Deformation properties of arched glass fiber reinforced plastics structure under static load: Considering the soil cover and rise-span ratio

Abstract

In this study, the load level, soil cover height, rise-span ratio, and arch foot constraint state were utilized to explore the mechanical properties of buried arch glass fiber reinforced plastics (GFRP) structures. Through the indoor scale-down test, the stress and deformation of arched GFRP structures under different load and soil cover height were investigated. Additionally, through the three-dimensional finite element method, the influence of the rise-span ratio and the constraint state of arch foot on the mechanical properties were obtained. The results indicate the new buried composite arch structure has excellent bearing capacity for the possible traffic load. Simultaneously, the semi-elliptical arch structure was believed to outperform the semi-circular arch structure when considering the external load. Specifically, increasing the soil cover height and reducing rise-span ratio were found to achieve the load-reduction effect.

Keywords

assembled arch culvert glass fiber reinforced plastics arch structure cover soil height rise-span ratio deformation and stress

Introduction

Culverts have been considered as a substitute for short-span highway bridges owing to the low cost and short construction period. Especially in China, a huge number of culvert projects have been implemented and there are about 3–4 underground culvert structures per kilometer on average. With the long-term construction plan of highway, the culvert structure projects are still meaningful. According to the statistics, the majority of underground culvert structures are rigid structures with reinforced concrete materials and under poor condition. About 63.5% of culverts appears cracks and other early diseases, and 70% of cracks are longitudinal cracks. The early failure of reinforced cement concrete rigid pipe culverts, caused by uneven settlement of foundation, excessive deflection, corrosion, and overload damage during construction, has become a common quality fault of culverts. As a new type of flexible composite pipe, glass fiber reinforced plastics (GFRP) pipe presents the advantages of high specific strength, high specific modulus, and excellent corrosion resistance (Hollaway, 2010). The application of GFRP pipe in highway culverts is believed to eliminate the early diseases of traditional rigid pipe culverts, as it is suited to the complex foundation conditions. For instance, the flexible deformation of the GFRP pipe can fix the uneven settlement of foundation or overload damage caused by cracks and water seepage. Therefore, the early disease and maintenance of culvert can be significantly reduced. In order to implement the GFRP culvert with reduced construction period and better adaptability in plain area, prefabricated GFRP arch culvert has become popular in highway culvert project. Thus, it is meaningful to investigate the mechanical characteristics and bearing capacity of the buried arch GFRP structure.

The deformation and mechanical properties of GFRP circular pipe have been examined in both engineering and academic fields. Design of GFRP pipe and culvert structure has considered the ring stiffness, fatigue characteristics, functional failure under internal pressure, long-term performance, etc. (Antoniou et al., 2009; Affolter et al., 2018; Buarque and Almeida, 2007; Luo et al., 2019; Roham and Ali, 2015; Roham and Mohammad, 2018a, 2018b; Roham and Mazhari, 2016; Roham, 2013a, 2013b). Moreover, most of the literature put emphasis on the material and production parameters, such as glass fiber, resin sand, winding angle, and thickness of each structural layer, which affected the deformation characteristics of buried GFRP pipe. Besides the deformation of GFRP pipe, the maximum load, bending strength, and shear strength that GFRP pipe bears are also important indexes for the GFRP pipe structure design.

Additionally, traffic load and culvert soil stress are considered as the main indexes in highway culvert structure design. For the GFRP structure in highway culvert, soil-structure interaction has become another important factor to determine whether the buried GFRP structure contains good serviceability. The "cyclic compression theory" was the representative theory to analyze soil-structure interaction of flexible structures. The full scale engineering test was employed by Lee et al. (2015) to examine the application of large diameter GFRP sand inclusion tubes for water supply and drainage pipeline. A total of 387 days data of the radial deformation of glass steel sand tube with 16 m burial depth was collected and compared to the estimation results of Iowa formula and finite difference method. The results showed that the vertical deformation of GFRP culvert after 60 years was less than 5% of its vertical deformation limit, which proved the long life and excellent mechanical properties of sand glass steel pipe culvert. In addition, Wei et al. (2018) proposed the calculation formula for vertical converging deformation of steel bellows in terms of the Spangle tube-soil interaction model. The proposed model considered the resistance and foundation bed coefficient of soil at the culvert side as well as the deformation and stress characteristics of steel bellows. These deformation calculation models assisted in the planning and design of buried flexible culvert structures.

