The wood selected for this experiment is Shandong cedar from Lishui City, chosen to closely match practical conditions, as this type of wood is commonly used in the construction of wooden arch corridor bridges. The physical and mechanical properties determined by wood testing methods are shown in Table 1. Six middle-section seedlings were fabricated for the three-segment arch bridge, consisting of three unreinforced components and three reinforced components, each illustrated in Figure 3. Figure 4 presents the moisture content of the wooden components reinforced with CFRP and those that are unreinforced. The selected moisture content reflects the levels typically encountered in the environmental conditions to which the wood is exposed, simulating the performance of CFRP reinforcement under normal drying conditions.

The moisture content of the wooden arch bridge components was measured using the ZTW1601a wood moisture tester produced by Zhengtai Network Technology Co., Ltd. The CFRP used in the experiment was carbon fiber cloth produced by Shanghai Zhinuo Decoration Materials Co., Ltd., with a model specification of Grade I 58,788 (200 g); the adhesive was epoxy resin impregnated adhesive produced by Shanghai Zhino Decoration Materials Co., Ltd., with a model of ZN-700. It consists of two components, A and B, mixed in a ratio of A:B = 2:1. The mechanical properties of CFRP and adhesive were tested by the National Building Materials Testing Center on behalf of the company. The test results are shown in Table 2.

The experiments were performed using a 5000 kN hydraulic testing machine at the Structural Laboratory of Lishui University. The loading process entailed concentrated loading at two points on the beam, with preliminary loading of the specimen to mitigate local voids and minimize their impact on the test results. Subsequently, graded loading was applied until failure ensued.

During the experiment, measurements primarily encompassed the mid-span displacement of the wooden arch bridge components, strain at mid-span cross-sections, and strain at adjacent points of CFRP bonding termination. Observations and records of damage to the wooden arch bridge components during loading were also conducted. The arrangement of the loading device and measurement points is depicted in Figure 5.

The components of the wooden arch bridge were reinforced using carbon fiber cloth. This paper conducted theoretical analysis on the small range of the two end points, as shown in Figure 6 (unit: mm).

For the small cross-sectional analysis around adjacent measurement points, it is assumed that after CFRP reinforcement of the wooden arch bridge components, the strain between the adjacent measurement points exhibits linear variation, meaning that the shear stress at the bonding interface between adjacent measurement points remains constant. The shear stress within this range can be obtained through the equilibrium relationship between adjacent CFRP points, namely, the average bonding interface shear stress τ. Assuming the distance between the two points is Δ L , and the strains at the two measurement points are ε ₁ and ε ₂ , respectively, the equilibrium relationship can be expressed as follows (Dai et al., 2015): F N 1 + F N b = F N 2 (1) F N 1 = b C δ C E C ε 1 F N 2 = b C δ C E C ε 2 F N b = b C △ L τ (2)

Where F _N1 and F _N2 are the axial forces of adjacent measuring points respectively; F _Nb is the axial force of the bonding interface layer.

According to Equations 1, 2, order Δ ε = ε 2 − ε 1 , the average shear stress τ between the two measuring points of CFRP and wooden arch corridor bridge members in Δ L section is: τ = E C δ C △ ε / △ L (3)

Where E _C is the elastic modulus of CFRP; Δ ε is the strain difference of CFRP between two measuring points in Δ L section, that is, the relative strain between the two measuring points.

According to Equation 3, the shear stress of the bonding interface of the member under different loads can be calculated.

