The Development of New Type GFRP Hollow Panels

Under the background of global energy transformation, pumped storage power stations are becoming more and more important. Most of their water retaining structures adopt face rockfill dams, but their concrete panels will have many problems such as durability. In this study, a new type of GFRP hollow panel was developed for face rockfill dam. The nonlinear behavior and damage process of the material were simulated by finite element analysis and UMAT subroutine. Through analysis and comparison, it is found that the triangular section form is superior to other forms in terms of stress distribution and bearing capacity. After optimization design, the optimal section takes into account the stability, safety and economic benefits of the structure. The research results provide a high-performance panel solution with high construction efficiency and low maintenance cost for the face rockfill dam, and provide an important design reference for the application of GFRP composite materials in water conservancy projects in the future.


Introduction
The effective integration of renewable energy by pumped storage power stations is an indispensable part of the global energy system, especially for improving the system's peak shaving and energy storage capacity.In the face of fluctuations in intermittent energy, this type of power station compensates for the instability of wind and solar energy by providing stable energy output.Face rockfill dam has become the first choice for many pumped storage power stations due to its excellent safety, economic and seismic performance.However, in northwest China, concrete slabs are prone to cracks and damage, resulting in higher maintenance costs.Fiber reinforced polymer (FRP) materials, with their light weight, high strength and corrosion resistance, show great potential as an alternative to traditional concrete structures.This composite combines the high bearing capacity of the fiber and the adhesion of the resin, as well as protecting the fiber from environmental damage.At the same time, the use of FRP hollow panels can reduce the material degradation caused by humid environment and temperature difference [1,2], and reduce the maintenance cost of face rockfill dams.
Domestic and foreign scholars have done a lot of research on FRP hollow slabs.For example, Plecnik [3] tested the X-section hollow slab of GFRP and proved that it meets the actual application requirements.Williams [4] explored a new type of hollow slab design, using core tube winding technology and FRP rods.At present, FRP hollow panels are mainly used in bridge engineering, but the application in water conservancy projects is limited.In this study, Abaqus software was used to analyze GFRP hollow panels with different sections, and the damage process was simulated by UMAT subroutine to determine the optimal design section.

Material Properties of GFRP Panels
The performance of FRP products depends on its composition and preparation process.The types of fiber and resin used in the FRP panel in this paper are glass fiber and vinyl resin.The fiber volume content of the single-layer plate in the panel is 50 %, and the fiber volume content in the core tube is 60 %.The elastic constant of the single-layer plate is calculated according to the calculation formula of mesomechanics [5], as shown in Table 1.In addition, the basic strength index of the single-layer plate can be determined according to the FRP material design manual [6], as shown in Table 2. Interlaminar shear strength S 30 30

Umat Subroutine
In order to effectively simulate the nonlinear behavior and progressive damage process of GFRP hollow panels, a user-defined material model (UMAT) subroutine was developed for the finite element software Abaqus.The progressive damage analysis method is mainly composed of three parts : stress solution, material failure analysis and material performance degradation.In this paper, the modified Hashin three-dimensional failure criterion with shear nonlinearity is selected as the initial criterion of material damage and the nonlinear degradation model proposed by Linde [7].

Example Verification.
In order to verify the validity and accuracy of the user defined material subroutine (UMAT) developed in this paper, the open-hole laminate test piece is selected as an example to study.The detailed size of the test piece is shown in figure 1, and the material properties are shown in table 3.In the finite element analysis, in order to accurately capture the stress concentration effect around the circular hole, the corresponding area is refined by mesh refinement, as shown in figure 2. The boundary conditions of the model are set as follows : a fixed constraint is applied to the left end face of the laminate, and a displacement load is applied to the right end face to simulate the loading condition.As depicted in figure 3, the fractograph of the specimen reveals that the primary failure occurred on both sides of the hole and is characterized by compressive fracture [8].The high numerical region ( greater than 1 ) in the damage distribution diagram represents the failure region of the material.The finite element analysis results are highly consistent with the experimental results, which proves the accuracy and reliability of the UMAT subroutine in predicting material failure.

Section Design
In the field of engineering, FRP hollow slabs are mainly divided into three categories : profile assembly plate ( AMP plate ), profile core and panel composite plate (CSC plate) and sandwich plate.Considering the machinability, mechanical properties, design flexibility and fiber content, CSC plate was selected as the research object in this paper.

Design Conditions
In the actual design of concrete face rockfill dam, the concrete strength grade of C30 or C40 is usually selected.In view of structural safety considerations and expectations for bearing capacity, this study determined to use concrete that meets the C40 strength level as a design basis to provide higher strength assurance.In practical applications, GFRP panels are laid side by side above the cushion through shear connectors in the transverse direction to form an overall panel structure.When analyzing the bearing capacity of the panel structure, the model is simplified to the constraint condition that the lower surface is hinged and the upper surface bears the load.This method can take into account the constraint and support mechanism of the panel system under the actual situation, and effectively evaluate the bearing capacity and overall mechanical performance of the panel.