On the other hand, numerical simulation has become a widely used method due to the environmental restrictions for field test. Yawa and Shuea (1996) and Ahmed and Ahmed (2019) investigated the mechanical properties of buried pipelines in elastic soft soil through numerical simulation. Specifically, pipeline parameters, buried mode, buried depth ratio, friction between pipes, and soil were found to be the main factors affecting the mechanical properties of buried pipelines. A finite element–based stress model was developed by Li et al. (2019) and Jeyapalan et al. (1989), based on the ABAQUS and FLUENT software. The model demonstrated that the depth of soil coverage has the greatest effect on stress and deformation of the pipeline, followed by traffic load, especially for the traffic load of shallow buried pipe culvert (below 3 m of soil). However, the difference between the mechanical characteristics of non-closed arch structure and annular pipe under load was not fully understood.

Recent researches mainly focused on the mechanical characteristics of steel bellows arch culvert, while the mechanical characteristics of buried arch GFRP structures under load still needs further studies. Walton proposed the indoor soil load test for steel corrugated arch culvert to examine a series of mechanical performance indexes, such as stress, bending moment, and deformation monitoring of the arch culvert soil. The results showed that soil compaction, load pressure, and soil cover height were significantly related to the mechanical properties of arch culvert. Moreover, the extreme state of steel corrugated plate arch culvert was examined and spandrel arch structure was found to be the weak position. Sezen et al. (2008) and Yeau et al. (2009) designed performance field tests of steel corrugated arch culverts under static and dynamic loads, which proved that the mechanical response of culverts was significantly affected by overburden height factor. Additionally, the maximum deflection of culverts showed a nonlinear relationship with overburden height, and the static load deflection was always greater than the dynamic load deflection. However, the risk of arch culvert instability caused by dynamic load cannot be ignored. In the study from Flener and Karoumi (2009), the actual dynamic response of long-span steel corrugated arch culvert under the action of train was investigated. Field test was utilized to measure the strain and deformation under different train speed. The results indicated that train speed greatly influenced on deformation of steel corrugated arch culvert, especially for the dynamic load condition. Through collecting strain and deformation data of highway steel corrugated arch culvert under dynamic load, Beben (2013) applied the fast Fourier transform method to determine dominant frequency of the culvert. Therefore, arch structure, bearing the filling stress and traffic load, was the critical part of the whole culvert structure.

The rise-span ratio was defined as the ratio of arch height to span length, which was an important parameter in arch culverts. The ratio significantly influenced on the mechanical characteristics of arch culverts as well as the design and construction of arch culverts. Existing studies had shown that the value of rise-span ratio was highly related to the mechanical characteristics and ultimate bearing capacity of buried arch culverts. (Houst et al., 2013). Thus, it was usually considered as one of the parameters for the structural optimization of buried arch culverts. Through the numerical simulation of different rise-span ratio, Huang et al. (2019) examined the ultimate bearing capacity of the concrete-filled steel tube arch. The study found the reduction factor of concrete-filled steel tubular arch structure was positively related to the rise-span ratio. When rise-span ratio is less than 0.25, the initial stress effect on ultimate bearing capacity is approximately 10%, which cannot to be ignored in the study.

Although the arched GFRP structure had better performance than the traditional cement concrete arched culvert, few studies had examined the soil-structure interaction, mechanical performance, stress, and deformation characteristics of arched GFRP structure under load. In order to further explore the mechanical characteristics, indoor tests, and numerical simulations were developed to monitor the hoop strain value, radial deformation value and soil stress value of shallow buried arched GFRP structures under static load. Consequently, the influence of load level, soil cover height, rise-span ratio and arch foot constraint factors on arched GFRP structures were analyzed, which provided further exploration of practical application and theoretical research of arched GFRP structures in highway culverts.

Experimental Study

Materials and specimens

The tested arch culvert was produced through the constant-length discontinuous winding process. On the 12-m-long steel mandrel, the glass fiber filament (or felt) infiltrated by cross and hoop winding resin, and resin quartz sand were made layer by layer within the length of pipe mold. The transmission system of fiber winding machine was used to control the reciprocating movement speed, mold speed, and fiber winding angle of the winding and sanding trolley. The production of fiber winding and resin quartz sand winding were completed according to the design requirements of the pipe wall structure, as shown in Figure 1. The winding angle was affected by the ratio of moving speed of winding trolley to the speed of the mandrel, which was controlled by computer. The design parameters are shown in Table 1. After the glass fiber winding and sand clamping process, the pipeline products were generated through infrared heating curing, pipeline dressing, and hydraulic demoulding.

Figure 1.

Production process of fixed length winding (a) Schematic diagram of winding production (b) Winding production equipment (c) Vibrator compaction resin sand layer.

Table 1.

Design parameters of winding production.

