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Experimental and Numerical investigation on Pile Foundation Underpinning Structure System in Urban Overpass

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13 September 2023

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14 September 2023

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Abstract
In view of the complexity of the pile foundation underpinning structure system and the stringent requirements of the construction process, this paper briefly describes the necessity of introducing epoxy resin reinforcing adhesive of planting rebar in the design of pile foundation underpinning beam structure to im-prove the mechanical properties of the underpinning beam new and old concrete joint surfaces and proposes a new type of pile foundation underpinning beam system construction method by “chiseling + prestressed reinforcement + epoxy resin reinforcing adhesive”. This paper uses an actual pile foundation underpinning project of an urban overpass as a prototype, designs and creates a model structure with a similarity ratio of 1/6, and performs repeated pro-gressive static loading tests to study the load carrying capacity, displacement change, and other properties of the underpinning structure, as well as analyses and distorts the overall working performance and failure mode of them. On this basis, the prototype structure's finite element analysis model was built, and the finite element analysis results were compared with the test results to get the mechanical properties and deformation characters of the actual pile foundation under-pinning structure system corresponding to the actual underpinning beam load. This paper's study can lay the theoretical and experimental foundation for the smooth development of similar projects.
Keywords: 
Subject: Engineering  -   Civil Engineering

1. Introduction

With the acceleration of urbanization, urban rapid rail transit systems, represented by subway tunnels, have been extensively constructed. However, due to the rapid growth in the number of urban structures, situations involving the construction of new bridges or subway tunnels near or through existing buildings have become increasingly common. In order to ensure the safety of the upper structures, pile foundation replacement technology is often employed to transfer the superimposed loads from existing piles, ensuring the smooth progress of new construction projects [1-6]. Pile cap replacement technology is an effective construction technique that involves the creation of a new replacement beam and replacement piles to efficiently transfer the existing load-bearing system. This process redirects the loads previously borne by the existing piles onto the newly constructed replacement piles, effectively managing the stresses and deformations in the existing upper structure [7-9].
As urban underground construction continues to grow rapidly, the significance of pile foundation replacement construction technology for urban development becomes increasingly prominent. The pile foundation underpinning technology was first applied to Winchester Cathedral in the United Kingdom. Divers dig a trench through the peat and chalk layers to access the gravel layer, then fill it with concrete to carry out underpinning construction [10]. Germany has conducted several theoretical and practical investigations into pile foundation underpinning technology since the 1950s, employed this technology in numerous projects, and included pile foundation underpinning technology in its industrial standard (DIN) [11,12]. Shan et al. [13] conducted pile underpinning research on an actual building, and the results indicated that the piles acted well as an underpinning role in transferring structure load into surrounding geomaterials, which may offer enough support for the rebuilt structure. Xu et al. [14-15] based on the engineering background of shield tunnel crossing through group pile foundation of a road bridge with pile underpinning technologies in Shanghai verified the feasibility of pile underpinning technology to solve this problem. Li et al. [16] investigated stress transfer mechanism during underpinning process by conducting the refined numerical simulation of the pile foundation underpinning construction using FLAC3D, and found that pile foundation underpinning technology could effectively transferred the overlying load on the underpinning pile to a new underpinning pile. That confirmed the significance of pile foundation displacement construction technology to urban infrastructure projects.
There are numerous factors that influence the safety of pile foundation replacement beam construction. Employing appropriate construction methods and effective safety control measures are essential safeguards for pile foundation replacement beam construction technology. In this regard, scholars both domestically and internationally have conducted extensive research. Li et al. [17], Dong et al. [18], Wang [19] and Huang et al. [20] investigated the mechanical performance of replacement piles under replacement loads and proposed a method for predicting the pile's bearing capacity. Huang Xi et al. [21], by analyzing the transfer of replacement loads, the settlement patterns of pile foundations when t tunnel traverses the pile foundation of flyover, and the impact of design parameters on the safety of pile foundation replacement construction, have found that active replacement is superior to passive replacement. Furthermore, they observed a positive correlation between the pile length, pile diameter, replacement beam height, and the safety of the pile underpinning replacement structure. Through the orthogonal experiment of scaled models of the wrap-underpinning joints under frame columns in moving engineering, Zhang et al. [22] investigated the influences of the shear-span ratio, longitudinal reinforcement parameter, and stirrup ratio in the underpinning joint surface on the orthogonal experiment of scaled models of the wrap-underpinning joints under frame columns. They