1. Introduction
With rapid economic development, many highways, bridges, and transmission towers need to be established on soft soil foundation. Soft soil, characterized by low strength and high compressibility, has a low capacity to resist lateral movement of the foundation, significantly impacting the pile foundation’s ability to resist load deformation. In regions with poor soil properties, shallow ground improvement is an effective method. There have been numerous studies on soil improvement both domestically and internationally.
The research on the horizontal bearing capacity of pile foundations has been widely studied by many scholars. Kellezi et al. [1] first used the finite element software ABAQUS 2022 to study the bearing characteristics of the single pile foundation of the Horns Rev offshore wind farm in Denmark. In the modeling, the Mohr–Coulomb constitutive model is used for the soil, and the soil parameters and layer thickness are selected according to the geological survey data of the engineering site. The analysis method of this model provides a reference for analyzing the horizontal bearing characteristics of the single pile foundation. Based on the field test data, Sun et al. [2] used ABAQUS to carry out a numerical analysis of very large-diameter, horizontal loaded single pile. The effects of soil strength parameters, pile size, load, and other factors on large-diameter, horizontal loaded piles were explored. Wang Jian [3] ed ABAQUS to analyze the horizontal bearing characteristics of reinforced composite piles in clay. The research shows that the horizontal ultimate bearing capacity of reinforced composite piles is related to the strength of the cement soil, the diameter of the cement soil piles, and the undrained shear strength of the soil. A simplified algorithm for the horizontal ultimate bearing capacity of reinforced composite piles is proposed. Wang Ge et al. [4] created a beam element analysis model through the three-dimensional, finite element analysis of checking the engineering test pile, clearing the horizontal load of large-diameter, single pile resistance composition, and change rule. Zhang Xin et al. [5] found through indoor pile-soil model tests and finite element numerical simulations that the pile bucket diameter ratio has a significant impact on the horizontal bearing characteristics of composite foundations. Wang Songyang et al. [6] used a strain wedge model to obtain a calculation method for the lateral bearing performance of a single pile under three-dimensional, asymmetric local erosion conditions, and revealed the influence of different erosion sizes on the mechanical and displacement properties of single piles. Ren Meng et al. [7] analyzed the stress characteristics of bridge pile foundations under fracture zones through on-site triaxial compression tests and numerical simulations, and found that the performance of pile foundations can withstand the influence of fracture zones during their service life.
Domestic and foreign scholars have also conducted extensive research on soil reinforcement. Adsero [8] and Rollins [9] used high-pressure jet grouting piles to reinforce around pile caps to improve the horizontal bearing capacity of pile groups. Experimental results showed that, compared to traditional methods of altering pile structure, using high-pressure jet grouting piles had better economic efficiency. Faro et al. [10,11] found that short piles’ horizontal load-bearing performance improved significantly after using cement to reinforce shallow ground. The horizontal bearing capacity of short piles increased with the widening of the reinforcement width, and there existed an optimal reinforcement depth. He Ben et al. [12] found that reinforcing shallow soil with 7.5 times the pile diameter had a decisive effect on the horizontal bearing capacity of flexible single piles. Static load test results showed a 100% increase in the ultimate bearing capacity of the pile foundation after reinforcement, along with a 50% reduction in the maximum pile bending moment. Taghavi et al. [13,14] compared and analyzed the horizontal bearing characteristics of pile groups before and after cement-soil reinforcement through centrifuge tests. The results showed a significant improvement in the horizontal bearing capacity of the pile group after reinforcement, and the seismic performance of the pile group was also enhanced. Wang Anhui et al. [15] discovered a 40% increase in the horizontal ultimate bearing capacity of PHC piles after cement-soil reinforcement by inserting precast concrete piles into cement-mixed piles, with significant reductions in the pile top horizontal displacement and maximum pile bending moment. Yu Guangming [16,17] and others, through field tests and numerical simulations, obtained a 43% increase in the horizontal bearing capacity of single piles reinforced with cement in gravel, proposing a suitably modified p–y curve formula based on their experiments. Zhang Dingwen et al. [18], relying on a solid engineering project for reinforcing a soft foundation with an interlayer of easily liquefiable silty soil, studied the applicability and reinforcement effects of jet grouting piles through field tests.