Parameter names	Numerical value	Parameter names	Numerical value
Mandrel diameter	1500 mm	Winding angle	±57.52°
Mandrel length	9850 mm	Core shaft revolution	2.7 r/min
Yarn slice width	97 mm	Number of winding round trips	31

The arched GFRP structure specimen was set with one-third scale-down factor, and the semi-elliptical specimen had a sectional long axis of 1500 mm and a short axis of 1200 mm, while the rise-span ratio was 0.40. The corresponding semi-circular specimen was taken from a 1500 mm diameter pipe and bisected along the diameter into two parts, while the rise-span ratio was 0.50. In addition, both types of arch structures have the same structural level. Thickness of the pipe wall, same to the actual applied structure, is 5 cm. Figure 2 showed the studied GFRP pipe wall structure. In the structure, the lining layer, about 1.6 mm thick, was mainly composed of gel coat, glass surface mat, alkali-free knitting mat, chemical fiber mesh cloth, ammonium polyphosphate flame retardant, and m-benzene resin materials. Three layers of resin sand layer, about 14 mm thick, were mainly composed of quartz sand, resin, pocket gauze, and other materials.

Figure 2.

Pipe wall structure.

The thickness of 1 layer of circular winding and 1 layer of cross-winding was about 1.2 mm. It is mainly composed of glass fiber untwisted roving, winding fiber, o-benzene resin, and other materials, with resin content between 15% and 25%. The thickness of 1 layer of ring winding and 2 layers of cross-winding was about 2 mm, and the material composition and resin content were the same as that of 1 layer of ring winding and 1 layer of cross winding. Table 2 presented mechanical properties of the materials used to produce the GFRP tube structural layers. The parameters for the winding layer are based on the standards "Fiber-reinforced plastics composites-Determination of tensile properties. (GB/T1447:2005)" and "Test method for longitudinal transverse (L-T shear) properties of fiber reinforced plastics. (GB/T3355:2005)." Additionally, the parameters of sand layer are obtained from theoretical calculations (Roham and Farshid, 2014; Roham, 2013a, 2013b).

Table 2.

Parameter values of each structural layer of pipes and culverts.

	Elastic modulus/GPa	Poisson’s ratio	Shear modulus/GPa
Sand layer	5.7	0.32	-
Hoop wrap	E₁=32.8 E₂=6.3 E₃=6.3	0.26	3.4
Cross winding layer	E₁=62 E₂=7.1 E₃=7.1	0.28	4.2

Experiment equipment and instrumentation

In order to simulate the mechanical characteristics of arch GFRP structure in the laboratory, the arch GFRP structure was placed in a steel model box with length of 3 m, width of 1.6 m, height of 2.4 m, and thickness of 50 mm. Fine sand with thickness of 0.15 m was used as culvert foundation, and steel pads with length of 1.6 m, width of 0.2 m and thickness of 0.1 m were embedded. The arch GFRP structure was placed on the steel pads to simulate rigid contact between arch foot and concrete. The experimental device was shown in Figure 3. Both sides of the arch structure in test box were backfilled with multiple sand layers, and thickness was 0.4 m for each layer. In addition, the compaction degree of soil reached 96% and the sand was filled up to required soil covering height of the arch. The mechanical parameters of sand were defined as the optimum moisture content of soil was 12%, the maximum dry density was 1.86 g/cm³, the internal friction angle was 37°, the cohesion was 14 kPa, the elastic modulus was 15 MPa, the bulk density was 1782 Kg/m³, and the Poisson’s ratio was 0.3. In order to simulate automobile axle load, the hydraulic jack was fixed on counterforce beam. Specifically, the load was applied to soil through I-beam, pad, and steel plate and transmitted to upper part of culvert roof. During loading process, all devices remain concentric to avoid eccentric loading.

Figure 3.

Experimental loading device.

Subsequently, the arch structure below loading point was utilized as test section, so as to record the strain and deformation of arch structure and soil stress at vault and arch foot. Five test points (measuring points 1, 2, 3, 4, and 5) were selected for internal test section of the pipeline. Circular-oriented SZ120-100AA strain gages were arranged at each test point. The deformation of culvert was measured through arrangement of YHD-100 deformation sensors on the vault and arch foot. The soil stress at vault and arch foot was measured by YLH soil stress sensor installed at test points (a, b, and c). The measurement points and instrument layout were shown in Figure 4. Experiment data were automatically recorded by computer system.

Figure 4.

Measuring points and instrument layout.