Design Size
In order to optimize the construction process and ensure the structural integrity of the dam, the concrete panel needs to be poured in layers according to the height in the design and construction stages.The panel height is usually layered in the range of 0.5 to 1.5 meters.The length of GFRP pultruded panel can be customized according to the project requirements.The length of this design is 1.6 meters.The thickness of concrete face slab will change with the height of the dam body.Small and medium-sized rockfill dams can choose 0.3 to 0.4 meters of equal thickness face slab.The thickness of the hollow panel manufactured by pultrusion should not be changed.In this paper, the equal thickness panel is selected to simplify the manufacturing process, and the thickness is 0.2 to 0.3 meters.The vertical joint spacing of the concrete panel is 8 to 16 meters.The width direction of the GFRP panel is a repeated arrangement of triangular or rectangular elements, and 4 rectangular elements and 8 triangular elements are selected for calculation and analysis.According to the literature analysis, the wall thickness of GFRP hollow panel core should be in the range of 4 to 10 mm, and the panel thickness should be in the range of 4 to 15 mm.

Design Scheme Comparison
3.3.1Finiteelement analysis.The boundary conditions for the GFRP hollow board model stipulate that the lower plate is affixed, whereas the upper plate is subjected to a uniformly distributed displacement load.This load propagates in the negative direction of the y-axis with a magnitude of 5 mm.The material parameters employed in the model are detailed in table 1-3.The maximum edge length of the model's elemental sides is set at 10 mm.After computational verification, this was found to adhere to the requisite convergence criteria.The finite element analysis model is depicted in figure 4. The total number of units for the T1 model amounts to 103,200, with an overall count of 155,526 nodes; as for the R1 model, it possesses 83,200 units in total and encompasses 126,546 nodes.Figure 5 presents the stress cloud and displacement cloud diagrams for each structural model.The finite element analysis reveals that the maximum stress in the triangular-sectioned compression members primarily converges at the ends of the lower panel, points of contact between the core tube and the panel, and the midpoint of the central tube wall.In contrast, the major stress in rectangular-sectioned structures tends to concentrate on the core tube wall and the contact regions.The stress distribution in triangular-sections outperforms those in rectangular ones demonstrated by a more even dispersion of load, thereby enhancing the structural stability and compressive performance.Moreover, the deformation patterns under both cross-sectional styles seem alike with minimal distortions occurring in the central portions of core tubes and larger ones at the edges.Figure 6 exhibits the degree of fibre damage and matrix damage for each component.Observations from the fibre and matrix damage indications signal that the R1 component suffers from the greatest area of destruction, with matrix damage traversing the upper and lower panels and core tube.On the contrary, the damaged zones in T1 components relatively appear restricted.Taking into account all factors, the T1 section was selected as the foundational cross-section for this design, thereby advancing to further detailed design and analysis.

Optimum Design of Sectional Sizing
After analysis, this paper developed five design schemes for comparison.After a comprehensive comparison of these schemes, the scheme with the best comprehensive performance, namely scheme 5, is selected as the optimal section.The specific scheme is shown in table 4, and scheme 5 has smaller deformation and higher bearing capacity when subjected to load.The detailed section size information of Scheme 5 can be seen in figure 7.

Conclusion
This research implements a systematic approach to the selection of materials, damage analysis, cross-section design and optimisation of GFRP panels, resulting in the development of hollow GFRP panels suitable for panel rockfill dams.
(1) The efficacy and accuracy of the chosen damage criterion and material degradation model were validated through the development and application of a UMAT subroutine.The results indicate that this method is reliably predictive of the incremental damage and final failure behaviour of composite materials.
(2) A comprehensive analysis of various cross-section schemes resulted in the selection of a triangular cross-section hollow board, which boasts high load-bearing capacity, minimal deformation, and efficient use of materials.
(3) By manipulating key parameters such as the height and width of the core tube and the thickness of the panel, an optimal cross-section was identified that balances structural stability, safety, and material economy.
In conclusion, the GFRP hollow panel design scheme proposed in this study is characterised by its high load-bearing capacity, minimal deformation, efficient use of materials, and economical and reasonable structure.

Figure 2 .
Figure 2. Finite element model of laminated plate.

Figure 3 .
Figure 3.The fracture of the test piece and the damage distribution of the component.

Figure 5 .
Figure 5.The stress and displacement distribution of each model.

Figure 6 .
Figure 6.Fiber and matrix damage distribution.

Table 1 .
Elastic constant of single layer plate.

Table 2 .
Basic strength index of single-layer plate (unit : MPa).

Table 3 .
Engineering constants and basic strength indexes of laminated plates.

Table 4 .
Performance comparison of each scheme.