It can be seen that current research on soil improvement focuses on studying the effects of different improvement methods, with less emphasis on the study of the influence of the same improvement method’s different improvement ranges. Additionally, most studies target a single soil layer, and research on multi-layer soil is limited. Therefore, a more in-depth study is needed on the influence of the improvement range on multi-layer soil. Based on the analysis of the existing reinforcement methods, the dynamic compaction method creates difficulties in controlling the scope of reinforcement and the strength of the soil after reinforcement. The electroosmotic method has the disadvantages of an uneven reinforcement effect, with good reinforcement effect near the cathode, poor reinforcement effect near the anode, and high fraud. Vacuum preloading also has disadvantages such as uncontrollable reinforcement range. Therefore, the cement mixing method is selected in this paper. This method can effectively control the reinforcement range, and the strength of the reinforced cement soil can be measured. Numerical simulation is used to simulate the change of horizontal bearing characteristics of reinforced concrete single pile under different reinforcement degrees, and the influence of reinforcement range on horizontal bearing characteristics of single pile is explored.
2. Finite Element Model Establishment
2.1. Model Design
This study focuses on the influence of two parameters, namely reinforcement width and reinforcement depth, on the load-bearing performance of the pile. Both parameters are simulated using a single controlled variable method based on the ABAQUS finite element model. The dimensions of the pile and the surrounding soil are introduced separately as follows.
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(1). Soil around the Pile
The soil around the pile is simulated as a rectangular block, as shown in Figure 1. To eliminate the influence of boundary conditions on the load-bearing capacity of the pile foundation, the soil is set up and down to a square with a side length of 20D, and the thickness of the soil is set to 2L (where D and L are the diameter and length of the pile, respectively). The soil is divided into three parts: the shallow soil around the pile reinforced with cement, the upper part of soft soil, and the bottom sand soil. Since the model pile and the applied horizontal load in the horizontal static load test have symmetry, to improve the computational efficiency, the numerical simulation model is created as half of the actual model.
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(2). Pile
As shown in Figure 2, the pile is a concrete pile with a length of 3 m and a diameter of 0.6 m, positioned in the middle part of the soil.
2.2. Simulation Groups
As shown below, Figure 3 provides a schematic diagram of the finite element simulation. In this figure, the reinforcement depth of cement reinforced soil is the amount that needs to be changed for research. The thickness of the silty soft soil and the dimensions of the pile are held constant.
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(1). Variation in Reinforcement Width
This section primarily investigates the influence of changes in reinforcement width on the horizontal bearing characteristics of the pile foundation. Therefore, while keeping the reinforcement depth constant, only the reinforcement width is altered. The specific groupings are outlined in Table 1, where Dcem is the depth of the reinforced soil and Lcem is the width of the reinforced soil.
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(2). Variation in Reinforcement Depth
This section primarily explores the impact of changes in reinforcement depth on the horizontal bearing characteristics of the pile foundation. Therefore, while keeping the reinforcement width constant, only the reinforcement depth is altered. The specific groupings are outlined in Table 2, where Dcem is the depth of the reinforced soil and Lcem is the width of the reinforced soil.
2.3. Element Selection and Material Definition
The soil surrounding the pile is divided into three categories: the shallow cement-stabilized soil around the pile, the shallow silt soft soil, and the sand at the bottom of the pile. Based on existing simulation studies, the silt clay adopts the Mohr–Coulomb elastic–plastic constitutive model [19]. Although the strength of the sand is higher than that of the soft clay, it is still much lower than the strength of the pile, and exhibits significant plasticity. Therefore, for the sand, the Mohr–Coulomb elastic–plastic model is also employed. For the cement-stabilized soft soil, according to the conclusions obtained by researchers like Jamsawang P. [20], the Mohr–Coulomb constitutive model is equally effective in simulating its deformation and failure under load. Therefore, all three types of soil are simulated using the Mohr–Coulomb model. In the simulation, the values for soft soil and sand are taken from a geological survey report of a location at the front edge of the Yangtze River Delta [21]. The pile is modeled using a linear elastic model. Detailed model parameters are shown in Table 3, where C is the cohesion, φ is the internal friction angle, μ is Poisson’s ratio, E is the elastic model, and ρ is the density.