Experimental scheme and process

The experiment proposed to measure the deformation and strain of arch culverts and soil stress distribution with various combination of arch culverts type and soil covering height. In this study, two kinds of arch shapes (semi-circular and semi-elliptical) and three kinds of arch soil covering heights (30 cm, 60 cm, and 90 cm) were proposed and evaluated, and six condition were tested, respectively. The detailed parameters were shown in Table 3.

Table 3.

Loading conditions and parameters.

Conditions	Height of covering soil, cm	Arch shape
Condition 1	30	Semi-circle
Condition 2	30	Semi-elliptical
Condition 3	60	Semi-circle
Condition 4	60	Semi-elliptical
Condition 5	90	Semi-circle
Condition 6	90	Semi-elliptical

The deformation, soil stress, and pipe wall strain of the arch structure were monitored and recorded during different test phases.

Phase 1: collect initial value after filling;

Phase 2: change load value with 10 kN increase for each level and measure parameters simultaneously;

Phase 3: measure the parameters immediately after load is removed and conduct additional strain measurements on arch structure after 20–30 min;

Phase 4: Once the vertical deformation of arch GFRP structure exceeds 15 mm (2%D, D represents the short axis length of the arch) or the backfilled soil shear failure occurs, the load process stops.

Three-dimensional finite element analysis

Establishment of numerical model

In this paper, the finite element software ABAQUS was used to establish tube-soil interaction model to analyze the influence of rise-span ratio and arch foot constraint on mechanical properties of arched GFRP structure with sand. To simplify model, only resin sand layer and FRP layer were considered. The sand layer was assumed to be isotropic material, while winding layer was anisotropic material. The appropriate material properties for the three solid parts, the created arched GFRP structure, soil, and steel plate, can be defined. Among them, the sand layer of the arched GFRP structure is defined as isotropic material, while the winding layer is defined as anisotropic material. The soil is defined as isotropic material, and the steel plate is defined as 3D Discrete Rigid. These components are assembled into a complete finite element model of the cladding arched GFRP structure. Through adjusting load in model, displacement and strain fields of model was recorded under different conditions.

The elastoplastic Mohr–Coulomb model was adopted for analyzing tube-soil contact relationship between arch structure and surrounding soil. The contact relationship was described as follows

τ_{e r i t} = μ p

(1)

In the equation, $τ_{e r i t}$ is the ultimate shear stress. If the friction is less than $τ_{e r i t}$ , the contact surface is considered in the state of bonding, otherwise slip occurs. $μ$ is the slip coefficient, 0.55, $p$ is the normal contact stress. In this paper, the "hard contact" type is adopted. It is believed that the normal pressure was transmitted only when the two objects were in a tight state, otherwise the normal pressure was not transmitted.

On the other hand, the steel box was removed from the finite element model and the soil size was adjusted to 8D, in order to ensure the soil was consistent with stress of arch GFRP structure and eliminate the constraint of test box size. Additionally, C3D8R type element was selected for soil model and SC8R type element was selected for arch GFRP structure. Then, three-dimensional finite element model was shown in Figure 5.

Figure 5.

Three-dimensional finite element model (a) Model of arched GFRP structure (b) Pipeline - soil contact model (c) Assembly model.

Model validation

In order to validate the simulation of arch GFRP structure, the output of indoor scale-down test and numerical simulation of semi-oval GFRP structure with 60 cm covering soil were compared and analyzed, as shown in Figure 6. The comparison results show that under the condition of 60 cm cover soil, the test and simulated force states of the arched GFRP structure at the same point are consistent with various load. The difference between the arched GFRP structure test and the hoop strain result in simulation is about 4.46%. Specifically, the differential values of vertical displacement and load are approximately 3.15% and 4.88%, respectively. The error may be caused by the narrow working space during the test and the large variation of soil compaction degree. Thus, the results validate the model performance, which can be adjusted to further explore the rise-span ratio and the constraint of the arch foot of the arch GFRP structure.

Figure 6.

Comparison of simulated value and test value at measuring point 3 under 60 cm of soil (a) Comparison of hoop strain data (b) Comparison of vertical displacement and load data.