also provided the formula to calculate the bearing capacity of underpinning joints. Xu et al. [15] conducted a seismic analysis of pile foundation replacement structures to elucidate the load transfer mechanism of bridge structures throughout the entire construction process. Meanwhile, Zhang et al. [23] established a numerical simulation model that accounted for the entire foundation replacement structure and construction steps to validate the feasibility of the pile foundation replacement construction scheme. Yue et al. [24] tested sixteen prototypes considering different shear span-to-depth ratios, underpinning joint heights, and reinforcement ratios and discovered that the underpinning beams can fail in shear or flexure-shear. During loading, the interface between the column and the beam would also be prone to failure. Yan et al. [25] studied the shear and slide characteristics of the joint and developed a revised method for determining shear capacity using three local node models of the underpinning structures with a similarity ratio of 1/1. Horpibulsuk et al. [26], Wang et al. [27], Kou. [28] Tu et al. [29] and Igba U.T. et al. [30] proposed an optimized pile cap replacement construction scheme based on practical engineering applications. The aforementioned research has elucidated the key factors affecting pile foundation replacement beam construction technology, including pile foundations, replacement beams, and replacement piles. It has also proposed relevant computational models, laying a solid foundation for the practical application of pile foundation replacement beam systems and paving the way for further exploration in novel pile foundation replacement techniques.
However, there is a notable lack of research addressing the issue of the connection between newly cast replacement beams and existing structures in pile foundation replacement beam construction technology, specifically, the adhesive properties at the interface between old and new concrete. bond slippage between the new and old concrete contact surfaces of pile foundation underpinning beam structures has become the key to limiting the use of underpinning construction technology in large-scale projects due to insufficient anchoring technology and bond material limitations. Fortunately, the development of polymer composite reinforcing adhesive anchoring technology for pile foundation underpinning has created new ideas. Epoxy resin reinforcing adhesive of planting rebar as a commonly used composite building structural adhesive materials, with excellent adhesive properties, chemical stability, and strong heat resistance, has attracted scholars in various fields of research [31-32], while also adding a variety of new polymers of composite epoxy resin materials and new epoxy resins with specific properties have also appeared one after another, such as the novel in-situ polytriazolesulfone modified epoxy and the epoxy resin modified with biodegradable polymer [33-35]. Liu et al. [36] pointed out that cracks in building structure adhesives can be self-healed in various ways and proposed a new epoxy with self-repairing properties for environment-friendly building structure adhesives, which is helpful to the prolongation of the reinforcing adhesive of planting rebar’s working life in complex climatic and engineering environments and also opens the door to the future application of a new type of the reinforcing adhesive of planting rebar to pile foundation underpinning technology. He et al. [37] conducted a study on the mechanical properties of a new epoxy resin reinforcing adhesive for planting reinforcement in highway engineering and discovered that the use of a new composite material can not only greatly improve bond strength between structures but also greatly improve over-all structural load-bearing performance. Gou et al. [6] proposed five different beam-column joint forms and demonstrated that the combination of “tongue and groove + anchor bar + prestressed force” can effectively guarantee the safety of beam-column joints. That provides a valuable reference for the combination of the new type of epoxy resin reinforcing adhesive and reinforcing bar construction technology. It can be seen that the epoxy resin reinforcing adhesive composite material has the high bonding characteristics that traditional planting reinforcement construction requires. Now, the epoxy resin composite material has been widely used in various fields with a good research foundation and technical reserve, which is beneficial to the realization of pile foundation underpinning technology in the complex project, and it is worth introducing into the attempts. However, aiming at reinforcing adhesives excel-lent material performance, it must be combined with reasonable planting reinforcement construction technology, such as the rough interface - prestressing - planting re-bar - reinforcing adhesive construction technology methods, such as joints with a rough interface + planting reinforcement + prestressing + epoxy resin reinforcing adhesive of planting rebar connections.
In summary, researchers have conducted more practical engineering applications for pile foundation underpinning technology; however, the safety of “chiseling - prestressed reinforcement - epoxy resin bonding” for treating the interface between old and new concrete has yet to be thoroughly tested and studied. Based on this, the paper uses an actual pile foundation underpinning project of an urban overpass as a prototype, employs a method involving chiseling - prestressed reinforcement - epoxy resin bonding simultaneously designs and creates a model structure with a similarity ratio of 1/6, and analyses and discusses the overall working performance and failure mode of them. We expect that this paper's study can lay the theoretical and experimental foundation for the smooth development of similar projects. It also lays the foundation for the future development of the deep integration between the novel epoxy resin reinforcing adhesive and the great planting rebar technology.