2.4. Meshing
The rationality of meshing is a crucial step in determining the accuracy of numerical simulation results. In this study, the sweeping neutral axis algorithm is employed for meshing the soil, excluding the soil at the pile bottom. The soil close to the pile is finely meshed, while the soil farther from the pile is sparsely meshed. Structural meshing is applied to the pile bottom soil and the pile itself. Additionally, four seed points are used for refining the mesh around the pile, and three seed points are used for the internal part of the pile. The reduced integration, three-dimensional element C3D8R is used in this modeling. The horizontal loading responses for different mesh sizes are shown in Figure 4. As observed in Figure 4, when the mesh size ranges from 50 mm to 200 mm, there is minimal variation in the ultimate horizontal bearing capacity at the pile top, gradually reaching a stable state. Considering the trade-off between computational accuracy and speed, a mesh size of 100 mm is chosen for this model.
2.5. Contact Definition and Boundary Conditions
Three steps of analysis are set up for this simulation. In the first step, the pile section is entirely deactivated using the birth–death element method. In the second step, the pile is activated, and the soil originally occupying the pile section is deactivated using the birth–death element method. This simulates the static press-in process of the pile and ensures a more reasonable distribution of initial ground stresses within the model. In the third step, horizontal loads are applied to the pile top.
The bottom boundary condition of the model is fully fixed, with all four sides subjected to normal constraints, and the top in a free state. The contact surfaces adopt the Mohr–Coulomb model, with the pile considered the master surface and the soil as the slave surface. The interaction on the contact surface is divided into the normal and tangential directions. In the normal direction between the pile and the soil, a “hard contact” method is applied. In the tangential direction, the Coulomb friction model is used for both soft soil and ordinary sand. The friction coefficient of soft clay to concrete is in the range of 0.3~0.5. Therefore, the tangential friction coefficient is selected as 0.3 in this range. For cement-reinforced soil, the tangential friction coefficient is in the range of 0.39~0.49, and the tangential friction coefficient is selected as 0.4 in this range [22].
2.6. Load Application and Control
The horizontal load on the top of the pile adopts the loading mode of concentrated force, and the size is set to 100 kN. The loading form is a concentrated force loading, the top surface of the pile is coupled to a point, and then a horizontal concentrated force is applied to it. According to the relevant provisions of the 2014 “Technical Code for detection of Building Foundation Piles”, one of the stopping criteria for the horizontal static load test is that the horizontal displacement of the pile top reaches 30~40 mm, so this paper applies 40 mm horizontal displacement to the pile top.
2.7. Validation of Finite Element Simulation
In order to ensure the rationality of the simulation method and the reliability of the relevant results, this paper takes the field test finished by Faro et al. [10] as a reference, establishes the corresponding finite element model, and carries out the numerical simulation analysis. The comparison between the simulation results and the field test results is shown in Table 4. It should be mentioned that the code Dcem is the diameter of the range of the soil reinforcement plane and Lcem is the depth of the soil reinforcement. It can be seen that a finite element simulation can provide accurate prediction of the bearing capacities under horizontal load, with a minimum relative error of 5.53%, a maximum error of 15.05%, and an average error of 9.35%. It is indicated that the numerical simulation method proposed in Section 2.1, Section 2.2, Section 2.3, Section 2.4, Section 2.5 and Section 2.6 is suitable for analyzing the coupling bearing mechanism of piles in marine soft foundation, considering the influence of the diameter of the range of the soil reinforcement plane and the depth of soil reinforcement.
3. Results and Analysis
To explore the impact of the reinforcement range on the horizontal response of the pile, this section extracts and analyzes data, such as pile bending moment, load displacement, etc., from the simulation results. The analysis is conducted in two directions: different reinforcement widths and different reinforcement depths, investigating their respective influences on the pile.