Results and discussion

Structure performance measurement of load value

The soil cover height above arch GFRP structure was selected as 60 cm, in order to investigate load value effect on stress of arch structure. The test results of model box were shown in Figure 7. With the increase of load value, the hoop strain, radial deformation, and soil stress of arch GFRP structure all increased significantly, which had been confirmed in many studies (Guedes, 2009; Roham and Farshid, 2014; Saghir et al., 2021; Wang et al., 2021). As shown in Figure 7(a) and (b), when the external load increased by 50 kN, the hoop strain of the semi-circular GFRP structure increased by about 47% at measuring point 1, 40% at measuring point 2, and 46% at measuring point 3. As a comparison, the hoop strain of semi-elliptical GFRP structure increased by 43%, 40% and 43%, respectively. In addition, the hoop strain values for points 4 and 5 were approximate to those for points 1 and 2 owing to the symmetry of arch GFRP structures. Figure 7(c) shows that the horizonal and vertical deformation of two arch structures presented positive and negative relationship with increasing load, respectively. The absolute value of vertical deformation was almost 6 times to the horizontal deformation. Additionally, the deformation of semi-elliptical arch structure was found to be larger than that of semi-circular GFRP structure considering the same increase of load. On the other hand, the absolute value of hoop strain at vault position (measuring point 3) under load was significantly larger than that at other measuring points. Thus, point 3 was the measuring point with maximum stress point and maximum deformation. It is mainly because the top structure beard the load, which was then transferred to both sides. Therefore, the vault position needed to be concerned in the construction and operation stage of arch GFRP structure, as it was the most unfavorable area for the whole arch structure. In practical engineering projects, it is also important to determine the load level of arch GFRP structure to ensure safe. Through test, the maximum external load for semi-circular and semi-elliptical GFRP structure were 380 kN and 410 kN, respectively, which proved better performance of semi-elliptical arch GFRP structure.

Figure 7.

Influence of load on arched glass fiber reinforced plastics structure (a) Semi-circular load-hoop strain (b) Semi-elliptic load-hoop strain (c) Load - radial deformation (d) Load - soil stress.

Figure 7(d) shows that the soil stress changed at top of vault and at foot of arch. The soil stress of arch structures was about 17 times to that at arch foot. The external load was transferred to bottom layer through arch foot and connected steel plate; thus, horizontal thrust generated by arch foot was small. It is mainly because the cushion blocks were set at the bottom of arch GFRP structure to restrain the lateral deformation in test process.

In order to simplify the construction process, arch foot was placed in groove in vertical wall to restrain the horizontal deformation, which can strengthen the stability of arch culvert and reduce the construction time of connection between arch culvert and vertical wall.

Structure performance measurement of soil cover height

The height of soil significantly affected the maximum external load that arch GFRP structure can bear. When radial deformation of arch structure was less than or equal to 15 mm, the maximum external load of two arch structures increased greatly with the increase of soil cover height, and the semi-elliptical GFRP structure has better performance than the semi-circular GFRP structure under the same conditions. As shown in Figure 8(a), the maximum external loads for semi-elliptic GFRP structure were 310 kN, 410 kN, and 520 kN when the soil cover height was 30 cm, 60 cm, and 90 cm, respectively. As a comparison, the maximum external loads for semi-circular GFRP structure were 280 kN, 380 kN, and 480 kN, respectively. Therefore, soil cover height was an important parameter for load-bearing and safe of arch structure.

Figure 8.

Influence of soil cover height on arched glass fiber reinforced plastics structure (a) Hoop strain under various conditions (b) Hoop strain under 280 kN load (c) Vertical deformation under various conditions (d) Horizontal deformation under various conditions (e) Soil stress under various conditions under 280 kN load.

In addition, Figure 8(b) shows that the strain of arch structure decreased significantly with the increase of soil cover height under a load of 280 kN. When the soil cover height increased by 30 cm, the absolute values of hoop strain at points 1, 2, and 3 of semi-elliptical GFRP structure decreased by 35%, 22%, and 55%, respectively. On the other hand, the hoop strain at points 1, 2, and 3 of semi-circular GFRP structure decreased by 36%, 25%, and 57%, respectively. The absolute values of hoop strain at measuring points 4 and 5 of two arches were approximate to those at measuring points 2 and 1. The load diffusion area expanded with the increase of soil cover height; thus, the load transferred to arch GFRP structure decreases. Simultaneously, the soil arching effect becomes significantly with the increase of the filling height. The increased area of the shear slip plane would result in load transfer and dissipate to the surrounding soil. In addition, it was found that the absolute value of hoop strain of semi-circular GFRP structure was greater than that of semi-elliptical GFRP structure.

It should be emphasized that at measuring points 2 and 4, the pipe walls of two arch structures demonstrated the contrary strain states of tension and compression. That is, measuring points 1, 2, 4, and 5 of semi-circular GFRP structure presented the compressive strain and measuring points 3 presented the tensile strain. On the contrary, measuring points 1 and 5 of semi-elliptical GFRP structure presented the compressive strain and measuring points 2, 3, and 4 presented the tensile strain. The difference of stress state explained the better mechanical performance of semi-elliptical GFRP structure. Through the analysis, low rise-span ratio was found to increase area of arch structure bearing external load. Moreover, the horizontal thrust at arch foot was large when rise-span ratio was low, which further restricted the deformation of arch culvert. The influence of rise-span ratio on mechanical characteristics of arch structures is further discussed in the following section.

