 104 | 704.3690 | 913.4800 | 0.0638 | General shear |
| 7 | 0.250 | 1 | 25 | 40 | 15 | 1400 | 1.00 × 105 | 490.8000 | 447.1100 | 0.3990 | Local shear |
| 8 | 0.250 | 1 | 25 | 25 | 30 | 1740 | 1.50 × 104 | 941.1730 | 889.8300 | 0.3992 | Local shear |
| 9 | 0.250 | 1 | 25 | 0.10 | 40 | 1950 | 2.40 × 104 | 632.1840 | 913.4800 | 0.0617 | General shear |
| 10 | 0.167 | 1.5 | 25 | 40 | 15 | 1400 | 1.00 × 105 | 504.6220 | 447.1100 | 0.3991 | Local shear |
| 11 | 0.167 | 1.5 | 25 | 25 | 30 | 1740 | 1.50 × 104 | 873.8600 | 889.8300 | 0.3993 | Local shear |
| 12 | 0.167 | 1.5 | 25 | 0.10 | 40 | 1950 | 2.40 × 104 | 677.0650 | 913.4800 | 0.0617 | General shear |
| 13 | 0.500 | 1 | 50 | 40 | 15 | 1400 | 1.00 × 105 | 496.5650 | 447.1100 | 0.3991 | Local shear |
| 14 | 0.500 | 1 | 50 | 25 | 30 | 1740 | 1.50 × 104 | 920.9610 | 889.8300 | 0.3992 | Local shear |
| 15 | 0.500 | 1 | 50 | 0.10 | 40 | 1950 | 2.40 × 104 | 733.3540 | 913.4800 | 0.0657 | General shear |
| 16 | 0.333 | 1.5 | 50 | 40 | 15 | 1400 | 1.00 × 105 | 507.5590 | 447.1100 | 0.3992 | Local shear |
| 17 | 0.333 | 1.5 | 50 | 25 | 30 | 1740 | 1.50 × 104 | 909.8120 | 889.8300 | 0.3992 | Local shear |
| 18 | 0.333 | 1.5 | 50 | 0.10 | 40 | 1950 | 2.40 × 104 | 646.2090 | 913.4800 | 0.0617 | General shear |
| 19 | 0.750 | 1 | 75 | 40 | 15 | 1400 | 1.00 × 105 | 506.5840 | 447.1100 | 0.3992 | Local shear |
| 20 | 0.750 | 1 | 75 | 25 | 30 | 1740 | 1.50 × 104 | 929.6590 | 889.8300 | 0.3993 | Local shear |
| 21 | 0.750 | 1 | 75 | 0.10 | 40 | 1950 | 2.40 × 104 | 656.7460 | 913.4800 | 0.0637 | General shear |
| 22 | 0.500 | 1.5 | 75 | 40 | 15 | 1400 | 1.00 × 105 | 507.7100 | 447.1100 | 0.3992 | Local shear |
| 23 | 0.500 | 1.5 | 75 | 25 | 30 | 1740 | 1.50 × 104 | 911.2680 | 889.8300 | 0.3991 | Local shear |
| 24 | 0.500 | 1.5 | 75 | 0.10 | 40 | 1950 | 2.40 × 104 | 660.8910 | 913.4800 | 0.0617 | General shear |
| 25 | 1.000 | 1 | 100 | 40 | 15 | 1400 | 1.00 × 105 | 508.0010 | 447.1100 | 0.3993 | Local shear |
| 26 | 1.000 | 1 | 100 | 25 | 30 | 1740 | 1.50 × 104 | 924.8770 | 889.8300 | 0.3994 | Local shear |
| 27 | 1.000 | 1 | 100 | 0.10 | 40 | 1950 | 2.40 × 104 | 665.3290 | 913.4800 | 0.0637 | General shear |
| 28 | 0.667 | 1.5 | 100 | 40 | 15 | 1400 | 1.00 × 105 | 508.9090 | 447.1100 | 0.3990 | Local shear |
| 29 | 0.667 | 1.5 | 100 | 25 | 30 | 1740 | 1.50 × 104 | 772.7800 | 889.8300 | 0.2950 | Local shear |
| 30 | 0.667 | 1.5 | 100 | 0.10 | 40 | 1950 | 2.40 × 104 | 601.3890 | 913.4800 | 0.0598 | General shear |
| 31 | 2.000 | 1 | 200 | 40 | 15 | 1400 | 1.00 × 105 | 503.2950 | 447.1100 | 0.3992 | Local shear |
| 32 | 2.000 | 1 | 200 | 25 | 30 | 1740 | 1.50 × 104 | 919.0260 | 889.8300 | 0.3992 | Local shear |
| 33 | 2.000 | 1 | 200 | 0.10 | 40 | 1950 | 2.40 × 104 | 657.1950 | 913.4800 | 0.0617 | General shear |
| 34 | 1.333 | 1.5 | 200 | 40 | 15 | 1400 | 1.00 × 105 | 492.3850 | 447.1100 | 0.3991 | Local shear |
| 35 | 1.333 | 1.5 | 200 | 25 | 30 | 1740 | 1.50 × 104 | 931.7800 | 889.8300 | 0.3992 | Local shear |
| 36 | 1.333 | 1.5 | 200 | 0.10 | 40 | 1950 | 2.40 × 104 | 692.0160 | 913.4800 | 0.0967 | General shear |
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Details
; Gheibi, Mohammad 3
; Reza Yeganeh Khaksar 1 ; Annuk, Andres 4
; Moezzi, Reza 5
1 Department of Civil Engineering, Sadjad University of Technology, Mashhad 9188148848, Iran;
2 Department of Civil Engineering, Faculty of Engineering, Islamic Azad University, Tabriz Branch 5157944533, Iran;
3 Institute for Nanomaterials, Advanced Technologies and Innovation, Technical University of Liberec, Studentská 1402/2, 461 17 Liberec, Czech Republic;
4 Institute of Forestry and Engineering, Estonian University of Life Sciences, 51006 Tartu, Estonia;
5 Faculty of Mechatronics, Informatics and Interdisciplinary Studies, Technical University of Liberec, 461 17 Liberec, Czech Republic; Association of Talent under Liberty in Technology (TULTECH), 10615 Tallinn, Estonia