2. Design of the Testing

2.1. Similarity Relation

The geometric similarity ratio of the model was chosen as 1/6 when combined with the test demand and test circumstances. Other model similarity constants were inferred using fundamental mechanics equations or the approach of comparable dimensional analysis, as indicated in Table 1.

2.2. Model Design and Construction

The similarity ratio was used to determine the dimensional correspondence between the model and prototype structures, as shown in Table 2 below. Figure 1 illustrates the intended model structure. The joints with rough interface, planting reinforcement, pre-stressing, and construction adhesive were applied to manufacture the model depicted in Figure 2 according to the structure design drawing.

2.3. Model Materials

The materials used for the underpinning beam model are the same as those used for the prototype construction. The concrete strength grade is C50, and the major reinforcement in the compression and tension zones of the underpinning beam is HRB400, while the other bars are HRB335 reinforcement. The underpinning beam's longitudinal prestressed tendons are made of high-strength, low-relaxation steel strands with a standard tensile strength of fpk = 1860MPa and a nominal diameter of 15.2mm. The results of material tests are displayed in the table below.
Table 3. Mechanical properties of steel and concrete.
Table 3. Mechanical properties of steel and concrete.
Type Physical Quantities Yield strength
（MPa)		 Ultimate tensile strength（MPa) Extensibility
Reinforcement Major reinforcement of the underpinning beam 396.33 548.33 6.5
Other bars 346 463 6.1
Prestressed tendons -- 1877 1.75
Concrete Underpinning beam
(The second pouring)		 53.41
The novel planting reinforcement anchoring method "joints with rough interface + planting reinforcement + prestressing + epoxy resin reinforcing adhesive of planting" is used for the interface between old and new concrete of underpinning beam. Epoxy resin as a planting reinforcement of thermosetting Resins, which has excel-lent mechanical properties, adhesion, and chemical stability, as well as low material shrinkage and a low cost of preparation, and is widely used in construction, adhesives, composites, and other fields. Therefore, the planting reinforcement anchoring technique employs epoxy resin glue as the adhesive of planting reinforcement and concrete. The material properties of epoxy resin are shown in Table 4.
The following is the construction process for planting reinforcement between the new pouring concrete and the existing concrete interface for the pile foundation underpinning beam structure: measuring the holes for planting rebar installation, drilling and cleaning holes, filling the epoxy resin anchoring adhesive of planting reinforcement, installing the planting rebar and maintaining, as shown in Figure 3.

2.4. Test Setup and Measuring Point

The geometric similarity ratio for the experimental model in this study is 1:6. The testing equipment used is a computer-controlled electro-hydraulic servo shear testing machine. The test loading system consists of a 5000kN hydraulic jack and a roller system. The loads are precisely measured using pressure sensors and collected and recorded through a data acquisition system. Throughout the entire loading process, a repeated progressive static loading method is employed, which includes loading, unloading, and then reloading. Before applying replacement load to the specimen, it is preloaded twice with a load of 100kN. Subsequently, loading is carried out in stages, with 150kN applied as the first stage, repeatedly, until reaching 1850kN. Finally, the load is incrementally increased by 100kN stages until the specimen reaches its ultimate load capacity. To ensure load and deformation values stabilize, two minutes holding period follows the completion of each stage of loading. The loading protocol used in the experiments were displayed in Table 5.
The test in this work is primarily intended to analyze the displacement response of the drag-replacement structure under load, and six displacement gauges are set, as shown in Figure 4 below. Simultaneously, Figure 4 is employed to vividly present the novel anchoring connection method with (1) chiseling (concrete roughening interface), (2) prestressed reinforcement, and (3) epoxy resin bonding.