On the other hand, the horizontal and vertical deformation of arch GFRP structure and soil stress of each measuring point demonstrated the downtrend with increase of soil cover height. Specifically, with the increase of soil covering height by 30 cm, Figure 8(c)–(e) indicated the horizontal deformation of semi-circular GFRP structure decreased by 38%–73%, the vertical deformation decreased by 32%–33%, and the soil stress decreased by 33%–52%. As a comparison, the horizontal deformation of semi-elliptical arch structure decreased by 30%–87%, the vertical deformation decreased by 35%–38%, and the soil stress decreased by 36%–63% with same condition. Additionally, the vertical deformation of two arch structures was much larger than the horizontal deformation, and the deformation of semi-elliptical GFRP structure was always smaller than that of semi-circular GFRP structure under the same load. For instance, when the soil cover height was 30 cm and load was 280 kN, the vertical deformation and horizontal deformation of semi-circular GFRP structure were 12% and 23% higher than that of semi-elliptical GFRP structure, respectively. When the soil cover height was increased to 60 cm, it was 18% and 19% higher, respectively. When the soil cover height was increased to 90 cm, it was 20% and 28% higher, respectively. Moreover, the soil stress of semi-circular GFRP structure was 7%–22% higher than that of semi-elliptical GFRP structure, and the vertical soil stress at the top of arch GFRP structure was significantly higher than the horizontal soil stress on both sides of the structure.

Structure performance measurement of arch parameters

Based on the numerical calculation model of buried arch structure, the deformation and mechanical characteristics of the structure were analyzed under various condition. The soil cover height was set as 60 cm, and the rise-span ratio was ranging from 0.35 to 0.45. The arch foot included fully constrained, semi-constrained, and unconstrained condition.

Effect of vector rise-span ratio on structural properties

Figure 9 provides the calculation results of three sensitive parameters of arch structure, namely, hoop strain, vertical deformation, and arch soil stress, with different rise-span ratios. As shown in Figure 9(a), the absolute value of hoop strain at each measurement point demonstrated a downtrend with the decrease of rise-span ratio. For the instance with 280k N load, the maximum absolute values of hoop strains with different rise-span ratios were all located at the vault (measuring point 3), which presented the tensile stress. However, points 1 and 5 presented the compressive stress. Additionally, the stress state of spandrel area (measurement point 2 and measurement point 4) was found to be the transition between tensile and compressive stresses with different rise-span ratios. When the rise-span ratio was 0.45, the compressive stress occurred at the measuring points 2 and 4. On the contrary, the compressive stress changed to tensile stress if the rise-span ratio decreased to 0.40 and 0.35. Simultaneously, the transition between tensile stress and compressive stress occurred in the range of arch shoulder, which resulted in a large shear stress. Figure 9(b) and (c) presents a downward trend of the vertical deformation and vertical soil stress, when the rise-span ratio of arched GFRP structure decreased. For the instance with 400 kN load, the vertical deformation with rise-span ratio of 0.40 and 0.35 decreased by about 6% and 15%, respectively, when compared to that of arch structure with rise-span ratio of 0.45. The soil stress of arch was found to be decreased by about 5% and 10%, respectively. The possible reason is that with the rise-span ratio decreases, the arch axis of the arched GFRP structure is similar to the reasonable arch axis, which eventually leads to the reduction of the internal stress and deformation.

Figure 9.

Influence of the rise-span ratio on mechanical properties of arched glass fiber reinforced plastics structures (a) Hoop strain for each rise-span ratio under 280 kN load (b) Vertical deformation for each rise-span ratio (c) Vertical soil stress for each rise-span ratio.

In addition, the bearing capacity of the arch structure tends to increase as the rise-span ratio decreases. The maximum load allowed for the arched GFRP structure with rise-span ratio of 0.35, 0.40, and 0.45 are 470 kN, 430 kN, and 400 kN, respectively. Reducing the rise-span ratio would be another effective means to improve the bearing capacity of the arched GFRP structure besides adjusting the cover soil height. Although an arch structure with a relatively low rise-span ratio can enhance its ability to resist deformation, extremely low rise-span ratio should not be chosen for the design of the structure, as it will increase the requirements for the mechanical properties of the material at the connection position. Moreover, low rise-span ratio will increase the horizontal thrust and bending moment of the section at the arch foot, which is not conducive to the force of the arch foot of the rigid-flexible (concrete and GFRP) assembly structure with two different characteristics of materials. However, the GFRP material have both excellent compressive and bending-tensile properties, which cannot be achieved by the sand layer materials with poor tensile strength. Notably, a lower rise-span ratio will reduce the headroom of the arch structure and make the assembled arch structure meaningless. Therefore, the range of the rise-span ratio was recommended to be 0.3–0.4 when designing the arch structure.