3.1. The Influence of Reinforcement Width
In this section, with reinforcement width as the variable, we investigate the impact of changing the reinforcement width on factors such as the pile’s horizontal ultimate bearing capacity, pile bending moment, displacement, etc., under the condition of constant reinforcement depth.
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(1). Pile Bending Moment
Figure 5 shows the variation of the pile bending moment with the increase in reinforcement width when the pile top load is 100 kN. From Figure 5, it can be observed that when the reinforcement depth is kept constant, the reinforcement width has a significant impact on the pile bending moment. When the pile is in intact clay, the maximum bending moment of the pile is 34.60 kN·m and is located 1.2 m below the mud surface. When the reinforcement depth is 0.3 m, with the increase in reinforcement width, the maximum pile bending moment decreases to 20.52 kN·m, 12.24 kN·m, and 9.29 kN·m, representing a reduction of 40.69%, 64.62%, and 73.15%, respectively, compared to the intact clay state. However, as the reinforcement width increases, the proportion of reduction in the pile bending moment gradually decreases. This is more evident in the bending moment curve when the reinforcement depth is 0.6 m. When the reinforcement depth is 0.6 m, the maximum pile bending moment decreases to 12.13 kN·m and 11.08 kN·m with the increase in reinforcement width. It can be concluded that the impact of reinforcement width on the pile bending moment diminishes gradually as the reinforcement width increases.
Regarding the occurrence position of the maximum pile bending moment, when the reinforcement depth is kept at 0.3 m, the positions with increasing reinforcement width are 1.1 m, 1.0 m, and 0.9 m below the mud surface, showing a slight upward trend. For a reinforcement depth of 0.6 m, the positions of the maximum pile bending moment are consistently 0.5 m below the mud surface with the increase in reinforcement width. Although there is a noticeable upward shift compared to intact clay, changing the reinforcement width does not alter the occurrence position of the maximum moment. In summary, the variation in the reinforcement width has a limited impact on the occurrence position of the maximum pile bending moment.
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(2). Pile Displacement
Figure 6 displays the change curve of pile deformation with the increase of the reinforcement width, when the pile top load is 100 kN. As shown in Figure 6, when the horizontal load is 100 kN, the pile displacement curve is presented. It can be seen that shallow soil reinforcement can effectively reduce the displacement deformation of the pile. From Figure 6, it can be seen that when the reinforcement depth is kept constant, the deformation gap of the pile displacement curve gradually decreases with the increase of the reinforcement width. Without reinforcement, the pile top displacement is 55.11 mm. When the reinforcement depth is kept at 0.3 m, the pile top displacement decreases with the increase of the reinforcement width, measuring 34.11 mm, 15.62 mm, and 10.58 mm, respectively. Although the pile top displacement is gradually decreasing, this reduction rate also decreases with the increase in reinforcement width. When the reinforcement width increases from 1.8 m to 2.4 m, the displacement reduction rate is only 32%.
When the reinforcement depth is kept at 0.6 m, the pile top displacements are 11.44 mm and 8.61 mm with the increase in reinforcement width. It can be observed that while shallow soil reinforcement can significantly reduce pile deformation, the efficiency of this reinforcement gradually decreases with the increase in reinforcement width.
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(3). Pile Horizontal Bearing Capacity
Figure 7 displays the displacement gradient curve obtained by changing the reinforcement width under the premise of keeping the reinforcement depth unchanged. According to the relevant provisions in the “Technical Specification for Building Pile Foundation Inspection” (JGJ106-2014) [23], the second inflection point of the curve in the figure corresponds to the horizontal ultimate load value of the single pile. According to the curve in the diagram, it can be determined that the ultimate load values of single piles under different reinforcement widths are 16.42 kN, 30.04 kN, 33.54 kN, and 53.27 kN, respectively.
Figure 8 displays the curve of the ultimate bearing capacity of the pile with the change of the reinforcement width. Compared with the unreinforced case, the ultimate load values of the piles increased by 82.95%, 104.26%, and 224.42%, respectively.