The components of wooden arch corridor bridge are strengthened with CFRP, and the micro elements of two adjacent measuring points dx are taken, then the shear strain γ of the bonding layer is: γ = d i x , y d y + d j x , y d x (4) where i(x,y) and j(x,y) are the horizontal and vertical displacement of the bonding layer respectively. According to Equation 3, the shear stress τ(x) at the bonding interface is: τ x = G A d i x , y d y + d j x , y d x (5) where G _A is the shear modulus of the bonding layer. It is assumed that the horizontal displacement of the bonding layer is linearly distributed along the vertical, that is: d i x , y d y = 1 δ A i C x − i W x (6) where i _C (x) and J _W (x) are the horizontal displacement of the outer surface and inner surface of the bonding layer respectively, that is, the horizontal displacement of the inner surface of CFRP and the outer surface of wood beam respectively; δ _A is the thickness of the tack coat. Substituting Equation 6 into Equation 5 and deriving, it obtains: d τ x d x = G A 1 δ A d i C x d x − d i W x d x + d 2 j x , y d x 2 (7)

Since the influence of shear deformation is very small, the shear deformation of single member of wooden arch corridor bridge and CFRP is ignored, then: d i C x d x = F N C x E C A C − M C x δ C 2 E C I C (8) d i W x d x = M W x d / 2 + δ A + δ C E W I W − F N W x E W A W (9) where F _NC (x) and F _NW (x) are the axial forces of CFRP and wooden arch corridor bridge components respectively; M _C (x) and M _W (x) are the bending moments of CFRP and wooden arch corridor bridge members respectively; E _C and E _W are the elastic modulus of CFRP and timber-arched lounge bridge members respectively; A _C and A _W are the sectional areas of CFRP and wooden arch corridor bridge components respectively; I _C and I _W are the section moment of inertia of CFRP and timber-arched lounge bridge components respectively; δ _C and δ _A are the thickness of CFRP and bonding layer respectively, and δ is the diameter of the member.

Because the stiffness and shear capacity of CFRP are very small, the bending moment and shear force borne by CFRP are ignored, that is: F S C x = 0 ;   F S W x = F S x ;   M C x = 0 (10) M W x = M x − F N C x d / 2 + δ A + δ C (11)

According to the relationship between curvature and bending moment in material mechanics: d 2 j x , y d x 2 = − M x E I (12) E I = E I C C + E A I A + E W I W (13)

The equation for EI represents the total section bending stiffness, where E _C , E _A and E _W denote the elastic modulus of CFRP, the elastic modulus of the bonding layer, and the elastic modulus of the wooden arch corridor bridge components, respectively; I _A signifies the cross-sectional moment of inertia of the bonding layer. By substituting Equation 8–13 into Equation 7, we can obtain: d τ x d x = G A δ A F N W x E W A W − d / 2 E W I W + δ A E I M x + 1 E C A C + d / 2 + δ A + δ C d / 2 E C I C F N C x (14)

By deriving from both sides of Equation 14: d 2 τ x d x 2 = G A δ A 1 E W A W d F N W x d x − d / 2 E W I W + δ A E I d M x d x + 1 E C A C + d / 2 + δ A + δ C d / 2 E C I C d F N C x d x (15)

Considering the balance of micro elements, it can be obtained that: d F N C x d x = d F N W x d x = b C τ x (16) d 2 τ x d x 2 = G A δ A ⁢ − d / 2 E W I W + δ A E I ⁢ F S ⁢ x + 1 E C A C + 1 E W A W ⁢ b C ⁢ τ ⁡ x + d / 2 + δ A + δ C d / 2 E W I W ⁢ b C ⁢ τ ⁡ x (17)

Order: λ 2 = G A b C δ A 1 E C A C + 1 E W A W + d / 2 + δ A + δ C d / 2 E W A W (18) m 1 = G A δ A λ 2 d / 2 E W I W + δ A E I (19)

According to Equations 15–19, can be obtained: d 2 τ x d x 2 − λ τ x + m 1 λ 2 F S x = 0 (20)

Equation 20 is the governing differential equation of shear stress at the bonding interface, and its solution is: τ x = C 1 e λ x + C 2 e − λ x + m 1 F S x (21) where C ₁ and C ₂ are coefficients, which can be obtained according to the two-point centralized loading, and the two-point centralized loading of wooden arch corridor bridge components as shown in Figure 6. In the shear span, q(x) = 0, F _S (x) = F/2; In the pure bending section, q(x) = 0, F _S (x) = 0. Substituting it into Equation 21, the interfacial shear stress is: τ x = τ 1 x = C 1 e λ x + C 2 e − λ x + m 1 F / 2 , 0 ≤ x ≤ L W − a τ 2 x = C 3 e λ x + C 4 e − λ x , L W − a ≤ x ≤ L C / 2 (22)