3. Test Results

3.1. Experimental Phenomenon

The specimen did not display a noticeable damage phenomenon at the start of loading due to the low loading force. When the load was increased to 550kN, for the first time, a little fracture occurred at the bottom of the underpinning beam below the loading point, and the specimen was still in the elastic stage. When loaded to 1150kN, multiple horizontal cracks appeared at the bottom of the beam between 1/2 section on the left side of the bearing platform and 1/2 section on the right side of the bearing platform and gradually developed to both sides of the beam, and multiple vertical and inclined cracks appeared on the south and north sides of the beam, with small crack widths. When loaded to 1750kN, the bottom of the beam appeared along the east-west direction with a number of horizontal newborn cracks, intersected with the original cracks, and gradually formed a network cracks, the original cracks continued to develop and form a number of north-south penetrating cracks, crack width increased, inclined cracks extended, and the slope gradually decreased; When loaded to 2750kN, the bot-tom of the beam formed a number of full-length cracks with a crack width of up to 0.5mm, and beam side inclined cracks near the loading point intersected. At the same time, the beam was heard to make an abnormal noise, displacement increased significantly, the load value reached its peak and appeared to decline, the maximum crack width reached 0.8mm, the specimen was considered damaged, and loading was stopped. Figure 5, Figure 6 and Figure 7 depict the specimen's ultimate cracking state.

3.2. Specimen Load Capacity

When the load on the displacement beam ranged from 0kN to -1900kN, the behavior of the underpinning beam exhibited linear elastic deformation. As the load continued to increase, a turning point appeared in the load-displacement curve with a decrease in the curve's slope. When the load reached the maximum design load of 2750kN during the test, a peak appeared in the curve, indicating that the specimen was approaching failure. The phase from the turning point in the curve to reaching the ultimate load represented the plastic deformation stage of the underpinning beam. Afterward, as the load continued to increase, cracks in the specimen rapidly developed and propagated until failure occurred.
The load-displacement curve for the transfer beam under transfer loads is similar to the deformation curve of the steel reinforcement. This similarity is attributed to the optimized bonding performance of the new planning rebar anchoring technology at the interface between old and new concrete in the underpinning beam. This optimization overcomes the weak points in the underpinning structural system, enhances the deformation performance of concrete, and thus allows the steel reinforcement to play a primary controlling role in the deformation of the underpinning structural system.
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Figure 8. Load displacement Curve.
Figure 8. Load displacement Curve.
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3.3. Specimen Load Capacity

The displacements of the underpinning beam at different load values and different measurement places were obtained by extracting the results of the displacement of the bottom of the beam under different load values in the underpinning beam model test, as shown in Figure 9. From this figure, when the load is 1000kN, the maximum dis-placement of the lower part of the underpinning beam is 1.27mm and the displacement of the original underpinning beam is 7.62mm, indicating that the displacement of the structure after the completion of the underpinning beam construction is smaller and the overall stiffness is greater under the action of the upper large-axis bridge load. The beam deformation is more coordinated in the elastic range, meaning that the internal concrete old and new bonding surfaces are reliable, and it is absolutely viable to finish the treatment of the underpinning structure's concrete bonding surface using this approach. The deformation of the abutment region clearly exhibits incoherence once the specimen reaches the yielding stage, indicating that the force in this region of the beam is more concentrated and that it is the weak area of the structural damage.