3.2. The Impact of Reinforcement Depth
In this section, with the reinforcement depth as a variable, the influence of changing the reinforcement depth on the horizontal ultimate bearing capacity, pile bending moment, displacement, and other factors is investigated, while keeping the reinforcement width constant.
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(1). Pile Bending Moment
Figure 9 depicts the distribution curve of the pile bending moment when changing the reinforcement depth, while keeping the reinforcement width constant. Similarly to the previous section, when the pile is in intact clay, the maximum bending moment is 34.60 kN·m, and the maximum moment occurs 1.2 m below the mud surface. From the two graphs above, it can be observed that although changing the reinforcement depth significantly reduces the pile bending moment compared to intact clay, the impact on the maximum bending moment is not significant when keeping the reinforcement width constant. When the reinforcement width is 2.4 m, with the increase in reinforcement depth, the bending moment even shows an increase. For reinforcement depths of 0.3 m, 0.6 m, and 0.9 m, the maximum bending moments are 9.29 kN·m, 11.08 kN·m, and 12.55 kN·m, respectively. It can be seen that changing the reinforcement depth does not have a significant impact on the maximum bending moment.
In Figure 9a, it is evident that with the increase in reinforcement depth, the location of the maximum bending moment shifts upward. Although the shift is not very pronounced in Figure 9b, it also gradually moves upward with the increase in reinforcement depth. Therefore, there is a certain relationship between the change in reinforcement depth and the occurrence location of the maximum bending moment.
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(2). Pile Displacement
Figure 10 represents the pile displacement curves obtained by changing the reinforcement depth while keeping the reinforcement width constant. Both before and after reinforcement, the pile exhibits the characteristics of a rigid pile, and shallow reinforcement significantly reduces the deformation of the pile. From the right graph, it can be observed that, with a constant reinforcement width of 2.4 m, the pile displacements increase with the reinforcement depth, measuring 10.58 mm, 8.61 mm, and 7.91 mm, respectively. Although the pile deformation is gradually decreasing, it becomes less significant when reinforcing beyond a width of 1.8 m.
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(3). Displacement Gradient
Figure 11 represents the displacement gradient curve obtained by changing the reinforcement depth under the premise of keeping the reinforcement width unchanged. According to the relevant provisions in the “Technical Specification for Building Pile Foundation Inspection” (JGJ106-2014) [24], the second inflection point of the curve in the figure corresponds to the horizontal ultimate load value of the single pile. According to the curve in the diagram, it can be determined that the ultimate load values of single pile under different reinforcement depths are 16.42 kN, 53.27 kN, 75.75 kN, 91.42 kN, 94.86 kN, and 96.09 kN, respectively.
Figure 12 displays the curve of the ultimate bearing capacity of the pile, changing with reinforcement depth. Compared to the unreinforced case, the ultimate load values of the piles increased by 224.42%, 361.33%, 456.76%, 477.71%, and 485.2%, respectively. As the reinforcement depth increases, the increase in bearing capacity does not increase linearly, but gradually decreases. From Figure 12, it can be seen that when the reinforcement depth exceeds 1.5D, which is 0.9 m, increasing the reinforcement depth again no longer significantly improves the horizontal bearing capacity of the pile. Compared to the case where the reinforcement depth is 0.9 m, when the reinforcement depth is increased to 1.2 m, the horizontal bearing capacity of the pile only increases by 3.76%. Compared to the case where the reinforcement depth is 1.2 m, when the reinforcement depth is increased to 1.5 m, the horizontal bearing capacity of the pile only increases by 1.30%. This indicates that simply increasing the reinforcement depth to improve the horizontal bearing capacity of the pile requires a comprehensive consideration of the reinforcement purpose and economy. From Figure 12, it can be seen that when the reinforcement depth exceeds 0.9 m, increasing the reinforcement depth again has little effect on the horizontal bearing performance of the pile. Considering the economy, it can be considered that the pile studied in this article has an optimal reinforcement depth of 1.5D, which is 0.9 m. Blindly carrying out deep soil reinforcement without comprehensive evaluation is not advisable.