Influence of arch foot constraints on structural performance

As a flexible structure, the arched GFRP structure was different from traditional rigid arch structure in allowable deformation. The arch structure numerical calculation model with rise-span ratio 0.40 and height of soil covering 60 cm was selected as example. Through numerical calculation, the distribution of stress and deformation of arch structure was obtained under three constraint treatments: unconstrained, fully constrained, and semi-constrained (only 2 mm horizontal deformation was allowed). Figure 10 showed the radial deformation results of arch structure under different arch foot constraints. The calculation results showed that the vertical deformation of whole arch structure can be reduced by 67% when the horizontal deformation at arch foot was completely constrained instead of unconstrained condition. This is mainly because the horizontal deformation of GFRP structure was restricted when arch foot position was under constraint.

Figure 10.

Radial deformation under different arch foot constraints.

Figures 11 and 12 show the hoop strain and strain cloud map of arch structure under different arch foot constraints. It can be found that when arch foot position of GFRP structure was changed from unconstrained state to constrained state, the absolute value of hoop strain at vault position presented a downward trend, while the absolute value of hoop strain at arch waist position presented an upward trend. In addition, the constraint state of arch foot changed the stress state and the most unfavorable position of internal stress. When arch foot was in the unconstrained state, the vault-waist-foot of arch structure presented gradually transitions from tensile strain to compressive strain, especially for the arch waist position with small internal stress. The arch vault was the most unfavorable position of the whole structure, while the maximum internal stress of arch foot was slightly less than that of arch vault. The results indicated no stress concentration phenomenon occurred.

Figure 11.

Hoop strain under different arch foot constraints.

Figure 12.

Hoop strain nephogram under different arch foot constraints (a) Arch foot unrestrained (b) Arch foot semi-restraint (c) Arch foot fully restrained.

When the arch foot was in a constrained state (complete or semi-constrained), the internal stress at arch waist position presented the stress concentration, which was the compressive stress. And the arch waist position was the most unfavorable position of the whole structure. On the contrary, arch foot and vault presented tensile stress. The main reason was arch foot generated horizontal thrust when the arch vault structure beard the load. If there was no rigid constraint on the position of arch foot, the arch GFRP structure can transfer the load to soil on both sides through larger radial deformation. The compaction requirements of surrounding soil were strict, while the internal stress of arch structure was low. However, if the arch foot position was implemented with rigid constraints, most of vault load can be transferred to the reinforced concrete side wall through arch foot. Consequently, the load transfer requirements on the surrounding soil were significantly reduced, but the internal stress of arch structure was high. This was consistent with the load transfer mechanism of traditional arch bridge structure. Therefore, the constraint of arch foot position had an important effect on stress distribution of arch GFRP structure, which was the unique load-bearing mechanism of flexible arch structure.

Figures 13 and 14 show soil stress around arched GFRP structure under different constraint conditions of arch foot. It can be found that the soil pressure around arch with different arch foot constraints varied greatly. When the arch foot position was in semi-constrained condition, the vertical soil stress decreased by about 20%, and the horizontal soil stress decreased by about 28 times compared to unconstrained condition. As shown in Figure 14, the maximum vertical soil stress emerged at vault position, and the distribution of vertical soil stress expanded as arch foot position changed from the constrained state to unconstrained state. When the arch foot was constrained, the vertical soil stress mainly concentrated on the upper part of arch GFRP structure. In the unconstrained state, higher soil stress was distributed around the whole structure, and the vertical soil stress concentration occurred in arch waist. The results indicate the arch deformation resulted in more load to be transferred to the surrounding soil when the arch foot was not restrained.

Figure 13.

Vertical soil stress nephogram under different arch foot constraints (a) Arch foot unrestrained (b) Arch foot half restraint (c) Arch foot fully restrained.

Figure 14.

Horizontal soil stress nephogram under different arch foot constraints. (a) Arch foot unrestrained (b) Arch foot half restraint (c) Arch foot fully restrained.

In practical projects, the filling ground and pavement structure above the vault cannot bear large deformation. Thus, the technical scheme with constraint of arch foot was recommended. Simultaneously, the tensile and compression characteristics of GFRP materials should be concerned owing to the higher internal stress state of arch structure.