4. Finite Element Simulation Analysis

4.1. Model

The general finite element software Abaqus is used in this research to create a proto-type simulation model of an underpinning beam structure. Firstly, concrete elements are modeled using C3D20R solid elements, while steel reinforcement, post-tensioned tendons, and prestressed tendons are simulated using T3D2 truss elements. The connection between steel reinforcement and concrete is modeled with “embedded” constraints, and the interface between old and new concrete are treated as hard contacts. The interaction between the existing platform and replacement beam is simulated using tie constraints to maintain deformation coordination between the two. Secondly, Concrete materials are characterized using a plastic damage constitutive model, which not only captures the differences in tensile and compressive behaviors of concrete materials but also exhibits good convergence properties, making it suitable for describing the deformation characteristics of concrete materials under cyclic loading conditions. Thirdly, Steel reinforcement is represented using a bilinear elastic-plastic constitutive model. Furthermore, the measured values were used for the constitutive relations of the materials in the underpinning beam. To accurately reflect the fact that the underpinning nodes of the beam and original pile foundation bearing platform are different batches of poured concrete, this paper employs the contact surface to describe this feature. That is, the underpinning beam and the existing piers are defined as two surfaces, and then the contact relationship between the two surfaces is defined, so that the contact surface becomes a kind of boundary condition, which is beneficial to the convergence of the calculation. According to the above modelling principles, the finite element model of a prestressed concrete underpinning node with interface contact between the old and new concrete is illustrated in Figure 10.

4.2. Comparison of test and finite element computation results

This paper conducted a finite element simulation analysis of the underpinning structure and plotted the corresponding displacement curves under underpinning load in Figure 11 for easy comparison and analysis with the experimental results (Figure 8) in order to study the load-bearing performance of the underpinning structure with the new reinforcement technology.
As can be seen from Figure 11, the load-displacement curves of the test and simulation are in good agreement, and the ultimate loads of the two are respectively 2750kN and 2600kN, with a 5.5% error, indicating that the scaled model of 1:6 is a good guide for the analysis of the prototype structure. The reason for the slight difference in displacement values between the above finite element results could be that the constitutive relationship of the material used in the finite element analysis differs from the actual values, resulting in the actual resistance of the structure being higher than the finite element analysis results. The elastic limit of the prototype structure in Figure 10 is approximately 68,400kN, while the maximum load in the actual project construction process is 17,000kN, indicating that the entire construction process is within the elastic stage of the underpinning beam structure and that this structure meets the basic bearing capacity requirements.

4.3. Displacement

The displacement cloud of the prototype structure was acquired when the load was in-creased to the maximum value of 17000kN during the actual construction, as shown in Figure 12.
The maximum displacement of the underpinning beam structure is 15.7mm, and the maximum deflection control value at the point of load is L/600, which calculates the allowable value of deflection for the structure to be 3.4cm, which meets the specification requirements and ensures the smooth implementation of the actual project.

4.4. Underpinning beam structures concrete stress analysis

Figure 13 depicts the stress state of concrete under construction load and ultimate load for underpinning beam structures. The underpinning beam concrete stress compression pattern in Figure 13 is in great agreement with the truss-arch model theory and in good accord with the theory presented in the literature [12]. As shown in Figure 13, when the load reaches its maximum value, the concrete strength is less than 6.41MPa, and the entire concrete of the underpinning beam is in the elastic stage, indicating that the transfer of the underpinning load can be well realized throughout the construction process and that the underpinning beam still has sufficient safety reserves. When the load is increased to 90,000kN, the underpinning beam local strength approaches the com-pressive strength of concrete, and it is generally between 10.49MPa-16.71MPa, indicating that the underpinning beam structure is still safe and trustworthy at this time.