4. Conclusions
In this paper, seven three-dimensional finite element models are established to study the influence of soil reinforcement width and soil reinforcement depth on the horizontal bearing capacities of single piles. The results are as follow:
(1). The comparison between the simulation carried out in this paper and the field test on the capacities of a single pile in shallow reinforcement soil showed good coincide, with a minimum relative error of 5.53%, a maximum error of 15.05%, and an average error of 9.35%. The simulation method proposed in this paper is suitable for analyzing the coupling bearing mechanism of piles in soft soil considering shallow reinforcement.
(2). Increasing the reinforcement width can significantly improve the bearing capacity of the pile foundation, and as the reinforcement width increases, the reinforcement effect will become better and better. Compared with the unreinforced case, the horizontal bearing capacity of the pile is increased by 83.0%, 104.3%, and 224.4%, respectively, corresponding to a reinforcement width of 2 times, 3 times, or 4 times the dimeter of the pile respectively. With the increase of the reinforcement width, the bending moment and deformation of the pile under the same horizontal load decrease significantly, while also having no significant effect on the location of the maximum bending moment of the pile.
(3). The bearing capacity of the pile foundation gradually increases with the increase of the reinforcement depth. However, unlike the reinforcement width, the effect of increasing the reinforcement depth on improving the bearing capacity of the pile is gradually weakening, and it can be considered that there is an optimal reinforcement depth of 1.5D. Compared with the unreinforced situation, when the reinforcement depth is 0.5 times, 1.0 times, 1.5 times, 2.0 times, and 2.5 times the pile diameter, the horizontal bearing capacity of the pile body is increased by 224.4%, 361.3%, 456.8%, 477.71%, and 485.2%, respectively.
(4). As the reinforcement depth increases, the increase in bearing capacity does not increase linearly, but gradually decreases. This indicates that simply increasing the reinforcement depth to improve the horizontal bearing capacity of the pile requires a comprehensive consideration of the reinforcement purpose and economy. Blindly carrying out deep soil reinforcement without comprehensive evaluation is not advisable.
(5). Due to space limitations, this article did not consider the combined effect of vertical and horizontal loads in the simulation analysis. Whether this has a significant impact on the relevant conclusions requires further research to confirm. In addition, further specialized research is needed to determine whether the conclusions of this article are applicable to piles with more aspect ratios and soil material properties.
Methodology, Q.S.; Software, F.C. and J.Z.; Investigation, G.B., H.Z., B.W., F.C. and J.Z.; Resources, Q.S.; Data curation, G.B., H.Z. and B.W.; Writing—original draft, G.B.; Writing—review & editing, Q.S.; Funding acquisition, Q.S. All authors have read and agreed to the published version of the manuscript.
Data are contained within the article.
Authors Guanglin Bai, Hong Zhang and Feng Chen were employed by the company Xuzhou Survey and Design Branch of State Grid Jiangsu Electric Power Design Consulting Co., Ltd. Author Bo Wang was employed by State Grid Jiangsu Electric Power Co., Ltd. Economic Research Institute. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. The authors declare that this study received funding from State Grid Jiangsu Electric Power Design Consulting Co., Ltd. The funder was not involved in the study design, collection, analysis, interpretation of data, the writing of this article or the decision to submit it for publication.
Footnotes
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Enlarge this image.Figure 1. Soil finite element model. (The black part in the picture is cement reinforced soil, the orange part in the picture is upper layer silt soft soil, and the yellow part in the picture is sandy soil).
Enlarge this image.Figure 4. The ultimate bearing capacity of the pile top varies with the grid size.
Enlarge this image.Figure 5. Bending moment distribution of pile shaft. (a) reinforcement depth of 0.3 m. (b) reinforcement depth of 0.6 m.
Enlarge this image.Figure 6. Pile displacement. (a) reinforcement depth of 0.3 m. (b) reinforcement depth of 0.6 m.