The boundary conditions are:x = L _C /2; τ(L _C /2) = 0; x = L _W -a; τ 1 x x = L W ‐ a = τ 2 x x = L W ‐ a ; d τ 1 x d x x = L W ‐ a = d τ 2 x d x x = L W ‐ a

Order: m 2 = G A δ A d / 2 E W I W + δ A E I ,

Obtain: d τ 1 x d x x = 0 = − m 2 M 0

According to the boundary conditions: C 1 = ‐ m 1 F 4 1 + e λ L C e λ L C ‐ L W + a + e λ L W ‐ a ‐ m 2 F a 2 λ 1 + e λ L C , C 2 = ‐ m 2 F a 2 λ 1 + e λ L C e λ L C ‐ m 1 F 4 1 + e λ L C e λ L C ‐ L W + a + e λ L W ‐ a , C 3 = m 1 F 4 1 + e λ L C e ‐ λ L W ‐ a ‐ e λ L W ‐ a ‐ m 2 F a 2 λ 1 + e λ L C , C 4 = m 2 F a 2 λ 1 + e λ L C e λ L C + m 1 F 4 1 + e λ L C e λ L C + L W − a − e λ L C − L W + a

Where a is the distance from the end of CFRP to the support; L _W is the distance from the action point of concentrated load to the support; L _C is the length of the CFRP.

The 1:5 scale model of the wooden arch bridge was placed under the MTS hydraulic testing machine for load testing, as shown in Figure 13. The displacement measurement points for the load test of the wooden arch bridge arches are illustrated in Figure 14.

Static load test was conducted on the wooden arch bridge arches, and the displacements at each measurement point are shown in Figure 15.

From Figure 15, it can be observed that the displacement curves at each measurement point exhibit a similar trend under static loading. The maximum displacement occurs at the mid-span of the wooden arch bridge arches under static loading, gradually decreasing towards the sides. This trend indicates that during flood periods when additional loads are applied to prevent the bridge from being washed away, reducing the load at the mid-span while distributing it towards the sides may be advisable.

A numerical model of the wooden arch bridge was established using SAP 2000, as shown in Figure 16A. The established numerical model was compared with the experimental results to validate its accuracy, and the obtained displacements are illustrated in Figure 16B.

As shown in Figure 16A, during the numerical modeling of the wooden arch corridor bridge using SAP 2000, the deck beams were modeled; however, since there were no deck beams in the experiments, the deck beams were assumed to bear no loads during the numerical calculations. Additionally, each node was subject to a relaxation of constraints, allowing for a limited movement of 5 mm in all six degrees of freedom, changing the constraints from fixed to movable. The current model is suitable for the performance of the specimens tested; however, its generalizability needs to be enhanced through additional experiments with different specimens for parameter calibration. As indicated in Figure 16B, the numerical model of the wooden arch bridge framework established using SAP2000 demonstrates a close agreement in mid-span displacement under static loading, indicating a certain level of accuracy in the model.

Using the data obtained from the CFRP reinforcement of components in Section 2, the spring elements representing CFRP are attached to the mid-span nodes of the wooden arch bridge framework and subjected to load simulation, with results shown in Figure 17.

From Figure 17, it is evident that the application of CFRP reinforcement significantly enhances the load-bearing capacity of the wooden arch bridge, resulting in a substantial reduction in mid-span displacement under the same load conditions. CFRP reinforcement of the wooden arch bridge’s framework can increase its load-bearing capacity by 20%. When subjected to flood periods, CFRP reinforcement of the wooden arch bridge’s framework ensures its structural integrity under applied loads.