4.5. Stress Analysis of Reinforcement in Underpinning Structure

Figure 14, Figure 15 and Figure 16 depict the stress analysis cloud for underpinning structure with conventional, planting, and prestressing reinforcement.
As shown in Figure 14, the stress of the reinforcement is less than 66.6MPa under the action of the maximum construction load, and the reinforcement of the entire under-pinning beam is in the elastic stage, indicating that the reinforcement has a high safety reserve throughout the underpinning beam construction. When the load is increased to 90,000kN, the underpinning beam’s local strength approaches the limit of tensile strength. However, the majority of reinforcement strength is maintained between 176.4MPa-294MPa, which is mostly in the elastic stage, and the tensile reinforcement corresponding to the bottom of the beam at the loading point has the largest tensile stress and has not yielded, indicating that the underpinning beam structure is still safe.
As shown in Figure 15, the planted reinforcement strength is under 21.3 MPa at the maximum construction load, and it is in the elastic stage, which indicates the planted bars still have enough strength reserve in the process of underpinning structure construction. When the load reaches to 90000kN, only a small amount of reinforcement reach-es the tensile strength limit, while the majority of the other reinforcement strength is between 84.37MPa-253.1MPa, which is in the elastic stage, and the planted reinforcement transmits the load of the bearing platform to the underpinning beam structure.
From Figure 16, it can be seen that the prestressed tendons strength is within the range of 1274MPa-1295MPa under the maximum construction load, and the prestressed ten-dons stress is less than the tensile strength limit. Because of this, the prestressed ten-dons have sufficient safety reserve. When the load reaches 90000kN, prestressed ten-dons stress is maintained between 1293MPa-1494MPa, which is less than the tensile strength limit of 1860MPa, and the prestressing tendon is still in a safe state under the ultimate load.

5. Conclusion

In this study, the displacements, stresses, and other properties of a pile foundation underpinning structure system in an urban overpass are explored using experimental and finite element analysis, and the following results are reached:
  • The damage condition of the pile foundation underpinning was slight under the test load, and there was no localized damage or general bending and shear damage, indicating the safety of “joints with rough interface + planting reinforcement + prestressing + epoxy resin reinforcing adhesive of planting rebar connection”.
  • The specimen deformation is small in the early loading stage, and the displacement curves of different measurement points are more coordinated, indicating that the combined surface of old and new concrete inside the underpinning beam body is still reliable. However, once the specimen enters the yielding stage, the deformation of the bearing platform section clearly shows an uncoordinated phenomenon, which indicates that the section of beam is more concentrated in the force and that it is a weak region for the whole pile foundation beam structure system, and it should be noticed during the design.
  • The displacement cloud, reinforcement stress cloud, and concrete stress cloud of the pile foundation underpinning beam structure system show that the underpinning structure is in the elastic stage under the construction load, and even under the ultimate load, the underpinning beam structure does not show any overall damage, which indicates that the underpinning beam safety reserve is large enough.
The text continues here.
4.
The finite element simulation analysis of the overall model of pile foundation beam structure shows that test results and simulation results are in great agreement, which verifies the accuracy of the modelling method and the test results. The finite element analysis results can be used as a supplement to the test, and then the detailed force conditions in the pile foundation beam structure system can be analyzed to guide the smooth implementation of the actual project.

Author Contributions

F Data curation—writing and editing: L. Y. and X. G.; Editing: Z. G; Supervision, L. Y. and K. Y; Project administration: X. Z. and Y. J.; Investigation X. R. and G. C. All authors have read and agreed to the published version of the manuscript.

Funding

This project was supported by the General Program of China Postdoctoral Science Foundation(2023MD734111), Chongqing Natural Science Foundation General Project (CSTB2023NSCQ-MSX0853), Sponsored by Natural Science Foundation of Chongqing, China (CSTB2023NSCQ-MSX0433), Scientific and Technological Research Program of Chongqing Municipal Education Commission (KJZD-K202301205), Wanzhou District Science and Technology Innovation Project (20210306, Study on bearing mechanism and buried depth optimization of corrugated guardrail column of low grade highway in mountainous area), Chongqing Three Gorges Reservoir Bank Slope and Engineering Structure Disaster Prevention and Control Center Civil and Hydraulic Master’s Degree Open Fund (SXAPGC23ZDI09), Cooperation projects between universities of Chongqing and institutes affiliated to the Chinese Academy of Sciences (HZ2021012).

Data Availability Statement

The data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest

The authors declare no conflict of interest.