Enlarge this image.Figure 7. Displacement gradient curve (reinforcement depth of 0.3 m). (a) not strengthened. (b) reinforcement width of 1.2 m. (c) reinforcement width of 1.8 m. (d) reinforcement width of 2.4 m.
Enlarge this image.Figure 7. Displacement gradient curve (reinforcement depth of 0.3 m). (a) not strengthened. (b) reinforcement width of 1.2 m. (c) reinforcement width of 1.8 m. (d) reinforcement width of 2.4 m.
Enlarge this image.Figure 8. Relationship between the horizontal bearing capacity of single pile and reinforcement width.
Enlarge this image.Figure 9. Pile bending moment. (a) reinforcement width of 1.8 m. (b) reinforcement width of 2.4 m.
Enlarge this image.Figure 10. Pile displacement. (a) reinforcement width of 1.8 m. (b) reinforcement width of 2.4 m.
Enlarge this image.Figure 11. Displacement gradient curve (reinforcement width of 2.4 m). (a) not strengthened. (b) reinforcement depth of 0.3 m. (c) reinforcement depth of 0.6 m. (d) reinforcement depth of 0.9 m. (e) reinforcement depth of 1.2 m. (f) reinforcement depth of 1.5 m.
Enlarge this image.Figure 11. Displacement gradient curve (reinforcement width of 2.4 m). (a) not strengthened. (b) reinforcement depth of 0.3 m. (c) reinforcement depth of 0.6 m. (d) reinforcement depth of 0.9 m. (e) reinforcement depth of 1.2 m. (f) reinforcement depth of 1.5 m.
Enlarge this image.Figure 12. Relationship between horizontal bearing capacity of single pile and reinforcement depth.
Reinforcement width variable simulation grouping.
| Notation | L/m | D/m | Dcem/m | Lcem/m |
|---|---|---|---|---|
| 1 | 3 | 0.6 | 1.2 | 0.3 |
| 2 | 3 | 0.6 | 1.8 | 0.3 |
| 3 | 3 | 0.6 | 2.4 | 0.3 |
| 4 | 3 | 0.6 | 1.8 | 0.6 |
| 5 | 3 | 0.6 | 2.4 | 0.6 |
Reinforcement depth variable simulation grouping.
| Notation | L/m | D/m | Dcem/m | Lcem/m |
|---|---|---|---|---|
| 1 | 3 | 0.6 | 1.8 | 0.3 |
| 2 | 3 | 0.6 | 1.8 | 0.6 |
| 3 | 3 | 0.6 | 2.4 | 0.3 |
| 4 | 3 | 0.6 | 2.4 | 0.6 |
| 5 | 3 | 0.6 | 2.4 | 0.9 |
| 6 | 3 | 0.6 | 2.4 | 1.2 |
| 7 | 3 | 0.6 | 2.4 | 1.5 |
Pile and soil properties.
| Soil Mass | C/kPa | φ/° | μ | E/MPa | ρ/(g/cm3) |
|---|---|---|---|---|---|
| Mucky moft soil | 10.9 | 17.2 | 0.35 | 3.77 | 1.75 |
| Silt | 2.5 | 30.8 | 0.3 | 8.71 | 1.93 |
| Cement-stabilized soil | 346 | 38.3 | 0.2 | 130 | 1.76 |
| Pile | / | / | 0.2 | 22,000 | 2.50 |
Comparison of horizontal bearing capacity between field measurement and numerical simulation.
| Notation | Dcem/D | Lcem/D | Hult/kN | Relative Error/% | |
|---|---|---|---|---|---|
| Experimental Data | Analog Data | ||||
| 1 | 0 | 0 | 80 | 88.26 | 10.32 |
| 2 | 2 | 0.5 | 140 | 150.87 | 7.76 |
| 3 | 3 | 0.5 | 160 | 170.43 | 6.52 |
| 4 | 3 | 1 | 220 | 186.90 | 15.05 |
| 5 | 4 | 1 | 250 | 225.14 | 9.94 |
| 6 | 4 | 1.5 | 250 | 236.17 | 5.53 |
| 7 | 0 | 0 | 80 | 88.26 | 10.32 |
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