Discussion about the assembled GFRP arch culvert

In cold regions around the world, temperature restricted the construction of concrete structures. As the concrete components poured on site needed high temperature, the construction time can only be satisfied for 6–7 months in a year in cold areas. In order to solve the problem of construction period, prefabricated structure is preferred in road engineering. In terms of the component prefabrication and on-site construction, short-term projects can be implemented (Marshall et al., 2014; Sawamura et al., 2019). In the future, prefabricated buried reinforced concrete and GFRP arch composite culverts are believed to be further utilized and studied in highway engineering.

As shown in Figure 15, assembled GFRP arch culvert is mainly composed of precast arch GFRP structure, precast reinforced concrete straight wall, horizontal culvert bottom, pile foundation, and other auxiliary components. The pipe pile foundation is connected to the precast reinforced concrete straight wall, which can improve the bearing capacity of straight wall through transferring the load to foundation. The top of straight wall is implemented with a groove for embedding arch foot, and the bottom is implemented with reserved bolts or reinforcing bars connected to pipe piles and horizontal culvert bottom. After the arch is connected to straight wall, GFRP material can be poured in the groove to protect arch foot and transfer the load better. The horizontal culvert bottom, the anchor bars of straight wall and pipe pile foundation can promote the stability of straight wall, prevent the overturning, and improve seismic performance of the structure effectively.

Figure 15.

Assembled glass fiber reinforced plastics arch culvert.

Assembled GFRP arch culvert is believed to overcome the inherent defects of cement concrete structure and improve the headroom. Thus, it is expected to be further utilized in the future.

Conclusion

The main purpose of this study was to investigate the mechanical properties of buried arch GFRP structures and provide a preliminary study for application of assembled GFRP arches and reinforced concrete composite culverts. Indoor arched GFRP structure of soil load scale-down test was proposed to explore the mechanical parameters under various conditions, such as load levels and soil cover height. In addition, the finite element numerical method was developed to examine the effect of rise-span ratio and arch foot constraints on arch GFRP structure performance. The main findings were summarized as follows:

1. The load value had a significant effect on the mechanical properties of the arched GFRP structure. When the load increased by 50 kN, the hoop strain increased by about 40%–47%, the radial deformation increased by about 28%–49%, and the soil stress increased by about 22%–27%. Arch vault was the most unfavorable area of the whole arch structure, which can be used as control point of the safety performance measure. The performance of the semi-elliptical GFRP structure was better than that of the semi-circular structure. With 60 cm soil covering height and 410 kN external load, the deformation of arch structure was only 2%D, which can meet the requirements of traffic load in highway engineering.

2. The increase of soil cover height can effectively reduce the external load. When the soil height increased from 30 cm to 90 cm, the hoop strain value decreased by 22%–57%, the radial deformation decreased by 30%–87%, and the soil stress decreased by 33%–63%.

3. The vertical deformation and internal stress of arch structure can be reduced by decreasing the rise-span ratio. Under 400 kN load, the vertical deformation of arch structure with rise-span ratio of 0.40 and 0.35 decreased by about 6% and 15%, respectively, and the stress of vault soil decreased by about 5% and 10%, respectively, compared to that of arch structure with rise-span ratio of 0.45. Therefore, reducing the rise-span ratio was another effective means to increase the load-bearing capacity of the arched GFRP structure. Moreover, the arched GFRP structure with rise-span ratio of 0.40 and 0.35 had a large tensile and compressive stress transformation in the range of arched shoulder, resulting in a large shear stress, which formed a complex stress state.

4. The arch foot constraint can restrict the deflection of arch and soil stress around the arch; however, it can also change the stress distribution in arch structure. The vertical deformation of the arch was reduced by about 67% and the vertical earth pressure was reduced by about 20%, while the constrained arch foot substituted the unconstrained arch foot.

In the future, the application of GFRP arch and precast reinforced concrete will be further studied, especially the connection between GFRP arch components and the design and maintenance of the whole structure.

Highlight

Buried arch GFRP structure with sand presents excellent bearing capacity to deal with the potential traffic load.

Through the indoor scale-down test, mechanical properties of buried arch GFRP structure with sand were found to be influenced by the load level, soil cover height and the constraint state of arch foot.

Semi-elliptical arch structure outperforms the semi-circular arch structure in bearing capacity owing to the load-reduction effect achieved by low rise-span ratio.

Proposed the approach and scenario to implement the assembled GFRP arch culvert with sand.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Natural Science Foundation of Tianjin of China [No.20JCYBJC00630].

ORCID iD

Qing-Zhou Wang

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