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  32. Ba, H. , Guo, L., Huan, H., Zhang, S., &Lin, Z. (2023). Multi-Objective Optimization of Epoxy Resin Adhesive for Pavement Toughened by Self-Made Toughening Agent. Polymers, 15, 1946. [CrossRef]
  33. Cai, W., Yuan, Z., G., Wang, Z., C., Guo, Z., Y., Zhang, L., L., Wang, J., &Liu, W., T. (2021). Enhancing the toughness of epoxy resin by using a novel hyperbranched benzoxazine. Reactive and Functional Polymers, 164. [CrossRef]
  34. Lee M K, Kwon W, Kwon D, Lee E, &Jeong E. (2019). Fracture toughness of the novel in-situ polytriazolesulfone modified epoxy resin for carbon fiber/epoxy composites. Journal of Industrial and Engineering Chemistry, 77: 461-469. [CrossRef]
  35. 임윤지, 박수진. (2017). Fracture toughness and ductile characteristics of epoxy resin modified with biodegradable polymer. 한국고분자학회 학술대회 연구논문 초록집, 42(2): 120-120.
  36. Liu, M., M. , Zhang, L., &Lee, C. (2021). New Epoxy with Self-Repairing Properties of Environmental-Friendly Building Structure Adhesives. Ecological Chemistry and Engineering S, 28: 39-48. [CrossRef]
  37. He X., G. (2012) Application of New-type Epoxy Resin Mortar in Planting Reinforcement Bar of Highway Engineering. Journal of Railway Engineering Society, 29(07): 62-66.
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Figure 1. Model design drawing.
Figure 1. Model design drawing.
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Figure 2. Model physical drawing.
Figure 2. Model physical drawing.
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Figure 3. Construction process of planting reinforcement.
Figure 3. Construction process of planting reinforcement.
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Figure 4. Layout of measuring points.
Figure 4. Layout of measuring points.
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Figure 5. Development of cracks on the south side.
Figure 5. Development of cracks on the south side.
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Figure 6. Development of cracks on the north side.
Figure 6. Development of cracks on the north side.
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Figure 7. Development of cracks on the bottom surface.
Figure 7. Development of cracks on the bottom surface.
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Figure 9. Deformation of the beam body.
Figure 9. Deformation of the beam body.
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Figure 10. Finite element model of underpinning structure.
Figure 10. Finite element model of underpinning structure.
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Figure 11. Test and finite element comparison.
Figure 11. Test and finite element comparison.
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Figure 12. Displacement contour plot.
Figure 12. Displacement contour plot.
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Figure 13. Stress distribution of concrete.
Figure 13. Stress distribution of concrete.
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Figure 14. Stress of ordinary reinforcement.
Figure 14. Stress of ordinary reinforcement.
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Figure 15. Stress of planting reinforcement.
Figure 15. Stress of planting reinforcement.
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Figure 16. Stress of prestressed tendon.
Figure 16. Stress of prestressed tendon.
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Table 1. Similar constants.
Table 1. Similar constants.
Type Physical Quantities Similarity Relation Similar Constants
Material performance Stress Sσ 1
Strain Sε 1
Elastic modulus Sσ 1
Poisson's ratio 1 1
Geometrical performance Geometrical size Sl 1/6
Linear displacement Sl 1/6
Angular displacement 1 1
Force concentrated loads Sl2 1/36
Table 2. Material properties of epoxy resin anchoring adhesive for planting reinforcement
Table 2. Material properties of epoxy resin anchoring adhesive for planting reinforcement
Items Prototype (cm) Model (cm)
Length 250 41.67
Width 130 21.67
Length 650 108.33
Width 650 108.33
Height 200 33.33
Length 2030 338
Width 870 145
Height 350 58.33
Table 4. Material properties of epoxy resin anchoring adhesive for planting reinforcement
Table 4. Material properties of epoxy resin anchoring adhesive for planting reinforcement
Thermal Distortion Temperature (℃) Fracture elongation
(%)		 Thermal expansion coefficient
(10-5m/(m•℃)		 Tensile strength
(MPa)		 Compressive strength
(MPa)
Epoxy 46-288 3-6 4.5-6.5 28-91 105-175
Table 5. Loading protocol.
Table 5. Loading protocol.
Preloading Loading
Loading protocol 0-100kN 100kN-1900kN 1900kN-2700kN
Loop loading twice Loading step with 150kN Loading step with 100kN
loading level L0 L0-L12 L12-L20
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Copyright: This open access article is published under a Creative Commons CC BY 4.0 license, which permit the free download, distribution, and reuse, provided that the author and preprint are cited in any reuse.
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